Structure and Properties of Ceramics

Materials Science and Technology Copyright © WILEY-VCH Verlag GmbH & Co KGaA. All rights reserved.

1 Crystal Structures of Principal Ceramic Materials Bruce G. Hyde, John G. Thompson, and Ray L. Withers

Research School of Chemistry, The Australian National University, Canberra, Australia

List of Symbols and Abbreviations 1.1 Introduction 1.2 Simple Structures 1.2.1 Bl, NaCl Type (cF8) 1.2.2 Cl, Fluorite Type (cF12) 1.2.3 A4, Diamond or Silicon Type (cF8); B3, SiC, BN, etc. Type (cF8); and A9, Graphite Type (hP4) 1.2.4 B h , Tungsten Monocarbide, WC (hP2) 1.2.5 C32, A1B2 Type (hP3) 1.2.6 D5 l 5 Corundum or oc-Alumina, A12O3 (hR10) 1.2.7 C16, Fe 2 B = CuAl2 Type (til2) 1.3 More Complex Structures 1.3.1 C43, ZrO 2 , Baddeleyite Type (mP12) 1.3.2 D2 1? Calcium Hexaboride, CaB 6 (cP7) 1.3.3 E2 1? Cubic Perovskites, ABX3 (cP5) 1.3.4 D0 l x , Cementite, Fe 3 C Type (oP16); Fe 5 C 2 (mC28); Fe 7 C 3 etc. [Cr 7 C 3 = D10 i ; Th 7 Fe 3 = D102]; B27, FeB (oP8); CrB (oC8); D7 b , Ta 3 B 4 (oI14); oc-MoB (til6) 1.3.5 H l l 9 Spinel, MgAl 2 O 4 (cF56) 1.3.6 Hexagonal Barium Ferrite Structures Related to the Magnetoplumbite (PbO • 6Fe 2 O 3 ) Type (hP66) 1.3.7 (3-Alumina (hP58) 1.3.8 HI3/SI3, P-Si3N4, and the (3'-Sialons (hP14) 1.3.9 Other (AIN-Related) Sialons 1.3.10 H5 7 , Apatite-Type Nitride Silicates of the Rare Earths (hP42); and the D8 8 , Mn 5 Si 3 Type (hP16) 1.4 High-Temperature Superconductors 1.4.1 The "1:2:3" Compound Ln 1 Ba 2 Cu 3 O 7 _ 5 [Ln = Y or Rare Earth(s)] 1.4.2 LnBa 2 Cu 4 O 8 1.4.3 (La, M) 2 CuO 4 (M = Sr, Ba) 1.4.4 The T1-, Bi- or Pb-Containing Families: (i) M 1 Ca w _ 1 M 2 Cu M O 2n + 3 (1 1 000 °C); anion-deficient ones particularly stabilised zirconias (Sec. 1.3.1) are widely used: and anion-excess ones such as zirconia "stabilised" with Nb 2 O 5 or Ta 2 O 5 (compounds

41

not yet widely used and therefore not discussed here, although they are of great structural interest). These all have in common the stable c.c.p. cation array. Other oxide, ceramic, solid-electrolyte materials include the pyrochlores (also with a c.c.p. cation array; Sec. 1.6.1) and P-aluminas [in which the mobile species is the low-valence cation, e.g., Na (sometimes Ag); Sec. 1.3.7]. Fluorides such as YF 3 (anti-structure of the Fe 3 C type) and LaF 3 (which is not very different in structure) are possibly useful electrolytes for high-temperature cells.

1.8 Notes 1 Note the convention, roman letters for anions, greek letters for cations (although, in this case the distinction is irrelevant since the structure and antistructure are identical). The equal spacing of the letters shows that the cations are midway between the anion layers, and vice versa. Because they occupy octahedral interstices in the array, atoms must have a position indicated by a letter different from those on either side (and of the other font), i.e., a between b and c, p between a and c, etc. Tetrahedral sites lie at one quarter of the distance between eutactic layers, and therefore correspond to the spaces between greek and roman letters in the present sequence, cf. the B 3 structure, below. They must be represented by a letter identical to that of the furthest adjacent layer, but of different font (cf. tetrahedral structures, below). We would prefer the term "eutactic" to (the usual) "close-packed" because it describes the geometry without implications about distance. For example, in the B1 type both anion and cation arrays have the same ("eutactic") geometry, but (logically) not more than one of the two is likely to be "close-packed". However, the latter term is now entrenched. 2 At 2.54 A (12 x), the second-nearest-neighbour distances in diamond are extremely short, and it has been suggested that it is this rather than strongly-directional bonding that is reponsible for its hardness and incompressibility. Third-nearest neighbours are not much more distant, 2.95 A (12 x). Cf. the van der Waals radius for carbon is 1.60 A (which may be compared with the inter-layer separation of 3.35 A in graphite), and its non-bonded radius (at which overlap repulsion is very high, ~ 15 kJ mol" 1 ) is 1.25 A (O'Keeffe and Hyde, 1981). 3 SiC is also extremely hard and incompressible, due to the short, second-nearest-neighbour, Si-Si distances, 67)(Si2O5)2(OH)2, can be converted to a calcium montmorillonite, Ca 0 . 17 (Mg 0 . 33 Al 1 . 67 )(Si 2 O 5 ) 2 (OH) 2 , through room temperature ion exchange in solution. The plasticity of the smectites is strongly affected by such exchange with sodium yielding a much higher degree of plasticity. Neither pyrophyllite (on which the smectites are based) nor the dioctahedral analogues talc and vermiculite exhibit swelling. A complete explanation for this difference is lacking (Van Olphen, 1977), but, as an aside, it is noted that the properties of the montmorillonites determined by crystal structure offer unique flexibility in processing. Sugahara et al. (1984,1988) developed processing schemes for P-SiAlON and aluminum silicon carbide using montmorillonite clay. The montmorillonite was first treated with a hexylammonium hydrochloride solution to exchange the interlayer alkali ions with hexylammonium which burn out during firing. After washing and drying, it was immersed in acrylonitrile monomer and allowed to stand for sufficient time to allow the monomer to penetrate between the layers after which polymerization was induced. The result was an extremely homogeneous distribution of a carbon source (polyacrylonitrile or PAN). Heating in a nitrogen bearing atmosphere caused carbothermic reduction of the silicate layer to form silicon nitride which interdiffused with the gibbsite layer to produce SiAlON. The ability to form an intimate mixture, an intercala-

61

tion compound, of the reactants leads to a significantly more efficient conversion than mechanical mixtures of carbon black and clay. More recently, Seron et al. (1992) have shown that the efficiency of carbon retention is increased if acriflavine ammonium cations are used. This is a direct result of ionic bonds which form between the Cl 3 N 3 Hi 3 f ions and the substituted sheets in the montmorillonite. Montmorillonite clays are also widely used as suspension aids, for example in ceramic glazes. Although a very different application from that discussed in the preceding paragraph, it is also based on the tendency of the clay to spontaneously dissociate when suspended in water. In this case, the colloidal nature of the montmorillonite produces a situation known as "hindered settling" which retards the settling rate of the coarser particles. The effect of heat on the phyllosilicates is also intimately dependent on the details of the structure. The first process which occurs during heating is the removal of physically bound water followed by dehydroxylation, or the removal of chemically bound water. In the case of halloysite the dehydration occurs around 50 °C. Dehydration results in a collapse of the interlayer spacing (from 1.0 nm to 0.7 nm) and a significant change in the degree of plasticity. Since it occurs at such a low temperature, the degree of hydration often changes during transport or storage. From an engineering point of view the material is therefore subject to uncontrolled variations which is a disadvantage. Similarly, heating vermiculites causes the dehydration of the interlayer magnesium ions, but at a higher temperature, 110°C. If heated rapidly the explosive conversion of the interlayer water to steam results in exfoliation, or separation of individual layers, yielding a volume expansion up to 100 times. Such

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behavior is exploited in, for example, the manufacture of thermal insulating refractories. At higher temperatures, the structure of the phyllosilicates breaks down. In the case of the dioctahedral materials mullite, Al 6 Si 2 O 13 , is usually one of the decomposition products whereas enstatite, MgSiO 3 , is usually formed from trioctahedral materials. In both cases decomposition usually involves the rejection of silica. The processes occurring upon firing kaolinite clay have been the subject of extensive investigation ever since the work of LeChatelier (1887). However, it was not until the work of Brindley and Nakahira (1957,1959) that the reaction sequence was essentially understood. Recently, Brown etal. (1985) and MacKenzie et al. (1985) have characterized the details of the threestage reaction sequence outlined below. The combined water in the clay is driven off at about 500 °C (dehydroxylation) and metakaolin is formed. Stage I Al 2 Si 2 O 5 (OH) 4 kaolinite 500 °C

metakaolin + 2H 2 O

Stage II metakaolin 970

°c

3A1 2 O 3

Al 6 Si 2 O 1 3

3SiO 2

defect spinel

alumina-rich mullite

glass

Stage III defect spinel -f silica glass 1125°C 2Al 6 Si 2 O 13 + SiO2 mullite

cristobalite

The metakaolin structure is essentially glassy consisting of anhydrous regions of distorted Al-O tetrahedra containing about 12% randomly-distributed, isolated, residual hydroxyls associated with A l - O

configurations of regular octahedral and tetrahedral symmetry. Decomposition of the metakaolin by removal of the final residual hydroxyl radicals at 970 °C triggers the separation of amorphous free silica and formation of both poorly crystalline mullite and a phase with a cubic, defective spinel, crystal structure similar to y-Al 2 O 3 . The mullite and spinel form in tandem, the former originating in the vicinity of Al-O units of regular symmetry. There is some disagreement as to whether the spinel phase formed is actually y-Al 2 O 3 or a defective spinel containing A12O3 and SiO 2 . The nuclear magnetic resonance studies of MacKenzie et al. (1985) suggest the former while the transmission electron microscopy study of Srikrishna etal. (1990) suggest the spinel has a 3Al 2 O 3 -2SiO 2 mullite composition. The spinel crystallites are about 10-50 nm diameter at 1020°C. Initially the mullite forms as alumina-rich but at higher temperatures it gains silica to approach the 3 A12O3 • 2SiO 2 composition. On further heating above 1125°C, the spinel phase is converted to mullite by reaction with some of the amorphous silica, the balance of which eventually becomes cristobalite (discussed in Sec. 2.2.3.1) if held at high temperature for sufficient time. The end products of firing the mineral kaolinite are mullite and silica. Natural clays often have impurities which yield a mixture of mullite crystals and a multicomponent siliceous glass. The temperature at which natural clays are fired depends closely on its alumina and flux content. Higher firing temperatures are required for clays with greater alumina and less flux. The decomposition of pyrophyllite also has a long history and is the subject of recent investigations (MacKenzie et al.,

2.2 Silicate Ceramics

63

1986). This material also undergoes a series of reactions upon heating ultimately forming mullite and cristobalite. The ratio of cristobalite to mullite is higher for pyrophyllite since it is a 2:1 structure. Although cristobalite forms during the decomposition of phase pure kaolinite or pyrophyllite, the final form of the liberated silica in a triaxial formulation is influenced by the presence of alkali and alkaline earths as is discussed in Sec. 2.2.2. Although they are unambiguously phyllosilicates, micas which contain relatively high concentrations of alkali ions are better classified as fluxes in the context of industrial ceramic manufacture. 2.2.2 Fluxes A flux is defined as "any substance which promotes the fusion and flow of a ceramic or glass mixture when subjected to heat" (O'Bannon, 1984). For silicate ceramics, fluxes are generally compounds which contain alkali or alkaline earth elements (although anionic fluxes such as fluorine are used in some applications). Fluxes are often described as breaking up the network structure of a glass. The classic (and highly schematic) illustrations of the effect of fluxes on the structure of silicate glasses are presented in Fig. 2-10. Figure 2-10 a and b represent the structural difference between a crystal and glass of the same composition. In the glass structure the coordination polyhedra are preserved (i.e., short range order is preserved), but the connectivity between the tetrahedra becomes randomized. The effect of fluxes on the structure of the glass is illustrated in Fig. 2-10c. The addition of the flux, for example Na 2 O, produces what are termed nonbridging oxygens decreasing the degree of connectivity of the structure (analogous to decreasing the molecular

Figure 2-10. Schematic illustration of (a) a crystal and (b) the corresponding glass. Although the long range order is lost in the structure of the glass the local order (i.e. tetrahedra) and the connectivity (two tetrahedra per vertex) are preserved. The addition of a flux decreases the connectivity of the structure as shown in (c).

weight of a polymer melt). The most commonly employed fluxes contain alkali; alkaline earth elements are less commonly used. The most widely employed mineral sources of fluxing elements are feldspars and feldspathoids. The general chemical formula for feldspars (Griffen, 1992) may be written MT 4 O 8 where M is either sodium, potassium, or calcium (less commonly, barium

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and ammonium) and T represents either aluminum or silicon. The significance of the symbol T is that both the aluminum and the silicon are in tetrahedral coordination within the crystal structures of these minerals. As in the case of micas, aluminum in tetrahedral coordination must be charge compensated. In the case of the sodium and potassium feldspars compensation is available for one aluminum per formula unit, NaAlSi 3 O 8 and KAlSi 3 O 8 respectively, whereas calcium provides compensation for two aluminums per unit cell, CaAl 2 Si 2 O 8 . All of these minerals can exist in more than one polymorph. In the case of the albite, NaAlSi 3 O 8 , and anorthite, CaAl 2 Si 2 O 8 , these are simply distinguished by the modifier low- or high-. However, potash feldspar, KAlSi 3 O 8 , is referred to either as orthoclase or microcline depending on the structure. Although microcline is the stable phase at room temperature and is the most commonly occurring mineral, the term orthoclase is more frequently encountered in the ceramics literature. An alternate flux somewhat higher in sodium and potassium is the mineral nepheline, sometimes reported as Na 2 Al 2 Si 2 O 8 and alternately as (Na 3 K)Al 4 Si 4 O 16 . Lithium is also used as a flux. Due to its relatively high cost, it finds application only where it offers unique properties. When substituted for sodium or potassium, lithium increases the elastic modulus, increases the surface tension, and increases the hardness (Taylor and Bull, 1986; De Guire and Brown, 1984) of a silicate glass. Many lithium chemicals, such as lithium chloride or carbonate are highly processed, but the principal mineral sources of lithium are spodumene and petalite. Spodumene, LiAlSi 2 O 4 , is somewhat richer in lithium than petalite, LiAlSi 4 O 6 .

2.2.2.1 Crystal Structure During the early stages of processing fluxing agents are generally molten and on cooling often form a glass. Therefore, the crystal structure of the flux is not directly related to the properties of the final ceramic, unless the glass is intentionally crystallized during the final stages of processing. The distinguishing characteristic of the feldspar structure is the existence of four membered rings of tetrahedra (Griffen, 1992). The minerals nepheline and petalite are tectosilicates, i.e., they have a crystal structure based on the silica polymorph tridymite (the tridymite structure is discussed in Sec. 2.2.3.1). Spodumene is classified as pyroxene, which is a chain silicate. In chain silicates SiO4 tetrahedra are linked, i.e., share corners, in only one direction, in contrast to the two dimensional linking in sheet silicates. 2.2.2.2 Mineral Sources

Feldspars rarely occur in nature as pure minerals. Since albite and anorthite form a complete solid solution series, they occur in nature as alloys. Even though orthoclase and albite form only limited solid solutions, deposits of orthoclase always contain some albite. The rock nepheline syenite is a mixture of orthoclase, albite, and nepheline with minor impurities. Typical compositions of mined materials (somewhat arbitrarily termed soda and potash feldspars) are compared to mineral compositions in Table 2-4. These materials are typically ground to a relatively coarse powder, on the order of 70 to 100 jam, for use in ceramic (or glass) manufacture.

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2.2 Silicate Ceramics

Table 2-4. Chemical composition of fluxes (Dinsdale, 1986). Oxide (%)

Minerals

Raw materials

Feldspars Orthoclase K2O Na 2 O A12O3 SiO2 K 2 O + Na 2 O

Albite

Nepheline

11.82 19.44 78.74 11.82

21.81 35.89 42.30 21.81

16.92 18.31 64.76 16.92

2.2.2.3 Characteristic Properties

The tendency to form a glass is strongly correlated to the viscosity of a melt. In general, molten feldspars are rather viscous which is ascribed to the existence of polymerized silicon-aluminum-oxygen tetrahedra in the liquid (Barth, 1969). Despite lower melting points, the alkali feldspars produce much more viscous liquids than anorthite. In the case of albite this is inter-

Potash feldspar

Soda feldspar

Cornish stone

Nephelinesyenite

11.9 2.8 19.0 65.8 14.7

2.2 8.0 19.9 67.2 10.2

4.6 3.7 12.0 76.0 8.3

9.8 7.4 24.0 57.0 17.2

preted as evidence for a higher degree of polymerization in the melt. In the case of orthoclase it is due to the formation of leucite, KAlSi 2 O 6 , crystals. In all cases glasses are produced under the cooling rates normally encountered in ceramic processing. As indicated in the phase diagram, Fig. 2-11, albite melts at the lower temperature than orthoclase, but the addition of anorthite increases the melting temperature of

CaAI 2 Si 2 O 8 (lime feldspar)

1348 ± 5°

NaAISi 3 O 8 (soda feldspar)

1078 ± 3°

KAISi 3 O 8 (potash feldspar)

Figure 2-11. Pseud oternary phase diagram of the feldspars anorthitealbite-orthoclase.

66

2 Oxide Ceramics

soda feldspar while decreasing that of the potash feldspar (down to a minimum at about 22% anorthite). Similarly a 50%: 50% mixture of albite and orthoclase melts at a lower temperature than either end member. Often mixtures of fluxes are employed in order to take advantage of eutectic melting. Lithium bearing minerals are often very effective fluxes when used in conjunction with feldspar since such combinations form deep eutectics.

a)

2.2.3 Fillers

Most fillers used in silicate ceramics do not undergo irreversible changes during processing. As a result, the fillers may be accurately regarded as the dispersed phase in an engineering composite. The properties of the resultant ceramic, therefore, are strongly influenced by the properties and relative volume fraction of the filler. The most commonly employed filler is silica (either as quartz or cristobalite), but other materials which are used as fillers include alumina, mullite (often in the form of calcined clay-alumina mixtures), wollastonite, and zircon. 2.2.3.1 Crystal Structure

From a naive point of view silica, SiO 2 , is the simplest of the silicates. It is, however, a remarkably complex material. There are six acknowledged equilibrium polymorphs of silica depending on temperature and pressure. In silicate ceramics, the crystalline forms of interest are quartz, tridymite, and cristobalite. In addition to equilibrium structures there are metastable modifications of each of these three. Further, vitreous (or fused) silica glass has properties which differ significantly from crystalline silica.

b) Figure 2-12. (a) The perforated hexagonal net of tetrahedra that may be stacked to make the tridymite and cristobalite crystal structures in which the apices of alternate tetrahedra point in opposite directions, (b) The B-type layer which may be alternately stacked on the A-type layer, shown in (a), to represent the high temperature polymorph of tridymite. Note that a Btype layer in this structure may be obtained by a simple translation of the A-type layer.

Although they are framework silicates (ionic/covalent bonding in all three dimensions), both the tridymite and cristobalite structures can be built from hexagonal nets of tetrahedra. However, in contrast to the phyllosilicates, the apical oxygens of adjacent tetrahedra point in opposite directions as illustrated in Fig. 2-12 a. The two structures differ in a manner analogous to f.c.c. and h.c.p. metals. Figure 2-12 illustrates the A-B stacking sequence of SiO 4 tetrahedra which leads to tridymite and Fig. 2-13 shows the latter two steps in the A - B - C stacking sequence corresponding

2.2 Silicate Ceramics

7 X

7

b) Figure 2-13. The stacking sequence of hexagonal nets of tetrahedra leading to the high temperature polymorph of cristobalite. (a) A two layer stack of A- and B-type layers. Note in this structure that a 180° rotation is required in addition to a translation to obtain a B-type layer from an A-type. (b) A three layer stack of A-, B-, and C-type layers which contains the unit cell for cristobalite and onto which another A-type layer could be joined.

67

to cristobalite. In both illustrations, the addition of another layer leads to a repetition of the original layer. The quartz structure is markedly different from tridymite or cristobalite. Rather than being described in terms of the stacking of sheets, quartz is described (Griffen, 1992) in terms of a double helixes of tetrahedra as illustrated in Fig. 2-14. Each of these phases is stable over a defined temperature range at atmospheric pressure. In addition to the structures illustrated in Figs. 2-12, 2-13 and 2-14, there are lower symmetry derivative structures which may be viewed as distortions of the high temperature phases. Thus the commonly cited polymorphs of silica are: oc- and (3-quartz; high, middle, and low tridymite; and high and low cristobalite. Polymorphic transitions become an important consideration during thermal processing of a ceramic containing silica. A summary of the transitions between polymorphs in silica is presented in Fig. 2-15. The crystal structures of wollastonite, CaSiO 3 , fosterite, Mg 2 SiO 4 , and zircon, ZrSiO 4 , are complicated. In all cases, the silicon is in tetrahedral coordination. In wollastonite, the tetrahedra are linked in infinite one dimensional chains which are

Figure 2-14. The structure of quartz, which may be viewed in terms of double helices of tetrahedra. In this figure the projection is on a plane perpendicular to the axis of the helix and the orientation of the tetrahedra is such that they project onto this plane as squares.

2 Oxide Ceramics

68

Polymorphic Forms of Crystalline Silica at Normal Pressures High quartz

Reconstructive \ N 867°c

Reconstructive u. . nign tridymite ^ 1 4 7 0 o C

Displacive

160°C Displacive 573°C

u'nh cristobalite

|h

vll Middle tridymite

Displacive 200-270°C

Displacive I h 105°C vll

Low quartz

Low tridymite

Low cristobalite

linked together by calcium ions in irregular octahedral coordination (Klein and Hurlbut, 1985). In zircon the tetrahedra are all separated and share edges with a ZrO 8 triangular dodecahedron to form a 3-D connected structure (Griffen, 1992). The crystal structures of alumina and mullite are discussed in Chapter 1 of this Volume. 2.2.3.2 Mineral Sources

Silica is present in a number of forms (Worrall, 1986; Klein and Hurlbut, 1985). Quartz is the most common polymorph; sources include sand, sandstone, ganister, quartzite, and flint. Sands are a widely occurring and familiar material, commercial deposits are characterized by being of sufficient volume and high purity. Sandstone is a sedimentary rock which is easily ground to the crystallite size. Quartzite is a metamorphic rock derived from sandstone characterized by interlocking grains which result from solution and reprecipitation reactions. Ganister is a form of quartzite commonly located along coal seams and is typically contaminated with clay minerals. Flint is an accessory mineral found in chalk (CaCO3) deposits and is referred to

Figure 2-15. Summary of the polymorphic transformations of silica.

as a cryptocrystalline quartz (i.e., the individual crystals are too small to be resolved under an optical microscope). Both tridymite and cristobalite occur naturally, but are limited to volcanic extrusions. They are both common constituents in fired ceramics as a result of effectively irreversible reconstructive transformations. Diatomaceous earth (or diatomite) is an unusual form of silica. It is a sedimentary rock composed of the fossilized skeletons of the diatoms. The result is a highly siliceous mineral with very low bulk density and high specific surface area which is not abrasive. This material finds application in the fabrication of insulating refractories. Wollastonite is a metamorphic rock which has recently become an important mineral in ceramics. It is a soft mineral which is mined and may be crushed to reduce the particle size down to the crystallites which are acicular reflecting the chain silicate crystal structure (Klein and Hurlbut, 1985). Zircon is mined from mineral sand deposits throughout the world (Adams, 1989). Alumina is a synthetic material. The preparation of alumina is discussed further in Sec. 2.4.2.

2.2 Silicate Ceramics

2.2.3.3 Characteristic Properties

The overriding characteristic of silica fillers is their unique thermal strain. There are, in general, two distinct contributions to thermal strain, thermal expansion (as a result of the anharmonicity of the pair potential) and phase or polymorph changes. Both are dependent on the particular form of silica which is used. It is important to distinguish between reconstructive and displacive transformations. The former require bond breaking and a rearrangement of the connectivity between tetrahedra whereas the latter may be viewed as the result of bond bending leaving the topology unchanged. The transformations between the basic structures (quartz, tridymite, and cristobalite) are necessarily reconstructive. Therefore, they are relatively slow and thermally activated. Some conversion of quartz to cristobalite may occur during anneals at high temperature, but the reverse transformation will not occur simply because the kinetics of transformation are extremely slow in the temperature regime in which, say, quartz is thermodynamically stable. For whitewares the duration of firing is usually too short for reconstructive transformations to be significant, although this may not the case for silica refractories which are typically fired above 1400 °C. Significant conversion to tridymite and cristobalite may also occur during service at high temperature, and the presence of a lime flux will enhance the rate of conversion. In sharp contrast, the displacive transitions within a polymorph cannot be suppressed and are extremely rapid. The details of the displacive transformations remain an area of active research and, in fact, speculation (Griffen, 1992). However, the key consequence of interest in ceramic processing is the dimensional changes which

69

occur during the oc- to f$-quartz, low- to high-tridymite, and low- to high-cristobalite transformations. The molar volume of quartz is a smooth function of temperature except for the phase transformation which occurs at 573 °C which causes a sudden change in volume on the order of one percent. Interestingly, high quartz exhibits a negative thermal expansion coefficient. Tridymite exhibits a smaller displacive volume change at 105 °C, but also exhibits negative expansion above 575 °C. In the case of cristobalite the transformation occurs at a low temperature, about 215 °C, and the volume change is roughly three percent, that is, significantly larger than in the case of the other two polymorphs. The thermal expansion of other fillers is also an important property. Over the temperature range of interest zircon, mullite, wollastonite, and alumina are all considered to have low thermal expansion coefficients, in the range 4.5 to 8.8xl0~ 6 /°C respectively. Conversely, fosterite is used as a filler for specific applications because it has a high thermal expansion, but exhibits no phase transformation. Other characteristics of fillers which are important are index of refraction, to achieve translucency, as well as the dielectric constant and loss tangent, for low loss electrical insulators. 2.2.4 Triaxial Formulations

There are a sizable number of commercially important triaxial compositions. Design of a specific system is nearly always the result of a compromise between demands related to processing and a desired set of properties. The processing of most oxide ceramics (excepting glass) is based on powder technology. One characteristic of powder processing is that the geometrical information

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2 Oxide Ceramics

is stored independent of densification and microstructural development. There are three basic steps in the process: i) a powder mixture, sometimes suspended in a liquid, is formed into the desired shape, ii) the shaped powder compact is subjected to heat, and iii) the fired component is often glazed. The structure of the raw materials, the chemical reactions which occur during firing and the final microstructure all impact important properties. Phelps (1976) and Lehman et al. (1984) have pointed out that complete characterization of a triaxial formulation requires specification of: average chemical composition; percentages of individual mineral phases; particle size distribution; colloidal content; and amount of organics. Nevertheless there are general families which serve to illustrate the influence of each material. 2.2.4.1 Clay-Quartz-Feldspar

There are many variations within this general category. The term triaxial is somewhat misleading in this case since it is conventional to distinguish between the amount of ball clay and china clay and therefore four independent variables are required to completely specify the composition. Increasing the relative amount of ball clay generally improves the plasticity as well as the green strength, but often leads to discoloration as a result of contamination by iron-bearing accessory minerals. Therefore applications where green strength is at a premium, and color is of less importance, employ larger amounts of ball clay. One example where ball clays are heavily used is high tension insulators (Norton, 1976). These are extruded as large cylinders, perhaps 0.5 m in diameter and 1.5 m in length and then machined in the green state to form the ribs; green strength is crucial. Fine china represents the oppo-

site end of the spectrum where aesthetics take priority. China clays are used in these formulations, because they are nearly phase pure (unlike ball clays) and do not occur as iron bearing solid solutions (as do the smectites and illites). The maturation of a triaxial formulation during thermal treatment is a complex process and is not understandable from the equilibrium viewpoint. In many triaxial formulations the filler may be regarded as chemically nonreactive. Usually this is the result of sluggish kinetics rather than thermodynamic equilibrium. The decomposing clay forms mullite and rejects silica which combines with feldspar (and other fluxes) to form a glass. The quartz filler undergoes a displacive polymorph transition during heating, undergoes some conversion to cristobalite or tridymite and dissolves slowly in the glass. The final microstructure of the fired ceramic contains unaltered filler (in fact, the "unaltered" filler has experienced displacive phase transformations during both heating and cooling), glass, and mullite. Therefore, the fired whiteware is, in essence, a glass matrix composite containing two different types of particulate and typical mixing rules apply to the properties. The extent of glass formation affects properties such as dimensional stability and degree of densification. In systems which require high dimensional stability such as structural clay products (i.e., large ceramic pipes and tiles) the extent of glass formation is kept to a minimum (Brownell, 1976). In contrast, dental porcelains must fuse at low temperatures to be compatible with metal substructures and therefore may contain in excess of 80% feldspars. The physical properties of the glass are of obvious importance to the performance of the fired ceramic. One method for controlling the properties of the glass, such as

2.2 Silicate Ceramics

strength and thermal expansion coefficient is through the control of the potassium to sodium ratio in the feldspars. The index of refraction of the glass, on the other hand, is insensitive to this ratio; glasses derived from orthoclase, albite and nepheline syenite all have indices very near to 1.5 (Kingery et al., 1976). This is closely matched by a silica filler regardless of polymorph (the indices of quartz, tridymite and cristobalite are 1.55, 1.47, and 1.49 respectively). Mullite has a somewhat higher index, 1.64, but most of the light which is scattered results from residual porosity and material fired to low porosity is translucent. The role of the quartz is to increase the effective thermal expansion coefficient. The need for a high thermal strain during cooling is dictated by the desire to glaze the surface. A glaze may be defined as a thin glassy coating fired on the surface of a ceramic article. Although always "glassy", many contain appreciable volume fraction crystalline phases. A glaze serves many purposes beyond decoration. Properly glazed ceramics are substantially stronger, present a smoother surface, are impervious to gases or liquids, have increased corrosion resistance, and (in the case of some electrical porcelains) may be semiconducting (Taylor and Bull, 1986). Glazes are typically designed to be in a state of residual compression during service. The stress state is determined during cooling after the glaze has congealed. If the effective thermal expansion coefficient of the substrate is higher than that of the glaze, residual compression is achieved. This is not always easy to achieve since glazes are usually more heavily fluxed than the body and most fluxes increase the thermal expansion coefficient. The thermal expansion mismatch is strongly affected by the silica content in both the glaze and the

71

substrate. Increasing the silica content of either tends to increase the level of residual compression in the glaze. This apparent paradox is understood when it is recognized that the silica in the glaze is a glass (and thus lowers the thermal expansion) whereas the silica in the substrate is crystalline. The contraction associated with the pto a-quartz transformation on cooling helps to increase the effective thermal expansion coefficient of the ceramic and achieve the desired state. When the glaze fuses at temperatures below 573 °C, cristobalite may be the desired polymorph since the displacive transformation occurs at 215°C. In this case, flint is the preferred form of quartz since the kinetics of conversion to cristobalite are relatively rapid (Worrell, 1986). The penalty to be paid for the use of displacive phase transformations as a mechanism for tailoring thermal expansion is poor mechanical properties. The abrupt contraction of quartz (or cristobalite) leads to the formation of microcracks (Warshaw and Seider, 1967). These authors observed that the extent and type of microcracks were dependent on particle size and that the efficacy of quartz in affecting the thermal expansion was diminished as the extent of cracking increased. Quartz particles on the order of 80-150 }im produced cracking which virtually eliminated any effect on expansion. The strength was observed to increase as quartz particle size was decreased to 25 jim. Further reductions did not increase strength. 2.2.4.2 Clay-Alumina-Feldspar, Clay-Zircon-Feldspar

The properties of triaxial formulations may be significantly modified by the choice of the filler. Although quartz is inexpensive

72

2 Oxide Ceramics

and provides some desirable properties, other fillers are sometimes used. The substitution of alumina for quartz increases the strength of the fired ceramic (Warshaw and Seider, 1967; Dinsdale, 1986). However, it increases density, decreases translucency, and reduces the effective thermal expansion coefficient. The density of alumina, 3.96 g/cm3, is roughly 50% larger than quartz, 2.65 g/cm3, therefore in formulations containing fifty weight percent filler the density difference is substantial. There is also a decrease in translucency due to the alumina's higher index of refraction, 1.76, which leads to a greater degree of internal light scattering. The reduction in thermal expansion coefficient is the result of a modestly lower thermal expansion coefficient and the absence of a phase transformation. This property leads to the need for specialty glazes. Electrical porcelains (ceramics used as electrical insulators) are one area in which the high strengths associated with alumina based formulations find application (Moulson and Herbert, 1991). Zircon has yet higher density (4.68 g/ cm3), higher index of refraction (1.95), and lower thermal expansion, roughly one-half of alumina. In fact, the most common application of zircon in the ceramic industry is as a crystalline phase dispersed in glazes. In this application, it serves to lower the thermal expansion, increase opacity and increase corrosion resistance of the glaze (Taylor and Bull, 1986). Zircon also tolerates substitutional solid solution of both transition metals and rare earths. This has lead to the development of a wide array of zircon pigments (Taylor and Bull, 1986). Zircon based ceramic bodies find application as low loss electrical insulators (Grimshaw, 1971) or as corrosion resistant refractories (Chesters, 1973; Adams, 1989). Zircon formulations exhibit good thermal

shock resistance; a product of low thermal expansion and high thermal conductivity. Ball clays and montmorillonite clays are typically employed in such formulations in order to increase the plasticity. 2.2.4.3 Pyrophyllite- and Talc-Based Formulations, Clay-Wollastonite-Nepheline Syenite

Pyrophyllite, talc, and wollastonite find wide application in the manufacture of both wall tile and electrical porcelain (both billion US dollar industries). Tile must be manufactured to precise dimensional tolerances. This is typically achieved by processing such that the piece experiences a minimum amount of firing shrinkage, usually through selection of raw materials and control of the firing schedule to minimize densification during firing. One result of this is that most wall tile is porous after firing. Although they have nominally similar formulations, electrical porcelains are densified in order to develop high strength and reproducible electrical properties. The thermal decomposition of pyrophyllite at 1000 °C produces a felted mass of cristobalite crystals and mullite that suffers negligible firing shrinkage (Grimshaw, 1971). The thermal strain associated with the cristobalite transformation aids in glazing. Whiteware grades of pyrophyllite contain appreciable amounts of sericite (very fine grained muscovite mica) and quartz with a small amount of kaolin (Reiger, 1992) and therefore are effectively a triaxial formulation as-mined. Two distinct types of talc based bodies are produced, cordierite and steatite (Worrall, 1986; Moulson and Herbert, 1991). (The names form a somewhat mismatched set, cordierite is the principal phase formed during firing of the former, whereas steatite is simply a mineralogical term referring to

2.2 Silicate Ceramics

a natural deposit of the mineral talc.) In both cases the major crystal phase is formed as a result of chemical reaction during firing. A typical steatite formulation contains 60-90% (by weight) talc, 5 - 8 % feldspar, 5-20% clay, with 7-20% alkaline earth carbonate. During firing to 1300°C the talc decomposes to form enstatite, MgSiO 3 , by the reaction Mg3(Si2O5)2(OH)2 -> 3MgSiO 3 Enstatite exhibits a very low dielectric constant and a high thermal expansion coefficient leading to its use in electrical applications (Lee and Heuer, 1987). Cordierite formulations are comprised of a mixture of clay (kaolinite) and talc with a low expansion filler. The trioctahedral and dioctahedral phyllosilicates react during firing to produce cordierite by the overall reaction 2Mg 3 (Si 2 O 5 ) 2 (OH) 2 -> 3Mg 2 Al 4 Si 5 O 18

6Al 2 Si 2 O 5 (OH) 4 10H 2 O.

In polycrystalline form, cordierite has a very low thermal expansion coefficient and finds applications requiring good thermal shock resistance, but glazing is difficult. Since the body is reactive there is the possibility of distortions during firing. This may be minimized by the addition of a nonreactive filler. In order to achieve a low thermal expansion coefficient, fillers such as mullite, calcined clay (fired clay products which are crushed and recycled are referred to as grog) (Worrall, 1990), or zircon are used (Grimshaw, 1971). Tremolitic talc is the preferred form of raw material (Johnson, 1992). This material contains in the range of 30-50% prismatic tremolite, Ca 2 Mg 5 Si 8 O 22 (OH) 2 , which aids in dry pressing.

73

Increasing cost of fuel(s) has provided motivation for firing schedules of shorter duration and lower maximum temperature. As a result, wollastonite is becoming an increasingly important filler (Reiger, 1992) particularly in wall tile formulations. A typical formulation is 65% (by weight) wollastonite, 30% china clay, and 5% nepheline syenite (Sainamthip and Reed, 1987). The wollastonite serves both as an auxiliary flux to the nepheline syenite and as a filler. Reaction between the clay and wollastonite produces some anorthite. The extent of the reaction depends on the firing cycle indicating the structure is not at equilibrium. As in the case of pyrophyllite, one of the desirable features of this system is the minimal firing shrinkage, on the order of one percent. 2.2.5 Summary and Analogies in Single Phase Ceramics

Silicate ceramics illustrate the close relationship between crystal structure, microstructure and properties. The crystal structure of the raw materials affects not only properties in the green state, such as plasticity, but also the microstructural development during firing. For example, the silicon in a densified clay-quartz-feldspar ceramic, although everywhere in tetrahedral coordination, is in at least three qualitatively different states: in mullite crystals; in the glass matrix; and a discrete crystalline phase. The system is designed to be far from equilibrium and the distribution of silicon is directly related to the crystal structure and particle size of the raw materials. Such a nonequilibrium partitioning is also characteristic of other elements. Although these materials are often classified as clay-based, many of the formulations have little or no clay. Also, many of the properties of a fired ceramic are con-

74

2 Oxide Ceramics

trolled by the nature and amount of the filler rather than the clay content. Finally many of the ceramics which are considered single oxides, e.g., commercial 96% alumina substrates and refractories as discussed in Sec. 2.4 or the liquid phase sintered tetragonal zirconia polycrystals discussed in Sec. 2.5.3.3 may be considered as limiting cases of triaxial formulations. One interesting area for research is to develop systems which behave in a manner analogous to a triaxial formulation in the green state, but which convert to single phase ceramics upon firing. An example is the production of a single phase alumina from a mixture of colloidal aluminum monohydroxide and alumina powder. There are two forms of aluminum monohydroxide, diaspore and boehmite. The latter is routinely synthesized and a commercial product. It has been recognized that the crystal structure of boehmite leads to the formation of high aspect ratio platey particles which exhibit rheological behavior similar to clays (Pierre and Uhlmann, 1986). Boehmite is a difficult material to process due to its small particle size and phase transformation behavior, see Sec. 2.4.1, but it has been shown that it significantly improves the rheological characteristics of alumina slips and pastes in the green state (Chen and Cawley, 1992; Chou and Senna, 1987; Kindl et al., 1991). During firing it is converted to a-alumina yielding a single phase ceramic.

2.3 MgO, Magnesia, Periclase Magnesia refractories are widely used particularly in the production of iron and steel because of their general availability, high thermal conductivity, refractoriness, and resistance to basic slags especially when combined with graphite. Section

2.3.2.3 will be concerned extensively with basic refractories including magnesia and doloma. There are presently few commercial applications of dense magnesia in engineering ceramics because it hydrates readily when exposed to air and has few property advantages over alumina. 2.3.1 Crystal Structure MgO is a highly ionic crystal with the M g - O bonds having about 80% ionic character. Its crystal structure is the simplest of any ceramic being cubic with the rock salt structure (discussed in Chapter 1). The cubic structure of MgO is maintained from room temperature to its melting point. Unlike many ceramics, it has no deleterious polymorphic transitions. 2.3.2 Mineral Sources and Production

MgO occurs rarely as the mineral periclase but is abundant as magnesite (MgCO3), and dolomite (Mg,Ca)CO 3 . High-purity magnesite ores can simply be beneficiated and calcined to MgO at 500-700 °C. Magnesia refractories are often called magnesites even though they contain MgO not MgCO 3 and may not even have been derived from magnesite ore. Doloma (CaO • MgO) refractories derived from dolomite are still widely used, particularly in Europe. Other commercial sources of magnesia are sea water, brines and deposits of Mg-rich salt. Sea water accounts for most MgO production in the USA, Japan and the UK. Worldwide mined natural magnesite accounts for about 67% of refractory MgO with synthetic sources for about 33% (Mikami, 1983). Sea water contains about 1 kg of MgO per 500 L as magnesium chloride and is reacted with an alkali source (usually lime or slaked doloma) to precipitate

75

2.3 MgO, Magnesia, Periclase

Mg(OH) 2 i.e

Table 2-5. Physical properties of raw materials used in refractory production (Brown and White, 1986).

(Ca,Mg)(CO)3 dolomite ore 1100

°C>

CaO 4- MgO burnt doloma

ZZ£>

Ca(OH)2 + Mg(OH)2

Composition (wt.%)

slaked doloma

2 Mg(OH)2 (s) + CaSO4(aq) + CaCl2 (aq) "spent" sea water

The hydroxide precipitate is washed, filter pressed, dried and calcined in large rotary kilns at 750-900 °C. The as-calcined crystal size from natural ores or hydroxide from sea water is well below 1 |im. Such powder has a large surface area and rapidly reacts with atmospheric CO 2 and H 2 O. Consequently, "mineralizers" such as NaCl or NaOH may be added to encourage grain growth and/or the ore is "dead burned" or calcined to high temperature (1500-1700 °C) to give 3-4 jim grains which are effectively resistant to water vapor and carbon dioxide. Adding silica or Fe 2 O 3 to the ore and partially melting while dead-burning gives sintered "clinker" grain which is used as the raw material for later brick or monolithic refractory production. Sea-water derived MgO contains enough excess lime and other impurities so that additions may not need to be made to produce adequate clinker. For the best quality refractories the MgO is fused above 2750 °C in an electric arc furnace which removes the undesirable, high-vapor pressure, impurities. Typical properties of the starting grains for refractory production are given in Table 2-5 (Brown and White, 1986). Very high purity MgO may be synthesized using chemical techniques. For example, Gardner and Messing (1984) used evaporative spray decomposition of solutions to prepare magnesia. Their results indicate that the efficiency of conversion and the state of agglomeration of the resultant powder are both dependent on the nature

MgO A12O3 Fe 2 O 3 CaO SiO2 B2O3

c/s

Bulk density (gem" 3 ) Grain porosity (vol.%)

Sintered MgO Clinker

Sintered Doloma Clinker

Fused MgO

96-99 39-40 97-98 0.05-0.25 0.3-0.8 0.1-0.2 0.05-0.2 0.6-1.0 0.1-0.5 0.6-2.4 57.5-58.5 0.9-2.5 0.1-0.5 0.6-1.1 0.3-0.9 0.005-0.6 0.004-0.01 2-4 1-5 3.5 3.4-3.45 3.15-3.25 2-3

5.5-7

0.5-2

of the precursor. Fine unagglomerated particles were obtained when an acetate precursor was employed, but either incomplete reaction or agglomeration was observed when chloride, sulfate, or nitrate precursors were employed. 2.3.3 Properties 2.3.3.1 Single-Crystal MgO MgO is often regarded as a model ionically bonded ceramic. Some useful physical property data are given in Table 2-6. It adopts the relatively simple rock salt crystal structure (see Chapter 1 of this Volume) which is a convenient structure for illustrating the effect of ionic bonding on crystal defect structure. As discussed more fully in Chap. 7, Sec. 7.4.2, the crystal structure of ionic materials increases the energy associated with both the generation and glide of dislocations. Both result from the localized charges associated with lattice sites. As illustrated in Fig. 2-16, a stable edge dislocation cannot be generated by the familiar hypothetical removal of a halfplane. Instead, pairs of half-planes must be

76

2 Oxide Ceramics

Figure 2-16. Illustration of the effect of electrostatic repulsion between next nearest neighbors on the hypothetical removal of a half-plane of atoms from a rock salt structure ionic ceramic.

Table 2-6. Physical property data for single-crystal MgO. Property 2800

Tm (°O Density (gem" 3 )

3.58

Thermal conductivity (W/mK)

100 °C 1000°C

7.1 37.6

Linear thermal expansion (xio-6/°Q

RT 200 °C 500 °C 1000°C

6.5 11 12.7 13.9

0-1000°C

13.5

Mean value Average refractive index Elastic modulus (GPa)

1.74 300

removed to achieve nearest neighbors with unlike charges in the relaxed structure. The formation of dislocations with such large Burger's vectors is energetically unfavorable. Permissible slip directions are also restricted by localized charges. Slip is restricted, at low temperature, to those com-

binations of planes and directions that do not require ions of like charges to be brought into contact in saddle point configurations. MgO is one of the few oxide ceramics to exhibit a high degree of plasticity. This is a result of the existence of slip planes with a minimum of electrostatic faulting, see Fig. 7-53. MgO has also been used as a model system to illustrate the consequence of ionic bonding on the formation of point defects. In discussing point defects, it is convenient to distinguish between the anion and cation sublattices. The thermal production of intrinsic defects may be described using the following pseudo-chemical reactions written in Kroger-Vink notation (Kroger, 1974), where the subscript refers to the site of species (V refers to a vacancy and i to an interstitial site), and the superscript refers to the charge relative to the lattice (' indicates negative, ' indicates positive, and x neutral relative charge), Anion Frenkel disorder

o o -> or + v o Cation Frenkel disorder Schottky disorder Null _> V "

4- V "

It is evident that the defect populations on the Mg and O sublattices are coupled through the Schottky defect reaction. Extrinsic defects produced by aliovalent impurities may also be written in pseudochemical form. For example, consider the dissolution of A12O3 in MgO, this may be written either as A12O3 or A12O3

MgOv

2.3 MgO, Magnesia, Periclase

The appropriate reaction depends on the energetics associated with the production of oxygen interstitials and magnesium vacancies. A qualitative argument based on ionic size is sometimes used to argue that the energy associated with the production of oxygen interstitials is prohibitively high and that trivalent impurities are more likely to be compensated by the production of vacant Mg sites. In principle, either direct spectroscopic measurements (Crawford, 1984) or indirect measurements of, for example, the effect of doping on mass transport can be used to determine the dominant defect species. However, it has become clear that the use of simple mass action laws based on the assumption of fully ionized point defects originally developed to describe the behavior of alkali halides does not give reliable predictions in the case of MgO (and other oxides). The first complication is the very high energies associated with the intrinsic defect reactions. As has been pointed out by Viera and Brook (1984), intrinsic diffusion will not be observed unless the total impurity level is below 10" 7 mole fraction (or 0.1 parts per million). This level of purity cannot be achieved in real materials; thus the observed behavior is determined by a competition between low level impurities, both intentional and incidental. Secondly, and more importantly, it has become clear the defect association, or clustering, is important in determining the defect structure of both undoped and doped MgO (Gourdin and Kingery, 1979; Yager and Kingery, 1984; Mackrodt, 1984). Defect clustering interferes with direct interpretation of experimental results in at least two ways. Firstly, it is difficult to estimate the energetics of defect clusters a priori, or to determine them from experiments of commercial purity. Secondly, when associa-

77

tion, or clustering, occurs during cooling the defect structure which is quantified through room temperature experiments may not correspond to either the equilibrium high temperature or room temperature structure, but a metastable mixture of point defects, associates, and clusters (Yager and Kingery, 1984). Due to these complications the details of the defect structure of even model oxide systems such as MgO are not completely determined. Single crystal MgO does not find wide commercial application. 2.3.3.2 Refractory Fabrication and Microstructure

The most important commercial use of magnesia is in the fabrication of basic refractories used in steelmaking. The historical development of basic bricks has been intimately linked with improvements in steelmaking techniques. Until the early 1970s most BOS (basic oxygen steelmaking) vessels had simple doloma linings. Doloma is an inexpensive material which is produced through the calcination of dolomite, (Mg,Ca)(CO 3 ) 2 , and has the nominal composition (Mg,Ca)O 2 . Blending doloma with magnesia or using all magnesia linings was observed to yield significantly increased vessel life. It was also noticed that vessels lined with bricks containing pitch or tar (added to prevent hydration) had longer lives. The less than 5% residual carbon left from the pitch after firing was beneficial since it inhibited wetting by slags and its high thermal conductivity improved thermal shock resistance. This led logically to systematic additions of much higher C levels (up to 20 wt.%) and the evolution of MgO-graphite bricks currently used to line BOS vessels. The simpler, but now less common, cases of magnesia and doloma bricks will be con-

78

2 Oxide Ceramics

Table 2-7. Chemical and physical properties of densified basic brick. Chemical analysis (wt.%) MgO Fe 2 O 3 A12O3 CaO SiO2 B2O3 Apparent porosity (%) Bulk density (gcm~ 3 ) Cold crushing strength (MPa) Thermal conductivity (W/mK) mean at 900 °C MOR (MPa) RT 1400°C 1600°C

91-97 0.4-5 0.1-2 1-3 0.8-2 1000°C). Unaffected by atmospheric exposure Unaffected by marine exposure Unaffected by in-vivo exposure Non-thrombogenic Non-reactive with body fluids

2.4 AI 2 O 3 , Alumina, Sapphire, Corundum

tion phases are denoted as y, %, r|, i, e, 8, 0 and K and are of particular importance because of their use as catalysts substrates and because the characteristics of oc-alumina can be affected by the crystal structure^) of the precursor(s). All of the metastable phases have partially disordered crystal structures based on a closepacked oxygen sublattice with varying interstitial aluminum configurations. As equilibrium is approached the structures become more ordered until stable oc-alumina is formed. The sequence of transition aluminas that form is strongly dependent on the starting material and how it is processed. For example, if the starting material is boehmite, AIO(OH), formed from solution or amorphous alumina then the most probable sequence is Y->8->9->OC. However, if the starting material is gibbsite, oc-Al(OH)3, then the sequence may include %-*Y-»X-> 0->a even though boehmite is formed prior to %. Diaspore, another polymorph of AIO(OH) transforms directly to a-Al 2 O 3 . Formation of the transition aluminas from hydrated compounds is often accompanied by development of a highly porous microstructure (Wilson, 1979). The crystal structures of the transition aluminas are characterized by the maintenance of an approximately f.c.c. anion sublattice (Wilson, 1979). While usually treated as cubic, y-alumina has a slightly tetragonally-distorted defect spinel structure (c/a about 0.99, the distortion varying with heat treatment). 5-alumina has a tetragonal superstructure with one unit cell parameter tripled with the cation vacancies thought to be ordered on the octahedral sites of the spinel structure. 0-alumina is monoclinic with space group A2/m but still similar to spinel and often observed to be twinned. r| is cubic spinel.

87

2.4.2 Mineral Sources and Chemical Synthesis Alumina occurs abundantly in nature, most often as impure hydroxides which are the essential constituents of bauxite ores. Bauxite is an impure mixture of boehmite and/or diaspore, which are a and P forms of AIO(OH), respectively, with gibbsite A1(OH)3. Most raw bauxite is refined by the Bayer process to remove impurities such as SiO 2 , Fe 2 O 3 and TiO 2 leaving a nominal 99.5% alumina product with Na 2 O as the dominant impurity. The high-purity grades of alumina manufactured from these ores of interest to the ceramics/refractories industries are: calcined, low-soda, reactive, tabular and fused. The production, composition and morphology of each of these powders will be discussed in the following sections. The refining of bauxite occurs in several stages. After physical beneficiation (crushing, grinding, and screening), the ore undergoes hydrothermal digestion to get the ions in solution using an NaOH solution under 0.5 MPa pressure at a temperature of 150-160°C. The aluminum hydroxides and much of the siliceous impurities go into solution, as sodium aluminate and sodium silicate respectively. Solid impurities such as TiO 2 and Fe 2 O 3 remain undissolved and are removed as red mud by filtration. After cooling the filtered solution is seeded with gibbsite and precipitation of gibbsite is induced by bubbling carbon dioxide through the solution. Since precipitation is heterogeneous, the temperature, alumina supersaturation and seed content all affect particle size. Drying of the precipitate invariably leads to agglomeration because the residual salts present in the solution precipitate as the water evaporates forming solid bridges between particles. A

88

2 Oxide Ceramics

Figure 2-26. SEM image of Bayer process gibbsite (from Southern, 1991).

typical Bayer gibbsite particle is shown in Fig. 2-26. Note the large number of angular crystallites about 20 jam diameter making up the agglomerate. Upon calcination, water loss begins at about 180 °C leading to high surface area, porous, transition alumina phases. Dehydroxylation of gibbsite begins by the opening of fissures parallel to (0001) as shown by the TEM image (Fig. 2-27). The surface area can reach over 350m 2 g~ 1 at about 400 °C although above this temperature the area decreases due to sintering. At 800 °C the surface area is reduced to about 100 m 2 g" 1 . As calcination proceeds a system of tubular pores parallel to [0001] of gibbsite and fissures parallel to the {0001} planes evolves. a-Al 2 O 3 finally forms at about 1150°C and the fissures are still clearly visible (Fig. 2-28). Consequently, the particle size and shape of the oc-alumina is determined by the crystal structure of the original hydroxide and the series of phase transformations which occur during calcination. Without the presence of mineralizers the structure is retained but the cell walls between the pores grow into small QC-A12O3

Figure 2-27. Bright-field TEM image showing fissures along (0001) forming in gibbsite upon dehydroxylation (courtesy of Alcan Chemicals Ltd., Banbury, UK).

Figure 2-28. SEM image showing fissures in a-Al 2 O 3 formed by dehydroxylation of gibbsite at 1150°C (courtesy of Alcan Chemicals Ltd., Banbury, UK).

2.4 AI 2 O 3 , Alumina, Sapphire, Corundum

89

Figure 2-29. Coral structure of unmincralizcd calcined Bayer alumina (from Southern, 1991).

crystallites while the aggregates retain a pseudomorphic relationship with the original gibbsite. This fine vermicular structure of the calcined alumina is often referred to as a coral structure (Fig. 2-29). As the calcination temperature increases the crystals grow eventually sintering together above 1600°C. Mineralizers such as fluorine, chlorine and boric acid are sometimes used to lower the transformation temperature to a although they also affect the crystal shape; for example, fluorine-mineralized alumina has very platey crystals (Fig. 2-30). Typical commercial aluminas are calcined at 1300-1400°C. High-temperature calcination produces almost 100% a-alumina while material calcined at lower temperatures, that has smaller crystallite size, may also retain some transition alumina phases, usually y. This may cause difficulties in subsequent processing of the powder. Although a-alumina is effectively insoluble in aqueous solutions, y-alumina readily dissolves in weak acid solutions. This leads to the formation of hard agglomerates upon drying of alumina suspensions since the dissolved y-alumina will precipitate at particle contacts as the water evaporates (Niesz and Bennett, 1978).

Figure 2-30. Platey calcined Bayer alumina crystals arising from addition of fluorine mineralizer (from Southern, 1991).

The Bayer process produces highly-aggregated powders which must be milled to release the crystallites and so enable high packing densities and reduced porosity in the green formed state. The degree of milling required depends both on the application and the alumina. The evolution of these commercial Bayer-process powder morphologies is controlled during precipitation and calcination to facilitate the formation of aggregates which are easiest to breakup during milling. Powder (aggregate and crystallite) size and shape control permits the production of aluminas having desired packing and/or sintering characteristics. Intense milling can produce very fine particle sizes but also may introduce intolerable amounts of contamination from the milling media. Careful control of the Bayer

90

2 Oxide Ceramics

process and calcination/milling conditions can give commercial aluminas of up to 99.99% purity. As shown in the Table 2-16 normal Bayer alumina grades contain about 0.5 wt.% Na 2 O which degrades many properties. The Na ion is mobile in an electric field causing deterioration of electrical properties and it can be leached during wet processing unfavorably influencing rheology, pH and slip stability. If sodium P alumina (Na 2 O • 11A12O3) forms on sintering the density, strength, thermal shock and corrosion resistance are all negatively impacted. Consequently, there is significant demand for low soda alumina. Table 2-17 indicates the Na 2 O contents required for common applications of calcined Bayer alumina powders (MacZura et al., 1992). Low soda alumina is produced by i) using low soda gibbsite prepared by adjusting the Bayer process precipitation conditions (US Patent 4014985); ii) washing alumina prepared at 900 °C that has a very high surface area followed by further hightemperature calcining to a alumina; or iii) adding chlorine, halides, sulfate or borates which react to form volatile or soluble sodium salts which can then be readily removed (e.g., French Patent 1389829, US Patent 3092452). Reactive alumina powders are defined (Southern, 1991) as those that give high fired densities at relatively low (i.e., about 1550-1600 °C) firing temperatures in a > 99.5% alumina body. For high reactivity the Bayer alumina is processed to be pure, fine, equiaxed and a phase. However, if the particle size is too small, handling and processing problems may give low green density and poor sintering. Reactive powders require low soda but high surface area. Table 2-18 (Southern, 1991) illustrates the effect of these variables on sintered density for several alumina powders, powder 3 be-

Table 2-16. Typical chemical analyses of Bayer process aluminas. Composition (wt.%) A12O3 SiO 2 Fe 2 O 3 Na 2 O

Normal Na 2 O >98.9-99.7 0.02-0.05 0.04-0.05 0.3-0.6

Low Na 2 O

Reactive

99.5-99.8 0.07-0.12 0.04-0.06 99.5 0.04-0.08 0.01-0.02 0.08

Table 2-17. Maximum Na 2 O content and particle sizes of aluminas for particular applications (MacZura et al., 1992). Application

]Median crystal Na 2 O content size (jam) range (%)

Electronic ceramics Sodium vapor lamps Structural ceramics Fused abrasives Ceramic fibers High tech. refractories Spark plugs

99.1 0.01-0.02 0-0.3 0.02-0.36

>99 0.02-0.05 0.03-0.15 0.02-0.5 0.02-0.02

3.56

3.86

95.5 1.2 0.18 0 2.6 0.45 3.92

3

3

1

2.4.2.1 Fused and Tabular Refractory Grades

Tabular grade refractory alumina powder is 99.9% pure with a low porosity and controlled particle size and shape (Fig. 2-31). Tabular aluminas are used extensively in alumina-graphite refractories, and

Figure 2-31. Milled tabular alumina powder.

in low-cement and ultra low cement castable refractory mixes. Tabular alumina crystals are produced by heating pellets of calcined alumina, 2 cm diameter, at temperatures > 1925 °C, just below the melting temperature, until near 100% conversion of the fine, oc-alumina crystallites into large (40 to > 200 pm), hexagonal, elongated tabletshaped crystals occurs. The recrystallized alumina is in the massive state and tabular alumina crystals are hard and dense with good thermal conductivity and high crushing strength. A wide range of particle sizes (25 jim to 6 mm) are made by crushing and grading the tabular alumina. Table 2-19 lists the composition and properties of tabular and fused alumina. In the process used to produce fused alumina the batch is mixed, charged and melted in a Higgins-type electric arc furnace using graphite electrodes with a removable, water-cooled, steel shell. The fused refractory grain is massive and requires crushing to obtain the desired particle size. Fused alumina is produced in two forms: white and brown. White fused alumina is made from calcined Bayer alumina

92

2 Oxide Ceramics

and different grades are available based on alkali content. It is used extensively in high-temperature refractory bricks as well as monolithic refractories. Brown fused alumina is made from bauxite ore under conditions which allow only partial removal of impurities as ferrosilicon. The residual impurities in the product lowers its melting temperature by about 50 °C, but it is much tougher than white fused alumina and has superior wear resistance. This less costly material is commonly used in refractories for blast furnace troughs and as induction furnace linings. X-ray diffraction of brown fused alumina reveals predominately a-Al 2 O 3 peaks whereas the higher Na 2 O content of white fused alumina (a residue from the Bayer process) produces detectable amounts of N a 2 O l l A l 2 O 3 ((3-alumina). 2.4.2.2 Abrasives

Alumina abrasives are commonly used in grinding wheels and coated abrasive paper (emery). The conventional route to synthesis of abrasive grain involves melting alumina powder, adding MgO dopant for grain size control, and allowing the melt to solidify. While used extensively, this route does have some drawbacks including: i) variations in cooling rate result in a variable product with a wide range of crystallite sizes and formation of unwanted MgAl 2 O 4 spinel; ii) the need to crush the solid abrasive which requires extensive, and energy intensive, grinding (unsuitablysized grains are discarded and recycled to the melt); iii) the high temperatures required are costly to achieve. An alternative sol-gel production route does not suffer from these disadvantages. Abrasive alumina can be made via a colloidal sol-gel production process in which aqueous pseudoboehmite particles are

peptized to a colloidal dispersion with acid addition. The sol is doped by adding an Mg salt, gelled and dried. The brittle, but soft, gel can be crushed and sieved prior to calcination to produce oc-alumina. This allows fine grit to be produced with far less energy consumption than is necessary when grinding dense oc-alumina. Calcination at 135O°C gives alumina with a 300 nm crystallite size which is much smaller than the melt-derived fused grain and imparts improved abrasive properties. Alumina-zirconia grain may also be manufactured using a similar route (Segal, 1989). 2.4.2.3 Fibers

Aluminosilicate ceramic fibers based on alumina have been commercially available for many years. The largest use for highalumina aluminosilicate refractory fibers (containing less than 28 wt.% silica) is as high-temperature low-thermal-mass furnace insulation. The non-continuous or wool-like fibers are used as loose wool, blankets, felts, paper and board. The loose wool is made by melt spinning or air jet blowing of kaolin-based materials. In the melt spinning process the molten material is fed onto a vertically oriented, rapidly rotating disc from which fibers are thrown by centrifugal force. In the blowing process the molten material is poured into the path of a high-velocity blast from a stream of compressed air which shreds the stream into droplets and elongates them into fibers (Cooke, 1991). Only melts containing substantial amounts of silica are suitable for these processing routes. The resultant fibers therefore are of limited refractoriness, which precludes their use in CMCs. However, fibers with 52% alumina can be used as insulation up to 1250°C and those containing 65% A12O3 can be used up to 1450°C.

2.4 AI 2 O 3 , Alumina, Sapphire, Corundum

Non-continuous alumina fibers were developed in the 1970s (Sowman, 1988) using a sol-gel processing route from a basic aluminum chloride salt starting solution. The sol is doped with a silica source which acts as a grain growth inhibitor. The fiber wool is made by dry centrifugal spinning of a controlled viscosity sol and the green fiber is then calcined to ceramic. The benefit of this route over using kaolin-based melts is that lower silica contents can be used since melt fluidity is not a factor in fabrication, yielding fibers that are more refractory. The room temperature fracture strengths of commercial alumina fibers are typically in excess of 1 GPa; note the fiber is still only 96% alumina. Continuous alumina fibers were developed in the late 1970s and are produced on a much smaller scale than the insulating fibers discussed above (Stacey, 1988). Commercial continuous alumina fibers are dry spun, drawn or extruded from an alumina precursor which may be a solution, sol or slurry dispersion to give green fibers which are calcined, often in several stages, to form the ceramic fiber. For example, one process uses a starting mixture of basic aluminum chloride in solution with 0.5 jim a-Al 2 O 3 and dissolved organic polymers such as polyvinyl alcohol. These processing routes are flexible in terms of the compositions that can be employed but require careful control of quite complex process conditions. The microstructure of the final product is strongly affected by purity, uniformity, molecular weight and size distribution of the starting material used as well as by processing conditions. During the development of the fiber microstructure from the amorphous precursor various intermediate transition aluminas form before the thermodynamically stable a-Al 2 O 3 . Grain growth and pore shrinkage accompany the formation of the

93

different transition aluminas as the temperature is increased. The main effect of silica or magnesia additions during processing is to increase the stability region of r| and 5 aluminas and to restrict grain growth, respectively. Most fibers are made from gel precursors fired at 1000-1300 °C so they may often consist of these intermediate polymorphs and not a-Al 2 O 3 . Grain growth and consequent strength degradation limits the temperature of fiber use as a reinforcing phase. Additionally, phase transformations may occur if the fiber is not in the thermodynamically stable state. A recent development is the growth of single-crystal pure alumina fibers from a melt using a modified Czochralski method termed edge-defined film-fed growth (EFG) developed by LaBelle (1980). In this technique the fiber is grown through a small diameter molybdenum crucible and wound continuously onto spools. Various crystal orientations can be grown and the properties of one commercial fiber are given in Table 2-15. Obvious benefits of single crystal fibers for high-temperature CMC reinforcements include the lack of weakening grain boundary phases and no propensity for grain growth. In addition to the EFG process, it is possible to grow continuous single crystal alumina fibers using the laser heated float zone (LHFZ) technique. In this method of fiber production a small molten zone is produced by local heating of a cylindrical rod using a CO 2 laser {X = 10.6 jim) as a focused heat source, see Fig. 2-32. The molten zone is held in place by surface tension. A tapered seed fiber is brought into contact with the molten tip of the feed rod and lowered until it is wet by the liquid. The pull rate of the seed fiber and feed rate of the feed rod are adjusted to allow growth of crystals with the required dimensions. The absence of containers eliminates

94

2 Oxide Ceramics

which failed at nearly the same applied stress are shown in Fig. 2-33 b. It was observed that the critical flaw in DS-eutectic fiber was considerably larger, implying a higher fracture toughness. 2.4.3 Ceramic Fabrication and Microstructural Evolution

Figure 2-32. Laser heated floated zone of a chromedoped single crystal alumina fiber. An extruded green rod is fed upwards through a brass mandrel into the region heated by the laser at which point fusion occurs. The dark band immediately above the fusion zone is carbon due to combustion of the organic binder. (Courtesy of A. Sayir, CWRU)

contamination from crucible corrosion, can allow for more efficient outgassing of the melt and permits the use of very large thermal gradients during growth (Haggerty etal., 1976). In addition to single-phase alumina fibers, it is possible to produce directionally solidified (DS) eutectics such as A12O3 -YAG (yttrium-aluminum-garnet). Data on the failure strength of experimental A12O3 and DS-eutectic A12O3-YAG fibers are compared in Fig. 2-33 a and the failure origins on two representative fibers

High density, high-alumina ceramics can be categorized as a) those densified with the aid of a liquid by viscous flow and b) those where there is essentially no liquid phase and sintering is via the solid state. Solid state sintered aluminas are highly pure (>99.7wt.% A12O3) requiring very pure starting powders and careful processing. They are used in the most demanding applications requiring good mechanical properties and/or extreme corrosion resistance at high temperature such as sodium vapor lamp envelopes. Liquid phase sintered, LPS, aluminas are less pure typically ranging from 80-99.7% A12O3. Although, it should be noted, there is some doubt as to whether 0.3% impurities is sufficient for LPS. Many high alumina LPS compositions with only small amounts of grain boundary glass are used for electrical and engineering applications. For example, 96% A12O3 compositions are used as substrates in microelectronic circuits. 2.4.3.1 Bulk Single Crystal Alumina

Bulk single crystal alumina is exploited in a number of commercial applications beyond the structural fibers discussed in Sec. 2.4.2.3. Historically, the first commercial uses of synthetic sapphires and rubies were as jewelry, abrasion resistant thread guides, components in the clockwork mechanism in watches and draw plates for wire drawing (Belyaev, 1980). Another more familiar applications is that of ruby, chromium doped single crystal alumina, as

2.4 AI 2 O 3 , Alumina, Sapphire, Corundum

ISiS (a) 4000 ,—

As-received ^sapphire fiber

3000

Tensile Strength MPa

200

As-grown YAG-AI fiber

°

1000

I (b)

0

I

I

1

1

1

1

200 400 600 800 1000 1200 1400

95

Figure 2-33. (a) A comparison of the fracture surfaces of directionally solidified A12O3/YAG eutectic fiber (left) and c-axis sapphire (right). The high tensile strength of the eutectic fiber, 911 MPa, in spite of the large flaw size (void) « 3.3 jim demonstrates the dramatic improvements against crack propagation (high toughness). The sapphire fibers have low toughness and are highly sensitive to small surface and internal flaws (voids). In this case, a fiber with a »1.4um flaw fractured with a tensile strength of 400 MPa. (b) The tensile strength of directionally solidified A12O3/Y3A15O12 (YAG) eutectic fibers as a function of temperature. This oxide-oxide aligned microcomposite fiber system has been engineered to have strength retention at elevated temperatures (800 MPa at 1400 °C). High temperature strength is retained in the eutectic system due to the presence of the non-twinable YAG phase. High temperature creep resistance is attributed to the large aspect ratio (thickness to length) of the eutectic structure along the fiber axis, resulting in a high dislocation climb barrier. (A. Sayir, CWRU and L. E. Matson, Wright Laboratories, Wright-Patterson Air Force Base, OH)

Temperature °C

the active optical element for an important class of solid state lasers. Variants of the EFG process have led to the exploitation of the unique combination of properties offered by single crystal alumina in diverse applications. These include: substrates for silicon-on-sapphire integrated circuits; arc tubes for lighting applications; hollow fibers as optical waveguides for medical applications of lasers; and (one of the most important

commercial applications) as abrasion resistant windows for supermarket laser scanners. One example of the flexibility of the EFG process is the hemispherical missile dome shown in Fig. 2-34. 2.4.3.2 Solid State Sintering

Solid state sintering of polycrystalline alumina developed from a commercial need (see, for example, Bennison and

96

2 Oxide Ceramics

Figure 2-34. An example of bulk single crystal aluminum oxide. A hemispherical missile dome fabricated using the EFG process. (Saphikon, Inc., Milford, NH)

Harmer, 1990 a). In the late 1950s researchers at the General Electric Company laboratories in the USA required a translucent material which was resistant to alkali attack at high temperatures for use in envelopes in sodium-vapor discharge lamps, the sort now used extensively for street lighting. The primary problem was the inherent opacity in sintered material due to the presence of pores which efficiently scatter visible light. Coble (1961) determined that the addition of 0.25 wt.% MgO enabled alumina to be sintered to a finegrained, low porosity, translucent state after firing at 1900°C in hydrogen atmosphere, see Fig. 2-35. This material was given the trade name Lucalox for transLUCent ALuminum OXide. Determining the mechanism(s) of grain growth inhibition in A12O3 by MgO has been a major research task ever since the pioneering work of Coble. However, early studies of solid state sintering were complicated by the presence of both liquid phases

at the grain boundaries (produced by unintentional impurities) and porosity due to agglomerates in the starting powder. Only recently have these difficulties been overcome. For example, Handwerker et al. (1989) have shown that the growth of large, anisotropic, and facetted grains in nomi-

Figure 2-35. SEM image of cquiaxcd grain structure in high-density MgO-doped alumina (from Handwerker et al., 1989).

2.4 AI 2 O 3 , Alumina, Sapphire, Corundum

nally undoped alumina was due to the presence of a liquid phase at sintering temperatures. In a set of experiments employing very high purity material, Bennison and Harmer (1990 b) have demonstrated that the MgO suppresses grain boundary migration rate by a factor of 50 times. Rodel and Glaeser (1990 a, b) have further shown that the effect of MgO is dependent on the crystallography of the individual grains. The effect of MgO doping in model experiments was to suppress the migration of the {1120} planes. The results of Baik and Moon (1991) suggest an indirect effect producd by MgO doping. Both Mg and Ca (always present, even in the most pure aluminas) segregate to grain boundaries. The segregation of Ca is highly sensitive to crystallographic orientation whereas Mg is insensitive. When both Ca and Mg are present, the anisotropy of Ca segregation is reduced. 2.4.3.3 Liquid Phase Sintering

Most commercial aluminas have intentional additions of CaO and SiO 2 . SiO 2 has low solubility in the alumina and segregates to the grain boundaries forming a liquid phase at high temperature. The effect of MgO-doping in liquid phase sintering is analogous to that observed for solid state sintering; the grains of LPS alumina without MgO are anisotropic and facetted whereas the presence of MgO in LPS A12O3 homogenizes the grain size distribution. The abnormal grain growth, see Fig. 2-36, in commercial-purity alumina comes from the presence of impurities, such as Ca and Si, in the glassy grain boundaries (Handwerker et al., 1989). Chemical inhomogeneities in the starting powders are, in fact, more likely to be responsible for ab-

97

Figure2-36. Microstructure after lOmin. at 1440 °C of an alumina containing substantial liquid-forming impurities (from Morrell, 1985).

normal grain growth than morphological inhomogeneities such as large grains or hard agglomerates. A qualitative correlation is observed between faceted discontinuously grown grains and a liquid phase at the facet-matrix interface during sintering. Song and Coble (1990) observed platelike abnormal grains in alumina doped with 0.25 mol.% of Na 2 O + SiO 2 , CaO + SiO 2 , SrO + SiO2 and BaO + SiO 2 . They determined that the driving force for platelike grain formation is the difference in solubility between growing and shrinking grains due to the curvature and anisotropic interfacial energies of A12O3 with respect to the liquid. Grain growth is controlled by pore drag until the compact reaches a critical density, beyond which the interfacial reaction step of the dissolution-precipitation process becomes controlling. The dopants both increase the interfacial reaction rate and make the basal plane the lowest energy plane. Hansen and Phillips (1983) observed facetting on the (0001), {1012} and {1120} planes in 99.8% LPS alumina. The addition of MgO in addition to other liquid forming impurities leads to an equiaxed microstructure with a narrow distribution of dihedral angles close to

98

2 Oxide Ceramics

120° suggesting that all grain boundary energies are about equal. MgO therefore has a homogenizing effect of the LPS microstructure and the MgO reduces the anisotropy of alumina similar to its effect in solid state sintered alumina. In LPS alumina, however, the grains may still be abnormally large compared to solid state sintered alumina. The mechanism of this homogenizing effect must be entirely different when liquid is present; it has been suggested that the MgO changes the wetting behavior of silicate liquids in alumina. It is known (Handwerker et al., 1989) that addition of MgO to the system increases the solubility of SiO 2 in alumina leading to a reduction in silica content at grain boundaries when MgO is present. Kaysser et al. (1987) determined that the growth rates of matrix grains decreased in the order: undoped A12O3, Al 2 O 3 + anorthite, Al 2 O 3 + anorthite + MgO, A12O3 + MgO. They attributed this behavior to differences in mobility between clean grain boundaries and those with intergranular glass. If the glass is inhomogeneously distributed throughout the microstructure this will lead to coarsening as grains grow at different rates. TEM studies have indicated that silicate liquid only wets the long facets on alumina grains and not the ends. Shaw and Duncombe (1991) also found that an anorthitic glass only wets some grain boundaries in alumina depending on the mismatch in crystallographic orientation across the boundary. In summary, MgO is a microstructural stabilizer in both solid state and LPS alumina. MgO reduces the grain boundary mobility through solid solution pinning leading to a reduced tendency for poregrain boundary separation, protection against abnormal grain growth arising from inhomogeneous green state components, and/or non-uniform liquid phase

distribution. It is interesting to note that the microstructures resulting from anisotropic grain growth and/or in the presence of liquid are more likely to display desirable R curve behavior since the elongated grains can serve as bridges to apply crack closure forces in the crack wake (see Chap. 7, Sec. 7.3.4.2). 2.4.3.4 Microstructures of Commercial Aluminas and Relation to Properties

The microstructures formed in commercial aluminas are closely related to the macroscopic properties. Morrell (1985) subdivides commercial aluminas into six categories in terms of the wt.% alumina content i.e. Solid state sintered: Liquid phase sintered:

>99.7 i) 99.0-99.7 ii) 96.5-99.0 iii) 94.5-96.5 iv) 86-94.5 v) 80-86

Pure a-Al 2 O 3 is denser, harder, stiffer and more refractory than most silicate ceramics so that increasing the proportion of second phase in an alumina ceramic tends in general to decrease the density, Young's modulus, strength, hardness and refractoriness (Morrell, 1987). However, fabricating products with the higher alumina contents is expensive requiring pure starting materials and high firing temperatures. Intentional additions are made to alumina for a number of reasons including: lowering the firing temperature, allowing cheaper, less pure starting materials to be used, improving rheology in shape forming and modifying the properties of the product (Morrell, 1987). A broad range of materials are commercially available with a concomitant broad range of properties. Trends in data given in the following sec-

99

2.4 A I 2 0 3 , Alumina, Sapphire, Corundum

tions are meant as a general guide, Other microstructural variables such as, porosity, grain size and second phase composition may also have important effects on properties such as strength and thermal conductivity. Solid state sintered alumina is produced from high purity powders which densify to give single-phase ceramics with uniform grain size. Products fired in air may contain some residual porosity but firing in reducing atmosphere (usually hydrogen) leads to complete elimination of porosity. Firing is usually in air at 1600-1700 °C. The reason for the persistence of ^ 5 % porosity is simply that in the last stages of sintering all of the pores are isolated within the oxide matrix. Therefore further shrinkage of the pore requires the gas within the pore to dissolve in the oxide and diffuse to the external surface. Nitrogen is not soluble in alumina at the sintering temperature and therefore the pores only shrink until the increased internal gas pressure balances the reduction in surface energy driving the process. Coarse-grained translucent alumina used for sodium vapor lamp envelopes is fired at 1700-1800 °C in hydrogen to improve the rate of elimination

of porosity. The material is fired in hydrogen since the hydrogen has a relatively large solubility and high diffusivity. It is fired at high temperatures to increase the average grain size. Since alumina has an index of refraction which is anisotropic (see Table 2-15), some light scattering occurs at each grain boundary. The large grain size reduces the linear density of grain boundaries and thereby increases the total transmission for visible light. When 99.8% A12O3 is used in very high temperature refractory applications, for example as crucibles, MgO cannot be used since it is prone to evaporation at high temperature. As a result, aluminas used in these applications typically have coarse-grained microstructures. These "recrystallized" alumina refractories are relatively weak, see Table 2-20, as a result of the large mean grain size. When even small amounts of MgO, as low as 0.1 % are added to control grain growth the resultant LPS alumina is much stronger and can be used in applications requiring high temperature insulating ability, i.e., in kiln furniture and thermocouple insulation and for small section and thin walled components, e.g., rods or tubes.

Table 2-20. Typical properties of high density alumina. A12O3 (wt.%) Density (g cm ~ 3) Hardness (GPa), HV 500 g RT Fracture toughness, XIC (MPa m1/2) Young's modulus (GPa) Bend strength (MPa) at RT Thermal expansion coefficient (10~6/K) 200-1200°C Thermal conductivity at RT (W/mK) Firing range (°C) a b

"recrystallized" without MgO with MgO

>99.9

>99.7 a

>99.7 b

99-99.7

3.97-3.99 19.3 2.8-4.5 366-410 550-600 6.5-8.9

3.6-3.85 16.3 — 300-380 160-300 5.4-8.4

3.65-3.85 15-16 — 300-380 245-412 5.4-8.4

3.89-3.96 15-16 5.6-6 330-400 550 6.4-8.2

38.9 1600-2000

28-30 1750-1900

30 1750-1900

30.4 1700-1750

100

2 Oxide Ceramics

Vehicle-

Film Substrate Grain boundary glass Wet Film

Dry Film

Underfired

Fired Film

Overtired

Figure 2-37. Schematic illustration of the firing of thick film circuitry on the surface of a debased (glass-containing) alumina substrate. During firing the glass forms a mechanical interlock between the substrate and the metallic layer. If the system is overfired the glass is rejected entirely from the metal, resulting in a weak bond.

Many engineering alumina ceramics contain 99-99.7% alumina and so have a significant glass content. Grain sizes in the range 2-25 jim are typical and the products can be particularly strong (Table 2-20). The fine grain sized 99% aluminas may be used in demanding applications such as hip prostheses whereas coarser grained materials are preferred for electrical insulation. Aluminas with 94.5-99% A12O3 have a large proportion of grain boundary glass which must be of carefully controlled composition to confer the required densification behavior and final state properties. The grain boundary glass is usually an aluminosilicate containing additional oxides such as CaO or MgO. Microstructures in aluminas where the glass is used simply as a densification aid show a uniform distribution of alumina crystals completely separated by glass. In other aluminas which are fired to higher temperatures some recrystallization of the alumina may occur to give an interconnected network. In these materials pores are usually located at the

interface between the alumina and the glass. Typical properties are given in Table 2-21. Although these aluminas cannot be used in applications requiring very high temperature stability they can be tailored for use in many electrical applications. The second phases present depend in general on the composition used, the firing temperature, and the cooling rate (more glass being present with faster cooling). Phases such as anorthite (CaAl2Si2O8), mullite (Al6Si2O13), cordierite (Mg 2 Al 4 Si 5 O 18 ) and celsian (BaAl2Si2O8) may form on cooling or be crystallized from the glass by prolonged heating above 900 °C. PowellDogan and Heuer (1990) characterized the microstructures of a series of 96% alumina ceramics containing 2 - 3 wt.% SiO 2 , 0.41.4wt.% MgO, 0.06-1.5 wt.% CaO and 0.05-0.25 wt.% Na 2 O. The ease of crystallization was observed to be strongly dependent on the MgO to CaO ratio in the intergranular glass phase. The mechanical properties of glass-containing alumina ceramics have been observed to depend on

101

2.5 Zirconia

Table 2-21. Typical properties of debased alumina. A12O3 (wt.%) Density (gcm~3) Hardness (GPa), HV 500 g Young's modulus (GPa) Bend strength (MPa) Thermal expansion coefficient (x 10"6/K) 200-800 °C Thermal conductivitiy at RT (W/mK) Firing range (°C)

99-96.5

94.5-96.5

86-94.5

80-86

3.73-3.8 12.8-15 300-380 230-350 8-8.1

3.7-3.9 12-15.6 300 310-330 7.6-8

3.4-3.7 9.7-12 250-300 250-330 7-7.6

3.3-3.4 — 200-240 200-300 —

24-26 —

20-24 1520-1600

15-20 1440-1600

— —

the thermal expansion coefficient of the glass and the extent of crystallization (Powell-Dogan etal., 1991; Knapp and Cawley, 1991). In particular, the volume change associated with the devitrification of the grain boundary glass appears to induce microcracking which degrades the fracture strength. The presence of a grain boundary glass is not, however, necessarily deleterious. For example, the metallization of a substrate is often necessary to allow brazing or soldering and to provide a conducting surface. Procedures such as the molymanganese process (Kohl, 1967), or thick-film circuitry (Harris and Lall, 1991) rely on interactions during firing between the powder particles, which are painted on, and pre-existing intergranular glass. Figure 2-37 provides a schematic of the microstructural development in a thick-film circuit. The thick-film paste, which is a mixture of desired metals or conductors and a low temperature melting glass frit, is painted on the desired region and the substrate. During firing the metal particles fuse together to provide the conduction path while the glass particles fuse and begin to dissolve the more refractory glass in the ceramic substrate. The result is a strong bond with graded properties.

Aluminas with 80-94.5% A12O3 are generally used as electrical insulators or low-temperature mechanical components or refractories. The glass-bonded insulators and mechanical components are fired < 1500 °C and may suffer viscous flow of the glass at comparatively low temperatures. If non-equiaxed alumina particles are used, the fluid nature of the glass during processing may allow their reorientation leading to anisotropic grain structures and properties.

2.5 Zirconia The traditional applications of ZrO 2 and ZrO 2-containing materials are foundry sands and flours, refractories, ceramic and paint pigments and abrasives. These applications still account for most of the tonnage used. However, the thermomechanical and electrical properties of zirconia-based ceramics have led to a wide range of advanced and engineering ceramic applications. Early reviews of the then state of knowledge of ZrO 2 are given by Ryshkewitch (1960) and Garvie (1970). The recent level of research interest in ZrO2 can be gauged by examining the series of conference proceedings on the Sci-

102

2 Oxide Ceramics

ence and Technology of Zirconia (published by the American Ceramic Society Volumes I-IV (1981, 1984, 1988, 1992). Tough, wear resistant and refractory, ZrO 2 is being developed for applications such as extrusion dies, machinery wear parts, and piston caps. Composites containing ZrO 2 as a toughening agent such as ZTA (zirconia toughened alumina) also show promise in applications such as cutting tools. Ionically-conducting ZrO 2 can be used as a solid electrolyte in oxygen sensors, fuel cells, and furnace elements (see Chap. 1, Sec. 7 and Chap. 11, Sec. 4 of this Volume). 2.5.1 Mineral Sources and Powder Production

The main source of zirconia is the mineral zircon (ZrSiO4) which typically contains significant A12O3, HfO2 and TiO 2 impurity. Commercial zircon is mined from beach sand sources with large deposits found in Australia, India, South Africa, Russia, China and the USA most of which are used directly in the manufacture of refractories for basic steelmaking and glass tank furnace linings, as investment and sand casting foundry sands and flours (for mold washes), and abrasives (Garnar, 1983). Another source of ZrO 2 is the mineral baddeleyite, which is 80-90% monoclinic ZrO 2 with TiO 2 , HfO 2 , SiO2 and Fe 2 O 3 as the major impurities. Commercial baddeleyite deposits are found in Brazil and South Africa. Production of zirconia can be considered in terms of four stages (Clough, 1985): a) zircon decomposition, b) dissolution of Zr species, c) precipitation of Zr species and d) calcination to ZrO 2 . There are two main processes used in zircon decomposition: thermal decomposition into SiO 2 and ZrO 2 ; and chemical decomposition into Zr and Si-containing compounds (Heathcote,

1991). The technique used depends on the purity, particle size, morphology and surface area required in the product. A common thermal decomposition method involves injection of zircon sand into a plasma arc above 6000 °C where it melts and dissociates into the constituent ZrO 2 and SiO 2 . The material is rapidly quenched as it leaves the plasma and therefore recombination does not occur. The spheroidised product is then either a) boiled with caustic soda to dissolve and remove the silica or b) treated with sulfuric acid to dissolve and remove the ZrO 2 as sulfate. Zircon is also thermally decomposed by reaction with carbon forming a cyanonitride which readily oxidizes to ZrO 2 . The chemical decomposition methods can be further subdivided into two groups, attack by chlorine and attack by alkalis. Zircon sand can be chlorinated by reacting it with coke and Cl 2 at 800-1200°C to produce gaseous ZrCl 4 and SiCl4 which are separated by condensers. The zirconium tetrachloride gas is bubbled through water to form a solution of ZrOCl 2 . Zircon can also be decomposed by reacting with oxides, hydroxides and carbonates from groups IA or IIA of the Periodic Table such as NaOH, Na 2 CO 3 and CaO. Reaction with NaOH or Na 2 CO 3 at high temperature forms sodium zirconate, sodium zirconate silicate and sodium silicate (Farnworth et al., 1980). The sodium silicate is removed by leaching with water, the zirconate ions hydrolize to form a complex hydrated hydroxide. In either process the Zr-containing decomposition product is dissolved in an acidic solution. Pure ZrO 2 is isolated from the acid-soluble impurities by precipitation and the product calcined. In some cases "stabilizing oxides," such as CaO, MgO or Y 2 O 3 (see Sees. 2.5.2 and 2.5.3) may be coprecipitated with the ZrO 2

2.5 Zirconia

or dispersed as a salt (e.g., yttrium nitrate) with the zirconia powder during spray drying. Many novel techniques for the production of ultrapure ZrO 2 powders are currently being examined. For example, powders have been prepared by fusion casting (Blackburn et al., 1988), vapor phase reaction (Hori et al, 1984), hydrothermal precipitation (Hishinuma et al., 1988) and solgel processing (Tokudome and Yamaguchi, 1988). In general, these techniques are characterized by high raw material and processing costs and therefore they are likely to be used only in specialized applications. 2.5.2 Crystal Structure, Polymorphism and Physical Properties of Single Crystal ZrO 2

Zirconia occurs in three well established polymorphs: monoclinic (m), cubic (c) and tetragonal (t), see Chap. 1, Sees. 1.3.1 and 1.7 of this Volume. In pure ZrO 2 the monoclinic phase is stable up to 1170°C above this temperature it transforms to tetragonal symmetry and then to cubic symmetry at 2370 °C before melting at 2680 °C. The transformation from monoclinic to tetragonal exhibits a hysteresis. The transformation from t to m on cooling occurs over a temperature range of about 100 °C below 1170°C. The transformation to monoclinic is martensitic and during cooling results in a volume increase on the order of 3-4%. This volume change is sufficient to exceed the elastic limit of the ZrO 2 grains and cause cracking. Thus the fabrication of large, pure zirconia bodies is impossible. However, Garvie et al. (1975) proposed using this transformation to improve both the strength and toughness of ZrO 2 ceramics. They suggested that metastable tetragonal particles constrained in a cubic matrix

103

could be caused to transform to monoclinic symmetry when a propagating crack relieves the constraint. The volume change and shear strain associated with the martensitic reaction oppose the opening of the crack so increasing the resistance of the ceramic to crack propagation i.e. increasing its toughness. Reviews of so-called "transformation-toughening" in zirconia alloys are given by Green et al. (1989), Evans (1984) and Claussen (1984). It should be recognised, however, that the toughness and strength increases arising from the presence of tetragonal ZrO 2 particles in a cubic matrix come from several sources including crack deflection (as found in all two phase ceramics), transformation toughening and microcracking (Faber and Evans, 1983). A more complete discussion of the toughening of ceramics in general and transformation toughening in particular is given in Chap. 8, Sec. 8.3, respectively. In powder mixtures, the polymorphs of pure ZrO 2 can be differentiated using Xray diffraction although distinguishing between cubic and tetragonal peaks is difficult. Garvie and Nicholson (1972) and Schmid (1987) describe XRD techniques for quantitative analysis of mixtures of the zirconia polymorphs. However, in a ternary system of cubic, tetragonal and monoclinic, there is no real possibility of quantitative analysis using XRD. Under such circumstances, the only accurate method is neutron diffraction (Howard and Hill, 1991). Distinguishing between polymorphs becomes more difficult in ZrO 2 alloy systems. The lattice constants are known to vary with the type and concentration of the anion and distortion of the unit cell affects the structure factor. Consequently, quantitative analysis in the alloy systems is difficult. Systematic experimental calibration is

104

2 Oxide Ceramics

Table 2-22. Physical properties of single crystal zirconia. Polymorph Melting point (°C) Density (g cm ~ 3) Hardness (GPa), HV 500 g Thermal expansion coefficient (xl0- 6 /K)0-1000°C Thermal conductivity (W/mK)

100 °C 1300°C

Refractive index

Cubic a

Tetragonal

Monoclinic

2500-2600 5.68-5.91 7-17 7.5-13

2677 6.10 12-13 8-10 || a-axis 10.5-13 || c-axis

— 5.56 6.6-7.3 6.8-8.4 || a-axis 1.1-3.0 || b-axis 12-14 || c-axis

1.675 2.094 2.15-2.18

Properties dependent on stabilizer type and content, typical ranges given.

needed and, while equations have been developed, they should only be applied to the specific system and thermal history for which they were determined (Evans et al., 1984). Table 2-22 lists some typical properties of single-crystal zirconia. 2.5.3 Ceramic Fabrication and Microstructural Control of Binary Zirconia Alloys

The high melting temperature and chemical inertness of pure ZrO 2 make it an attractive material for applications as a refractory. However, during thermal cycling the displacive tetragonal-to-monoclinic transition leads to gross cracking. Most applications of zirconia therefore require that the structure be fully- or partially-stabilized through alloying with alkaline earth or rare earth oxides. The term "stabilized" refers to a kinetic stabilization of a solid solution in the cubic polymorph to room temperature. By avoiding formation of a tetragonal phase at intermediate temperatures the displacive transformation of that polymorph to monoclinic is avoided at low temperature. Full stabilization refers to compositions which exhibit single phase behavior from absolute zero

to the solidus. Although such alloys avoid the deleterious volume change of the t - m transition, thermal shock resistance is still an important issue. This is due to a simultaneous increase in the thermal expansion coefficient and a reduction in the thermal conductivity. The low thermal conductivity tends to cause steep thermal gradients during heating or cooling and the high thermal expansion coefficient results in large thermal strains, or high stresses. The discovery that thermal shock resistance was improved by only adding enough of the alloying element to partially stabilize the cubic phase led to the use of the partially stabilized zirconia (PSZ) as a refractory and its later development as an engineering ceramic due to its high toughness arising from transformation toughening. In addition to the most commonly used stabilizers (the oxides of Ca, Mg, Ce, and Y) virtually all the rare earth elements form solid solutions with zirconia. In general, where the zirconium ion is in eight fold coordination (i.e. tetragonal or cubic) ions will stabilize the zirconia phase provided that the ionic radius is within approximately 40% of that of Zr 4 + . The exact mechanism of stabilization remains unclear. In some cases it appears that the pro-

2.5 Zirconia

portion of ionic bonding is increased which renders the cubic structure more stable. In addition, many alloy additions promote anion ordering (the cations remain disordered) rendering a more stable lattice. The behavior, processing and microstructure of partially stabilized zirconias are discussed in terms of the binary phase diagrams and the type of heat treatments used in processing the material to obtain the optimum microstructure in the following sections. 2.5.3.1 ZrO 2 -MgO The diagram reported by Grain (1967) is the most widely reported and is shown in Fig. 2-38. A typical composition for a magnesia-partially stabilized zirconia, MgPSZ, may be around 8 mol.% MgO. The first step in processing involves a solution heat treatment in the cubic single phase field (2-4 h at about 1800°C depending on composition) followed by a rapid cool. This quench is too rapid to allow the equi-

105

librium amount of tetragonal phase to precipitate out, but it does promote homogeneous nucleation of very fine tetragonal precipitates. The maximum cooling rate must, however, be limited to avoid thermal shock. Reheating to 1400 °C and holding isothermally (aging) leads to coarsening of the tetragonal particles by rejection of MgO into the cubic matrix. If overaging is avoided, the resultant microstructure is one of finely divided precipitates in a cubic matrix. Small tetragonal particles, 0.2 |im, may be metastably retained upon cooling due to the presence of the cubic matrix. Coarser particles spontaneously transform to monoclinic symmetry during cooling. The microstructure of an optimally processed Mg-PSZ containing metastable tetragonal or monoclinic precipitates in a cubic matrix is shown in Fig. 2-39. If the tetragonal precipitates are above a critical size they will transform to monoclinic symmetry either spontaneously or as a result of applied stress. It should be noted that this critical size depends on many

2200

p

1800 -

HI

cc Z>

LU £L

1400

-

1000

-

LU

5

10

MOLE % MgO

15

Figure 2-38. Zirconia-rich end of the ZrO 2 -MgO phase diagram (from Grain, 1967). The shaded region indicates the composition range of commercial MgPSZs.

106

2 Oxide Ceramics

Figure 2-39. Bright-field TEM image of the microstructure of an optimally-aged Mg-PSZ consisting of oblate tetragonal precipitates in a cubic matrix (courtesy of A. H. Heuer, CWRU).

factors including the degree of constraint (whether particles are in a bulk matrix or powder form), temperature and composition. The influence of the precipitates including the effect of particle shape and size on the fracture strength and toughness of dense ceramics is discussed in detail in Chap. 8, Sec. 8.3.1. Commercial Mg-PSZ undergoes a further sub-eutectoid ageing treatment at 1100°C to improve the room temperature properties. The microstructure of commercial PSZ is rarely optimized; more usually it is that produced by a furnace cool after sintering in the single cubic phase field, or possibly a rapid cool from the sintering temperature to an isothermal hold temperature. This heat treatment schedule allows more heterogeneous nucleation of tetragonal particles to take place. Consequently, a thicker grain boundary tetragonal film is produced which spontaneously transforms to monoclinic on cooling. In addition, heterogeneously nucleated precipitates form within the grains. Such precipitates grow rapidly during a subsequent isothermal hold at 1400 °C. The precipitates thus formed, are also large enough to transform to monoclinic on cooling, thereby reducing

the total residual metastable tetragonal available for transformation toughening. It is well known that grain boundary structure strongly influences the properties of ceramics, for example, impurity grain boundary phases can provide crack nucleation sites and reduce high temperature strength. With PSZ materials, the starting powders invariably contain 0.1-0.4% SiO 2 , some A12O3 together with other impurities (Leach, 1987). The SiO 2 arises from two main sources. In coprecipitated powders, SiO2 is derived from the precursor ZrSiO 4 . If the powder is further milled using silica milling media, the SiO2 level increases, arising from wear debris of the milling media (Ruhle et al., 1984). In MgO and Y 2 O 3 doped zirconia ceramics, a silicate grain boundary liquid forms which acts as a sintering aid. In MgO-PSZ, the grain boundary phase, its distribution and wettability, depend on the Mg silicate formed. Forsterite (Mg2SiO4) occurs as isolated pockets and appears to be nonwetting whereas enstatite (MgSiO3) exhibits wetting behaviour spreading along all grain boundaries. The isolated forsterite particles, strongly associated with monoclinic regions, are thought to reduce the extent of microcracking by making nucleation of the tetragonal to monoclinic transformation more difficult. The loss of MgO from the matrix to the grain boundary does, however, promote the formation of monoclinic to the detriment of mechanical properties. Recently, Drennan and Hannink (1986) have discovered that addition of 0.25% SrO enhances mechanical properties by altering the grain boundary phases. 2.5.3.2 ZrO 2 -CaO There are strong analogies between CaPSZ and Mg-PSZ. Although there have

2.5 Zirconia i

^^^

2500 -

v

2000 -

i

L + CaZrO 3

i

\

Css

LJJ QC

QC

107

C s s + CaZrO3

1500

LU

1 3 1 0 ± 40°C

1140 ± 4 < \ y - • - ^ C s + CaZr O S 4 9

LU

TS8-*- CaZr 4 Og

M

/ "

/

0 ZrO2

CaZr4O9 +

CaZrO 3

30

40

Mss+ CaZr4O9 10

20 CaZr 4 O 9

50 CaZrO 3

Figure 2-40. Part of the ZrO 2 -CaO phase diagram (from Hellman and Stubican, 1983).

MOLE % CaO

been numerous examinations of the C a O ZrO 2 phase diagram, the version proposed by Stubican and Ray (1977) and further refined by Hellman and Stubican (1983 a, b) has been generally adopted and is shown in Fig. 2-40. The stability of the CaZr 4 O 9 has not been definitively proven, and consequently it is omitted in some versions (e.g. Stubican et al, 1984) which include instead Ca 6 Zr 1 9 O 4 4 (at 27 mol.% CaO). Different temperatures and compositions have been reported for the eutectoid decomposition. Marder et al. (1983) reported a temperature of 1000 °C and 15 mol.% CaO when decomposing a cubic solid solution. Alternatively, Hellman and Stubican (1983 a, b) report a eutectoid temperature of 1140±40°C and a composition of 17 + 0.5 mol.% CaO, on prolonged heat treatment of reactive powders. The latter technique would be expected to achieve equilibrium more rapidly and therefore may be regarded as more reliable.

As with other zirconia systems, the eutectoid transformation is very sluggish, and is, therefore, not usually seen in conventionally heat treated samples, and metastable extensions of the phase fields dominate. A large cubic phase field exists which, in conjunction with the sluggish eutectoid transformation, allows a fully cubic structure to be retained by rapid cooling, and this is the basis of e.g. calcia stabilized zirconia solid electrolytes. In particular, as with the MgO system, the structure actually consists of cubic containing a fine distribution of homogeneously nucleated tetragonal particles. Suitable heat treatment allows the growth of these particles to a point where they become metastable and will transform with the application of stress from a propagating crack. The best mechanical properties are achieved at a particle size of about 0.1 jim. However, the temperature/composition window where such a treatment is practicable is small.

108

2 Oxide Ceramics 2500

2000

iilk

\ UJ

\ U. (

1500

cr

tss

< UJ

a.

PSZ

1

\

'

\

*ss +

V \

1000

Css

\

c

TZP

ssM 500

\

\ m

m

ss

ss + c ss \ \

1

2 Y2O3

t

1

1

4

6

8

10

Figure 2-41. Zirconia-rich end of the ZrO 2 -Y 2 O 3 phase diagram (Scott, 1975). The shaded regions indicate the compositions and processing temperatures for commercial partially stabilized zirconia (PSZ) and tetragonal zirconia polycrystals (TZP).

CONTENT (mole %)

OOiVmj

Figure 2-42. Bright-field TEM image of the microstructure of Y-TZP. Note the fine grain size and lack of porosity (courtesy A. H. Heuer, CWRU).

2.5.3.3 ZrO 2 -Y 2 O 3 The phase diagram proposed by Scott (1975), Fig. 2-41, is universally quoted since it agrees well with experimental findings, although there have been more recent studies. In particular, those of Riihle et al. (1984) and Lanteri et al. (1984) have at-

tempted a more accurate assessment of the position of the t / t + c and t + c / c phase boundaries. The most significant feature of this diagram is the extensive solubility for Y 2 O 3 in the terminal tetragonal solid solution. Up to approximately 2.5 mol.% Y 2 O 3 will be taken into solid solution which, in conjunction with the low eutectoid temperature, allows a fully tetragonal ceramic to be obtained (so-called tetragonal zirconia polycrystals or TZP) first reported by Rieth et al. (1976). Fine grain sizes are obtained by using ultra fine powders and sintering in the range 1400-1550 °C where the coarsening rate can be controlled (see Fig. 2-42). Similar to the critical precipitate size in PSZ materials, TZP ceramics exhibit a critical grain size (about 0.3 jim) above which spontaneous transformation occurs leading to low strength and toughness. The critical size depends on the composition (being about 0.2 jim for 2 mol.% Y 2 O 3 and 1.0 ^m for 3 mol.% Y2O3) and the degree of mechanical constraint.

2.5 Zirconia

TZPs have a significant advantage over Mg-PSZs because sintering can be carried out at comparatively low temperatures (1400-1550 °C compared to 1800°C) bringing the production of TZPs within the scope of existing furnaces in ceramic manufacturing plants. The bulk of commercial TZPs contain 2-3mol.% Y 2 O 3 and mainly consist of fine equiaxed tetragonal grains of a diameter typically in the range 0.2-2 jim. In addition, many materials contain a small amount of cubic phase, the grain size of which is usually larger than the tetragonal phase. Although cubic is more common in the highly stabilized materials, being ubiquitous in those with 3 mol.% Y 2 O 3 and above, it is also present with lower solute additions especially where inhomogeneous powders are used. The uncertainty of the ZrO 2 rich end of the phase diagram, in particular the position of the t /1 + c phase boundary makes an accurate prediction of the amount of cubic difficult. In a survey of 10 commercially available TZPs containing 2 - 3 mol.% Y 2 O 3 Riihle et al. (1984) found cubic phase ranging from 0 to 42%. The morphology of the cubic phase varied, but often contained fine (10 nm) tetragonal precipitates, believed to form during slow cooling from sintering. The grain morphology of the polycrystals varies; although well faceted grains are more typical, rounded grains are observed in materials containing an appreciable amount of silicate glass phase at the grain boundary. A grain boundary glass often plays an important role in sinterability. In one experimental study ultra-pure coprecipitated powders were difficult to sinter whereas the same powders sinter easily after milling. This effect was presumed to be the result of the presence of a silicate liquid produced by contamination from the milling media. However, the composition of the glass can

109

have a significant effect on properties. Lin et al. (1990) showed that an aluminosilicate glass leached out the Y stabilizer whereas a borosilicate glass did not. Leaching of the stabilizing component led to less desirable mechanical properties in the sintered TZP. In a systematic study Riihle et al. (1984) found a wide variation in the microstructures of commercial TZPs. Large solute variations were reported both within grains and throughout the ceramic. The variation within a grain is a result of the slow diffusion of the solute within ZrO 2 , although transport is rapid along the grain boundary glassy phases. However, the dramatic variations in solute concentration from grain to grain in many TZP's indicated that they had not reached equilibrium at the end of sintering. This was thought to be a result of the mixed oxide powder processing route employed. It was also suggested that A12O3 had been added deliberately by some manufacturers. Different starting powders gave a variation in toughness from 5.5 to 11 MPa m 1/2 for nominally identical solute levels. A large cubic plus tetragonal phase field exists in the ZrO 2 -Y 2 O 3 system which permits the formation of a PSZ structure. In this region, sintering has to be conducted at higher temperatures (up to 1700°C) to ensure sufficient yttria is taken into solution for the generation of fine, metastable tetragonal particles. Although in many ways analogous to Mg-PSZ and Ca-PSZ, the structures formed in Y-PSZ are more complex. Under conditions of slow cooling from sintering and subsequent aging, a diffusional reaction occurs giving tetragonal precipitates in a cubic matrix. The morphology of the tetragonal precipitates depends on the aging temperature and time. However, under more rapid cooling conditions a displacive transformation occurs which gives another tetrag-

2 Oxide Ceramics

110

onal phase, commonly called t' (t-primed), which has a lower c/a ratio than the normal tetragonal and contains the same quantity of yttria as the cubic. The microstructures generated in the zirconias with higher yttria contents than 3 mol.% >Y2O3 are generally referred to as partially stabilized since, as with the Mg-PSZs the structure is two phase. 2.5.3.4 ZrO 2 -CeO 2 This system shows a very wide tetragonal phase field as shown in Fig. 2-43 (Tani et al., 1983), with a solubility limit of 18 mol.% CeO 2 . The eutectoid temperature, 1050 °C is somewhat higher than in the Y 2 O 3 system but the size of the tetragonal phase field still makes it possible to retain a fully tetragonal structure as in the Y 2 O 3 system. Sintering temperatures are very similar, with 1550°C being common,

20

40

(wt7o) 60

80

100

2800 -

Liquid 2400-

V Cubic * 1600

Tet. j Tet.

D • Ol-tr o g. 1200 R D O D

^

Cubic (1050±50'C) A

t—

800

400

and again an ultra fine powder is required to generate a fine grain size in the ceramic. There are many similarities between the Ce and Y-TZPs although a fully tetragonal structure can be obtained in Ce-TZP for CeO 2 additions between 12 and 20 mol.%, representing a much wider range than with Y-TZPs (Tsukuma and Shimada, 1985). The minimum composition required for a fully tetragonal structure clearly depends on the sintering temperature and the grain size produced. Ce-TZPs densify via liquid phase sintering in a similar manner to YTZPs. Ultra-pure powders give low densities, with impurities such as Si and Ca essential for full densification. In addition, Ce-TZPs are more susceptable to reduction during sintering. Even with a plentiful oxygen supply during sintering, the center of a large sample will become discolored, turning orange to brown to black, attributed to a reduction in the oxygen content. For an equivalent fracture toughness, the grain size is larger in Ce-TZP compared to Y-TZPs. For example, a K1C of 12 MPa m 1/2 could be achieved in a YTZP with a grain size of 2 pxn compared to 8 jim in a Ce-TZP (Tsukuma and Shimada, 1985). Very high toughness values can be achieved in these materials, with nominal values of up to 30 MPa m 1/2 being reported, although the absolute value depends strongly on the test method used.

A Mono.

0 ZrO 2

o

\

2.5.4 Properties and Applications of Selected Zirconia Ceramics

o

\

o

2.5.4.1 Mg-PSZ Monoclinic Cubic

20

40 60 (mol°/o)

80

100 CeO2

Figure 2-43. ZrO 2 -CeO 2 phase diagram constructed by Tani et al. (1983).

Representative mechanical and thermal properties for commercial PSZs are given in Table 2-23. While a useful guide the data should be treated with caution since the particular values obtained depend on the test method especially for K1C. Further, these general values are, of course, affected

111

2.5 Zirconia Table 2-23. Physical properties reported for commercial partially stabilized zirconias (PSZ).

Wt.% stabilizer Hardness (GPa) RT fracture toughness, K1C (MPa m 1/2 ) Young's modulus (GPa) Bend strength (MPa) RT Thermal expansion coefficient (x 10~ 6 /K) at 1000°C Thermal conductivity at RT (W/mK) 2.8% MgO,

b

4% CaO,

c

Mg-PSZ

Ca-PSZ

Y-PSZ

Ca/Mg-PSZ

2.5-3.5 14.4a 7-15 200 a 430-720 9.2a

3-4.5 17.1 b 6-9 200-217 400-690 9.2 b

5-12.5 13.6C 6 210-238 650-1400 10.2c

3 15 4.6 — 350 —

1-2

1-2

1-2

1-2

5% Y 2 O 3

700 -

Modulus of Rupture (MPa)

2

3 4 Stabilizer (wt. % MgO)

by material variables in the ceramic microstructure (stabilizer content, grain size etc.) and external variables such as atmosphere and temperature. Figure 2-44 shows the effect of MgO content on the bend strength and fracture toughness of various MgPSZs while Fig. 2-45 shows the effect of temperature on the bend strength and fracture toughness of a commercial Mg-PSZ (Dwovak et al., 1984). 2.5.4.2 Y-TZP Typical mechanical and thermal properties for commercial TZPs are given in Table 2-24. The exact yttria content in Y-

Figure 2-44. Bend strength and fracture toughness behavior of various Mg-PSZ ceramics at room temperature (from Dworak et al., 1977).

TZP plays an important role in the transformability of the tetragonal phase and therefore the toughness (Fig. 2-46). Toughness is also a strong function of grain size (Fig. 2-47). A major obstacle to the full exploitation of TZP ceramics is that spontaneous surface transformation of tetragonal to monoclinic occurs if the ceramic is held at temperatures in the range of 150-250°C at times ranging from hours to days, which can lead to severe degradation in strength. In the worst case, complete material disintegration can occur. The extent of surface degradation is greatly enhanced by the presence of water vapor at temperatures

112

2 Oxide Ceramics

Test Conditions 4 point bending dG/d = 1.75MPa/sec

Fired Temp. • 1400°C A 1 500°C O 1600°C

12

Bend Strength 400(MPa) 300-

\

2001000 0

250 500 750 Temperature (°C) ->

1000

3

4

Mol % Y 2 O 3

Figure 2-46. Fracture toughness (Klc) of Y-TZP ceramics as a function of Y 2 O 3 content and sintering temperature (from Tsukuma et al, 1984). 10 Mg - PSZ (ZN40) Single Edge Notched Beam

- 2 m/o yttria - zirconia

A'

12 Fracture 5Toughness (MPaVm)

K,c MPax/m 4 _-

0

250 500 750 Temperature (°C) ->

1000

0

A i

i

1

2

Grain Size Gum)

Figure 2-45. Bend strength and fracture toughness, Klc, of a commercial Mg-PSZ as a function of temperature (Dworak et al., 1984).

Figure 2-47. Grain size dependence of the fracture toughness (XIC) for a 2mol.% Y-TZP (from Swain, 1986).

Table 2-24. Typical physical properties of tetragonal zirconia polycrystals (TZP).

below 200 °C and is accelerated as the water vapor pressure is increased (Sato et al., 1985; Sato and Shimada, 1985). The final amount of monoclinic produced at 200 °C is constant, indicating that water vapor effects the rate of degradation rather than the equilibrium. Matsumoto (1985) has demonstrated that full strength recovery is possible if the degraded sample is annealed at 1000 °C for 24 h. This is little comfort for engineers, however. Alternative strategies lie in the addition of ceria and alumina to the TZP (Sato etal., 1986; Nettleship and Stevens,

Y-TZP Mol.% stabilizer Hardness (GPa) RT fracture toughness, Klc (MPa m1/2) Young's modulus (GPa) Bend strength (MPa) Thermal expansion coefficient (x 10 " 6 /K) 20-1000 °C RT thermal conductivity (W/mK)

2-3

10-12 6-15

Ce-TZP 12-15 7-10 6-30

140-200 800-1300 9.6-10.4

140-200 500-800

2-3.3

—

—

2.5 Zirconia

1987) or reducing the grain size below that at which microcracking occurs. Additions of CeO 2 decrease the amount of degradation to the point that no monoclinic is observed with the addition of 10% CeO 2 to 3 Y and 4 Y, and 15% CeO 2 to 2 Y (Sato and Shimada, 1985; Sato et al., 1986). However, additions exceeding 6 - 8 % CeO 2 yield a material with compromised mechanical properties (Sato et al., 1984). Additions of A12O3 to TZP reduce transformability by increasing matrix constraint and reduce, but do not eliminate, the degradation (Sato and Shimada, 1986; Tsukama and Shimada, 1985). Zirconia ceramics have the highest toughness of any ceramic which, combined with high strength, hardness and chemical resistance, should allow their application in harsh environments under severe loading conditions. Wear resistant applications of Mg-PSZ as drawing dies, bearings, seals and bone replacement devices (mostly ball and socket joints) have been developed. The low thermal conductivity of ZrO 2 can be used to advantage in automotive engines in piston crowns, head face plates and piston liners so that heat loss from the combustion chamber can be reduced and flame temperature increased resulting in higher efficiency. Wear resistant applications in engines include those in the valve train as cams, cam followers, tappets and exhaust valves. The thermal expansion coefficient of zirconia closely matches that of cast iron so that these materials can be joined (typically by an active substrate process with a Ti-based bond) to give relatively inexpensive automotive components. PSZ refractory crucibles, shaped by slip casting or isostatic pressing are used in vacuum induction or air melting of refractory metals such as Co-base alloys or precious metals such at Pt, Pd or Rh. The relatively high cost of ZrO 2 compared to

113

other refractories limits its use to special applications where it has particularly desirable properties. PSZ is comparatively stable to both acid and basic slags and molten steel. This amphoteric behavior, combined with its superior erosion and thermal shock resistance, enables its use for submerged entry tundish nozzles in continuous casting of steel. PSZ inserts are also used in alumina-graphite sliding and rotary gate valves when high oxygen or calcium-bearing steels are used and increased corrosion/erosion resistance is required. Zirconias are also used in a number of cutting applications for difficult materials such as glass fibres, magnetic tape, plastic film and paper items such as cigarette filters (Stevens, 1986). 2.5.4.3 ZTA Composites

Zirconia has been added to a variety of other oxide matrices such as mullite, spinel, cordierite, zircon and MgO in order to improve their toughness. The first system developed was zirconia toughened alumina (ZTA) simultaneously with the PSZ systems (Claussen, 1976). This material demonstrated that the inclusion of unstabilized zirconia can lead to retention of t-ZrO 2 in the sintered product if the particle size is small enough. The toughening mechanism primarily involves transformation and microcrack formation although dispersion strengthening is also active in this system. Less than 20 vol. % zirconia unstabilized particles are typically used although subsequent work has attempted to increase the ZrO 2 content by partial stabilization of the zirconia with Y 2 O 3 , CeO 2 or TiO 2 (Lange, 1982). Unstabilized ZTA's can have strengths of 1200 MPa and toughnesses of 16MPam 1 / 2 with about 15vol.% ZrO 2 compared to values of 600 MPa and 4 MPa m 1/2 respectively for

114

2 Oxide Ceramics

Figure 2-48. Backscattered electron SEM image of ZTA containing 18 vol.% ZrO 2 . The light phase is the

typical dense alumina. The dual phase microstructure is clearly seen in the backscattered SEM image of Fig. 2-48 where the zirconia is the light phase. ZTA was first used as toughened abrasive for industrial grinding wheels where large improvements in grinding efficiency were detected over conventional materials. Other applications are found in metal cutting tools and engine components.

2.6 Summary The crystal structures, mineral sources and powder synthesis, processing methods, and microstructure-property relationships of the industrially important single oxides share many common features. However, the end uses of MgO, A12O3, and ZrO 2 vary greatly. MgO is rarely used as a polycrystalline ceramic due to its large thermal expansion and tendency to react at room temperature with atmospheric water and carbon dioxide. Instead, it is used in refractories (where its high melting point is an advantage) with a coarse grain and some form of prophylactic protection such as an organic resin. A12O3 suffers no such problem and is most commonly liquid phase sintered to give a polycrystalline

ceramic whose microstructure can be tailored to give a range of properties. Alumina is a "workhorse ceramic", which, while having no outstanding single property, offers an exceptional combination of very reasonable properties (mechanical, optical, and electronic). With ZrO 2 , proper chemistry and careful microstructural control allow phase transformations to be exploited to yield ceramics with outstanding strength and toughness. Zirconia is being applied to uses previously thought outside the realm of ceramics, notably in engine components. Furthermore, its unique electrical properties lead to a wide variety of applications in sensor applications. While the properties of these ceramics and the silicates may differ considerably, one of the intentions of this chapter was to illustrate that the principles behind the microstructure-processing-property relations are in essence the same for dinnerware, a refractory brick, or a hip prosthesis. Oxide ceramics were one of the first materials utilized by mankind and as a result of recent developments, some of which were discussed in this chapter, it is clear that exciting new applications will continue to be found for them in the future.

2.7 References Adams, W T. (1989), Am. Ceram. Soc. Bull. 68,10241027. Baik, S., Moon, J. H. (1991), J. Am. Ceram. Soc. 74, 819-822. Barth, T. F. W. (1969), Feldspars. New York: Wiley, pp. 165-171. Belyaev, L. M. (1980), in: Ruby and Sapphire. New Delhi: Amerind, pp. vi-xiv. Bennison, S. I, Harmer, M. P. (1990a), in: Ceramic Transactions, Vol. 7: Sintering of Advanced Ceramics, pp. 13-49. Bennison, S. X, Harmer, M. P. (1990b), /. Am. Ceram. Soc. 73, 833-837. Blackburn, S., Kerridge, C. R., Senhenn, P. G. (1988), in: Advances in Ceramics, Vol. 24: Science and Technology of Zirconia III. Columbus, OH: American Ceramic Society, pp. 193-199.

2.7 References

Brant, P. O. R. C , Button, T. W, Rand, B. (1989), Br. Ceram. Proc. 42, 179-192. Brindley, G. W., Nakahira, M. (1957), / Am. Ceram. Soc. 40, 346-350. Brindley, G. W., Nakahira, M. (1959), J. Am. Ceram. Soc. 42, 311-314; 314-318; 319-324. Brinker, C. X, Scherer, G. W (1990), Sol-Gel Science: The Physics and Chemistry of Sol-Gel Processing. New York: Academic Press. Brown, A. I , White, I (1986), Met. Mater., 632-639. Brown, I. W. M., MacKenzie, K. J. D., Bowden, M. E., Meinhold, R. H. (1985), J. Am. Ceram. Soc. 68, 298-301. Brownell, W. E. (1976), Structural Clay Products. Vienna: Springer. Chen, A. Y, Cawley, J. D. (1992), J. Am. Ceram. Soc. 75, 575-579. Chesters, J. H. (1973), Refractories: Production and Properties. London: The Iron and Steel Institute. Chou, C. C , Senna, M. (1987), Am. Ceram. Soc. Bull. 66, 1129-1133. Claussen, N. (1976), J. Am. Ceram. Soc. 59, 49. Claussen, N. (1984), in: Advances in Ceramics, Vol. 12: Science and Technology of Zirconia II. Columbus, OH: American Ceramic Society, pp. 325-351. Clough, D. J. (1985), Ceram. Eng. Sci. Proc. 6, 12441260. Coble, R. L. (1961), J. Appl. Phys. 32, 793-799. Cooke, T. F. (1991), J. Am. Ceram. Soc. 74, 29592978. Cooper, C. F. (1980), Refractories, J. 6, 11-21. Cooper, C. F. (1987), Interceram 36, 79-84. Cooper, C. R, Alexander, I. A., Hampson, C. J. (1985), Br. Ceram. Trans. J. 84, 57-62. Crawford, J. H. (1984), in: Advances in Ceramics, Vol. 10: Structure and Properties of MgO and A12O3 Ceramics. Columbus, OH: American Ceramic Society, pp. 791-798. De Guire, M. R., Brown, S. D. (1984), /. Am. Ceram. Soc. 67, 270-273. Dinsdale, A. (1986), Pottery Science: Materials Process and Products. New York: Wiley. Drennan, X, Hannink, R. H. J. (1986), /. Am. Ceram. Soc. 69, 541-546. Duwez, P., Odell, R, Brown, R H. (1952), /. Am. Ceram. Soc. 35, 107. Dworak, U., Olapinski, H., Thamerus, G. (1977), Sci. Cer. 9, 543-550. Dworak, U., Olapinski, H., Fingerle, D., Krohn, U. (1984), in: Advances in Ceramics, Vol. 12: Science and Technology of Zirconia II. Columbus, OH: American Ceramic Society, pp. 480-487. Evans, A. G. (1984), in: Advances in Ceramics, Vol. 12: Science and Technology of Zirconia II. Columbus, OH: American Ceramic Society, pp. 193-212. Evans, P. A., Stevens, R., Binner, J. G. P. (1984), Br. Ceram. Trans. J. 83, 39-43. Faber, K. T., Evans, A. G. (1983), Ada Metall. 31 (4), 565-576.

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Farnworth, R, Jones, S. L., McAlpine, I. (1980), in: Specialty Inorganic Chemicals: Thompson, R. (Ed.). London: Society of Chemistry, pp. 248-284. Gardner, T. J., Messing, G. L. (1984), Bull. Am. Ceram. Soc. 63, 1498-1504. Garnar, T. E. (1983), Ceram. Eng. Sci. Proc. 4, 170185. Garvie, R. C. (1970), in: High Temperature Oxides, Part II: Alper, A. M. (Ed.). New York: Academic Press, pp. 117-166. Garvie, R., Nicholson, P. (1972), J. Am. Ceram. Soc. 55, 303-305. Garvie, R. C , Hannink, R. H., Pascoe, R. T. (1975), Nature 258, 703. Gourdin, W. H., Kingery, W. D. (1979), J. Mater. Sci. 14, 2053-2073. Grain, C. R (1967), J. Am. Ceram. Soc. 50, 288-290. Green, D. X, Hannink, R. H. X, Swain, M. V. (1989), Transformation Toughening of Ceramics. New York: CRC Press. Griffen, D. T. (1992), in: Silicate Crystal Chemistry. New York: Oxford University Press, Chaps. 1 and 2. Grim, R. E. (1962), Applied Clay Mineralogy, New York: McGraw-Hill Grimshaw, R. W. (1971), The Physics and Chemistry of Clays. Pairfax, V: TechBooks. Haggerty, X S., Menashi, W. P., Wenckus, X R (1976), U.S. Patent (No. 3944640), March 16th, 1976. Hancock, X D. (1988), Practical Refractories. Huddersfield, U.K.: Cartworth Industries. Handwerker, C. A., Morris, P. A., Coble, R. L. (1989), J. Am. Ceram. Soc. 72, 130-136. Hansen, S. C , Phillips, D. S. (1983), Phil. Mag. A47, 209-234. Harris, D. H., Lall, P. (1991), in: Handbook of Electronic Package Design: Pecht, M. (Ed.). New York: Marcel-Dekker, pp. 101-152. Heathcote, R. (1991), Br. Ceram. Proc. 47, 37-44. Hellman, X R., Stubican, V. S. (1983 a): J. Am. Ceram. Soc. 66, 260-264. Hellman, X R., Stubican, V S. (1983 b), J. Am. Ceram. Soc. 66, 265-267. Hishinuma, K., Kumaki, T., Nakai, Z., Yoshimura, M., Somiya, S. (1988), Advances in Ceramics, Vol. 24: Science and Technology of Zirconia III. Columbus, OH: American Ceramic Society, pp. 201 -209. Hori, S., Yoshimura, M., Somiya, S. (1984), in: Advances in Ceramics, Vol. 12: Science and Technology of Zirconia II. Columbus, OH: American Ceramic Society, pp. 794-805. Howard, C. X, Hill, R. X (1991), J. Mater. Sci. 26, 127-134. Johnson, R. L. (1992), Bull. Am. Ceram. Soc. 71, 818-819. Kaysser, W. A., Sprissler, M., Handwerker, C. A., Blendell, X E. (1987), J. Am. Ceram. Soc. 70, 339343. Keller, W. D. (1982), Geol. Soc. Am. Bull. 93, 27-36.

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Kendall, K. (1978), Proc. Roy. Soc. A361, 245. Kindl, B., Carlsson, D. X, Deslandes, Y, Hoddenbagh, J. M. A. (1991), J. Can. Ceram. Soc. 60, 5 3 58. Kingery, W. D., Bowen, H. K., Uhlmann, D. R. (1976), Introduction to Ceramics, 2nd ed. New York: Wiley. Klein, L. C. (1987), Sol-Gel Technology for Thin Films, Fibers, Preforms, Electronics, and Specialty Shapes. Park Ridge, NJ: Noyes. Klein, C , Hurlbut, C. S. (1985), Manual of Mineralogy, 12th ed. New York: Wiley. Knapp, X X, Cawley, X D. (1991), Metal-Ceramic Joining: Kumar, P., Greenhut, V. A. (Eds.). Warrendale, PA: TMS, pp. 181-204. Kohl, W H. (1967), Handbook of Materials and Techniques for Vacuum Devices. New York: Reinhold. Kroger, F. A. (1974), in: The Chemistry of Imperfect Crystals, Vol. 2; 2nd ed. New York: North-Holland, p. 14. LaBelle, H. E. (1980), / Cryst. Growth 50, 8-17. Lange, R R (1982), /. Mater. Sci. 17, 255. Lanteri, V., Heuer, A. H., Mitchell, T. E. (1984), in: Advances in Ceramics, Vol. 12: Science and Technology of Zirconia II. Columbus, OH: American Ceramic Society, pp. 118-130. Le Chatelier, H. L. (1887), Bull. Soc. Fr. Mineral 10, 204-211. Leach, C. A. (1987), Mater. Sci. Technol. 3, 321 -324. Lee, W. E., Heuer, A. H. (1987), /. Am. Ceram. Soc. 70, 349-360. Lehman, R. L., Weinstein, J. G., Phelps, G. W, Adams, K. M. (1984), Bull. Am. Ceram. Soc. 63, 1039-1050. Lin, Y-X, Angelini, P., Mecartney, M. L. (1990), /. Am. Ceram. Soc. 73, 2728-2735. MacKenzie, K. J. D., Brown, R W. M., Meinhold, R. H., Bowden, M. E. (1985), J. Am. Ceram. Soc. 68, 293-297. MacKenzie, K. J. D., Brown, I. W. M., Meinhold, R. H., Bowden, M. E. (1986), J. Am. Ceram. Soc. 68, 266-272. Mackrodt, W. C. (1984), in: Advances in Ceramics, Vol. 10: Structure and Properties of MgO and A12O3 Ceramics. Columbus, OH: American Ceramic Society, pp. 62-78. MacZura, G., Moody, K. X, Anderson, E. M. (1992), Bull. Am. Ceram. Soc. 71, 780-782. Marder, J. M., Mitchell, T. E., Heuer, A. H. (1983), Ada Metall. 31, 387. Matsumoto, R. (1985), J. Am. Ceram. Soc. 68, C213. McColm, I. J. (1983), Ceramic Science. Glasgow: Blackie and Sons. Mikami, H. M. (1983), Ceram. Eng. Sci. Proc. 4, 9 7 118. Millot, G. (1978), Sci. Am. 240 (4), 109-118. Morrell, R. (1985), Handbook of Properties of Technical and Engineering Ceramics, Part 1: An Introduction for the Engineer and Designer. London: HMSO.

Morrell, R. (1987), Handbook of Properties of Technical and Engineering Ceramics, Part 2: Data Reviews. London: HMSO, Sec. 1. Moulson, A. X, Herbert, J. M. (1991), Electroceramics: Materials, Properties and Applications. London: Chapman and Hall, pp. 206-221. Nettleship, I., Stevens, R. (1987), Int. J. High Tech. Ceram. 3, 1-32. Niesz, D. E., Bennett, R. B. (1978), in: Ceramic Processing Before Firing: Onada, G. Y, Hench, L. L. (Eds.). New York: Wiley. Norton, F. H. (1976), Fine Ceramics: Technology and Applications. New York: McGraw Hill. O'Bannon, L. S. (1984), Dictionary of Ceramic Science and Engineering. New York: Plenum Press. Phelps, G. W. (1976), Bull. Am. Ceram. Soc. 55, 528532. Pierre, A. C , Uhlmann, D. R. (1986), in: Materials Research Society Proceedings. Vol. 73: Better Ceramics through Chemistry. New York: Elsevier, pp. 481-487. Powell-Dogan, C. A., Heuer, A. H. (1990), /. Am. Ceram. Soc. 73, 3670-3676; 3677-3683; 36843691. Powell-Dogan, C. A., Heuer, A. H., Readey, M. X, Merriam, K. (1991), J. Am. Ceram. Soc. 74, 648649. Reed, J. S. (1988), Introduction to the Principles of Ceramic Processing. New York: John Wiley. Reiger, K. C. (1992), Bull. Am. Ceram. Soc. 71, 821. Rieth, P. H., Reed, J. S., Naumann, A. W. (1976), Bull. Am. Ceram. Soc. 55, 111. Robertson, I. D. M., Eggleton, R. A. (1991), Clays Clay Miner. 39, 113-126. Rodel, X, Glaeser, A. M. (1990a), / Am. Ceram. Soc. 73, 3292-3301. Rodel, X, Glaeser, A. M. (1990b), /. Am. Ceram. Soc. 73, 3302-3312. Riihle, M., Claussen, N., Heuer, A. H. (1984), in: Advances in Ceramics, Vol. 12: Science and Technology of Zirconia II. Columbus, OH: American Ceramic Society, pp. 352-370. Ryshkewitch, E. (1960), Oxide Ceramics. New York: Academic Press. Sainamthip, P., Reed, J. S. (1987), Bull. Am. Ceram. Soc. 66, 1726-1730. Sato, T., Shimada, M. (1985), / Am. Ceram. Soc. 68, 356. Sato, T., Shimada, M. (1986), in: Ceramics for Engines, Proc. 2nd Int. Conf. Mat. Engines, LubeckTravemunde. pp. 291-298. Sato, T., Ohtaki, S., Endo, T., Shimada, M. (1984), in: Advances in Ceramics, Vol. 12: Science and Technology of Zirconia II. Columbus, OH: American Ceramic Society, pp. 29-37. Sato, T., Ohtaki, S., Shimada, M. (1985), /. Mater. Sci. 20, 1466-1470. Schmid, H. K. (1987), J. Am. Ceram. Soc. 70 (5), 367-376. Scott, H. G. (1975), / Mater. Sci. 10, 1527-1537.

2.7 References

Segal, D. (1989), Chemical Synthesis of Advanced Ceramic Materials. London: Cambridge University Press. Seron, A., Beguin, R, Bergaya, R (1992), Mater. Set Forum, 91-93. Shaw, T. M., Duncombe, P. R. (1991), /. Am. Ceram. Soc. 74, 2495-2505. Shinohara, K. (1991), in: Powder Technology Handbook, Iinoya, K., Gotoh, K., Higashitani, K. (Eds.). New York: Marcel-Dekker, pp. 481-501. Singer, R, Singer, S. S. (1963), Industrial Ceramics. London: Chapman and Hall. Song, H., Coble, R. L. (1990), /. Am. Ceram. Soc. 73, 2077-2085. Southern, X C (1991), Brit. Ceram. Proc. 47, 1-12. Sowman, H. G. (1988), Am. Ceram. Soc. Bull. 67 (12), 1911-1916. Srikrishna, K., Thomas, G., Martinez, R., Corrall, M. P., De Aza, S., Moya, J. S. (1990), J. Mater. Sci. 25, 607-612. Stacey, M. H. (1988), Br. Ceram. Trans. J. 87, 168172. Stevens, R. (1986), An Introduction to Zirconia. Twickenham, UK: Magnesium Elektron. Stubican, V. S., Ray, S. P. (1977), /. Am. Ceram. Soc. 60, 534-537. Stubican, V. S., Corman, G. S., Hellman, J. R., Senft, G. (1984), in: Advances in Ceramics, Vol. 12: Science and Technology of Zirconia II. Columbus, OH: American Ceramic Society, pp. 96-106. Sugahara, Y, Kuroda, K., Kato, C. (1984), J. Am. Ceram. Soc. 67, C-247-C-248. Sugahara, Y, Sugimoto, K., Kuroda, K., Kato, C. (1988), /. Am. Ceram. Soc. 71, C-325-C-327. Swain, M. V. (1986), /. Mater. Sci. Lett. 5, 11591162. Tani, E., Yoshimura, M., Somiya, S. (1983), /. Am. Ceram. Soc. 66, 506-510. Taylor, J. R., Bull, A. C. (1986), Ceramics Glaze Technology. Oxford: Pergamon Press, 21 -22; 132-134.

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Tokudome, K., Yamaguchi, T. (1988), in: Advances in Ceramics, Vol. 24: Science and Technology of Zirconia III. Columbus, OH: American Ceramic Society. Tsukuma, K., Shimada, M. (1985), J. Mater. Sci. 20, 1178-1184. Tsukuma, K., Kubota, Y, Tsukidate, T. (1984), in: Advances in Ceramics, Vol. 12: Science and Technology of Zirconia. Columbus, OH: American Ceramic Society. Van Olphen, H. (1977), Colloidal Chemistry of Clays. New York: Wiley. Velde, B. (1985), Developments in Sedimentology, Vol. 40: Clay Minerals: A Physico-Chemical Explanation of Their Occurrence. Amsterdam: Elsevier. Viera, J. M., Brook, R. J. (1984), in: Advances in Ceramics, Vol. 10: Structure and Properties ofMgO and A12O3 Ceramics. Columbus, OH: American Ceramic Society, pp. 438-463. Warshaw, S. I., Seider, R. (1967), /. Am. Ceram. Soc. 50, 337-343. White, J. (1970), in: High-Temperature Oxides, Part 1: Magnesia, Lime and Chrome Refractories, Alper, A. M. (Ed.). New York: Academic Press, pp. 77141. Williams, P., Taylor, D., Soady, X S. (1990), in: Proc. Conf. Refractories for the Steel Industry Commission of European Community. Amsterdam: Elsevier. Wilson, S. X (1979), Br. Ceram. Soc. Proc. 28, 281294. Worrall, W. E. (1986), Clays and Ceramic Raw Materials. London: Elsevier. Yager, T. A., Kingery, W D. (1984), in: Advances in Ceramics, Vol. 10: Structure and Properties of MgO and A12O3 Ceramics. Columbus, OH: American Ceramic Society, pp. 139-151. Yamaguchi, A. (1984), Taikabutsu Overseas 4,14-18.

3 Nitride Ceramics Stuart Hampshire

Materials Research Centre, University of Limerick, Limerick, Ireland

List of 3.1 3.2 3.3 3.3.1 3.3.2 3.3.2.1 3.3.2.2 3.3.3 3.3.3.1 3.3.3.2 3.3.4 3.3.5 3.3.5.1 3.3.5.2 3.3.5.3 3.3.5.4 3.3.6 3.3.6.1 3.3.6.2 3.3.6.3 3.3.7 3.3.8 3.3.9 3.4 3.4.1 3.4.2 3.4.3 3.4.4 3.4.5 3.4.5.1 3.4.5.2 3.4.5.3 3.4.6

Symbols and Abbreviations Introduction Transition Metal Nitrides Silicon Nitride Historical Development Crystal Structure Structures of a and (3 Silicon Nitrides The ot-p Silicon Nitride Phase Transformation Reaction-Bonded Silicon Nitride (RBSN) Overview of the Reaction-Bonding Process Reaction Mechanisms and Microstructural Development Formation of Silicon Nitride Powders Formation Routes for Dense Silicon Nitride Hot-Pressed Silicon Nitride (HPSN) Sintered Silicon Nitride (SSN) Sintered Reaction-Bonded Silicon Nitride (SRBSN) Hot Isostatically Pressed Silicon Nitride (HIPSN) The Role of Additives in the Densification of Silicon Nitride Formation of Oxynitride Liquids in Silicon Nitride Ceramics Sintering Kinetics Phase Relationships, Microstructure and Effects on Properties Properties of Silicon Nitride Ceramics Oxidation of Silicon Nitride Ceramics Summary of Approaches to Optimisation of Properties Sialons p'-Sialons Phase Relationships in the S i - A l - O - N and Related Systems Sintered P-Sialons Properties of (3-Sialon Ceramics a'-Sialons Introduction The Structure of oc-Sialons Formation of oc-Sialon Ceramics oc/P-Sialon Ceramics

Materials Science and Technology Copyright © WILEY-VCH Verlag GmbH & Co KGaA. All rights reserved.

121 122 122 123 123 124 124 127 127 127 129 132 133 133 134 135 135 136 136 137 140 142 144 148 149 149 150 151 152 153 153 153 154 155

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3.5 3.5.1 3.5.2 3.5.3 3.5.4 3.5.5 3.6 3.6.1 3.6.2 3.6.3 3.6.4 3.6.5 3.7 3.7.1 3.7.2 3.7.3 3.7.4 3.8 3.8.1 3.8.2 3.8.3 3.8.4 3.8.5 3.9 3.10 3.11 3.12

3 Nitride Ceramics

Silicon Oxynitride Introduction The Silicon Oxynitride Structure Sintering and Properties of Silicon Oxynitride Ceramics O'-Sialon Ceramics O'-P'-Sialons Oxynitride Glasses and Glass Ceramics Introduction Solubility of Nitrogen in Glasses Sialon Glasses Nitrogen Coordination in Oxynitride Glass Structures Nucleation and Crystallisation in Oxynitride Glasses Aluminium Nitride Introduction Structure of Aluminium Nitride Synthesis of Aluminium Nitride Fabrication and Properties of Aluminium Nitride Ceramics Aluminium Oxynitride (A1ON) Ceramics Introduction Structure of A1ON Phase Relationships in the A l - O - N System Formation of A1ON Ceramics Properties of A1ON Ceramics Boron Nitride Future Potential of Nitride Ceramics Acknowledgements References

155 155 155 156 157 157 158 158 158 159 161 161 163 163 163 163 163 165 165 165 166 166 166 167 167 168 168

List of Symbols and Abbreviations

List of Symbols and Abbreviations E AG° AH A//e k M P T Tg

Young's modulus change in Gibbs free energy activation enthalpy enthalpy change of reaction Boltzmann constant Ca, Li or Y ion partial pressure absolute temperature glass transition temperature

Q

density

A1ON AN CVD FTIS HIP HIPSN HPSN RBSN sialon SN SRBSN SSN XPS YAG YAM YN

aluminium oxynitride ceramic aluminium nitride chemical vapour deposition Fourier transform infrared spectroscopy hot isostatic pressing hot isostatically pressed silicon nitride hot-pressed silicon nitride reaction-bonded silicon nitride ceramic from the S i - A l - O - N or related system silicon nitride sintered reaction-bonded silicon nitride sintered silicon nitride X-ray photoelectron spectroscopy yttrium aluminium garnet yttrium aluminate, monoclinic yttrium nitride

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3.1 Introduction One of the major advantages of ceramics over metals is their high temperature behaviour, reflected in the fact that ceramics have higher strengths at temperatures above 1000 °C and better oxidation and corrosion resistance. In addition to these advantages, one class of ceramic materials, the nitrides, combine superior hardness with high thermal and mechanical stability, making them suitable for applications as cutting tools, wear-resistant parts and structural components at high temperatures. Transition metal nitrides, because of their extremely high hardness and stiffness, have been developed for wear-resistant applications. They have also generated considerable interest because of their high thermal and electrical conductivities. However, the greatest impetus to research and development on nitride ceramics has been the attempt to produce a ceramic gas turbine engine for which application silicon nitride has been a main contender. Silicon nitride is the primary material in a family of nitride or "nitrogen" ceramics developed for engineering applications and is a generic term used for a variety of types made by different processing methods or having different compositions or both. The attainment of their intrinsic properties requires that attention be given to control of processing and microstructural development. Sialon (Si-Al-O-N) ceramics retain the structure of silicon nitride with incorporation of aluminium and oxygen in solid solution. These ceramics have already been successfully commercially exploited as cutting tool inserts. The other nitride ceramics within the S i - A l - O - N system include silicon oxynitride and aluminium nitride. The latter has intrinsically a very high thermal conductivity, the achieve-

ment of which depends on careful optimisation of processing and microstructure. This chapter provides an overview of nitride ceramics and a more in-depth exploration of silicon nitride and aluminium nitride ceramics including their structure, microstructure, properties and processing.

3.2 Transition Metal Nitrides Nitrides of the transition metals including titanium, vanadium, zirconium, niobium, molybdenum, hafnium and tantalum are extremely hard refractory materials with thermo-mechanical stability and thus find applications as cutting tools, wear-resistant parts (Sproul and Rothstein, 1985) and high-temperature structural components. Previous methods of preparation are outlined by Toth (1971). Several methods involve contact of a metal oxide with solid carbon under nitrogen to achieve reduction and nitridation. Later refinements (Oyama et al., 1988) involve passing a gas over the precursor oxide to produce the nitrides in high surface area form (NbN: 3.6 m 2 g" 1 ; Mo 2 N: 22 m 2 g" 1 ). No report is given of the sinterability of these powders. TiN and ZrN powders are available commercially and they are being used as dispersed phases in other ceramic matrix composites, notably alumina and silicon nitride. In the former case, starting from Al 2 O 3 -TiN, the product consists of A1NTiO 2 . With TiN as a second phase in ceramic composites, electrical discharge machining is feasible in view of the very high electrical conductivity of TiN, which approaches the range for metals. In wear, bearing and cutting applications, transition metal nitrides are applied as coatings, and the chemical vapour deposition (CVD) method has been the most frequently used technique (Stinton et al.,

3.3 Silicon Nitride

1988). This involves depositing the nitride material from gaseous precursors onto a substrate, typically a hard metal such as tungsten carbide. Table 3-1 lists the gaseous mixtures used in CVD processes for transition metal nitrides and the deposition temperatures. Titanium nitride has received more attention than the other nitrides and has been successfully commercialised as a coating for a range of materials including Cobonded WC tool inserts. The coating provides increased hardness and wear-resistance but also prevents reaction of the cobalt binder with the metal workpiece at the high temperatures generated by machining. However, titanium nitride is susceptible to oxidation above 800 °C. Laugier (1988) showed that TiN coatings have a good scratch resistance at all temperatures up to 1050 °C confirming the excellent adhesion of these types of coating. This is due to interdiffusion of Ti and N into the underlying material at the relatively high processing temperature and this produces very high strength bonding at the interface. The use of transition metal nitrides as bulk ceramics rather than coatings has reTable 3-1. Transition metal nitrides produced by CVD (after Stinton et al., 1988).

Coating TiN HfN ZrN TaN VN NbN

Gas mixture

Deposition temperature

TiCl 4 -N 2 -H 2 HfCl x -N 2 -H 2 HfI 4 -NH 3 -H 2 ZrCl 4 -N 2 -H 2 ZrBr 4 -NH 3 -H 2 TaCl 5 -N 2 -H 2 VC14-N2-H2 NbCl 5 -N 2 -H 2

900-1000 900-1000 >800 1100-1200 >800 800-1500 900-1200 900-1300

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ceived relatively little attention compared with the large research effort on ceramics based on silicon and aluminium nitrides.

3.3 Silicon Nitride 3.3.1 Historical Development Silicon nitride was first mentioned in 1857 by Deville and Wohler and later, in 1910, Weiss and Engelhardt observed the formation of a bluish-white coating on silicon after heating to 1320°C in nitrogen. The chemical formula was given as Si 3 N 4 but it remained a chemical curiosity to researchers, mainly in Germany, until over forty years later, when refractories utilising silicon nitride as a bond for silicon carbide and other materials were developed (Wroten, 1954). At the same time, silicon nitride with good thermal stability was developed for use as thermocouple tubes, crucibles for molten metals and also rocket nozzles (Collins and Gerby, 1955). This type of material was formed by nitriding silicon powder compacts and was later termed reaction-bonded silicon nitride (RBSN). Interest began to grow in this new ceramic material, particularly in Britain, for potential use in gas turbines. Physical, chemical and structural characteristics were investigated and it was clearly established that silicon nitride existed in two crystallographic modifications, a and (3. By 1960, Parr, Martin and May had published a comprehensive review of the properties and structure of silicon nitride (RBSN), outlining the technology which they had developed which would be the major processing route for silicon nitride ceramics for at least the next decade. One of the major obstacles to the use of RBSN in engine applications was its limited mechani-

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3 Nitride Ceramics

cal strength as a result of the presence of 20-30% microporosity. In 1961, Deeley et al. succeeded in achieving increased densities by hot-pressing previously formed silicon nitride powder with various sintering additives. With magnesium oxide, full density material was produced by hot-pressing at 1850°C under 23 MPa and strength was substantially improved over that of RBSN. Magnesia was also used as the densification additive in the first commercial development of HPSN, although the precise role that the oxide played in densification remained unknown at that time. However, the initial predominantly a silicon nitride powder was observed to transform to the (3 modification during the hot-pressing process, and this was thought to be responsible for the development of high strengths (Lumby and Coe, 1970). In 1971, a full-scale effort to produce the ceramic gas turbine was initiated in the USA. It was realised early in the programme that the objectives would not be achieved, because a major problem was the difficulty of component fabrication, since hot-pressing is limited to simple shapes. It was therefore necessary to consider the possibility of sintering without pressure where shaping could be carried out by more conventional methods. One breakthrough was the discovery of the "sialons" in Japan and Britain (Oyama and Kamigaito, 1971; Jack and Wilson, 1972). These are silicon nitride ceramics in which oxygen can replace nitrogen in the P silicon nitride structure if at the same time silicon is replaced by aluminium to maintain charge neutrality. Pressureless sintering to theoretical density proved feasible provided that a sintering additive such as MgO or Y 2 O 3 is included. Since the 1970s, the search for improved materials has led to a better understanding

of the role of additives in the densification and microstructural development of silicon-nitride-based ceramics and the consequences for final properties. Improvements in powder manufacture and forming techniques and the development of alternative firing process has led to a wide range of materials including RBSN, HPSN, sintered sialons of different types, sintered silicon nitrides (SSN), sintered reaction-bonded silicon nitride (SRBSN) and hot isostatically pressed silicon nitride (HIPSN). 3.3.2 Crystal Structure 3.3.2.1 Structures of a and P Silicon Nitrides

Vassiliou and Wilde (1957) obtained the first evidence for the existence of two forms of silicon nitride by reporting a "hexagonal" type (II) with a different X-ray diffraction pattern from that of the "orthorhombic" (I) silicon nitride extracted from silicon steels by Leslie et al. (1952). Turkdogan et al. (1958) described how changes in the time and temperature of nitriding of silicon affected the X-ray diffraction pattern, some peaks completely disappearing after prolonged nitriding above 1600°C. The silicon nitride remaining was designated |3 and the apparently lower temperature form which disappeared was designated a, both with the same chemical composition (Si3N4) and the same measured densities (3.19 + 0.01 gcm~3). Popper and Ruddlesden (1957) had claimed that the two forms observed previously were (I) orthorhombic and (II) rhombohedral. Following these early misinterpretations of X-ray diffraction patterns, Hardie and Jack (1957), using samples from Turkdogan et al. showed that both forms are hexagonal, the essential difference being that the c dimension of a is approximately twice that of (3, as shown in Table 3-2.

3.3 Silicon Nitride

125

Table 3-2. Comparison of unit cell parameters for oc and p silicon nitrides (Hardie and Jack, 1957). Silicon nitride

Unit cell contents

a (A)

c(A)

c/a

F(A3)

Calculated density (gem" 3 )

a

Si 12 N 16 Si6N8

7.748 7.608

5.617 2.9107

0.7250 0.3826

292.0 145.9

3.184 3.187

P

A complete structure determination assigned P silicon nitride to space group P63/m. The structure is based on the phenacite type, Be 2 SiO 4 , in which the oxygen atoms are replaced by nitrogen and the beryllium atoms by silicon. A further structure refinement (Wild et al., 1972 a) was in broad agreement with the earlier work and the two sets of data for the atomic positions are compared in Table 3-3. The bonding leads to a framework of SiN4 tetrahedra (slightly distorted) joined by sharing nitrogen corners so that each ni-

Table 3-3. Final parameters for (3-Si3N4 (space group P6 3 /m-C 6 2 h , No. 176).

trogen is common to three tetrahedra. The (3 structure is composed of puckered rings of alternating Si and N atoms as shown in Fig. 3-1 (Hampshire etal., 1978). Because the fractional heights are z = 0.25 and 0.75, these joined rings can be considered as layers with a stacking sequence ABAB and forming long continuous channels in the c direction as shown in Fig. 3-2 (Redington, 1989). The oc silicon nitride structure has aroused more controversy. Hardie and Jack (1957) deduced a space group of P 31c.

Idealised Si - N layers

(a) From Hardie and Jack (1957). X

6 Si in 6 (h)at 6N1 in 6 (h)at 2N2 in 2 (c) at

0.172 0.333 0.333

y -0.231 0.033 0.667

z 0.250 0.250 0.250

(b) From Wild et al. (1972 a). X

y

z

6 Si in 6 (h) at

0.1773 ±0.0003

-0.2306 0.0003

0.2500 0.0000

6 Nl in 6 (h) at

0.3323 ±0.0008

0.0314 0.0007

0.2500 0.0000

2 N2 in 2 (c) at

0.3333 ±0.0000

0.6667 0.0000

0.2500 0.0000

Reliability index R = 0.021; number of planes in refinement 61; total number of planes 68.

^•ABAB

Figure 3-1. The AB layers in the crystal structure of (3 silicon nitride (after Hampshire et al., 1978).

126

3 Nitride Ceramics Idealised Si-N layers

OOABCD

Figure 3-2. The ABAB stacking of layers in the p silicon nitride structure giving rise to long continuous channels in the c direction (after Redington, 1989).

Where the layers of atoms in P are linked along the [001] direction in the sequence ABAB, the a structure has the sequence ABCDABCD. The CD layer, shown in Fig. 3-3, is similar to the AB layer except that it is rotated by 180° on the c-axis. The long continuous channels seen in the P (ABAB) form are thus closed off into two large interstices, centred at 1/3, 2/3, 3/8 and 2/3, 1/3, 7/8 (see Fig. 3-4). Wild et al. (1972a), from data on bond lengths and angles, abnormal site occupation numbers, density and oxygen content, concluded that oc silicon nitride was a defect structure with up to 1 in 30 nitrogen atoms replaced by oxygen with corresponding silicon vacancies as in: 1.5-^15

0.5

They proposed that a and p, respectively, are high- and low-oxygen-potential modifications. Roberts et al. (1972) nitrided F e Si alloys at low temperatures (500- 720 °C)

Figure 3-3. The CD layers in the crystal structure of a silicon nitride (after Hampshire et al., 1978).

Figure 3-4. The ABCD stacking of layers in the a silicon nitride structure giving rise to two closed interstices per unit cell (after Redington, 1989).

and found that pure p was only precipitated at very low oxygen potentials whereas oc was formed at higher oxygen potentials, again suggesting that a and P are not merely low and high temperature forms of the same compound. An extensive thermo-

3.3 Silicon Nitride

dynamic investigation of the S i - O - N system, also by Wild et al. (1972 b), supported these conclusions. Marchand et al. (1969) previously found no significant variation in bond lengths and no evidence for segregation of oxygen atoms in the nitrogen positions. Further work by Kohatsu and McCauley (1974) and Kato et al. (1975) concluded that a can exist without a small amount of "stabilising" oxygen. Priest et al. (1973) and Edwards et al. (1974) showed that a forms at much lower oxygen contents than those previously proposed by Wild et al. (1972 a). Jack (1983) later provided evidence showing that 26 different a silicon nitride samples from these different preparation routes had a relatively wide range of unitcell dimensions (a = 7.7491 -7.7572 A; c = 5.6164-5.62213 A), but similar c/a ratios, and concluded that this must be due to variations in their compositions, particularly oxygen content. Clearly, oxygen may indeed stabilise the oc structure, but it is not a necessary requirement. However, as discussed in Sec. 3.3.3, during nitriding of silicon, the formation of a silicon nitride is favoured by the presence of oxygen in the nitriding environment. 3.3.2.2 The a-p Silicon Nitride Phase Transformation The a->p transformation in silicon nitride requires a lattice reconstruction. This type of process occurs usually only when the transforming material is in contact with a solvent. The greater solubility of the more unstable form drives it into solution after which it precipitates as the less soluble, more stable form. A variant of this process may occur in the vapour phase. The transformation is observed during liquid phase sintering of silicon nitride (see Sec. 3.3.6) at temperatures in excess of

127

1400°C where the original a phase is in contact with a metal-silicon-oxynitride liquid. Further discussion of this topic is given in Sec. 3.3.6.2. The thermodynamic investigation of Wild et al. (1972 b) showed that a (containing oxygen) becomes unstable with respect to (3-Si3N4 + Si 2 N 2 O at 1400 °C with R ~10~ 2 0 atm. o2 If p and a silicon nitrides are true high and low temperature polymorphs with a specific transformation, then it should be possible to transform p to oc. However, this has never been observed experimentally, giving further credence to the idea that a is a defect structure. 3.3.3 Reaction-Bonded Silicon Nitride (RBSN) 3.3.3.1 Overview of the Reaction-Bonding Process Reaction-bonded silicon nitride was the first commercially available form of the ceramic and relies on a simple inorganic chemical reaction, the nitridation of silicon: 3Si + 2N 2

(3-1)

The required shape is first formed from silicon powder by techniques such as isostatic pressing or injection moulding. Because the reaction tends to be slow, for useful production rates, high surface area silicon powders must be used (mean particle size Si(NH)2 + 4NH 4 C1 (3-12a) 3Si(NH)2 -* Si 3 N 4 + 2NH 3 (3-12b) Each method yields powders suitable for sintering but with different morphologies, crystallinity, specific surface area, oxygen, carbon and impurity contents, all of which can significantly influence the rate of densification. The ideal powder should have the following characteristics: (i) equiaxed particle morphology for good green compaction; (ii) high surface area for good sinterability;

(iii) high a silicon nitride content to favour better microstructural development during sintering; (iv) low levels of impurities to avoid unwanted reactions and to allow development of better high-temperature mechanical properties. In all cases the oxygen is present usually as a surface layer of SiO 2 around each powder particle. Typical characteristics of silicon nitride powders produced by the four different routes are given in Table 3-5 (Wotting and

3.3 Silicon Nitride

133

Table 3-5. Characteristics of Si 3 N 4 powders, processed by different preparation methods Technique:

Nitridation of Si

Sample no.:

1

2

23 1.4 0.2 0.07

11 1.0 0.25 0.4

Chemical vapour deposition

Carbothermal

Diimide precipitation

tuuvuuii

Specific surface area (m2 g" 1 ) O (wt.%) C (wt.%) Fe,Al,Ca(wt.%) Other impurities (wt.%) Crystallinity (%)

a/(a + p) (%) Morphology

100 95 E

100 92 E

1

2

4 10 1.0 3.0 _ 0.005 0.005 f Cl: 0.04 [Mo + Ti:0.02 60 0 95 E+R E+R

10 2.0 0.9 0.22

1

2

11 1.4 0.1 0.01

13 1.5 0.1 0.015

Cl: 0.1 100 98 E+R

98 86 E

0.005 95 E

E: equiaxed; R: rod-like.

Ziegler, 1986). An understanding of the effect of powder characteristics on densification behaviour and microstructural development is essential to produce materials with better properties. 3.3.5 Formation Routes for Dense Silicon Nitride For an intrinsically high strength, high hardness material such as silicon nitride, the high energy covalent chemical bonds giving rise to these properties are a disadvantage in fabrication. Self-diffusivity in silicon nitride is quite low and species only become sufficiently mobile for sintering at temperatures where the decomposition of silicon nitride commences (>1850°C). Thus, alternative approaches have been developed by the use of densification additives to create the conditions for liquidphase sintering either with or without applied pressure to assist the process. These techniques include hot-pressing, pressureless sintering, of both silicon nitride powder compacts and reaction-bonded silicon nitride, and hot-isostatic-pressing of all of the previously formed types. Initially, ad-

ditives such as MgO or Y 2 O 3 were used to densify silicon nitride, and this resulted in the formation of secondary phases at the silicon nitride grain boundaries. Later, mixed oxide additives such as Y 2 O 3 + A12O3 and various rare earth oxides were explored to develop specific microstructures by modifying the nature of the grain boundary phase. The role of the additives in the liquid phase sintering process and microstructural development is discussed in Sec. 3.3.6. 3.3.5.1 Hot-Pressed Silicon Nitride (HPSN) Hot-pressing of silicon nitride, which involves the application of both heat and uniaxial pressure, is carried out in graphite dies heated by induction to temperatures in the range 1650-1850 °C for 1 to 4 hours under an applied stress of 15 to 30 MPa. Boron nitride is applied as a coating to the graphite die and plungers to prevent reaction of these with the silicon nitride. Boron nitride powder is also used as a solid high temperature lubricant to facilitate removal of the hot-pressed material from the die,

134

3 Nitride Ceramics

but surface contamination is usually a problem. This can be minimised by prepressing the powder mix in a metal die to form a compact prior to its introduction into the graphite die. Material produced by Coe et al. (1972) by hot-pressing high-oc phase silicon nitride powder with only 1 wt.% MgO had a mean bend strength of 900 MPa, which reduced to 800 MPa at 950 °C. However, HPSN is limited to simple shaped (cylindrical) billets and components must be machined from these using expensive grinding. A typical microstructure is shown in Fig. 3-8.

Figure 3-8. Scanning electron micrograph of a polished etched section of HPSN (after Ziegler et al., 1987).

3.3.5.2 Sintered Silicon Nitride (SSN) A more cost-effective method of production of complex-shaped components in dense silicon nitride, without the requirement for machining to any extent, is pressureless sintering, which involves firing of the shaped component at 1700-1800 °C under a nitrogen atmosphere at 0.1 MPa. As with hot-pressing, the additives provide conditions for liquid phase densification but, in the absence of applied pressure, the reduction in surface energy becomes the major driving force for sintering and so the use of high surface area powders is necessary. This increases the oxygen content of the powders, which can also affect the quantity of liquid phase formed and affect the overall composition of the secondary phase. A typical microstructure is shown in Fig. 3-9. Without pressure, dissociation of Si 3 N 4 becomes a problem at high temperatures. During pressureless sintering at temperatures much above 1700°C, Terwilliger and Lange (1975) showed that density starts to decrease at longer times as a result of increasing weight losses. The use of so-called "powder beds", where the component to

11 jim

Figure 3-9. Scanning electron micrograph of an etched fracture surface of SSN.

be sintered is surrounded by a mixture of powder of its own composition and inert boron nitride, has proved successful in reducing volatilisation (Wotting and Hausner, 1983). This creates a local gas equilibrium immediately adjacent to the silicon nitride compact, thus minimising volatilisation. An alternative is to increase the nitrogen pressure to higher levels (10 MPa), and development work, particularly in Japan, has demonstrated substantial improvements in properties by this method. Densities of 97-99% of the theoretical value are routinely achieved with bend strengths of >1000 MPa.

3.3 Silicon Nitride

3.3.5.3 Sintered Reaction-Bonded Silicon Nitride (SRBSN) Silicon nitride powder compacts have low green densities (~45-55% theoretical) and, thus, sintering to high densities requires volume shrinkages of 45-55%. Consequently, control of the firing process for complex shapes becomes more difficult. As RBSN has a density within the range 70-85% of the theoretical value, it was considered as a suitable starting material for sintering by Giachello and Popper (1979) and Mangels and Tennenhouse (1980). Additives such as MgO or Y 2 O 3 are mixed with the silicon prior to shaping and nitriding as for RBSN. A further heattreatment in the range 1800=2000 °C under a nitrogen atmosphere (0.1 to 8 MPa), and using a protective powder bed to reduce volatilisation, allows densification to 98% theoretical density with only 6% linear shrinkage. A typical microstructure is shown in Fig. 3-10. Bend strengths of 700 MPa have been reported (Mangels, 1983).

135

^ ,. \

Figure 3-10. Scanning electron micrograph of a polished and etched section of SRBSN (after Kleebe and Ziegler, 1989).

3.3.5.4 Hot Isostatically Pressed Silicon Nitride (HIPSN) Hot isostatic pressing (HIP) was originally developed for processing metals, special alloys and hard metals. Further development of the technique for ceramic parts required parallel developments in special HIP equipment to allow sintering by HIP at temperatures above 1700°C. The silicon nitride components are placed in an "autoclave" and subjected to high temperature and high pressure using argon or nitrogen as the pressure transmission medium to consolidate a shaped powder compact or to remove porosity from pre-fired, RBSN, SSN or SRBSN. In all cases, a small amount of sintering additive is required but because a lower quantity may be used,

Figure 3-11. Transmission electron micrograph of HIPSN (after Rouxel, 1990).

properties should be superior to those of other forms of Si 3 N 4 . A typical microstructure is shown in Fig. 3-11. For HIP of a powder compact or RBSN, where there is a large volume fraction of open porosity, an encapsulation technique is used to prevent penetration of the pressurised gas into the open pore network (Larker, 1979). The green or reaction-

136

3 Nitride Ceramics

bonded body is coated with a layer of glass powder and the pressure vessel is evacuated to "degas" the component. The temperature is then raised to melt the glass to form an impermeable barrier and the gas pressure increased to 200 MPa as the peak temperature reaches 1700-1900°C. During controlled cooling, the glass capsule cracks off and the component is given a surface treatment such as sandblasting. For pre-sintered materials such as SSN and SRBSN where there is no open porosity, encapsulation is unnecessary (Larker, 1983) and the major reason for applying the HIP treatment is to remove residual porosity. Ziegler and Wotting (1985) show that HIP of SSN results in a substantial improvement in reliability (higher Weibull modulus) because of flaw-healing and removal of porosity. 3.3.6 The Role of Additives in the Densification of Silicon Nitride 3.3.6.1 Formation of Oxynitride Liquids in Silicon Nitride Ceramics

In the early development of hot-pressed silicon nitride, it had not been realised that every powder particle of silicon nitride is surrounded by a surface layer of silica. Oxide additives react with this silica and some of the nitride to form an oxynitride liquid at high temperature which cools as an intergranular phase. Wild et al. (1972 c) showed, by detecting silicon oxynitride and enstatite (magnesium silicate) as devitrification products in silicon nitride hotpressed with magnesia, that this phase was a glass containing nitrogen. The glass was first observed directly by electron microscopy by Drew and Lewis (1974), who suggested that the mechanism of sintering involves solution and reprecipitation of silicon nitride crystals. Attempts were made to determine the glass composition (Powell

and Drew, 1974), and it was found that impurity ions such as calcium could be accommodated in the glass. The glass softening temperature is lowered as a result, and there is a clear correlation between this and the drastic reduction in strength observed at high temperatures. The characteristics of the oxynitride liquids formed with different densification additives differ widely, and the second phase formed on cooling may be crystalline or vitreous. The role of the additives is summarized by a-SLN, + SiO. + MYOV -> P-Si3N4 + M - S i - O - N phase

(3-13)

Hampshire and Jack (1981) observed that the temperature of initial liquid formation with additions of metal oxide to silicon nitride containing 4 wt.% surface silica is appreciably lower than the lowest solidus temperature in the corresponding metal oxide-silica system, confirming that nitrogen, as an additional component, lowers the eutectic temperature. For example, liquid formation occurs with MgO at 1390°C and with Y 2 O 3 as low as 1450°C. With A12O3 the lowest eutectic is at 1470 °C, and extra additives will lower this further. During sintering, shrinkage usually starts at the temperature of liquid formation and is subsequently accompanied by the a->p phase transformation. Weston and Carruthers (1973) showed that, during hotpressing with MgO, full densification could be achieved via liquid silicate formation before any a-»P transformation had taken place. Terwilliger and Lange (1974) suggested that the liquid would allow transport of Si and N, but they did not consider that oc->P transformation was required for densification. Figure 3-12 shows the shrinkage and transformation at different temperatures (constant time: 30 min) during pressureless

137

3.3 Silicon Nitride 40 -|

7wt. c /o Y 2 O 3

4U-

5 wt. % MgO p = 0.95

30-

30-

J 20-

20-

o _2~-

"O

p

O

= 0.75

10-

10-

y

0—i— 1300

'

1400

i

i

1500

i

1600

100-1

i

i

1

1700

-o—o-c

50-

1300

1400

1500

1600

1700

1600

1700

100-i

50U'

CO

CO.

™_«V oJ

01300

1400

1500

1600

1700

T (°C)

—r 1300

1400

1500

T CC)

Figure 3-12. Shrinkage and transformation as a function of temperature for pressureless sintering of silicon nitride with Y 2 O 3 and MgO (after Hampshire and Jack, 1981). Q is the relative density.

sintering of silicon nitride (Hampshire and Jack, 1981) and emphasises the differences between magnesia and yttria as additives. With MgO, nearly complete densification is achieved with only partial transformation to (3 during hot-pressing, as found by Weston and Carruthers (1973) and Bo wen et al. (1978 a), whereas with Y 2 O 3 complete transformation occurs with only limited densification. Clearly, the behaviour of different additives requires interpretation and studies of the densification and transformation kinetics are thus important. 3.3.6.2 Sintering Kinetics

Terwilliger and Lange (1974) were the first to study the kinetics of densification of

silicon nitride hot-pressed with 5wt.% MgO, and their results were interpreted using the liquid phase sintering model of Kingery (1959) without any firm conclusions regarding the model itself. Mitomo (1976) also used the Kingery model in analysing hot-pressing kinetics. The only systematic study of pressureless sintering kinetics is that by Hampshire and Jack (1981), again using the Kingery liquid-phase sintering model in which three stages are identified, as summarized by the log-shrinkage/log-time plot of Fig. 3-13. The stages are: (i) particle rearrangement within the initial liquid, where the rate and the extent of shrinkage depend on the volume and vis-

138

3 Nitride Ceramics

u-

-1/

2-

SolutionDiffusionReprecipitation

Elimination of closed porosity

Particle rearrangement

Log time

Figure 3-13. Three stages during the liquid phase sintering of silicon nitride (after Hampshire and Jack, 1981).

cosity of the liquid; this is the incubation period for the a ->(3 transformation; (ii) solution-diffusion-reprecipitation, where shrinkage can be expressed as (see Kingery, 1959) AF/F 0 oc tlln

(3-14)

where t is time, n = 3 if solution into or precipitation from the liquid is rate controlling and n = 5 if diffusion through the liquid is rate-controlling, assuming that the particles are non-spherical; the oc->(3 transformation begins in this stage; (iii) final elimination of closed porosity during which the liquid acts to form a more rounded grain morphology; final density is greater than 95% of the theoretical value. During pressureless sintering of silicon nitride with 5 wt.% MgO and 7wt.% Y 2 O 3 respectively, Hampshire and Jack (1981) observed that the rearrangement stage with MgO accounts for half of the total shrinkage required for full densification, whereas with Y 2 O 3 it is responsible for less than a quarter of the shrinkage required. The reason for the difference is the larger volume and lower viscosity of the magnesium silicon oxynitride liquid compared with the yttrium-containing

liquid. Different silicon nitride powders, containing different levels of impurity and surface silica, densify to different extents during this first stage, as these affect the volume of liquid formed. During the stage (ii) solution-precipitation, for MgO, n = 3, indicating a reactioncontrolled process; for Y 2 O 3 , n = 5 and this suggests that diffusion through the more viscous liquid is rate controlling. This is confirmed by the fact that for Y 2 O 3 transformation starts immediately after stage (i) rearrangement and is complete at a relative density of 0.75. Solution-precipitation is more rapid than diffusion and so the oc->p transformation occurs with little material transport and hence with very little densification. On the other hand, with MgO, a reasonable level of densification is attained by rearrangement, which corresponds to the incubation period for oc-> P transformation. During stage (ii), the relatively rapid transport of material through the low-viscosity liquid ensures that transformation is accompanied by shrinkage. Figure 3-14 illustrates schematically the liquid phase sintering process. For both additives, solution of oc into the oxynitride liquid occurs preferentially at the contact areas between the particles. With MgO, rapid transport of material allows precipitation of p on the free surfaces so that the distance between particle centres is reduced allowing shrinkage to occur. With Y 2 O 3 , diffusion is slow, and appreciable precipitation of P occurs in the contact areas without significant material transport. Thus, transformation takes place without much densification. In hot-pressing silicon nitride with MgO, Brook et al. (1977) also observed the rearrangement and solution-diffusionreprecitation stages, but interpretation of the kinetics is based on a grain boundary diffusion-controlled creep model of Coble

3.3 Silicon Nitride

Ideal

Complete densification

Solution control e.g. MgO

Partial transformation

Incomplete densification

Diffusion-Control e.g. Y 2 O 3

Full transformation

Kingery Model Figure 3-14. Schematic illustration of the stage (ii) solution-precipitation process during liquid phase sintering of silicon nitride (after Hampshire and Jack, 1981).

(1963,1970), in which surface energy effects are assumed to be negligible in comparison with applied pressure, and therefore this is not applicable in the case of pressureless sintering. Brook et al. suggested that, following a rapid rearrangement process, the major part of the densification occurs by dissolution of a silicon nitride at points of compressive stress, diffusion of material through a grain-boundary phase down the stress gradient, and then reprecitation of P silicon nitride at unstressed points, with diffusion being the rate-controlling step. The densification rate is given by At

47 QWDPA kTG3

(3-15)

where Q is the volume transported by each atom of the slow-diffusing species, W the boundary thickness, D the diffusion coeffi-

139

cient, PA the applied stress, and G the grain size. W is related to the quantity of second phase present, which is in turn proportional to the amount of additive used, and the linear dependence of W with densification rate was confirmed. Although transformation occurs together with densification, it was not seen by Brook et al. as a necessary factor in bringing about densification, even though the activation energies for both densification and transformation were found to be similar. Changes in the slopes of the Arrhenius plots were found at 1550°C, i.e., close to the solidus in the MgSiO 3 -SiO 2 system, and according to the authors indicated a change from diffusion through a "secondphase solid" boundary to diffusion through a liquid grain-boundary film. The activation enthalpies were found to be: Below 1550°C Densification AH = — 450 kJ mol ~* Transformation AH = — 500 kJ mol~ x Above 1550°C Densification AH= - 6 9 5 k J m o r 1 Transformation AH = - 6 9 0 k J m o l " 1 The concept of liquid silicate formation is oversimplified, since there is general agreement that a magnesium silicon oxynitride liquid is formed, and at a lower temperature (1515 °C: Lange, 1978; 1390°C: Hampshire and Jack, 1981). While Brook et al. (1977) and Bowen et al. (1978 a) found that the activation enthalpies for transformation and densification with MgO were the same, suggesting that mass transport mechanisms are the same for both processes, this was not found to be the case for Y 2 O 3 , Y 2 Si 2 O 7 and Li 2 SiO 3 additions (Bowen et al., 1978 b). In the pressureless sintering study by Hampshire and Jack (1981), the activation energies for the oc->p transformation were

140

3 Nitride Ceramics

found to be the same for both MgO and Y 2 O 3 additives and are similar to the dissociation energy of the Si-N bond, i.e., 435 ±38 kJ mol" 1 . The mechanism of transformation seems to be the same for both additives, each merely providing a solvent for a reconstructive transformation involving the breaking of Si-N bonds, which would usually occur only when there is contact between solid and a solvent. The less stable, more soluble form (a) goes into solution and is precipitated as the less soluble, more stable form (P). So the free energy change AG(a_p) may be expected to contribute to the driving force for solution-precipitation densification, especially as the temperature is increased. 33.6.3 Phase Relationships, Microstructure and Effects on Properties As well as limiting or aiding densification, the type and amount of additive determines the nature and quantity of the resulting grain boundary phase as indicated in Eq. (3-13), and this can affect hightemperature strength, creep resistance and oxidation resistance. Thus it is important to understand the phase equilibria in M - S i - O - N and related systems and then apply this knowledge to processing, the development of beneficial microstructures and the relationship between these and properties. The concept of "grain boundary engineering" sought to control the structure of, and reactions occurring at, the grain boundary in silicon nitride based materials. Significant advances in materials development were realized as a result of this new approach. The original work by Gazza (1973,1975) suggested that improvements in high-temperature properties could be achieved by finding a system in which the softening point of the intergranular glass phase is

increased, and this was the reason for investigating Y 2 O 3 as an alternative to MgO as the densifying additive. However, with Y 2 O 3 , one or more of four quaternary, crystalline yttrium-silicon oxynitrides can be formed in preference to glass, depending on the amount of surface silica on the silicon nitride powder. Figure 3-15 shows the Y - S i - O - N behaviour diagram (Jack, 1986). This representation is the same as that of a reciprocal salt system, and the concentrations are expressed in equivalents. The bottom right hand corner is Si 3 N 4 (3Si 4+ and 4N 3 ") and, maintaining 12 positive and 12 negative valency units throughout, the other corners are then Si 3 O 6 , Y 4 O 6 and Y 4 N 4 . For any composition, the equivalent concentrations of silicon (eq.% Si) and nitrogen (eq.% N) are given by eq.% Si =

4[Si] x 100 4[Si] + 3[Y]

(3-16)

3[N] x 100 2[O] + 3[N]

(3-17)

where [Si], [Y], [O] and [N] are, respectively, the atomic concentrations of silicon, yttrium, oxygen and nitrogen.

6/5(Y 2 Si0 5 )

2/5(Y 6 Si 3 N 10 )

6/7(Y 2 Si 2 0 7 ) 2/3(Y 2 Si 3 N 6 ) 4/5(YSi3N5)

Figure 3-15. The Y - S i - O - N behavior diagram: (1) N-apatite, (2) N-YAM, (3) N-oc-Wollastonite and (4) N-melilite (after Jack, 1986).

141

3.3 Silicon Nitride

Earlier work by Rae et al. (1978) shows slightly different compatibility, as YN was obviously not used as a starting component. Similar phase relationships are also reported in the earlier studies of Wills et al. (1976) and Lange et al. (1977), but in these cases the diagram is shown as the Y 2 O 3 SiO 2 -Si 3 N 4 ternary system in molar units. The four phases in the system are: (1) (2) (3) (4)

N-melilite, Y 2 Si 3 O 3 N 4 N-apatite, (Y, [ ])10(SiO4)6(O,N)2 N-YAM, Y 4 Si 2 O 7 N 2 N-oc-wollastonite, YSiO2N

where (Y, [ ])10 means ten lattice sites for Y but with some vacancies and YAM is yttrium aluminate, monoclinic. All are isostructural with the corresponding silicates or aluminates and may accommodate in solid solution the impurities such as calcium that would otherwise be incorporated into a glass. Thus the strengths, at temperatures in excess of 1200 °C, of silicon nitrides densified with yttria are much higher than materials in the M g - S i - O - N system because of the much larger volumes of residual glass of lower viscosities formed with MgO. Unfortunately, materials containing the quaternary crystalline oxynitrides undergo much worse strength degradation at lower temperatures (900-1200°C) because these phases, particularly N-melilite, oxidize to form a yttrium silicate and silica with a marked change in specific volume, which leads to induced stresses in the surface scale and catastrophic failure (Lange et al., 1977; Rae et al., 1978) (see Sec. 3.3.8). It is desirable to produce a final product within the compatibility region Si 3 N 4 Si 2 N 2 O-Y 2 Si 2 O 7 in order to have good oxidation resistance, but this must then contain glass and will have poor creep resistance.

Giachello et al. (1980) developed materials using a combination of Y 2 O 3 + MgO as the densifying additives. The grain boundary glass phase can be crystallized to form Mg 5 Y 6 Si 5 O 24 , and strength at 1000°C is improved as a result. Figure 3-16 shows the effect of MgO additions on the densification of silicon nitride with 7 wt.% Y 2 O 3 at 1650°C for 30min (Hampshire, 1986). There is a substantial increase in densification with MgO while the difference in oc->(3 transformation is negligible. In addition to the requirement of a crystalline second phase, it appears that the morphology of the |3-Si3N4 grains is im-

50-

0

2

4

6

8

wt. % MgO

Figure 3-16. Effect of MgO additions on densification and transformation of silicon nitride with 7 wt.% Y 2 O 3 at 1650°C for 30 minutes (after Hampshire, 1986). •: apparent solid density; o: bulk density; •: % P-Si3N4.

142

3 Nitride Ceramics

portant in determining high-temperature strength. Materials in which the p-phase particles have a very fibrous morphology have better strengths and improved fracture toughness. Lange (1973) suggested that the aspect ratio (length: diameter), R, of the grains is empirically related to the starting a: P ratio through the relationship K= l + |

(3-18)

However, Wotting and Ziegler (1984) showed for silicon nitrides sintered with different Y2O3-AI2O3 mixtures but with the same level of porosity and the same grain size that fracture toughness and aspect ratio vary in the same way with composition. Other studies, concerned with sintering of silicon nitride with MgO-Y 2 O 3 mixtures (Hampshire and Pomeroy, 1985), have also shown that the aspect ratio of grains is dependent on composition and firing time. Prismatic growth in the longitudinal direction occurs to give aspect ratios of 8 to 9 as shown in Fig. 3-17. As the grain boundary

composition changes, the aspect ratios of P grains vary and there is also evidence of grain coarsening as the firing time is increased. Aspect ratio may vary not only with the volume of liquid phase but also with viscosity and nitrogen solubility in the liquid. In particular, the use of rare earth oxides (Nd 2 O 3 , Sm 2 O 3 , Dy 2 O 3 , etc.) usually in combination with MgO (Hampshire etal., 1986, 1987) results in the formation of microstructures with high aspect ratio P silicon nitride grains. These microstructural features have a crucial effect on subsequent mechanical properties. 3.3.7 Properties of Silicon Nitride Ceramics

Mechanical properties of silicon nitride ceramics are shown in Table 3-6. Even within each material type, the properties, particularly fracture strength and fracture toughness, show large variations, again attributable to micro structural differences. Young's modulus of elasticity, £, for RBSN decreases with an increase in total porosity according to (Moulson, 1979) = E0 e x p ( - 3 P )

Figure 3-17. ture surface MgO/Y 2 O 3 grains (after

Scanning electron micrograph of fracof silicon nitride sintered with mixed additives showing high aspect ratio (3 Hampshire, 1984).

(3-19)

where P is the total volume fraction of porosity and Eo is the Young's modulus for silicon nitride with zero porosity, taken as 300 GPa. Materials with the same total porosity but different pore size distributions have very similar elastic moduli. For dense silicon nitrides, values of Young's modulus vary between 260 and 330 GPa, depending on the amount and orientation of other phases present in the material, including porosity. For RBSN, fracture strength is dependent on the volume fraction of porosity but, more particularly, on the size of the largest pores which are created by the melting out of iron impurities present in the original silicon powders. Thus, for a

143

3.3 Silicon Nitride

Table 3-6. Mechanical properties of silicon nitride ceramics. Material type:

RBSN

HPSN

SSN

Relative density 70-88 (% of theoretical) 99-100 95-99 Young's modulus E (GPa) 120-250 310-330 260-320 0.20 0.27 0.25 Poisson's ratio Flexural strength a{ (MPa) 150-350 450-1000 600-1200 at 25 °C 140-340 250-450 340-550 at 1350°C 19-40 15-30 10-25 Weibull modulus m Fracture toughness 5.0-8.5 4(MPam1/2) 1.5-2,8 4.2-7.0

given density, the strength of RBSN shows significant scatter. For the achievement of high strength, it is better to have a homogeneous microstructure with a narrow pore-size distribution at moderate densities than a high density material with large voids present (Ziegler et al., 1987). The grain size, which is finer than the macropore size, has much less effect on strength. Typical average fracture strength values at ambient temperature for HPSN are 600 MPa with MgO additive and 800 MPa with Y 2 O 3 additive, the major difference being the morphology of the (3 grains in the microstructure. With MgO, the liquid phase during hot-pressing allows easy densification but an equiaxed grain morphology, whereas the liquid formed with Y 2 O 3 has a higher viscosity resulting in c-axis growth of the (3 grains and hence a higher aspect ratio (Hampshire and Pomeroy, 1985) giving higher strength and fracture toughness. Improvements in the processing of sintered silicon nitride have resulted in values as high as or exceeding those of HPSN. Weibull modulus tends to be higher for the HPSN and, in particular, the HIP processes as these result in flaw-healing and pore size reduction.

SRBSN

HIP-SN HIP-RBSN HIP-SSN

93-99

99-100

280-300 0.23

310-330 0.23-

0.27

500-800 350-450 10-20

600-1050 350-550

500-800 250-450 20-30

600-1200 300-520

5.0-5.5

4.2-7.0

2.0-5.8

4.0-8.0

For any particular material type, the room temperature mechanical strength and fracture toughness are dependent on, firstly, the aspect ratio of the (3 silicon nitride grains and, secondly, the overall grain size. Figure 3-18 shows schematically how fracture strength and fracture toughness change during the sintering process for silicon nitride. As the ot-form transforms to |3-phase? the aspect ratio changes from equiaxed crystals to fine elongated crystals giving improved strength and toughness but, once the a-»(3 transformation is complete, grain growth results in an increase in grain diameter with a consequent decrease in these properties. The reason for the improvement with higher aspect ratios is that the interlocking, elongated (3 grains have better resistance to crack propagations because of crack branching and deviation as well as grain pull-out, resulting in higher energy requirements for crack growth. The high strength values now achieved for sintered silicon nitrides are a result of process optimisation including modifications to the type and composition of the grain boundary phase by varying the amount and type of sintering additive. The use of mixed oxide additives (e.g., Y 2 O 3 + A12O3, MgO + Nd 2 O 3 , etc.) allows control

144

3 Nitride Ceramics ASPECT RATIO: varies with powder properties, volume, viscosity of liquid phase, processi ng parameters (t,T)

800

100 .

600

90 CL

80

fc 400-^ I

§ 200

L

70 60

Figure 3-18. Schematic plot showing changes in aspect ratio and grain diameter (thickness) of Si 3 N 4 as a function of sintering (soaking) time and resulting strength and fracture toughness (KIc). 2 3 4 Soaking time (h)

of the properties of the sintering liquid such as volume and viscosity which determine the growth of the J3 grains along the preferred c-axis direction and also the grain diameter. The variation of strength with temperature for the different types of silicon nitride based ceramics is shown in Fig. 3-19. Because of the presence of porosity, RBSN has the lowest flexural strength (150350 MPa) at ambient temperature but since there is no glass phase the strength is retained up to very high temperatures (>1400°C). With SSN, much higher strengths are achieved (600-1200 MPa) at ambient temperature but, at temperatures exceeding 1000 °C, this may decrease rapidly due to the softening of the intergranular glass.

Strength is retained to much higher temperatures when the secondary phase is crystalline (Katz and Gazza, 1977; Lewis et al, 1987; Ziegler et al, 1987). HPSN and HIPSN, with zero porosity and much lower levels of additives and hence less glass, generally have higher strengths than SSN at higher temperatures. 3.3.8 Oxidation of Silicon Nitride Ceramics

Oxidation of silicon nitride in air begins as low as 800 °C and a thin protective layer of amorphous SiO2 is formed on the surface of the silicon nitride according to Si 3 N 4

3O 2 ^ 3 S i O 2 + 2N 2

(3-20)

This simple equation describes the situation for reaction-bonded silicon nitride

145

3.3 Silicon Nitride

FLEXURAL STRENGTH (MPa)

Figure 3-19. The ranges of flexural strength values for silicon nitride ceramics and the effect of temperature. 200

400

600

800

1000

1200

1400

1600

TEMPERATURE (°C)

with no additives and for hot-pressed silicon nitride at lower temperatures. However, Tripp and Graham (1976) found that oxidation of commercial silicon nitrides hot-pressed with magnesia was much more complex because the reaction products at 1400 °C include, as well as SiO 2 , magnesium silicate (enstatite). Some of the silica was crystalline and present as oc-cristobalite but conferred a protective layer on the nitride which remained coherent for several hundred hours. These workers and others report that the weight-gain versus time curves at all temperatures follow classical parabolic kinetics. Figure 3-20 shows parabolic plots of oxidation at 1400°C of silicon nitrides densified with different additives. The rate of oxidation varies according to the amount and type of additive used. The parabolic kinetics suggest that the rate of oxidation is a diffusion-controlled process, limited by inward diffusion of oxygen and outward diffusion of nitrogen as shown schematically in Fig. 3-21. Parabolic oxidation behaviour was observed by Cubicciotti et al. (1977), but they demonstrated that the rate of oxidation is

unaffected by removal of the oxide layer suggesting that diffusion through the layer is not rate-controlling. They concluded that the rate of oxidation was limited by outward diffusion of metallic impurity ions from the grain boundary glass phase within the material into the SiO2 scale. Clarke + 5MgO + 10Sc2O3 + 5Y0O3-5AI2Of10CeO ? 20CeCL


1000 °C, healing of flaw-tips occurs (assisted by oxidation) as a result of softening of the vitreous phase enabling stress relaxation and crack-blunting. However, the Napatite phase is unstable and decomposes to an amorphous phase. This degradation, together with softening of residual glassy films containing large concentrations of impurity cations that remained at the grain boundaries following crystallisation, is responsible for the marked decrease in strength at high temperature. 3.5.4 O'-Sialon Ceramics

Trigg and Jack (1984) showed that approximately 0.8 mol% alumina could be incorporated into the structure of silicon oxynitride to form an O'-sialon solid solution. Its range of composition is shown in Fig. 3-23. A suitable additive such as Y 2 O 3 is used as a sintering aid to mixtures of silicon nitride/silica/alumina which react at 16001800°C to form a much larger volume of

157

liquid than in the case of pure silicon oxynitride. Thus, pressureless sintering of O sialon to near theoretical density can be achieved and the constituents of the liquid phase are subsequently incorporated into the O' solid solution, leaving only a small volume of intergranular glass phase. This can be devitrified by suitable post-preparative heat-treatment to give Y 2 Si 2 O 7 . These ceramics have flexural strengths of over 400 MPa, low coefficients of thermal expansion (a = 2.9 x 10~6 K" 1 ) and good thermal shock resistance. 3.5.5 O'-P'-Sialons

Figure 3-23 shows that there exists a two-phase O'-p' region in the S i - A l - O - N system extending up to a p'-sialon of z = 0.8. Sun et al. (1986) prepared these two-phase composites by sintering in the range 16001800°C using Y 2 O 3 as the densification aid. Reaction proceeds rapidly above 1600°C to form O' in a Y - S i - A l - O - N liquid matrix with undissolved a silicon nitride. As the temperature is raised, a dissolves and P'-sialon is precipitated from a liquid with a constantly changing composition. At lower temperatures the liquid is more oxygen-rich, precipitating the moreoxygen rich product (O'), whilst at the higher temperature the liquid becomes more nitrogen-rich, precipitating the more nitrogen-rich product (p'). The selective precipitation of the two phases allows the possibility of tailoring the microstructure by carrying out heat treatments at intermediate temperatures. Devitrification of the intergranular glass gives Y 2 Si 2 O 7 and YAG. The production of high aspect ratio crystals of O' in a P' matrix should lead to a material with good mechanical properties, but the potential of these newer sialon ceramics is still being assessed.

158

3 Nitride Ceramics

3.6 Oxynitride Glasses and Glass Ceramics

produce a more rigid glass network as follows: - S i - O - S i - -> - S i - N - S i -

(3-28)

I

3.6.1 Introduction

The ease of shaping glasses, the possibility of producing glass ceramics containing refractory oxynitride crystalline phases, and the occurrence of oxynitride glasses as grain-boundary phases in silicon nitride based ceramics has provided the impetus for a number of investigations on oxynitride glass formation and properties. Originally, small concentrations of nitrogen in oxide glasses were reported to increase their softening temperature, viscosity and resistance to devitrification. Crystallization of selected glasses has been investigated principally to complement more extensive studies of phase equilibria in M - S i - A l - O - N systems and the effects of vitreous phases on high-temperature mechanical properties of silicon nitride based ceramics including sialons and silicon oxynitride. 3.6.2 Solubility of Nitrogen in Glasses

Mulfinger (1966) was one of the first investigators to study the solubility of nitrogen in glasses and found, by bubbling nitrogen gas through the glass melt, that the physical solubility of nitrogen in glasses was very low. However, by bubbling ammonia gas through the glass melt for five hours at a temperature of 1400 °C, the chemical solubility of nitrogen in the melt reached a value 105 times higher. Using this method, 0.33 wt.% nitrogen was introduced into soda-lime-silica glass. Mulfinger suggested that the substitution of nitrogen for oxygen must lead to a higher than average coordination of non-metal atoms and that increased cross-linking should

-SiElmer and Nordberg (1967) observed that devitrification of certain glasses could be induced electrolytically. Incorporation of nitrogen into these glasses inhibited the electrolytically-induced devitrification and this they attributed to increased viscosity, due to the presence of (=NH) and (=N-) groups in the glass structure. This was one of the first observations of an improvement in some physical property resulting from the incorporation of nitrogen into the glass structure. In this case, ammonia was again used as the nitriding agent and nitrogen contents of the order of 3 wt.%, or ten times that reported by Mulfinger, were obtained. Davies and Meherali (1971) suggested that the solubility of nitrogen in glass melts was chemical rather than physical, and they found that severe reducing conditions had to be imposed in order to dissolve significant amounts of nitrogen in the glass melts. They discovered that the solubility of nitrogen increased with increasing basicity, indicating that bridging rather than non-bridging oxygen atoms were involved in the dissolution reaction. Dancy and Janssen (1976) investigated the solubility of nitrogen in CaO-SiO 2 A12O3 slags. They compared physical and chemical methods of dissolving nitrogen in these melts and found that under one atmosphere of nitrogen an equilibrium solubility of 0.25-2.5 wt.% nitrogen was achieved after 24 h. By contrast, when Si 3 N 4 was added to the melt, again under an atmosphere of nitrogen, nitrogen incorporation was very rapid and reached significantly higher levels (4 wt.%).

3.6 Oxynitride Glasses and Glass Ceramics

3.6.3 Sialon Glasses Jack (1976) observed the close similarity between the building units for the structure of silicate glasses (SiO4 tetrahedra) and those in silicon nitride (SiN4 tetrahedra) and also the similarity between the lengths of Si-N, Si-O and Al-O bonds, and proposed that nitrogen could be incorporated into the network of silicate and aluminosilicate glasses. Jack (1977) prepared oxynitride glasses in the following systems: Si 3 N 4 -Al 2 O 3 SiO 2 , Si 3 N 4 -MgO-SiO 2 , and A1NY 2 O 3 -SiO 2 , with nitrogen levels up to 10at%. Changes in physical properties due to incorporation of nitrogen were not reported at this point. Subsequently, considerable investigation by Drew et al. (1981, 1983, 1984) has been carried out on glass formation and glass properties in a wide range of M - S i - O - N and M-Si-AlO - N systems where M=Y, Mg, Ca, Al or Nd and the effects of increasing nitrogen content on properties of these glasses have also been reported. Both Shillito et al. (1978) and Loehman (1979,1980) were among the first to report correlations between amounts of nitrogen incorporated into oxynitride glasses and changes in their physical properties. Shillito et al. reported a linear increase in the Knoop hardness of a Y - S i - A l - O - N glass as the nitrogen content increased. Loehman produced more detailed results of changes in physical properties due to incorporation of nitrogen when he prepared glasses in the same system with up to 7 at.% nitrogen. Glass transition temperature (Tg), microhardness and relative fracture toughness all increased with increasing nitrogen content, whilst the thermal expansion coefficient decreased. IR spectroscopic analysis carried out by Loehman indicated that the incorporated nitrogen

159

became chemically bonded to silicon in the glass network, and by substitution for oxygen, produces a more tightly and highly linked structure. However, whilst these results did indicate improvements in properties of glasses related to incorporation of nitrogen, these property changes could not be attributed solely to the incorporation of nitrogen, since it is well known that viscosities of glasses may increase or decrease depending on field strength, polarisability and size and coordination requirements of the modifying cation. Thus for glasses with a constant nitrogen: oxygen ratio, changes in Al or M concentration may cause changes in viscosity, Tg and hardness and these variances remained unaccounted for. Drew et al. (1981, 1983) carried out extensive systematic studies on nitrogencontaining glasses in M - S i - O - N and M - S i - A l - O - N systems. Glasses with a fixed cation composition with varying nitrogen: oxygen ratios were prepared, to allow direct comparison between different M - S i - A l - O - N systems and determination of the effect on properties of replacing oxygen by nitrogen within each system. The Janecke prism representation was adopted by Drew et al. (1981, 1983) and Hampshire et al. (1985) to describe the limits of glass formation in different metal sialon systems. The limits of the metal alumino-silicate glass regions were plotted on the oxide face of the prism and it was possible to observe how the glass region extended into the M - S i - A l - O - N prism on replacing oxygen by nitrogen. The three dimensional representation of the complete glass forming regions in both the M g - and Y^Si-Al-O-N systems is shown in Figs. 3-29 and 3-30 respectively. Prior to this, investigation of these systems had been carried out by Jack (1977) and Loehman (1979) but adequate exploration

160

3 Nitride Ceramics Mg6N4

Mg 6 O (

3/2MgAI 2 O 4

Figure 3-29. Glass formation region in the Mg-sialon Janecke prism.

Y.O,

Figure 3-30. Glass formation region in the Y-sialon Janecke prism. Si 3 O 6

of the full extent of glass formation in these systems was not completed. From Fig. 3-29 it can be seen that the extent of the glass forming region in the M g - S i - A l - O - N system expands away from the oxide face with increasing replacement of oxygen by nitrogen. This increase continues until 10eq.% nitrogen is incorporated, after which the glass forming region contracts with a simultaneous shift towards slightly more Mg-rich compositions. This also shows that whilst MgO is a network modifier in oxide systems, in oxynitride glasses

it appears to act as a network former. In the Y - S i - A l - O - N system (Fig. 3-30) the expansion away from the oxide face is less at 10 eq.% N but the maximum nitrogen solubility is much greater. Depending on the particular system it was found that a limit of 17-25 eq.% of the oxygen could be replaced by nitrogen. Drew et al. (1981) found that, for glasses with a constant cation ratio, incorporation of nitrogen resulted in increasing viscosity, Tg, resistance to devitrification, refractive index, dielectric constant and ac conductivity, in all the

3.6 Oxynitride Glasses and Glass Ceramics

Mg-, Ca-, Y- and Nd-sialon glasses. The corresponding M - S i - O - N systems displayed a much smaller glass-forming region, thus showing the ability of A12O3 to extend the range of glass formation. 3.6.4 Nitrogen Coordination in Oxynitride Glass Structures

The resulting improvements in glass properties by substitution of nitrogen for oxygen was usually attributed to the replacement of a 2-coordinated bridging oxygen atom, by a nitrogen atom coordinated by three silicon ions. Thus, it was assumed that properties were improved due to an increase in the cross-linking of the silicate network due to the 3-coordinated nitrogen. Published IR data by Loehman (1979) and Schrimp and Frischat (1983) only suggested the presence of Si-N bonds in the structure. Brow and Pantano (1984) carried out more extensive studies on the coordination of nitrogen in oxynitride glasses by analysis using Fourier Transform Infrared Spectroscopy (FTIR) and X-ray Photoelectron Spectroscopy (XPS). At this point direct evidence of the formation of Si-N bonds and of the presence of 3-coordinated (nitride-like) nitrogen groups was obtained. It was concluded that nitrogen was present in the structural network, because introduction of the nitrogen caused shifting of the position of the Si-O-Si stretching peak towards that of Si-N. If nitrogen existed as precipitated Si 3 N 4 the position of the Si-O-Si peak would not be expected to change. Rand and Roberts (1973) also observed a similar shift of the Si-O-Si stretching vibration to lower wavelengths in nitrided silicon thin films. XPS studies by Brow and Pantano also revealed that nitrogen is usually present in more than one form, and they proposed

161

that non-bridging nitrogen ions may also be present, similar to the following: -Si-N--Si=Si-N 2 ~

(3-29) (3-30)

The interpretation of the XPS analysis was based on an analogous situation involving bridging and non-bridging ions in silicate glasses. The local charge on the non-bridging nitrogen ions is balanced by the presence of interstitial metal ions in their vicinity. Thus, while it has not been proven beyond doubt that nitrogen is present in oxynitride glasses in a 3-coordinated state, all evidence indicates that this is the symmetry that it accepts. No theory to indicate that it is present in some other form has been put forward to date. 3.6.5 Nucleation and Crystallisation in Oxynitride Glasses

Reports of formation of various Msialon glasses have been described with resultant changes in physical properties due to incorporation of nitrogen. After formation of these glasses, suitable heat-treatment results in the formation of tiny nuclei, upon which crystals then grow. This process results in the formation of glass ceramics which have superior properties to the parent glass. Using suitable heat treatments, properties of glass ceramics can be tailored to particular requirements. Many glasses require the addition of a nucleating agent to promote the crystallisation process, but in general oxynitride glasses are self-nucleating. Abromovici and Ish-Shalom (1985) investigated the effect of nitrogen on nucleation and crystallisation in SiO 2 -Al 2 O 3 MgO and related glass forming systems. In the SiO 2 -Al 2 O 3 -Li 2 O system they found the presence of nitrogen to influence the phase composition of crystallised samples

162

3 Nitride Ceramics

to only a limited extent. In the SiO 2 Al 2 O 3 -MgO system they reported that in samples with TiO 2 as a nucleating agent the addition of nitrogen leads to a more advanced and finer crystallisation. They concluded from this that nitrogen promotes nucleation and in some cases advances crystallisation, but they failed to give any explanation. Nitrogen is known to be an inhibitor of crystallisation because it increases viscosity, and a more probable explanation of their observation is that nitrogen does in fact inhibit growth of large crystals, but in some cases this may be compensated for by a more extensive growth of smaller crystals, where less matter transport would be required for their propagation. The crystalline phases formed in glasses on heat-treatment and the extent of their formation will determine the properties of the particular material. The phases formed will depend on both the composition of the parent glass and the heat-treatment process. Ahn and Thomas (1982) carried out preliminary studies on crystallised Y-sialon glasses. Appreciable crystallisation was only effected after glasses were doped with up to 5 wt.% ZrO 2 which acted as a nucleating agent. The main crystalline phase was Y 2 Si 2 O 7 . Winder and Lewis (1985) carried out further work in this system and reported that low nitrogen: oxygen ratios again favour formation of yttrium disilicate (Y2Si2O7), whilst the increased glass viscosity associated with an increase in the nitrogen: oxygen ratio favoured suppression of Y 2 Si 2 O 7 crystallisation and preferential formation at higher temperatures of yttrogarnet (Y3A15O12). More extensive studies of crystallisation in Y-sialon glasses were carried out by Lewis and Leng-Ward (1985). On heattreatment at 1250 °C the oxide glasses fully

crystallised to yttrium disilicate, mullite and A12O3. Again, with increasing nitrogen content the disilicate phase was progressively replaced by yttrium aluminium garnet and nitrogen was mainly incorporated into Si 2 N 2 O. Heat-treatment of the nitrogen glasses at 1100°C produced partial crystallisation involving intermediate phases related to nitrogen wollastonite. In further investigations, Lewis et al. (1986 b) investigated crystallisation in the Mg-sialon system and found that fosterite was the main crystallising phase. They also identified secondary phases and these included a magnesium substituted p'-sialon, designated as p" which was first reported by Drew et al. (1981). At higher temperatures, this is replaced by a Mg-Si-AlO - N petalite phase. More recent work by Morrissey et al. (1990) and Lonergan et al. (1991) reports on a two-stage heat treatment process for formation of glass ceramics in the N d - S i A l - O - N and M g - N d - S i - O - N systems. Figure 3-31 shows a typical microstructure of apatite crystals crystallised from the parent glass. The area of oxynitride glasses and glass ceramics offers encouraging possibilities for developing improved materials, but more detailed property evaluation must be

Figure 3-31. Micrograph of apatite crystals crystallised from a Mg-Nd-Si O - N glass.

3.7 Aluminium Nitride

carried out before these materials can be exploited fully. Whilst several investigators have demonstrated the benefits of nitrogen inclusion in oxide glasses, few have produced any detailed property measurements on the corresponding glass ceramics. The possibility of developing quality oxynitride glass ceramics by suitable heat-treatments makes the future of this field very attractive.

3.7 Aluminium Nitride 3.7.1 Introduction

Aluminium nitride was developed as an insulating substrate and packaging material for high power, high-speed microelectronic applications where its high thermal conductivity allows good heat dissipation. In this regard, it is a cheaper, non-toxic alternative to beryllium oxide. The intrinsic thermal conductivity of aluminium nitride is 3 2 0 W m ^ K ' 1 (Slack, 1973), but until recently values for the polycrystalline ceramics were in the range 50-80 Wm" 1 • K 1 . Because of the growing interest in A1N for electronic purposes, there have been further developments of improved powders and processing, which have led to better materials and renewed consideration of the ceramic for thermo-mechanical applications. 3.7.2 Structure of Aluminium Nitride

As with other covalent nitrides with equal numbers of metal and non-metal atoms, aluminium nitride adopts the wurtzite structure (2H) with nitrogen atoms in a close-packed hexagonal arrangement (ideally) and with aluminium atoms occupying half of the tetrahedral interstitial sites in the structure. The cell dimensions are a = 3.114 A, c = 4.986 A.

163

3.7.3 Synthesis of Aluminium Nitride

Aluminium nitride was reported as early as 1907 (Fichter) by reacting molten aluminium with nitrogen. This is the simplest method of synthesis of the powder according to: 2A1 + N ,

2A1N

(3-31)

but the reaction is highly exothermic and careful control is required to avoid the formation of large molten globules of aluminium. Long nitriding times result in crystal growth, and the product requires extensive milling which introduces impurities. The powder can also be produced by carbothermal reduction of alumina in nitrogen according to: A12O3 + 3C + N 2 -> 2A1N + 3 CO (3-32) Any excess carbon is removed by a low temperature oxidation step (Kuramoto and Taniguchi, 1986). Aluminium compounds may be reacted with ammonia according to: A1CL + N H , -+ A1N + 3HC1

(3-33)

but this has only limited commercial interest because of the HC1 by-product. The purity, particle size and particle size distribution, oxygen content and specific surface area all affect the sinterability and properties of A1N ceramics. 3.7.4 Fabrication and Properties of Aluminium Nitride Ceramics

The ceramic is fabricated from aluminium nitride powder mixed with densification additives such as CaO, Y 2 O 3 or a rare earth oxide by a process of die pressing or tape casting into thin sheets followed by blanking out. The green shapes are then sintered at 1650-1900 °C in a nitrogen atmosphere. Hot pressing has been

164

3 Nitride Ceramics

employed to fabricate material for assessment of mechanical properties. Aluminium nitride powder always contains oxygen within the surface layers, and reaction occurs with the additives to form a liquid phase which allows sintering to near theoretical density (3.26gem"3). With yttrium oxide as a sintering aid, the yttrium aluminium garnet (YAG) is formed at the grain boundaries. In addition to aiding densification, the oxide additive forms a secondary phase (usually an aluminate) which removes the oxygen from the aluminium nitride grains. In order to improve the thermal conductivity, secondary phases should be localised at triple points or removed completely. Russel etal. (1991) show that the thermal conductivity increases dramatically with Y 2 O 3 content. This is because at low yttrium levels (6) (SiSi) = SiB2 89 which is attributed to an Si-Si chain and two sites in the icosahedron being partially occupied by Si (Matkovich and Economy, 1977 a; Hoard and Hughes, 1967; Magnusson and Brosset, 1962). 4.2.1.2 Structure and Polytypes of Silicon Carbide The fundamental structural units of the silicon carbide lattice are the covalently bonded coordination tetrahedra SiC4 and CSi 4 . These tetrahedra are assembled in

plane layers having common edges and one apex out of the layer plane which forms the connection to the next stack of tetrahedra. Thus four tetrahedra are linked through each corner to satisfy the four-fold coordination at any point of the resulting framework. This structure can equally be described as a close-packing of spheres with a constant radius and smaller spheres occupying a quarter of the tetrahedral positions yielding two formula units per unit cell. If the stacking sequence of the tetrahedra is ABC, a cubic zinc blende structure results, but if it is ABAB, a hexagonal wurtzite structure is the result. In contrast to these regular structures of the ZnS-type, however, the tetrahedra in SiC are not regular but possess acentric apices. In the layers of reverse stacking sequences ACAC, the A and C layers are rotated relative to each other. While both cubic and simple hexagonal stacking sequences can be found in SiC, known as /? and a structures, respectively, these sequences may alternate in a more complex, intermixed order resulting in large periods of stacking. Disordering and short-range twinning are common. The phenomenon of different one-dimensional ordering of structures is called polytypism, and the resulting structures are called polytypes. The most common hexagonal, hightemperature polytype consists of a zigzag stacking of three layers in the odirection (i.e. perpendicular to the layers) which may be derived from the cubic polytype by insertion of rotation twin boundaries every three layers (Fig. 4-3). The stacking sequence may then be described as ABCB'A'C'-with A', B', C indicating a plane rotation of that particular layer. According to the notation of Ramsdell (1947), this polytype is named 6/7, indicating that after six stacking sequences the initial layer position is obtained again.

4.2 Chemical Bonding and Crystal Chemistry

3C (cubic)

SH (hexagonal)

2H (hexagonal)

&H (hexagonal)

181

UH (hexagonal)

15/? (rhombohedral)

Figure 4-3. Atomic arrangement in the most common SiC polytypes (Ryan et al, 1968).

In that nomenclature the capital is related to the Bravais lattice type, i.e. C means cubic, H hexagonal, and R rhombohedral. In Fig. 4-3 the most common polytypes are visualised (Ryan et al., 1968). Long-range ordering with sequences of 90 layers have been observed. Although the various polytypes can be readily distinguished by structural analysis their differences in physical properties can

almost be neglected. Since all structures are close-packed and the density is constant at 3.17 g/cm3 because of the same next-neighbor relation, all polytypes have nearly the same energy of formation. Calculations of stability between room temperature and 2300 °C, taking wide-range neighborhoods into account, show only slight differences between 3C and 6H polytypes (Bind, 1979). This means that

182

4 Boride and Carbide Ceramics

neither pressure nor temperature can satisfactorily explain the preferential formation and relative stability of certain poly types. Attempts to do so therefore involve the influence of impurities or different dislocation energies (e.g., Verma and Krishna, 1966). Heine et al. (1991) showed by ab initio quantum calculations of the relative polytypes in bulk that the cubic /? phase should not be stable at any temperature. Taking impurities acting as electron donors into account and allowing for the formation of differently oriented double layers, Heine et al. (1991) demonstrated that jS-SiC is the favored structure. Nevertheless, more or less exact conditions for polytype transitions during sintering or heat-treatment of ceramics have been established empirically (see Sees. 4.4.1.4 and 4.5.2.4). 4.2.1.3 Structure of Transition Metal Carbides

The structure of metallic carbides is generally governed by the ratio of the atomic radii of the metal and the carbon atom (Hagg's rule). Starting with the closepacked lattice of the metallic elements, the successive incorporation of the smaller C atoms into the octahedral sites results in the development of structures with various sequences of occupied carbon layers. A simple, systematic model for the formula type of transition metal carbides can be derived from geometrical considerations of the degree of interstitial site occupation. Complete occupation of the octahedral sites in a space-centered cubic host-lattice yields the face-centered cubic sodium chloride structure of the IVa and Va group monocarbides. The characteristic structural element is thus the M 6 C octahedron (where M stands for metal) with the possibility of defect structures resulting in a

huge homogeneity range. In the primitive hexagonal lattices of the monocarbides MC, half of the six-fold coordinated carbon positions are unoccupied. The structural unit of the hexagonal phases is thus the M 6 C triangular prism with carbon in the center, or the C 6 M with a six-fold coordinated metal atom. Hence this so-called WC structure type shows similarities to the nickel arsenide structure in which the metal atom is located in an octahedral coordination sphere (Fig. 4-4). In the hemicarbides M 2 C of the IVa, Va and Via group elements, the hexagonal Cdl 2 structure (P3 m 1) and the Z/3 structure (P63/mmc) are predominant, which can be derived from half occupied, octahedral sites of a close-packed hexagonal host-lattice. Due to the presence of such a high amount of vacancies, ordering can occur in the metalloid sublattice, which has a comparatively narrow homogeneity range M 2 C 1 _ ;c . Problems of carbon sublattice ordering have been intensively discussed by Epicier (1990 a, b). In carbides with a carbon-to-metal ratio exceeding unity, the carbon atoms form couples resulting in tetragonally distorted NaCl lattices (CaC2-type). The dicarbides of the lanthanide and actinide elements crystallize in this structure and have a less metallic character. The C2-coordination is

Figure 4-4. Crystal structure of hexagonal tungsten monocarbide; black: carbon, white: tungsten.

4.2 Chemical Bonding and Crystal Chemistry

183

Crystal lattice

^ - Bonding

t 2g Orbitals T

- Bonding

ddCT- Bonding

also present in space-centered cubic M 2 C 3 carbides of the actinides. As the ratio of carbon and metal radii for carbon accommodation in closepacked host-lattices approaches the critical value of 0.59 (optimum packing at rc/rM = 0.414) elements of the iron and chromium group react with small atom fractions of carbon to form interstitial structures of the M 23 C 6 -type. With both an increasing ratio of the radii and an increasing content, complex structures of low symmetry become stable (e.g. hexagonal M 7 C 3 , orthorhombic M 3 C 2 and M 3 C) and can also be found in carbides of iron and chromium group elements. In the following sections, the carbides used in ceramic composites as reinforcing particulates are treated in more detail since their metallic behavior brings about interesting prospects for the mechanical behavior and transport properties of these usual-

Figure 4-5. Crystal structure of TiC with orbital overlapping; black circles titanium, white circles: carbon (Neckel, 1990).

ly more ionically or covalently bonded matrix materials. Cubic Monocarbides The technically important monocarbides of the six group IV and V transition metals TiC, ZrC, HfC, VC, NbC, and TaC are isotypic and crystallize in the face-centered cubic NaCl structure (space group Fm3m). Every metal and carbon atom is surrounded by eight next-neighbors of the respective other species in an octahedral configuration (Fig. 4-5). Hence the unit cell consists ideally of two atoms of each species, i.e. of two formula units. The real composition of the transition metal carbides exhibits, however, a huge non-stoichiometry represented by the formula MCX where x is the carbon-to-metal ratio. Within the range of x = 0.5-0.97 the crystal structure does not change. The carbon

184

4 Boride and Carbide Ceramics

deficiency is accounted for by carbon atom vacancies in the carbon sublattice. This high vacancy concentration of at least 2 - 3 % exceeds that obtained in metals or semiconductors by mechanical or radiation damage. Ordering is observed in VC and NbC at certain carbon-to-metal ratios (e.g., at x - 0 . 8 3 3 - 5 / 6 or at x = 0.875 = 7/8). Since a decreasing stoichiometry is related to the reduction of C-M bonds relative to x=l, the concentration of vacancies influences systematically the bonding strength-related properties such as the cohesive energy, the melting point, elastic constants, the hardness, and the plastic deformation behavior at high temperatures, as well as defect-related transport properties such as heat, electrical conductivity and diffusion behavior (Williams, 1988). Analysis of the binding character in this NaCl-type structure by self-consistent Augment Plane Wave calculations reveals that there are contributions from all three main types of chemical bonding (Neckel, 1990). The metallic fraction is due to nonvanishing densities of states at the Fermi energy and a relatively high electron density in the region between the atomic spheres. Ionic bonding is caused by charge

transfer from the metal atom to the carbon yielding electrostatic forces. According to calculations for TiC, approximately 0.36 electrons are transferred from a titanium atomic sphere relative to the charge of a hypothetical crystal of non-interacting neutral atoms. The covalent bonding fraction was calculated for TiC by linear combination of molecular orbitals (Neckel, 1990), taking degeneration of energy levels by octahedral ligand field of the carbon atoms into account. The five 3 d orbitals of a Ti atom are thus split into three orbitals of t2g symmetry and two of eg symmetry. The lobes of the Ti eg orbital thus extend towards the neighboring carbon 2p x orbitals and form pd a bonds (Fig. 4-6), whereas the Ti t2g orbitals overlap forming pd n bonds with the adjacent C 2p y orbitals as well as forming dd a bonds with the corresponding t2g orbitals of the neighboring Ti atom. It is established that the latter intermetallic bonds are strengthened by an increased substoichiometry. More detailed studies on the nature of chemical bonding in transition metal carbides and their nonstoichiometry have been published by, e.g., Neckel (1983), Schwarz and Blaha (1983), De Novion and Landesmann (1985), and Redinger et al. (1985, 1986).

Figure 4-6. Electron density in the (100) plane of three occupied band states of TiC for wave vector k = n/a (1, 0, 0) (Schwarz and Blaha, 1983). Ay U22mRyd

A2. 62QmRyd

As 636mRyd

4.2 Chemical Bonding and Crystal Chemistry

Hexagonal Monocarbides Tungsten monocarbide, WC, crystallizes in a primitive hexagonal structure (space group P6m2, resembling the NiAs structure type) consisting of alternating W and C layers with ordered C vacancies (Fig. 4-4), where the W atoms occupy the 0, 0, 0 positions (i.e. the simple hexagonal hostlattice) and the C atoms are in the Va, 2/a, Vi positions and thus occupy only half of the triangular prismatically coordinated holes. The c/a-ratio of the unit cell is 0.98. The cell thus contains a single formula unit (Ishizawa and Tanaka, 1986). Due to the close structural relationship to the closepacked cubic transition metal monocarbides, solid solutions of WC in other IVa and Va group metal carbides exhibit an NaCl structure with huge homogeneity ranges and probable complete mutual solubility at very high temperatures (see Sec. 4.3). Examples are (M, W)x _x with M = Ti, Zr, Hf, Nb, V, Ta. Because of the various MoC x _x structures, (MOi .yWyC^ -x solid solutions of the hexagonal P6m2 and P63/mmc, as well as the cubic Fm3m, space group exist (Rudy et al., 1978). 4.2.2 Chemical Bonding of Borides

The nature of the chemical bonding in boron compounds is governed by the wellknown two-electron-three-center bond, i.e., three boron atoms share two common electrons. These electrons are thus more or less delocalized. The resulting sp2 hybridization leads to the plane B 3 X 3 hexagon as the main structural element in BN, B 2 O 3 , H 3 BO 3 and related compounds, and to the B 3 triangle as a fraction of the typical five-fold symmetric icosahedron of elemental boron, the group of boranes and their derivatives. Depending on the saturation of the electron deficiency, soft and non-conducting, salt-like com-

185

pounds or semimetallic to metallic materials of exceptionally high melting point and hardness and excellent electrical conductivity can exist. As pointed out in the following section, the latter boron compounds, like the corresponding carbides, may contain ionic, metallic and covalent fractions of bonding forming very stable compounds due to the well-balanced electron transfer between metal and boron sublattice. 4.2.2.1 The Crystal Structure of Borides

Similar to silicates, the crystal structures of borides can easily be classified according to the arrangement of the boron atoms. Boron may occur as an isolated atom or form B-B bonds with an increasing degree of interconnection in the chains, double chains, layers and frameworks and combinations thereof (Fig. 4-7). Due to the strong covalent bonding between the boron atoms and the electron deficiency of the three-center bond a number of complex and unique structures result which have been the subjects of investigation for many years (Kiessling, 1950; Lundstrom, 1969 a). In general, compounds with a boron-to-metal ratio of less than 1.0 are built up of isolated boron atoms or pairs with a low B-B interaction (e.g., Ni 3 B, Ru 7 B 3 , Fe 2 B, Cr 5 B 3 ), in zigzag chains with additional, isolated B (e.g., #-Ni4B3). At a ratio of 1.0 to 1.3, infinite chains are formed which may be parallel to one or even two crystallographic axes (e.g., mNi 4 B 3 , FeB, CrB, MoB), whereas in M 3 B 4 borides double chains are predominant (e.g., Cr 3 B 4 ). With increasing boron content, two-dimensional nets are stable, yielding preferential stoichiometries between M 2 B 3 and MB 4 . The most important structure type group thereof is the A1B2 type, which is covered in more detail

186

4 Boride and Carbide Ceramics

[No [connections

[Chainsl

Partial

Single

Multiple

O

o o

o-o

o

I

o

o-o

| 2-D netsj

|Units helping to form 3-D frameworks]

B12-Type

sp 2 -Type

later on. Three-dimensional frameworks exist in so-called higher borides with typical stoichiometries of MB 4 , MB 6 , MB 1 2 , and MB 6 6 . Channels with rectangular cross-sections were found in e.g. CrB 4 and MnB 4 which is unique for the three-center bond of boron (Andersson and Lundstrom, 1968). A rigid boron skeleton consisting of B 6 octahedra is a characteristic of the CaB 6 structure group (important member: LaB6), whereas the UB 1 2 structure contains B 1 2 cubo-octahedra. Other borides of MB 6 and MB 1 2 stoichiometry or a higher boron-to-metal ratio, especially the main group element borides, can be derived from the trigonal rhombohedral a-boron or /?-boron structure with the B 1 2 icosahedron as the most important structural unit. Some general systematics on chemical bonding and crystal chemistry have been published by Matkovich and Economy (1977 a), and Aronsson et al. (1965, 1968), who also refer to the struc-

B 6 -Type

Figure 4-7. Structural classification units of the borides (Spear, 1977).

tural similarities in silicides and phosphides. 4.2.2.2 A1B2-Type Structures

The transition metal borides of the A1B2 structure type group are of great technical interest for ceramics, as are the ternary co, cp and x type borides as compounds for cermets and coatings. The A1B2 structure is conveniently described as a sequence of alternating metal and boron layers of hexagonal symmetry. The metal layers are close-packed and stacked in an A-A-A sequence, resulting in a basal-centered unit cell. The boron atoms are six-fold coordinated and situated in the center of trigonal prisms of metal atoms (//position). Hence they generate a planar primitive hexagonal, two-dimensional, graphite-like network (Fig. 4-8). The total stacking sequence is then AHAHAH. . . and belongs to the space group

4.2 Chemical Bonding and Crystal Chemistry

o

Metal

187

Boron

Figure 4-8. The A1B2 structure type (redrawn after Spear, 1976 a; Higashi and Takahashi, 1986). a2

P6/mmm. The unit cell contains one formula unit MB 2 . Since this structure is very versatile at accommodating metal atoms of various sizes and electron configurations, M could be Mg, Al, group IVa, Va, Via, actinide or lanthanide elements. Additionally, other transition metal borides of various stoichiometries can be derived from the A1B2 structure type by introducing the metal layer positions B and C in analogy to close-packings and the boron layer types A^and K', which may be slightly puckered. By allowing stacking sequences

such

as

AHAK-BHBK-CHCK. . .

(MoB 2 . 3 = "Mo 2 B 5 "), AHAK'-BHBK. . . (WB2.o-2.7 = "W 2 B 5 "), or AH'AK'BH'BK'. . . (Ru 2 B 3 ) and AK'BK'. . . (ReB2), and vacancies in the boron K layers, other structures and symmetries can be generated (Fig. 4-9) (Lundstrom, 1969 b; Aronsson et al., 1968). Calculation of the band structures of AlB2-type compounds shows that no band gaps are present, and all the compounds are predicted to be conductors, which is in agreement with experimental results. For the main-group element diborides the boron 2 p a and 2p7i orbitals are the main

constituents of the states at the Fermi edge, while for the transition metal diborides it is the localized metal 3 d orbitals which are the predominant component of the valence and conduction bands. All diborides exhibit a strong electron transfer from the metal atom to the boron which gives rise to a strong ionic contribution to the bonding. In the transition metal diborides, the charge transfer decreases from 2.28 electrons in ScB2 to 1.09 electrons in MnB 2 (Armstrong, 1987); lower values have been presented by Samsonov and Kovenskaya (1977 a, b). The additional electrons occupy the 2p7i orbitals of the boron where the electrons are involved in both the B-B bonding as well as the metal-boron interactions. Cluster calculations of main group element diborides show that the metal-metal bonds are weak, the metal-boron interaction is significant and the boron-boron interactions are very strong. In the transition metal diborides the metal-metal bonds within the layers are considerably stronger than in main-group diborides and reaches a maximum for VB 2 . This internal bonding within the layers is clearly of a metallic type and is thus re-

188

3 ^

4 Boride and Carbide Ceramics

2.983 A

A.B: metal H,K': boron

Figure 4-9. The Mo 2 B 5 structure type (Higashi and Takahashi, 1986).

sponsible for the metallic transport properties. The metal-metal interlayer bonding, as well as the metal-boron interactions, also increase from ScB2 to MnB 2 , whereas the contribution of the boron-boron bonding decreases in this order. Due to the existence of vacancies in the boron layer and the possible occupation of interstitial sites by additional boron atoms, the boron sheets may also exhibit metallic or semimetallic conductivity. The considered metallic fraction does not, however, account very much for the transport properties. In contrast, the interaction between metal and boron layers contains a more efficient metallic portion which explains the electric conductivity along the oaxis (Aravamudhan, 1967). In ideal boron layers, the donor capability of the metal governs the extent of electron localization in the sp states of the boron atoms. Thus the covalent character of the B-B bonds decreases from group IV to group VI metal diborides (Samsonov et al., 1972). As it has been established that the boron network is rather rigid and governs the lattice expansion in the a direction whereas

the lattice dilatation perpendicular to the metallic layers strongly depends on the metal species, it seems likely that the metal atoms are distorted in some cases (Hoard and Hughes, 1967; Spear, 1976 a). The c/a ratio is thus a function of the rmetal/rboron ratio and depends furthermore on the valency electron concentration (Aravamudhan, 1967).

4.3 Phase Systems Knowledge of the phase diagrams for compounds of technical interest and of the environmental phases in contact with these compounds is the key for materials development and for the understanding of materials behavior in application. Not only can the thermal stability of particular phases be calculated by means of thermodynamic data, but suitable sintering procedures can also easily be considered and decomposition in aggressive media can be predicted. Generally recommended data books on binary and ternary systems are, e.g., Hansen (1958), Elliott (1965), Shunk

4.3 Phase Systems

(1969), Mofatt (1976, 1979), Massalski (1990), and Petzow and Effenberg (1988ff.). Phase diagrams of the most important carbide and boride phases will be presented and discussed, starting with the binary systems, then selected ternary systems that are of technical interest. In the subsequent sections particular phase systems will be treated in respect to sintering of B4C, SiC, and TiB2 (Sec. 4.5) or in the context of microstructural design and mechanical strengthening (Sec. 4.6). 4.3.1 Binary Phase Diagrams Containing Carbides

Problems in the presentation of binary systems containing carbon usually arise from uncertainties in the stoichiometry range of the particular carbides due to the formation of vacancies or from uncertainties concerning the very high melting or decomposition points which are not readily accessible by experiments. Generally, this work concentrates on data accepted by the Office of Standard Reference Data of the U.S. National Institute of Standard and Technology, as published by e.g., Massalski (1990). A special review treatise on binary and ternary transition metal carbide phase diagrams is published by Holleck (1984). Most of these data are based upon the important experimental work by Rudy et al. (1965) and Rudy (1973) or thermodynamic calculations. 4.3.1.1 The B-C System In contrast to early publications by Samsonov and Schuravlev (1956) and Schuravlev and Makarenko (1961) considering several boron carbide phases it is generally accepted today that only one binary phase B 13 C 2±JC exists with a wide homogeneity range of 8.8 to 20.0 at.% C.

189

This phase melts congruently at 2450 °C (Elliott, 1965) at the composition B 13 C 2 (18.5 at.% C, 20.2 wt.% C). For the B-rich corner of the phase diagram, Bouchacourt and Thevenot (1979) proposed a degenerated peritectic with elemental boron at 2075 °C, according to measured element distribution coefficients. In this diagram the melting point of boron is placed at 2020 °C. Since the melting point of B accepted today is 2092 °C the resulting reaction with boron carbide should be a eutectic one, assuming that the nonvariant equilibrium at 2075 °C is correct. The maximum carbon content is usually given as 20.0 at.% corresponding to the stoichiometry of B4C. Beauvy (1984) suggested a carbon content steadily increasing with temperature from 21A at.% (20°C) to 23.1 at.% (2375°C). Recent microprobe analyses by Schwetz and Karduck (1991) indicated, however, that the maximum carbon content of fused boron carbide being in equilibrium with graphite, is only 19.2 at.%, corresponding to the formula B 4 3 C. The eutectic with carbon is given at 2375± 5°C and 29 at.% C, which is in agreement with thermodynamic calculations (Lukas, 1990) stating 2357 °C as the eutectic temperature. The phase diagram is presented in Fig. 4-10. 4.3.1.2 The Si-C System Silicon carbide (SiC) is the only intermediate solid compound in the Si-C system that crystallizes either in the cubic /?-form or in the hexagonal a-form with many poly types (stacking variations). SiC has no nominal solid solubility for C or Si, but non-stoichiometries due to carbon vacancies have been reported leading to 2 at.% Si in excess (Prochazka, 1989). The £-to-a transition is discussed extensively in Sees. 4.2.1.2, 4.4.1.4, and 4.5.2.4 in respect to

190

4 Boride and Carbide Ceramics

2600

(Kleykamp, 1992) report the peritectic reaction at 2830 °C, yielding Si liquid of 13 at.% C which is actually partially vaporized at normal pressure. SiC and Si react eutectically at 1404 + 5 °C and 0.75 + 0.5 at.% (Dolloff, 1960), whereas Kleykamp (1992) gives 1412 °C and 0.02 at.% C as the correct eutectic point. A comprehensive summary of the conflicting data up to 1984 is given by Olesinski and Abbaschian (1984 a). 1

1"

10

20 C (atom-%)

M

1 30

4.3.1.3 The Ti-C System

Figure 4-10. The B-C phase diagram; uncertainties arise from the localization of carbon in the crystal structure indicating that the C-rich limit may be B 4 3C rather than B4C. The degenerated reaction at the B-rich corner is most probably a eutectic.

crystal structure, materials preparation and sintering. SiC decomposes peritectically forming liquid silicon and solid carbon. The assessed phase diagram (Fig. 411) presents this reaction at 2545 +40 °C involving Si liquid with 27 at.% (13.7 mass %) C (Dolloff, 1960). Uncertainties arise from the high vapor pressure of Si at this temperature. More recent investigations

10

£500

20

Transition metal-carbon systems contain a monocarbide phase with an extraordinarily wide homogeneity range due to more than 2-3 % of vacancies in the f.c.c. carbon sublattice of NaCl type structures. In the case of T i C ^ ^ , the maximum homogeneity range is 32 to 48.8 at.% at 1870°C, while the phase melts congruently at 3067°C with a composition of 44 at.% C (Fig. 4-12; Rudy et al., 1965). Other melting points reported range between 1940 and 3250 °C. At approximately 1900°C, another carbide Ti 2 C (33 at.% C) apparently forms congruently having ordered vacancies. This ordered phase is in

wt.% C 30 £0 50 60 7080 100 3000 G a s

4000^ 3500- 3200 ° C

0 Si

10

20 30

G+C

G+L

"y""-""-"-"-•

£0

50 60

at.% C

70

80

90 100 C

Figure 4-11. The Si-C phase diagram (Massalski, 1990); the decomposition of SiC results in an Si vapor phase.

0 Ti

10

20

30 £0 at.% C

50

60

70 C

Figure 4-12. The Ti-C phase diagram (Rudy et al., 1965).

4.3 Phase Systems

eutectic equilibrium with jS-Ti solid solution at 1648 °C and 1.8 at.% C. The phase relations at lower temperatures are unknown, but TiC 1 _ x undergoes a peritectoidal reaction with /?-Ti to form a-Ti solid solution. There is probably another ordered phase of Ti 8 C 5 stoichiometry present at low temperatures, Towards the carbon-rich corner, TiC 0 97 forms a eutectic with C at 2776 °C and approximately 63 at.% C (Rudy et al, 1965). A summary of the data available on the Ti-C system up until 1987 is presented by Murray (1990). 4.3.1.4 The W-C System Figure 4-13 shows the tungsten-rich part of the binary W - C equilibrium diagram basically taken from Sara (1965), and Rudy and Hoffman (1967), as assessed by Massalski (1990). Three stoichiometries of condensed phases have been proven, hexagonal W 2 C crystallizing in three modifications, the PbO 2 , Fe 2 N, and Cdl 2 types, denoted /?, /?', and /?", respectively, the cubic subcarbide W C ^ , crystallizing in the NaCl type structure denoted y, and the hexagonal WC denoted 3. W 2 C exhibits a mass-% C 2 3 U 3000

5

191

comparatively wide homogeneity range of 25.5 to 34 at.% C at 2715°C. This phase originates from a eutectoidal reaction between elemental W and <S-WC at 1250 °C and melts congruently at 2785 +10 °C. /?W 2 C reacts eutectically with the W solid solution at 2715 + 5 °C and with y - W C ^ at approximately 2758 °C. Phases of W 2 C stoichiometry are obtained as intermediate products during WC production. The yphase results from a eutectoidal reaction between /? and 5 at 2535 °C and melts at approximately 2785 °C. It can be obtained at room temperature by extremely rapid cooling, e.g., in plasma sprayed layers. The technically important liquid), 2016°C (TiB2 + B 4 C ss + B^liquid), and 1510°C (TiB + TiC! _ x + Ti -> liquid), and one peritectic at 2160 °C (TiB2 + TiC1_JC -•TiB + liquid). Figures 4-17 and 4-18 show isothermal sections of the T i - B - C system at 1700 °C and 2300 °C, respectively (Rudy et al., 1965). The corresponding sec-

3225±20

_) 0) 3J

o CD Q_ CD f—

Liquid

\ 3000 A I

\ TiB 2+ L

28002600-

X,

^

\ 2620 + 15

20

30 TiC,., 50 60 at.% C

70

80

90

C

10 20

10

20

A

A

A

A~

30 TiC^ 50 60 at.% C

70

80

90

C

Figure 4-18. Isothermal section of the ternary T i - B C system at 2300°C in at.% (Rudy et al., 1965). Three liquid phases appear but TiB 2 , TiC 1 _ x and C form solid phase equilibria.

57±2

SiC + 4HC1 (+ C)

(4-13)

4.4.1.3 Organometallic Precursors Laboratory-scale procedures can be used to produce extremely well-defined materials comprising monomeric, organometallic compounds which are pyrolyzed at relatively low temperatures in a vacuum, hydrogen or an inert gas atmosphere. For the synthesis of SiC without a free carbon residue it is important to start with precursors which exhibit an Si/C ratio close to unity. Suitable processes are: (a) Pyrolysis of dichloromethylsilane or trichloromethylsilane

4.4.1.2 High-Purity Material

CH 3 SiHCl 2 iooo-i5oo°c)

High-purity SiC single crystals, whiskers or powders are synthesized from the elements, silicon melts, and by vapor phase

CH 3 SiCl 3 >noo-i9oo°c )

S i C + 2 HCl

+ H2

S i C + 3 HCl

+ H2

(4-14) (4-15)

204

4 Boride and Carbide Ceramics

Below 1400 °C, polycrystalline material and coatings are obtained whereas above this temperature stoichiometric single crystals and whiskers can be grown (Brenner, 1960; Bonnke and Fitzer, 1966). Various techniques for the fabrication of fibres and laminates including kinetic data have been extensively described by Fitzer et al. (1987). (b) Pyrolysis of methylsilane, CH 3 SiH 3 , tetramethylsilane (CH3)4Si or other organopolysilanes, (c) 1,1,1,2,3,3,3-heptamethyl-2-vinyltrisilane II

I

H 3 C-Si—Si—Si-CH 3 I I I CH3CH CH3 CH2 (d) Tetraphenylsilane Ph4Si (Ph = phenyl)

SiC+C+CH 4 (4-16) (6-50% yield)

(e) Diphenyldipropenylsilane PhSi(CH2CH = CH 2 ) 2 (3-15% yield) (f) Triphenylvinylsilane Ph 3 Si-CH = CH 2

CH3

-hSi-CH2-h H

(2-69% yield)

(g) Phenyltrimethylsilane Ph-Si(CH 3 ) 3 (1-27% yield) (h) Triphenylsilane Ph3SiH

purity if a carbon residue can be avoided, the process can be carried out at relatively low temperatures and yields near-netshape parts of high surface quality. Furthermore, the resulting material is usually amorphous and may be crystallized at temperatures above 1800°C. Thus a tailored microstructure of desired grain size can be grown by annealing treatments. Disadvantageous effects are the relatively small yield and the vaporization of pyrolysis byproducts such as methane, hydrogen, hydrochloric acid, ammonia and others which create high porosity or rupture of the ceramic body. Another difficulty is the control of the resulting stoichiometry of Si and C which can easily lead to a strong excess of free carbon. The starting materials for the SiC synthesis are polycarbosilanes, polysilanes and polycarbosiloxanes (e.g., Yajima et al., 1981; Schilling et al., 1983),

(1-15% yield)

Since approximately 1974, the molding and pyrolysis of polymerized organometallic compounds have been investigated in detail and a promising method was developed for the preparation of continuous fibres, coatings, and monolithic or composite SiC material by a "non-ceramic process" in which the powder route is avoided. In the case of coatings and bulk material, the advantages of using pyrolysis are that the material obtained is of high

Polycarbosilane

Ph CH3 I I -Si—Si— I I CH 3 CH 3

R I -r-Si-O-f I R

Polysilane

Polycarbosiloxane (4-17) SiC —Si3N4 composite materials have been synthesized from (a) Polysilazanes (Verbeek, 1974) R R I I 4-Si-N-f I R (b) Alkalenetrisilazane

(10-20% yield)

-CH2 I —N-Si-N-Si-N-Si-N(CH3)2 (CH3)2_ 3) H2C-

4.4 Material Preparation

(c) 7V,Af-Diphenyltetraphenylcyclodisilazane (5-15% yield) ph I N / \ Ph2Si SiPh2 \ / N I Ph (d) iV-6,9-Bis (trimethylsilyl) adenine (1-33% yield) [-Si(CH 3 ) 2 ] n I C N I

CN II

c c c N

N Si(CH3)3

(e) Bis (diethylamino) dimethylsilane

The preparation of crack-free ceramic bodies derived from polycarbosilane was achieved by the conversion of dichlorodimethylsilane and dichloromethylvinylsilane in an N a - K alloy at 68 °C with 94% yield. The product consists of an insoluble and infusible polycarbosilane with reacted vinyl groups that can be processed as premolds and subsequently pyrolyzed at 1100°C. The final products are monolithic amorphous SiC parts with a hardness of HV 18.5 GPa (Riedel et al., 1990). The considerably lower value compared to crystalline SiC is attributed to the presence of residual carbon. In a similar process (Riedel et al., 1992), infusible black polysilazane was synthesized by heat-treating commercial polysilazane at 350 °C for 3 h. Formation of the infusible black polysilazane was attributed to a cross-linking reaction (4-18)

(CH 3 ) 2 Si[N(CH 2 CH 3 ) 2 ] 2 (f)

205

1,1,33-Tetramethyldisilizane

(CH3)2Si-N-Si(CH3)2 I I H H Precursors for SiC — B4C composites are (a) Carboran-siloxane

(60-65% yield)

CH 3 -Si-CH 3 (BB8C2B)

C6H5

H3C-Si-O-Si-OI

I

CH3

C6H5

(b) Poly(borodiphenyl)siloxane (43% yield)

(CH 3 ) 3 -Si-f-O—Si—O-j-Si-(CH 3 ) 3 phBH2

Subsequently, the product was milled to powder and molded by cold isostatic pressing. Pyrolysis of that organometallic green body yields an amorphous silicon carbonitride material of the composition Sii.5N1#35C1>0, if carried out in an argon atmosphere at 1000 °C. In an ammonia atmosphere, a pure, colorless Si 3 N 4 is obtained that starts to crystallize at 1200 °C. The resulting ceramic material is almost dense and crack-free since the volatile pyrolysis products can degass easily due to the open porosity of the green compact. Another method starting with polysilsesquioxanes of the general formula (RSiO 15 ) n with R = H, CH 3 , C 6 H 5 and CH = CH 2 , mixed with reactive fillers of metallic titanium limits the strong release of gaseous pyrolysis by-products to hydrogen, which can easily diffuse due to its

4 Boride and Carbide Ceramics

small ion size (Greil and Seibold, 1993). In this process called "active filler controlled pyrolysis" the polymer compound and the filler metal are molded at 200 °C and annealed for 60 min to allow a cross-linking reaction to occur in the green compact due to an addition mechanism e.g. in the vinylsubstituted polysiloxane

H CH I I -Si- + -Si-

200°C ,

H H I I I I -Si-C-C-SiI I I I H H (4-19)

A pore-free, green part is obtained which can easily be machined. Upon pyrolysis at 900-1400 °C for 1 h the precursor is converted to SiC, C and CH 4 . Since C and CH 4 react with metallic fillers such as, e.g., titanium to form TiC, only hydrogen is released. No porosity or cracking was thus found. As an additional benefit, dispersed TiC works as a reinforcing phase. Almost dense parts of complicated near-net-shape morphology have been produced up to 40 mm in size. It is possible also to use other reactive fillers such as silicides, as well as inert materials such as transition metal carbides or borides in fiber or platelet shape which reduce shrinkage to almost zero. 4 A.I A Poly type Formation During SiC Synthesis a-SiC is generally obtained by vaporliquid-solid mechanisms or the Lely process and related methods (Knippenberg, 1963), preferentially in the temperature range 2300-2700 °C, whereas the formation of /?-SiC is favored by growth from silicon melts or by hydrogen reduction of organo-silanes at temperatures below

2000 °C. Upon heat-treatment between 2100 and 2300 °C j8-SiC transforms irreversibly to the a-polytype. In contrast to this general picture which indicates that a-SiC may be the high-temperature form, some a-polytypes also form at temperatures as low as 1300-1600 °C, e.g. 2Hwhiskers produced by the decomposition of methyltrichlorosilane CH3SiCl3 (Merz and Adamsky, 1959; Merz, 1960), or by traveling solvent processes. On the other hand, yS-SiC has been obtained above 2600 °C (Scace and Slack, 1959). Ryan et al. (1968) stated that a small excess of atmospheric pressure may favor the formation of a jS-polytype at any temperature (Fig. 4-29). Furthermore, impurities such as aluminum, nitrogen or boron may influence the generation of screw dislocations or stacking faults, which also determine the polytype. Kistler-De Coppi and Richarz (1986) have shown that particle size and shape must also be taken into account. Figure 4-30 gives some general temperature/process-dependent stability fields of both polytypes (Ryan et al., 1968). Other comprehensive treatments of polytype stability may be found in Verma and Krishna (1966). Polytype transformation and other reaction processes related to sintering phenomena and important microstructural features will be dealt with in Sec. 4.5.2.4. uu -

a _Q

CD

c o

p-SiC

10 -

ieco mpoj

206

i"n

1 -

/ ^

tx-SiC

/vapor! 0.1 -

i

i

i

i

i

i

i

1800 2200 2400 Temperature °C) Figure 4-29. Influence of atmospheric pressure on the formation of a- and /?-SiC polytypes (Ryan et al., 1968).

uoo

4.4 Material Preparation

[3-Polytype

207

a-Polytype

3000Decomposition 28002600 o

2Z.00-

g

2200-

Vapor phase processes at 35 bar Ar or 1-35 bar N2

P to a trcinsformation

a. — 2 2000 1800-

Lely-process vapor phase processes

Growth from silicon melts

Films and coatings Travelling solvent method

nt 2B + 3CO 2

Boron carbide powder is produced on a technical scale by the carbothermic reduction of boron oxide with graphite or petroleum coke 2B 2 O 3 + 7C

4C +

6COt

formed, the reaction of Eq. (4-20) is accelerated to the benefit of B 4 C. Both volatilized boron oxides and carbon monoxide generate an internal Boudouard equilibrium within the raw material mixture and thus contribute to a self-propagating purification process, which can be expressed by

(4-20)

The process is carried out in huge electric arc or resistance furnaces and is comparable to the Acheson process. The reaction takes place between 1500 and 2500 °C, is strongly endothermic and requires 1812kJ/mol, i.e. 9.1 kWh/kg (Lipp, 1965, 1966 a). Since large quantities of carbon monoxide (approximately 2.3 m3/kg) are

2 CO

B4C + 6MgO (4-25) The process is performed by single point ignition (thermite process) or in a carbon tube furnace in a hydrogen atmosphere. The problem is the removal of magnesia, magnesium borides, and unreacted magnesium metal which are usually extracted by hydrochloric or sulfuric acid. Since MgO acts as a grain growth inhibitor, submicron powders with Mg compounds as the only impurities are produced (Schwetz and Lipp, 1985; Thevenot, 1990b). Further chemical refinement by high-temperature vacuum treatment, however, induces an undesirable coarsening of the particles. The 1990 total annual production of boron carbide in the western world is estimated at approximately 500-600 t. 4.4.2.2 High-Purity Material In laboratory-scale production, boron carbide can also be synthesized in the form of high-purity powders or coatings: (a) from the elements by arc melting at 2500 °C, or self-propagating synthesis above 1100°C 4B + C -> B4C

(4-26)

(b) by chemical vapor deposition reducing boron trichloride in the presence of carbon in a hydrogen atmosphere 4BC13 + 6H

B4C + 12HC1 (4-27)

(c) by pyrolysis of boron trihalides with methane or carbon tetraiodide as carbon carriers, in high-frequency furnaces 4B(Cl,Br) 3 + CH 4 + 4H 2 900-1800°C * B4C + 12HCl(HBr)

(4-28)

4BI 3 -hCI 4 900-1100°C

(4-29)

The latter methods yield boron-enriched solid solutions with a maximum of 20.4 wt.% carbon. Very fine boron carbide powders of spherical shape and 20-30 nm in size have been prepared by chemical vapor deposition according to (c). In an A r - H 2 - C H 2 BC13 atmosphere a radio frequency plasma produces stoichiometries between B 1 5 8 C and B 3 9 C (McKinnon and Reuben, 1975; Ploog, 1974). Also laser-induced pyrolysis of similar gas mixtures with or without acetylene has been employed for the preparation of nano-sized particles (Knudsen 1987). With similar success, composites of B4C and SiC have been produced by the pyrolysis of boroncontaining polysilanes (Walker et al., 1983). The general problem associated with the production of submicron powders by pyrolysis is the comparatively low yield of these highly expensive procedures and the excess of free carbon which cannot usually be avoided. The advantages of high purity and well-defined composition are limited due to the pick-up of oxygen by the large and hence extremely reactive surface area of the particles when exposed to air.

4.4 Material Preparation

4.4.3 Preparation of Transition Metal Carbides The production of transition metal carbides on an industrial scale occurs by sinter-carbonization of the oxides or hydroxides with carbon black in huge induction furnaces between 1500 and 2000 °C (ZrC, HfC, VC? NbC, TaC) or 2000-2200 °C (TiC) in a vacuum or hydrogen atmosphere TiO2 + 3C -> TiC + 2COt

(4-30)

Other reduction processes for oxides are aluminothermic and, less common, silicothermic reactions. The reaction then occurs above the melting point by arc melting or by induction melting. Only mixed carbides with relatively low melting temperatures [e.g., (Cr, Mo)C, (V, Ta, Nb)C] or eutectic mixtures (e.g., WC/W2C) are usually produced by this method. Purer melt-derived carbides are prepared by the auxiliary bath technique {menstruum process) by dissolution and re-crystallization of contaminated carbides in a liquid metal of no or little solubility. The melt temperature ranges between 1700 and 2000 °C; after cooling the refined carbide crystals of 100-1000 jim in size are extracted by an acid treatment of the metallic matrix. High-purity tungsten carbide (WC), molybdenum carbide (Mo 2 C), and Cr 3 C 2 are produced by the strongly exothermic reaction of the metals with carbon black under hydrogen or in a vacuum between 1400 and 1600 °C. Powder blends of Ti, Zr, Hf and carbon black are flammable. Solid solutions of the transition metal carbides are obtained by homogenization annealing between 1600 and 1800°C. Recent developments include direct tungsten and tungsten carbide production from the raw material scheelite (CaWO4) with several tungsten oxides as intermediate products.

209

In combined methods, a mixture of oxides and metals is carburized. Recycled chunks of metals are hydrogenized for embrittlement, crushed and milled. The metal hydrides are then added for carburization. Thus, ungraded commercial metal carbides are usually prepared from a large amount of recycled material, and they therefore contain other transition metal carbides and solid solutions thereof as significant impurities. The total WC production is estimated to be approximately 12000 tons/year. Vapor phase deposition methods yielding chemically well-defined powders or coatings make use of reactions of volatilized transition metal chlorides: (a) Conversion of titanium tetrachloride and methane by a heated wire H2 1600-2000°C

TiCL+CH 4

TiC + 4HCl (4-31)

(b) Decomposition of titanium tetrachloride with acetylene in hydrogen plasma + §H 2 ^ TiC + 4HCl (4-32) (c) Reaction of titanium trichloride with metallic aluminum powder and carbon black 2

TiCl3 + Al + C

700 1100 c

~

° > TiC + AlCl 3 (4-33)

All these reactions are strongly endothermic. The formation of MC in (a) and (b) occurs via CH radicals as a product of the methane and acetylene pyrolysis and yields particles of 10-100 nm diameter. More recently, the preparation route via organometalic precursors has become of increasing interest. Tfre aim is the synthesis of extremely pure, fine-grained powders or

210

4 Boride and Carbide Ceramics

pre-alloyed composite powders, fibers, coatings, or even monolithic materials. Possible precursors for titanium carbide are: - Ti2 + : titanocene and its derivatives: Cp 2 Ti(CO) 2 ,Cp 2 Ti(PMe 3 ) 2 , CpTiPh • 2OEt 2 and Ph 2 Ti. - Ti 3 + : (Cp 2 TiPh) 2 , Cp 2 TiMe. - Ti 4 + : Cl x TiR 4 _ x . Cp = cyclopentadienyl and Me = methyl.

4.4.4 Preparation of Transition Metal Borides Large-scale production of metal borides occurs preferentially in electric furnaces by the following high-temperature reactions: (a) Carbothermic reduction of the metal oxide, graphite or carbon black + B2O3

MB 2 + 5CO (4-34)

The carbothermic method yields carbon contaminated powders and is suitable for materials in which a C content of 2MB 2 + 4CO (4-35) M 2 O 3 + 3B 4 C -> MB 6 + 3CO (4-36) where M = rare earth elements. The boron carbide process can also start from blends of metal carbides, metal hydrides, boron oxide, boron carbide and carbon black 3MB 2 + 9COt

(4-37)

MC + MO 2 + B4C (4-38)

-> 2MB 2 + 2COT

This material usually contains only small amounts of residual carbon or boron carbide but no metals, and is thus the favored process for the technical synthesis of less contaminated borides. The process is carried out in tunnel furnaces under hydrogen or in a vacuum at 1600-2000°C, i.e., below the melting point of the boride. It is thus a reaction sintering procedure yielding a high-porosity product which can easily be crushed and milled. Additional refinement is obtained by multiple vacuum treatments with metallic or B4C additives to compensate non-stoichiometries. The final product is then called "vacuum quality". (c) Aluminothermic, silicothermic, magnesiothermic reduction of mixtures of metal oxides and hydroboric acid + B 2 O 3 + Al(Si,Mg) + Al 2 O 3 (SiO 2 ,MgO)

(4-39)

The yield is usually contaminated by residual metals or oxides and thus has to be purified by subsequent leaching, or a hightemperature vacuum treatment. High-quality borides of the transition metals with defined stoichiometry and crystal structure are synthesized by the following laboratory-scale methods: (a) From the elements or metal hydrides by fusion in an arc or resistance furnace, or by diffusion during sintering or hot pressing M + 2B -> MB 2

(4-40)

MH 2 + 2B -> MB 2 + H 2

(4-41)

(b) Borothermic reduction of metal oxides MO 2 + 4B

+ B2O2t

(4-42)

4.5 Sintering Behavior of Carbide and Boride Ceramics

(c) Conversion of metal carbides with boron and/or boron carbide yielding powder mixtures or - carried out during powder metallurgical densification, i.e., sintering or hot pressing - composites MC + 2B

MB 2 + C

(4-43)

MC + 6B

MB 2 + B4C

(4-44)

2MC + B X -> 2MB 2 + 3C

(4-45)

(d) Electrolysis of fused salts containing metal oxides, boron oxide or hydroboric acid plus alkaline borates and fluorides. (e) Molten metal/boron dissolved in Al, Cu, Sn, or Pb melts (auxiliary-metal bath method). (f) Chemical vapor reaction of metal halides and boron halides in a hydrogen atmosphere under plasma conditions. This method yields, however, material of varying stoichiometry and crystallinity. Limiting factors for commercial fabrication are the relatively high costs of elemental boron and the low production rate in the reactors.

4.5 Sintering Behavior of Carbide and Boride Ceramics Sintering of covalently-bonded materials is generally much more difficult than densification of oxide ceramics or metals. This is not only due to the low self-diffusion (poor tendency for grain boundary and volume diffusion), high ratio of grainboundary-to-surface energies and high vapor pressure of particular constituents (strong tendency for surface diffusion and evaporation-recondensation), but also due to their extreme sensitivity to environmental factors such as sintering atmosphere, traces of contaminants, particle size and shape distribution, temperature

211

gradients, etc. The phenomenon of a "terminal" density, i.e., the density obtained after sintering which is far below the theoretical density for pore closure, above which neither an increase in the temperature nor a prolonged sintering time would assist further densification, was frequently observed for B4C, SiC and Si 3 N 4 . The reason for this, as proposed by DeHoff et al. (1966), Greskovich and Rosolowski (1976) and Prochazka (1989), is that upon sintering the decrease in the specific surface area (driving force for densification) is consumed to a much greater extent for pore and particle coarsening (Ostwald ripening) than for grain boundary movement and pore removal. Figure 4-31 shows a socalled DeHoff diagram correlating the specific surface area and the fractional density on which the path of an ideally densifying material is illustrated by the diagonal line. The lines plotted for A12O3, SiC and B4C powders make it obvious that in the first step of sintering, the surface energy is dissipated very fast due to coarsening (Prochazka, 1989). Since a doubling in particle size corresponds to a decrease in the densification rate by a factor of ten, it is no wonder that densification comes to an end before pore closure is achieved. As pores are favorably removed by grain boundary movement, it is essential to generate a pore size distribution below a critical size above which pores are stable or even tend to grow (i.e., the driving force for pore shrinkage is 90%), pore eliminating mass transport mechanisms such as grain boundary and volume diffusion become effective at temperatures above 2000°C, i.e., at temperatures close to the melting point. At lower temperatures, surface diffusion and evaporation-recondensation reactions are the favored mechanisms, resulting in neck formation (increase of contact area), pore coalescence and particle rounding (decrease of specific surface area), or euhedral growth of particles by vapor phase reactions, respectively. Grabchuk and Kislyi (1976) proved that the regime of predominant surface diffusion extends from

1500°C to 1800°C, whereas sublimation occurs above 1800 °C with boron being the more volatile species. Only the latter sintering mechanism causes an enhanced shrinkage of the ceramic body. However, a poor tendency for plastic deformation, a high resistance to grain boundary sliding, and low surface energies hinder a considerable particle rearrangement or shape accommodation before grain boundary or volume diffusion is effective. Even submicron powders cannot thus readily be densified completely by pressureless sintering if they are not mechanically or chemically activated. The general preconditions for the densification of pure stoichiometric boron carbide are to start with very fine powders (preferably 90 %) and Grabchuk and Kislyi (1974) (2300°C: 99-99.5% density) who

4.5 Sintering Behavior of Carbide and Boride Ceramics

used finer powders. A considerable reduction in temperatures can be achieved by microwave sintering using 2.45 GHz radiation. After a 12 min treatment at 2000 °C, 95% of the theoretical density was obtained (Katz et al., 1988). The energy conservation compared to hot-pressing is, however, rather low. Starting from powders with a smaller particle size, e.g. < 1 pxn, would possibly result in lower sintering temperatures and higher final densities. Boron carbide, however, becomes pyrophoric with increasing specific surface area and is hence strongly oxygen-loaded or even dangerous in handling. 4.5.1.2 Pressureless Sintering with Additives

Activation of grain boundary and volume diffusion and thus densification at lower temperatures is possible by increasing the density of point defects or dislocations: (i) mechanically by high-energy milling (attrition milling), (ii) by doping with trivalent ions which substitute for carbon and thus introduce electron deficiencies and vacancies, e.g., by adding boron or aluminum, (iii) by introducing sintering additives which remove oxide layers on the surface of the boron carbide particles and thus increase the surface energy, e.g., by adding carbon, aluminum carbide, silicon carbide or related compounds which also inhibit exaggerated grain growth (Dole and Prochazka, 1985). Other methods make use of additives which possess a comparatively low melting point and have a suitable wetting behavior on boron carbide to provide a rapid path for mass transport via the melt and thus to initiate liquid phase sintering. Dense bodies of boron carbide have also been obtained by liquid phase infiltration of highly porous

213

powder compacts or presintered ceramic bodies. Kislyi and Grabchuk (1975) reported that volume diffusion is enhanced in the boron-rich area of the homogeneity range of boron carbide due to the generation of point defects. In fact, pressureless sintering with boron additives results in an onset of shrinkage at temperatures which are 300 K lower than those required for stoichiometric B4C. Since aluminum also substitutes for carbon, a similar mechanism may be activated. Accordingly, 95-99.2% of the theoretical density is obtained at 21002200°C with 3-15%, preferentially < 1 % Al additive (e.g., Kriegesmann, 1989). Other Al-providing sintering additives are A14C3, A12O3 and A1F3 (Lange et al., 1980; Kanno et al., 1987; Kriegesmann, 1989) which also use carbon or fluorine as deoxidizing agents. The use of metallic additives is limited due to the low thermodynamic stability of boron carbide reacting with metals to form metal borides and free carbon, except in the case of Cu, Zn, Sn, Ag, and Pb. Nevertheless, Mg, Cr, Co, and Ni have been used (Glasson and Jones, 1969; Janes and Nixdorf, 1966, Lange et al., 1980), with minor success. Stibbs et al. (1973) have proposed additions of 5 10 wt.% Al, Mg or TiB2 to obtain > 9 9 % density between 2150 and 2250 °C. TiB 2 , CrB 2 , and W 2 B 5 additives inhibit grain growth by grain boundary pinning or, as in the case of W 2 B 5 at >2220°C, initiate liquid phase sintering if a eutectic reaction occurs (Zakhariev and Radev, 1988). Sintering of submicron powder with an addition of 1 wt.% Be2C resulted in 94% density when sintered between 2200 and 2280 °C (Prochazka, 1977). The only technically important sintering additive for boron carbide is carbon, as discovered almost simultaneously by Schwetz and Vogt (1977), Henney and

214

4 Boride and Carbide Ceramics

Jones (1978), and Suzuki et al. (1979). An amount ranging from 1 to 6 wt.% is sufficient to obtain almost theoretical density. Schwetz and Grellner (1981) added phenolic resin (corresponding to 1-3 wt.% C) to a submicron B4C powder and obtained > 9 8 % density at 2150°C. The sinter activation was attributed to an increase in surface energy due to the removal of oxide layers. Moreover, residual graphite particles which have been observed at the grain boundaries may inhibit surface diffusion and evaporation and may also control the grain boundary movement (Dole and Prochazka, 1985; Dole et al., 1989). Firing of B4C with 6 wt.% C additive at 2220°C results in a 97% dense microstructure of 1-5 jLim equiaxed particles, i.e. almost no coarsening has occurred. Abnormal growth of individual grains to 10-30 jim starts above 2235 °C; at 2250 °C, extensive Ostwald ripening and twinning is observed. The local growth of faceted grains exceeding 500 jim in size was attributed to liquid phase sintering processes due to the presence of low melting impurities (Dole and Prochazka, 1985). The method of in situ pyrolysis of organic additives such as Novolaque-type resins to amorphous carbon was also studied by Bougoin et al. (1985). The advantage of the precursor method is the improved homogeneity of the carbon distribution and the extraordinarily fine, resulting average grain size of 2 |im and less. Furthermore, the resin may act as a molding aid upon cold isostatic pressing, or may even be the plasticizer for injection molding. Thus complicated parts can be fabricated easily and subsequently pyrolyzed and pressureless sintered. Combined additives consisting of carbon and a metal carbide or boride make use of both the deoxidizing effect of carbon and the diffusion-enhancement by the

metal, or the grain growth inhibiting and reinforcing effect of nonreacting phases, e.g., B + C, SiC + C, SiC + Al, or TiB2 + C (e.g., Bougoin et al., 1985; Grabchuk and Kislyi, 1975; Oh et al., 1985). Weaver (1982 a, b) sintered relatively coarse (average size 9 jim) boron carbide powders with 2-40 wt.% SiC and 0-10 wt.% Al additives to > 85 % density. In similarity to the decomposition of an A14C3 addition, metallic Al is dispersed very homogeneously by evaporation and condensation in the still porous ceramic body (Borchert and Kerler, 1975; Kriegesmann, 1989). Starting from submicron powders, Schwetz et al. (1983) prepared composite materials consisting preferentially of 9-10 wt.% SiC and 1-3 wt.% C with 97-99.7% density at 2000-2100 °C. Residual porosity was removed completely by a post-HIP (hot isostatic pressing) treatment at 19502050 °C. Both C and SiC may also be introduced in the form of organometallic precursors, e.g., by infiltration of a porous B4C body with polycarbosilane and phenolic resin, and subsequent pyrolysis. Bougoin and Thevenot (1987) reported on the fabrication of composite bodies containing 5 wt.% SiC residue but no free graphite. Sintering for 15 min at 2175 °C results in a density of > 9 2 % . The microstructure of 7.5 wt.% polycarbosilane material exhibits relatively large, faceted B4C particles (20-50 jim) with entrapped pores and local enrichments of SiC implying that liquid phase sintering may be active. Increasing the amount of polycarbosilane to 17.5 wt.% results in a more uniform microstructure that is characterized by /?-to-a transformed SiC platelets of 50 Jim size. Pressureless sintering with liquid phases was studied in the B 4 C-A1 and B 4 C-Si systems. Since Al melts below 600 °C and exhibits a significant vapor pressure at only slightly higher temperatures, the equilib-

4.5 Sintering Behavior of Carbide and Boride Ceramics

rium between 1000 and 1880 °C, at which liquid Al is stable with an Al-saturated B 12 (B, C, Al) 3 solid solution (Fig. 4-32, Lukas, 1990), cannot readily be utilized for liquid phase sintering. Moreover, problems in wetting due to oxide layers on the surface of both Al and B4C powder particles have to be overcome. As shown by Halverson et al. (1989), it is more effective to infiltrate compacted or presintered porous B4C bodies with liquid Al. Since the resulting material is a metal-reinforced B4C cermet rather than a liquid-phase sintered B4C ceramic, it will be treated in detail in one of the following sections. According to the B-C-Si phase diagram, liquid phase sintering of B4C should generally be possible above 1560°C with a B-rich Si liquid (Telle, 1990; Telle and Petzow, 1987 b). Starting from powder mixtures of B4C, B, and Si, the first unit is generated at 1380°C, which is in equilibrium with SiB6 and SiC and thus may cause the partial decomposition of B 4 C. Above

215

1560°C, however, a B 12 (B, C, Si)3 solid solution is in equilibrium with the liquid (Fig. 4-33). Besides the complications due to iterative changes of the wetting behavior due to dissolution and precipitation reactions upon heating, a strong limitation on the final densification arises from the continuous evaporation of Si, which may cause degassing channels and thus even open porosity (Fig. 4-34).

2600 2400220020001 800 — E 1600-

U0012001000

Figure 4-33. Isopleth through the ternary B-C-Si system parallel to the B-C edge at 5 at.% Si. The B 12 (B,C,Si) 3 solid solution forms a ternary eutectic with Si (B) liquid.

90

80 (B 4 C)

B AIB12 20

30

£0 50 60 at.% Al

70

80

90

Al

Figure 4-32. Isothermal section of the ternary A l - B C system at 1600 °C after Lukas (1990); liquid Al is stable with an Al-saturated B12(B,C,A1)3 solid solution.

Figure 4-34. Degassing channels in a B 12 (B,C,Si) 3 ceramic; pressureless liquid phase sintered at 2050 °C (SEM micrograph).

216

4 Boride and Carbide Ceramics

4.5.1.3 Hot-Pressing and Hot Isostatic Pressing Since pressureless sintering allows the fabrication of complex shapes but results in coarse microstructures and approximately 3-7 vol.% of residual porosity, this process is only applicable for wear parts or shieldings which are not subjected to high stresses because these materials exhibit a low strength (ah < 300 MPa) and a low fracture toughness (Xlc < 3 MPa m 1/2 ). Hence, for high densification at reasonable temperatures a hot-pressing treatment that causes particle rearrangement and plastic flow is required. Grain boundary sliding, strain-induced twinning, creep and, at a later stage, bulk diffusion combined with recrystallization were identified as the mechanisms of mass transport (Kuzenkova et al., 1979; Ostapenko et a l , 1979; Brodhag et al., 1983). Densification maps and diffusion diagrams of B-rich boron carbide and C have been established by Beauvy and Angers (1980), and Bouchacourt et al. (1981). Figure 4-35 shows the predominant mechanisms of densification related to the fraction of re-

Phase D: volume diffusion

Phase C: plastic flow

20 feO

10 ft

Phase B: rearrangement of particles

o

1700

1800

1900

2000

2100

2200

Temperature (°C) Figure 4-35. Densification map of boron carbide (Beauvy and Angers, 1980).

sidual porosity. Suitable preconditions are (i) the use of submicron powders, (ii) temperatures in the range 2100-2200 °C, (iii) pressures of 25-40 MPa, (iv) 15-20 min hold, and (v) a vacuum or an argon atmosphere. To resist the high pressures at these temperatures and to provide carbon as a sintering aid, the use of boron nitridecoated, graphite crucibles is favored. In Fig. 4-36, literature data on the obtained fractional densities of pure B4C are related to the particular hot-pressing conditions. It is obvious that both high temperatures and high pressures are required to achieve a density of > 9 5 % . Only formation of sinter necks is obtained at 20 MPa pressure and 2000 °C (Fig. 4-37). However, a strong coarsening has to be taken into account at higher temperatures and average particle sizes of > 100 jam in commercial ceramics are not rare. Similar to pressureless sintering, additives may be used for hot-pressing of boron carbide to reduce temperatures required for grain boundary and bulk diffusion and to retard grain growth. Figure 4-38 shows a typical microstructure of a hot-pressed stoichiometric and B-doped material with strain-induced polysynthetic twinning. Suitable dopants are B (Ekbom and Amundin, 1980; Champagne and Angers, 1979), C (Schwetz and Grellner, 1981), Mg, Al, Si, Ti, V, Cr, Fe, Ni, and Cu (Glasson and Jones, 1969; Janes and Nixdorf, 1966; Stibbs et al., 1973; Ekbom and Amundin, 1980; Telle and Petzow, 1987b). As demonstrated by Telle and Petzow (1988), combined B-Si or B-Si-Ti additions lubricate the grain boundary sliding and prevent coarsening by forming a thin SiC or TiB 2 grain boundary phase (Fig. 4-39) which pins the grain boundary movement and controls the surface diffusion. Compounds used as additives are various glasses, A12O3, sodium silicate with

4.5 Sintering Behavior of Carbide and Boride Ceramics

217

70 601 :E CD \

5040 -

I 30-

CD

• * • o A v o X

99-100 97-98 95-96 90-94 80-89 70-79 60-69 < 59 th. D. O

O

7

V

A

•

«

•

•

•

•

2010 1800

2000

2200

Temperature ( ° C ) Figure 4-36. Density-hot-pressing condition map of pure B4C (literature survey); the continuous line separates the conditions which lead to closed porosity (% th.D. = fraction of theoretical density).

Figure 4-37. Fracture surface of stoichiometric B4C, hot-pressed at 2000 °C; only the formation of sinter necks was initiated.

Mg(NO 3 ) 2 , and Fe 2 O 3 which may reduce the hot-pressing temperature down to 1750 °C (Vasilos and Dutta, 1974). A comparison between isothermal densification of pure B4C and a multiple additive material is shown in Fig. 4-40. MgF 2 , A1F3 (Lange et al., 1980) and ethyl silicate (Furukawa and Kitahira, 1979) are other additives which are active at particle surfaces and grain boundaries. Hot-pressing with

Figure 4-38. Microstructure of hot-pressed, coarsegrained B4C; note the presence of polysynthetic twinning in large grains due to pressing stresses.

218

4 Boride and Carbide Ceramics

Figure 4-39. Thin SiC grain boundary phase between B12(B, C, Si) 3 particles pinning the grain boundary movement and thus controlling the grain growth; transient liquid phase-assisted, hot-pressing of B 4 C~ Si-B powder blends; SEM micrograph.

10

40

100

400

1000

Time [min]

Figure 4-40. Comparison between isothermal densification of pure (•) and multiply-doped (o) B4C (Vasilos and Dutta, 1974).

l-5wt.% of the above-mentioned additives usually requires a temperature of 1750-1900 °C to obtain > 9 5 % density. In most cases, grain size refinement and distributed second phases result in improved mechanical properties such as strength and fracture toughness.

Hot isostatic pressing (HIP) of boron containing ceramic powders creates special difficulties due to the choice of the canning material. In general, containers made from metals or usual glasses cannot be used because of reactions with the sample material. In the presence of metals, boron carbide decomposes forming metal borides plus graphite which embrittles the capsule. In the case of silica glass, boron diffusion from the outer layers of the specimen into the glass strongly changes the viscosity and the glass transformation temperature. Hence the softening of the container and the pressure transfer to the specimen cannot be controlled reliably. Moreover, boron oxide gas may be released from both the capsule and the sample and hence result in blowing of the container. Promising techniques have been developed by Asea Cerama AB, Sweden, and Elektroschmelzwerk Kempten, Germany, using diffusion barriers and a special type of boron oxide glasses (Larker et al., 1988). These methods are also applicable to silicon nitride and silicon carbide ceramics and make the fabrication of complex parts, e.g., injection-molded sand blasting nozzles, in large-scale production feasible. In the case of boron carbide, this treatment was applied to additive-free submicron powder obtained by sedimentation of commercial powder in an aqueous suspension by changing the pH value from 10 for dispersion to 3 for flocculation. The sedimented powder exhibited a particle diameter 9 5 % density) can be fully densified by a postsintering HIP-treatment (Schwetz et al, 1986). Best results for C-SiC-doped B4C are obtained at 2000 °C and 200 MPa isostatic pressure. 4.5.2 Densification of Silicon Carbide

Densiflcation of silicon carbide is carried out by various techniques leading to different microstructures, mechanical properties, and capabilities of manufacturing large parts which are of particular importance for specific applications. Material which has been densified by pressureless sintering is known as SSiC (sintered silicon carbide), /zot-/?ressed material as HPSiC, hot zsostatically pressed material as HIPSiC or, if the HIP-treatment was one on pre-sintered parts to remove the residual porosity, the material is called HIPSSiC.

219

These materials are usually of high-quality with a homogeneous microstructure, a small amount of residual porosity, and a well-defined phase composition. Parts prepared in this manner have optimum strength and toughness for use as structural ceramics (wear parts, components in engines, heat exchangers, electronic devices, etc.). Low-cost materials used for large parts, e.g., kiln furniture or other refractory applications, are fabricated by recrystallization, known as RSiC, or by infiltration of a porous SiC-C body with liquid Si9 called SiSiC or RBSiC (reaction-bonded SiC). The advantage of the latter processes is that almost no shrinkage occurs on sintering, thus these methods are preferred for the manufacture of large parts that are not subjected to high loads, since their microstructure exhibits a considerable amount of residual porosity, carbon or metallic silicon and an exaggerated grain size. In the following sections, the state of the art in SiC sintering will be treated according to the various techniques. 4.5.2.1 Pressureless Sintering with Additives

Like other covalently bonded compounds, SiC does not sinter without specific additives. The reason for this behavior was attributed to the relatively poor volume diffusion due to the strong unidirectional bonding, as well as to vapor transport mechanisms (evaporation-recondensation) which generate neck-formation between adjacent particles but do not contribute to shrinkage (Popper and Davies, 1961). One precondition for densification by grain boundary or volume diffusion is the use of submicron powder either of the hexagonal a- or the cubic /J-polytype. The

220

4 Boride and Carbide Ceramics

amount of sintering additives is relatively small compared to that required for boron carbide and ranges between 0.2 and 3.0wt.%. Prochazka (1973a, b, 1974a) demonstrated that the simultaneous additon of 0.3 wt.% B and 0.2 wt.% C to fine £-SiC powder yields 95-99% of the theoretical density upon sintering at 2040 °C in a flowing He atmosphere. No shrinkage was only observed with a carbon addition. The absence of any detectable second phase except carbon led to the conclusion that densification had occurred by solid state diffusion. Normally, B substitutes for C, but it may also enter an Si site. A possible defect reaction as proposed by Prochazka (1981) is B

(4-46)

i.e., B enters the sublattice trivalently, acquires an electron to complete its bonding pairs and creates a neutral hole h° and a vacancy V in the other C or Si sublattice, respectively. Another reaction which does not require the formation of a vacancy is B + C -> BSi

(4-47)

Here B occupies an Si site and creates a hole, whereas C enters a C site. According to Shaffer (1969), and Vodakohov and Mokhov (1973), the solid solubility of B in a-6H SiC is limited to 0.2 mol%, which is considered to be the reason for the lower limit of the B additive. Investigations of the self-diffusion of Si and C in doped SiC reveal, however, that the formation of electronic defects is not sufficient to obtain complete densification by volume diffusion. Data on diffusion coefficients in both a- and /?-SiC are presented by Hong et al. (1979), Hon et al. (1980), and Birnie (1986). According to Prochazka (1974 b), another crucial precondition for pore closure is that the grain boundary energy to sur-

face energy ratio should be small. The advantageous effect of combined B and C doping is attributed to an increase in the surface energy of SiC, since oxide layers are removed by C to form SiO gas, CO gas, and secondary SiC, as well as to a decrease in grain boundary energy due to the segregation of B at the grain boundaries. Prochazka's hypothesis is strongly supported by the observation that silica and silicon inhibit sintering of B-doped SiC (Prochazka, 1973 b). More recent studies on the role of B and C in sintering SiC have revealed contradictory results. Microstructural studies with high-resolution techniques have shown that no B is enriched at the grain boundaries (Hamminger et al., 1983 a, b; More et al., 1986; Carter et al., 1988); the contrary was observed by Riihle and Petzow (1981) and Browning et al. (1987) who found B, C, BN, or B4C inclusions at the interfaces. Graphite inclusions of < l - 5 |im within the SiC grains have been reported by Hamminger et al. (1987), intra-SiC inclusions of B12(B, C, Si)3 were identified by More et al. (1986). Since these particular observations on the studied materials have not usually been easily related to the processing techniques nor to the sintering steps, these results may not be used as excluding arguments against the proposed sintering mechanisms. Investigations of the various sintering stages of aSiC by Wroblewska et al. (1990) have revealed that a thin (> 100 nm), uniform layer forms on the SiC particles at 1500°C, which also contains B and O impurities. A rapid migration of B was observed at 1350 °C by Suzuki and Hase (1979). At approximately 1900 °C, SiO2 reacts with C forming secondary SiC particles while the C layer becomes significantly thinner ( « 1 jim) and is almost depleted of B and O. The final, dense material was found to consist of B-enriched SiC and polycrys-

4.5 Sintering Behavior of Carbide and Boride Ceramics

talline C inclusions. Thus the study by Wroblewska et al. (1990) implies a combined deoxidizing and volume-diffusionenhancing sintering mechanism to be active. In addition to the solid state sintering processes in the previous discussion, liquid phase sintering was proposed, in which a B-containing liquid was considered to generate dissolution-reprecipitation mechanisms which would explain the rapid growth of faceted grains (Lange and Gupta, 1976; Bocker and Hausner, 1978; Prochazka, 1981). A recent re-investigation of the B-C-Si system by Telle and Petzow (1987 a) and Telle (1990) proves the existence of ternary B 12 (B, C, Si) 3 -SiCliquid and B 12 (B, C, Si)3-SiB5-liquid equilibria above 1560°C which have to exist if B or, specifically, B4C is present in an amount exceeding the solid solubility in SiC. This generally happens locally at phase boundaries between additive particles and SiC grains. Another explanation for the presence of a liquid phase considers the segregation of Si at the grain boundaries which is due to the recrystallization of stacking faults and point defects, yielding an excess of 2at.% Si (Prochazka, 1989). B can be introduced as B 4 C, BN, BP, A1B4, or SiB 6 . LiBH 4 and C mixtures (decomposing into the elements above 270 °C) or H3BO3 + C blends have been proven not to contribute to the densification to a similar extent since boron is lost by evaporation (BH 3 , B 2 O 3 ). Carbon may suitably be added in the form of carbon black or as an organic compound, preferentially a phenolic resin or a novolak to obtain an optimum distribution, whereas graphite seems to be ineffective due to its poor dispersability. Besides B, aluminum is also an effective sintering aid if combined with C or B, as

221

demonstrated by Billington et al. (1965), Bocker and Hausner (1978), Bocker et al. (1978, 1979), and Schwetz and Lipp (1980). Starting with submicron a-SiC powder and Al additives of 97 % have been obtained at temperatures between 2050 and 2250 °C. The doping was successfully carried out with metallic Al, A1N, A14C3, A1B2, A1P, and Al 4 SiC 4 . A12O3 and LiAlH 4 were not found to be very efficient due to evaporation of volatile reduction or decomposition products. There is evidence that a-SiC exhibits a solid solubility for Al compounds such as A14C3 and A1N (Cutler et al., 1978; Schwetz and Lipp, 1980) which stabilize the AH polytype. Thus, similar to B, the beneficial effect of Al is the enhancement of volume diffusion. In comparison to the SiC-B-C sinter system, Al additives result in a lower temperature of onset of sintering or of the maximum densification rate (Bocker and Hausner, 1979; Inomata et al., 1980). This was also observed for materials sintered with combined B, Al, and C additions and is mainly attributed to the formation of a liquid phase which significantly triggers a rapid grain growth by active dissolution-reprecipitation mechanisms (Fig. 4-42). This strong coarsening can be suppressed by minimizing the amount of additives to a transformation. 15 R and 4 H are the initial phases formed above 1850°C, with 6H appearing above 1950 °C. Both 15 R and 6H are transitory, whereas 4 H is the dominant phase above 2100 °C (Fig. 4-49). In sintered a-SiC, the particle morphology is governed by the B/C ratio (Bocker and Hausner, 1979). At 2060 °C, a B/C ratio of 0.125 yields a fine, uniform microstructure of equiaxed particles, whereas B/C = 0.33 results in faceted platelets of

225

Figure 4-47. Large, elongated, lath-like a-SiC particles in pressureless sintered material grown at 2100 °C at the expense of /?-SiC.

Figure 4-48. Typical microstructure of B-doped /?SiC sintered at above 2200 °C; note the large, feathershaped particles due to the enhanced /?-to-a transformation (courtesy of D. Peuckert).

rather uniform size. An increased ratio of B/C = 0.8 promotes the rapid growth of very large plates of several hundred microns in size. Sintering of B-doped a-SiC above 2100 °C induces abnormal grain growth of the 6H polytype stabilized by B. A growth rate of 3 mm/h was reported by Prochazka (1974 b) causing entrapped porosity inclusions of silicides and unreacted boron carbide (Fig. 4-50). Above 2200 °C, a conversion of 6H to 4H was

226

4 Boride and Carbide Ceramics

100

o

1000

A

- 98 % at a lower binder content. Cemented borides with a metallic matrix have also been fabricated from the ternary transition metal borides of T-, cp- and cotypes since these composites can easily be liquid phase sintered with metallic melts. The T-phase with a general composition of M 2 1 M 2 B 6 has been observed in ternary systems where MJ = Fe, Ni, or Co and M n = Zr, Hf, Nb, Ta, or W, with M1 as the liquid phase (Schobel and Stadelmaier, 1965; Lugscheider et al., 1980, 1982). T-phase-containing cermets are successfully used for the production of wear and corrosion resistant coatings by plasma spraying, flame spraying and reactive welding (Lugscheider and Eschnauer,

235

4.6 Microstructural Reinforcement of Boride and Carbide Ceramics

1987). The stoichiometries of the cp- and co-phases are IV^M11!* and M I 2 M II B 2 , respectively, where M1 represents Cr, Mo, Ta, or W and M n holds for Fe, Ni, or Co and solid solutions thereof. As an example, an isothermal section of the B-Co-Mo system is shown in Fig. 4-60 in which both the T- and the (^-phases are linked with Co as the binder (Haschke et al., 1966). However, in systems with Fe replacing Co, a cp-phase does not exist. Hence co is in equilibrium with liquid metal and is thus likely to form a cermet material with Fe (Fig. 461). Phase compositions situated in the pseudo-binary equilibria with a metal can easily be pressureless liquid phase sintered at temperatures between 1500°C and 1700 °C. Wear-resistant parts have been developed from Mo 2 FeB 2 -Fe cermets with Ni or Cr additives (Takagi et al., 1984, 1987 a, b).

10 20

Co

10

20 M o C o 3

Z,0Mo6Co7 60 at.% Mo

70

80

90

Mo

Figure 4-60. Isothermal section of the B-Co Mo system at 1000°C in at.%; formation of liquid phase in the vicinity of T indicated by "liq." (Haschke et al., 1966).

4,6 Microstructural Reinforcement of Boride and Carbide Ceramics Most of the strengthening and toughening concepts which have been derived from considerations of fracture mechanics and successfully applied to oxide and nitride ceramics have also been shown to be effective for boride- and carbide-based materials. The first steps for the improvement of the mechanical propertiers of a ceramic should always be

Fe

10

20

30

40 M ° 6 i = e 7 60 at.% Mo

70

80

90

Mo

Figure 4-61. Isothermal section of the B-Fe-Mo system at 1000°C in at.% (Haschke et al., 1966).

- sintering to densities > 9 8 % , - avoiding flaws and microstructural inhomogeneities such as large pores, inclusions, agglomerates, abnormally grown particles etc., - reducing grain growth, and - devitrification of glassy grain boundary phases.

In addition, strengthening and toughening strategies such as - metal matrix reinforcement, - grain size refinement using sintering additives, - transformation toughening,

236

4 Boride and Carbide Ceramics

- crack impediment, crack deflection or crack branching, and - crack bridging and flank friction have been studied intensively. In contrast to oxide ceramics, the applicability of these mechanisms for boride and carbide materials is much more limited because of chemical complications. In the following sections particular materials combinations are discussed in detail with respect to the preparation techniques and the improvement obtained in the mechanical properties. Special attention is given to the micro structural features which make the desired toughening and strengthening mechanisms operational. 4.6.1 Metal Matrix Reinforcement The fabrication of metal matrix cermets with boron carbide as a dispersed phase is very limited under equilibrium conditions since B4C reacts with all metals, except Ag, Cu, Sn, and Zn, forming metal borides and graphite or metal carbides (e.g., Hamjian and Lidman, 1952). In systems with sluggish reaction kinetics, however, complex low-temperature materials with interesting mechanical properties have been investigated. A development from the Ukraine makes use of a Ti-containing bronze as a binder phase in which the reaction of Ti with B4C to give TiB 2 is employed for active brazing and improvement of the wetting behavior. The use of pure Cu, Sn, or Zn, or alloys thereof for the infiltration of B4C power compacts usually fails since the wetting behavior is rather poor (wetting angle > 90°), but this can be improved by adding Cr or other metals which may react with the B4C when approaching equilibrium conditions. Other metal matrix composites with B4C-particulates have been obtained using

aluminum because of slow reaction kinetics. The process is based on an infiltration of liquid Al into a porous body of B4C at temperatures between 700 °C and 1200 °C. Since Al melts at 600 °C and exhibits a significant vapor pressure at only slightly higher temperatures, the equilibrium between 1000 and 1880°C at which liquid Al is stable with an Al-saturated, B12(B, C, Al)3 solid solution cannot readily be utilized for liquid phase sintering with small volume fractions of liquid. A shown by Halverson et al. (1989), it is more effective to infiltrate compacted or presintered, porous B4C bodies with liquid Al. The resulting material is a metal-reinforced, B4C cermet rather than a liquid-phase sintered B4C ceramic. The wetting behavior is strongly influenced by oxidation layers formed on the surface of the B4C particles (Halverson et al., 1985), but can be improved by superheating the melt. Between the melting point of Al and approximately 1000°C, wetting angles of 100-150° are observed which decrease to reasonable values with prolonged soaking for thousands of hours (Halverson et al., 1989). Hence, in that temperature range, only hot-pressing or hot isostatic pressing result in high-density cermets. Above 1000-1200 °C, a suitable wetting behavior is obtained within minutes of annealing. Due to capillary forces and phase reactions both densification and adhesion of the metal-ceramic interface are excellent. During infiltration, reactions of Al with B4C occur. Below 1200 °C, A14BC, A1B2, A1B12, and A1B12C2 are formed within tens of hours whereas above 1200 °C the generation of A14C3, A1B12, and A1B24C4 is more favored (Halverson et al., 1989). If the composite is prepared by fast heating, infiltration and rapid cooling, most of the aluminum matrix is retained unreacted. The matrix can then be hardened by a subse-

4.6 Microstructural Reinforcement of Boride and Carbide Ceramics

quent heat treatment at 800 °C for 20 hours due to the precipitation of aluminum carbides and borides. Since the mechanical properties are determined by the Al matrix, a Klc of 5-16 MPa m 1/2 and a flexural strength of 200-680 MPa can be obtained depending on the quality and volume fraction of the metallic binder. The Vickers microhardness of 15.70 GPa for a 31 vol.% Al composite is improved by annealing to 19.40 GPa. Similar metal matrix composites with B4C, SiC, and TiB2 as fillers have been fabricated by the so-called Lanxide- or Dimox-process (direct metal oxidation) where an Al- or Ti-based liquid mixed with ceramic particles - preferably of whisker or platelet shape - is slowly converted in air, oxygen or nitrogen to alumina or titanum nitride, respectively (Newkirk et al., 1986; Antolin and Nagelberg, 1992; Nagelberg et al., 1992). This self-propagating reaction yields columnar crystals of the oxide or nitride phase, with B4C, SiC, or TiB2 inclusions and residual metal-filled channels which contribute significantly to the strength and toughness. SiC-Al 2 O 3 composites have an excellent fracture toughness of 8-15 MPa m 1/2 and a flexural strength of 500-800 MPa. They have also been demonstrated to be highly resistant against erosive wear (Weinstein, 1989). Another approach to fabricate metalmatrix-based boride and carbide composites according to the Lanxide process starts with reactive blends of B4C and Ti or Zr metal. Upon conversion to TiB 2 or ZrB 2 , respectively, a strong heat release is observed which can easily lead to partial melting of the composites. Depending upon the starting composition, residual metallic Ti or Zr, or B4C may be found after reaction. Interesting microstructures can also be obtained if TiC or ZrC are added as fillers (Johnson et al., 1991).

237

An excellent literature survey on SiCparticulate reinforced, metal matrix composites is given by Ibrahim et al. (1991) with special emphasis on the processing and mechanical behavior of Al-based alloys with SiC contents of less than 40 vol.%. According to the thermodynamics of the SiC-Al system (Lee et al., 1988), SiC reacts with Al below 1820°C 4Al + 3SiC ->Al 4 C 3

(4-51)

4Al + 4SiC -> Al 4 SiC 4 + 3Si

(4-52)

These reactions are kinetically enhanced above the ternary eutectic at 580 °C where Al is in the liquid state. Above 1820°C an Si and C rich Al-melt is in equilibrium with SiC but this high temperature is certainly not suitable for the fabrication of composites because of the high evaporation rate of Al. The formation of interfacial A14C3 reaction layers has to be taken into account during low-temperature wetting and infiltration; these give good adhesion but may also increase the risk of interfacial cracks and voids. Accordingly, a variety of manufacturing processes have been developed such as liquid metal-ceramic particulate mixing, e.g., SiC powder injection into the melt or several stirring procedures, liquid metal infiltration of powder or fibre preforms, rheocasting of particles dispersed in metallic melts, formation of blended pellets by atomization of a metal melt together with injected SiC particles (Osprey process) or solid state sintering (Ibrahim et al., 1991). Transition metals such as Co and Ni are useful for liquid phase sintering of TiB2type borides causing Ostwald ripening, but they react chemically to form M^B^-type or more complex ternary phases which are very brittle. No metal-reinforced composites can thus be produced except where reactions can be at least partially avoided

238

4 Boride and Carbide Ceramics

by fast heating during hot-pressing. In contrast, Co- and Ni-based alloys can be successfully improved for wear resistance by the incorporation of TiB 2 and CrB 2 particles if reaction layers of lower hardness can be tolerated. Cemented borides with a metallic matrix have recently been developed using the TiB 2 -Fe system (Yuriditsky, 1990; Sigl and Schwetz, 1991a, b; Ottavi et al., 1992a,b; Ghetta et al., 1992; Jungling et al., 1991 b). Although there are still some uncertainties on the phase diagram which the synthesis of pure two-phase cermets is based upon (Fig. 4-58), the authors agree that the presence of oxygen and carbon impurities introduced by carbothermic synthesis of the TiB 2 starting powder is detrimental to the wetting behavior and responsible for the presence of the embrittling but hardening Fe2B phase which controls the sintering behavior and thus the properties, see also Sec. 4.5.3.2. The characteristic mechanical property compared to that of WC-based hard metals is the significantly higher hardness with HV10 ranging from 1500 to

1800 GPa at 16-20 vol. % binder and 2000-2300 GPa at 6vol.% binder, while the bending strength of 550-900 MPa and the fracture toughness of 6-10 MPa m 1/2 are lower than for commercial hard metals with an intermediate Co content (Yuriditsky, 1990; Sigl and Schwetz, 1991). Fig. 4-62 shows a comparison between the hardness/toughness relationship of TiB 2 -Fe cermets and various WC-Co hard metals. Additions of metals such as Mo, Cr, Ni, and Co to the Fe matrix may be used to fabricate composites with improved mechanical and corrosion properties. Figure 4-63 shows significant variations in the bending strength with increasing amounts of Mo in the binder phases of different volume fractions (Yuriditsky, 1990). As discussed in Sec. 4.5.3, hard metallike composites can be prepared by pressureless sintering of ternary borides with Fe, Ni, or Co melts. Materials with T-phase ( M ^ M ^ B ^ where MJ = Fe, Ni, or Co, and M11 = Zr, Hf, Nb, Ta, or W with M1 as the matrix phase) have not been developed for technical use but Ni-based alloys with

\ •

3000

single phase TiB 2

o

2500 -

CO

single phase WC C/) C/)

CD

2000 -

c

"P

TiB2-20 vol.% Fe

05

1500 -

Figure 4-62. Hardness-toughness relationship between hard metals and TiB 2 -Fe composites (courtesy of L. Sigl, ESK).

* WC/Co numbers are vol.% Co

20

1000 5

10

15

Fracture toughness, MPa Vm

20

4.6 Microstructural Reinforcement of Boride and Carbide Ceramics 900 o QL

800 en c CD

_b 700

c600 CD

500

0

10 20 30 40 Mo in binder phase, wt.%

Figure 4-63. Variation of strength with Mo content in the binder phase of TiB2-Fe-based cermets (Yuriditsky, 1990). A, 12.5 vol.% of binder; •, 15vol.%; • 17.5 vol.%.

T are in use as wear- and corrosion-resistant coatings on steels (Lugscheider and Eschnauer, 1987). (p- and co-phases have M ! M n B and ! M 2 M11 B 2 stoichiometry, respectively, where M1 = Cr, Mo, Ta, or W and M n = Fe, Ni, or Co and solid solutions thereof. Although the ternary phases are rather brittle, the cermets exhibit excellent toughness and strength (4. Matkovich, V. I., Economy, J. (1977b), in: Boron and Refractory Borides: Matkovich, V. I. (Ed.). Berlin: Springer, pp. 98-106. McCauley, J. W. (1988), Am. Ceram. Soc. Bull. 67(12), 1903. McCauley, J. W., Corbin, N. D., Resetar, X, Wong, P. (1986), in: Proc. 10th Ann. Conf Composites and Advanced Ceramic Materials, Cocoa Beach, FL, Jan. 19-24 (1986): Messier, D. R. (Ed.). Westerville, OH: Am. Ceram. Soc, pp. 538-554. McHale, A. E., Scott, R. S. (1986), J. Am. Ceram. Soc. 69(11), 827. McKinnon, I. M., Reuben, B. G. (1975), J. Electrochem. Soc. 122(6), 806. McMeeking, R. M. (1986), J. Am. Ceram. Soc. 69, C-301. McMurtry, C. H., Bocker, W. D. G., Seshadri, S. G., Zanghi, J. S., Gamier, J. E. (1986), Am. Ceram. Soc. Bull. 66, 325. Meerson, G. A., Kiparisov, S. S., Gurevich, M. A. (1966), Sov. Powder Metall. Met. Ceram. 5(3), 223. Mehrwald, K.-H. (1992), Ceram. Forum Int./Ber. Dtsch. Keram. Ges. 69(3), 72.

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Yamada, O., Miyamoto, Y, Koizumi, M. (1985), Am. Ceram. Soc. Bull. 64(2), 319. Yuriditsky, B. Y. (1990), Refractory Mater. Hard Mater. 3, 32. Zakhariev, Z., Radev, D. (1988), J. Mater. Sci. Lett. 7, 695. Zdaniewski, W. A. (1987), J. Am. Ceram. Soc. 70(11), 793.

General Reading Binder, F. (1975), Radex-Rundschau 4, 531. Clougherty, E. V., Pober, R. L. (1964), Nucl. Metall 10, All. Emin, D., Aselage, T., Beckel, C. T., Howard, I. A., Wood, C. (Eds.) (1986), Boron-Rich Solids. New York: Am. Inst. Phys. Fluck, E. (Ed.) (1986), Gmelin Handbook of Inorganic Chemistry, Si, Suppl. Vol. B3: Silicon Carbide, Part 2. Berlin: Springer. Freer, R. (Ed.) (1990), The Physics and Chemistry of Carbides, Nitrides and Borides. Dordrecht: Kluwer. Matkovich, V. I. (Ed.) (1977), Boron and Refractory Borides. Berlin: Springer. Post, B., Glaser, F. W, Moskowitz, D. (1954), Acta Metall. 2, 20. Thevenot, F. (1990), /. Eur. Ceram. Soc. 6, 205.

Recommended Periodicals Planseeberichte fur Puhermetallurgie, Ortner, H. M. (Ed.), Reutte: Plansee-Tizit. Journal of Less-Common Metals, since 1992: Journal of Alloys and Components, Lausanne: Elsevier Sequoia. Raub, C. (Ed.). Journal of Hard Materials, Brookes, C.A., Field, X E., Warren, R. (Eds.). Abingdon: Carfax.

5 Glass-Ceramics Bruce Aitken and George Beall Corning Glass Works, Research and Development Division, Corning, NY, U.S.A.

List of 5.1 5.2 5.2.1 5.2.2 5.2.3 5.3 5.3.1 5.3.1.1 5.3.1.2 5.3.1.3 5.3.2 5.3.2.1 5.3.2.2 5.3.2.3 5.3.2.4 5.3.2.5 5.3.3 5.3.3.1 5.3.3.2 5.3.4 5.3.4.1 5.3.4.2 5.3.4.3 5.3.4.4 5.3.5 5.3.5.1 5.3.5.2 5.4 5.4.1 5.4.2 5.4.3 5.4.4 5.4.5

Symbols and Abbreviations Introduction Nucleation and Crystallization of Glass-Ceramics Theoretical Considerations Practical Considerations Examples Classification by Chemical Composition Silicate Glass-Ceramics Lithium Silicates Calcium Silicates Magnesium Silicates Aluminosilicate Glass-Ceramics p-Quartz Solid Solution (3-Spodumene (Keatite) Solid Solution Indialite (Hexagonal Cordierite) Nepheline Other Aluminosilicates Fluorosilicate Glass-Ceramics Mica (Sheet Silicates) Chain Silicates Phosphate Glass-Ceramics Apatite BPO 4 NZP SiP 2 O 7 Oxide Glass-Ceramics Spinel Perovskite Microstructure Dendritic Ultrafine Grained Cellular Membrane Relict House-of-Cards

Materials Science and Technology Copyright © WILEY-VCH Verlag GmbH & Co KGaA. Allrightsreserved.

269 270 270 271 272 274 276 276 276 277 277 278 278 279 280 280 280 280 281 283 285 285 286 286 286 287 287 287 288 288 289 290 290 290

268

5.4.6 5.4.7 5.4.8 5.5

5 Glass-Ceramics

Acicular Interlocking Coast-and-Island Lamellar-Twinned References

291 292 293 294

List of Symbols and Abbreviations

List of Symbols and Abbreviations a, c AG h H / k n ns nv t T 7^

crystal axes molar free energy change upon crystallization Planck constant enthalpy of fusion steady state nucleation rate in a one-component system Boltzmann constant composition variable steady state nucleation rate per unit volume of the epitaxial phase number of formula units per unit volume of liquid temperature in °C absolute temperature melting temperature

Vm x

molar volume of the crystal stoichiometric variable

£ rj A v a i

crystal growth rate viscosity diffusion j u m p distance vibrational frequency surface tension between crystal a n d liquid time

AVC Crb. FKR NZP r.e.m. TTT

automatic viscosity control cristobalite fluorrichterite NaZr 2 (PO 4 ) 3 replica electron micrograph transformation-temperature-time

269

270

5 Glass-Ceramics

5.1 Introduction The development of glass-ceramics is a recent advance in the science of materials. The dramatic growth in applications for these novel materials since the serendipitous discovery, some thirty years ago, of internal nucleation and crystal growth in lithium silicate glass (Stookey, 1985), is a testament to their usefulness and great versatility in a wide range of applications. Glass-ceramics are polycrystalline solids prepared by the controlled crystallization of glass. They are generally well over 50% crystalline by volume and are fine-grained with crystal sizes below 10 jam. A key feature of glass-ceramics is the maintenance of shape of a previously-formed glass article. This is most effectively achieved through internal nucleation and growth of crystals. There are several important requirements for choice of a glass-ceramic system. The composition must form a glass with adequate viscosity at the liquidus to allow shaping of the required glass article. Internal nucleation must be efficient, in order to produce a fine-grained body, and to avoid the adverse effects of directional crystallization from the glass surface. Crystal growth upon the nuclei must also be controlled to avoid large crystals whose grain boundaries frequently act as planes for ease of fracture propagation. In order to maintain the shape of the original glass article, deformation through gravitational sag or warpage due to volume changes during crystallization in a thermal gradient must be controlled. Glass-ceramics have significant advantages over traditional powder-processed ceramics. One is in the flexibility and ease of forming afforded by high speed processes such as rolling, pressing, blowing, and drawing. A total lack of internal

porosity is an important characteristic of glass-ceramics. The uniformity of microstructure and reproducibility of properties which depend on structural consistency is another major advantage resulting from the homogeneous nature of the melting process. The ability to produce unique properties inherent in extremely finegrained crystalline materials is also important. For example, transparency can be achieved in glass-ceramics from a combination of efficient nucleation and sluggish crystallization at high viscosities resulting in crystallites smaller than the wavelength of visible light. Also, homogeneous, low thermal expansion characteristics can be achieved because the stresses accompanying crystal anisotropy are minimized by the fine-grained nature of the crystallites. There are manufacturing advantages in the process economy associated with high volume glass making. Also, any defects present in the glass can be observed prior to crystallization allowing simple reject inspection. Although the published literature on glass-ceramics is not as extensive as that for glasses, for additional information the interested reader is directed to the books by Strnad (1986) and McMillan (1979).

5.2 Nucleation and Crystallization of Glass-Ceramics The properties of glass-ceramics are controlled by the physical properties of the crystalline phases developed in the glass upon heat treatment and by their microstructure - the textural relationship between the crystalline phases and the residual glass. The uniformity and reliability of these properties in glass-ceramics is a consequence of the uniform grain size of the crystalline phases. An important prerequi-

5.2 Nucleation and Crystallization of Glass-Ceramics

site, therefore, to the formation of glass-ceramics is efficient nucleation of the crystalline phases. Accordingly, the heat treatment (ceramming) of glasses to produce a glass-ceramic typically involves two or more steps: a lower temperature step to induce nucleation, and one or more higher temperature treatments to promote growth of the crystalline assemblage and to develop the desired microstructure. 5.2.1 Theoretical Considerations

Various workers have attempted to derive a mathematical model for the processes of nucleation and crystal growth. For example, James (1982) has derived the following expression for the steady state nucleation rate, /, in a one-component system:

nvkT I = -—^r-expl

-

3AG2kT

(5-1)

where nv is the number of formula units of crystal per unit volume of liquid, T is the absolute temperature, I is the diffusion jump distance, rj is the viscosity, a is the surface tension between crystal and liquid, vm is the crystal's molar volume, AG is the molar free energy change upon crystallization, and k is Boltzmann's constant. This relationship is strictly applicable to the case of homogeneous nucleation, i.e. where crystallization occurs within a homogeneous liquid without addition of foreign particles. Homogeneous nucleation, however, is a relatively rare phenomenon, occurring in only a few glasses, such as Li 2 Si 2 O 5 , BaSi 2 O 5 , and Si 2 P 2 O 7 , whose composition is the same as that of the crystallizing phase. No glass-ceramic systems of industrial importance are known to nucleate homogeneously. In most glass-ceramic systems, internal nucleation is heterogeneous and occurs by

271

the epitaxial growth of the dominant crystalline phase upon nuclei of an earlierformed phase. The latter is most commonly a relatively refractory and/or insoluble phase, such as rutile, anatase, ZrO 2 , ZrTiO 4 , Cr 2 O 3 , or one of the noble metals, but can also be the exsolved globules of an inmiscible glass. As a result, "nucleating agents" or "nucleants" such as TiO 2 , ZrO 2 , P 2 O 5 , Au, or Ag are specifically included as essential components in the bulk composition of most commercial glass-ceramics. Nevertheless, the process of heterogeneous nucleation is governed by essentially the same parameters that affect homogeneous nucleation, and, as a result, the equations describing heterogeneous nucleation have the same form as the above, but with ny replaced by ns, the number of formula units per unit volume of the epitaxial phase in contact with the nucleant, and with a replaced by the surface tension between the epitaxial phase and the nucleant. The latter is a measure of the degree of lattice mismatch between the nucleant and crystallizing phase, and, therefore, the effectiveness of heterogeneous nucleation depends in part on the structural relationship between nucleant and epitaxial phase. Although exact evaluation of the nucleation rate equation is not possible due to the lack of relevant data, this equation can be used as a crude guide for adjusting the composition and/or heat treatment of a glass-ceramic to achieve efficient internal nucleation. For example, the nucleation rate is expected to increase as AG becomes large. Although AG is largely beyond experimental control, introduction of components which preferentially enter into solid solution with the crystalline phase may lower its free energy relative to the liquid, thus increasing AG and, hence, the nucleation rate. The rate equation further

272

5 Glass-Ceramics

suggests that increasing viscosity will lower the nucleation efficiency, presumably due to impeded transport of nutrients to the nucleus. Thus reducing the viscosity at the optimum nucleation temperature is desirable, although in practice this is limited by sagging of the material during the nucleation hold. Finally, the presence of the factor a 3 in the above equation indicates that lowering the interfacial energy should have the largest effect on increasing nucleation efficiency. This might be accomplished by variations in glass composition, for example through the addition of small amounts of WO 3 or MoO 3 , which components are known to be effective in reducing surface tension. The rate of crystal growth is also governed by parameters similar to those used in the description of nucleation. This can be illustrated using an equation derived by Jackson (1967) for continuous growth by random attachment of atoms to surface sites:

hv

HAT

£ = 6nX2rjkT T exp m

H

-

(5-2)

The rate of crystal growth £ is, in this description, dependent on the enthalpy of fusion H, the diffusion jump distance X, the viscosity r\, the vibrational frequency v, and AT, the temperature difference between the melting temperature Tm and the growth temperature T Although the parameters governing nucleation and crystallization are similar, the dependence of the nucleation rate and the crystal growth rate on these parameters is not. Consequently, nucleation and crystal growth rates generally peak at distinct temperatures, with the maximum for crystal growth occurring at a higher temperature than that corresponding to nucleation (for an illustration of this effect, as well as a more complete treatment of the theoretical

basis of nucleation and growth, the interested reader is referred to Chap. 3 by Scherer in Vol. 9 of this Series). The heat treatment of a glass to form a glass-ceramic therefore typically includes at least two steps. The first of these is the nucleation hold: a soak or gradual heating ramp at relatively low temperature, usually about 50 to 100 °C above the annealing point of the glass. Following the nucleation hold, the temperature is raised rapidly to that of the crystallization step, at which point the nucleated glass is heated isothermally or at a slow rate until crystal growth is complete and the desired microstructure attained. 5.2.2 Practical Considerations In actual practice, the existing mathematical models have proven to be of little utility in determining the optimum conditions for the efficient internal nucleation of glass. Thus compositional adjustments, including the selection of appropriate nucleants, as well as changes in the temperature and time of heat treatment steps have relied mainly upon empirical observations. Nevertheless, it is possible to infer an experimental time-temperature profile for ceramming by controlling the apparent viscosity of a heated glass within a specified range, typically 109 to 10 11 N s m " 2 . An experimental automatic viscosity control (AVC) curve for a phosphate glass-ceramic is shown in Fig. 5-1. The viscosity of crystallizing glass should be held below l O ^ N s m ^ t o allow viscous flow to release stresses caused by differential crystallization and thereby prevent fracturing. The lower limit of 109 N s m " 2 is due to the need to avoid gravitational sag, which can lead to unacceptable distortion if the viscosity of the residual glass becomes too low.

5.2 Nucleation and Crystallization of Glass-Ceramics

273

CONTROL VISCOSITY = 1 x 1010 N • s • m"2

500

During the crystallization hold, distortion can arise not only from gravitational sag of the glass, but also from thermal gradients across the article, which can cause one portion to crystallize before the rest. As most crystalline phases are denser than the precursor glasses, shrinkage of several percent is typical and must be accommodated uniformly throughout the article. This is particularly true of massive glass bodies, which are slow to heat in the central portions because of their low thermal conductivity. Furthermore, exothermic effects can be severe in large articles for the same reason: thermal waves due to the crystallization of massive articles can cause the central portion to become up to 50 °C hotter than the other areas of the ceramming furnace. In view of the typical temperature regime, the heat treatment of glass to produce glass-ceramics can be described as subsolidus crystallization. The expected crystalline phases in glass-ceramics, therefore, are those of the equilibrium subsolidus assemblage appropriate for the bulk composition of the precursor glass and the temperature of the crystal growth step. However, in many glass-ceramic systems, the crystalline phases observed are metastable so that, with glass rather than a

Figure 5-1. Experimental automatic viscosity control curve for a phosphate glass-ceramic.

melt as the initial state, it is possible to form solid phases which never develop under conditions of "equilibrium crystallization". Perhaps the best example of this phenomenon is the precipitation of p-quartz solid-solutions from lithium aluminosilicate glasses when these are cerammed at about 900 °C for a relatively short time. (3-Quartz is not only metastable at this temperature, it also has no thermodynamic stability, i.e. this phase is not a member of any equilibrium assemblage at any temperature for these bulk compositions. Prolonged heating at 900 °C, or raising the ceram temperature, causes the P-quartz glass-ceramic to invert to a stable assemblage containing P-spodumene solidsolution, as illustrated by Fig. 5-2 a. Nevertheless, the early formed p-quartz glassceramics persist indefinitely when cooled to room temperature and such glass-ceramics can withstand indefinite thermal cycling between room temperature and 900 °C without inverting to a p-spodumene glass-ceramic. A convenient technique for displaying the relationship between metastable and stable phases for a given glass-ceramic composition is the use of a "TTT" diagram, which plots phase transformation boundaries as a function of temperature

274

5 Glass-Ceramics

you

V

900

9

(3 SPODUMENE SS /3 QUARTZ SS + /3 SPODUMENE SS

^^c^rr——

*n8A4 0

o

S.

CL

/3 QUARTZ SS

780 GLASS

•

,

f3 QUARTZ SS

720

1600

1 ' 1 ' 1 ' I

GLASS

-

^S^

1 15

J>^ T V ~ ""

M

1

1200

1 10 TIME (h)

t,

1400-

o

(a)

^

T

-

r^—^-^ K ^ ^ X .

(

— "

-

1000-

800-^L

^

-

^

^

^

^

^

*2£ff-s;

^

"

P

(b) 1 O.I

1

1.0 —^

1

10

1 100

•

^

^

*

Figure 5-2. (a) Time-temperature metastable phase diagram for the glass-ceramic composition SiO2 65 wt.%, A12O3 23 wt.%, Li2O 3.8 wt.%, MgO 1.8 wt.%, with excess TiO 2 2 wt.%, ZrO 2 2 wt.%, and As 2 O 5 1 wt.% (after Beall and Duke, 1969). (b) Crystallization in MgO • A12O3 • 3SiO 2 glass with addition of ZrO 2 , depicted as TTT diagram. QP (s.s.): solid solution of |3-quartz, K: cordierite, P: Mg-petalite, S: spinel, C: cristobalite, M: mullite, ZT: tetragonal ZrO 2 , ZM: monoclinic ZrO 2 , ZS: zircon, Q: phase similar to a-quartz, tx and tg: liquidus and glass-transformation temperatures (after Conrad, 1972).

r(h)

and time. Figure 5-2 a is a rather simple example for a multicomponent lithium aluminosilicate glass-ceramic nucleated with zirconium titanate, where the oxide nuclei separation temperatures and times were difficult to measure. A more complete TTT-curve was developed by Conrad (1972) for a simpler composition MgO • A12O3 • 3SiO2 with the addition of 6% ZrO 2 (Fig. 5-2 b). The typical C-shaped curves of metastable and stable phases are shown. This simple fourcomponent glass shows no fewer than

eight metastable phases (glass, P-quartz solid solution, a-quartz solid solution, Mgpetalite, spinel, mullite, tetragonal and monoclinic zirconia), as well as the stable assemblage cordierite, silica (cristobalite over the main thermal range), and zircon. 5.2.3 Examples As noted above, a good example of a glass that displays homogeneous nucleation is BaSi 2 O 5 . Heat treatment of barium disilicate glass by nucleating at 700 °C

5.2 Nucleation and Crystallization of Glass-Ceramics

for one hour and crystallizing at 850 °C for one hour suffices to convert this material to a fine-grained glass-ceramic consisting of a mixture of dendritic a-BaSi2O5 crystals and residual glass (MacDowell, 1965). During the nucleation hold, submicrometer, spherulitic nuclei of 0c-BaSi2O5 develop randomly throughout the glass, which has remained homogeneous up to the nucleation temperature with no evidence of liquid-liquid phase separation. The commercial lithium aluminosilicate glass-ceramics based on phases with either the P-quartz or P-spodumene structure are good examples of heterogeneous nucleation by a well-dispersed insoluble phase (Beall, 1986). In this case, the nucleating agent TiO 2 or the combination of TiO2 + ZrO 2 is deliberately added to the base glass. Ceramming is accomplished by subjecting the glass to a nucleation hold at about 800 °C, followed by a crystallization hold at about 900 °C (P-quartz glass-ceramic) or 1100°C (P-spodumene glass-ceramic). During the nucleation hold, the spherical droplets of an exsolved Ti-rich liquid phase crystallize to form a uniform dispersion of exceedingly fine-grained (Ce4 + + Ag° By subjecting the exposed glass to a nucleation hold, the silver particles coalesce to the point where they can serve as the substrate for the subsequent crystallization of dendritic lithium metasilicate (Li2SiO3). By using a mask during the exposure step, nucleation and, hence, later crystallization can be confined to selected areas of the glass. Heterogeneous nucleation in glass-ceramics can take place on substrates other than insoluble crystalline phases. In the case of mullite glass-ceramics, aluminarich droplets separate from the siliceous matrix as the precursor aluminosilicate glass is quenched from the melt (MacDowell and Beall, 1969). Heat treatment of this phase-separated glass at 950 °C or above causes the aluminous droplets to crystallize to mullite. Thus, the physical surface between the two immiscible glasses acts as the nucleation site.

276

5 Glass-Ceramics

5.3 Classification by Chemical Composition Class-ceramics are most conveniently classified by their bulk chemical composition and more particularly by the composition of the major crystalline phase. The broadest classification includes silicates, phosphates, and oxides. Silicates can be further subdivided into simple silicates, aluminosilicates, and fluorosilicates. 5.3.1 Silicate Glass-Ceramics Simple silicate glass-ceramics are composed primarily of alkali and alkaline earth silicate crystals whose properties dominate that of the glass-ceramic. The most important are the lithium silicates, both lithium metasilicate (Li2SiO3) and lithium disilicate (Li2Si2O5), enstatite (MgSiO3), diopside (CaMgSi2O6), and wollastonite (CaSiO3). 5.3.1.1 Lithium Silicates Lithium silicate glass-ceramics consist of two composition groups, both of commercial importance. The first, nucleated with P 2 O 5 , develop high expansion glassceramics which match the thermal expansion of several nickel-based superalloys, and are used in a variety of high-strength hermetic seals, connectors, and feedthroughs (Headley and Loehman, 1984). The second group, photosensitively nucleated by colloidal silver, produce a variety of chemically machined materials which are useful as fluidic devices, display screens, lens arrays, and other patterned devices. Lithium disilicate glass-ceramics nucleated with P 2 O 5 are characterized by high body strength, 140-210 MPa, good fracture toughness, ~ 3 MPa • m 1/2 , and moderate to high thermal expansion coef-

ficient, 80-130 x 10" ^C"" 1 . The compositions typically comprise 70-85 weight percent SiO 2 , 10-15 Li 2 O, 3-10 A13O3, 1-5 P 2 O 5 as well as a minor amount of other modifiers including K 2 O, Na 2 O, CaO and ZnO. The glasses phase separate on heat treatment and lithium orthophosphate (Li3PO4) precipitates as the first crystal phase. Lithium metasilicate and/or lithium disilicate then form, the latter predominating with further heat treatment. Cristobalite and P-spodumene are often auxiliary phases, and residual glass is usually present in excess of 15 volume percent. The microstructure consists of tabular interlocking lithium disilicate crystals typically from 1 to 10 |im in diameter encased in residual glass and other crystalline phases. The randomly oriented tabular crystals appear to deflect or blunt cracks in such a way as to impede crack growth, thus accounting for the high strength and toughness. Dielectric properties are surprisingly good, with dielectric constants below 6 and loss tangents below 0.01 over a wide range of temperature and frequency. Photosensitive lithium silicate glass-ceramics contain metals, namely 0.1% Ag and 0.001% Au, which can be precipitated thermally after ultraviolet sensitization. The metallic colloids so produced nucleate a dendritic form of lithium metasilicate which is far more easily etched in hydrofluoric acid than is the parent glass, allowing an irradiated pattern to be selectively removed. The resulting photo-etched glass can then be flood exposed to ultraviolet rays and heat-treated beyond the temperature region of metastable lithium metasilicate. The stable lithium disilicate phase is then produced and the resulting glass-ceramic is strong (~140 MPa), tough, and faithfully replicates the original photoetched pattern.

277

5.3 Classification by Chemical Composition

Table 5-1. Silicate glass-ceramic compositions. wt.%

Fotoform/ Fotoceram Corning 8603

SiO 2 Li 2 O MgO CaO A12O3 Na 2 O K2O Ag Au CeO 2 SnO 2 Sb 2 O 3 B2O3

79.6 9.3 — — 4.0 1.6 4.1 0.11 0.001 0.014 0.003 0.4 — —

P2O5

Major crystal phases

Li 2 O-SiO 2 G.E./Sandia

71.8 12.6 — — 5.1 _ 4.8 — — — — — 3.2 2.5

MgO-SiO 2 Corning

58.0 0.9 25.0 — 5.4 —

ZnO MnO Fe 2 O 3 S ZrO.

lithium lithium disilicate, metasilicate, lithium metasilicate, lithium disilicate cristobalite

Specific applications include magnetic recording head pads, fluidic devices, cellular faceplates for gas-discharge displays, and charged plates for ink-jet printing. 5.3.1.2 Calcium Silicates For over two decades, inexpensive glassceramics based on blast furnace slags have been produced in Eastern Europe. Referred to as "slag-sitall" in the Soviet Union, these glass-ceramics presently constitute the largest volume application for crystallized glass. The most popular slag-sitall is a white product manufactured in the U.S.S.R. from low-iron (4 have disordered Si/Al distributions and are truly isostructural with P-SiO2. Li-rich compositions from

the latter range have been referred to as "virgilite". P-Quartz glass-ceramics are made by crystallizing TiO2- or TiO 2 + ZrO2-nucleated Li aluminosilicate glasses at 850-900 °C (Beall and Duke, 1969). Despite the metastability of P-quartz, these glass-ceramics persist indefinitely and can survive repeated thermal cycling provided that a maximum temperature of about 900 °C is not exceeded. If heated above 900 °C, P-quartz will transform to P-spodumene. A more general compositional representation of the P-quartz solid solution is (Li 2 ,R)O- Al 2 O 3 -«SiO 2 , where R is a small divalent cation, typically Mg or Zn. Replacement of Li by Zn and, in particular, Mg results in an increase in the thermal expansion coefficient of P-quartz. Thus, whereas the expansion coefficient of a pure Li P-quartz is about -15 x 10 " 7 °C ~ * from 25 to 300 °C, Mg- and/or Zn-substituted varieties can have zero or very small positive expansion coefficients. In commercial glass-ceramics, advantage is taken of the compositional flexibility of p-quartz. In the first place, Mg and Zn are included to produce materials with near zero thermal expansion and, consequently, excellent thermal shock resistance. Furthermore, n in the above formula is selected to range between 6 and 8, because the high silica content of these compositions furnishes a melt that is sufficiently viscous to be rolled, pressed, blown, and vacuum formed. The combination TiO 2 + ZrO 2 has proven to be the most effective nucleating agent in precipitating p-quartz from lithium aluminosilicate glasses. Heat treatment of glasses so nucleated yields ZrTiO 4 , a phase with the fluorite structure, which serves as the substrate for the subsequent nucleation and epitaxial growth of P-quartz crystallites. P-Quartz crystals with grain sizes on the order of 60 nm can be

5.3 Classification by Chemical Composition

produced if the nucleant concentration is on the order of 4 weight percent, resulting in a transparent glass-ceramic. The combination of transparency, low thermal expansion, optical polishability, and strength greater than glass has generated a multitude of applications for P-quartz glass-ceramics, including see-through cookware, telescope mirror blanks, woodstove and fire windows, infrared-transmitting range tops, and optically stable platforms, including ring-laser gyroscopes.

279

from heat treatments at temperatures in excess of 1000°C (Stookey, 1959). Glass-ceramics containing p-spodumene are coarser-grained than their P-quartz analogues. Grain sizes are typically in the range of 1-2 |im and, as a result, these glass-ceramics are opaque. If TiO 2 is used as a nucleating agent instead of the combination TiO 2 + ZrO 2 , the phase transition from P-quartz to P-spodumene, which occurs between 900 and 1000 °C during the ceramming process, is accompanied by crystallization of rutile, yielding a glass-ceramic with a high degree of opacity. As with p-quartz glass-ceramics, the thermal expansion of these materials is very low and can be tailored to the desired value by adjusting the Li/Mg ratio or the total silica content (cf. Fig. 5-3). Corningware is a good example of a P-spodumene glass-ceramic, and is formed by crystallizing a TiO2-nucleated aluminosilicate glass at a maximum temperature of 1125°C. This material is highly crystalline (>93vol.%) containing P-spodumene as the dominant phase and minor amounts of spinel, rutile, and residual siliceous glass. The coarse-grained, interlocking microstructure of p-spodumene crystals gives this material its relatively

5.3.2.2 p-Spodumene (Keatite) Solid Solution p-Spodumene is a tetragonal phase that is isostructural with keatite which, like P-quartz, is a polymorph of SiO 2 . p-Spodumene is therefore characterized by the same stoichiometry as P-quartz, although the compositional range of the solid solution is more restricted, with n ranging from 4 to 10. P-Spodumene glassceramics can be made from the same glasses that yield p-quartz glass-ceramics simply by altering the heat treatment: pquartz glass-ceramics are formed by crystallizing at or below 900 °C, whereas Pspodumene glass-ceramics are obtained

n= 4

0.28 Co 0

101

en
the electrical and chemical forces may be combined in the

304

6 Diffusion in Ceramics

6.3.3 Diffusion as a Random Walk

electrochemical potential

The transport coefficients, Lik, can be related to experimentally measurable quantities. Their value is to enable a complete description of mass transport to be made under a general set of driving forces and with no interactions between different particle fluxes being omitted (Howard and Lidiard, 1964). In simple cases the coefficients can be expressed in terms of measurable diffusion coefficients or electrical conductivities (Wagner, 1975). Often it is convenient to ignore the cross term (i.e., put Lik = 0 for i =# /c), in which case

In solids the atoms take up reasonably well-defined positions. Mass transport occurs by atoms making transitions between these positions in such a way that the time of transit is much less than the residence time at any particular position. Thus, diffusion can be thought of as occurring by particles hopping in a random way on a lattice of sites distributed in space. If an individual atom is labelled its motion can be followed and related to the phenomenological tracer diffusion coefficient. For a cubic lattice (i.e., diffusion is isotropic) the tracer diffusion coefficient is given by (Lidiard, 1957)

Jt~ -BtC^

D*=\fTr2

rjt = fit -\- zte D*. Comparing Eqs. (6-18) and (6-21) shows that, for the vacancy mechanism, DY = a% w 0

(6-22)

The tracer self-diffusion coefficient is related to the partial diffusion coefficient by Df = f Dt for pure compounds having only small deviations from stoichiometry (the thermodynamic factor in Eq. (6-15) being unity in such a case). 6.3.5.2 Tracer Solute Diffusion

There are two experimental regimes which must be considered for diffusion of a solute (or impurity) tracer. When the solute is present only as a very small concentration of diffusing tracer the

point defect populations will be the same as in the pure host ceramic. However, jump rates of atoms in the neighbourhood of the solute atom will be different. The case of both solute and host diffusing by a vacancy mechanism in an f.c.c. lattice has been treated using a five-frequency model (Fig. 6-3). The jumps of frequency w3 lead to dissociation of the solute and vacancy whereas those of frequency w4 lead to association. Their combination can be accounted for by the enthalpy of association, /zA, between the vacancy and solute (with hA being negative for an attractive interaction between them). The tracer diffusion coefficient in the dilute limit then becomes - n *2 = a w 2 / 2 [V]exp

-

(6-23)

where the subscript 2 denotes the solute atom. The correlation factor, / 2 , is now a complicated function of the jump frequencies in Fig. 6-3. The maximum value of f2 is unity and is approached when w2w0, f2 tends to wo/w2 and can be very small. This corresponds to a situation in which

Solute Figure 6-3. The "five frequency model" for solute diffusion in an f.c.c. lattice. The other exchange frequencies are w0 (no solute present) and w4 (the reverse of w3). (After Howard and Lidiard, 1964.)

6.3 Theory of Diffusion

the solute and vacancy spend most of their time repeatedly exchanging places. (In this discussion we have assumed that w1 « w3 «w 0 .) Equation (6-23) indicates that the activation energy for tracer solute diffusion, Q2, in the dilute limit, has extra contributions from hA and the temperature dependence of / 2 , in addition to the contributions from defect concentration and defect-solute exchange. When the solute is present as a significant dopant (of uniform concentration) as well as a tracer (of non-uniform concentration) the influence of the solute on the point defect population must be taken into account.

307

same valency [e.g., a solid solution (A, B) O], the interdiffusion coefficient is given by (Manning, 1968) n AB

where yB is the activity coefficient of B in the solid solution. Expressions such as Eq. (6-25), in which the component with lower mobility tends to dominate the result, are said to be of Nernst type. When the interdiffusing ions in an ionic conductor have different valency the more general form of Eq. (6-25) is (Cooper and Heasley, 1966) , 91nyB

6.3.5.3 Interdiffusion

Interdiffusion occurs when two components of a solid solution migrate in opposite directions down their coupled chemical potential gradients. A typical example would be the homogenising of two substitutional metal ions in a metal oxide solid solution. The simplest case occurs when the interdiffusing species have the same valency and the other component (oxygen in this example) is effectively immobile. Since electrical neutrality must be maintained, an internal electric field (Nernst field) will be generated to couple the transport of electrically charged particles. This is known as ambipolar diffusion and the resulting electrical potential is known as the diffusion potential. The interdiffusion is defined in the laboratory frame of reference by the equations JA (laboratory) = — DAB dx =

^AB —~ = ~ JB (laboratory)

(6-24)

If the ceramic is an ionic conductor and the interdiffusing atoms A and B have the

In metallic and semiconducting systems (or for uncharged particles) the electronic carriers redistribute themselves so as to prevent the generation of a diffusion potential. Provided that there are sufficient internal sources and sinks through which the point defect populations can maintain local equilibrium, the interdiffusion coefficient is given by (6-27)

This equation, in which the more mobile component dominates, is called a Darken type of interdiffusion equation. Even in metallic and semiconducting ceramics strong coupling between the interdiffusing fluxes will occur if there are no internal sources and sinks for point defects. The resulting requirement to preserve all the lattice sites couples the fluxes in a similar way to the electric field in ambipolar diffusion and the final expression for interdiffusion will be of the Nernst type. However, for interdiffusion in dilute solid solutions ([B] -> 0) of all systems the interdiffusion

308

6 Diffusion in Ceramics

coefficient tends to the same limit (6-28) which is equivalent to Eq. (6-23). More complicated situations arise if diffusion of the third component cannot be neglected (Allnatt and Lidiard, 1987). A typical example of such a case is when Ca and Zr interdiffuse in zirconia where the tracer diffusivities of the two cations are both much slower than that of oxygen. Interdiffusion can be approached alternatively in an atomistic formalism rather than the phenomenological one. A common example of interdiffusion in ceramics arises for a trivalent solute in a divalent host. If diffusion is by a vacancy mechanism the pair association model of Lidiard (1957) can be used to provide an atomistic description. In this model the solute (B2O3) in AO) can only diffuse if it is associated with a vacancy on a neighbouring site, leading to Dg = Dcp, where p is the fraction of solute atoms associated into vacancy-solute complexes and Dc the diffusion coefficient of the complex. Dc may be formulated in terms of the jump frequencies in Fig. 6-3. Thus the thermodynamic factor in Eq. (6-28) is equivalent to the variation of p with concentration of solute. 6.3.5.4 Chemical Diffusion

Most ceramics are compounds and therefore even a pure ceramic can support a gradient in the chemical potentials of its two components. In an oxide ceramic this is often established experimentally as a gradient in molecular oxygen activity. A gradient in oxygen activity will generate a gradient in composition through the point defect-forming reactions. Thus chemical self-diffusion may be regarded as interdiffusion between crystal components and

lattice defects (e.g., by placing two crystals of the same compound, but having different degrees of non-stoichiometry, in contact). The fluxes in the laboratory frame define the chemical diffusion coefficient, D, in the same way as for DAB in interdiffusion. Wagner (1975) has shown how, in a non-stoichiometric semiconducting oxide Mi +

33

+2c12)

'12

-c

(7-11)

(7-13)

X2

^22

5

and the c0- and stj are referred to as components of the stiffness and compliance matrices. Crystal symmetry can further reduce the number of independent components in the stiffness or compliance matrices. In cubic crystals, which constitute many ceramic materials (e.g., MgO and NaCl), there are

44 — -44

Table 7-1 gives the stiffness constants for some cubic crystals. In an isotropic material, such as a silicate glass or a polycrystalline aggregate, symmetry reduces the number of indepenent stiffness constants to two, with the ad-

Table 7-1. Independent elastic constants of ceramic single crystals and glasses. Symmetry

Ref.

Material (GPa)

(GPa)

79 70 83

15 20 22

(GPa)

(GPa)

(GPa)

Isotropic (glasses)

silica borosilicate soda-lime

Cubic

MgO MgAl 2 O 4 ZrO 2 CaF 2 NaCl ZnS ZnSe TiC

286 279 410 164 49 108 81 500

87 153 110 47 12 72 49 113

148 153 60 34 13 41 44 175

Hexagonal

A12O3 ZnO

465 210

124 121

233 43

563 211

117 105

Tetragonal

BaTiO 3

158

64

44

153

63

Trigonal

SiO 2

87

8

57

108

15

a e

(GPa)

17

Holloway (1973); b Ingel and Lewis (1988); c Landolt-Bornstein Tables (1984); d Gilman and Roberts (1961); Huntington (1958); f Bateman (1962); g Pisarenko et al. (1985).

349

7.2 Elasticity

ditional constraint imposed on Eqs. (7-12) and (7-13) of

In this case the isotropic Young's modulus, £, relating longitudinal stress and strain,

In general, the elastic response of a crystal depends on the loading direction, leading to orientation-dependent Young's moduli and shear moduli (Nye, 1957). In particular, the Young's modulus of a cubic crystal in a specific direction is given by

(7-15 a)

(7-19 a)

C4.4. — (en

—

(7-14)

c12)/2

a = Es is given by

B-±-

(7-15 b)

an

d °f a hexagonal crystal by 2

The isotropic Poisson's ratio, v, relating lateral to longitudinal strain under longitudinal stress, S2 —

(7-16 a)

—V81

is given by S

12

(7-16b)

V=

The isotropic shear modulus, G, relating shear stress and strain. T

= Gy

(7-17 a)

(writing atj and stj, i =f=j, as t and y, respectively) is given by G=

1 2(Sll-s12)

2(1+v)

(7-17 b)

and the bulk modulus, defined in Eq. (7-5) is given by K=

3(Sll

1 + 2s 12 )

3(1-2v)

(7-18)

which also pertains for cubic crystals. The stiffness constants of some amorphous, isotropic materials are given in Table 7-1. For hexagonal crystals (e.g., A12O3), trigonal crystals (e.g., SiO2) and tetragonal crystals (e.g., BaTiO3), more elastic constants are independent. Table 7-1 gives the independent stiffness constants for some crystals of these symmetries as well.

Sll(l-li)

+

(7-19 b)

+ 533/S + (2^3+544) ( 1 - / 1 ) / I where l{ are the direction cosines of the axis of loading relative to the directions for the cubic crystal, and l3 is relative to the [0001] direction for the hexagonal crystal. Figure 7-3 shows the variation of Young's modulus of some cubic crystals and some hexagonal crystals, using Eq. (7-19) and Table 7-1. Note that the variation for hexagonal crystals is symmetric for rotations about [0001], but that the variation for the cubic crystals is not symmetric for rotations about .

7.2.3 Elastic Moduli of Polycrystalline Ceramics A polycrystalline aggregate displays isotropic elastic responses representative of the weighted average of the anisotropic elastic constants of the constituent crystals. The weighting of the constants may be performed in different ways, producing bounds on the predicted polycrystalline moduli dependent on the assumptions used to model the distribution of stresses and strains in the polycrystal (Hashin and Shtrikman, 1962; Ingel and Lewis, 1988). For cubic crystals it is convenient to express the bounds on the Young's modulus in terms

350

7 Mechanical Properties of Ceramics

The uniform strain, or Voigt, bound for the polycrystalline shear modulus, is given by

[001]

(7-22 a)

G* =

and the uniform stress, or Reuss, bound, by 450

[100]

G* =

5GtG2

(7-22 b)

Bounds based on minimizing the potential energy or complementary energy of the solid are more restrictive than the uniform stress and strain bounds, and have been calculated by Hashin and Shtrikman (1962):

[0001]

(7-23a) 5

Gi-G [1120]

Figure 7-3. Variation of Young's modulus in the (010) plane for the cubic crystals MgO and ZrO 2 , and perpendicular to the [0001] direction for the hexagonal crystals A12O3 and ZnO.

of the bulk modulus (using Eqs. (7-13) and (7-18)): +2c12

(7-20)

and the two single-crystal shear moduli (using Eqs. (7-13) and (7-17)): '12

G2 = c 44

where

The polycrystalline Young's modulus is then given by (combining Eqs. (7-17) and (7-18))

AI 2 O 3

c12

- 6 j » 2 V (7-23 b)

(7-21)

E=

9XG* 3K + G*

(7-24)

where the shear modulus for the appropriate bound, G*, is chosen. Figure 7-4 plots measured polycrystalline Young's moduli for some cubic materials against the predicted bounds given above, using the data in Table 7-1 and Table 7-2. Agreement is evident in most cases. Table 7-2 also gives the measured polycrystalline Young's moduli for other non-cubic ceramics and glasses. 7.2.4 Elastic Moduli of Two-Phase Ceramics

Many ceramics are multiphase, and the elastic properties of such materials are rep-

351

7.2 Elasticity

resentative of the weighted average of the elastic constants of the constituent phases. As with single-phase polycrystalline materials the weighting of the constants may be performed in different ways to produce bounds on the moduli (Christenson, 1982, gives a good review). The simplest bounds are those assuming uniform strain or uniform stress in the solid. Hence, for a two phase material, the uniform strain, Voigt bound on the Young's modulus of the composite is given by EY ==

V

2

E2 + V1 Ei

(7-25 a)

and the uniform stress, Reuss bound by R

~

E±E2 V2 + E2

v,

(7-25 b)

where Ei,E2 are the Young's moduli of the constituent phases, and V±, V2 are the respective volume fractions. We note that these bounds represent materials in parallel and in series, respectively. Bounds calculated by Hashin and Shtrikman (1963) are once again more restrictive than the Voigt and Reuss bounds and are expressed in terms of the bounds on the effective bulk and shear moduli of the composite:

0 100 200 300 400 500 PREDICTED YOUNG'S MODULUS, E (GPa)

Figure 7-4. Plot of measured polycrystalline Young's moduli for cubic crystals vs. predictions based on Voigt, Reuss, and Hashin-Shtrikman bounds. The Hashin-Shtrikman bounds are shown as the shaded boxes, the Voigt-Reuss bounds as the open boxes. Nominal 10% uncertainty is assumed in the observed moduli.

lower bound suggesting some porosity in the composite in those cases. 7.2.5 Elastic Moduli of Porous Ceramics Many ceramic materials are frequently less than fully dense, in which case the second phase in the material is porosity which

Kf =

(7-26 a)

[6(Kt + 2 Gt) Vt]/[5 Gt (3Kt + 4 Gt)] where ij = 1,2. The bounds on the Young's modulus are then given by Eq. (7-24), using both G* and K* as appropriate. Figure 7-5 plots the measured Young's moduli of some composite ceramics as a function of the relative volume fraction of the phases, and compares the behavior with the bounds calculated above. The observations lie within the Hashin-Shtrikman bounds, although in some materials nearer to the

(7-26 b)

has zero modulus. A brief inspection of any of the bounds in Eqs. (7-25) and (7-26) shows that a porous material will have a lower modulus than a fully dense material. Figure 7-6 plots the Young's modulus of some ceramic materials as a function of the volume fraction porosity - the general decrease is evident. Only the Voigt and Hashin-Shtrikman upper bounds on the

352

7 Mechanical Properties of Ceramics

Table 7-2. Young's modulus of polycrystalline and amorphous ceramics. Material

E (GPa)

Silica glass Borosilicate glass Soda-lime glass MgO MgAl 2 O 4 ZrO 2 CaF 2 ZnSe ZnS TiC SiC

Ref.

74 61 74 305 258 220 160 69 98 430 435 393 300

BaTiO.

123

a

Holloway (1973);b Chung (1963);c Stewart and Bradt (1980); d Ingel and Lewis (1988); e Rice etal. (1980); f Freiman etal. (1975); g Marshall etal. (1982); h Ceramic Source (1990); * Cook (1985); j Material Data Sheet of Coors Porcelain Co. (1985).

J

Q O

0.0 0.2 0.4 0.6 0.8 1.0 0.0 0.2 0.4 0.6 0.8 1.0 VOLUME FRACTION SECOND PHASE, V2

Figure 7-5. Young's moduli of composite ceramics vs. volume fraction of the more rigid phase. The dashed lines show the Voigt and Reuss bounds and the solid lines the Hashin-Shtrikman bounds. Data from the collation of Shaw and Uhlmann (1971) (Co-WC), Binns (1962) (glass-Al2O3), Stock etal. (1979) (Cement-sand), and Lange (1975) (ZrO 2 -Al 2 O 3 ).

0.0 0.1 0.2 0.3 0.4 0.5 POROSITY, P

Figure 7-6. Young's modulus as a function of porosity for some ceramics. Data from Marlowe and Wilder (1965) (Y2O3), and the collations of Datta et al. (1989) (Si3N4), and Wang (1984) (A12O3). The solid lines are linear best-fits to the data.

Young's modulus can be calculated in this case (the Reuss and Hashin-Shtrikman lower bounds are zero). However, the infinite ratio of the moduli of the constituent phases means that the stress and strain distribution in the solid depends critically on the pore morphology chosen. Hence, there is no single model which appears capable of describing all the observations such as those shown in Fig. 7-6 as a function of the single parameter characterizing the volume fraction of the porosity. Dean and Lopez (1983) have carefully examined data on a wide range of materials, and the large number of semi-empirical expressions suggested for the Young's modulus, and conclude that the best-fitting equation is of the form E = E0(l-bP) (7-27)

7.3 Fracture

where Eo is the Young's modulus in the absence of any porosity, P is the volume fraction of porosity, and b is an empirical constant which characterizes, amongst other things, the pore morphology. Such linear fits are shown in Fig. 7-6. Dean and Lopez also make the point that the apparent concave-upward trends in the E — P data of A12O3 and Si 3 N 4 observed in some collations (see Fig. 7-6) may be an artifact caused by the wide range of materials (and hence pore morphologies) examined in such cases.

7.3 Fracture

353

Figure 7-7. Plot of Fappl (r) from Eq. (7-28), using n = 1 and m = 9 appropriate to an ionic solid, and Fc = F(rc). The separation rc is a critical extension beyond which the bond can no longer stably support an applied force, and rupture occurs.

7.3.1 Fracture at the Atomic Level

To consider brittle fracture at the atomic level we invoke the applied force-separation function Fappl(r% for a single atomic bond. Taking the negative of Eq. (7-2) we gain

nA *.«+!

mB

(7-28)

This function is shown in Fig. 7-7. It can be seen that there is a critical applied force, Fc, beyond which the interatomic bond can no longer sustain stably an increased extension. To evaluate the critical separation, r c , at which instability occurs (the extension at maximum force in Fig. 7-7), the condition dFaappl /dr = 0 is imposed on Eq. (7-28) to yield =1.22 for n = l,m = where Eq. (7-3) has been used. A material consisting of many bonds as described by Eq. (7-28) will thus require a strain of about 22% for homogeneous rupture of a plane of bonds.

Table 7-3 gives typically observed strength values for some common ceramics: a typical fracture strength of a ceramic material is about 400 MPa, whilst a typical Young's modulus is about 200 GPa (Tables 7-1 and 7-2). Observed strains at fracture for ceramics are thus of order 0.2%, clearly much less than that required to cause homogeneous separation of the interatomic bonds across the fracture plane. Hence, some strain (and stress) concentration mechanism must be acting in order to generate the requisite conditions for bond rupture, and hence macroscopic fracture, in real materials. Inglis (1913) showed that the stress, c tip , at the tip of an elliptical hole in a uniformly stressed solid (see Fig. 7-8) was given by

2c b

(7-30)

where aa is the applied stress, which is uniform at large distances from the hole, 2 c is the length of the major axis of the ellipse, and 2 b is the length of the minor axis. If we imagine the ellipse to be extremelyslender,

354

7 Mechanical Properties of Ceramics

Table 7-3. Strength, fracture resistance, and toughness values of ceramics. Material

Strength Fracture Toughness Ref. (MPa) resistance (MPam 1/2 ) (Jm~ 2 )

Glasses Soda-lime Fused silica Bulk Fiber

140

8

0.75

a

90 1000

8 8

0.75 0.75

b

7.3.2 Energy Balances in Fracture b

Polycrystals A12O3 1 = 3 um A = l l jim

1 = 25 urn MgO Y2O3 SiC Si 3 N 4 ZrO 2 Ca-PSZ Y-TZP BaTiO 3

7.3.2.1 Unstable Equilibrium: The Griffith Equation Scaling Relations

488 400 302 275 300 600 520

39 36 54 10 13 39 65

3.9 3.3 4.6 1.8 1.5 4.1 4.4

800 2200 124

500 125 10

10 5 1.1

300 170

60 51

2.5 1.8

c d d

c d e f 8

,h i,j

k k c

Glass-Ceramics Pyroceram Macor

neous fracture. Fracture is then seen as the sequential rupture of interatomic bonds, with only the stresses and strains near a crack tip approaching those required for instability as shown in Fig. 7-8 and Eq. (7-30).

1d

Although the Inglis analysis provides a mechanism for fracture, by the concentration of stress at crack tip bonds, the analysis allows no mechanics to be derived, as the stress developed is scale invariant: large and small cracks of the same aspect ratio (c/b) have the same crack-tip stress, and therefore would be expected to fail at the same applied stress. The connection between crack size and specimen strength, and the beginnings of the mechanics of

1, d

The strengths are those observed for polished bars or discs, the toughness and fracture resistance values are those for complete saturation of any microstructural toughening effects. 1 is the grain size. a Dabbs et al. (1982);b Dabbs and Lawn (1985);c Cook etal. (1985); d Cook et al. (1987); e Davidge (1979); f Cook and Pascucci, unpublished work; 8 Cook and Roach (1986);h McHenry et al. (1976); ! Marshall et al. (1983 b); j Trantina (1979); k Swain and Rose (1986); Fairbanks etal. (1986).

approximating a crack, such that c > b, the stress concentration at the tip can be appreciable. In ceramic materials cracks typically have dimensions of c ~ 10 |im, with openings of b ~ 25 nm, such that stress concentrations of approximately 1000 are obtained. Hence, the conditions for bond rupture are achieved for applied stresses well below those required for homoge-

i

i 4(2c/b)o- a

Figure 7-8. Schematic diagram of the stress field around an elliptical slit in a solid under uniaxial tension.

7.3 Fracture

fracture were made made by Griffith (1920). Griffith realized that the critical condition for the fracture of a specimen containing a crack is really a manifestation of a critical energy balance. The first half of the energy balance was the surface energy introduced into the system by the ruptured bonds on the crack surface. For a specimen containing a crack of dimension c under uniform applied stress 0 (Table 7-4). Determination of M or 2 y is made in each case by measurement of a critical value of load or stress needed to propagate the crack, and the crack length and specimen geometry. Glaesemann et al. (1987) used measurements of 2 y from the double cantilever beam geometry for soda-lime glass, and predicted the strength of glass bend-specimens containing carefully characterized elliptical surface flaws (and hence known xj/). The agreement with the experimentally observed strengths was excellent, as shown in Fig. 7-1 l b , reinforcing in quantitative detail the Griffith condition of Eq. (7-39). Table 7-3 gives the 2y values of some ceramic materials with homogeneous fracture resistance, measured using the geometries of Fig. 7-12.

Mechanical energy release rate, #

Unstable I//2(T2C/E Tension Double cantilever beam \l/2P2c2/(Ed3w2) Single edge-notched ij/2P2s2c/{Ed4w2) beam \l/2P2(2s + c)2/[E(s-cfw2] Compact tension Stable ij/2A2E/c Displacement Double cantilever beam i//2A2Eh3/c4 \j/2P2l(Ec3) Indentation \l/2P2/{Ecw2) Wedge Neutral Double cantilever beam i//2 M2/(E d3 w2) V P2 s2/(E d w4) Double torsion ij/2A2E/d Infinite slab The width of the specimen is w, the geometry parameter \j/ is given in Tada et al. (1973), Atkins and Mai (1985), or Fuller (1979). Specimen dimensions and loading configurations are given in Figs. 7-12, 7-13 and 7-15.

358

7 Mechanical Properties of Ceramics

librium position. The stability condition

DISPLACEMENT A

DCB

— P*) we have the usual P~1/3 dependence (Eq. (7-58)):

(a)

^

(7-66 a)

(b)

and in the small flaw limit (P 1) the toughness tends to &~0, and that in the large crack limit (c/S -» oo) to another invariant quantity (using Eq. (7-60))

Figure 7-30 plots the measured strengths of a series of alumina materials as a function of indentation load, normalized by the parameters in Eqs. (7-65) and (7-66 b). The definite ^?-curve tendencies of these materials are reflected in the ability of the model to describe the strengths - at low indentation loads the strengths become quite insensitive to the scale of the flaw used to initiate failure (compare the strength degradation with that of the untoughened ma-

(7-64) characterizing the saturation of the bridging process. Effect of Bridging on Specimen Strength For a stabilized (e.g., indentation) crack subjected to an applied stress in a material described by Eqs. (7-63) and (7-64), the strength as a function of indentation load may be derived by imposing the equilibrium instability condition as before. To do this it is useful to define the quantity P* =

(7-65)

'1O~3

10" 2 10" 1 10° 101 INDENTATION LOAD, P/P*

10 2

Figure 7-30. Strength vs. indentation load for A12O3 specimens containing Viekers indentation flaws. The solid line is a best fit to the data in accord with Eq. (7-67), the dashed lines are the asymptotes of Eq. (7-66) (data from Cook, 1987).

370

7 Mechanical Properties of Ceramics

terials of Fig. 7-26). The data of Fig. 7-30 may be used to predict successfully the maximum strength of such materials, as shown in Fig. 7-31. Ductile Particle and Fiber Reinforcement The behavior discussed above is simply one example of the way ligamentary bridging elements may toughen ceramics. The underlying general principle is that of energy dissipation caused by the deformation of the ligament imposed by increasing crack opening displacement at the ligament site. Explicit treatment of the energy balances during fractue is best handled by the path-independent J-integral (Rice, 1968), especially for steady-state crack propagation. Here we calculate the energy balances for a propagating crack with a ligamentary bridged zone, showing how such a zone manifests itself as toughening in an energy framework, and showing how various deliberately-added bridging elements in ceramics toughen on the basis of their constitutive equations for deformation.

The J-integral involves the integration of the strain energy density and tractions along paths beginning and ending on opposing crack faces. Making a circuit beginning at the crack mouth, around the exterior of the specimen, followed by return to the starting point traversing the crack surface, as shown in Fig. 7-32, leads to J. - J,, - Jo = 0

(7-68)

where J a is the contribution to the path from the applied loadings, JM the contribution from the superposed microstructural tractions, and J o the contribution from the interatomic bond rupture processes. Now, J a is simply ^ a = Jf^/E and j 0 = 2 y = ^Q2/E, and we are left with the evaluation of the contribution from the ligamented zone. For paths along the crack face there is no contribution from the strain energy and the J-integral is simply expressed in terms of the tractions exerted (Rice, 1968): J^= j

-T-(du/dr)ds-

c-b c-b

-

J -T'(du/dr)ds

(7-69)

c

where J i s the traction exerted on the crack faces in the bridged zone, u is the crack opening displacement, r is a radial coordinate, and ds is a path element. Making the assumption that the tractions are normal to the crack face such that T = a(u) and that ds = dr, Eq. (7-69) may be written as

200 300 PREDICTED STRENGTH (MPa)

Figure 7-31. Observed maximum strengths for the A12O3 materials in Fig. 7-30 vs. the values predicted from the bridging model.

c) = - 2 J a (u) du (7-70) o where 2 a is the crack opening at the end of the bridged zone (i.e., at r = c — b). The toughening effect of the bridging zone as a function of crack length may thus be calculated by explicitly inserting a constitutive equation for the bridging, o(u\ and a crack length dependence for the

371

7.3 Fracture

Figure 7-32. ./-integral path used to calculate contributions to fracture resistance from bridging ligaments.

crack opening, u(r,c\ and integrating Eq. (7-70). As the opening depends on the degree of toughening, an implicit equation for I±3t(c) results (Marshall et al, 1985), which is generally not analytic. However, the increase in fracture resistance resulting from a bridging process is easily seen from Eq. (7-70) to be proportional to the integrated area of the constitutive equation for ligament deformation. Figure 7-33 shows the form of the constitutive equations for several bridging processes in ceramics: ductile particles (e.g., WC-Co) (Sigl et al., 1986); debonding fibers (e.g., SiC-glass-ceramic) (Marshall et al., 1985); sliding fibers; debonding grains (e.g., A12O3 polycrystals). Obviously the greater area under the constitutive equation the greater the degree of toughening. In steady-state crack propagation the crack opening at the end of the bridging zone is equal to that necessary to cause ligament rupture. This crack opening is 2a = 2M*, and hence the integral in Eq. (7-70) may then be evaluated explicitly: Afmax = - 2) a(u)du = irx 0

(7-71)

(T*

ur

u

Figure 7-33. Schematic of bridging processes in ceramics and their constitutive relations: debonding fibers, ductile particles, sliding fibers or whiskers.

372

7 Mechanical Properties of Ceramics

The maximum increment in the work of fracture is equal to the work per unit area necessary to rupture a ligament. 7.3.4.3 Toughening by Phase Transformations Toughening

Mechanics

Zirconia ceramics may be toughened by phase transformation processes ahead of the crack tip, and considerable effort has been expended in this area since the original suggestion of Garvie et al. (1975), which is covered in some detail in the monograph of Green et al. (1989). If particles of the tetragonal phase of ZrO 2 are metastably retained by appropriate processing of the material, the enhanced crack tip stresses may trigger the transformation to the stable monoclinic phase. Associated with this phase transformation are dilational and shear strains which act to toughen the material. The toughening may be viewed as either a shielding of the crack by compressive stresses associated with the strained particles (in a stress intensity factor view) (McMeeking and Evans, 1982), or, by the work done in moving the particles through their constitutive relation for deformation (in a mechanical energy release rate view) (Mashall et al., 1983 a). Figure 7-34 shows particles in various states of deformation around a crack tip: Particles remote from the tip (extreme right) are simply elastically deformed. At a critical distance from the crack tip (shown as the cardioid-shaped process zone boundary) the stress field reaches a critical level which triggers the transformation, and a stress-free transformation strain develops. For particles closer to the crack tip (i.e., in the process zone) additional elastic strain may ensue. Particles in the crack tip wake region are elastically destraining, and at points remote from the tip (extreme left)

J/x=/ W 2Udz

Figure 7-34. Schematic of the crack-tip process zone and wake region for a transforming material, showing the movement through the constitutive equation for a transforming element.

such that no stress enhancement is felt, the particles are unstressed at the transformation strain sT. The strain energy density change °U * associated with the right-to-left cycle in Fig. 7-34 is simply the integrated area under the o (&) response of the transforming particles. For the same /-integral path as shown in Fig. 7-32 the only contribution in this case comes from the remote wake region (Fig. 7-34) (Rice, 1968): (7-72)

where °ll is the strain energy density along the path dz, and w is the width of the wake region. Once again the maximum increase in fracture resistance may be estimated without exact knowledge of the deformational constitutive equation. If all particles have been moved through the full transfer-

373

7.3 Fracture

mation cycle along the J-integral path in the wake then % in Eq. (7-72) may be written as

TC8T

(7-73)

where Vf is the volume fraction of transformed particles, e* is the maximum particle strain reached during the cycle, ac is a mean critical stress for particle transformation, and ah (e), and ov (s) are the loading and unloading parts of the constitutive relation, respectively. In this steady-state case, the integral of Eq. (7-72) reverts to = 2VfeTacw

(7-74)

Most analyses assume the critical mean stress at the process zone boundary to be unaltered from its form in the absence of transformation, such that the above equation is written generally as lx

= ?|F f £ T £w

(7-75)

where E is the Young's modulus of the matrix material, and rj is a dimensionless constant (~ 0.2) which accounts for the exact details of the constrained transformation process (Green et al., 1989). The linear dependence of A^ m a x on w predicted from Eq. (7-75) is reasonably well obeyed experimentally, as shown in Fig. 7-35. Figure 7-36 shows an indentation in a ZrO 2 material with transformation zones surrounding the contact impression and the initiated cracks.

5

10 15 20 ZONE WIDTH, w Qm)

25

Figure 7-35. Fracture resistance vs. zone width for Mg-ZrO 2 materials, showing the linear relation (Eq. (7-75)) (data of Swain, 1985).

tary bridging to increase fracture resistance. Such increases in fracture resistance are of course only obtained with correct processing. In particular, long heat treatments of ZrO 2 materials reduce the toughening as the tetragonal particles are coarsened. If the particles become too large, the metastability of the tetragonal phase is lost (i.e., the tetragonal phase particles become stable) and transformation and toughening disappear.

•*.•* ,J-J

>.

Transformation Toughening Effects in Zirconia Materials Figure 7-37 shows the ^-curves of a ZrO 2 material and a polycrystalline A12O3 demonstrating the power of the transformation process compared with ligamen-

Figure 7-36. Micrograph of an indentation flaw in a Y-TZP material, showing surface uplift indicative of the tetragonal to monoclinic transformation adjacent to the contact impression and the cracks. (Micrograph courtesy L. M. Braun.)

374

7 Mechanical Properties of Ceramics 0.12

key to this improved performance: the data shown in Fig. 7-39 are for a material optimized for thermal shock resistance at 11.5 vol.% ZrO 2 , greater or lesser amounts ZrO 2 added to the base A12O3 lead to weaker enhancement in properties or even degradation.

0.06 -

0.00

7.3.5 Non-Equilibrium Fracture 7.3.5.1 Crack Velocities in Destabilizing and Stabilizing Fields Zirconia

Crack motion is a non-equilibrium process reflecting the underlying kinetics of

0 1 2 CRACK EXTENSION, Ac (mm)

Figure 7-37. Fracture resistance vs. crack extension for polycrystalline A12O3 and a partially stabilized ZrO 2 showing the ability of the transformation process to considerably enhance fracture resistance. The data for A12O3 are from Swain (1986), and the data for ZrO 2 are from Readey et al. (1987).

1000 Toughened

Q_

• to

A

200 -

A

The ^-curves of ZrO 2 materials give rise to significant flaw tolerance in the strength characteristics. Figure 7-38 shows the strength of two ZrO 2 materials vs. indentation load. The material aged for peak toughening shows almost no decrease below the maximum strength with increased indentation load, whereas the over-aged material, although still showing some flaw tolerance, is less strong and shows a greater dependence of strength on indentation load. Ceramics containing ZrO 2 can also show increased resistance to thermal shock. Figure 7-39 shows the strength after thermal shock for a ZrO2-containing A12O3 material, in comparison with the base A12O3. The enhanced strength, and retained strength with increasing temperature drop, in comparison to the base, are obvious. Again it should be noted that processing is

50 10°

A

A

Overaged

100 i

•

A

A A

i

101 102 10 3 INDENTATION LOAD, P (N)

104

Figure 7-38. Strength vs. indentation load for ZrO 2 specimens containing indentation flaws, showing the significant flaw tolerance of specimens processed for optimum transformation toughening (data from Marshall, 1986).

1500 500 1000 TEMPERATURE DROP (°C) Figure 7-39. Strength of thermally shocked A1 2 O 3 ZrO 2 specimens vs. temperature drop showing the increase in strength and increased resistance to thermal shock (data from Becher, 1981).

7.3 Fracture

5

10 15 TIME (min.)

20

Figure 7-40. Crack length vs. time for a DCB glass specimen loaded beyond the unstable equilibrium point (data from Wiederhorn, 1967).

the atomic bond-rupture processes. If the kinetics of bond rupture are rapid then small perturbations of the system from equilibrium can lead to catastrophic results: crack lengths perturbed beyond unstable equilibrium points (Fig. 7-10) lead to rapid failure under such conditions - the specimen breaks. However, not all fracture kinetics in ceramics are rapid on human time-scales, as observed experimentally by Wiederhorn (1967). In fact, the common process of moisture-enhanced crack propagation in oxides, particularly glasses, is

375

quite slow. Figure 7-40 shows crack propagation vs. time in a soda-lime silicate glass for a load-controlled DCB specimen perturbed beyond unstable equilibrium. The crack velocity and crack length increase with time, as the system moves further from equilibrium (Table 7-4). Figure 7-41 shows crack propagation in a similar glass for rapidly initiated indentation cracks. The velocity decreases with time in this case as the system moves closer to equilibrium. The separation of the data for the different environments is an indication of the different environment-dependent kinetics operating, whilst the tendency to an environment-independent crack length value at long times is indicative of approach to a similar equilibrium point (c 0 , Eq. (7-42)). Figures 7-40 and 7-41 are characteristic of cracks propagating in destabilizing and stabilizing fields, respectively. Perturbations of the unstable geometries in Fig. 7-12 lead to similar increasing crack velocities (the most common of which is simple tension, which is regarded as a strength test when the kinetics are rapid). Perturbations of the stable geometries of Fig. 7-13 lead to decreasing velocities, and perturbations of the neutral geometries of Fig. 7-15 lead to constant velocities. Just as knowledge of

Figure 7-41. Crack length vs. time for rapidly initiated indentation radial cracks in soda-lime glass. Time, t(s)

376

7 Mechanical Properties of Ceramics

the geometry parameters (Table 7-4) allows 0i to be determined using these specimens, crack velocity as a function of mechanical energy release rate, v (^), can also be determined. The v (^) curve plays an analogous role in non-equilibrium fracture to that of 01 in equilibrium fracture, as both are specimen independent and only reflect material-environment interactions. Data such as Figs. 7-40 and 7-41 suggest that v (^) should be a monotonic increasing function of Si-OH • • • HO-Si

(7-80)

10" 10" 10- 1 2 0 2 4 6 8 Mechanical Energy Release Rate, # (J m~2)

Figure 7-43. Crack velocity data for glass specimens, showing the fit of the reaction and transport model. Data for soda-lime (SLS) and borosilicate (BS) glasses from Wiederhorn and Bolz (1970), and for sodiumaluminosilicate (NAS) glasses from Gehrke and Ullner (1988).

20000

Figure 7-43 shows some crack velocity data in glass, demonstrating the ability of 500 the model of Eq. (7-78) to describe experi10 mental data. Three aspects of behavior are 10~ displayed: (a) different materials have separate v {*&) responses reflecting differences in 7 10~ surface and reaction chemistry; (b) increas10ing temperature increases crack velocity in Alumina the reaction-controlled region, but has lit10'-10 tle effect in the transport-controlled region; 30 34 38 42 46 (c) increasing the viscosity of the surroundMechanical Energy Release Rate, $ (J m~ ) ing medium decreases the velocity in the Figure 7-44. Crack velocity data for a polycrystalline transport-controlled region, truncating the alumina (Pletka and Wiederhorn, 1982), PMMA, and steel (Williams and Evans, 1973). reaction-controlled region but without

378

7 Mechanical Properties of Ceramics

where a strong, primary, ionic/covalent bond is replaced by a weak, easily ruptured, hydrogen bond. Similar processes may be imagined for Al, Mg, Zr, etc., cations. Michalske and Freiman (1982) have considered the reaction of Eq. (7-80) and have provided generalized constraints on the environmental species which may make the primary -> secondary bond switch in ceramics, thereby allowing slow nonequilibrium fracture. Michalske and Freiman consider a three step reaction, shown in Fig. 7-45: (1) A lone pair from the reacting molecule is attracted to the Si site; (2) A proton from the reacting molecule is transferred to the bridging oxygen at the same time as electrons are transferred to the Si; (3) The hydrogen bond between the transferred proton and the remaining portion of the reacting molecule is broken. As a consequence of this scenario Michalske and Freiman propose three constraints on the allowed reactive species:

(3) The acid and base site separation on the reacting molecule must conform to the Si-O bond length.

(1) The reacting species must possess a non-bonding electron pair, i.e., be able to act as a Lewis base. (2) The reacting species must have a labile proton, i.e., be able to act as a Bronsted acid.

Figure 7-46. Failure time vs. applied stress for abraded glass bend specimens tested in water. The stress is normalized by the strength in liquid N 2 , and the lifetime by the lifetime at half this stress level. Data from Mould and Southwick (1959).

Si

Predictions based on these constraints suggest that species other than H 2 O will be able to enhance crack propagation in ceramics. Experiments on NH 4 , N 2 H 4 , and CH 3 NO confirm these predictions, whilst the absence of effect in N 2 , nitrobenzene,

0.0

0.2 0.4 0.6 0.8 APPLIED STRESS, Ofjo^

1.0 N

Si 0

\

H

H-0 H;

H

I

Si

0

si

Si

| \

I 2 3 Figure 7-45. Schematic of the three stage reaction process envisaged for the rupture of silicate bonds in the presence of water.

200 250 300 350 400 450 APPLIED STRESS, aA (MPa)

Figure 7-47. Failure time vs. stress at failure for alumina specimens containing sawing flaws tested in water. The shaded band represents the strength in an inert environment.

7.3 Fracture

(a) Static Fatigue Applied Stress

Time (b) Dynamic Fatigue Applied Stress

Time

Figure 7-48. Applied stress vs. time behavior for the delayed failure data of Figs. 7-46, 7-47, and 7-49, representing two extremes of loading.

acetonitrile, diethyl ether, and pyridine is explained (Freiman et al., 1985). 7.3.5.3 Time-Dependent Failure

A consequence of the finite reaction rates for bond rupture is that specimens perturbed in destabilizing fields will have finite times-to-failure. Figure 7-46 shows

379

the failure time for abraded glass bend specimens as a function of the applied stress; the decrease in lifetime with increasing stress is apparent. Figure 7-47 shows a similar plot for some alumina bend specimens containing flaws associated with sawing damage. In Fig. 7-46 the data reflect a stress history of the sort shown in Fig. 7-48 a: the applied stress is constant until failure. In Fig. 7-47 the data reflect that of a constant stressing rate to failure, Fig. 7-48 b. Figure 7-49 shows some data for the same polycrystalline alumina specimens containing indentation flaws for this latter condition, using the more common strength vs. stressing rate plot. The connection between the results of Figs. 7-46 to 7-49 and v (^) curves may be made by integration procedures, and this has been considered in some detail by Fuller et al. (1983). Cyclic loading effects per se have been observed in transformation-toughened ZrO 2 materials (Dauskardt et al., 1987), suggesting that lifetimes for these materials will be reduced under cyclic loading conditions compared with monotonic or static loading (i.e., as in Fig. 7-48). Such effects were not present. However, in a polycrys-

500

Figure 7-49. Stress at failure (strength) vs. stressing rate for alumina specimens containing indentation flaws. 10-2 Stress Rate,a~/MPa s -1

380

7 Mechanical Properties of Ceramics

talline A12O3 toughened by ligamentary bridges, as observed lifetimes under cyclic loading merely reflect the integrated response of the v (^) curve over the stressing cycle (Lathabai et al., 1989). Clearly, the ^-curve behavior in a material depends on the exact stress-state of a specimen, and different mechanisms of toughening will depend in different ways on cyclic loading. The implication from the work on ZrO 2 and A12O3 is that the toughening induced by phase transformation is more susceptible to reduction by cyclic effects than that induced by bridging, at least for tensiontension fatigue.

7.4 Plasticity 7.4.1 Slip at the Atomic Level Just as fracture, plasticity is mediated by localized defects. To see this we consider the yield strain for homogeneous shear of two atomic planes in a perfect crystal (Fig. 7-50). Under the action of an applied

shear stress, one entire plane of atoms slips over the adjacent plane. At low shear stresses the atoms resist motion and undergo elastic deformation. As the stress is increased, the atoms ride up on those in the adjacent rows until, at a yield point, they attain an unstable position where forward or backward motion can occur. If the stress is increased beyond the yield stress, the atoms will slip over those in the adjacent rows. Easy slip, or glide, results as one row "bumps" over another. If the stress is removed, permanent deformation results. Quantitatively, the homogeneous slip model overestimates the yield stress and strain. If the three close-packed atoms represented on the left in Fig. 7-51 are subjected to a shear stress, their positions at the yield point are those shown on the right of the Figure. If the interatomic separation is b, the shear displacement at yield is b/2 and the original length perpendicular to this displacement is b cos (TC/6). Thus the shear strain at yield is y = (fe/2)/[fecos(7c/6)] -0.6

Figure 7-50. Schematic diagram of homogeneous shear of atomic planes.

That is, the homogeneous slip model predicts a shear strain of ~ 60% at yield. In practice yield strains are considerably less than 1%. Clearly the model is inadequate, and we must turn to a defect-based model to describe the observed behavior. Although the homogeneous slip model fails in the macroscopic sense portrayed in Fig. 7-50, the process of deformation shown in Fig. 7-51 must occur. Hence, some strain localization mechanism must be acting in order to generate macroscopic yield in real materials (just as a crack causes localized bond rupture strains during macroscopic fracture). Figure 7-52 shows how such a localization - a dislocation - may be produced. The dislocation

7.4 Plasticity

381

7.4.2 Dislocation Glide in Ceramics 7.4.2.1 Inherent Resistance to Glide b cos 30

Figure 7-51. Schematic diagram of local atomic configurations for calculation of yield strain in homogeneous shear. extra , half-plane !

i

Figure 7-52. Schematic diagram of rows of atomic planes showing the localization of strain at a disclocation.

may be thought of as an extra half-plane of atoms inserted into the structure, and the shear stresses necessary to drive dislocations are quite small. At the ends of the atomic planes in Fig. 7-52, far from the dislocation core, the atoms are almost in their correct lattice sites, and strains of order 60% are needed to cause slip. At the dislocation core, however, the bonds are highly strained and the atoms are close to the unstable position of the homogeneous slip model. Very small additional strains are required to move the extra half-plane to the left. Thus, a small macroscopic stress may be applied to a specimen as a whole, causing plastic deformation via the motion of dislocations at which the conditions for bond shear are met locally. The local shear distortions, characterized by the Burgers vector A, may be perpendicular or parallel to the line of dislocated atomic planes, and the dislocations are referred to as "edge" or "screw", respectively, in each case.

The predominant mechanism of plasticity in metals is dislocation glide because the inherent resistance of the crystal lattice to dislocation motion, the Peierls-Nabarro force, is small. This is largely due to the fact that metallic bonding is non-directional, so that distortions in the atomic arrangement near the core of a moving dislocation do not produce large increases in strain energy as the dislocation moves from one equilibrium position in the lattice to the next. The same, however, is not true of most ceramics. Dislocation glide is difficult, and as a consequence, most ceramics fracture before they plastically deform, at least at room temperature. The reasons for the resistance to glide can be understood largely in terms of bonding and complexities in ceramic crystal structures. Atomic bonding in most ceramics is covalent, ionic, or a mixture thereof. As shown in Fig. 7-53 a, dislocation glide in covalent materials is inherently difficult because it requires the breaking and bending of strongly directional bonds. As a consequence, glide plasticity in ceramics like diamond, SiC, and Si 3 N 4 is observed only at the extremes of temperature and stress. In ionic materials, it is the formation of electrostatic faults which produces the resistance to glide. Slip along the horizontal plane of the simple ionic structure in Fig. 7-53 b, for example, brings like signed ions into registry, so that the atomic arrangement near the dislocation core in the half-slipped configuration is a high energy one. Slip is thus possible only on those slip systems for which electrostatic faulting is minimized, like the 45° plane in Fig. 7-53 b.

382

7 Mechanical Properties of Ceramics

covalent bonds

(a)

(b)

®

©

®

0

®

©

®

©•'

©

®

©

®

©

®

e

©

®

e

®

®

©

®

*

®

'

©•'©

e/® ®

•

©

©• ® // ©

Figure 7-53. Schematic illustrations of slip in (a) covalent and (b) ionic materials (after Ashby and Jones, 1986).

As in most close packed structures, slip occurs most easily on the close packed plane - in this case, the basal or (0001) plane - and the slip direction is that of the smallest unit repeat in the structure. On casual examination, one might thus expect [lOTO] slip, i.e., slip in the direction of closest packing in the anion plane (see Fig. 754 (a)). However, because the cation planes are not as closely packed as the anion planes, the smallest unit repeat in the structure is actually much larger, and the observed slip direction is rotated by 30° from [1010]. The Burgers vector b is 1/3 [1120], as shown by the large arrow in Figs. 7-54 a and b. The nature of this slip geometry led Kronberg to suggest that an edge dislocation in the a-Al 2 O 3 structure should dissociate into 4 quarter partial dislocations. The dissociation reactions are 1/3 [1120] -> 1/3 [1010] + 1/3 [0110]

Dislocation glide in ceramics can also be difficult due to complexities in crystal structure. One material in which crystal structure is thought to play a very important role is a-Al 2 O 3 (sapphire), in which significant slip occurs only at temperatures in excess of 900 °C. Details of the slip process in a-Al 2 O 3 , as first considered by Kronberg (1957), are now discussed. Figure 7-54 a shows the a-Al 2 O 3 structure. It consists of planes of oxygen anions in hexagonal arrays stacked in the A - B - A - B • • • stacking sequence, with aluminum cations occupying two thirds of the octahedral interstices. In a given cation plane, the aluminum ions form an ordered array, but the relative position of the array is shifted in consecutive aluminum layers to form three distinct cation planes. The hexagonal unit cell used to describe the structure is thus quite tall, consisting of three anion and three cation planes.

and 1/3 [1010] -> 1/9 [2110] + 1/9 [1120] and the slip steps corresponding to the formation of the partial dislocations are shown in Fig. 7-54 b. Kronberg further suggested that the motion of the partials is made difficult by the crystalline arrangement. The physical origin of the difficulty can be appreciated by considering the relative motion of the anions and cations during the advance of the first quarter partial, shown for selected atoms by the arrows in Fig. 7-54 c. Note that since the anion at point 1 displaces to a position which is occupied by a cation, the cation must simultaneously displace to an adjacent unoccupied octahedral site in the anion array, such as that made available by the movement of anion 2. The direction of motion of the anions and cations is thus different, and an inherently cooperative movement of the

7.4 Plasticity

383

[1120]

O

upper oxygen layer

#

lower oxygen layer

©

aluminum layer

two ionic species is required for the partial to advance. Referred to as "synchroshear", this process acts as a fundamental impediment to glide in A12O3 and other ceramics with complex structures, such as MgAl 2 O 4 (Poirier, 1985). 7.4.2.2 Observations of Glide Plasticity While dislocation glide is difficult in most ceramics, it is, nevertheless, observed. At elevated temperatures, for instance, many of the aforementioned constraints are eased, and at least a limited amount of dislocation glide occurs in almost all ceramics. In addition, in some ceramics, glide is possible even at room temperature and below. In general, these are strongly ionic

Figure 7-54. (a) The structure of alumina parallel to the basal plane showing two oxygen layers and the aluminum layer in between. The large arrow indicates the Burgers vector, (b) The slip steps corresponding to the dissociation of a dislocation into 4 quarter partial dislocations drawn in terms of the relative motion of two adjacent oxygen planes, (c) The motion of anions and cations during the first partial slip step showing that the two species move in different directions and thus require coordinated movement (after Kronberg, 1957).

materials with the rock salt structure, like the alkali halide salts. As mentioned, the Peierls barrier for slip in ionic materials is usually high because of electrostatic faulting. However, for rock salt materials, electrostatic faulting does not develop on the (110) [110] slip system (such as the slip system oriented at 45° in Fig. 7-53 b), and as a result, relatively pure single crystals exhibit substantial glide plasticity over a wide range of temperature. Figure 7-55 a, for example, presents room temperature stress-strain curves for NaCl which demonstrate that tensile strains in excess of 20% can be achieved in single crystals (Stokes, 1966). The conventional rule of thumb for determining slip systems in crystalline mate-

384

7 Mechanical Properties of Ceramics

NaCI room temperature

20 ' ().035mm

" •

0.07mm ,

A lO.IOmm

1b -

tri0.50mm crystal A 25mm h o / I bi-crystal IL ~2mm/l

CO

(a) a

/w-

10 .

r

LJJ

DC

5 .

jy I I

1 1j _

^ ^ \" 1 x• w

i

/i/

crystal /W ~2mm / /

j

'

bi-crystal^^Xsinglecrystal

I/VV^-^ n'

t

/ *

0 1 2 3%

If 1 II STRAIN

20

NaCI d-0.2mm

20°C 15 -96°C

(b)

~

CO CO LJJ

10

oc

0

0.5

1.0%

Figure 7-55. Tensile stress-strain curves for NaCI. (a) Room temperature data showing effects of grain size, (b) Data for fixed grain size of 0.2 mm showing effects of temperature (after Stokes, 1966).

STRAIN

rials is that slip occurs on the planes of highest packing density in the direction of the smallest unit repeat in the structure. This rule was previously applied to aA12O3, and it works well for most other ceramics, as well. However, for strongly ionic materials, the rule is sometimes broken because of the electrostatic constraint. In NaCI, for example, the planes of highest density are the (100) types, but slip at room temperature occurs predominantly on (110). While (100) slip is possible, it occurs only at higher temperatures where the electrostatic constraint is relaxed by expansion of

the lattice. Table 7-5 summarizes the slip systems of many ceramics. 7.4.2.3 Limitations on Slip and Loss of Ductility in Polycrystals The stress-strain curves for NaCI shown in Fig. 7-55 a, which include data for both single crystals and polycrystals of various grain sizes, demonstrate that the room temperature ductility exhibited by single crystals does not extend to polycrystals; in fact, all the polycrystals of grain size less than 0.50 mm are effectively brittle. This

7.4 Plasticity

385

Table 7-5. Slip systems in ceramics3. Material

A12O3 BeO C (diamond) C (graphite) CaF 2 CsBr Cu 2 O LiF KC1 MgO MgO • A12O3 NaCl PbS PbTe (3-SiC (3-Si3N4 p-SiO2 TiC TiO 2 UC UO 2 ZrB 2

Crystal structure

hexagonal hexagonal cubic (diamond) hexagonal cubic (fluorite) cubic (CsCl) cubic cubic (rock salt) cubic (rock salt) cubic (rock salt) cubic (spinel) cubic (rock salt) cubic (rock salt) cubic (rock salt) cubic (zinc blende) hexagonal hexagonal cubic (rock salt) tetragonal (rutile) cubic (rock salt) cubic (fluoride) hexagonal

Primary slip system

(0001) [1120] (0001) [1120] (l!l)[H0] (0001) [1120] (001) [110] (110) [001] (100) [001] (110)[110] (110)[lT0] (HO)[iTo] (111) [110] (110) [110] (001) [110]

Secondary slip system

several several

(110)[110]

(001) [110] (001) [110] (001) [110] (001) [110]

(ooi)[iio] (iii)[iio] (1010) [0001] (0001) [1120] (Hi)[iT0] (101) [101] (lll)[lT0] (001) [110] (0001) [1120]

(110)[110]

Number of independent slip systems

Minimum temperature for appreciable secondary slip

Primary

Secondary

2 2 5 2 3 3 3 2 2 2 5 2 3 3 5 2 2 5 4 5 3 2

2 or 3 2

- 0 . 8 Tm -0.8 T m

2

- 0 . 3 Tm

3 3 3

-0.5 Tm

3

- 0 . 5 Tm

2

~0.5T m

-0.5Tm

a

Table compiled from Davidge (1979), Evans and Langdon (1976), Kingery et al. (1976), Sprackling (1976), and Gilman (1961).

peculiar behavior, which is exhibited by many ceramics, is explained in terms of limitations on slip which don't exist in most metals. The usual explanation follows from the argument of von Mises (1928), that in order to produce an arbitrary change in shape in a crystalline material, 5 independent slip systems must operate. A slip system is indepenent if it produces slip which cannot be achieved by any combination of slip on other systems (Groves and Kelly, 1963; 1969). The basis of the argument is that an arbitrary shape change can be described by the 6 independent components of the strain tensor (three normal and three shear strains). However, since volume is con-

served during plastic deformation by slip, the normal strains must sum to zero, so that only 5 of the components are independent. Given that the shear produced by one slip system determines the value of one of the components of the strain tensor, 5 independent slip systems are needed to produce an arbitrary change in shape. The application to deformation in polycrystalline materials follows from the argument that if a grain is not free to change its shape, strain incompatibilities which develop at the boundaries with other grains will produce high local stresses and fracture. Metallic materials generally possess the 5 requisite slip systems and are thus ductile in both single crystal and polycrystalline

386

7 Mechanical Properties of Ceramics

form. However, as indicated in Table 7-5, most ceramics do not. In the case of rock salt materials like NaCl, only two of the six physically distinct (110) [110] slip systems which operate at room temperature are independent, thus explaining the loss of ductility in Fig. 7-55 a. As shown in Fig. 7-55 b, the ductility of poly crystalline NaCl increases markedly at a temperature of about 200 °C, corresponding to the activation of slip on the (001) [110] system which increases the number of independent slip systems to 5. Similar brittle-to-ductile transitions are observed in polycrystalline MgO (T=1700°C) (Day and Stokes, 1966 a; 1966 b) and polycrystalline KC1 (T = 250 °C) (Stoloff et al., 1963). The data in Fig. 7-56 for polycrystalline KC1 demonstrate how abrupt the transition can be. From a microstructural standpoint, the transition from brittle to ductile behavior is often correlated with the onset of wavy slip, that is, slip which is not confined to a single slip plane; see, for instance, Davidge (1979). In rock salt structures, wavy slip becomes possible at higher temperatures because of the activation of secondary slip systems. However, careful studies have

shown that it is not the onset of wavy slip, but rather the disappearance of all straight slip (slip confined to a narrow glide bands), which controls the transition (Stoloff et al., 1963). For example, appreciable wavy slip is observed during the deformation of polycrystalline KC1 at temperatures as low as 150°C, but straight slip persists to 250 °C, and it is the latter temperature which correlates with the marked increase in ductility (see Fig. 7-56). This suggests that ductility is limited by the nucleation of cracks by stress concentrations developed at the intersections of straight slip-bands and grain boundaries, and from this standpoint, the von Mises explanation for the loss in ductility in polycrystals is not entirely adequate. 7.4.2.4 Effects of Solutes and Impurities on Dislocation Glide Substitutional solutes and impurities, even at concentrations in the parts per million range, can have significant effects on the glide mobility of dislocations and therefore the flow stresses of ionic ceramics. Fig. 7-57, for instance, shows that the criti-

100 POLYCRYSTALLINE KCI 80

60

40

Figure 7-56. The ductility of polycrystalline KCI as a function of temperature showing a brittle-ductile transition at about 250 °C (after Stoloff et al., 1963).

20

100

200

300

TEMPERATURE (°C)

400

500

7.4 Plasticity

Q_ CO CO

ALKALI HALIDE SALTS

LU

A -

15

i
fc"1,

{6-11) _ W

max —

4 U

\

S

~

*) ~

~^t

The length lc of a fully developed zone can be determined from Eq. (8-27) by setting For cases where the bridging reinforcements can transmit the applied stress without failing, the bridging response under monotonic loading can be simulated by

(8-29 b) k that is, for long cracks, Ktip becomes independent of crack length, asymptoting to a value characteristic of an unbridged crack of half-length (nky1. This crack length (nky1 for the transition from the shortcrack to the long-crack regime can alternatively be regarded as the characteristic

8.2 Mechanics of Toughening

length introduced by bridging, instead of fc"1. However, micromechanical models of bridging lead more directly to the spring constant /c, which is related to the loadtransfer length to the reinforcement. Similar results also hold for nonlinear springs, in particular for the parabolic traction law which results from frictional sliding of bridging fibers relative to a brittle matrix (Sec. 8.2.4.3). An important application of the limiting value of Ktip for long cracks is for estimating the matrix cracking stress erM for continuous fiber-reinforced ceramic matrix composites, which for linear springs, would be given by

r

E = K™Ul-Vf)k— J

/2

(8-30)

on using Eqs. (8-29 b) and (8-21), £ m , Km denoting the Young's modulus and intrinsic toughness of the matrix phase, and E the modulus of the composite in the fiber direction. 8.2.4.2 Experimental Determination of the Traction Law

Two approaches can be used to determine the G-U relation directly. The first requires direct measurement of the crack opening within the bridged zone, coupled to the solution of an inverse problem of stress analysis to determine the transmitted stress corresponding to the observed crack profile (Cox and Marshall, 1991), Such detailed measurements and calculations have already been used extensively to characterize crazes in glassy polymers (Kramer, 1983; Doll, 1990). There are serious practical difficulties, both with achieving sufficient resolution for the experimental measurements and with numerical ill-conditioning for the inverse problem.

433

The second method, which is particularly appropriate for fiber-reinforced composites, is based on introducing a crack across the whole of the specimen's section, leaving the two halves held together by the bridging ligaments or reinforcements. This approach has been used for characterizing particulate rubber-phase toughening of epoxy (Kunz-Douglas et al, 1980) and more recently for ductile fiber toughening of intermetallics (Deve and Maloney, 1991) and model materials (Ashby et al., 1989). The influence of specimen gage length and machine compliance need to be taken into account in the design and interpretation of these experiments, as discussed earlier in connection with deformation bands (Sec. 8.2.2). A third approach relies on measuring parameters such as interfacial toughness or friction stress, which can be used in conjunction with a micromechanical model of bridging to generate the a-u relation. In particular, Marshall and Oliver (1987, 1990) have developed an indentation technique for measuring the frictional and residual stresses between fibers and matrix in ceramic-matrix composites. 8.2.4.3 Micromechanics of Bridging

The principal value of a micromechanical model is to provide insights into the influence of microstructural parameters (such as the fiber diameter or grain size, the interfacial toughness, frictional and residual stresses), which can be used to guide microstructural control of properties. Valuable insights can often be derived from little more than dimensional considerations (Bennison and Lawn, 1989; Campbell et al., 1990; Vekinis et al., 1990). The case of fiber reinforcement lends itself most readily to detailed .modeling (Marshall etal, 1985; Budiansky et al., 1986; Gao

434

8 Toughening Mechanisms in Ceramic Systems

etal, 1988; McCartney, 1987, 1989; Hutchinson and Jensen, 1990), and it can serve as a useful paradigm for other cases of bridging. Some of the more important results which have been obtained are summarized in this subsection. Figure 8-13 shows the principal features of the G-U curve for crack bridging by continuous fibers, based on a shear-lag analysis for a single fiber transferring load to a suitably constrained cylindrical sheath of matrix material (Gao et al., 1988; Hutchinson and Jensen, 1990). Debonding initiates at a bridging stress ai controlled primarily by (i) the interfacial fracture energy yi9 (ii) the volume fraction of fibers Vf, (iii) 2 r the fiber diameter, (iv) the residual stress in the matrix due to thermal expansion mismatch with the fibers. If it is assumed, for simplicity, that matrix and fibers have the same (isotropic) elastic constants E, v, so that the residual stress can be characterized by axial and radial strains sj, sj, corresponding to the integrated difference in expansion coefficients over the cooling range AT from

frictional sliding along full debond zone

the stress-free temperature, AT

6,%= J « z - a » ) d T

(8-31)

0

the following expression is obtained for o{ (Hutchinson and Jensen, 1990)

The bridging stress 10K0\ T

AKT equals

2 1/2

[EAG /(1 - v) ] . For the case where AKT is reasonably large (i.e., AKT is 3 to 6 times Ko)9 AKT can be approximated as 0.8[£AG T /(l-v 2 )] 1 / 2 or:

T

t

m*

112

where AK * is again dependent on the applied Kj level and m* equals m/(l — v2). In order to determine the value when the transformation zone is fully developed, we must account for the crack shielding effect of AKT on the applied stress intensity to advance the crack tip. The crack tip will advance when Kx equals or exceeds the sum of Ko, the fracture resistance of the material at the crack tip (in the absence of any transformation) plus the transforma-

tion toughening component, AKT, that is, KY > Ko + AKT. Substituting this condition into Eq. (8-45) and rearrangement yields (Becher et al., 1992): AK1

Ko

(8-46)

JAT{\-col

where co equals sT (2 / m* E/AS1"" m ) 1/2 , and AT equals (Ms — T). Thus for each composition, for example, ZrO 2 content, the AKT term will increase as M s is raised towards T, the test temperature, as well as with increase in / or E.

8.3.1.4 Zirconia Ceramics

The influence of decreasing (Ms — T) on AKT can be seen for a fine-grained zirconia containing an yttria solute in Fig. 8-17. In this case the M s temperature is constant and the test temperature, T, is the variable. The included photomicrograph shows that the increase in AKT is also accompanied by an increase in the transformation zone surrounding the crack as the test temperature is decreased. A similar temperature dependence of the fracture toughness occurs in partially stabilized zirconia (PSZ ceramics exhibited a peak in the toughness versus test temperature curves. This occurs as the test temperature is decreased to just above the M s temperature for the particular PSZ ceramic. In the PSZ ceramics, the tetragonal phase is present as precipitates in a cubic phase matrix with the M s temperature increasing with increase in precipitate size. Obviously, the temperature dependence of the fracture toughness of transformation toughened ceramics must be considered in the application of such materials. One would like to tailor the ceramic so that the toughness is optimized in the temperature range of interest. This can be accomplished

8.3 Toughening Mechanisms

I

I

443

I

18 16 \

>CO

14

—

z

Q_

12 $

X

10

\

c x: O)

o

8

0 i_

3 O

co ul

—

\

>>

6 4 2

— — I

0

(a)

—

100

I

i

200 300 Temperature (K)

,\w

:

,

400

.

500

,

(b)

Figure 8-17. The fracture toughness of transformation toughened fine-grained (0.4 um) zirconia (containing 2 mol% yttria) displays a significant increase with decreasing test temperature (a) which is associated with an increase in the size of the transformation zone generated around the crack as the test temperature is decreased towards the Ms temperature (b). This zirconia also exhibits a remarkably low M s temperature 2)

b

Zr0 2 (12mol%Ce0 2 )

c

AI 2 O 3 20 vol.% ZrO2(12 mol % CeOJ

70

110

150

|M

(a)

190

230

270

310

r| (K)

*-

• ALOo 40 vol.% Zr0 0 (12 mol c A ZrO 2 (12mol%CeO 2 ) , 20 vol.% ZrO2(12 mol % CeO2)

70

(b)

110

150 \MS~T\

190

230

270

310

(K)

Figure 8-21. Predicted transformation-toughening contribution (curves) at room temperature increases with increase in martensite start temperature, i.e., increase in tetragonal zirconia grain size (a). The observed transformation-toughening contribution exhibits a Ms temperature (and grain size) dependence similar to that predicted for the alumina-zirconia composites (b).

thermodynamically stable as the temperature is increased and thus the fracture toughness will exhibit a decrease with increase in temperature. Keeping this in mind, one can alter the ability to transform the tetragonal phase in the crack tip region and the fracture toughness by controlling the solute type and amount, the size (and

8.3 Toughening Mechanisms

447

Figure 8-22. Whisker bridging and whisker pullout are observed in the crack tip wake region of a SiC whisker reinforced alumina.

shape) of the tetragonal phase, and, in the case of composites, the matrix toughness and the mismatch in zirconia-matrix properties. 8.3.2 Reinforcement Processes There are a number of toughening processes which can be classified as part of the reinforcement approach to toughening ceramics. The name implies the use of a second phase which strengthens the matrix by carrying a portion of the applied stress, for example, as in reinforced cement which utilizes carbon steel rods as the reinforcing phase. Concrete, on the other hand, which incorporates gravel as a second phase may be reinforced or toughened by other processes. In the case of whisker-reinforced ceramics, bridging of the crack surfaces behind

the crack tip by strong whiskers imposes a closure force on the crack or a deflection of the crack tip by the whiskers or both, so that it moves out of the mode I fracture plane have been observed in the SiC whisker-reinforced aluminas (Becher et al., 1988 a; Claussen and Petzow, 1986; Becher et al., 1990; Becher, 1991). And in some instances, bridging whiskers are found to be pulled out of the matrix further behind the crack tip, Fig. 8-22. The extent of pullout, that is, the pullout length, of the whiskers is generally quite limited but still contributes to the toughness achieved. In continuous fiber-reinforced ceramics, extensive use is generally made of the fiber pullout process to attain improved fracture toughness (Evans, 1988; Marshall and Evans, 1985). While continuous fiber reinforcement will not be discussed here, various aspects of whisker bridging and pull-

448

8 Toughening Mechanisms in Ceramic Systems

out are, of course, appropriate to fiber reinforcement although the emphasis on pullout may require modifications for fiber-reinforced ceramics. For greater detail on fiber reinforcement, the reader is initially referred to earlier publications (Evans, 1988; Evans and McMeeking, 1986; Faber and Evans, 1983). Crack deflection models analyze the influence of the angular and linear displacements out of the mode I crack plane by different shaped particles using numerical analysis to define the toughness. This could be thought of as accounting for the resistance imposed by local mode II and III components of the crack and does show that geometry, for example, particle versus disk versus rod, has a significant effect as does aspect ratio consistent with experimental results (Faber and Evans, 1983). These approaches, however, do not reveal what properties of matrix, reinforcing phase, and the intervening interfaces are important. The approach to the contribution from whisker bridging analysis taken here considers the bridging effects of whiskers whose longitudinal axis are normal or near normal to the crack plane (Becher, 1990) while the real composite systems are not so highly aligned. However with the typical meandering path generally taken by the main crack through the matrix microstructure, the local crack plane may be oriented normal to a great many whiskers. One should note that the analysis obtained using the J-integral approach for whisker arrays with random texture (Krause and Fuller, 1987) arrive at the same dependence on material parameters as those predicted below. Whiskers at greater inclination to the crack plane are subject to bending stresses and act like leaf springs when they bridge the crack - a feature not addressed by current models.

8.3.2.1 Analysis of Toughening by Whisker Reinforcement

The bridging contribution to the toughness for uniaxially aligned whiskers (Becher etal, 1988 a; Becher, 1991) is: (8-47)

AKwr = Kc-K0

= [Ec(J

AJ cb )] 1/2

where Kc and Ec arc, respectively, the toughness and Young's modulus of the composite, Ko is the matrix toughness, and J m and AJcb are, respectively, the energy dissipated by extension of the crack tip in the matrix and by the crack bridging processes. One can then define in terms of the crack-opening displacement, uc, at the end of each particular zone and the bridging stress profile ah (w) within that zone: AJ c b =

\oh{u)du (8-48) o The bridging stress profile for a region where the whiskers remain intact and span the crack surfaces can be simply described as a linear increase with increase in crack opening displacement. For the present case, the maximum closure stress on the crack is defined as: ab=V(a7

(8-49)

where o™ is the tensile fracture strength of the whiskers. By equating the crack-opening displacement at the end of the bridging zone to the tensile displacement in the whisker at failure, one can define the energy dissipated by friction when intact bridging whiskers are elastically stretched while in contact with the matrix, AJfb: A/ fb =

6P,. w

31-*

(8 S0)

-

where aj, £ , r, and V{ are, respectively, the tensile strength, the Young's modulus, the radius, and the volume fraction of whiskers, and T 0 is the interfacial shear resistance. This contribution increases as more inter-

8.3 Toughening Mechanisms

facial debonding occurs to allow greater displacement for a given whisker fracture strength. The extent of interfacial debonding, /db, is defined using the analysis of Budiansky etal. (1986). Thus, a critical aspect of toughening by whisker bridging is whether or not the whisker-matrix interface debonds when the main crack tip approaches the whisker especially in the ceramic-ceramic systems where the toughness of each phase is approximately the same. The stress transferred to the whiskers increases with distance behind the crack tip, and the stress imposed on the bridging whiskers rapidly increases resulting in whisker fracture immediately behind the crack tip when no interfacial debonding occurs, Fig. 8-23. Very short elastic bridging zones are generated and measurable toughening occurs only with extremely high whisker strengths. Debonding of the interface, Fig. 8-24, occurs when the conditions are such that either the interface just ahead of the crack tip debonds or the crack tip deflects out of plane onto the interface plane. When debonding occurs, the stresses acting on the bridging whiskers is substantially reduced. The debonded length of the interface on either side of crack plane can be defined in terms of the whisker versus interface failure stresses (Hsueh and Becher, 1988) or that of the matrix (or whisker) to interface fracture energies (Budiansky et al., 1986). The bridging stress in this frictional bridging zone rises quite slowly which leads to a longer bridging zone prior to whisker fracture. Fracture of whiskers at positions away from the main crack surface can participate in the formation of a whisker pullout bridging zone and contributes additional toughening. Within the pullout zone, the bridging stress decreases as the crack-opening displacement increases behind the crack tip.

449

,- Debonded interface Crack tip

Crack opening displacement Elastic bridging

Pullout bridging cr*- Whisker failure

Distance behind crack tip X

Figure 8-23. When whisker-matrix interface debonding occurs (a), the magnitude of the bridging stress supported by the whisker is reduced, resulting in a large bridging zone length (b). Eventually the bridging stress again is sufficient to cause whiskers to fail; those failing away from the crack plane can participate in whisker pullout which further enhances the toughness. (Reproduced, with permission, from the Annual Review of Materials Science, Vol. 20. © 1990 by Annual Reviews Inc.)

Figure 8-24. Debonding-interface fracture accompanies crack propagation as observed in a SiC whiskerreinforced alumina composite.

450

8 Toughening Mechanisms in Ceramic Systems

Using the above approaches, the frictional energy dissipated by pullout of whiskers which is the most effective mechanism for dissipating energy even when the pullout lengths (/po) are only a few times the diameter of the whiskers. The pullout contribution is defined as: A/ po =

(8-51)

po

where /po is related to the debonded length of the interface and thus increases with increase in whisker diameter according to the analysis of Budiansky et al. Generally whisker-reinforced systems have moderate to high T 0 values, and thus limited pullout lengths, that is, quite different from continuous fiber-reinforced composites where T 0 values are purposely made low so that large pullout lengths are achieved. The frictional interfacial shear stress T 0 for a debonded interface will be a function of the coefficient of friction fi and the stress acting normal to the interface an (Outwater, 1956): xo = fi(jn

(8-52)

1

EO

4

-

3

-

i

The radial stress will be influenced by differential contraction induced by differences in therma expansion and elastic properties between the matrix and whisker (Angelini et al., 1987). One can calculate the magnitude of these stresses using Selsing's equations (Seising, 1961); for the alumina-SiC whisker system one finds that the radial stress acting on the interface is quite high, for example, a few hundred MPa. Using interfacial films, these stresses can be considerably reduced, for example, film must have higher thermal expansion coefficient and lower Young's modulus than alumina in this case (Hsueh et al., 1988). This latter analysis has been confirmed by X-ray studies of SiC whisker-reinforced aluminas containing uncoated and carbon coated SiC whiskers (Predecki et al., 1988). Greater toughening is predicted with increases in whisker strength, diameter, and volume content, in ease of interface debonding, and matrix thus composite Young's modulus. Experimental results, for example, Fig. 8-25, for various ceramic and glass matrix composites confirm the responses

i

i

Figure 8-25. The fracture toughness ratio (composite toughness/matrix toughness) increases with increase in SiC whisker content. Improved toughness observed in alumina, mullite, and glass matrices with addition of selected SiC whisker (radius r = 0.4 urn). (Reproduced, with permission, from the Annual Review of Materials Science, Vol. 2. © 1990 by Annual Reviews Inc.)

oQ

crfw = 10 GPa CO CO

I

r

*• 2

-

THEORY

o o — —i -

= 0.4Mm

EXP. MATRIX •

AI2O3

•

Glass

i

i

I

I

10

20

30

40

SiC WHISKER CONTENT (Volume %)

50

8.3 Toughening Mechanisms

451

Table 8-2. Toughening behavior or various whisker reinforced brittle matrix composites. Matrix

SiC whiskers (vol.%)

Fracture toughness (MPa^/m)

Reference

0 20 0

3.0-3.2 5.3 5

Becher et al. (1990)

30

7.5-8

Glass-ceramic Alumina

0 20 0 20 25 0

5.3 8.2 0.8 2.0-2.5 4.5 3

2 um grain size

20

8.5

Mullite:

0 20

2 4.7

20 20 0 20

7-8 10-11 6 8 to > 13

B4C Si 3 N 4 :

MoSi2 Glass

Mullite-20 vol.% ZrO 2 : m-ZrO2 t-ZrO 2 Zirconia-toughened alumina:

predicted by the whisker-bridging model. In fact, whisker reinforcement has been applied to a wide variety of ceramics; a portion of these are listed in Table 8-2. 8.3.2.2 Whisker Characteristics

From Eq. (8-50), it is obvious that high whisker tensile strengths impart significant toughness to the matrix at modest whisker contents. As expected from brittle-fracture behavior, internal (Nutt, 1985) and surface defects can degrade the whisker strengths. Large surface steps are also observed on some SiC whiskers. As described by Marsh (1963), surface steps or offsets can act as stress concentrators which reduce the tensile strength achieved; the magnitude of the reduction depends upon the inclination and height of the surface step and the radius at

Shaleketal. (1986) Buljan etal. (1987) Shaleketal. (1986) Buljanetal. (1987) Gac and Petrovic (1985) Gac and Petrovic (1985) Becher etal. (1988a) Becher etal. (1988a) Gadkaree and Chyung (1986) Becher etal. (1988a) Wei and Becher (1985) Becher etal. (1988a) Wei and Becher (1985) Becher and Tiegs (1987) Becher and Tiegs (1987) Becher Becher Claussen Claussen

and and and and

Tiegs (1987) Tiegs (1987) Petzow (1986) Petzow (1986)

the apex of the step (Marsh, 1963). When such defects can be minimized, very high strengths can be achieved as evidenced by average tensile strengths of approximately 8GPa and 16GPa obtained with long (> 10 mm) (Petrovic et al., 1985) and short ( < 5 m m ) (Petrovic and Hoover, 1987) 5 micrometer diameter SiC whiskers. Finally as predicted in Eqs. (8-50) and (8-51), the toughness contribution of whisker reinforcement should increase with increase in whisker diameter. Experimental measurements of fracture toughness of alumina - composites with 20 vol.% SiC whiskers - show that the toughness increased from approximately 6.5 to about 9 to about ^ M P a ^ / m for increases in mean diameter of the SiC whiskers from 0.4 to 0.75 to 1 -1.5 jam, respectively. However, mismatch in thermal expansion coef-

452

8 Toughening Mechanisms in Ceramic Systems

ficients and elastic properties between this whisker and matrix system introduces hoop and axial tensile stresses (Angelini et al., 1987) which can lead to cracking and loss of mechanical integrity with increasing whisker diameter. Therefore one must balance the expected gain in toughness for a given whisker-matrix combination accrued from increasing the whisker diameter with the effects of local stresses generated by mismatch in properties. 8.3.2.3 Interfacial Characteristics

Increasing the ratio of the whisker to interface fracture conditions [either yw/y1 or 0f7TDB (TDB i s ^ e interface strength)] also increases the extent of interface debonding and whisker pullout for a given whisker diameter. In the alumina composites containing SiC whiskers of a selected diameter, the greatest toughening effect was associated with the largest pullout lengths (/po) which were about 3-5 times the whisker radius (Becher etal., 1988 a). The Zpo and toughness values were sensitive to surface treatments given the whiskers prior to incorporating them into the composites. 8.3.3 Microstructural Tailoring

Observations show that the fracture toughness of ceramics can be influenced by microstructure, especially in noncubic ceramics, that is, aluminas (Rice and Freiman, 1981; Mussler etal., 1982; Claussen etal., 1982; Steinbrech etal., 1983; Knehans and Steinbrech, 1982). Such behavior has been attributed to microcrack generation in the crack tip region due to the interaction of the crack tip stresses and the tensile TEA stresses generated at grain boundaries due to differential crystallographic thermal contraction, the compressive TEA stresses which locally inhibit fracture to form bridging grains in the

wake of the crack tip, or combinations of these (Rice and Freiman, 1981; Swain, 1986; Swanson et al., 1987; Mai and Lawn, 1987; Wu et al., 1978). It is very likely that all these mechanisms are interrelated, for example, crack tip microcracking and local TEA compressive stresses lead to the formation of bridging grains in the crack tip wake. Most observations on grain size effects have related the occurrence of microcracking due to local residual stress intensity factors which are the product of the magnitude of the local TEA stress and the square root of the grain size (Evans and Clarke, 1980; Fu and Evans, 1982). Other studies also indicate that increased toughness in silicon nitride ceramics can be obtained by the formation of elongated grain structures (Lange, 1979). This can be understood by noting the similarity of the toughening from elongated grains with that derived from whisker reinforcement. Thus there appear to be several ways to tailor microstructure to achieve improved fracture toughness. 8.3.3.1 Matrix Bridging: Grain Size Effects

Here grain size effects on toughness are considered for the case where bridges are formed by matrix grains which are left intact behind the crack tip. Such bridges may form due to crack branching, microcracking, compressive grain boundary stresses, or combinations of these effects. The bridging stress versus the crack opening response utilized in this discussion is that where the maximum crack opening at the end of the grain bridging zone depends on the matrix grain size. In fact, the bridging component considered is simply the frictional pullout of these grains. The bridging stress is the product of the frictional shear stress t gb supported by the fracture surfaces as the grain is pulled out times the fraction

453

8.3 Toughening Mechanisms

of bridging grains Fgb. The energy contribution of the pullout of these grains can be defined through Eqs. (8-48) and (8-51) by relating the pullout length to the grain size. For the convenience of our discussion, we assume that the grain pullout length is one half the grain size d so that the maximum crack opening displacement wmax equals d/2, the energy dissipated by this process then is: ~

(8-53)

and the grain bridging toughening contribution - square root of the matrix grain size - is predicted (Becher et al., 1990). The fracture resistance Km of the matrix will then include the energy to rupture the lattice, J o , and the grain bridging contribution, AJgb: Km =

r£m ^

+

A J gb )] 1/2

(8-54)

where Em is the Young's modulus of the matrix. The Jo term is akin to the average fracture toughness value of the various crystallographic fracture planes. Indeed, one observes that the fracture toughness of alumina ceramics determined for large crack extensions increases with increasing grain size (Rice et al., 1981). A maximum is achieved due to extensive microcracking and crack linkage which diminishes the toughness above a critical grain size. Furthermore, R-curve behavior accompanies the increase in toughness due to the grain size effects (Steinbrech et al., 1983; Knehans and Steinbrech, 1982; Swain, 1986). The observations are consistent with the grain-bridging processes described above, and the fracture toughness of aluminas exhibits the predicted yjd dependence, Fig. 8-26.

1.0

2.0

3.0

U.O

5.0

Figure 8-26. Alumina ceramics and SiC whisker-reinforced aluminia exhibit greater fracture resistance with increase in matrix grain size d. Data from Becher et al. (1989). (Reproduced, with permission, from the Annual Review of Materials Science, Vol. 20. © 1990 by Annual Reviews Inc.)

8.3.3.2 Matrix Bridging: Influence of Grain Geometry

Studies of the approaches to develop more thermal shock resistant alumina ceramics revealed that the growth of platelike alumina grains in a medium sized (5-10 jam) equiaxed grained matrix yielded significant toughening (Tiegs and Becher, 1985). Fracture toughness values of 7 to 8 MPa y/m were achieved for samples containing about 25 vol.% large (up to 100300 (im wide times up to 10-30 jim thick) single crystal alumina plates. The cracks were found to be deflected along the interface between the matrix and the large platelike grains. Thus fracture around the platelike grains produces crack bridges which contribute to the toughness. While the strengths of the aluminas with such large platelike grains is reduced as they act as large flaws, these composite microstructures led to much increased thermal shock resistance. Aluminas with similar equiaxed grain sizes but without these platelike grains had toughness values of 4 to 4.5 M P a J m while very fine grained

454

8 Toughening Mechanisms in Ceramic Systems

(1-2 jim) equiaxed aluminas exhibit values below 3 MPa^/m. On a similar note, the fracture resistance of both Si 3 N 4 and SiAlON (Lewis, 1981) ceramis has been found to be substantially improved by the in situ growth of whiskerlike grains. This approach has proven to be a potent toughening process leading to fracture toughness values of Kc > lOMPa^/m (Lange, 1979; Li and Yamanis, 1989; Himsolt etal., 1979). At the same time, quite high fracture strengths (> 700 MPa) can be achieved in these materials by controlling the elongated grain dimensions. One then has whiskerlike grains which reinforce the matrix while not introducing large area defects. It should be noted that the increase in fracture toughness of these nitride ceramics is consistent with the response predicted for and observed in whisker reinforced ceramics, Eqs. (8-39 a-c), (8-47), and (8-51) (Becher, 1990). The observations indicate that the fracture resistance increases with volume content (Lange, 1979; Himsolt et al., 1979) and grain dimensions. In fact, recent results illustrate that the fracture toughness of silicon nitride containing elongated grains increases as the square root of the elongated grain diameter (Kawashima et al.? 1991). This is comparable to the increase in toughness predicted for increase in ^/whisker diameter, Eqs. (8-47), (8-50), and (8-51). The similarity in toughening response is not surprising as the fracture process in both of these classes of ceramics involve bridging of the crack surfaces by the reinforcing phase, for example, either whiskers or elongated grains, Fig. 8-27. 8.3.4 Coupled Toughening Responses

There is considerable interest in combining various toughening processes to ex-

(a)

u 12 -.10 o

•_ Si 3 N 4 + (2wt%AI°3 2 + 5 wt% Y2

L A

2 ': 0 (b)

0.5

1 2.5 1.5 [Grain diameter (pm)] 1/2

3.5

Figure 8-27. (a) Observations of the fracture path in micro structurally toughened silicon nitride ceramics reveal that the elongated grains bridge the crack much like whiskers do in reinforcement ceramics. [Reproduced, with permission, from Li and Yamanis (1989).] (b) The fracture toughness increases as the square root of the elongated grain diameter increases, as predicted for crack bridging toughness processes.

plore means to further enhance the fracture resistance of ceramic systems. In this section, only two of the many possible combinations will be addressed: whisker reinforcement and transformation toughening and whisker reinforcement and matrix microstructural-grain size effects.

8.3 Toughening Mechanisms

8.3.4.1 Whisker Reinforcement Transformation Toughening

trix toughness:

The fracture toughness of zirconia toughened composites, Kc, can be described by Kc = K

(8-55)

where Km is the matrix toughness, AKT is the contribution associated with the transformation of tetragonal ZrO 2 particles. This latter term can be defined by Eqs. (8-44 a-c), that is AKjc is proportional to AGT and hence h1/2. The size of the maximum transformation zone, /i, is a function of the ratio of the matrix toughness, Km, to the critical transformation stress, defined by Eq. (8-38). Combining these equations, one obtains:

ABll2fEc{sT)2

v

o

455

(8-56)

which indicates a strong dependence of the composite toughness upon the matrix toughness. Equation (8-56) shows that the composite toughness is significantly raised by increasing the matrix toughness as an increase in both toughness components on the right hand side of Eq. (8-56) results (Becher and Tiegs, 1987). Microcrack toughening can be associated with the presence of monoclinic ZrO 2 particles and toughness may be achieved by microcracks which are introduced by the transformation or introduced during postfabrication cooling AKUC', or those initiated by the combination of the m-ZrO 2 particle stresses and the crack tip stress AKUC. If only pre-existing microcracks contribute, then the toughness should be the sum of AXUC' and Km. On the other hand, toughness from stress-induced microcracking will also increase as the microcracked zone the main crack increases in size. The zone size, ruc, again depending on the ma-

(8-57)

2 5-fold and > 3fold respectively (Becher and Tiegs, 1987). (Reprinted by permission of the American Ceramic Society.)

456

8 Toughening Mechanisms in Ceramic Systems

zirconia is approximately 1.5 as tough as the mullite matrix. The inclusion of 20 vol.% m-ZrO 2 particles to a mullite20 vol. % SiC whisker composite yields a toughness which is about 3.5-fold greater than the matrix. As noted in Fig. 8-28, these effects - whisker reinforcement, zirconia toughening, and their combined effects - appear to be additive. On the other hand, when the zirconia particles are in the tetragonal phase in a condition, for example, at a test temperature just above their M s temperature, the result of the combined toughening processes is greater than a simple additive effect, Fig. 8-28. Similar coupled toughening effects have been described by Claussen and Petzow (1986). One can see from the earlier discussion of transformation-toughened ceramics that (1) the toughness of the above composite will be a function of temperature when transformation toughening is initiated and (2) the degree of the transformation-toughening contribution will be determined, at least, by the alloy content, volume content, and size of the transformable zirconia particles. The latter factors also indicate that processing of such composites requires careful selection of compositions and advanced processing technology to achieve the desired microstructures. However, it is clear that a multiple toughening mechanism approach provides a means of obtaining substantial further increases in fracture resistance. 8.3.4.2 Whisker Reinforcement Matrix Grain Bridging

As discussed earlier, the fracture resistance of ceramics, especially, noncubic ceramics, will increase with increase in the grain size as a result of grain bridging in the wake of the crack tip. In addition, altering the matrix grain size to form whisker-

like grains can result in improved toughness due to bridging effects which are similar to those derived from whisker reinforcement. Thus the overall fracture toughness of the composite can also be influenced by the intrinsic matrix toughness, the microstructural component of the matrix toughness, especially in the case of noncubic matrices, and the whisker reinforcement contribution (Becher et al., 1991). These mechanisms may be simply additive in which case the overall composite toughness Kc will be: Kc = Km + AKgh = m

gb

= [E (J0 + AJ )]

(8-58) 1/2

c

cb 1/2

+ {E AJ )

where A J gb is the energy dissipated by matrix grain bridging, Eq. (8-53). Substitution of Eq. (8-53) into Eq. (8-58) shows that toughness of whisker-reinforced composites (also fiber-reinforced and other types of composites) with polycrystalline noncubic brittle matrices will increase with increase in matrix grain size. Experimental results for SiC whisker reinforced aluminas having various whisker contents and matrix grain sizes are in agreement with the grain size dependent toughness predicted by Eq. (8-58), Fig. 8-26. Note that these data are for samples fabricated using the sample whisker source and size. These results again illustrate how one aspect of matrix microstructure can be manipulated to enhance the fracture toughness of a composite by utilization of multiple toughening mechanisms and point to the need to control microstructure.

8.4 Summary The fracture resistance of ceramic systems can be substantially improved by a number of different approaches, and these can be combined to obtain additional

8.4 Summary

toughening effects. The successful application of these various approaches demands that attention be paid to the influence of microstructure and the chemical composition on the toughening response and how the response may be modified by the temperatures that the ceramic is exposed to. The text here has obviously not exhausted all the possible toughening mechanisms but has chosen instead to examine those of transformation toughening, whisker and related reinforcement approaches such as matrix grain size and shape, and the combined effects of these. An obvious omission which is quite similar to the above reinforcement processes is the introduction of equiaxed or platelike second phase particles or both. Dispersions of equiaxed TiC particles and TiB 2 particles can substantially increase the fracture toughness of SiC ceramics. The introduction of platelike grains has been shown to increase the toughness of alumina and recent results show that the incorporation of SiC platelets into an alumina matrix can also result in increasing the fracture resistance. These processes result in toughening behavior and fracture path characteristics which are quite similar to those for whisker and grain reinforcement effects. In the case of the use of equiaxed particles, especially for those with differing thermal expansion and mechanical properties from those of the matrix, several approaches have been proposed to describe the toughening effects. These include crack deflection, crack pinning, and crack branching and bridging. The local stresses introduced by expansion mismatch in the vicinity of second phase particles could also arrest or divert the main crack locally leading to the formation of a bridging matrix ligament. Additional attention is needed here to develop a more comprehensive model which relates mate-

457

rial properties and microstructure to the toughening response. The behavior of transforming toughening zirconias are quite well described by the existing models. Keeping account of the influence of size of the tetragonal phase particles or grains and of the solute, one can realistically design toughening zirconias. Further insight into the alloying behavior of these systems, for example, what solute characteristics influence the strength of its stabilizing effect, would be of great benefit. In the case of toughening approaches as relates to zirconia toughened ceramic composites, one can draw on the knowledge of the transformation-toughened zirconias. However, one must account for the effects of the mismatch in matrix versus zirconia particle properties and resultant local stresses on the ability to transform the tetragonal phase particles. One can ascertain how these stresses might overlap and change with increase in zirconia particle content and how this influences the transformation. While we can suggest how particle size and possible size distribution will modify the ease of transforming tetragonal zirconia particles in a ceramic matrix, this and the influence on toughness need to be systematically explored experimentally. These and matrix microstructure effects are seen as critical factors in the variability in the fracture toughness often observed in zirconiatoughened ceramics. Progress in the area of reinforced ceramics is providing a wealth of new insights into the toughening of ceramic systems. The advances in the theoretical description of the toughening response in whisker- and fiber-reinforcement ceramics provide details of how to begin to design tougher materials and directions where more insight is needed, for example, interfacial property-structure relationships. These

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two systems, whisker versus fiber reinforced, cover a range of systems - those based on very weak interfaces to those utilizing quite strong interfaces and those in between - which only strengthens the need to understand interfacial phenomena and their effects on fracture resistance. In addition, the models for whisker reinforcement point to a need to develop techniques to synthesize whiskers where size and strength can be altered in a controlled manner. The use of microstructural control to toughen ceramics offers considerable potential, and along with the reinforcement approaches suggests other avenues for toughening. We need to examine the factors influencing the toughening response in systems like the silicon nitrides with elongated grain structures to determine what and how grain and interfacial-grain boundary properties alter crack propagation and the toughness. This area and the ability to combine toughening processes are exciting new fields for exploration and exploitation in the design of ceramic materials.

8,5 Acknowledgements The success of such a venture was only possible with the support and contributions of our colleagues, each of whom have contributed to this field, and our families. P.F.B. gratefully acknowledges the continued support of the Materials Sciences Division, Office of Basic Energy Sciences, U.S. Department of Energy, which has provided him with the opportunity to conduct his own research activities in this field under contract DE-AC05 840R21400 with Martin Marietta Energy Systems, Inc.

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Patel, J. R., Cohen, M. (1953), Acta Metall. 1, 532538. Pellini, W. S. (1977), Principles of Structural Integrity Technology. Washington, D.C.: U.S. Government Printing Office. Petrovic, X X, Hoover, R. C. (1987), /. Mater. Sci. 22, 517-522. Petrovic, J. X, Milewski, X V, Rohr, D. L., Gac, F. D. (1985), J. Mater. Sci. 20, 1167-1177. Pickens, J. P., Gurland, X (1978), Mater. Sci. Eng. 33, 135-142. Predecki, P., Abuhasan, A., Barrett, C. S. (1988), in: Advances in X-ray Analysis, Vol. 13: Barrett, C. S., Gilfrich, X V, Jenkins, R., Russ, X C , Richardson, J.W., Jr., Predecki, P. K. (Eds.). New York: Plenum Press, pp. 231-243. Prewo, K. M., Brennan, X X (1980), J. Mater Sci. 15, 463-468. Prewo, K. M., Brennan, X X, Layden, G. K. (1986), Bull. Am. Ceram. Soc. 65, 305-313. Rao, K. T. V, Odette, G. R., Ritchie, R. O. (1992), Acta Metall. Mater. 40, 353-361. Rao, S. S. (1991), Ph.D. Dissertation, Rutgers. Rice, X R. (1968), Trans. ASME, J. Appl. Mech. 35, 379-386. Rice, R. W, Freimann, S. W (1981), J. Am. Ceram. Soc. 64, 345-350. Ritchie, R. O. (1988), Mater. Sci. Eng. 103, 15-28. Rose, L. R. F. (1986 a), J. Am. Ceram. Soc. 69, 208212. Rose, L. R. F. (1986b), J. Mech. Phys. Solids 34, 609616. Rose, L. R. F (1987a), Proc. R. Soc. London A412, 169-197. Rose, L. R. F (1987 b), /. Mech. Phys. Solids 35, 383405. Rose, L. R. F , Swain, M. V. (1986), /. Am. Ceram. Soc. 69, 203-207. Rose, L. R. E, Swain, M. V. (1988), Acta Metall. 36, 955-962. Riihle, M., Evans, A. G. (1989), Prog. Mater. Sci. 33, 85-167. Riihle, M., Kriven, W. M. (1983), Ber. Bunsenges. Phys. Chem. 87, 222-228. Riihle, M., Evans, A. G., McMeeking, R. M., Charalambides, P. G., Hutchinson, X W. (1987), Acta Metall. 35, 2701-2710. Schmauder, S., Schubert, H. (1986), /. Am. Ceram. Soc. 69, 534-540. Schubert, H. (1986), /. Am. Ceram. Soc. 69, 270-272. Seising, X (1961), J. Am. Ceram. Soc. 44, 424. Seyler, R. X, Lee, S., Burns, S. X (1984), in: Advances in Ceramics, Vol. 12: Claussen, N., Riihle, M., Heuer, A. H. (Eds.). Columbus, OH: Am. Ceram. Soc. Shalek, P. D., Petrovic, X X, Hurley, G. F , Gac, F. D. (1986), Am. Ceram. Soc. Bull. 65, 351-356. Sigl, L. S., Mataga, P. A., Dalgleish, B. X, McMeeking, R. M., Evans, A. G. (1988), Acta Metall. 36, 945-953.

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Steinbrech, R., Knehans, R., Schaarwachter, W. (1983), J. Mater. Sci., 265-270. Sternstein, S. S. (1977), in: Treatise on Materials Science and Technology, Vol. 10 B: Schultz, J. M. (Ed.). New York: Academic Press. Stump, D. M., Budiansky, B. (1989), Int. J. Solids Struct. 25, 635-646. Sun, Q. P., Hwong, K. C , Yu, S. W. (1991), /. Meek Phys. Solids 39, 507-524. Swain, M. V. (1983), in: Fracture Mechanics of Ceramics, Vol. 6: Bradt, R. C , Evans, A. G., Hasselman, D. P. H., Lange, F F. (Eds.). New York: Plenum Press. Swain, M. V. (1985), Acta Metall. 33, 2083-2091. Swain, M. V. (1986), / Mater. Sci. Lett. 5, 1313-1315. Swain, M. V, Rose, L. R. F. (1986), J. Am. Ceram. Soc.69, 511-518. Swanson, P. L., Fairbanks, C. I, Lawn, B. R., May, Y.-W, Hockey, B. J. (1987), / Am. Ceram. Soc. 70, 279-289. Tada, H. (1985), The Stress Analysis of Cracks Handbook, 2nd ed. St. Louis: Paris Productions Inc. Taya, M., Hayashi, S., Kobayashi, A. S., Yoon, H. S. (1990), J. Am. Ceram. Soc. 73, 1382-1391. Tiegs, T. N., Becher, P. F. (1985), Alumina Composites, in: Proc. 22nd Auto. Tech. Dev. Contractors' Coord. Meeting, Vol. P-155. Warrendale, PA: Soc. Automotive Eng., pp. 479-485. Tsukuma, K., Shimada, M. (1985), /. Mater. Sci. 20, 1178-1184. Urquhart, A. W. (1991), Adv. Mater. Processes [7], 25-29. Vekinis, G., Ashby, M. F , Beaumont, P. W. R. (1990), Acta Metall. Mater. 38, 1151-1161.

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General Reading Fracture Mechanics of Ceramics, Vol. 1-4 (19741978): Bradt, R. C , Hasselman, D. P. H., Lange, F. F. (Eds.). New York: Plenum Press. Fracture Mechanics of Ceramics, Vol. 5-8 (1983, 1986): Bradt, R. C , Hasselman, D. P. H., Evans, A. G., Lange, F. F. (Eds.). New York: Plenum Press. Green, D. X, Hannink, R. H., Swain, M. V. (1989), Transformation Toughening of Ceramics. Boca Raton, FL: CRC Press. Kelly, A. A., Macmillan, N. H. (1986), Strong Solids, 3rd ed. Oxford: Clarendon Press. Lawn, B. R., Whilshaw, T. R. (1975), Fracture of Brittle Solids. Cambridge: Cambridge University Press. Series on Science and Technology of Zirconia, Adv. Ceram. 3,12, 24. Columbus, OH: Am. Ceram. Soc.

9 Mechanical Behavior of Cellular Ceramics Rasto Brezny and David J. Green Department of Materials Science and Engineering, The Pennsylvania State University, University Park, PA, U.S.A.

List of 9.1 9.2 9.3 9.4 9.4.1 9.4.2 9.4.3 9.5 9.6 9.6.1 9.6.1.1 9.6.1.2 9.6.2 9.7 9.7.1 9.7.2 9.7.2.1 9.7.2.2 9.7.2.3 9.7.3 9.8 9.8.1 9.8.2 9.8.3 9.8.3.1 9.8.3.2 9.8.4 9.9 9.9.1 9.9.2 9.9.2.1 9.9.2.2 9.9.3 9.10

Symbols and Abbreviations Introduction Classification of Cellular Materials The Structural Role of Porous Materials Modelling Mechanical Behavior of Cellular Ceramics Structure of Foams Density-Microstructure Relationships Gibson and Ashby Model Macro- and Microstructural Characterization Elastic Behavior Open Cell Ceramics Effect of Density Effect of Cell Size Closed Cell Ceramics Fracture Toughness Theoretical Approach Experimental Work on Open Cell Ceramics Measurement of Strut Strength Effect of Density Effect of Cell Size Experimental Work on Closed Cell Ceramics Tensile Strength Theoretical Approach Specimen Size Effects Experimental Work on Open Cell Ceramics Effect of Density Effect of Cell Size Experimental Work on Closed Cell Ceramics Compressive Strength Theoretical Approach Experimental Work on Open Cell Ceramics Effect of Density Effect of Cell Size Experimental Work on Closed Cell Ceramics High Temperature Mechanical Behavior

Materials Science and Technology Copyright © WILEY-VCH Verlag GmbH & Co KGaA. Allrightsreserved.

465 467 468 469 471 472 472 473 474 475 476 476 478 479 480 480 482 482 486 489 491 492 492 494 496 496 498 500 500 500 503 504 506 508 509

464

9.10.1 9.10.2 9.11 9.12 9.13

9 Mechanical Behavior of Cellular Ceramics

Thermal Shock Behavior Creep Behavior Conclusions Acknowledgements References

509 512 513 514 515

List of Symbols and Abbreviations

465

List of Symbols and Abbreviations a A A{ B C t , . . . , C7 D E Es / G Gc, Gcs KIC Klcs L Mf n N P r rt t Tt, T 2 ATC Y

critical macroscopic flaw size constant depending on the cell geometry and solid material properties mirror and branching constants exponent related to the actual deformation mode of the unit cell geometrical constants constant characteristic of the end condition on the beam Young's modulus Young's modulus of the struts number of faces shear modulus critical strain energy release rate of the cellular and solid (strut) materials fracture toughness toughness of the solid material length of the cell edges fracture m o m e n t creep constant of the strut material number of edges per face volume fraction of porosity radius of gyration radii of the mirror-mist a n d mist-hackle boundaries thickness surface temperature of a solid critical temperature change crack geometrical constant

a ft 8 £ £Os v Q gs gt a aOs oc afc crfs 0.70). Although these two related groups of materials have more complicated structures than cellular materials, their mechanical behavior should possess similarities.

9.3 The Structural Role of Porous Materials Cellular structures abound in nature and although they can be complex, they are often aesthetically pleasing and intriguing. Figure 9-5 shows the cellular struc-

• I ",,,,

'-. t Mi

\•,--

(a)

(b) Figure 9-4. Macrostructure of sintered hollow glass spheres at (a) low degrees of sintering, showing both open and closed porosity (Green and Hoagland, 1985, reprinted by permission of the American Ceramic Society), and (b) high degrees of sintering exhibiting only closed porosity.

(b) Figure 9-5. Natural cellular structures found in (a) spine of sea urchin, (b) sea sponge.

470

9 Mechanical Behavior of Cellular Ceramics

tures of a sea urchin spine and natural sponge. It is reasonable to suppose natural cellular structures are not a result of random events but rather a careful evolutionary optimization process. These structures must fulfill a variety of functions but of relevance here, is the ability to withstand various types of mechanical forces. It is important, therefore, to determine whether porous materials possess some special characteristics in their mechanical behavior and if so, can man-made versions of these materials be used in structural applications. A clue to the answer to the former question can be gained from some recent calculations of Ashby (1989), in which he considers design of structures that minimize weight for a given stiffness or strength. In particular, he demonstrated the mode of loading can have a strong influence on the design process. Table 9-1 shows a few examples of these calculations, in which the weight has to be minimized for a given stiffness or brittle strength. The optimization process simply involves maximization of certain combinations of 3 parameters, E, the Young's modulus, KIC, the fracture toughness and Q, the density of the bulk material. The use of Klc, rather than strength as a brittle design parameter assumes one can specify the critical flaw size. As shown in Table 9-1, for the loading geometries considered, the minimization of weight for a given stiffness depends on maximizing the parameters, E/Q, E/Q2 and E/Q3, whereas for strength it depends on KIC/Q, KIC/Q3/2 and KIC/Q2. Thus one concludes for some loading geometries, density can play a pivotal role in producing an optimum design. In order to appreciate this effect, several materials are compared in Table 9-2, in terms of the parameters that optimize stiffness. In this table, the parameters are normalized to those of

wood, as this is the most utilized natural material for structural applications. The values used for these calculations are given in Table 9-3. There are several important observations from the data in Table 9-2. In comparing the value of E/Q for wood with dense ceramics and metals one finds wood is comparable to metals but inferior to dense ceramics. For the values of E/Q2 and E/Q3, however, wood can be substantially superior. Next, comparison of wood with data for ceramic foams (open cell alumina and closed cell glass) shows wood is only slightly better and in one case is outperformed. It should be noted that the corn-

Table 9-1. Parameters required to maximize stiffness or strength for minimum weight for selected modes of loading (after Ashby, 1989). Design parameters

Mode of loading

stiffness Rod in tension Bending of rod Bending of plate Internal pressure in cylinder

E/Q

strength KIC/Q

3I2

E/Q2

KZ/Q2 Klc/Q

E/Q

Table 9-2. Values of stiffness design parameter for various materials. Material

E/Q

E/Q2

E/Q3

Wood Steel Aluminium alloy

1 1.1 1.2

1 0.06 0.19

1 0.003 0.03

4.4 4.2 5.7 1.6

0.49 0.58 0.78 0.12

0.06 0.08 0.11 0.009

0.36 0.86

0.41 1.5

Dense ceramics Aluminum oxide Silicon nitride Silicon carbide Zirconium oxide

Cellular ceramics (10% dense) Aluminum oxide (open cell) 0.3 Glass (closed cell) 0.5

All values have been normalized to that of wood.

9.4 Modelling Mechanical Behavior of Cellular Ceramics

471

Table 9-3. Values used for design parameter calculations. Material Wood Steel Aluminum alloy

E (GPa)

e(kg/m3)

10.5 207 75

450 8000 2750

Gibson and Ashby (1988) Gibson and Ashby (1988) Gibson and Ashby (1988)

400 304 418 205

3970 3180 3210 5750

Lackey Lackey Lackey Lackey

Reference

Dense ceramics Aluminum oxide Silicon nitride Silicon carbide Zirconium oxide

et al. (1987) et al. (1987) et al. (1987) et al. (1987)

Cellular ceramics (10% dense) Aluminum oxide (open cell) Glass (closed cell)

3.0 2.9

parison of ceramic foams with a natural cellular material is a little unfair, especially as we are considering the most stiff direction of the wood. Presumably, ceramic honeycombs can give values superior to wood for the axial and transverse directions. The high values for the closed cell glass are surprising but may indicate that closed cell (crystalline) ceramics could be attractive materials for maximum stiffness with minimum weight. Unfortunately, there are very few experimental data on these types of materials. An important conclusion of the above calculations is that porous materials can offer advantages in structural applications over dense materials. Clearly, the structural design process involves more than design for maximum stiffness and one must consider many other features, such as strength, thermal shock resistance, chemical and thermal stability, etc. Moreover, there may be non-structural features involved in the design. Some of the features that could be useful in design and are present in porous ceramics include permeability (open cell), impermeability (closed cell), high surface area, low thermal conductivity, low dielectric constant, thermal and

397 255

Hagiwara (1986) Zwissler and Adams (1983)

chemical stability. Currently, cellular ceramics are not a particularly common material, unlike their polymeric counterparts, but the above discussion implies they could be used in structures. A theme of this chapter is that the mechanical behavior of currently-available cellular ceramics could be substantially improved.

9.4 Modelling Mechanical Behavior of Cellular Ceramics It clearly would be useful to derive analytical equations that relate the mechanical behavior of cellular materials to their microstructure. Such an approach is helpful in the design process as one could predict properties. It also allows the critical parameters that control the deformation process to be identified. This latter process is particularly important in the development of new materials and improved fabrication procedures. The major scientific approach that has been used to accomplish this type of theoretical analysis has been to identify a unit cell and analyze the deformation behavior of the cell. For honeycombs, unit cells that fill a plane in two

472

9 Mechanical Behavior of Cellular Ceramics

dimensions are any triangle, quadrilateral or hexagon with a center of symmetry (Gibson and Ashby, 1988). Man-made honeycombs utilize these shapes, often with a high degree of precision whereas natural honeycombs are less uniform, showing dispersion in cell shape and size (Gibson and Ashby, 1988). The uniformity of the man-made honeycombs can be analyzed in detail and a variety of deformation mechanisms have been identified (Gibson and Ashby, 1988). Analytical expressions have been put forward for the various mechanisms and confirmed by experimental data (Gibson and Ashby, 1988). In this work, we have chosen not to discuss ceramic honeycombs in detail, primarily as a result of the lack of experimental data. Such materials are expected to be elasticbrittle with creep deformation becoming important at high temperatures. The rest of the chapter will emphasize ceramic foams and the approach will be to compare theoretical expressions with experimental data. 9.4.1 Structure of Foams

Compared to honeycombs, a greater variety of space-filling, cell shapes is possible in three dimensions (foams), viz, triangular, rhombic and hexagonal prisms, rhombic dodecahedra and the tetrakaidecahedra. These types of cells have often been used as idealizations for the unit cell (Gibson and Ashby, 1988). Other geometric figures, such as tetrahedra, icosahedra and pentagonal dodecahedra have also been analyzed but these shapes fill space, only if distorted. The difficulty with the unit cell approach is that most foams do not involve a regular packing of a particular cell shape and there are variations in both shape and size, such that the cells have differing numbers of faces and edges. There are, however, topological laws that govern the connectivity of

cellular solids. For example, Euler's Law can be used to relate the average number of edges per face (n) to the number of faces (/) in an isolated cell (Gibson and Ashby, 1988), i.e., (9-1) This relationship indicates the reason most foams possess faces with 5 edges, regardless of the cell shape. For example, N is found to be 5.0, 5.14 and 5.4 for dodecahedra, tetrakaidecahedra and icosahedra respectively. Although many foam-like structures, such as grain boundaries in ceramics and metals, have / ~ 14 and N = 5.1, the topology of the foam will depend on the process by which the foam is made. For example, in man-made foams, the volume expansion during foaming is often constrained to one (rise) direction and the cells become elongated in this direction. This anisotropy in cell shape can in some cases, give significant anisotropy in mechanical properties. For this review, however, we will consider the foams to be isotropic. Gibson and Ashby (1988) have demonstrated the analysis for isotropic foams can be modified to describe anisotropy in structure or properties. 9.4.2 Density-Microstructure Relationships

An important property of a foam is its relative density, i.e., the density of the bulk foam (Q) normalized by the theoretical density of solid that forms the cell edges and faces (£t). For cellular ceramics, this definition of density does pose some problems, in that cell edges (or struts) and faces are not always theoretically dense. Indeed, as will be seen later, many open cell ceramics have struts that are hollow and even the apparently solid portion can contain fine-scale

9.4 Modelling Mechanical Behavior of Cellular Ceramics

porosity. Thus we will also define a parameter termed the normalized density of the foam, where the bulk density of the foam is normalized with respect to the density of the cell edges and faces (QS). That is, the volume used to calculate Q/QS includes the porosity within the cell edges and faces. For cases in which the cell edges and faces contain porosity or are hollow, g/gt < Q/QS. At this point, it is worth emphasizing another important point with respect to the microstructure. The microstructure should be thought of at two levels, the first we will call the macrostructure and refers to the cellular structure itself, i.e., the arrangement of the cells. The finer structure that should be considered is the structure within the cell edges and faces and we will call this the microstructure. At low densities (Q/QS < 0.2), Gibson and Ashby (1988) have shown that the normalized density can be related to the macrostructure by the following simple expressions for open and closed cell foams respectively (9-2)

473

9.4.3 Gibson and Ashby Model

The complications in defining the macrostructure of a foam and a unit cell led Gibson and Ashby (1982) to consider a simple geometry for this unit cell, as shown in Fig. 9-6 for the open cell case. As seen in this figure, deformation of the unit cell even under axial loads leads to cell edge bending and the unit cell was chosen as a result of visual observations of such bending in honeycombs and foams. Thus, provided the identification of the deformation modes is correct, it is assumed that dimensional analysis will give the correct dependence on the critical parameters that describe the deformation, and the geometric effects can be combined into a single parameter. Thus the scaling from the unit cell to the bulk properties, is incorporated into the geometric constant and presumably, the value of this parameter can be found by comparing experimental data with the theoretical expressions. By simplifying the geometry, the mechanics analysis is substantially facilitated and expressions have been derived for most of the critical mechanical properties of cellular materials. In particular for brittle cellular foams, expressions have been derived for the elastic constants, tensile

(9-3) where t is the thickness of the cell edges or faces, L is the length of the edges and C1 and C 2 are numerical constants (approximately unity) that depend on cell shape. At higher densities, these relationships become more complicated (Gibson and Ashby, 1988). Similarly, the manner in which the solid is distributed can be important. For example, collection of solid in the nodes of the struts (open cell materials) and the relative thickness of the cell faces to the cell edges (closed cell materials), will impact these relationships.

Figure 9-6. Unit cell used by Gibson and Ashby to derive mechanical relationships for open cell materials (Brezny et al., 1989, reprinted by permission of the American Ceramic Society).

474

9 Mechanical Behavior of Cellular Ceramics

and compressive strength, fracture toughness, hardness and creep rate (Gibson and Ashby, 1988). The approach in this review is to use the Gibson and Ashby model and the subsequent analytical expressions to discuss the experimental behavior found in ceramic foams. In particular, emphasis will be given to any modifications to the theory that are needed for brittle foams.

9.5 Macro- and Microstructural Characterization Following the discussion in Sec. 9.4, it is clearly important to carefully characterize both the macro- and microstructures of cellular materials. It is also advantageous to have some idea of the fabrication procedure. A common processing approach for open cell ceramics is to coat an open cell polymer foam, usually with a ceramic powder dispersed in a liquid (e.g., Lange and Miller, 1987). This approach approximately replicates the polymer and gives a rather distinctive macrostructure for the material, in that the cell struts are hollow (Fig. 9-7). The central hole represents the original shape and position of the polymer, which was removed by pyrolysis during the firing of the ceramic. Moreover, in many of these materials, the struts or faces contain microscopic porosity. Before applying any theoretical model to the mechanical properties of cellular materials, it is important to determine whether the assumed relationship between the density and macrostructure [Eqs. (9-2) and (9-3)] is valid. To keep these simple equations, it is important to determine the normalized density, i.e., the value of QS must include the total volume associated with the strut porosity. This makes the characterization process more difficult but

Figure 9-7. Fracture surface of a single strut in an open cell ceramic made by coating and burnout of polymer foam. Triangular hollow region results from polymer removal.

optical measurement of the hole size and shape and the determination of pore volume using mercury porosimetry have been used to calculate £s(Brezny and Green, 1989). Quantitative optical microscopic measurements can be used to determine the average values of t and L for a particular material. Figure 9-8 shows the logarithm of the normalized density as a function of log(t/L) for three commerciallyavailable, alumina-based, open cell ceram-

1-

0.1^r

A Q • —

yr yr yS 0.01- ^0.1

,

,

Alumina Alumina-zirconia Alumina-mullite Eq. (9-2) , ,—, , . 1

Strut thickness /length

Figure 9-8. Normalized density as a function of the thickness/length ratio of the struts in alumina materials. Solid line represents the slope predicted by Eq. (9-2) for entirely open cell material.

9.6 Elastic Behavior

ics and the solid line is that predicted by Eq. (9-2) with C± = 1 (Brezny and Green, 1989). It is clear that only one of the materials, alumina-mullite, gives good agreement with the equation. Visual observation indicated the other two materials possessed an increasing number of closed faces, as the density increased and thus one obtains materials that are partially closed. Figure 9-9 shows the type of macrostructure observed in the partially-closed cell materials. The steeper slopes for the two non-ideal materials were interpreted to be a result of the extra material being used for cell face formation rather than changing the strut dimensions (Brezny and Green, 1989). Recently, similar data was gathered by Van Voorhees (1990) for an open cell alumina with a slightly finer cell size. In this work, he found the power dependence of (t/L) on density was < 2 and this was interpreted as additional material being deposited in the nodes, where cell struts meet. Overall, it is clear that the ways in which the solid material is distributed throughout the cell (faces or nodes) can significantly impact the density-macrostructure relationships. Two other materials will be mentioned in some detail in the remainder of the chapter and it is worth briefly discussing some of their macrostructural characteristics as they were fabricated using a different procedure than discussed above. The first of these is an open cell vitreous carbon foam that is formed by pyrolysis of a polymeric foam (Sherman et al., 1991). These materials usually possess a completely open cell structure with solid struts, as shown in Fig. 9-10. The density -macrostructure data for these materials have been obtained for a single density and are consistent with Eq. (9-2), with C± = 0.75. These vitreous carbon foams are also used as the basis for a third type of fabrication ap-

475

Figure 9-9. Macrostructure of a partially closed cell material showing some face filling. Arrows indicate longitudinal strut cracks.

Figure 9-10. Macrostructure of reticulated vitreous carbon which exhibits completely open cells over a wide range of sizes.

proach, in which chemial vapor processes are used to deposit a variety of oxides, borides, nitrides and carbides onto the carbon foam (Sherman et al., 1991). Figure 9-11 shows an example of an open cell SiC material. The fractured strut shows the deposited layers of SiC and the carbon core that is used as the cellular substrate.

9.6 Elastic Behavior The initial response of cellular ceramics to stress is linear elastic and for isotropic

476

9 Mechanical Behavior of Cellular Ceramics

9.6.1 Open Cell Ceramics Using standard beam theory Gibson and Ashby (1982) determined the deflection of the cell struts in the unit cell (Fig. 9-6), and by relating the applied stress to the force acting on the struts obtained T

(a)

(9-4)

where E and £ s are the Young's moduli of the foam and the struts and C 3 is a geometric constant. By substitution of Eq. (9-2) and assuming C± = I, one can relate the modulus to the normalized density, (9-5) The analysis for the shear modulus of the foam (G) is similar and Gibson and Ashby (1982) obtained (9-6)

ip) Figure 9-11. (a) Macrostructure of SiC foam made by chemical vapor deposition of SiC onto reticulated vitreous carbon foam, (b) Fracture surface of a single strut reveals carbon core and several layers of deposited SiC.

materials, one usually requires two elastic constants, e.g., the Young's and shear moduli. Lakes (1986,1991) has suggested cellular solids may not obey classical elasticity theory. Such non-classical behavior has many ramifications (Lakes, 1991) but for this work, the cellular ceramics will be treated as being classical. Cell strut bending has been identified as the major (linear elastic) deformation mode in open cell materials (Gibson and Ashby, 1988).

Gibson and Ashby (1982) considered a variety of corrections to these simple equations but found offsetting effects and thus they suggest Eqs. (9-5) and (9-6) are valid, at least as a first approximation, for all densities. Comparing Eqs. (9-5) and (9-6) with experimental data on open cell materials, Gibson and Ashby (1988) conclude C 3 « 1 and C 4 = 0.375. As pointed out earlier, foams can show significant anisotropy and this complicates the theoretical analysis. In addition, some foams can show unusual elastic behavior, such as negative values of Poisson's ratio (Lakes, 1987, 1991). 9.6.1.1 Effect of Density Initial elastic constant measurements on open cell alumina by Hagiwara and Green (1987) showed Eqs. (9-5) and (9-6) gave

9.6 Elastic Behavior

good agreement in terms of the exponent (2) but the values of the geometric constants (C3 and C4) were less than suggested by Gibson and Ashby (1988). Clearly the choice of values of £ s and QS are critical in determining these constants. Hagiwara and Green (1987) recognized the presence of the hollow struts is a feature that would impact the theoretical analysis. From beam theory, Hagiwara and Green (1987) showed that the hollow strut would actually increase the geometric constant if one considers the variation of modulus with respect to relative density. That is, hollow struts are actually more efficient than solid, in terms of stiffness at a given relative density. This is a result of the hole significantly reducing the density but not the flexural rigidity of the struts. In order to keep the simplicity of Eqs. (9-5) and (9-6), the parameter {Q/QS) has to be interpreted as normalized density and not relative density (see Sec. 9.5). The choice of Es will be influenced by the hollow nature of the struts but as discussed above, this effect is not expected to be as critical as the density correction. It would be useful if Es could be measured directly but currently we are not aware of any such experimental technique. In order to estimate £ s , it is important to be aware of the phase content of the strut material. For example, we have recently studied an alumina-mullite (AM), open cell ceramic, the same one described in Fig. 9-8. The strut walls in these materials were found to possess ~ 25% porosity and the mullite volume fraction was 0.28. A Young's modulus for dense alumina/28% mullite of 328 GPa can be obtained from the average of the upper and lower bounds (Young's moduli of alumina and mullite are assumed to be 380 and 225 GPa respectively, Kingery et al, 1976; Wu, 1990). The value of Es must also account for the porosity and using the

477

form of the correction suggested by Davidge (1979), the value of Es was estimated to be 190 GPa. In the original work of Hagiwara and Green (1987), such a careful estimation of QS and Es was not performed and thus we have analyzed some more recent elastic constant data (Brezny, 1990; Dam, 1988; Orenstein, 1990). These data were gathered on materials from a single manufacturer, at constant cell size. The Es value of 190 GPa, as calculated above, was used for the modulus normalization (ignoring the small effect of the central hole) and the approach used by Brezny and Green (1989) was used to change relative to normalized density. Figure 9-12 shows the results of these calculations. As can be seen, the modulus data for these open cell aluminas shows considerable scatter and this was considered to be a result of material variability. The slopes of the log-log plots for the Young's and shear moduli were 1.9 and 2.2 respectively and these are in good agreement with the value of 2 predicted by Gibson and Ashby (1982). Forced fits, using a power dependence of 2, are shown in Fig. 9-12 and the values for C 3 and C 4 were 0.42 and 0.17 respectively. These values are similar to the ones origi-

Young's modulus • Shear modulus "D O •o (D N

75 E 0.01

0.001 0.1 Normalized density

Figure 9-12. Relative Young's and shear moduli of cellular alumina as a function of normalized density. Data exhibits good agreement with Eqs. (9-5) and (9-6).

478

9 Mechanical Behavior of Cellular Ceramics

nally suggested by Hagiwara (1986) and Hagiwara and Green (1987), i.e., 0.363 and 0.142 for a different open cell alumina. Overall, it appears for these open cell ceramics, the values of C 3 and C 4 are substantially less than those suggested by Gibson and Ashby (1988). Zhang and Ashby (1989) have recently refined the Gibson and Ashby model using a tetrakaidecahedron as the unit cell, obtaining values of 0.5 and 0.17 for C 3 and C 4 respectively. These latter values are in good agreement with the data on the open cell alumina (C 3 = 0.42 and C 4 = 0.17) shown in Fig. 9-12. It is important to note that the AM material discussed here, was found to agree with Eq. (9-2) (see Fig. 9-8). Cellular materials that are partially-closed, such as the other materials shown in Fig. 9-8 would not be expected to satisfy Eqs. (9-5) and (9-6) and this was confirmed by Dam (1988).

8000 CO CL

o RD = 0.11 • RD = 0.16

6000

3

o

4000

?

2000

0

1

2

3

4

5

Cell size (mm)

Figure 9-13. Relative Young's modulus of an alumina mullite material increases with cell size, for two different relative densities (RD).

9.6.1.2 Effect of Cell Size According to Eqs. (9-5) and (9-6), one does not expect any variation of the elastic constants with cell size. In the AM material discussed above, it appeared initially there may be a cell size effect. For example, Fig. 9-13 shows data for 3 different cell sizes (Dam, 1988). Macrostructural observation showed the materials with the finest cell size often contained longitudinal strut cracks, Fig. 9-14 a. Clearly, this would be expected to reduce Es for these materials. In order to gain more detailed insight into the effect of cell size, elastic constant measurements were made on vitreous carbon, open cell foams (Brezny and Green, 1990 a). These materials possess solid struts and do not appear to have the complications of partial cell closure or cracked struts. The data are shown in Fig. 9-15 and there is no significant influence of cell size. Another interesting aspect of the carbon foam is the

(a)

(b) Figure 9-14. Microstructure of fine cell alumina mullite foam exhibited (a) an increase in the number of longitudinal strut cracks (marked by arrows) and (b) fracture of this material occurred primarily by strut splitting.

9.6 Elastic Behavior

4Pa)

140 120-

jng's modulu

100-

O

80-

6040-

I

i

I ••

*-

2000

1

2

3

4

5

Cell size (mm)

Figure 9-15. Young's modulus of RVC exhibits no cell size dependence in agreement with Eq. (9-5).

low material variability, especially compared to the open cell aluminas. For the data in Fig. 9-15, 20 specimens were tested for each cell size and the point to point variability was considered to be related to variations in Es (Brezny and Green, 1990 a). 9.6.2 Closed Cell Ceramics

Gibson and Ashby (1988) have derived analytical equations for the elastic constants of closed cell materials, recognizing some faces must be placed in tension in either tensile or compressive loading. Another contribution that can be important in some circumstances is the compression of any liquid or gas that is present within the cells. Ignoring this latter effect, the analysis gave

479

C 4 = C 4 = 0.375. These equations show a transition in density exponent from 1 to 2 as 4> increases from 0 to 1, i.e., as the faces become thinner. The limiting condition, (/> = 1, gives the equations for open cell materials, i.e., Eqs. (9-5) and (9-6). Equations (9-7) and (9-8) predict the lower the value of (/>, the higher the modulus at a given density, thus it appears the cell faces can substantially increase the foam stiffness. Using a comparison with prior experimental data, Gibson and Ashby (1988) suggest $ may be in the range 0.6 to 0.8 for many closed cell foams. For these values, cell edge bending no longer appears to be the dominant deformation mechanism as it is being constrained by the attached faces. There is very little data on the elastic behavior of closed cell ceramic foams. Zwissler and Adams (1983) and Morgan et al. (1981) have studied foamed glasses and their Young's modulus data are shown in Fig. 9-16. The data, show the predicted decrease in the power dependence of the relative density compared to open cell ceramics and the values of E/Es are substantially higher (see Fig. 9-12). The implication is that the elastic constants of closed cell, polycrystalline ceramics may be in the

B Zwissler and Adams • Morgan et al. 0.1

-ct>)U)

(9-7)

Uj

0.01

and ^

(9-8)

0.001 0.01

where C 3 and C4 are geometric constants and (j) is the volume fraction of solid in the cell edges. Gibson and Ashby (1988) suggest values of C 3 = C 3 = 1 and

0.1 Relative density

Figure 9-16. Young's modulus of closed cell foamed glass material after Zwissler and Adams (1983) and Morgan et al. (1981).

480

9 Mechanical Behavior of Cellular Ceramics

range of one-tenth to one-fiftieth of the modulus of the dense materials, making their specific stiffness values very attractive for structural applications. Ashkin et al. (1990) have compared their data on gel-derived, porous silica to Eq. (9-4) and found density exponents > 2 and similar to the work on the open cell alumina discussed in Sec. 9.6.1.1, the geometric constants was < 1. Similarly, in studies on the mechanical behavior of sintered hollow glass spheres (Green and Hoagland, 1985), deviations were also seen from the Gibson and Ashby predictions. Green and Hoagland (1985) suggested the elastic constants would be very sensitive to the size of the sintered contact areas in the initial stage of sintering and demonstrated this could explain the higher density exponent. Thus although Eq. (9-4) gives a reasonable approximation to the work on other high porosity systems, such as sintered gels, there can be deviations in the region where the materials are approaching a powder, i.e., with little or no connectivity between the particles.

9.7 Fracture Toughness Ceramics that are considered for high temperature applications are often elasticbrittle at temperatures below ~1000°C. In this temperature range, the initial tensile response of ceramics is linear elastic until at a maximum load, a crack propagates through the material. For this type of behavior, one expects the strength to be determined by the fracture toughness of the material and the size of the flaws within the material. For some porous materials, it has been suggested that failure can be more appropriately described by a cumulative damage type of analysis (Meiser and Tressler, 1981). For this review, we will

consider the fracture toughness approach at least for tensile stresses, as this is the type of behavior we have observed in open cell ceramics. 9.7.1 Theoretical Approach

The fracture toughness of brittle foams was originally discussed by Maiti et al. (1984 a) using two types of analyses. Both approaches are based on the unit cell considered by Gibson and Ashby (1982). The first was derived from a linear elastic fracture mechanics argument whereas the other was a simple energy balance approach. The fracture mechanics approach initially treats the foam as a linear-elastic continuum and determines the forces acting ahead of a crack tip. The discrete nature of the macrostructure is then introduced by considering the action of these forces on an array of unit cells. The crack is considered to advance when the moment on the struts at the crack tip exceeds their fracture moment, Mf = in Eq. (9-23) for the foam relative to the dense material. As pointed out by Gibson and Ashby (1988), the thermal conductivity of a foam depends on a variety of factors, e.g., cell size, density, gas conductivity, etc. Clearly, inclusion of these effects will complicate the simple ideas put forward in Eq. (9-25). An important distinction is expected to occur between open and closed cell materials. For an open cell material, one expects convective flow of the quenching medium to be very important, as the medium (gas or liquid) can flow into the center of the material. In particular, if this flow is rapid, it will allow the bulk temperature gradient, from the outside of the foam to the interior, to be rapidly reduced. For a closed cell material, such flow between cells is much more difficult such that radiation effects and conductivity through the gas and solid become more important than convection (Gibson and Ashby, 1988). A recent study has considered the thermal shock resistance of an alumina-mullite, open cell ceramic (Orenstein, 1990, Orenstein and Green, 1991). Initial experiments considered the change in compressive and flexural strength for specimens quenched into water. The intent was to simulate very rapid temperature changes. Figure 9-42 shows the results of these experiments and indicates a gradual loss in strength with increasing AT, rather than an abrupt change. Such behavior is often observed in ceramics as one increases the amount of porosity (Davidge, 1979). This implies a damage accumulation process rather than the rapid extension of a few flaws. The latter process is usually ob-

O)

Q.

O

O

200

400

600

800

600

800

A7-(°C)

0 200

400

A7TC) Figure 9-42. Strength shows a gradual decrease with increasing degrees of thermal shock in an open cell alumina mullite material: (a) compressive strength and (b) bend strength as a function of quenching temperature difference.

served in dense ceramics and there is an associated sudden drop in strength at the critical condition. The onset of damage for the cellular ceramics appeared to occur in the range AT = 200 to 300 °C. This damage initiation is somewhat difficult to define as the strength has substantial variability and the reduction in strength occurs gradually. Calculation of ATC, using Eq. (9-24), gave values of ~80°C, and thus it appears that 0 < 1.

511

9.10 High Temperature Mechanical Behavior

Figure 9-43, shows the type of damage incurred in the thermal shock and it involves struts cracking, where the number of cracks was found to increase with increasing severity of thermal shock (Orenstein, 1990). The morphology of these cracks suggest they are a result of a temperature gradient across a strut rather than across the bulk of the material. Such a situation can clearly occur in an open cell material, as the quenching medium (e.g., water) flows into the material. Measurement of the Young's and shear modulus, showed these parameters were also changing as a result of the thermal shock, Fig. 9-44. Such behavior is expected as the strut elastic constant (£s) will be effectively reduced by strut cracking [see Eqs. (9-5) and (9-6)]. Thus, for these materials, elastic modulus measurements can be used to assess the damage. Such an approach is attractive, in that the measurement is nondestructive, allowing the effect of stress and thermal fatigue to be assessed, and there is typically less scatter in the experimental data. To assess the thermal shock damage in the open cell ceramics, Young's modulus measurements were made before and after thermal shock (Orenstein, 1990, Orenstein

2.5

^

-•- Young's modulus -*•- Shear modulus

2.0 p

03

S »

1.5 1.0

0.5

200

400

600

800

A 7" (°C)

Figure 9-44. Young's and shear moduli exhibit a decrease with higher degrees of thermal shock as further damage is introduced into the struts.

and Green, 1991). For these experiments the onset of significant damage was defined as the value of AT when the modulus is reduced by 10% and is termed AT10. The values of AT10 for both oil and water quenches are shown in Table 9-8 for materials with a variety of densities and cell sizes. The experimental data show the thermal shock resistance is strongly dependent on cell size (increasing with increasing cell size) and weakly on density (increasing with increasing density). The change with density is opposite to that predicted by

Table 9-8. Thermal shock resistance of open cell, alumina-mullite materials quenched in water or oil. Relative density * (%)

Figure 9-43. Micrograph showing typical damage to the struts resulting from thermal shock (Orenstein and Green, 1991, reprinted by permission of the American Ceramic Society).

11 16 8 11 16 22 11 16

Cell size*

AT10(°C)

(mm)

Water

Oil

3.6 3.6 1.3 1.3 1.3 1.3 0.4 0.4

321 + 14 379 + 35 287 + 36 288 + 43 299 + 10 304 + 35 231 + 11 240 ±14

1096 + 157 1120+174 525+ 57 560+ 68 739 + 122 830+ 68 333+ 53 354+ 43

* Nominal values from manufacturer.

512

9 Mechanical Behavior of Cellular Ceramics

Eq. (9-25) and there is a strong effect of the choice of quenching medium. From the damage observations and the magnitudes of the AT10 values, it is clear that the ideas used to derive Eq. (9-24) need to be re-evaluated. Initial calculations indicated the water will reach the specimen center prior to any significant reduction in the temperature of the struts, thus removing the bulk temperature gradient before a thermal stress develops across the struts (Orenstein, 1990). It was assumed initially the thermal shock resistance of these materials could be considered by simply considering the quenching of the struts. This allows Eq. (9-23) to be written as (9-26) The removal of the bulk temperature gradient has an important effect on reducing the value Biot's modulus as the specimen dimension of concern in the modulus is that of the strut rather than the bulk sample. Unfortunately this approach does not explain the trend of the data in Table 9-8. The parameter 0 used in Eq. (9-23) is retained in Eq. (9-26) as it is likely to be less than unity even for a rapid water quench as a result of the reduced /? associated with a strut. For example, one expects /? to increase (decreases d>) with increasing density and cell size; an effect that is opposite to the data trend in Table 9-8. It was suspected that another source of thermal stress existed and it was postulated that the quenching medium undergoes heating as it infiltrates the specimens. For the fine cell material, the flow is expected to be more difficult giving more chance for the fluid to heat. For increasing density, the volume of the quenching liquid that can infiltrate the foam decreases, and the thermal mass of the solid is higher, both of which would tend to increase the heat transferred to the

quench liquid. Temperature measurements made at the specimen centers confirmed this was the observed trend (Orenstein, 1990). Thus, it was concluded that the thermal stresses arose from two sources; the temperature difference across the struts and the bulk temperature gradient that occurred as the quenching medium was heated (Orenstein, 1990). Comparison of the predicted and experimental retained elastic modulus for a given quench temperature difference showed fair agreement. The heating of the quench media explained the dependence of the thermal shock resistance on cell size but the source of the density dependence was less clear. For example, although it was found that E and the quench media heating increased with increasing density, this was offset by the increases in foam strength and decreases in Poisson's ratio. 9.10.2 Creep Behavior

Gibson and Ashby (1988) have put forward equations to describe the creep behavior of cellular materials. The steady state creep behavior of the struts was assumed to follow the power law behavior observed in most materials, i.e., 8 = 8 Os

(9-27) ;

0s,

where s and a are the strain rate and stress associated with a strut and n, 80s and aOs are creep constants of the strut material. By a similar approach to the derivation of the elastic constants, the unit cell can be analyzed to determine the relationship between the bulk and microscopic stresses and strain rates. For open cell materials this analysis gives (9-28)

Os

9.11 Conclusions

The value of n depends on the particular mechanism of creep that is predominating in some particular stress and temperature range. Equation (9-28) shows creep strain rate for the foam has the same stress dependence as the strut material but the dependence on relative density involves n. For example, diffusional creep that is often found in ceramics, has n = 1. For this situation, the strain rate of the foam will be linearly dependent on stress and on (Q/QS)2. Thus the cellular structure will amplify the strain rate compared to the dense strut material but one would expect rather large creep rupture strains for these materials. Goretta et al. (1990) showed the strength and fracture toughness of an open cell alumina-mullite material degraded above 1200 °C, as creep mechanisms became important. Creep testing showed deformation mechanisms which were apparently linear viscous at the lower stresses, consistent with stress-assisted diffusional processes that are typical of creep in dense polycrystalline alumina (n = 1). On a rather limited data set, the density exponent was estimated to be 1.8, slightly less than that obtained by using n = 1 in Eq. (9-28). An in-

Figure9-45. The open cell ceramic exhibited creep cracks at high levels of strain, the morphology of the cracks supports a bending deformation within the struts even under axial loads.

513

crease in strain rate was observed at the higher stresses and this was associated with the creep cracks formed in the struts. An example of this cracking is shown in Fig. 9-45 and is reminiscent of the damage that occurs when dense ceramics undergo creep in flexure.

9,11 Conclusions For a variety of scientific and technological reasons, there is a need to understand the physical properties of porous ceramics and this chapter has considered one group of such materials: cellular ceramics. These materials can be obtained in the form of open and closed cell, solid foams as well as honeycombs. Cellular ceramics possess a variety of attributes that make them attractive in non-structural applications but, as indicated in this chapter, they could also be used in structural applications. For cases when maximum stiffness or strength for minimum weight are required, porous ceramics can lead to an efficient design and for some modes of loading can outperform their theoretically dense counterparts. This advantage could be further exploited if these porous ceramics were used as a component in composite systems, such as cores for sandwich laminates or as a matrix in a fiber-reinforced material. The work of Gibson and Ashby has laid a strong foundation for understanding the mechanical behavior of cellular ceramics. This approach considers a simple unit cell that attempts to mimic the expected deformation processes in the bulk cellular solid. The approach also assumes the complex geometry can be scaled by geometric constants in a simple fashion. Recent experimental studies on the elastic, toughness and tensile strength behavior of open cell ceramics have been found to be in reason-

514

9 Mechanical Behavior of Cellular Ceramics

able agreement with the theory, especially their dependence on density. Measured values of the geometric constants for open cell ceramics were, however, substantially less than suggested by Gibson and Ashby. In order to apply the theoretical analyses to cellular ceramics, it is critical to have a detailed understanding of the macro- and microstructure of the foams and the physical properties of the individual struts that compose the reticulated macrostructure. Thus, it is important to measure the structures of these materials quantitatively, especially the way in which they change with density and cell size. In some cases, the presence of non-ideal structural features, such as strut cracks, or cell faces in open cell materials can significantly influence the macroscopic mechanical properties. A critical assessment of the theoretical framework is only possible with measurement of the strut properties. Strut strength is a key item in determining the toughness and tensile strength behavior of brittle, open cell foams, and techniques have been introduced to measure this property. For brittle open cell materials, it is found that strut strength may increase or decrease with cell size. Experimental data on closed cell ceramics is extremely sparse but analysis of the data on closed cell glasses indicates closed cell ceramics may have a structural advantage over their open cell counterparts. The tensile strength of a brittle cellular foam is sensitive to the presence of flaws at both a macroscopic and microscopic level. Macroscopic flaws in commercial, open cell ceramics are often close to their theoretical limit (i.e., the cell size), but at a microstructural level it is believed substantial improvements could be made. Analysis of the strut strength data indicates strength > 1 GPa should be easily feasible and this would increase the strength and toughness of the bulk open cell ceram-

ics by a factor of at least 2, but in some cases by an order of magnitude. Such improvements represent a strong challenge to the scientists involved in the processing of ceramics. Although brittle crack propagation in response to applied tensile stresses is a key feature of cellular ceramics, damage accumulation can occur in these materials. In compressive loading some degree of damage occurs prior to reaching the maximum load. The behavior in compression is also sensitive to the uniformity of loading and, in some cases, the theoretical analysis does not clearly describe the measured properties. It is clear the effect of strut strength variability on the fracture process and the behavior of small cracks (~ cell size) are areas that are yet to be fully understood. Damage mechanisms are also important in thermal shock and at high temperatures, where extensive creep cracking can occur. For thermal stresses, it appears that open cell ceramics may possess a distinct advantage over the closed version. This advantage is a result of the convective heat flow that occurs when the pore space is interconnected, allowing bulk temperature gradients to be rapidly reduced.

9.12 Acknowledgements This work is supported by the National Science Foundation under Grant No. DMR-8818908. The authors wish to acknowledge the students and staff of the Materials Science and Engineering Department who assisted in this study. Special thanks are extended to Chuong Dam, Ken Goretta, Bob Orenstein, Hiroshi Hagiwara, Dave Price, Sam Salamone and Eric Van Voorhees for their technical contributions and many helpful discussions regarding this work.

9.13 References

9.13 References Anderton, G. E. (1975), /. Appl. Polym. Sci. 19, 3355-3359. Ashby, M. F. (1983), Metall Trans. A14 A, 17551769. Ashby, M. F. (1989), Ada Metall 37, 5, 1273-1293. Ashkin, D., Haber, R. A., Wachtman, J. B. Jr. (1990), /. Am. Ceram. Soc. 73, 3376-3381. Brezny, R. (1990), PhD Thesis, The Pennsylvania State University. Brezny, R., Green, D. J. (1989), /. Am. Ceram. Soc. 72, 1145-1152. Brezny, R., Green, D. J. (1990a), Ada Metall Mater. 38, 2517-2526. Brezny, R., Green, D. I, (1990 b), J. Mater Sci. 25, 4571-4578. Brezny, R., Green, D. J. (1991), /. Am. Ceram. Soc. 74, 1061-1065. Brezny, R., Green, D. I, Dam, C. Q. (1989), J. Ceram. Soc. 72, 885-889. Chan, R., Nakamura, M. (1969), /. Cell. Plast. 5,112. Dam, C. Q. (1988), M.S. Thesis, The Pennsylvania State University. Dam, C. Q., Brezny, R., Green, D. J. (1990), /. Mater. Res. 5, 163-171. Davidge, R. W. (1979), Mechanical Behavior of Ceramics. Cambridge: Harvard University Press, pp. 118-131. Fowlkes, C. W. (1974), Intl. J. of Fract. Mech. 10, 99-108. Gent, A. N., Thomas, A. G. (1959), J. Appl Polym. Sci. 1, 107-113. Gibson, L. X, Ashby, M. F. (1982), Proc. R. Soc. London, Ser. A 382, 43-59. Gibson, L. X, Ashby, M. F. (1988), Cellular Solids: Structure and Properties. New York: Pergamon Press. Goretta, K. C , Brezny, R., Dam, C. Q., Green, D. X, De Arellano-Lopez, A. R., Dominguez-Rodriguez, A. (1990), Mater. Sci. Eng. A124, 151-158. Green, D. X (1984), Industrial Materials Science & Engineering: Murr, L. E. (Ed.). New York: Marcel Dekker, Inc., pp. 123-143. Green, D. X (1985), /. Am. Ceram. Soc. 68, 403-409. Green, D. X, Hoagland, R. G. (1985), J. Am. Ceram. Soc. 68, 395-398. Green, D. X, Brezny, R., Nader, C. (1988), Mat. Res. Soc. Symp. Proc. v. 119, Pittsburgh, pp. 43-48. Green, D. X, Nader, C , Brezny, R. (1990), Sintering of Advanced Ceramics: Handwerker, C. A. et al. (Eds.). Westerville, OH: American Ceramic Society, pp. 347-356. Hagiwara, H. (1986), M.S. Thesis, The Pennslyvania State University. Hagiwara, H., Green, D. X (1987), /. Am. Ceram. Soc. 70, 811-815. Hengst, R. R., Tressler, R. E. (1983), Chem. and Concrete Res. 13, 127-134.

515

Hobbs, S. Y. (1977), J. Appl. Phys. 48, 4052-4057. Huang, X S., Gibson, L. X (1990), submitted to Ada Metall Mater. Kendall, K., Alford, N. McN., Birchall, X D. (1987), Proc. R. Soc. London A412, 269-283. Kingery, W. D., Bowen, H. K., Uhlman, D. R. (1976), Introduction to Ceramics. New York: John Wiley & Sons, p. 777. Lackey, W. X, Stinton, D. P., Cerny, G. A., Schaffhauser, A. C , Fehrenbacher, L. L. (1987), Adv. Ceram. Mater. 2, 24-30. Lakes, R. S. (1986), Int. J. Solids Structs. 22, 55-63. Lakes, R. S. (1987), Science 235, 1038-1040. Lakes, R. S. (1991), Trans. ASME, J. Engg. Mater. Tech. 113, 148-155. Lange, F. R, Miller, K. T. (1987), Adv. Ceram. Mater. 2, 827-831. Lederman, X M. (1970), /. Appl Polym. Sci. 15, 693703. Maiti, S. K., Ashby, M. F., Gibson, L. X (1984a), Scripta Metall 18, 213-217. Maiti, S. K., Ashby, M. F., Gibson, L. X (1984b), Acta Metall. 32, 1963-1975. Matonis, V. A. (1964), SPE Journal, 1024-1030. Mecholsky, X X, Freiman, S. W, Rice, R. W. (1976), J. Mater. Sci. 11, 1310-1319. Meiser, M. D., Tressler, R. E. (1981), Am. Ceram. Soc. Bull 60, 901-905. Menges, G., Knipschild, F. (1975), Polym. Eng. Sci. 15, 623-627. Morgan, X S., Wood, X L., Bradt, R. C. (1981), Mater. Sci. Eng. 47, 37-42. Mclntyre, A., Anderton, G. E. (1975), Polymers 20, 247-253. McLaughlin, L. M., Kite, H. T (1970), Oak Ridge Document # Y-SB-10 (Rev. 1). Orenstein, R. M. (1990), M.S. Thesis, The Pennsylvania State University. Orenstein, R. M., Green, D. X (1991), submitted to /. Am. Ceram. Soc. Patel, M. R., Finnie, I. (1970), /. Mater. 5, 909-932. Price, D. A. (1990), M.S. Thesis, The Pennsylvania State University. Schmitt, C. R. (1970), Materials Research and Standards 10, 26-28. Sherman, A. X, Tuffias, R. H., Kaplan, R. B. (1990), Bull Am. Ceram. Soc. 70, 1025-1029. Stevens, K. K. (1979), Statics and Strength of Materials, Prentice-Hall Inc., NJ. Van Yoorhees, E. X (1990), M.S. Thesis, The Pennsylvania State University. Verweij, H., deWith, G., Keeneman, D. (1985), J. Mater. Sci. 20, 1069-1078. Weibull, W. (1951), /. Appl. Mech. 18, 293-297. Wu, M. (1990), PhD. Thesis, The Pennsylvania State University. Zhang, X (1989), Private Communication. Zhang, X, Ashby, M. F. (1989), Cambridge University Engineering Department Report #CUED/CMATS/TR 158.

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9 Mechanical Behavior of Cellular Ceramics

Zwissler, X G., Adams, M. A. (1983), in: Fracture Mechanics of Ceramics, Vol. 6: Bradt, R. C , Evans, A. G., Hasselman, D. P. H., Lange, F. F. (Eds.). New York: Plenum Press, pp. 211-241.

General Reading Cellular Materials Almgren, Jr. F. X, Taylor, J. E. (1976), Sci. Am. 235, 1, 82. Ashby, M. F. (1983), Metall Trans. A 14A, 17551769. Gibson, L. X, Ashby, M. F. (1988), Cellular Solids: Structure and Properties. New York: Pergamon Press. Sieradzki, K., Green, D.X, Gibson, L. X (Eds.) (1991), Mechanical Properties of Porous and Cellular Materials, Materials Research Symposium Pro-

ceedings, Vol. 207, edited by Materials Research Society. Stevens, P. S. (1974), Patterns in Nature. Boston, MA: Little and Brown. Thompson, D. W. (1961), On Growth and Form, abridged edition: Bonner, X T. (Ed.). Cambridge: Harvard University Press. Wainwright, S. A., Biggs, W. D., Curry, I D , Gosline, X M. (1976), Mechanical Design in Organisms. Princeton, NJ: Princeton University Press. Fracture of Brittle Materials Davidge, R. W. (1979), Mechanical Behavior of Ceramics. Cambridge: Harvard University Press. Evans, A. G. (1990), /. Am. Ceram. Soc. 73, 2, 187206. Gordon, X E. (1978), Structures or Why Things Don't Fall Down. New York: Plenum Press. Lawn, B. R., Wilshaw, T. R. (1975), Fracture of Brittle Solids. Cambridge: Harvard University Press.

10 High Temperature Engineering Ceramics Katsutoshi Komeya Department of Materials Chemistry, Yokohama National University, Yokohama, Japan Minoru Matsui Materials Research Laboratory, Research and Development Laboratories, NGK Insulators Ltd., Nagoya, Japan List of Symbols and Abbreviations 518 10.1 Introduction 520 10.2 Material Property Requirements 520 10.3 Mechanical Properties of Ceramics 522 10.4 Oxides 523 10.4.1 Oxide Ceramics for High Temperature Engineering Applications 523 10.4.2 Alumina Ceramics 524 10.4.3 Zirconia Ceramics 526 10.4.4 Mullite Ceramics 527 10.4.5 Low Thermal Expansion Coefficient Ceramics 528 10.5 Non-oxide Ceramics 530 10.5.1 Non-oxide Ceramics for High Temperature Engineering Applications .. . 530 10.5.2 Silicon Nitride Ceramics 531 10.5.2.1 The Intrinsic Character of Silicon Nitride 531 10.5.2.2 Synthesis of Silicon Nitride Powder 531 10.5.2.3 Progress in Sintered Silicon Nitride 533 10.5.2.4 Practical Applications of Silicon Nitride Ceramics 543 10.5.3 Silicon Carbide Ceramics 544 10.5.3.1 The Intrinsic Character of Silicon Carbide 544 10.5.3.2 Synthesis of Silicon Carbide Powder 545 10.5.3.3 Progress in Sintered Silicon Carbide 546 10.5.3.4 Practical Applications of Silicon Carbide Ceramics 549 10.5.4 Evaluation of Silicon-Based Ceramics 549 10.5.4.1 Fast Fracture Strength and Its Dependence on Volume 549 10.5.4.2 Fatigue Strength 550 10.6 Ceramic Matrix Composites 557 10.6.1 Definition and Classification 557 10.6.2 Dispersants for Composites 557 10.6.3 Ceramic Matrix Composites 559 10.6.3.1 Ceramic Nanocomposites 559 10.6.3.2 Whisker Dispersed Composites 561 10.6.3.3 Long Fiber Reinforced Composites 562 10.7 Acknowledgements 563 10.8 References 563 Materials Science and Technology Copyright © WILEY-VCH Verlag GmbH & Co KGaA. All rights reserved.

518

10 High Temperature Engineering Ceramics

List of Symbols and Abbreviations A a a0 C

Y

constant flaw size atomic radius half the length of an interior crack constant Young's modulus Weibull distribution function frequency enthalpy stress intensity factor fracture toughness or critical stress intensity factor Weibull modulus constant number of cycles to failure L a r s o n - M i l l e r parameter stress ratio absolute temperature thermal shock resistance temperature static fatigue lifetime or equivalent time time to failure time to creep rupture lifetime effective volume geometrical factor

y 7 gb y{ ysv a aa cre Ceramics \ Applied stress

Figure 10-2. Candidate materials for particular operating conditions.

Figure 10.1. Engineering ceramics.

peratures and stresses and the various materials that satisfy them are shown in Fig. 10-2. There are a large variety of applications which require different fabrication processes. This can be compared with other classes of materials such as electroceramics, magnetoceramics, and so on. There are different kinds of manufacturing processes, e.g., turbocharger rotors are fabricated by injection molding and slip casting methods, whereas antifriction ball bearings are made by die-pressing. This situation is quite different from that for electronic ceramics such as substrates and packages, which are fabricated mainly by tape casting or extruding methods. The large variety of potential applications for engineering ceramics make the development strategies for these materials very complicated. Each application needs much development engineering and requires considerable funding. Another problem is brittleness, which must be understood and overcome, which dictates that fracture strength and reliability are very important properties. As is well known, the strength depends on the microstructure. Ifflawslike pores, cracks, defects, inclusions and so on exist in the ma-

522

10 High Temperature Engineering Ceramics

Table 10-2. Properties evaluated for engineering ce-

Elastic properties Thermal properties

Young's modulus [R-1602(RT), R-1605 (HT)]a, Poisson's ratio, shear modulus Thermal expansion coefficient, thermal conductivity [R-1611]a, specific heat [R-1611]a, emissivity, softening temperature Strength Bending strength [R-1601 (RT), R-1604 (HT)]a, tensile strength [R-1606]a, compressive strength [R-1608 (RT)]a, shear strength, fracture toughness [R-1607(RT)]a, fracture energy, impact strength, thermal shock resistance, bonding strength, statistical evaluation Fatigue Fatigue life, slow crack growth, creep [R-1612] Friction Hardness [R-1610 (RT)]a, friction coeffiand wear cient, wear resistance [R-1613]a, erosion, machinability Corrosion Oxidation [R-1609]a, corrosion [R-1614] Others Nondestructive evaluation, residual stress, surface roughness, chemical analysis of silicon nitride powder [R-1603]a a

[R

(- -)]: [JIS No. (temperature)]

terial, they will act as points of fracture. The consequent range of strength values depends on the flaw distribution parameters, and is a result of the processing including the raw powder characteristics. For engineering ceramics establishment of the processing conditions for minimal scatter in the mechanical properties is particularly important. There are also many other properties that require evaluation for the fabrication and application of engineering ceramics. Table 10-2 lists a number of the properties evaluated for engineering ceramics, for which fourteen Japanese standards have been determined in the last ten years.

10.3 Mechanical Properties of Ceramics To better understand the mechanical properties of ceramics, the difference between those of metals and ceramics is shown in Table 10-3. The intrinsic difference in the mechanical properties is due to the chemical bonding. Namely most metals have metallic bonds, while ceramics generally have ionic and/or covalent bonds. For instance, alumina and zirconia are principally ionic structures, whereas silicon nitride and silicon carbide are typically covalent structures. Consequently ceramics exhibit brittle fracture without plastic deformation up to temperatures of half the melting point. Plastic deformation at low temperatures is not expected as dislocation multiplication and motion is very restricted in ceramics due to the complicated crystal structure (large Burgers vector) and a large Peierls stress (caused by the covalent/ionic bonding), see Chap. 2 of Volume 6. It must be remembered that the fracture of ceramics is very sensitive to microflaws such as pores, cracks, machining Table 10-3. Differences in properties between metals and ceramics3. Property Density Young's modulus Thermal expansion coeff. Hardness Room temp, strength High temp, strength Deformation Impact strength Fracture toughness Heat resistance Oxidation/corrosion Wear resistance Machinability L>M>S>SS

Ceramics

Metals

S L S L M-L M SS

L S L S L S L L L S-M S-M S L

s s

L L L S

10.4 Oxides

flaws and residual stress. A more detailed account of the effect of these flaws on the strength and why it is much lower than the theoretical stress of these materials is given in Chap. 7 of this Volume. The fracture strength of an ideal solid is essentially determined by the nature of the bonding and its arrangement. That is, the theoretical strength (crth) is given by the following equation, which relates the strain energy release rate for the bonding fracture to the energy to create two new fracture surfaces; (10-1) where y is the thermodynamic surface energy, E is Young's modulus, and a0 is an atomic radius. A theoretical strength of about 5000 MPa for alumina can be calculated by using a surface energy of 100 Jm~ 2 , which is about 1/10 of the Young's modulus. This value is compared with 200300 MPa for practical usable alumina ceramics. This decrease in the strength of ceramics is due to the existence of flaws. This is explained by Eq. (10-2), derived from the Griffith flaw model (Griffith, 1920), namely

523

where y{ is the fracture energy (usually y{ > y), Klc is the fracture toughness or critical intensity factor, C is the flaw size and Y is a geometrical factor. In this case flaw size means not only crack size, but also the maximum size of grains, pores and inclusions. From Eq. (10-4) it can be seen that ceramics with higher Klc are less sensitive to the flaw size. Mechanical property requirements for engineering ceramics depend upon the intended applications, as described above. Namely, a turbocharger rotor requires a high strength and toughness, excellent thermal shock resistance for the materials, as well as a higher level of shaping and joining technology. Anti-friction bearing parts also require excellent wear resistance, minimization of flaws and excellent machining and lapping ability. It should in particular be remembered that engineering ceramics require different characteristics and different shaping technologies but with costs competitive to metals, unlike other ceramic components like substrates and ferrites. It has recently been found that some monolithic ceramics such as silicon nitrides show nonlinear fracture behavior. Therefore nonlinear fracture mechanics has been developed in recent years (see Chap. 6 of this Volume).

(10-2) where C is half the length of an interior crack. However, the strength ( Si 3 N 4 (s) AH =-175

kcal/mol

(1)

(1600 K)

careful temperature control is necessary in order to obtain a higher content of a-phase silicon nitride.

Table 10-11. Synthesis methods for silicon nitride powders. £-50

Synthesis method

-

Silicon direct nitridation method Silica reduction and nitridation method Imide decomposition method

£ -100 in

_a JO

CD

-150 1500

2000 2500 Temperature (K)

Figure 10-10. Formation free energies.

3000

Gas phase synthesis method

Reaction formula 3Si + 2 N 2 ^ S i 3 N 4 3 S i O 2 + 6 C + 2N 2 -» Si 3 N 4 + 6CO SiCl 4 +6NH 3 ^Si(NH) 2 + 4NH4C1 3 Si(NH)2 -+ Si 3 N 4 + 2 NH 3 3SiCl4 + 16NH 3 -+Si 3 N 4 + 12NH 4 Cl

532

10 High Temperature Engineering Ceramics

• ' ,.

'**

f-i

2a(CuKa)

Figure 10-11. SEM micrographs of silicon nitride powders synthesized by the silica reduction and nitridation method: (A) SiO 2 -C-N 2 , (B) SiO 2 -C-Si 3 N 4 -N 2 (bar = 10 urn). Electron diffraction of B reveals that it is almost entirely a phase.

Pure and fine powder is produced by grinding and refining the synthesized silicon nitride block. This method produces silicon nitride powder at a lower cost compared to other methods. Silica Carbothermal Reduction and Nitridation Silicon nitride powder is formed by an endothermic reaction of the system SiO 2 -C-N 2 according to 3SiO2(s) + 6C(s) + 2N 2 (g) -+ Si 3 N 4 (s) + 6CO(g)

(2)

AH = 303 kcal/mol (1700 K) It was found that the addition of silicon nitride to the SiO 2 -C mixture strongly affected the grain morphology, as shown in Fig. 10-11, and, in consequence, more aphase particles of controlled size and shape were obtained (Inoue et al., 1982). Although the powder synthesized is of a granular type with accompanying sharp edges and shows a lower green density in molding, it is meaningful that this powder gave rise to the development of high strength silicon nitride. Recently a silicon nitride powder which exhibits good sinterability has been synthesized from a new system, the SiO 2 -

L P G - N H 3 system (LPG: liquefied petroleum gas). Silicon Imide Decomposition Amorphous silicon nitride is synthesized by the following two-step process: SiCl4 + 6NH 3 -> Si(NH)2 + 4NH 4 Cl (room temperature) (3) 3Si(NH)2(s) -+ Si3N4(s) + 2NH 3 (g) (1200-1500 °C) (4) Fine grained silicon nitride powder of high oc-form content is obtained by crystallization of the amorphous silicon nitride product, as shown in the SEM micrograph in Fig. 10-12. The powder formed by this method shows high purity, excellent sinterability, and is widely used worldwide to fabricate the highest quality silicon nitride parts (Yamada and Kotoku, 1989). The quality of silicon nitride raw powders has improved in recent years. Table 10-12 lists typical characteristics of the above three kinds of silicon nitride powder. The characteristics required for the raw powder are mainly high purity, fine grains of controlled size and shape, high oc-silicon nitride content, and so on. To achieve good densification according to

533

10.5 Non-oxide Ceramics

o Silicon imide decomposition a Silica reduction nitridation A Silicon direct nitridation

0.3 0.2

10

20 30 LQ 50 Sputter depth (nm)

60

100 300

Figure 10-12. SEM micrograph of silicon nitride powders synthesized by silicon imide decomposition.

Figure 10-13. Oxygen distribution from the surface to the inside of silicon nitride particles, measured by Auger electron spectroscopy.

Table 10-12. Typical compositions (in wt.% of the elements) and characteristics of silicon nitride powders.

able microstructures, as described later. However, there are many things to be explained, such as the role of existing oxygen, relations between raw powder characteristics and microstructures and properties of sintered products. Figure 10-13 shows some unexplained experimental results (Jenett et al., 1989), where the distribution of oxygen from the surface to the interior is different for the different synthesis methods. It is of particular note that in the powder from the imide decomposition method, the oxygen exists only as a surface silica layer. It is likely that characterization of the raw powder will remain a perennial problem until the next century. Anyway, the present status of these powder production routes is that direct nitridation is available for low cost, imide decomposition is to be used for good sinterability, and silica reduction and imide decomposition are to be used for high strength and toughness development.

Method:a

Ab

Ab

Composition Si 59.4 N 39.7 O C Al 0.06 Ca Fe 0.01 Mg 50 / Q. 10

O LL

. A SUJ

2

Ceramics

5 10 50 100 No. of stress cycles (*106 cycles)

Figure 10-34. Rolling fatigue life of silicon nitride in comparison with SUJ2 alloy.

Typical photographs of some of the components in practical use are shown in Fig. 10-33. The realization of all of these parts has required much work on fabrication, evaluation and component testing.

For instance, the antifriction bearing has been put into practice by attainment of the attractive rolling fatigue life shown in Fig. 10-34 (Komeya and Kotani, 1986) and development of a more reliable fabrication process. Although ceramic gas turbines are under development for early next century, several projects are already well underway. 10.5.3 Silicon Carbide Ceramics 10.5.3.1 The Intrinsic Character of Silicon Carbide

Silicon carbide is an even more covalent compound than silicon nitride with an ionicity of only 0.19 and a higher decomposition temperature of about 2500 °C under atmospheric pressure. It can exist in a (hexagonal) and p (cubic) crystal structures, the a-type of which can consist of many polytypes, as shown in Table 10-18. Silicon carbide is characterized by higher hardness, excellent high temperature creep resistance, high thermal conductivity, semiconducting properties and excellent oxidation/corrosion resistance. From these characteristics, silicon carbide has applications for service at high temperatures under corrosive conditions and in areas where wear must be prevented. It is also widely used for heating elements which must operate at temperatures up to

10.5 Non-oxide Ceramics

Table 10-18. Silicon carbide polytypes and their lattice constants. Polytype

a (A)

2H 3C 4H 6H 15R

3.076 4.348 3.095 3.095 3.095

c(k) 5.048

10.09 15.17 37,95

1500°C in air. Recent progress has been made in the use of this material for high performance applications such as gas turbine and heat engine parts, ball bearings, pump seal components and so on, applications where it competes with silicon nitride. However, one of the most critical problems still to be overcome for silicon carbide ceramics is its low fracture toughness (3-4 MPa m 1/2 ), which will be discussed later.

545

ous recrystallization, polycrystalline silicon carbide ingots are produced according to SiO2(s) + 3C(s) -• SiC(s) + 2CO(g) AH= 132 kcal/mol

(5)

(2700 K)

Synthesized silicon carbides consist of octype crystals of mainly 6H and 15R polytypes. After crushing, the products are selected into several grades according to their level of quality. Higher grade silicon carbides are ground and purified so as to obtain pure and fine grains of silicon carbide powders. Low grades of silicon carbide are generally used as refractories and abrasive grits. Silicon carbide powder from the Acheson method is classed as a low cost powder. Table 10-19 compares the characteristics of the Acheson method silicon carbide powders with those from other synthesis methods. Low Temperature Carbonization of Silica

10.5.3.2 Synthesis of Silicon Carbide Powder Three kinds of synthesis methods for SiC powder have been developed: the Acheson method, low temperature carbonization of SiO2, vapor phase reaction, including direct carbonization of silicon and carbon and thermal decomposition, of which the first two are currently available. Outlines of these three methods are described below. Acheson Method The Acheson method has been carried out since the beginning of the new ceramic age. A graphite core is prepared as an electrolyte, and powder mixtures of silica and coke are placed around the core. By electrical resistance heating, the temperature is elevated to over 2500 °C. Through a carbothermal reduction reaction and continu-

The carbothermal reduction reaction of fine silica and carbon powder mixtures gives fine-grained and pure P-type silicon carbide powder, for which the reaction is carried out at 1400-1800 °C. Although the reaction is similar to the Acheson method, it is different in that the synthesizing temperature is lower and the crystal structure produced is p-type. This method is the one of choice for preparing high quality, finegrained silicon carbide powder. Typical characteristics of synthesized powders are shown in Table 10-19. Ultrafme powders of less than 100 nm in particle size have recently been developed using the sol-gel method. Vapor Phase Reaction Ultrafme silicon carbide powders are also synthesized by vapor phase reaction between SiCl4 or SiH 4 and hydrocarbons,

546

10 High Temperature Engineering Ceramics

Table 10-19. Characteristics of silicon carbide powders. Method:3 Structure: Composition (wt.%) SiC Fb-C Fb-SiO2 Fb-Si Fe Al Ca Mg Na B Cr Ni Diameter (jam) Specific surface (m2/g) 1

A a

A a

B

B

Sol-gel B

C

C

P

P

P

P

P

99 0.3 0.1 0.02 0.01 5.0 -

97 1.4 0.7 0.06 0.01 0.45 14

>98 0.4 0.3 0.04 0.03 0.27 17.5

>99 0.10 0.14 0.012 0.048 0.004 0.001 0.003 0.002 0.2-0.3 20

>99 10" 4 Q" 1 cm~ 1 at the device operating temperature), electronic conductivity is insignificant, and on application of an applied electric field, material transport can take place. These materials are electrolytes in the true sense which have ionic conductivity in the solid state as opposed to the molten or the liquid state. Unlike in liquid electrolytes, the conductivity in solids is selective and there is usually one mobile ionic species. Such materials have been known for several decades. For example, Nernst (1899) demonstrated that the electrical conduction through ZrO 2 -Y 2 O 3 at elevated temperatures was mainly due to mobile oxygen ions. Often in solid electrolytes the ionic conductivity is defined in terms of electrolytic domain. This is the region of conduction with respect to temperature and the chemical potential of the electroactive species over which the ionic transport number is > 0.99 (Patterson, 1971, 1974; Heyne, 1977). Ionic conductors can be divided into three main classes of materials. These are: (i) crystalline compounds e.g. oxygen-ion conductors such as zirconia, ceria, thoria and bismuth oxide based materials, cation conductors such as Na + , and substituted (Li + , K + , Ag + , NH+, H 3 O + )p(p>aluminas; Agl; RbAg 4 I 5 ; Li3N; Nasicon and several others, (ii) amorphous materials such as glasses (Na + , Li + and K + conductors) and (iii) polymers (ion exchanged or solvated with alkali metal salts, e.g. Nafion and polyethylene oxide). The ceramic superionic conductors covered in this chapter fall into the first category of materials.

Ceramics are insulators, electronic conductors (metallic or semiconduction) or ionic conductors. The mode of conduction depends in general on the crystal structure of the material, the concentration of each type of charge carrier [ionic and electronic (n or p-type)], temperature and the band gap. In crystalline compounds the ionic conduction occurs in a well defined host lattice whose composition and structure play a major role in determining the level of ionic conductivity at any given temperature. At room temperature many materials are insulators or poor conductors but with increasing temperature they become good conductors (e.g., ZrO 2 based electrolytes). The majority are mixed conductors i.e. transport takes place by simultaneous motion of electronic and ionic defects. However, for a material to qualify as an electrolyte, the concentration of electronic charge carriers must be several orders of magnitude smaller than that of ionic defects. Ever growing global population and the associated increasing demand for energy in both developing and developed countries has put an unsustainable pressure on our environment. Therefore, if we are to preserve the environment for future generations and improve and/or sustain living standards, then new technologies have to be developed which contribute to the reduction of pollution, greenhouse gases and assist in preserving the limited resources available. It is in this area that superionic conductors have the potential to play an increasingly important role. Superionic materials are already been used in sensors, batteries and fuel cells and are playing an ever increasing role in pollution monitoring and control, energy conservation and conversion. Several different types of technologies based on superionic conductors are commercially available and

11.2 Basic Theory of Superionic Conduction

others are currently under development. Gas sensors based on fast ionic conductors are in use in the chemical and metallurgical industries for process or quality control, in small to medium size boilers and thermal power plants for improving combustion efficiency, in automobiles for increased fuel efficiency and reduced emission and in general for pollution control and monitoring. Significant advances have been made on secondary batteries based on beta alumina or other similar electrolytes for vehicle traction and stationary energy storage. Earlier versions of solid oxide or ceramic (also known as the third generation) fuel cells with combined heat and power generation capability are undergoing extensive trials and high power density cell designs are under development. This chapter has been planned as follows. Initially a brief outline of the basic theory behind superionic conduction is given. This is followed by description of various techniques used to study transport, thermodynamic and kinetic properties of superionic conductors. The galvanic cells utilizing ceramic superionic conductors are inherently accurate in providing reproducible thermodynamic data. The section on thermodynamic properties also discusses applications of the galvanic cells for determining the free energy of formation of binary and ternary metal oxides, fluorides and carbides, the activity of an electrochemical species in solid or molten mass (e.g., oxygen activity in molten metals, alloys or nonstoichiometric oxides). Next a number of classes of materials are described, with emphasis on two main types of materials of great technological significance. These are the oxygen-ion conductors (zirconia, ceria, bismuth oxide, thoria) and Na + or substituted (Ag + , K + , H 3 O + , NH^, etc.) beta 0 , p'O-aluminas. A section is devoted to the relationship between

571

the ceramic microstructure and transport properties. Finally, applications of ceramic superionic conductors in new technology areas and several devices based on them are described.

11.2 Basic Theory of Superionic Conduction In this section a brief account of the basic theory behind superionic conduction is given. A detailed discussion on the relationship between the nature and formation of point defects responsible for ionic conduction, crystal structure and lattice disordering, and transport mechanisms is not within the scope of this chapter and readers should consult some excellent books and articles written on the subjet (Geller, 1977; Glasser, 1973; Hagenmuller and Van Gool, 1978; Hladik, 1972; Mahan and Roth, 1976; Mitoff, 1966; Seltzer and Jeffee, 1973; Sorensen, 1981, Subbarao, 1980; Tallan, 1974; Van Gool, 1973; Vashishta et al., 1979; Wheat et al, 1983). In superionic conductors, the point defects, whose concentration is fixed by the composition, are responsible for the high ionic conduction. In general, the concentration of ionic defects is much larger than that of electronic defects and solids behave almost like pure ionic conductors. However, distinction must be made between low point defect concentration (or dilute) solids such as alkali metal halides, AgBr etc., which in the solid state have very low conductivity and high activation energy for ionic transport and those with high concentration of point defects [e.g., doped zirconia - vacant lattice sites in the anion sublattice (Etsell and Flengas, 1970)] or high cation disordered sublattice (e.g., (3 or |3"-alumina, RbAg4I5) (Heyne, 1977;

572

11 Ceramic Superionic Conductors

Kasper, 1978; Kennedy, 1977; Powers and Mittof, 1978). Often cations with different valence (aliovalent) are added to create large concentrations of defects. These cations may substitute for an ion in the normal lattice site or alternatively enter an interstitial site. Anion conduction results from anions being present at interstitial sites or from anion vacancies. The cation conduction may arise due to the presence of interstitial cations or cation vacancies. For example in fluorite-related solid solutions of zirconia (ZrO2), ceria (CeO2) or thoria (ThO2) with dopants such as CaO, MgO, Y 2 O 3 , Sc 2 O 3 , Yb 2 O 3 , the dopant cation occupies a normal lattice site. To preserve charge neutrality, vacancies are created in the oxygen sublattice to compensate for the charge difference between Zr 4+ and the lower-valent dopant cation. These vacancies are randomly distributed in the crystal lattice and are responsible for the high ionic conduction. In Na + beta ((3, |3")-alumina, the Na + is the disordered cation present in crystallographic loose layers. The number of available sites in the layer for Na + to occupy are larger than the number of Na + ions. The Na + ions are therefore distributed over a large number of sites. Many solid electrolytes (e.g., oxygen-ion conductors, substituted beta aluminas, CaF2) are poor conductors at room temperature but become good conductors at higher temperatures with increasing disorder in the sublattice but without any phase transition. Other materials such as Bi 2 O 3 and some silver and copper salts (Takahashi and Iwahara, 1973; Wiedersich and Geller, 1970) undergo a first order transition from a poor conduction state at low temperature to a high conducting state at elevated temperature. Nevertheless, in the superionic conductors, from a structural point of view, there are clear pathways for ions to migrate with more avail-

able sites for them to occupy than the number of mobile ions. The ionic conductivity and transport of material results from hopping of ionic defects into adjacent available sites under the influence of an applied electric field and is given by: er^C^ZeJft

(11-1)

where [i{ is the ionic mobility Cx is the concentration of ionic defects or conducting ions per unit volume and Z e is the charge on the ionic charge carriers. Typically in a solid, the mobility of electronic defects is several orders of magnitude higher than that of the ionic defects. Therefore for a material to be a predominantly ionic conductor, the defect concentration for ions must be significantly high (in the percent range) and that of electronic charge carriers should be negligible. The dependence of ionic conductivity on temperature is usually expressed in the form of the Arrhenius relationship:

where A{ is the pre-exponential term and is independent of the temperature, E is the activation energy, k is the Boltzmann constant and T is the temperature. Kilner and Steele (1981) have given the following general equation for anion mobility in oxygenion conducting solid electrolytes: tt

= [Z e/(fc T)] 3j /o y exp [- AGJ(k T)] (11-3)

where J d is the jump distance, f0 is the jump attempt frequency, y is a geometric factor and AGm is the Gibbs free energy for the jump. Similar expressions are used for other ionic conductors (Goodenough, 1983). For dilute solid solutions (low dopant concentration), substituting for the concentration of vacancies ([Fo]), the number of anion sites per unit volume, JV0, and the

573

11.3 Techniques for Studying Transport and Kinetic Properties in Superionic Conductors

mobility term in Eq. (11-1) the following expression can be written for the ionic conductivity (Kilner and Steele, 1981):

•exp(ASm//c)exp[-Atfm/(/cT)] = A{exp[-AHJ(kT)]

(11-5)

where AHm is the enthalpy of ion migration. A plot of log (conductivity x T) versus reciprocal temperature should be a straight line whose slope gives the enthalpy for ion migration and intercept the preexponential term. However, it is common to observe a continuous change in the slope of the Arrhenius plots towards a lower activation energy with increasing temperature (Abelard and Baumard, 1982; Adham and Hammou, 1983; Badwal, 1984; Badwal and Swain, 1985; Baumard and Abelard, 1984; Casselton, 1970; Ioffe et al, 1975). In the case of fluorite-type oxide solid electrolytes this has been attributed to the formation of complexes of varying degree between vacancies and dopant cations at low temperatures and their increasing dissociation as the temperature rises (Baumard and Abelard, 1984; Hohnke, 1981; Kilner, 1983; Kilner and Faktor, 1983; Kilner and Waters, 1982; Nakamura and Wagner, 1980, 1986; Schmalzried, 1977; Wang et al., 1981). Several of these authors have discussed the formation of neutral complexes for divalent and charged complexes in the case of trivalent dopant cations. In the dilute solid solution range simple associates and for concentrated solid solutions higher order complexes (involving several nearest neighbors) between dopant cations and vacancies and ordering of vacancies have been considered. At low temperatures the activation energy term in Eq. (11-2) consists of the enthalpy for defect formation as well as

enthalpy for migration of vacancies. In the high temperature range when clusters are completely dissociated the activation energy equals the enthalpy of vacancy migration. The binding energy for associate formation depends on the type of the dopant and ionic charge on the dopant cation and its size. The conductivity is also related to the diffusion coefficient (DJ by the Nernst-Einstein relationship:

The correlation factor (/) should be included if Eq. (11-6) is to be applied to isotopic diffusion (Dt) and is given by: Dt

(11-7)

The correlation factor is usually between 0.5 and 1, depends on the transport mechanism and is often written as the Haven ratio, HR (Compaan and Haven, 1956; Haven, 1978; LeClaire, 1973).

11.3 Techniques for Studying Transport and Kinetic Properties in Superionic Conductors Several techniques are commonly used to study transport, kinetic and thermodynamic properties of superionic conductors or solid electrolyte cells based on these materials. These techniques have been described below. The electrical or electrochemical measurements alone are not sufficient to fully understand the transport mechanism. It is necessary to combine these measurements with characterization techniques such as X-ray diffraction, neutron diffraction, scanning and transmission electron microscopy, DTA/TGA, optical microscopy, NMR, infra-red and Raman

574

11 Ceramic Superionic Conductors

spectroscopy. Often there is a complex relationship between the transport properties, crystal structure and the ceramic microstructure (phase assemblage, grain size distribution, porosity, surface area, grain boundary density and impurity segregation) of the system under study. Powder synthesis, ceramic fabrication techniques and sintering conditions also play a major role in influencing kinetic and transport properties. Measurements only on fully characterized systems are valuable in understanding the nature of transport processes.

Power supply/ Current source/ Measurement

Electrolyte

Voltmeter

Electrode

Electrolyte

Electrode

11.3.1 Conductivity Measurements 1,2 Current probes 3,4 Potential probes

11.3.1.1 DC Techniques

In solid electrolyte cells, major contributions to the total cell resistance come from the electrolyte resistance (in the case of polycrystalline materials both the grain boundary and the lattice resistivity) and the electrode resistance at the cathode/ electrolyte and anode/electrolyte interfaces. The cell resistance can be determined from a simple relationship between the current flowing through the cell and the steady state potential difference between a pair of electrodes reversible to the charge carrying species. The two-probe DC technique has been used in the past to determine the electrolyte resistivity. The circuit for this method is shown in Fig. 11-1. The electrolyte conductivity, cr, for a specimen of length L and cross sectional area A is given by: a = (I/V)(L/A)

(11-8)

where / is the current flowing through the cell and V is the voltage drop between the pair of electrodes. This is the simplest technique requiring a minimum of instrumentation but it is one of the most error prone methods of measuring conductivity of su-

Figure 11-1. An equivalent circuit and cell arrangement for a two-probe conductivity technique.

perionic conductors. A simple two-probe DC method may be adequate to give a reasonable estimate of electrolyte resistance provided that there is good contact between the electrode and the electrolyte, that the electrodes maintain a constant composition during the measurement and that the electrode resistance is negligible compared with the electrolyte resistance. It is difficult to attain a near perfect contact between the electrolyte and electrodes. Furthermore in a solid electrolyte cell, the contribution of the electrode resistance is often too significant to be ignored. All these parameters change with temperature and the measurement procedure in a different fashion. Let alone measuring the true electrolyte conductivity, the two-probe DC technique can not be relied upon to even furnish reproducible results as a function of temperature. In order to eliminate the contribution from the electrode/electrolyte interface, a

11.3 Techniques for Studying Transport and Kinetic Properties in Superionic Conductors

four-probe technique, in which the current passes through two current probes and the potential drop is measured with a high input impedance voltmeter across another two probes, should be used. The equivalent circuit of a four-probe technique is shown in Fig. 11-2. In this technique all the four probes are physically isolated and when measuring the ionic conductivity, must also be reversible to the charge carrying species within the material. L in Eq. (11-8) is now the distance between the potential probes. With proper considerations to the positioning of the probes and selection of the probe material, the technique is capable of providing accurate information about the electrolyte conductivity. The technique can be surface sensitive especially if the composition of the material is not uniform and is affected by the temperature and the gas environments. The major drawback, however, is that although very useful for single crystals, it is incapable of

Power supply/ Current source/ Measurement

Electrolyte

T Voltmeter

Electrode

Electrolyte

Electrode

h/wv 1,2 Current probes 3,4 Potential probes Figure 11-2. An equivalent circuit and cell assembly for the four-probe technique.

575

distinguishing between intergrain (grain boundary) and intragrain (lattice resistivity) in polycrystalline materials. Nevertheless, the four-probe technique is fast, extremely useful in providing information about the total conductivity over a much wider temperature range and is very accurate for studying time dependent conductivity (ageing-phase decomposition or precipitation) behaviour at a constant temperature. Information about phase transformation and/or phase precipitation can be easily obtained as shown by some examples in Figs. 11-3, 11-4. 11.3.1.2 AC Techniques

Several different AC techniques are used for measuring the conductivity of superionic conductors. These include measuring the current voltage response at a constant frequency of between 1 to 10 kHz using a two or a four-probe cell arrangement discussed above. The underlying assumption in this approach is that at all measurement temperatures the electrode processes must relax below this constant measurement frequency to allow only electrolyte resistance to be measured. Both these methods give erroneous results as with increasing temperature the time constant of various electrode and electrolyte processes increases and the frequency response of each shifts to a high frequency region. Moreover, these vary with the type of the electrode or the electrolyte material used, the cell geometry, nature of the transport processes and the gas concentration. Figure 11-5 compares the results of electrolyte resistivity obtained using fixed frequencies of 1 and 10 kHz with the total and lattice resistivity values determined using impedance spectroscopy for a Pt/ZrO 2 -Y 2 O 3 /Pt cell. The error inherent in measuring electrolyte resistance at a constant frequency is quite

U.UDO

(a) 3mol% Y 2 0 3 -Zr0 2

1000°C

0.056 \ 7 E

0.054

o

£ 0.052

0.050

(a) 0048

1000

2000 3000 Time in min

(b) 7.8mol% Sc 2 0 3 -Zr0 2

4000

5000

1000°C

0.30 0.28

T

E CJ0.26 .S b 0.24

Figure 11-3. Ageing behaviour studied by the four-probe DC conductivity technique at 1000 °C in (a) 3 mol% Y 2 O 3 -ZrO 2 and (b)7.8mol% Sc 2 O 3 -ZrO 2 .

0.22

(b) 0.20 1000

2000 3000 Time in min

4000

5000

Figure 11-4. Arrhenius plots for two Sc 2 O 3 -ZrO 2 specimens with different amounts of monoclinic zirconia investigated by the four-probe DC conductivity technique. The jumps occur due to the transformation of monoclinic (present as twinned regions in the microstructure-inset) to tetragonal zirconia on heating (D) and the reverse transformation on cooling (o).

-4.0

a— Heating cycle o - Cooling cycle -5.0

75

9.0

10.5 12.0 Temperature in 10AK"1

13.5

15.0

11.3 Techniques for Studying Transport and Kinetic Properties in Superionic Conductors

577

Figure 11-5. Arrhenius plots for a Pt/3 mol% Y 2 O 3 -ZrO 2 /Pt cell showing the effect of measurement technique on the measured electrolyte resistance. At 500 °C the contributions of the grain boundary and the volume resistivity are equal, o - At 1 kHz, A - a t 10kHz, • - total (grain boundary and lattice) resistivity, o - lattice resistivity. 12.0

13.0

U.O

15.0

16.0

17.0

Temperature in 104-K"1

clear. Impedance spectroscopy (described below) in which the response of the cell is studied over a wide frequency range, is obviously a more versatile technique and therefore is most commonly used. It is a powerful technique for separating the contributions of various processes in a solid electrolyte cell in the frequency domain and offers considerable advantage over other techniques. Recent advances in instrumentation and data analyses have further contributed to its versatility. For polycrystalline electrolyte materials it can separately provide information about migration of charge carrying species within the grains (intragrain or lattice resistivity) and across grain boundaries (intergrain or grain boundary resistivity) and is an excellent technique for studying the effect of impurity segregation at grain boundaries. For studying transport properties of superionic conductors with AC methods, the use of reversible electrodes is not necessary. 11.3.2 Transport Number Determination

Transport (transference) number of mobile species is an important factor in estab-

lishing the suitability of a conductor as an electrolyte. High ionic conductivity and an ionic (anionic or cationic) transport number close to unity over wide cell operating conditions are some of the criteria which must be fulfilled by a material to be a good electrolyte. Many materials are mixed conductors and the ionic transport number varies with the cell operating conditions. Even small electronic conductivity can limit the use of a material as an electrolyte. The ionic conduction in a solid electrolyte is characterized by the ionic transport number t{ which is the ionic fraction of the total current (anionic, cationic and electronic charge) flowing through the system. (11-9) and aT = ai + ae (11-10) Several different techniques are available for separating the ionic and electronic contributions to the total conductivity in solid electrolytes and the most common ones are described below (Etsell and Flengas, 1970; Goto and Pluschkell, 1972; Heyne, 1977; Sequeira, 1985).

578

11 Ceramic Superionic Conductors

(i) A sample can be electrolyzed between a pair of electrodes reversible to the mobile ionic species for a period of time and composition at the anode and cathode sides of the specimen measured and compared to the quantity of the charge passed (Bottelberghs, 1978). Alternatively the specimen can be electrolyzed between two or more pellets of materials reversible to the charge carrying species. The transport numbers can be determined by comparing the weight change of the pellets with the amount of charge passed. This method is named after Tubandt who first introduced it and can furnish information about both cation and anion transport numbers at the same time. (ii) The more commonly used and simple technique for determining transport numbers is the EMF method. In this, the material under investigation is placed between two reversible electrodes which define the chemical potential for the mobile component of the material at each electrode/electrolyte interface. If both interfaces are at a different chemical potential then the EMF signal across the cell, for example for an oxygen concentration cell, is given by (Wagner, 1933): \

equal to some average value t\w then Eq. (11-12) can be approximated to: (11-13) The ionic transport number nevertheless varies with the composition and the need to have a different chemical potential on either side of the cell means that the ionic transport number will not be constant throughout the material. Thus it is not possible to integrate Eq. (11-12) and the ionic transport number can not be taken in front of the integral. However, Eq. (11-13) may be a reasonable approximation provided that the chemical potential gradient across the electrolyte is kept very small and the ionic transport number then equals the ratio of the measured to the theoretical values of the electromotive force. In order to overcome this problem Schmalzried (1962, 1963) derived the following expression for the ionic transport number t{ in oxygen-ion conducting solid electrolytes by assuming n-type and ionic conductivity and a (p O2 )~ 1/4 ^ aw f° r e^ec" tronic conductivity variation as a function of oxygen partial pressure:

ln/io

(11-11) where n'Ol and y!'O2 are the chemical potentials of oxygen on either side of the specimen, F is the Faraday constant and n is the number of electrons required to complete the electrode reaction. Since fiO2 = fio2 + R Tlnp O 2 , the above equation can be written as: RT

(11-12)

If the ionic transport number can be assumed to be constant in the material and

where p& is the oxygen partial pressure at which t{ = 0.5 (or o{ = cre). This expression can be used to determine the ionic transport number by substituting Eq. (11-14) in Eq. (11-12). Goto and Pluschkell (1972) have discussed the various limiting cases under which these expressions are valid. One serious problem with this EMF technique is that if the electronic transport number is appreciable (te > 0) then material transport takes place from one electrode to the other due to internal short circuiting of the cell. This has the effect of altering the oxygen concentration at the

11.3 Techniques for Studying Transport and Kinetic Properties in Superionic Conductors

electrode/electrolyte interface. Also both electrodes become polarized due to passage of current as the electrode reactions take place at finite rates. These effects cause deviation from the true equilibrium chemical potential. The measured EMF signal falls below the actual value causing overestimation of the electronic transport number. The technique is most suitable when the material is mainly an ionic conductor and has been widely used for determining the electrolytic domain of various materials (Etsell and Flengas, 1970; Goto and Pluschkell, 1972). (iii) Another method is to study the conductivity of a mixed conductor as a function of the partial pressure of a component related to the mobile ionic species in the mixed conductor under study. This technique has commonly been used in oxygenion conducting solid electrolytes such as stabilized zirconia, doped thoria and doped ceria to determine the electrolytic domain. In these materials the ionic defect concentration is controlled by the dopant concentration and ionic conductivity is essentially independent of oxygen partial pressure. However, the number of electronic defects" is markedly influenced by small deviations from stoichiometry and therefore the electron or hole conductivity varies significantly with oxygen partial pressure. Thus the ionic transport number can be determined by analyzing curves of conductivity versus oxygen partial pressure. (iv) A most direct way of determining small electronic transport numbers is the polarization technique. This technique has been used quite extensively and involves the use of one reference electrode and one electronically or ionically blocking electrode (Fig. 11-6). A small DC voltage signal is applied to the cell to set up a chemical potential gradient between the reference and the blocking electrode. In the case

Reversible electrode

579

Ion or electron blocking electrode

Figure 11-6. A schematic of the DC polarization technique (with ion or electron blocking electrode) for determining electronic or ionic conductivity in a mixed conductor. 3, 4 are potential probes reversible to ionic or electronic charge.

of the ionic blocking electrode no ionic current and in the case of the electronic blocking electrode no electronic current flows under steady state conditions. With the use of two additional probes positioned on the specimen, reversible only to the electronic or ionic current, electronic or ionic conductivity can be measured. The polarization method has been discussed in detail by a number of authors (Dudley et al, 1980; Heyne, 1977; Mizusaki and Fueki, 1982; Sequeira, 1985; Wagner, 1957,1975) and successfully employed in a number of systems. In the case of oxygenion conductors it has limited application as the interference from electrode reactions involving oxygen in the gas phase can not be completely eliminated. 11.3.3 Thermodynamic Measurements

Since the work of Kiukkola and Wagner (1957 a, 1957 b), who reiterated interest in the usefulness of galvanic cells for studying thermodynamics of solid state reactions,

580

11 Ceramic Superionic Conductors

considerable advances have been made. Solid electrolyte cells have been and are frequently used for determining the solubility of oxygen in molten metals and alloys, thermodynamic stability (or free energy of formation) of binary and ternary compounds and chemical potential of various species in solids, molten metals, alloys, and nonstoichiometric oxides. One of the most commonly used applications of galvanic cells is in relation to determining the free energy of formation of binary or ternary compounds. For example for the cell, reference electrode (aro) |O 2 ~ conductor | M - MO (a£), provided that the ionic transport number is unity and constant throughout the electrolyte, the free energy of formation for the metal oxide (M +1/2 O 2 -> MO) is given by: AG°= -

aro/a%) (11-15)

where aro and a^ are the oxygen activities at the reference and test electrodes respectively. The EMF technique is inherently accurate for obtaining thermodynamic information from a reversible galvanic cell. The measurements of EMF signal are made in the open circuit mode with respect to a reference electrode with a voltmeter with sufficiently high input impedance to avoid electrode polarization. The technique is simple, requiring a minimum of instrumentation. The main limitation is the availability of suitable reference electrode materials over the desired temperature range. Many extensive review articles have been written describing the applications of solid electrolytes for thermodynamic measurements, on the theoretical treatment of galvanic cells and limitations of the technique (Alcock, 1968; Chandrasekharaiah etal, 1980; Goto and Pluschkell, 1972; Kubashewski and Alcock, 1979; Markin et al., 1967; Seetharaman and Abraham,

1980; Shores and Rapp, 1971; Steele, 1968; Steele and Alcock, 1965; Steele and Shaw, 1978). Oxygen-ion conducting solid electrolytes such as stabilized zirconia, doped thoria and doped ceria are most commonly used for determining the free energy of formation of binary and ternary metal oxides, binary intermetallics, and oxygen activity in molten metals and nonstoichiometric oxides. In these galvanic cells the reference electrodes used include Pt (air), (U,M)O 2±:c (air), Ni/NiO, Fe/Fe x O, Cu/Cu 2 O, Cr/ Cr 2 O 3 , Nb/NbO and Ta/Ta 2 O 5 (Bannister, 1984; Etsell and Flengas, 1970; Goto and Pluschkell, 1972; Hladik, 1972 b; Patterson et al., 1967; Steele and Alcock, 1965; Worrell and Iskoe, 1973; Yuill and Cater, 1967). Other electrolytes employed include metal fluorides (e.g., CaF 2 , BaF 2 , SrF2) and metal-ion conducting beta alumina (Na + , Ag + ). Metal fluorides have been used for determining the free energy of formation of metal oxides, fluorides and carbides in addition to thermodynamic information on the activity of a metal in binary alloys. However, their use is somewhat restricted because of the limited and less reliable free energy data available on reference metal fluorides and their high volatility. Beta alumina electrolytes have been used for determining metal (Na, Ag) or sulfur activity. Table 11-1 lists some examples of galvanic cells used for obtaining different types of thermodynamic data. Recent review articles (Chandrasekharaiah et al., 1980; Seetharaman and Abraham, 1980; Steele and Shaw, 1978) give more detailed accounts of various systems studied by the galvanic cell technique. The simplicity of the galvanic method can be deceptive and extreme care needs to be given to the selection of the reference electrode and electrolyte materials and

11.3 Techniques for Studying Transport and Kinetic Properties in Superionic Conductors

581

Table 11-1. Some examples of thermodynamic measurements with galvanic cells. Type of measurement

System

Electrolyte

Free energy of formation

binary and ternary metal oxides, silicates, spinels intermetallic compounds (TiPt3, HfPt3, ZrPt 3 , Co3W) metal fluorides, carbides molten glasses, silicates, metal slags binary intermetallics (Co-W, Fe-Nb, Zr-Pt, U-Co) binary liquid alloys

zirconia or thoria based, metal fluorides zirconia or thoria based

UO 2 + J B ,CeO 2 _,,Nb 2 O 5 _,, (U,Pu)O 2±;c , TiO 2 _ x , (U,Zr)O 2+x , VO 2 _ X ,WO 3 _ X Cu, Pb, Sn, Ag, Fe, Na Na-Pb, Na-Hg, Ag, Ag-compounds, metal sulfides

zirconia or thoria based

Free energy of formation Free energy of formation Oxygen activity Metal activity

Nonstoichiometry in oxides

Oxygen dissolved in molten metals metal or sulfur activity

various physical parameters in designing experiments. A brief account of the important factors which should be considered when designing galvanic cells for obtaining thermodynamic data, is given below. The selection of a suitable electrolyte and reference electrode materials is of utmost importance as these together put limits on the accuracy of the thermodynamic data and the range over which measurements can be made. The electrolyte must be free of cracks and connecting pores to avoid molecular transfer of gas from one side of the cell to the other as this will have an effect on the equilibrium EMF signal. This is not a serious problem as with the modern ceramic powder and fabrication techniques it is possible to obtain high density crack free electrolytes with a built in strenghtening and toughening mechanism (Green et al., 1989). Also for accurate thermodynamic measurements both electrode compartments should be hermetically sealed to avoid gas phase transfer of the electroactive species between the two electrodes.

CaF 2 zirconia or thoria based zirconia or thoria based CaF 9

zirconia or thoria based beta-alumina

Over the experimental chemical potential and temperature ranges, the electrolyte used in the galvanic cell should have an ionic transport number close to unity with a minimum of interference from secondary phases and the omnipresent impurities at grain boundaries in polycrystalline ceramics. As discussed previously, even small electronic conductivity can lead to internal short circuiting, transport of mass from one electrode to the other and polarization of the electrodes. This has the effect of disturbing the local chemical equilibrium especially if the electrode kinetics are slow. Therefore it is necessary to study only those systems and use reference electrodes which do not impose chemical potentials at the electrode/electrolyte interface beyond the ionic stability domain of the electrolyte (t{ > 0.99) (Heyne, 1977; Patterson, 1971, 1974). The selection of the reference electrode is to some degree dictated by the experimental conditions over which thermodynamic data are required. However, the reference electrode must be capable of maintaining

582

11 Ceramic Superionic Conductors

accurately the chemical potential at the electrode/electrolyte interface. Electrodes with fast kinetics (high exchange current density) are desirable. It has been indicated that the Cu/Cu 2 O reference electrode can more easily adjust to small perturbations than Fe/Fe x O and Ni/NiO electrodes (Worrell, 1977), the latter having most difficulty in maintaining appropriate chemical potential at the electrode/electrolyte interface. Kinetic data on solid electrolyte systems is not extensive and for a given system under study it is advisable to check for the reversibility of the cell (both reference and test electrodes). This can be easily done by perturbing the system from its equilibrium position in both directions by superimposing a small voltage signal or passing a small current for a short period and observing restoration of the previous EMF signal with time. Inert atmosphere is maintained over the metal/metal oxide reference electrode to minimize gas phase interference and to avoid mixed potentials arising from electrode reactions involving the gas phase especially in cells based on oxygen ion conducting solid electrolytes. Purification of the gas is desirable to remove traces of oxygen. Titanium or copper gettering furnaces are normally used to achieve this. The effect of gas flow rate on the stability of the EMF signal, provided there is no cooling of the cell by fast gas flow rates, can be used to check for the gas phase interference. Alternatively the use of vacuum or a sealed reference electrode compartment may be more satisfactory. The system under study must be thermodynamically well defined and there should not be any chemical reactions between the electrode and electrolyte components. Any new phases formed at the electrode/electrolyte interface can establish

their own chemical potentials and give misleading results. Thermal EMF's due to temperature gradients across the galvanic cells (thermoelectric effect) is another major source of error in obtaining thermodynamic information. A mere 1 °C difference in the temperature of two electrode/electrolyte interfaces can produce about 0.5 mV signal (Goto and Pluschkell, 1972). It is either added on or subtracted from the isothermal EMF due to the true chemical potential gradients characteristic of the system under study. The temperature gradient on the same side of the cell but across the electrolyte can lead to mixed potentials due to the thermoelectric effects (Goto and Pluschkell, 1972). Care should be taken in designing experiments to minimize such temperature gradients. Finally errors inherent in the thermodynamic data for reference electrodes can not be avoided and the accuracy of the information obtained from such cells should reflect this additional source of error. In the absence of all the sources of error discussed above and proper designing of the cell, the reproducibility of the galvanic cell technique for obtaining thermodynamic data is acceptably high. 11.3.4 Kinetic Measurements

Several techniques are used to separate the contributions of various polarization processes in solid electrolyte cells and to study the kinetics of electrode reactions in the time or frequency domain. Numerous books and review articles have been written describing various theoretical and experimental aspects of these transient techniques (Gabrielli, 1980; Gileadi et al, 1975; Koryta and Dvorak, 1987; Macdonald, 1977; Sequeira, 1985; Vetter, 1967; Yeager and Salkind, 1972). Only an overview of

11.3 Techniques for Studying Transport and Kinetic Properties in Superionic Conductors

some techniques more relevant to studying solid electrolyte systems will be described here. In any given study, the use of a technique is dictated by the information required, the accuracy, experimental parameters and limitations imposed by the cell design. A combination of techniques may be necessary to satisfactorily understand the mechanism of charge transfer processes in a solid electrolyte system. Often kinetic parameters are related to the physical state of the electrode (microstructure-grain size, porosity and surface area, etc.) which may also need to be investigated. The impedance technique is extremely versatile for determining the contribution of electrode or electrolyte processes as the detail contained in an impedance spectrum can be quite significant. A single impedance spectrum can provide information about diffusion, charge transfer and adsorption/dissociation processes at the electrode/electrolyte interface as well as about the grain conductivity (intragrain) and grain boundary (intergrain) blocking in polycrystalline electrolytes. Impedance studies are usually carried out in the linear region under an applied signal of low magnitude when the system is near equilibrium. However, in order to study the use of superionic conductors in devices such as batteries, fuel cells, electrochemical reactors, etc. it is essential to study the current carrying capabilities of electrode/electrolyte interfaces. In principle, it is possible and the instrumentation is available to make impedance studies in the dynamic mode when the cell is perturbed from its equilibrium position either in the potentiostatic mode (constant applied DC potential) or in the galvanostatic mode (constant current). However, the technique is slow and limited in supplying information about currentpotential behaviour of solid electrolyte cells. Moreover, accurate measurements

583

can be made only for those systems which are sufficiently stable over the time required to collect several impedance spectra. The galvanostatic current interruption technique is beneficial for studying polarization events in solid electrolyte systems where ohmic losses are significant. This method is fast, and accurate irrespective of the size of the ohmic potential and no prior model assumptions are necessary about the nature of the electrode polarization processes. Potentiostatic methods are used extensively in solution electrochemistry and are useful when ohmic losses in a cell are small. For solid electrolyte systems these techniques have limited applications because of the significant ohmic contribution and have been used mainly to study charge/discharge characteristics of batteries. 11.3.4.1 Impedance Spectroscopy

The impedance spectroscopy technique involves applying an AC signal (sinusoidal) of varying frequency to the solid electrolyte cell and comparison of the input and output signals to get information about the phase shift and the impedance modulus. A sine wave is used because for a sinusoidal signal applied to a linear system the input and output have the same form and at a specific frequency there is a linear relationship between them. The impedance of the cell is the ratio of the voltage to current as Ohm's law holds in the time domain. The resultant response of a solid electrolyte cell can be displayed in the complex plane either in the more commonly used impedance or admittance formulations. Each electrode (diffusion, charge transfer, or adsorption/dissociation) and electrolyte (grain boundary or lattice) process has a different time constant and therefore relaxes over a

584

11 Ceramic Superionic Conductors

different frequency range. If the frequency range is large enough, then the contribution of each process can be separated in the frequency domain. In general, the time constant associated with each process decreases with increasing temperature and the response of the cell shifts to a higher frequency spectrum. In the simplest form, a solid electrolyte cell can be represented by a series combination of several resistance (R) and capacitance (C) elements (subcircuit) in parallel as shown in Fig. 11-7, each corresponding to a different electrode or electrolyte process characterized by a different time constant. The resistor in the subcircuit corresponds to the flux flow for the relevant process and the capacitor represents the space charge effects. The simulated response of the circuit of Fig. 11-7 is shown in Fig. 11-8 and is somewhat similar to that observed for solid electrolyte cells using polycrystalline electrolytes. From impedance circuit theory, it can be shown that the response of each subcircuit (a resistor in parallel with a capacitor) is a semicircle in the complex impedance plane with its origin on the real impedance axis (Badwal, 1988). The difference of intercepts of the semicircle on the real axis gives the value of the resistor, and the value of the capacitor can be obtained from the apex frequency [T0 = l/coo = RC =

l/(2nF0)].

Impedance spectroscopy has been used extensively for a number of years to investigate the kinetic processes in aqueous electrochemistry and several review articles have been written describing both experimental and theoretical aspects of this technique (Archer and Armstrong, 1980; De Bruin and Badwal, 1978; Gabrielli, 1980; Macdonald, 1987; Sluyters-Rehbach and Sluyters, 1970). It is only in the last 1 5 20 years that this technique has been ap-

Hh

Hh

Hh

Hh

Figure 11-7. A simple equivalent circuit of a solid electrolyte cell.

Frequency

Figure 11-8. Response of the circuit shown in Fig. 11-7 in the complex impedance plane. T1S t gb and rel are relaxation times and Rl9 Rgh and # e l are resistivities associated with electrolyte bulk (intragrain), grain boundary (intergrain) and electrode processes respectively.

plied to study the electrical and electrochemical properties of solid electrolyte cells (Macdonald, 1987). Impedance spectroscopy is useful in providing information about the nature of various rate limiting processes at the electrode/electrolyte interface and within the solid electrolyte, on the grain boundary blocking effects by the grain boundary phases and the lattice resistivity. It is an extremely sensitive technique for studying how various ceramic processing variables (sintering temperature, time, heating and cooling rates), post-sinter treatments and impurities in the starting powders have an effect on the nature and segregation sites for the grain boundary phase and precipitation of secondary phases (in the bulk of the grain or at grain boundaries).

11.3 Techniques for Studying Transport and Kinetic Properties in Superionic Conductors

In general, in solid electrolyte cells, arc I in Fig. 11-8 arises from charging of the electrode/electrolyte interface and electrode reactions occurring at or near the interface. It may consist of two or more overlapping relaxations and may include contributions from diffusion, charge transfer and adsorption/dissociation processes. It is usually observed at low frequencies (10kHz) and is influenced by the geometric dimensions of the specimen. For single crystals, the intermediate grain boundary arc is not observed. The frequency domain over which each process relaxes varies with temperature, the cell geometry and the nature of the transport processes at the electrode/electrolyte interface and within the solid electrolyte. Each process has a different dependence on temperature, gas concentration, and the electrode and electrolyte type and microstructure. In real electrochemical systems each electrode or electrolyte process can not be represented by a simple resistor-capacitor (in parallel) subcircuit as described previously and which gives rise to a perfect semicircular arc in the complex impedance plane. The arcs are usually depressed below the real impedance axis. Such a behaviour in general indicates a distribution of time constants and heterogeneity in the system. The symmetric distribution of relaxation times can be represented by ColeCole relationships for the real (Z'o) and imaginary (ZQ) parts of the impedance given by (Bottcher and Bordewijk, 1978):

Z'

585

(11-16)

" 1 + 2 (cy t o ) 1 ' a sin (a TC/2) +(co T 0 ) 2(1 " a) Z'o (H-17) _ R(coxo)1'cc cos (an/2) ~ 1 +2(coT o ) 1 - a sin(a7r/2) + (a;T o ) 2(1 - a) where a is a distribution parameter and a n/2 is the angle of depression of the semicircle below the real impedance axis. In general the impedance response of a polycrystalline electrolyte is simple and can be represented by two Cole-Cole type distributions. Various models describing impurity segregation in solid electrolytes and their relationship to the grain boundary resistivity have been discussed in detail by Badwal et al. (1991). The electrode behaviour is often complex and is affected by both the physical and chemical nature of the electrode and electrolyte materials. A prior knowledge of various physical processes is necessary to delineate impedance spectra. The equivalent circuit approach, in which the circuit is constructed on the basis of previous understanding of the system, is simple and therefore more commonly used to analyze impedance data. Nonlinear least squares techniques for fitting experimental data to analytical expressions for the impedance of a plausible equivalent circuit are extremely useful. Macdonald (1989) has developed versatile nonlinear least squares programs for this purpose which allow for fitting of the experimental data to a range of equivalent circuits consisting of both ideal and distributed elements. The details of cell designs, instrumentation and data analyses techniques have been reviewed elsewhere (Badwal, 1988; De Bruin and Badwal, 1978; Dickinson and Whitfield, 1977; Gabrielli, 1980; Macdonald, 1987; Schouler, 1985; Spinolo et al., 1988; Tsai and Whitmore, 1982).

586

11 Ceramic Superionic Conductors

11.3.4.2 Gal vanostatic Current Interruption

The galvanostatic current interruption technique involves passing a constant current through a two or a three electrode cell for a sufficiently long time to achieve steady state potential. The current is then interrupted with a fast electronic switch and the potential-time transient is recorded with a fast storage oscilloscope or a transient recorder within microseconds of current interruption. The voltage decays almost instantaneously across the electrolyte for the ohmic (IR) potential losses (usually less than 1 JIS) and no trace on the oscilloscope or data on the transient recorder is recorded. The slow part of the transient corresponds to polarization losses at the electrode/electrolyte interface as shown in Fig. 11-9. The principle of operation of the galvanostatic current interruption technique can be easily understood in terms of an equivalent circuit (Fig. 11-10) representing the basic polarization processes in the solid electrolyte cell. In this circuit Z o is the nonlinear faradaic impedance associated with the electrode (anode and cathode) reac-

Current on

tions, Cdl is the double layer capacitance, Rl and Rgh are respectively the lattice and grain boundary resistance in the solid electrolyte, Cg is the geometric capacitance of the cell and Cgb is the grain boundary capacitance associated with blocking of mobile charge carriers at grain boundaries in polycrystalline materials. For each resistorcapacitor subcircuit, at the instance the current pulse is applied, it is divided between two parallel paths. Initially most of the current goes towards charging of the capacitor and little current flows through the resistor. However, the current through the capacitor path decreases rapidly with time. Under steady state conditions when the capacitor is completely charged all the current flows through the resistor. The reverse of this occurs when the current is switched off. In general Cg and Cgb (Cgb > Cg) in solid electrolyte cells are several orders of magnitude smaller than the interfacial double layer capacitance (Cdl). Thus the time constants associated with the electrolyte processes are much lower than that for the electrode process and charging and discharging of the electrode/ electrolyte is a much slower process. The

Current switch off

Figure 11-9. Transient response of the solid electrolyte cell to switching on or off of a constant current.

Zero Time

11.3 Techniques for Studying Transport and Kinetic Properties in Superionic Conductors

587

Figure 11-10. A schematic of the galvanostatic current interruption technique along with the three electrode cell arrangement. WE is the working electrode, CE is the counter electrode, and RE the reference electrode.

(a) Anode

WEI1I

777/777/////////, Solid electrolyte

\

Y77/77/A CE(3)

V7/7A RE(2)

galvanostatic technique allows for separation of the electrode and electrolyte contributions in the time domain. With the two electrode assembly, the electrode contribution includes overpotential losses at both the cathode/electrolyte and anode/electrolyte interfaces. However, as shown in Fig. 11-10, with the use of a third (reference) electrode through which no current passes, it is possible to separately study anodic or cathodic polarization processes. A versatile computer controlled current interruption technique for studying polarization processes in solid electrolytes has been described by Nardella et al. (1988). 11.3.4.3 Other Transient Techniques

Potentiostatic techniques commonly used in liquid electrolyte systems essentially involve controlling the potential be-

tween a working or test electrode and a reference electrode and allowing the current to vary between the test and a counter electrode in a three cell configuration. These techniques have limited application in solid electrolyte systems as ohmic losses can be significant and can cause distortion of the polarization curves. The Luggin probe approach used commonly in liquid electrolyte cells to reduce IR or ohmic potential drop across the electrolyte is not always feasible. Moreover, it does not completely eliminate ohmic losses. Several methods are available to compensate for the electrolyte resistance. These include, built in electronic circuitry in the potentiostats, galvanostatic current interruption and impedance spectroscopy or AC bridge methods. Linear potential sweep and cyclic voltammetry are the common and most versatile potentiostatic techniques used in the study of solid state battery system (Sequeira, 1985). Both methods involve imposing a linear voltage ramp between working and reference electrodes and measuring the current response between working and counter electrodes. The voltage ramp rates can vary from a few mVh" 1 to several V h" 1 and the voltage scan range is

588

11 Ceramic Superior!ic Conductors

usually within ± 3 V. In the linear potential sweep the voltage ramp is applied only in one direction from a rest potential whereas in cyclic voltammetry the direction of sweep is reversed frequently and the whole procedure repeated several times. In a sequence of measurements, as the applied voltage nears the standard potential for the electrode process, the current begins to flow the magnitude of which increases rapidly, but once the applied potential exceeds the standard potential for the electrode process the current starts decreasing. The general characteristics of a cyclic voltammetry curve are shown in Fig. 11-11. The technique is useful for studying charge/discharge behaviour and cycle life in battery systems as the areas under the peaks correspond to the charge or discharge capacity of the battery. It is not unusual to observe more than one peak for oxidation or reduction sweeps if the solid electrolyte system contains more than one electroactive species and their oxidation or reduction potentials are sufficiently separated. The other less frequently used techniques in solid electrolyte systems to study electrode kinetics are chronopotentiome-Ve

Potential over time

Figure 11-11. Cyclic voltammograrn of a cell with reversible electrodes.

try and chronoamperometry. In the former the potential is monitored as a function of time for a system under constant current control. In the latter, the current response of a system to a potential step perturbation is investigated as a function of time. Both these techniques have been extensively used in solid electrolyte cells especially those based on oxygen-ion conductivity for studying diffusion of oxygen in metals (both in the solid and molten states), for determining chemical diffusion of oxygen in nonstoichiometric oxides and diffusion/ solubility product in metals (Hladik, 1972 c; Tare et al, 1980).

11.4 Types of Ceramic Superionic Conductors 11.4.1 Oxygen-Ion Conductors

The use of oxygen-ion conducting materials in solid electrolyte devices and as a tool for studying thermodynamic and kinetic properties is wide spread. A majority of solid electrolytes which are fast oxygenion conductors have either the face centered cubic (fluorite-type) or the distorted face centered cubic structure (see Ch. 1, Sec. 1.2.3 for structure model of fluorite lattice). These materials contain a large number of vacancies created by the incorporation of lower valent cations into the fluorite lattice (extrinsic defects). In the fluoritetype structure, cations are grouped in a face centered cubic arrangement with oxygen ions occupying all the tetrahedral sites. The lower valency dopant cation substitutes on a zirconium lattice site thus creating vacancies in the oxygen sublattice for charge compensation. Oxygen-ion vacancies have been confirmed to be the dominant defects by X-ray and density measure-

11.4 Types of Ceramic Superionic Conductors

ments. One anion vacancy is introduced for one divalent cation or two trivalent cations substituted in the host cation sublattice. The ionic conductivity in the fluorite-type structure is isotropic in nature and results from migration of oxygen-ion vacancies distributed randomly in the oxygen sublattice. There is a rather large scatter in the conductivity and activation energy data reported in the literature. This can be attributed to different preparation techniques used and to the level of impurities in the materials all of which affect the total conductivity, to different measurement techniques used by various authors all of which do not furnish the same information, and to incomplete characterization of the ceramics. In addition, the contribution from the grain boundary resistivity, the level of interaction between vacancies and between dopant cations and vacancies are a function of the temperature. Unless the role of each process is fully appreciated and its contribution to the total conductivity is isolated, the interpretation of the data can be subjective. 11.4.1.1 Zirconia Based Materials Pure zirconia (ZrO2) exists in three polymorphs. The monoclinic (m) phase is the stable form at room temperature but is mainly an electronic conductor with a very low value for conductivity (Kumar et al., 1972; Nasrallah and Douglas, 1974). It undergoes phase transformation to the tetragonal (t) modification on heating at 1170°C which itself transforms to the cubic phase at 2370 °C. The cubic phase is stable up to the melting point of zirconia (2680 °C). On cooling the reverse transformations take place. These phase transformations are martensitic in nature. The tetragonal to monoclinic phase transformation is

589

accompanied by about 3 - 5 % volume change which is enough to cause severe cracks in the ceramic. The t -> m transformation can be avoided and the high temperature cubic and tetragonal phases can be stabilized at lower temperature by the addition of a number of metal oxides (CaO, MgO, Y 2 O 3 , Sc 2 O 3 and rare earth oxides). These metal oxides form solid solutions with zirconia and stabilize the tetragonal and the cubic phases in addition to introducing vacancies in the anion sublattice which are responsible for the observed high ionic conduction. The phase diagrams for ZrO 2 based materials are complex and there is a considerable disagreement in the literature as to the exact location of the phase boundaries. Methods of powder and ceramic fabrication also have a significant influence on the phase assemblage. The existence of metastable phases, ordering and precipitation as a function of heat treatments further add to the complexity of the system. For technological applications CaO, MgO, Y 2 O 3 , Sc 2 O 3 and Yb 2 O 3 systems have been more widely studied and as superionic conductors the tetragonal and the cubic phases of stabilized zirconia are of main interest. The composition range over which these phases exist is narrow and is temperature dependent. The amount of the dopant required to fully stabilize the cubic phase is about 8 mol% Y 2 O 3 (Scott, 1975; Yoshimura, 1988), corresponding to about 3.75% vacancy concentration, 8-9mol% Yb 2 O 3 (Perez y Jorba, 1962), 8 mol% Sc 2 O 3 (Ruh etal, 1977; Thornber et al., 1970), and 12-13 mol% CaO (6-6.5% vacancy concentration) (Stubican and Hellmann, 1981). The amount of other rare earth oxide (Dy 2 O 3 , Sm 2 O 3 , Gd 2 O 3 , Nd 2 O 3 ) required to stabilize the cubic phase varies between 8-12 mol% (Col-

590

11 Ceramic Superionic Conductors

longues et al., 1961; Etsell and Flengas, 1970). The cubic phase range varies with the temperature and it exists over 8 to 50mol% Y 2 O 3 at 1600 °C (Scott, 1975), 12-13 to 20 mol% CaO at 1500 °C (Etsell and Flengas, 1970; Stubican and Hellmann, 1981) and 8-12 to 40-50 mol% rare earth oxides at 1000 °C (Collongues etal, 1961; Etsell and Flengas, 1970). In the Sc 2 O 3 -ZrO 2 system, the cubic phase exists only over the composition range of &9 to 15mol% Sc 2 O 3 at 1200°C but in compositions containing more than about 10 mol% Sc 2 O 3 , a low conducting rhombohedral (P) phase usually coexists with the cubic phase (Bannister and Skilton, 1983; Ruh et al, 1977). In the ZrO 2 -MgO system, the cubic solid solutions are stable only at higher temperatures and decompose below about 1300 °C (Grain, 1967). If the stabilizer content is insufficient then the structure of the material consists of two or more phases which may be in the metastable form depending on the thermal history of the ceramic. Such materials are known as partially stabilized zirconia (PSZ). Although some of these properties have been exploited to advantage in MgO and CaO-ZrO 2 systems and materials with high strength, toughness and thermal shock resistance have been developed (Garvie et al., 1975; Green et al., 1989), they nevertheless have serious consequences for ion transport properties. In the ZrO 2 -Y 2 O 3 system, the phase assemblage between 2 - 3 and 8.5 mol% Y 2 O 3 consists of a mixture of cubic, tetragonal and sometimes monoclinic phases. At about 2 - 3 mol% Y 2 O 3 a low-dopant tetragonal (t) phase is formed. This phase has a fine grain size, has extremely high strength and toughness and transforms to monoclinic zirconia under stress (Nettleship and Stevens, 1987). The lattice conductivity of this phase is higher than that of

fully stabilized zirconia, below about 600700 °C (Badwal and Swain, 1985). A metastable dopant-rich tetragonal phase known as the t'-phase has also been reported in ZrO 2 -Y 2 O 3 and ZrO 2 -Sc 2 O 3 systems. This phase does not transform under a stress field but slowly decomposes with time at elevated temperatures to a cubic phase and tetragonal ZrO 2 precipitates (Heuer et al., 1988). The transformation of the t'-phase is diffusion controlled, leading to a decrease of the ionic conductivity (Ciacchi, 1990). In the ZrO 2 -Y 2 O 3 system, the t'-phase is formed by quenching the ceramic from a temperature in the cubic phase field (Y2O3 < 7 mol%). In the ZrO 2 -Sc 2 O 3 system, the t'-phase is formed under normal sintering conditions (quenching is not necessary) between 4.58mol% Sc 2 O 3 . For detailed discussion of the phase diagram work, fabrication techniques, thermal and mechanical properties readers should refer to several review papers and articles written on various aspects (Claussen etal., 1984; Green et al., 1989; Heuer and Hobbs, 1981; Heuer, 1987; Koehler, 1984; Somiya et al., 1988; Stevens 1986; Stubican and Hellmann, 1981; Swain, 1989; Yoshimura, 1988). There seems to be some correlation between the minimum amount of the dopant required to fully stabilize the cubic phase and the conductivity maximum observed as a function of the dopant concentration (12-13 mol% CaO, 8-9 mol% Y 2 O 3 , 8-9mol% Yb 2 O 3 and 8-12 mol% other rare earth oxides) (Dixon et al., 1963; Etsell and Flengas, 1970; Schmalzried, 1977; Strickler and Carlson, 1965; Takahashi, 1972; Tannenberger et al., 1966). In the cubic phase field, the conductivity decreases rapidly with increasing dopant concentration. Such a behaviour is shown in Figs. 11-12 and 11-13 for a number of

11.4 Types of Ceramic Superionic Conductors

591

-075

Figure 11-12. Conductivity as a function of dopant content in zirconia based systems. The data for Yb 2 O 3 (o), CaO (D) and Gd 2 O 3 (A) from Tannenberger et al. (1966). Sc 2 O 3 data (o) from author's laboratory.

-3.25 m o l % M 2 0 3 (MO)

-0.75 O Single grain # Polycrystalline

1000°C

0.90 o c b o)-1.20

-1.35 -1.50

(a) -3.70

-3.90 T

-4.10

-A.50

Figure 11-13. Variation of conductivity as a function of Y 2 O 3 concentration in the ZrO 2 -Y 2 O 3 system at (a)1000°C(total)and(b) 400 °C (lattice resistivity), o - Single grain; • - polycrystalline specimens.

O Single crystal • Polycrystalline

-4.70 13

1

(b)

mol% Y203

592

11 Ceramic Superionic Conductors

ZrO2-based system. The trend, however, is different at higher and lower temperatures as shown in Fig. 11-13 for the more extensively studied ZrO 2 -Y 2 O 3 system. At 400 °C there is no sharp maximum as observed at 1000 °C. In fact there is little change in the lattice conductivity up to about 8 mol% Y 2 O 3 above which conductivity decreases rapidly with increasing dopant concentration. A maximum in the conductivity at 1000 °C has also been observed for doped CeO 2 and ThO 2 systems at about the same vacancy concentration (see below). Both CeO 2 and ThO 2 in the pure form have the cubic structure and the dopant is added only to increase the concentration of extrinsic defects (vacancies). Thus the relationship between the conductivity maximum and the minimum amount of the stabilizer required to fully stabilize the cubic phase in zirconia is somewhat ambiguous unless the conditions which require the crystal lattice to be fully stabilized in the cubic structure also give rise to a maximum conductivity. In zirconia based electrolytes if conductivity measurements are made over a wide temperature range (300-1100 °C), a continuous change in the slope of the Arrhenius plots is observed (Abelard and Baumard, 1982; Badwal, 1984; Badwal and Swain, 1985; Casselton, 1970; Ioffe et al., 1975). This behaviour is obvious in both single crystals (or grains) and high purity materials and is not due to the higher contribution of the grain boundary impedance at lower temperatures. The activation energy decreases monotonically with increasing temperature. The activation energies reported in the literature are for different temperature ranges and some caution is necessary in directly comparing values reported by different authors. In general, an increase in the activation energy with in-

crease in the dopant concentration has been reported (Dixon et al., 1963; Etsell and Flengas, 1970; Ioffe et al, 1978; Strickler and Carlson, 1965). However, the change in the slope of the Arrhenius plots with temperature as well as the activation energy over a given temperature range are functions of the dopant concentration. In both Y 2 O 3 and Sc 2 O 3 systems the curvature in the Arrhenius plots is less marked as the dopant concentration decreases (Badwal, 1987; Badwal and Ciacchi, 1990) and is shown in Fig. 11-14 for the Z r O 2 Y 2 O 3 system. The isothermal change in the conductivity with the dopant concentration and the conductivity behaviour as a function of temperature for different dopant contents have been discussed by several authors (Hohnke, 1979, 1981; Kilner, 1983; Kilner and Waters, 1982; Nakamura and Wagner, 1980, 1986; Schmalzried, 1977). Models with varying degrees of interactions and nearest neighbours involving dopant cations and vacancies and ordering of vacancies have been considered. In general, over the entire temperature range, two broad regions for ionic conduction exist for fluorite-type ionic conductors. At the low temperature end (below 600-700 °C), simple associates form between dopant cations and vacancies for dilute solutions and the activation energy consists of the energy for defect pair association and the enthalpy for vacancy migration. With increasing temperature the defect pairs begin to dissociate and at higher temperatures, as vacancies become free, the conductivity is determined mainly by the concentration of charge carrying defects and the activation energy equals the enthalpy for vacancy migration. The transition between the two regions occurs over a very broad temperature range. For concentrated solutions, complexes involving several near neigh-

11.4 Types of Ceramic Superionic Conductors

593

2.0 E

i

1.0

Log

jo 0.0

-1.0

-2.0 7.5

o3mol% A8mol% Di2mol% Y 2 0 3 -Zr0 2

9.0

10.5 12.0 Temperature in 10*K~1

bours can form. Moreover, interactions between vacancies can lead to ordering of vacancies. This may explain the observed rapid decrease in the conductivity with increasing dopant content for concentrated solutions. However, in the dilute solution range the phase assemblage in zirconia based materials, below the minimum amount of dopant required to fully stabilize the cubic phase, may consist of two or more phases in addition to variants of the same phase with varying degrees of solute distributions. As a result interpretation of the data in the dilute solid solution range is somewhat obscured. In Z r O 2 - M 2 O 3 systems, in general, an increase in the conductivity and decrease in the activation energy with decreasing ionic radius of the dopant cation is observed (Kilner and Brook, 1982; Stafford etal., 1989; Strickler and Carlson, 1965; Takahashi, 1972). This behaviour has been explained in terms of the steric blocking effect of the dopant cation and binding energy between the dopant cation and vacancies. Larger ions are more effective in blocking vacancy migration. Also the binding energy, which is a combination of coulombic and strain (caused by different Zr 4 +

L ^

13.5

^*^

Figure 11-14. Arrhenius conductivity plots as a function of the stabilizer content, o - 3 mol%, A 8 mol% and n - 12 mol% Y 2 O 3 -ZrO 2 .

15.0

and dopant cation size) factors, is affected by the dopant cation size (Kilner and Brook, 1982; Stafford et al., 1989). Conductivity studies in Sc 2 O 3 -Y 2 O 3 -ZrO 2 (Ciacchi, 1990) and Yb 2 O 3 -Y 2 O 3 -ZrO 2 (Corman and Stubican, 1985) at a constant dopant concentration (8 or 10 mol%) but as a function of Sc 2 O 3 (Yb 2 O 3 )/Y 2 O 3 ratio clearly demonstrate that the dopant cation size has an effect. The ionic radius of both Sc 3+ and Yb 3 + is close to that of Zr 4 + but smaller than that of Y3 + and in both systems conductivity increased with increasing Sc 2 O 3 or Yb 2 O 3 content. In the high temperature region (850-1000 °C) where most of the vacancies are expected to be dissociated and free to migrate, the activation energy has been reported to increase with increase in the Y 2 O 3 content in the Sc 2 O 3 -Y 2 O 3 -ZrO 2 system. Figure 11-15 compares the conductivity behaviour over a large temperature range for several zirconia based electrolytes. Amongst various zirconia based electrolytes, the maximum conductivity has been observed for Sc 2 O 3 stabilizer (smallest cation size) followed by Yb 2 O 3 , Gd 2 O 3 and Y 2 O 3 . Table 11-2 gives conductivity and activation energy data for several compositions.

594

11 Ceramic Superionic Conductors

Figure 11-15. Arrhenius plots for various stabilized zirconia electrolytes, o - 13mol% CaO (Tien and Subbarao, 1963), A - 10mol% Y 2 O 3 , n - 8 mol% Sc 2 O 3 (author's data).

0.0 o I

-1.0

-2.01— 7.5

• 8mol% Sc2O3 A 10mol% Y 2 0 3 O 13mol% CaO 9.0

10.5 12.0 Temperature in 10^-K"1

A larger number of materials show a continuous change in the conductivity with time (ageing) at higher temperatures (800-1200 °C) (Badwal, 1987; Ciacchi, 1990; Etsell and Flengas, 1970; Vlasov and Perfiliev, 1987). The conductivity deterioTable 11-2. Ionic conductivity and activation energy data for zirconia based electrolytes. Composition

(ZrO 2 ) 0 . 88 (Y 2 O 3 ) 0 . 12 a (ZrO2)0.90(Y2O3)0.10a (ZrO 2 ) 0 . 92 (Y 2 O 3 ) 0 . 08 a (ZrO 2 ) 0 . 97 (Y 2 O 3 ) 0 . 03 a (ZrO2)0.92(Sc2O3)0.08a (ZrO2)0.87(CaO)0.13b (ZrO 2 ) 0 . 92 (Yb 2 O 3 ) 0 . 08 c (Zr0 2 )o. 90 (Gd 2 0 3 ) 0 . 10 d (ZrO 2 ) 0 . 81 (In 2 O 3 ) 0 . 19 e a

G in Q^cm"1 (1000 °C)

E in kJmol" 1 (±3) (Temperature range in °C)

0.11

95(850-1000) 115(400-550) 0.12 88(850-1000) 105 (350-500) 0.15 75(850-1000) 100(300-425) 0.055 72(850-1000) 88 (300-450) 0.18-0.31 75(850-1000) 130(400-500) 0.06 115(750-1000) 0.2 80(600-1000) 0.02 (800) 0.04 (800) 146 (400-800)

Data from Author'sJ laboratory; b Dixon etal. (1963); c Yamamoto et al. (1989); d Tannenberger et al. (1966); e Hohnke (1980).

13.5

15.0

rates continuously over a long period (usually rapidly in the first few hours and then more slowly) when the sintered materials are annealed as shown previously in Fig. 11-3 for a ZrO 2 -Y 2 O 3 and a ZrO 2 -Sc 2 O 3 composition. The rate of conductivity deterioration is a function of the annealing temperature, previous thermal history, the type and concentration of dopant and is determined by thermodynamics and kinetics of phase equilibrium reactions. For each system or composition there is usually an upper and a lower temperature beyond which no ageing and deterioration in the conductivity occurs. In most of these systems the ageing can be reversed by heating the materials to higher temperatures. The ageing in single crystals and within the grains of polycrystalline ceramics occurs as a result of slow decomposition of the metastable phases, formation and growth of precipitates of low conducting phases and ordering of cation or anion sublattices (Allpress and Rossell, 1975; Baukal, 1969; Etsell and Flengas, 1970; Green et al., 1989; Hannink, 1978; Rossell, 1981; Stubican and Ray, 1977; Stubican etal., 1977; Subbarao and Sutter, 1964; Tien and Subbarao, 1963; Vlasov and Per-

11.4 Types of Ceramic Superionic Conductors

filiev, 1987). These processes require diffusion and rearrangement of cations and, therefore, are limited by the slow cation migration at the annealing temperatures and often proceed through the formation of intermediate metastable phases. Even materials whose phase assemblage consists of a single phase may not be in thermodynamic equilibrium at the annealing temperatures. The existence of short or long range ordering in cubic solid solutions on annealing has been observed in zirconia based systems (Allpress and Rossell, 1975; Stubican and Ray, 1977; Stubican et al., 1977). The strongest evidence for the formation and growth of microdomains or ordered compounds on annealing exists in the ZrO 2 -CaO system (Allpress and Rossell, 1975; Stubican and Ray, 1977) and the observed decrease in the conductivity with time in the vicinity of 1000 °C for higher dopant concentrations (18-20mol% CaO) has been attributed to an order/disorder transition (Subbarao and Sutter, 1964; Tien and Subbarao, 1963). In the single phase ZrO 2 -Y 2 O 3 compositions, the effect of ordering on the conductivity has not been quantified and in any case appears to be relatively small (Etsell and Flengas, 1970). No ageing occurs for the 10mol% Y 2 O 3 composition at 1000 °C (Badwal, 1984). In the ZrO 2 -Sc 2 O 3 system all compositions between 4.5 and 8 mol% Sc 2 O 3 are essentially single phase materials in the as-sintered form but show a decrease in conductivity with time at 1000 °C. This results mainly from the slow disproportionation of the dopant-rich metastable t'-phase present in the sintered materials into a cubic phase matrix and tetragonal (low dopant level) precipitates (Badwal, 1987; Ciacchi, 1990). For 7.8mol% Sc 2 O 3 -ZrO 2 , the maximum conductivity deterioration occurred at 900 °C (Fig. 11-16) (Ciacchi, 1990).

595

150

600

700 800 900 1000 Annealing temperature in °C

1100

Figure 11-16. Percentage resistivity increase in 7,8 mol% Sc 2 O 3 -ZrO 2 at different annealing temperatures after 9500 min.

In the two phase ceramics, the phase assemblage in the sintered materials is usually not in thermodynamic equilibrium, and a significant deterioration in the conductivity occurs with time in all partially stabilized zirconias in the vicinity of 1000 °C as a result of solute partitioning and precipitation and in the growth of low conducting phases. In ZrO 2 -Y 2 O 3 , at 1000 °C, conductivity deterioration has been observed for all compositions (2-8 mol% Y2O3) in the two phase (cubic and tetragonal) field (Badwal and Ciacchi, 1990). The conductivity of both MgO and CaO-PSZ deteriorates even more rapidly with time in the vicinity of 1000 °C (Fig. 11-17). In MgO-PSZ, ageing below the sub-eutectoid temperature leads to the transformation of the tetragonal precipitates to monoclinic zirconia, development of fine monoclinic structure within tetragonal zirconia precipitates and the formation of an ordered anion vacancy phase Mg 2 Zr 5 O 1 2 within the grains (Hannink and Garvie, 1982). Also increased precipitation of monoclinic zirconia takes place at the grain boundaries. Similarly precipitation and coarsening of low conducting phases also occur in CaO-PSZ during annealing (Hannink et al., 1981).

596

11 Ceramic Superionic Conductors

-2.0 3.Awt.% MgO —PSZ

1000°C

E -2.1 o C

b o-2.2 Figure 11-17. Ageing be-2.3

haviour of 3.4wt.% MgOPSZ at 1000 °C. 1000

2000 3000 Time in min

In polycrystalline materials, apart from a change in the conductivity in the bulk of the grains, increase in the grain boundary resistivity due to annealing has also been reported (Ciacchi, 1990; Kleitz et al., 1981; Vlasov and Perfiliev, 1987). In addition to the ageing behaviour discussed above, phase transformations during heating or cooling of zirconia ceramic can lead to sudden changes in conductivity. For example the presence of monoclinic zirconia (due to incomplete phase reaction or formed as a result of phase decomposition) leads to jumps in the Arrhenius plots for the conductivity and hysteresis effects as shown above in Fig. 11-4. Such phase transformations are accompanied by a volume change, leading to microcracking and deterioration in the conductivity on thermal cycling (Badwal, 1983). The conductivity of zirconia based electrolytes is independent of oxygen partial pressure over a wide range of temperatures and oxygen partial pressures with oxygenion transport number close to unity (Etsell and Flengas, 1970). Despite considerable scatter attributable to the techniques used for determining the ionic transport number, the electrolyte domain at 1000 °C extends at least from 1 to 10~ 20 atm oxygen

4000

5000

partial pressure. It narrows with increasing and widens with decreasing temperature. At lower oxygen partial pressures the mode of conduction is n-type. In zirconia-based ceramics segregation of low conducting impurities during sintering and subsequent heat treatments considerably modifies the total conductivity. The contribution to the total resistivity from grain boundaries is a function of the powder and ceramic processing procedures used. The effect of grain boundary resistivity is more marked in small grain size ceramics with a large grain boundary surface area such as yttria tetragonal zirconia (Badwal, 1990). This subject will be discussed in more detail in Sec. 11.5 on "Microstructure and Transport Properties". 11.4.1.2 Ceria Based Materials Pure ceria (CeO2 _x) exists in the fluorite structure over a wide temperature and oxygen partial pressure range (x « 0.3, Bevan and Kordis, 1964). For small values of x9 ceria is a mixed conductor but the electronic (n-type) conductivity dominates with increasing degree of nonstoichiometry (VanHandel and Blumenthal, 1974). In pure ceria both oxygen vacancies and

597

11.4 Types of Ceramic Superionic Conductors

cerium interstitials have been reported as the nonstoichiometric defects although most of the data point to an oxygen-ion vacancy model (Blumenthal and Hofmaier, 1974; Panlener et al., 1975). On addition of low valence dopants (CaO, Y 2 O 3 , Gd 2 O 3 , Nd 2 O 3 , Yb 2 O 3 , La 2 O 3 , etc.), the concentration of oxygen vacancies increases well above that of electronic defects and the material becomes a predominantly ionic conductor. The solubility of the added oxides is quite high (Bevan etal., 1965 a, 1965 b; Etsell and Flengas, 1970) and the solid solutions with the fluorite-type structure exist over a wide dopant concentration range. In doped ceria, oxygen vacancies are the main charge compensating defects (Blumenthal etal., 1973). In the CeO 2 -CaO system, the maximum in the conductivity between 500 and 1000 °C has been reported at 11 -12 mol% CaO (5.5-6% vacancy concentration) by Adham and Hammou (1983) and Blumenthal etal. (1973) whereas No wick etal. (1979) observed no such maximum. The activation energy does not change significantly with the dopant content between 3 and 14mol% CaO. In the CeO 2 -Y 2 O 3 system, Wang et al. (1981) have studied the effect of Y 2 O 3 content over a large concentration range (0.05-40 mol%) and observed a sharp maximum at 182 °C in the conductivity [Fig. 11-18 (a)] and a minimum in the activation energy at 4 mol% Y 2 O 3 . With further increase in the dopant concentration to 40 mol%, the conductivity decreased by more than four orders of magnitude at 182°C. However, Adham and Hammou (1983) observed a conductivity maximum at 8 mol% Y 2 O 3 (500600 °C). A careful examination of the data reported by Wang etal. (1981) at 560°C also revealed a broad maximum above 6mol% Y 2 O 3 [Fig. ll-18(b)]. Like with zirconia based materials, the Arrhenius

plots of ionic conductivity show a change in slope towards lower activation energy with increasing temperature. Wang et al. (1981), Kilner (1983) and Hohnke (1981) have interpreted the conductivity behaviour in doped CeO 2 in terms of interactions between vacancies and dopant cations at low temperatures as discussed previously for the zirconia based electrolytes. The effect of dopant cation type and its concentration is more meaningful in ceria based systems in the dilute solid solution range as the same fluorite structure is maintained throughout. Amongst various CeO2-based electrolytes the maximum conductivity has been reported for Gd 2 O 3 doped CeO 2 (Gerhardt-Anderson and No wick, 1981; Gerhardt and No wick, 1986; Kudo and Obayashi, 1975). Table 11-3 gives values for ionic conductivity and activation energy for various doped CeO 2 compositions. Some ambiguity results from different temperature ranges over which the activation energy data has been reported.

Table 11-3. Conductivity and activation energy data for doped ceria electrolytes Composites

(CeO2)0.92(Y2O3)0.08a (CeO2)0.95(Y2O3)0.05b (CeO2)0.90(CaO)0.10b (CeO2)0 90 (Gd 2 O 3 ) 0 1OC (CeO 2 ) 0 . 82 (Gd 2 O 3 ) 0 . 18 d (CeO 2 ) 0 . 82 (Nd 2 O 3 ) 0 . 18 d (CeO2)0.82(La2O3)0.18d a

a in

E in

(T in °C)

(temperature range in °C)

0.0091 (600) 0.003 (500) 0.145 (1000) 0.10 (1000) 0.0064 (600) 0.25 (1000) 0.235 (1000) 0.23 (1000) 0.154(1000)

68 (450-700) 73 (400-1000) 88(400-1000) 72 (450-700) 68 (700-1000) 81 (700-1000) 78 (700-1000) 78 (700-1000)

Adham and Hammou (1983); b Tuller and Nowick (1975); c Reiss etal. (1981); d Kudo and Obayashi (1975).

11 Ceramic Superionic Conductors

-2.0

Figure 11-18. Variation of conductivity with Y 2 O 3 content in the CeO 2 -Y 2 O 3 system, (a) 182°C(Wang etal., 1981). (b) n - 5 6 0 ° C (Wang et al., 1981); o 600 °C, A - 500 °C (Adham and Hammou, 1983).

Grain boundary resistivity in ceriabased materials makes a major contribution to the total resistivity and has been reported to be dependent on the type and concentration of dopant in addition to impurities (Adham and Hammou, 1983; Gerhardt and No wick, 1986; Tanaka etal., 1987; Wang and No wick, 1980). In general, higher grain boundary resistivity has been observed for low dopant content. The origin of grain boundary resistivity is similar to that in zirconia based electrolytes. Impurities segregate at grain boundaries

and have been suggested to form a continuous glassy film surrounding each grain or aggregates of grains (Gerhardt et al., 1986; Tanaka et al., 1987). The ionic conductivity regime is narrow in ceria based electrolytes and is a function of the dopant concentration. These materials easily develop n-type electronic conduction in low oxygen partial pressures and at high temperatures (Adham and Hammou, 1983; Blumenthal etal., 1973; Hurley and Hohnke, 1980; Tuller and No wick, 1975). For example for

11.4 Types of Ceramic Superionic Conductors

(CeO2)0 95 (Y 2 O 3 ) 0 0 5 , Tuller and Nowick (1975) have reported that the electrolyte domain (t{ > 0.99) extended to 10" 1 3 atm at 600 °C and only to about 10 " 6 atm oxygen partial pressure at 1000 °C. Doped ceria electrolytes have limited application in low oxygen concentration environments and at high temperatures despite their high ionic conductivity compared with zirconia based materials. 11.4.1.3 Thoria and Hafnia Based Materials

Thoria (ThO2) exists in the cubic fluorite-type structure and in the pure form exhibits p-type conductivity (Bauerle, 1966; Etsell and Flengas, 1970; Lasker and Rapp, 1966). In high oxygen partial pressures, the predominant defects are electron holes (h) and interstitial anions Of~. Oxygen dissolves in the lattice according to the reaction: O 2 (g) = 2Of~ + 4 h \ Any variation in the oxygen partial pressure changes the relative concentration of ionic and electron defects. Dopants such as CaO, MgO, Y 2 O 3 , Gd 2 O 3 , Yb 2 O 3 are added to introduce anion vacancies and thus to increase the concentration of ionic defects over electronic charge carriers. The solubility of the added oxide varies considerably with the dopant-type and with temperature; the solubility limit increases with temperature. Around 1700 °C a solubility of about 10 and 20 mol% for CaO and Y 2 O 3 dopants respectively have been reported (Curtis and Johnson, 1957; Hund and Metzger, 1952; Mehrotra et al., 1973; Mobius, 1964; Subbarao et al., 1965). In doped thoria, p-type conductivity is a function of temperature and the electrolyte composition. For example, in ThO 2 -Y 2 O 3 , both ionic and p-type conductivity as well as the ionic transport number increase with Y 2 O 3 content (Hammou, 1975; Lasker and Rapp, 1966). In general, for Y 2 O 3 and

599

CaO dopants, for oxygen partial pressures less than about 10" 6 atm and at 1000 °C, the conductivity is predominantly ionic. Lasker and Rapp (1966) and Steele and Alcock (1965) have reported that the total conductivity of thoria-yttria solid solutions is independent of oxygen partial pressure over the range 10~ 6 -10~ 2 8 atm. The p-type conductivity in pure and doped thoria follows a (Po2)1/4 law (Lasker and Rapp, 1966). Amongst thoria based materials, most of the electrical conductivity studies have concentrated on ThO 2 -Y 2 O 3 and ThO 2 -CaO systems. The ionic conductivity occurs by migration of oxygen ions. A comparison of the measured and theoretical densities strongly points to an anion vacancy model for the fluorite-type solid solution (Subbarao etal., 1965; Wimmer et al., 1967). The maximum in the conductivity has been observed at about 8 mol% Y 2 O 3 (3.75% anion vacancy concentration) (Hammou, 1975; Lasker and Rapp, 1966) and 5 10mol% CaO (Steele and Alcock, 1965; Maiti and Subbarao, 1976). It is worth mentioning here that the solubility of CaO in ThO 2 is much lower than that in ZrO 2 and CeO 2 . The conductivity of ThO 2 -CaO compositions is about an order of magnitude lower than that of ThO 2 -Y 2 O 3 . The ionic conductivity in doped thoria materials is one to two orders of magnitude lower than that in corresponding zirconia based materials of similar compositions (Fig. 11-19). Table 11-4 lists conductivity and activation energy values for several ThO 2 -Y 2 O 3 (CaO) compositions. The electrolytic conductivity domain extends to much lower oxygen partial pressures in doped thoria. From DC polarization experiments on the ThO 2 -Y 2 O 3 system, Patterson etal. (1967) have estimated t{ to be > 0.99 at 1000 °C for oxygen

600

11 Ceramic Superionic Conductors

Figure 11-19. Arrhenius plots for various solid electrolytes all doped with 8mol% Y 2 O 3 . o - Z r O 2 , A-HfO 2 , n - T h O 9 .

-2.0

9.0

10.5

12.0

13.5

15.0

Temperature in 10A-K"1

Table 11-4. Ionic conductivity and activation energy data for doped thoria and stabilized hafnia electrolytes. Composition

o in Q 1 cm {T in °C)

1

(ThO2)0 92 (Y 2 O 3 ) 0 08 a (ThO 2 ) 0 . 92 (Y 2 O 3 ) 0 . 08 b (ThO 2 ) 0 . 92 (Y 2 O 3 ) 0 . 08 c (ThO2)0.93(CaO)0.07d (ThO2)0.95(CaO)0.05e (HfO 2 ) 092 (Y 2 O 3 ) 008 f (HfO2)0.80(Y2O3)0.20f

0.018(1045) 0.013(1000) 0.0075 (1000) 0.002(1000) 4.5 x l 0 ~ 4 (1000) 0.025 (1000) 0.0053 (1000)

Ein (temperature range in °C) 106(1045-1400)

112(1000-1300) 70(800-1000) 128(800-1000)

a

Hammou (1975); b Bauerle (1966);c Lasker and Rapp (1966); d Maiti and Subbarao (1976);e Steele and Alcock (1965);f Schieltz et al. (1971).

partial pressures down to 10 34 atm. Other authors have also reported similarly high ionic transport numbers at very low oxygen partial pressures (Etsell and Flengas, 1970; Hammou, 1975; Lasker and Rapp, 1966; Wimmer et al., 1967). There is general consensus that for ThO 2 -Y 2 O 3 at 1000 °C, the electrolyte conductivity domain is at least between 10~ 6 and 10~25 atm oxygen partial pressure. The ionic conductivity domain decreases with increasing temperature, a behaviour similar to that observed for zirconia based materials. The major advantage of doped thoria electrolytes compared with zirconia based materials is their

high stability in extremely reducing environments. For this reason these materials are more attractive for use in galvanic cells for measuring low oxygen concentrations, for example in liquid metals (Chandrasekharaiah et al., 1980; Jagannathan et al., 1980). These electrolytes are not serious contenders for use in fuel cells and oxygen gauges because of their low ionic conductivity and the presence of p-type conductivity at high oxygen partial pressures. Pure hafnia (HfO2) undergoes several polymorphic transformations with temperature and does not exists in the fluoritetype phase at low temperatures. The cubic

11.4 Types of Ceramic Superionic Conductors

structure has to be stabilized by the addition of dopants such as Y 2 O 3 , La 2 O 3 , Gd 2 O 3 , and CaO (Etsell and Flengas, 1970; Komissarova et al., 1964; Spiridinov etal, 1968). HfO 2 -CaO cubic solid solutions are not stable below 1450 °C and decompose to monoclinic HfO2 and CaHf 4 O 9 (Delamarre and Perez y Jorba, 1965). In HfO 2 -Y 2 O 3? the most extensively studied electrolyte amongst the HfO2 based systems, 7-8mol% Y 2 O 3 is required to fully stabilize the fluorite phase. The fluorite phase at 1500°C is stable for Y 2 O 3 additions up to about 50mol% (Spiridinov etal., 1969). Besson et al. (1966) and Schieltz et al. (1971) have studied the electrolytic behaviour of this system. The defect structure consists of a filled cation sublattice and anion vacancies. The maximum in the conductivity was observed at 8 mol% Y 2 O 3 . In the fluorite phase, the activation energy for conduction increases with increase in the dopant concentration. A maximum in the activation energy and minimum in the conductivity (1000 °C) have been reported at 33.3 mol% Y 2 O 3 . At this composition the existence of a compound Y2Hf2O7 was postulated (Caillet et al., 1967). Below this composition, the conductivity behaviour has been attributed to increasing anion vacancy ordering as the Y 2 O 3 content increased in the fluorite lattice (Schieltz et al., 1971). More recently Saly et al. (1989) have reported the conductivity of several rare earth doped (15 mol% Ln 2 O 3 ) - HfO2 single crystals and observed an order of magnitude higher conductivity for Sc 2 O 3 dopant compared with other rare earth oxides. The ionic conductivity of HfO 2 based materials is low compared with stabilized zirconia (Fig. 11-19) and the electrolytic conductivity regime is narrow (1 to 10 ~ 16 atm oxygen partial pressure at 1000°C) (Schieltz etal., 1971). Therefore

601

these materials offer no significant advantages over either zirconia or thoria based electrolytes. 11.4.1.4 Bismuth Oxide Based Materials Bi 2 O 3 exists in the stable monoclinic form (oc-phase) at room temperature. On heating the a-phase transforms to the fluorite-type 8-phase at around 730 °C. The monoclinic a-phase is a predominantly electronic conductor whereas the 8-phase is mainly an oxygen-ion conductor. The Arrhenius plot of the conductivity shows a large jump (about three orders of magnitude increase in the conductivity) around 730 °C during the heating cycle (Fig. 11-20). The oxygen-ion conductivity arises from the large vacancy concentration in the defect fluorite-type structure. It is the best oxygen ion conductor known with up to about two orders of magnitude higher conductivity than that of fully stabilized zirconia in the same temperature range (Fig. 11-20). However, the 5-phase is stable only in the narrow temperature range (730-825 °C) up to the melting point of bismuth oxide. On cooling, the 8-phase persists as a metastable phase and transforms to the tetragonal p-phase at about 650 °C or to the body centered cubic yphase at about 640 °C which in turn transfers to the a-phase below 640 °C (Cahen, 1980; Harwig, 1977; Takahashi and Iwahara, 1973; Verkerk, 1982). All the phase transformations may or may not occur at the temperatures given above depending on the cooling rate. Different stability regimes for both the P and the y-phases dependent on the cooling rates have been reported. Both p and y-phases have several orders of magnitude lower ionic conductivity than the 8-phase (Cahen, 1980; Harwig, 1977; Verkerk, 1982; Verkerk and Burggraaf, 1981). All the phase transformations

602

11 Ceramic Superionic Conductors

Figure 11-20. A comparison of the conductivity of some bismuth oxide and zirconia based electrolytes. 1 Bi 2 O 3 ; 2-(Bi 2 O 3 ) 0 8 (Er 2 O 3 ) 0 2 ; 3-(Bi 2 O 3 ) 0 . 75 (Y 2 O 3 ) 0 . 25 ; 4-(Bi 2 0 3 ) 0 . 715 (Dy 2 0 3 )o. 285 ; 5-(ZrO 2 ) 0 . 92 (Sc 2 O 3 ) 0>08 ; 6-(ZrO 2 ) 0 . 9 (Y 2 O 3 ) 0 . 1 .The data for Bi 2 O 3 electrolytes as per Table 11-5.

-5.0 10.5 12.0 Temperature in 10*-K

9.0

required to fully stabilize the fluorite-type phase at room temperature is 25-32 to 43 mol% Y 2 O 3 , 28.5 to 50mol% Dy 2 O 3 , 35 to 50mol% Gd 2 O 3 , 17.5 to 45 mol% Er 2 O 3 , 22-28 mol% WO 3 , 15-25 mol% Nb 2 O 5 , 18-25 mol% Ta 2 O 5 (Kruidhof et al., 1990; Takahashi and Iwahara, 1973; Takahashi et al., 1975; Takahashi et al., 1977; Verkerk etal., 1980; Verkerk and Burggraaf, 1981; Verkerk, 1982). The phase assemblage in Bi 2 O 3 -M 2 O 3 systems is quite complex and is dependent upon the prethermal history (for example

are accompanied by a large volume change. The high oxygen-ion conducting face centered cubic (f.c.c) 5-phase can be stabilized to much lower (and even room) temperatures by the addition of a number of other metal oxides such as Y 2 O 3 , Dy 2 O 3 , Er 2 O3,Nb 2 O 5 ,Ta 2 O 5 ,WO 3 ,andGd 2 O 3 . Verkerk and Burggraaf (1981) have discussed the effect of ionic radius of the dopant cation on the minimum amount of the dopant required to stabilize the cubic phase. This correlation is shown in Fig. 11-21. The amount of the stabilizer

Doped-Bi 2 0 3 OYb

Gd3-

3+

• 0.3

Dy3* O

o 0.2

15.0

13.5

/

o

y^

Figure 11-21. A correlation between the minimum amount of dopant (Dmin) required to stabilize the face centered cubic phase in Bi 2 O 3 and the dopant cation size, o - After Verkerk et al. (1981), • -more recent data for Y 2 O 3 .

o

\

X

\ o

0.1 0.097

0.099

0.101 0.103 Ionic radius in nm

0.105

0.107

603

11.4 Types of Ceramic Superionic Conductors

the cooling rate from the sintering temperature and subsequent heat treatments) of the specimens. Figure 11-22 summarizes the overall phase assemblage detected in various Bi 2 O 3 -M 2 O 3 systems. The cubic phase exists in the metastable form (at low temperatures) in compositions containing up to about 5-10 mol% lower stabilizer than that required to fully stabilize the cubic f.c.c phase. However, on extended annealing, the f.c.c phase slowly transforms to the hexagonal or the rhombohedral phase (e). This phase has been reported to have a much lower conductivity than the 5-phase. In the Bi 2 O 3 -Gd 2 O 3 system, Takahashi et al. (1975) reported that for Gd 2 O 3 compositions below 30 mol%, the fluorite phase was the high temperature phase which transformed to the tetragonal (for lower stabilizer content) or the rhombohedral (higher stabilizer content) phase at lower temperatures. In the system Bi 2 O 3 -Y 2 O 3 , Kruidhof et al. (1990) have reported that as-prepared compositions between 22 and 32.5 mol% Y 2 O 3 had a face centered cubic structure but on annealing at 650 °C a sluggish phase transformation took place from cubic to the hexagonal structure; the amount of the hexagonal phase decreases with increasing Y 2 O 3 content. At 31.8 mol% Y 2 O 3 only cubic and at 22 mol% Y 2 O 3 only the hexagonal phase existed. Somewhat similar behaviour was also observed in the Bi 2 O 3 -Dy 2 O 3 and Bi 2 O 3 -Er 2 O 3 systems (Kruidhof et al., 1988; Verkerk and Burggraaf, 1981). Watanabe and Kikuchi (1986) have reported that while cubic to hexagonal phase transformation is very sluggish, the reverse transformation from hexagonal to cubic phase is fast. Joshi et al. (1990) for 25 mol% Y 2 O 3 in Bi 2 O 3 also reported a slow decomposition of the 5-phase with time between 600 and 700 °C. These reports are contrary to the expectation of the phase

Low temp, range

High temp, range

600°-700°C M203 + 6

+(15-25)%

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M203 + 6

6

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(M203)m -(5-10)%

6 {metastable) or

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6

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5-10% 0

a

+ FeCl2 + 2Na). Many of the chemical corrosion, operational and fabrication problems associated with the sodium/sulfur battery are significantly reduced in the Zebra battery. This battery is well thought out and has the potential to replace the sodium/sulfur battery. 11.6.7 Miscellaneous Applications

Apart from the use of superionic conductors in applications discussed above these materials have been tried in several other devices such as timers, capacitors, coulometers, heating elements for furnaces and thermoelectric convertors. With the appropriate selection of electrodes, the charging characteristics of an electrode/ electrolyte interface and hence the capacitance can be changed. Such devices have high capacitance and can be used to store energy temporarily. The major drawback is their low decomposition voltage. The cells of the type, reversible electrode/electrolyte reversible electrode-blocking electrode have been suggested as timers. On application of a constant current, the material is transported from the right side of the cell to the left. Once the reversible electrode has been exhausted no further current can flow and the voltage rises sharply. By controlling the value of the constant

current and the amount of the reversible electrode on the right hand side of the cell, timers of duration ranging up to several months can be made. A coulometer works in a similar fashion to the timer except that the charge passed is determined by measuring the amount of the material transported through the cell from the Faraday law. Furnaces utilizing zirconia-based solid electrolyte as the heating elements and capable of operating in oxidizing environments up to 2000 °C are now commercially available. The alkali metal thermoelectric convertor or the sodium heat engine based on Na + beta-alumina electrolyte is under development (Prasad et al., 1983; Takahashi, 1988) for direct conversion of heat to electricity (efficiency around 20-25%). The thermoelectric convertor is a sodium concentration cell in which electric power is obtained from heat by generating different sodium vapour pressures on either side of the electrolyte.

11.7 Acknowledgements The author is thankful to Drs. K. Foger and M. J. Bannister for reviewing this manuscript.

11.8 References Abelard, P., Baumard, X F. (1982), Physical Rev. B 26, 1005-1017. Adham, K. EL, Hammou, A. (1983), in: Progress in Solid Electrolytes: Wheat, T. A., Ahmad, A., Kuriakose, A. K. (Eds.). Ottawa: Energy Mines and Resources, ERP/MSL 83-94 (TR), pp. 313345. Alcock, C. B. (1968), in: Electromotive Force Measurements in High Temperature Systems. London: The Institute of Mining and Metallurgy. Allpress, J. G., Rossell, H. X (1975), J. Solid State Chem. 15, 68-78. Ansell, R. O. (1986), / Mater. Sci. 21, 365-379. Archer, W. I., Armstrong, R. D. (1980), Electrochemistry 7, 157-202.

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Markin, T. L., Bones, R. X, Wheeler, V. J. (1967), Brit. Ceram. Soc. Proc. 8, 51-66. McCartney, M. L. (1987), /. Am. Ceram. Soc. 70, 54-58. McDonough, W. X, Flinn, D. R., Stern, K. H., Rice, R. W. (1978), /. Mater. Sci. 13, 2403-2412. McGeehin, P. (1981), /. Brit. Ceram. Soc. 80, 37-42. Mehrotra, A. K., Maiti, H. S., Subbarao, E. C. (1973), Mat. Res. Bull. 8, 899-908. Michaels, I N , Vayenas, C. G. (1984), J. Electrochem. Soc. 131, 2544-2550. Mitoff, S. P. (1966), Progr. in Ceram. Sci. 4, 217-264. Mizusaki, X, Fueki, K. (1982), Solid State Ionics 6, 85-91. Mobius, H. H., (1964), Z. Chem. 4, 81-94. Moseley, P. T., Tofield, B. C. (1987), in: Solid State Gas Sensors. Bristol: Adam Hilger. Munshi, M. Z. A., Nicholson, P. S. (1990), Solid State Ionics 42, 63-68. Nakamura, A., Wagner, X B. (1980), J. Electrochem. Soc. 127, 2325-2333. Nakamura, A., Wagner, X B. (1986), /. Electrochem. Soc. 133, 1542-1548. Nardella, N., Ho, D. V, Badwal, S. P. S. (1988), Mater. Sci. Forum 34-36, 237-241. Nasrallah, M. M., Douglas, D. L. (1974), J. Electrochem. Soc. 121, 255-262. Nernst, W (1899), Z. Elektrochem. 6, 41-43. Nettleship, I., Stevens, R. (1987), Int. J. High Tech. 3, 1-32. Nicholson, P. S. (1988), in: Proc. Solid State Ionic Devices, July 18-23, Singapore: Chowdari, B. V. R., Radhakrishna, S. (Eds.). Singapore: World Scientific, pp. 639-662. Nicholson, P. S., Nagai, M., Yamashita, K. (1985), Solid State Ionics 15, 317-326. Nowick, A. S., Wang, D. Y, Park, D. S., Griffith, X (1979), in: Fast Ion Transport in Solids: Vashishta, P., Mundy, X N., Shenoy, G. K. (Eds.). Amsterdam: Elsevier, pp. 673-679. Ohta, T., Harata, M., Imai, A. (1976), Mat. Res. Bull. 11, 1343-1350. Panlener, R. X, Blumenthal, R. N., Gamier, X E. (1975), / Phys. Chem. Solids. 36, 1213-1222. Patterson, X W. (1971), in: /. Electrochem. Soc. 118, 1033-1039. Patterson, X W. (1974), Electrical Conductivity in Ceramic and Glasses, Part B: Tallan, N. M. (Ed.). New York: Marcel Dekker Inc., pp. 453-558. Patterson, X W, Bogren, E. C , Rapp, R. A. (1967), /. Electrochem. Soc. 114, 752-758. Perez y Jorba, M. (1962), Ann. Chim. 7, 479-511. Poulsen, F. W. (1989), in: High Conductivity Solid Ionic Conductors, Recent Trends and Applications: Takahashi, T. (Ed.). Singapore: World Scientific, pp. 166-200. Powers, R. W, Mitoff, S. P. (1978), in: Solid Electrolytes, General Principles, Characterisation, Materials, Applications: Hagenmuller, P., van Gool, W (Eds.). New York: Academic Press, pp. 123144.

11.8 References

Prasad, S. E., Roy, R., El-Assal, K., Murthy, M. K. (1983), in: Progress in Solid Electrolytes: Wheat, T. A., Ahmad, A., Kuriakose, A. K. (Energy Mines and Resources) (Eds.). Ottawa: Erp/MSL 83-94 (TR), pp. 529-547. Rajendran, S., Drennan, X, Badwal, S. P. S. (1987), J. Mater. Sci. Lett. 6, 1431-1434. Ray, A. K., Subbarao, E. C. (1975), Mat. Res. Bull. 10, 583-590. Reiss, I., Braunshtein, D., Tannhauser, D. S. (1981), /. Electrochem. Soc. 64, 479-485. Rossell, H. J. (1981), in: Advances in Ceramics, Vol. 3, The Sci. and Tech. of Zirconia I. Heuer, A. H., Hobbs, L. W. (Eds.). Columbus: The Am. Ceram. Soc., pp. 47-63. Ruh, R., Garrett, H. I, Domagala, R. E, Patel, V. A. (1977), / Am. Ceram. Soc. 60, 399-403. Riihle, M., Claussen, N., Heuer, A. H. (1984), in: Advances in Ceramics, Vol. 12, The Sci. and Tech. of Zirconia II. Claussen, N., Riihle, M., Heuer, A. H. (Eds.). Columbus: The Am. Ceram. Soc, pp. 352370. Saly, V, Hartmanova, M., Glushkova, V. B. (1989), Solid State Ionics 36, 189-192. Scheetz, B. E., White, W. B. (1979), /. Am. Ceram. Soc. 62, 468-470. Schieltz, I D., Patterson, J. W, Wilder, D. R. (1971), /. Electrochem. Soc. 118, 1257-1261. Schmalzried, H. (1962), Z. Elektrochem. 66, 572-576. Schmalzried, H. (1963), Z. Phys. Chem. 38, 87-102. Schmalzried, H. (1977), Z. Physik. Neue Folge Bd. 105, 47-62. Scholtens, B. B., van Gool, W. (1978), in: Solid Electrolytes, General Principles, Characterization, Materials, Applications: Hagenmuller, P., van Gool, W. (Eds.). New York: Academic Press, pp. 463482. Schouler, E. I L. (1985), in: Solid State Protonic Conductors III: Goodenough, J. B., Jensen, X, Potier, A. (Eds.). Odense: Odense University Press, pp. 16-60. Scott, H. G. (1975), /. Mater. Sci. 10, 1527-1535. Seetharaman, S., Abraham, K. P. (1980), in: Solid Electrolytes and their Applications: Subbarao, E. C. (Ed.). New York: Plenum Press, pp. 127-163. Seiyama, T, Fueki, K., Shiokawa, X, Suzuki, S. (1983) (Eds.), in: Chemical Sensors, Analytical Chemistry Symp. Series, Vol. 17. Amsterdam: Elsevier. Seltzer, M. S., Jaffee, R. I. (1973) (Eds.), in: Defect and Transport in Oxides. New York: Plenum Press. Sequeira, C. A. C. (1985), in: Solid State Batteries, Sequeira, C. A. C , Hooper, A. (Eds.). Dordrecht: Martinus Nijhoff Publishers, pp. 219-240. Shores, D. A., Rapp, R. A. (1971), /. Electrochem. Soc. 118, 1107-1111. Shores, D. A., Rapp, R. A. (1972), J. Electrochem. Soc. 119, 300-305. Singhal, S. C. (1989), in: Proc. First Int. Symp. on Solid Oxide Fuel Cells. Pennington: The Electrochem. Soc.

631

Sluyters-Rehbach, M., Sluyters, X H. (1970), in: Sine Wave Methods in the Study of Electrode Processes, Electroanalytical Chemistry, Vol. 4: Bard, A. X (Ed.). New York: Marcel Dekker Inc., pp. 1-128. SOFC-Nagoya (1989), Proc, Int. Symp. on Solid Oxide Fuel Cells, November 13-14, Nagoya. Somiya, S., Yamamoto, N., Yanagida, H. (1988) (Eds.), in: Advances in Ceramics, Vol. 24 A, 24 B. Westerville: The Am. Ceram. Soc. Sorensen, O. T. (1981) (Ed.), Nonstoichiometric Oxides. New York: Academic Press. Spacil, H. S., Tedmon, Jr., C. S. (1969), J. Electrochem. Soc. 116, 1618-1626, 1627-1633. Spinolo, G., Chiodelli, G., Tamburini, U. A., Magistris, A. (1988), Solid State Ionics 28-30, 16021606. Spiridinov, F. M., Stepanov, V. A., Komissarova, L. N., Spitsyn, V. I. (1968), / Less-Common Metals i4t 435-443. Spiridinov, F. M., Komissarova, L. N., Kocharov, A. G., Spitsyn, V I. (1969), Russ, J. Inorg. Chem. 14, 1332-1335. Stafford, R. X, Rothman, S. X, Routbort, X L. (1989), Solid State Ionics 37, 67-72. Steele, B. C. H., Alcock, C. B. (1965), Trans. Metall. Soc. AIME233, 1359-1367. Steele, B. C. H. (1968), in: Electromotive Force Measurements in High Temperature Systems: Alcock, C. B. (Ed.). London: The Institute of Mining and Metallurgy, pp. 1-27. Steele, B. C. H., Shaw, R. W (1978), in: Solid Electrolytes, General Principles, Characterisation, Materials, Applications: Hagenmuller, P., van Gool, W. (Eds.). New York: Academic Press, pp. 483495. Steele, B. C. H. (1989), in: High Conductivity Solid Ionic Conductors, Recent Trends and Applications: Takahashi, T. (Ed.). Singapore: World Scientific, p. 402-446. Stevens, R., Binner, X G. P. (1984), /. Mater. Sci. 19, 695-715. Stevens, R. (1986), in: Zirconia and Zirconia Ceramics, Magnesium Electron Publication No. 113. Stoukides, M. (1988), Ind. Eng. Chem. Res. 27, 17451750. Stoukides, M., Vayenas, C. G. (1984), /. Electrochem. Soc. 131, 839-845. Strickler, D. W, Carlson, W. G. (1965), J. Amer. Ceram. Soc. 48, 286-289. Stubican, V S., Hellmann, X R. (1981), in: Advances in Ceramics, Vol. 3, The Sci. and Tech. of Zirconia I: Heuer, A. H., Hobbs, L. W (Eds.). Columbus: The Am. Ceram. Soc, pp. 25-36. Stubican, V. S., Ray, S. P. (1977), /. Am. Ceram. Soc. 60, 534-537. Stubican, V S., Hink, R. C , Ray, S. P. (1977), J. Am. Ceram. Soc. 61, 17-21. Subbarao, E. C. (1980) (Ed.), in: Solid Electrolytes and their Applications. New York: Plenum Press. Subbarao, E. C , Sutter, P. H. (1964), J. Phys. Chem. Solids 25, 148-150.

632

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Subbarao, E. C , Sutter, P. H., Hrizo, X (1965), /. Am. Ceram. Soc. 48, 443-446. Suzuki, Y, Takahashi, T., Nagae, N. (1981), Solid State Ionics 3/4,483-487. Swain, M. V. (1989), Materials Forum 13, 237-253. Takahashi, T. (1972), in: Physics of Solid Electrolytes, Vol. 2: Hladik, J. (Ed.). London: Academic Press, pp. 989-1049. Takahashi, T. (1988), in: Proc. Solid State Ionic Devices, July 18-23, Singapore: Chowdari, B. V. R., Radhakrishna, S. (Eds.). Singapore: World Scientific, pp. 95-103. Takahashi, T, Iwahara, H. (1973), /. Appl Electrochem. 3, 65-72. Takahashi, T., Esaka, X, Iwahara, H. (1975), /. Appl. Electrochem. 2, 197-202. Takahashi, T, Iwahara, H., Esaka, T. (1977), /. Electrochem. Soc. 124, 1563-1569. Takeuchi, T. (1986), in: Proc. 2. International Meeting on Chemical Sensors, July 7—10, Bordeaux: Aucouturier, X-L., Cauhape, X-S., Destriau, M., Hagenmuller, P., Lucat, C , Menil, R, Portier, X, Salardenne, X (Eds.). Bordeaux, pp. 69-78. Tallan, N. M. (1974), in: Electrical Conductivity in Ceramic and Glasses, Parts A and B. New York: Marcel Dekker Inc. Tanaka, X, Baumard, X R, Abelard, P. (1987), / Am. Ceram. Soc. 70, 637-643. Tannenberger, H., Schachner, H., Kovacs, P. (1966), Revue Energie Primaire 2, 19—26. Tare, V. B., Ramana Rao, A. V., Ramanarayanan, T. A. (1980), in: Solid Electrolytes and their Applications, Subbarao, E. C. (Ed.). New York: Plenum Press, pp. 165-199. Thornber, M. R., Bevan, D. X M., Summerville, E. (1970), J. Solid State Chem. 1, 545-553. Tien, T. Y, Subbarao, E. C. (1963), /. Chem. Phys. 39, 1041-1047. Tsai, Y X, Whitmore, D. H. (1982), Solid State Ionics 7, 129-139. Tuller, H. L., Nowick, A. S. (1975), /. Electrochem. Soc. 257, 255-259. van Dijk, T. (1981), Thesis, Twente University of Technology, Enschede, Netherlands. van Dijk, T., Helmholdt, R. B., Burggraaf, A. X (1980 a), Phys. Stat. Sol. (b) 101, 765-774. van Dijk, T, de Vries, K. X, Burggraaf, A. X (1980 b), Phys. Stat. Sol (a) 58, 115-125. van Dijk, M. P. (1985), Thesis, Twente University of Technology, Enschede, Netherlands. van Dijk, M. P., ter Maat, J . H . H , Roelofs, G., Bosch, H., van de Velde, G. M. H., Gelling, P. X, Burggraaf, A. X (1984), Mat. Res. Bull. 19, 11491156. van Gool, W. (1973), in: Fast Ion Transport in Solids. Amsterdam: North Holland Publishing Company. Van Handel, G. X, Blumenthal, R. N. (1974), /. Electrochem. Soc. 121, 1198-1202.

Vashishta, P., Mundy, J. N., Shenoy, G. K. (1979) (Eds.), in: Fast Ion Transport in Solids, Electrodes and Electrolytes. New York: North Holland. Vayenas, C. G., Bebelis, S., Neophytides, S., Yentekakis, I. V. (1989), Appl. Phys. A 49, 95-103. Verkerk, M. X (1982), Thesis, Twente University of Technology, Enschede, Netherlands. Verkerk, M. X, Burggraaf, A. X (1981), J. Electrochem. Soc. 128, 75-82. Verkerk, M. X, Keizer, K., Burggraaf, A. X (1980), /. Appl. Electrochem. 10, 81-90. Verkerk, M. X, Van de Valde, G. M. H., Burggraaf, A. X (1982), J. Phys. Chem. Solids. 43, 1129-1136. Vetter, K. X (1967), in: Electrochemical Kinetics, Theoretical and Experimental Aspects. New York: Academic Press. Virkar, A. V, Tennenhouse, G. X, Gordon, R. S. (1974), /. Am. Ceram. Soc. 57, 508. Vitter, G., Foster, P., Lahlou, M., Gutierrez Monreal, RX (1983), Solid State Ionics 9110, 12731276. Vlasov, A. N., Perfiliev, M. V. (1987), Solid State Ionics 25, 245-253. Wagner, C. (1933), Z. Phys. Chem. B21, 25-41. Wagner, C. (1957), in: Proc. Int. Committee Electrochem. Thermodyn. Kinetics (CITEC) 7, 361377. Wagner, C. (1975), Progr. Solid State Chem. 10, 3-16. Wang, Da Yu, Nowick, A. S. (1980), /. Solid State Chem. 35, 325-333. Wang, Da Yu, Park, D. S., Griffith, X, Nowick, A. S. (1981), Solid State Ionics 2, 95-105. Watanabe, A., Kikuchi, T. (1986), Solid State Ionics 21, 287-291. Weber, N., Kummer, X T. (1967), Proc. Annu. Power Sources Conf. 21, 37-39. Weppner, W, Schulz, H. (1988), in: Solid State Ionics - 87 Confr. Proc. Amsterdam: North Holland. Wheat, T. A., Ahmad, A., Kuriakose, A. K. (1983) (Eds.), in: Progress in Solid Electrolytes, Energy Mines and Resources: Wheat, T. A., Ahmad, A., Kuriahose, A. K. (Eds.). Ottawa: Erp/MSL 83-94 (TR). Whittingham, M.S., Huggins, R. A. (1971a), J Chem. Phys. 54, 414-416. Whittingham, M. S., Huggins, R. A. (1971 b), /. Electrochem. Soc. 118, 1-6. Whittingham, M.S., Huggins, R. A. (1972), NBS Special Publication 364, Solid State Chemistry, Proc. 5th Mater. Res. Symp., 139-154. Wiedersich, H., Geller, S. (1970), in: The Chemistry of Extended Defects in Non-metallic Solids: Eyring, L., O'Keefe, M. (Eds.). Amsterdam: North Holland, pp. 629-650. Wimmer, X M., Bidwell, L. R., Tallan, N. M. (1967), /. Am. Ceram. Soc. 50, 198-201. Wing-Kit, L., Nowick, A. S. (1986), Solid State Ionics 18/19, 989-993.

11.8 References

Williams, D. E., McGeehin, P. (1984), Electrochemistry 9, 246-290. Worrell, W. L. (1977), Solid Electrolytes: Geller, S. (Ed.). New York: Springer-Verlag, pp. 143-168. Worrell, W. L., Iskoe, J. L. (1973), in: Fast Ion Transport in Solids: Van Gool, W. (Ed.). Amsterdam: North Holland Publishing Company, pp. 513-521. Worrell, W. L., Liu, Q. G. (1986), US patent No. 4, 627, 892. Yamamoto, O., Takeda, Y, Kanno, R., Kohno, K., Kamiharai, T. (1989), J. Mater. Sci. Lett. 8, 198 — 200. Yeager, E., Salkind, A. J. (1972), in: Techniques of Electrochemistry, Vol. 1. New York: Wiley Interscience. Young, C. T. (1983), in: Progress in Solid Electrolytes, Energy Mines and Resources: Wheat, T. A., Ahmad, A., Kuriakose, A. K. (Eds.). Ottawa: Erp/MSL 8394 (TR), pp. 549-580. Youngblood, G. E., Gordon, R. S. (1978), Ceramurgia International 4, 93-98. Youngblood, G. E., Virkar, A. V, Cannon, W. R., Gordon, R. S. (1977), Am. Ceram. Bull. 56, 206210, 212. Yoshimura, M. (1988), Am. Ceram. Soc. Bull. 67, 1950-1955. Yuill, W. A., Cater, E. D. (1967), J. Phys. Chem. 71, 1436-1441. Zu-Xiang, L. (1989), in: High Conductivity Solid Ionic Conductors, Recent Trends and Applications: Takahashi, T. (Ed.). Singapore: World Scientific, pp. 223-241.

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General Reading Adham, K. EL, Hammou, A. (1983), Progress in Solid Electrolytes, Energy Mines and Resources: Wheat, T. A., Ahmad, A., Kuriakose, A. K. (Eds.). Ottawa: Erp/MSL 83-94 (TR), pp. 313-345. Bates, X, Farrington, G. C. (1981) (Eds.), in: Fast Ionic Transport in Solids. Amsterdam: North Holland. Chandra, S. (1981), Superionic Solids. Amsterdam: North Holland. Chowdari, B. V. R., Radhakrishna, S. (1988) (Eds.), in: Solid State Ionic Devices. Singapore: World Scientific. Green, D. X, Hannink, R. H. X, Swain, M. V. (1989), in: Transformation Toughening of Ceramics. Boca Raton: CRC Press Inc. Hagenmuller, P., van Gool, W. (1978) (Eds.), in: Solid Electrolytes, General Principles, Characterization, Materials, Applications. New York: Academic Press. Hladik, X (1972) (Ed.), in: Physics of Solid Electrolytes, Volumes 1 and 2. London: Academic Press. Macdonald, X R. (1987) (Ed.), in: Impedance Spectroscopy. New York: John Wiley & Sons. Subbarao, E. C. (1980) (Ed.), in: Solid Electrolytes and their Applications. New York: Plenum Press. Takahashi, T. (1989) (Ed.), in: High Conductivity Solid Ionic Conductors, Recent Trends and Applications. Singapore: World Scientific.

12 Ferroelectric Ceramics Kenji Uchino Materials Research Laboratory, Pennsylvania State University, University Park, PA, U.S.A.

List of Symbols and Abbreviations 12.1 General View of Ferroelectrics 12.1.1 Crystal Structure and Ferroelectricity 12.1.2 Origin of Spontaneous Polarization 12.1.3 Origin of Field Induced Strain 12.1.4 Electrooptic Effect 12.1.5 Example of a Ferroelectric 12.1.6 Applications of Ferroelectrics 12.2 High-Permittivity Dielectrics 12.2.1 Relaxor Ferroelectrics 12.2.2 Multilayered Capacitors (MLC) 12.3 Pyroelectric Devices 12.3.1 Temperature/Infrared-Light Sensors 12.3.2 Infrared Image Sensors 12.4 Piezoelectric Devices 12.4.1 Piezoelectric Materials 12.4.2 Piezoelectric Resonance 12.4.3 Piezoelectric Transformers 12.4.4 Piezoelectric Vibrators 12.4.5 Ultrasonic Transducers 12.4.6 Surface Acoustic Wave Devices 12.4.7 Piezoelectric Actuators 12.4.7.1 Deformable Mirrors 12.4.7.2 Impact Dot-Matrix Printers 12.4.7.3 Ultrasonic Motors 12.5 Electrooptic Devices 12.5.1 Transparent Electrooptic Ceramics 12.5.2 Bulk Electrooptic Devices 12.5.3 Waveguide Modulators 12.6 Positive Temperature Coefficient (PTC) Materials 12.6.1 The PTC Phenomenon 12.6.2 PTC Thermistors 12.6.3 Grain Boundary Layer Capacitors 12.7 Conclusions 12.8 Appendix 1: Tensor Representation of Physical Properties Materials Science and Technology Copyright © WILEY-VCH Verlag GmbH & Co KGaA. All rights reserved.

637 639 639 640 642 643 644 645 646 646 648 649 649 650 651 651 654 657 658 658 658 659 661 661 662 664 664 665 666 668 668 669 669 670 670

636

12.8.1 12.8.2 12.8.3 12.9 12.9.1 12.9.1.1 12.9.1.2 12.9.2 12.9.2.1 12.9.2.2 12.10

12 Ferroelectric Ceramics

Tensor Representation Crystal Symmetry and Tensor Form Reduction of the Tensor (Matrix Notation) Appendix 2: Phenomenology of Ferroelectricity Landau Theory of the Phase Transition Second-Order Transition First-Order Transition Phenomenology of Electrostriction Case I: X = 0 Case II: X 4= 0 References

670 671 673 674 674 674 674 675 675 676 676

List of Symbols and Abbreviations

List of Symbols and Abbreviations C

P

cd D E /A

fR F

9

I k k,k' L M n P P Ps Q QM

r s To

Tc u

U V

wdip Welas X

xs X a y

r

specific heat Curie-Weiss constant piezoelectric coefficient electric displacement electric field antiresonance frequency resonance frequency Landau free energy piezoelectric coefficient, secondary electrooptic coefficient light intensity electromechanical coupling factor force constants optical pathlength electrostrictive coefficient refractive index pyroelectric coefficient dielectric polarization spontaneous polarization electrostrictive coefficient mechanical quality factor primary electrooptic coefficient, voltage rise ratio of a piezoelectric transformer elastic compliance Curie-Weiss temperature Curie temperature displacement of an ion from the equilibrium position energy sound velocity energy of the dipole moment elastic energy of displacement strain spontaneous strain stress ionic polarizability Lorentz factor Dhase retardation relative permittivity vacuum permittivity dipole moment of the unit cell of a crystal barrier height of the Schottky barrier

637

638

D-TGS GBL MLC OA PLZT PMN PTC PTCR PVFD PZT rpm SAW VTR

12 Ferroelectric Ceramics

deuterated triglycine sulphate grain boundary layer multilayered capacitor office automation (Pb,La)(Zr,Ti)O 3 lead magnesium niobate positive temperature coefficient positive temperature coefficient of resistivity polyvinylidene fluoride lead zirconate titanate revolutions per minute surface acoustic wave video tape recorder

12.1 General View of Ferroelectrics

12,1 General View of Ferroelectrics 12.1.1 Crystal Structure and Ferroelectricity

In so-called dielectric materials, the constituent atoms are considered to be ionized to a certain degree and are either positively or negatively charged. In such ionic crystals, when an electric field is applied, cations are attracted to the cathode and anions to the anode due to electrostatic interaction. The electron clouds also deform, causing electric dipoles. This phenomenon is called the electric polarization of the dielectrics, and the polarization is expressed quantitatively as the sum of the electric dipoles per unit volume (C/m2). Figure 12-1 shows schematically the origin of the electric polarization. There are three kinds; electron, ion and dipole reorientation-related polarizations. Compared with vacuum capacitors, dielectric capacitors can store more electric charge due to the dielectric polarization P as shown in Fig. 12-2. The physical quantity corresponding to the stored electric charge per unit area is called the electric displacement Z>, and is related to the electric field by the following expression: (12-1)

= 80E+P=8 80

639

Here, s0 is the vacuum permittivity (= 8.854 x 10" 12 F/m), £ is the material's relative permittivity (also simply called permittivity or dielectric constant, and in general it is a tensor). Depending on the crystal structure, in some crystal lattices, the centers of the positive and negative charges do not coincide even without the application of external electric field. In this case, it is said that there exists spontaneous polarization in the crystal, and, especially when the polarization of the dielectric can be altered by an electric field, it is called ferroelectric. Not every dielectric can be a ferroelectric. Crystals can be classified into 32 point groups according to their crystallographic symmetry, and these point groups can be divided largely into two classes, one with a center of symmetry and the other without. There are 21 point groups which do not have a center of symmetry. In crystals belonging to 20 of these point groups [except for the point group (432)], positive and negative charges appear on surfaces when stresses are applied. These materials are known as piezoelectrics. Pyroelectricity is the phenomenon in which, because of the temperature dependence of the spontaneous polarization, as the temperature of the crystal is changed, electric charges cor-

Electronic polarization
3*

D2d

(21) Polar (pyro) (10) a

10

6mm

6

4mm

4

Qt,

C

C

C

6

4v

Ar

Piezoelectric crystals are those in the area enclosed by the thick line.

C

3v

3 C

3

2mm C

2v

m

C

l

641

12.1 General View of Ferroelectrics

Figure 12-3. Concept of the local field. Eloc is given by

4neorf

This is the driving force of the ion shift. Here y is called the Lorentz factor. For an isotropic and a cubic system, it is known that y = 1 (Kittel, 1966). e0 is the permittivity in vacuum and is equal to 8.854 x 10" 1 2 F/m. If the ionic polarizability of ion A is a, then the dipole moment of the unit cell of this crystal is:

trics, k! plays an important role in determining the magnitude of the dipole moment. By rewriting Eq. (12-6) using: P = Nqu (q is the electric charge) (12-7) Combining with Eq. (12-5), the total energy can be expressed as follows (see Fig. 12-4):

(12-3)

= [ay/(3fio)]P

The energy of this dipole moment (dipoledipole coupling) is c

2

2

Wdip = - /i • £'° = - [a y /{9 e )] P

2

(12-4)

Per unit volume, it is: WW = N w dip = -[Na

y2/(9 s2)] P2

(12-5)

On the other hand, when the A ions are displaced from their nonpolar equilibrium positions, the elastic energy also increases. If the displacement is u, and the force constants k and k\ then the increase of the elastic energy per unit volume can be expressed as: (12-6) Here, k' (> 0) is the higher-order force constant. It should be noted that in pyroelec-

(12-8) :

Nay 9s2

k!

4N33q v*

From this, one can see that if the coefficient of the harmonic term of the elastic energy is equal or greater than the coefficient of the dipole-dipole coupling, then P = 0, i.e., the A ions are stable and remain at their non-polar equilibrium positions. Otherwise, a shift from the equilibrium position {P2 = [2Nay2/(982)-k/(Nq2)]/[kf/(N3qAn is stable. In the perovskite-type crystal structure (as in barium titanate) as described in the next section, it is thought that because of the occurrence of a larger Lorentz factor y ( « 10) (Kinase et al., 1969) than found for other crystal structures, spontaneous polarization can occur more easily.

642

12 Ferroelectric Ceramics

(a)

Dipole interaction

two types of strain (defined by the ratio AL/L: the amount of deformation with respect to the original length) that may be induced by an electric field depending on the nature of the interaction "springs" between the ions which is, in turn, determined by the crystal structure (Uchino et al., 1983). As shown in Fig. 12-5 a, in crystals where there is no centrosymmetry, strain, x, is generated in proportion to the electric field E. This is the converse piezoelectric effect, and the tensor quantity, d, defined by the relationship x = 6E

Elastic energy

(c)

\y Figure 12-4. Energy explanation of the origin of spontaneous polarization. (a) Dipole interaction Wiip =

-[Nocy2/(9e20)]P2

(b) Elastic energy W

_ e l a s

p2

~

(c) Total energy

12.1.3 Origin of Field Induced Strain With the application of an electric field, the dielectric material inevitably induces strain or crystal deformation. There are

(12-9)

is referred to as the piezoelectric coefficient. On the other hand, in centrosymmetric crystals, as shown in Fig. 12-5 b, the expansion and contraction of the "spring" are such that the net response is nearly zero. However, the anharmonic nature of the "spring" motion will still bring about a small induced strain that is proportional to the square of the electric field E. This is referred to as the electrostriction effect which is expressed in terms of the strain, x, the applied electric field, E, and the electrostriction coefficient, M, as:

x = ME2

(12-10)

The system pictured in Fig. 12-5 a also possesses a spontaneous bias of electrical charge, or a spontaneous polarization. When a large reverse bias electric field is applied to a crystal that has a spontaneous polarization in a particular polar direction, a transition "phase" is formed which is another stable crystal state in which the relative positions of the ions are reversed (in terms of an untwinned single crystal, this is equivalent to rotating the crystal 180° about an axis perpendicular to its polar axis). This transition, referred to as polarization reversal, also causes a remarkable change in strain. This particular class of

643

12.1 General View of Ferroelectrics x=(6 2 -6 1 )/a 0 =dE

Ion pair potential energy

Ion pair potential energy

\\

// /

\

(a) Piezoelectric strain

\ \ \v

/

^

/

(b) Electrostriction

Figure 12-5. Diagrammatic explanation of the origins of piezoelectric strain (a) and electrostriction (b).

substances are referred to as ferroelectrics, as mentioned in Sec. 12.1.1. Generally, what is actually observed as a field-induced strain, is a complicated combination of the three basic effects just described. 12.1.4 Electrooptic Effect Since light is an alternating electromagnetic wave with electric and magnetic field directions crossing each other, it induces electric polarization in a dielectric crystal and the light itself is influenced by the crystal. The alternating frequency of the light is so high ( ^ 1 0 1 5 H z ) that only the electronic polarization should follow the field change, and the relative permittivity of the crystal is small, not exceeding 10. The permittivity 8 at this high frequency is related to the refractive index n by the following equation: e=n

(12-11)

When an external electric field is applied to the crystal, ion shift is induced, deforming the shape of the electron cloud, and consequently the refractive index is changed. This phenomenon is called the electrooptic effect. Generally, refractive indices are symmetrical 2-R tensor quantities and represented by using a refractive indicatrix (Eq. 12-12), where n^,n2 and n3 are principal refractive indices. _

n\

+

£L + _

n\

=

i

(12-12)

n\

With the application of an electric field, the change in refractive index is given by an expansion expression:

(12-13)

644

12 Ferroelectric Ceramics

Here rijk is a primary electrooptic coefficient {PockeVs effect) and gijkl is a secondary coefficient (Kerr effect). Considering a paraelectric phase of a perovskite crystal (m3m) as an example, the Kerr coefficients are represented in the following matrix: 011

012

012

012

011

012

012

012

011

0 0 0

0 0 0

0 0 0

0 0 0 044

0 0

0 0 0 0 044

0 0 0 0 0

0

044

(12-16) This is the principle of a light shutter/ valve, and the voltage required for the first intensity maximum (i.e., Fy = n) is essential and called the half-wavelength voltage.

Then, the refractive indicatrix under the electric field applied along z-direction can be expressed as: 2

2

x +y n [l~(n2/2)g12E2] 2

2i2

= 1

d is the electrode gap and L is the optical path length (see Fig. 12-6). Putting a crystal between crossed polarizers arranged at the 45° direction with respect to z-axis, the output light intensity can be modulated as a function of applied voltage in the following way:

(12-14)

When light is transmitted along the ^-direction, the phase retardation Fy between an ordinary and an extraordinary light is given by: (12-15)

12.1.5 Example of a Ferroelectric A typical ceramic ferroelectric is barium titanate, which is used here as an example to illustrate some properties of the ferroelectrics. As shown in Fig. 12-7, BaTiO 3 has a perovskite crystal structure. (See also Chap. 1, Sees. 1.3.3 and 1.6.2 of this Volume for a more complete description of the crystal structures of perovskites.) In the high-temperature paraelectric phase (nonpolar phase) there is no spontaneous polarization (the symmetry is O h — m3m). Below the transition temperature T c called the

Unpolarized light

Polarizer Crystal

Polarizer

Figure 12-6. Optical phase retardation through an electrooptic crystal. Notice the crossed polarizer configuration.

645

12.1 General View of Ferroelectrics

(a) Ba2

T>TC 4+

• Ti

T To, the unique solution Ps = 0 is obtained. For T < TQ the minimum of the Landau free energy is obtained at: >C)

(A 28)

The phase transition occurs at Tc = To and the polarization goes continuously to zero at this temperature; this is called a secondorder transition. Relative permittivity e is calculated as: 1/8 = so/(dP/dE) = 80 (a + 3 p P2)

(A 29)

Then, £

=

(C/(T- T0) \C/[2(T0-T)]

(T > To) (To < T)

(A 30)

Figure 12-A1 shows the variations of Ps and 8 with temperature. It is notable that the permittivity becomes infinite at the transition temperature. Triglycine sulphate is an example exhibiting the second-order transition. 12.9.1.2 First-Order Transition

When /? is negative in Eq. (A 24) and y is taken positive, the transition becomes first order. The equilibrium condition for E = 0 (A 31) leads to either Ps = 0 or (A 32).

(T-To).

(A31)

l(2y) (A 32)

675

12.9 Appendix 2: Phenomenology of Ferroelectricity

1i 1 i i

\

j /

Spontaneous ^ v polarization Ps \J\

I il

1 I \ \

i

\

Permittivity t

/

y

Spontaneous polarization Ps

/ /

;

Permittivity e

Inverse permittivity l/e

Inverse permittivity l/e , —- *"" TQ

Temperature

TQ

(Curie Temp.)

Temperature

(Curie Temp.)

Figure 12-A1. Second-order transition in a ferroelectric.

Figure 12-A 2. First-order transition in a ferroelectric.

The transition temperature 7^ is obtained from the condition that the free energies of the paraelectric and ferroelectric phases are equal: i.e., F = 0, or:

the elastic compliance and the electrostrictive coefficient. Note that the piezoelectric coupling term PX is omitted and the electrostrictive coupling term P2 X is introduced when the paraelectric phase has centrosymmetry (non-piezoelectric). This leads toEq.(A36)and(A37).

(A 33) Therefore:

E = (dGJdP) = aP + pP3 + yP5 -2QPX

(A 34)

16(

(A36) 2

x= - {dGJdX) = s i + QP .

Note that the Curie Temperature Tc is slightly higher than the Curie-Weiss temperature T09 and that the discrete jump of the Ps appears at Tc. Also, the permittivity exhibits a finite maximum at Tc for a first-order transition (Fig. 12-A 2). Barium titanate is a good example.

12.9.2.1 CaseI:J*T=0 When an external stress is zero, the following equations are derived: (A38) x = QP2

(A39) 2

12.9.2 Phenomenology of Electrostriction Let us assume that the elastic Gibbs energy should be expanded in a one-dimensional form: G±(P,X, T) = |aP 2 + y 2

2

-\sX -QP X,

\

[a = (T-T0)/(e0Q]

P, X, T are polarization, stress and temperature, respectively, and s and Q are called

(A37)

l/e o e = a + 3/3P + 5yP*

(A40)

If the external electric field is equal to zero (E = 0), two different states are derived; P = 0 and P2 = {^Jp2-4ay - P)/(2y). (I) Paraelectric phase: Ps = 0 or P = eosE (under small E) Permittivity: e = C/(T - To) (Curie-Weiss law)

(A41)

676

12 Ferroelectric Ceramics

Electrostriction: Q8282E2

X=

(A42)

(8T0/6p) = (8Tc/8p) = - 2 Q s0 C

(II) Ferroelectric phase:

Ps2 = (yJP2 — 4ay-

2s08QPsE+Qs2e2E2

(A43)

Spontaneous strain:

12.10 References (A 44)

Piezoelectric constant: (A 45)

d = 2sosQPs

Piezoelectricity is equivalent to the electrostrictive phenomenon biased by the spontaneous polarization. Temperature dependence of the spontaneous strain and the piezoelectric constant is plotted in Fig. 12-A3.

Piezoelectric constant d Spontaneous

ti

T c Temperature (Curie Temp.)

Figure 12-A 3. Temperature dependence of spontaneous strain and piezoelectric constant.

12.9.2.2 Case II: X * 0 When a hydrostatic pressure p (X = — p) is applied, the inverse permittivity is changed in proportion to p: l/808 =

(A48)

In general, the ferroelectric Curie temperature is decreased with increasing hydrostatic pressure.

(under small E) +

Therefore, the pressure dependence of the Curie-Weiss temperature To or the transition temperature Tc is derived as follows:

Akiyama, Y. (1986), Ultrasonic Motors/Actuators. Tokyo: Triceps. Andrich, E. (1965-66), Electr. Appl. 26, 123. Bhalla, A. S., Newnham, R. E., Cross, L. E., Schulze, W. A., Dongherty, I P., Smith, W. A. (1981), Ferroelectrics 33, 139. Cross, L. E., Jang, S. I , Newnham, R. E., Nomura, S., Uchino, K. (1980), Ferroelectrics 23, 187. Furuta, K., Uchino, K. (1986), Advanced Ceram. Mater. 1, 61. Heywang, W. (1964), /. Am. Cer am. Soc. 47, 484. Jaffe, B., Roth, R. S., Marzullo, S. (1955), /. Res. Nat. Bur. Stds. 55, 239. Kaminow, I. P. (1975), Trans. IEEE, M.T.T. 23, 57. Kanzig, W. (1951), Helv. Phys. Ada 24, 175. Kawai, H. (1969), Jpn. J. Appl. Phys. 8, 975. Kinase, W, Uemura, Y, Kikuchi, M. (1969), /. Phys. Chem. Solids 30, 441. Kittel, C. (1966), Introduction to Solid State Physics. New York: John Wiley & Sons, Inc. Klicker, K. A., Biggers, X V., Newnham, R. E. (1981), J. Amer. Ceram. Soc. 64, 5. Krause, H. B., Cowley, J. M., Wheatley, J. (1979), Acta Cryst. A 35, 1015. Kumada, A. (1985), Jpn. J Appl. Phys. 24, Suppl. 24-2, 739. Kumada, A., Kitta, K., Kato, K., Komata, T. (1977), Proc. Ferroelectric Mater. & Appl. -2, p. 205. Nikkei Mechanical (1983), Feb. 28 Ed., p. 44. Ohmura, K., Murai, Y, Uchino, K., Giniewitcz, J. (1989), Interaction. Display Research Confer., Proc, IEEE, p. 138. Ota, T., Uchikawa, T., Mizutani, T. (1985), Jpn. J. Appl. Phys. 24, Suppl. 24-3, 193. Rolov, B. N. (1963), Fiz. Tverdogo Tela 6, 2128. Rosen, C. A. (1957), Proc. Electronic Component Symp., p. 205. Sato, T., Ichikawa, H., Ikeda, O., Nomura, S., Uchino, K. (1982), Appl. Optics 21, 3669.

(Ferroelectric) 5yP* + 2Qp (T -T0 + 2Qs0Cp)/(80 C) (Paraelectric)

(A46) (A47)

12.10 References

Shibata, K., Takeuchi, K., Tanaka, T., Yokoo, S., Nakano, S., Kuwano, Y (1985), Jpn. J Appl. Phys. 24, suppl. 24-3, 181. Skanavi, G. I., Ksendzov, I. M., Trigubenko, V. A., Prokhvatilov, V. G. (1958), Soviet Phys. - JETP 6, 250. Smolensky, G. A., Isupov, V. A., Agranovskaya, A. I., Popov, S. N. (1961), Sov. Phys. - Solid State 2, 2584. Taylor, R. G. R, Boot, H. A. H. (1973), Contemporary Phys. 14, 55. Uchino, K. (1986), Bull. Amer. Ceram. Soc. 65, 647. Uchino, K., Cross, L. E., Newnham, R. E., Nomura, S. (1980), /. Phase Transition 1, 333. Uchino, K., Kuwata, X, Nomura, S., Cross, L. E., Newnham, R. E. (1981), Jpn. J. Appl. Phys. 20, Suppl. 20-4, 171. Uchino, K., Nomura, S. (1983), Oyo Butsuri 52, 575. Warner, D. J., Pedder, D. X, Moody, I. S., Burrage, X (1981), Ferroelectrics 33, 249. Yano, T., Fukui, L, Sato, E., Inui, O., Miyazaki, Y (1984), Electr. & Commun. Soc, Proc. 1-156.

677

General Reading Herbert, X M. (1982), Ferroelectric Transducers and Sensors. New York: Gordon and Breach. Jaffe, B., Cook, W. R., Jaffe, H. (1971), Piezoelectric Ceramics. New York: Academic Press. Jona, K, Shirane, G. (1962), Ferroelectric Crystals. Oxford: Pergamon Press. Levinson, L. M. (1988), Electronic Ceramics. New York: Dekker. Nowotny, X (1992), Electronic Ceramic Materials. Brookfield: TransTech Publ. Nye, X F. (1969), Physical Properties of Crystals. Oxford: Oxford University Press. Smolenskii, G. A. (1984), Ferroelectrics and Related Materials. New York: Gordon and Breach. Uchino, K. (1986), Piezoelectric/Electrostrictive Actuators. Tokyo: Morikita PubL Uchino, K. (1991), Piezoelectric Actuators - Problem Solving. Tokyo: Morikita Publ.

13 Ferrimagnetic Ceramics Bhaskar B. Ghate AT&T Bell Laboratories, Mesquite, TX, U.S.A. Alex Goldman Ferrite Technology Worldwide, Pittsburgh, PA, U.S.A.

List of Symbols and Abbreviations 13.1 Introduction 13.2 Historical 13.3 Basic Concepts 13.3.1 Atomic Magnetic Moments 13.3.2 Ferrimagnetism 13.3.3 Saturation Magnetization and Curie Temperature 13.3.4 Domains and Bloch Walls 13.3.5 The Hysteresis (B-H) Loop 13.4 Ferrite Crystal Structures 13.4.1 The Spinel Structure 13.4.2 The Hexagonal Ferrite Structure 13.4.3 The Garnet Structure 13.5 Intrinsic and Extrinsic Properties 13.5.1 Magnetization of Zn-Substituted MnZn Ferrite 13.5.2 Magnetic Anisotropy 13.5.3 Magnetostriction 13.5.4 Types of Hysteresis Loops 13.6 Ferrite Processing 13.6.1 Introduction 13.6.2 Powder Preparation 13.6.2.1 Conventional Processing 13.6.2.2 Nonconventional Processing 13.6.2.3 Calcining 13.6.2.4 Milling 13.6.2.5 Organic Binders and Additives 13.6.2.6 Spray Drying 13.6.3 Challenges in Pressing 13.6.4 Sintering 13.6.4.1 Ferrite Kilns 13.6.4.2 Sintering Cycles 13.6.4.3 Fast Firing Materials Science and Technology Copyright © WILEY-VCH Verlag GmbH & Co KGaA. All rights reserved.

681 683 684 684 684 685 687 687 688 689 690 691 691 692 693 693 694 695 696 696 696 696 700 700 701 701 702 702 702 703 704 706

680

13.6.5 13.6.6 13.7 13.7.1 13.7.2 13.7.3 13.8 13.9 13.10 13.11 13.12

13 Ferrimagnetic Ceramics

Vacuum Sintering, Hot Pressing, and Hot Isostatic Pressing Machining, Lapping, and Tumbling Case Studies High Permeability Ferrites Ferrites for High Frequency Power Supplies Ferrites for Recording Heads Hard Ferrites Microstmcture and Grain Boundary Chemistry Recent Developments Future Prospects References

707 709 711 711 717 720 722 723 725 725 726

List of Symbols and Abbreviations

681

List of Symbols and Abbreviations a A, B b B Bm BT £ s , Bsat Bmax d DCT Ea / H Hc k K K09Ki9K2

atmosphere parameter ion sublattices constant magnitude of magnetic induction or flux density magnitude of peak induction or flux density magnitude of remanent magnetization magnitude of saturation magnetization magnitude of maximum usable flux density density; minimum dimension normal to flux direction critical diameter anisotropy energy frequency magnitude of magnetic field strength magnitude of coercive field proportionality constant proportionality constant magnetocrystalline anisotropy constants referring to the zero, first, a n d second orders of the E a series L inductance m, n exponents M molecular weight MA,MB saturation moments of A, B site ions Ms saturation magnetization N Avogadro or Loschmidt number nB number of Bohr magnetons Pe power loss due t o eddy currents Ph hysteresis loss PO2 equilibrium oxygen pressure Ptot total power loss due to eddy currents Q quality factor R resistance Rp high core loss resistivity r oct>rtet radius of octahedral, tetrahedral sites T absolute temperature Tc Curie temperature T o (A), To (B) temperatures at which the S M P occurs for two concentrations (A a n d B) of F e 2 + ions x, y stoichiometric variables alJa2,a3 y d X

direction cosines of the ion moment relative to the three crystal directions stoichiometric variable loss angle magnetostriction coefficient

682

II', II"

,A

13 Ferrimagnetic Ceramics

saturation magnetostriction coefficient magnetostriction coefficients in the cube-edge and cube-diagonal directions permeability of a material real and imaginary (loss) components of permeability Bohr magneton initial, maximum permeability parallel permeability

/*0

aosoiuie permeaoiiiiy 01 iree space

Q

electrical resistivity

AC AES E, EP, Q EMI ESCA HDTV HIP HPF HRTEM MIG MOSFET OD PVA SEM SIMS SMD SMPS SMP SMT TEM VCR VHS YIG

alternating current Auger electron spectroscopy different shapes of ferrite cores electromagnetic interference electron spectroscopy for chemical analysis high-definition television hot isostatic press hot pressed ferrite high-resolution transmission electron microscopy metal-in-gap metal-oxide semiconductor field-effect transistor outside diameter polyvinyl alcohol scanning electron microscopy secondary ion mass spectrometry surface mount device switched mode power supply secondary maximum in permeability surface mount technology transmission electron microscopy video cassette recorder video home system yttrium - iron - garnet

683

13.1 Introduction

13.1 Introduction Oxide ceramics which exhibit ferrimagnetic behavior play an important role in the electronics industry and are commonly known as ferrites. Today's technology of high frequency recording, power supplies, telecommunications, television and entertainment electronics would have been very different were it not for the many useful properties of ferrites. Ferrites are the mixed metal oxides containing iron oxide as their main component. There are three important classes of commercial ferrites, each one having a specific crystal structure: (1) Soft ferrites with the cubic spinel structure such as NiZn-, MnZn-, and MgMnZn ferrites; (2) soft ferrites with the garnet structure such as the microwave ferrites, for example, yttrium iron garnets; and (3) hard ferrites with the magnetoplumbite (hexagonal) structure such as Ba and Sr hexaferrites.

Like ferromagnetic materials, ferrimagnetic ceramics exhibit spontaneous magnetization in the absence of an external field, consist of self saturated domains, and show the characteristic hysteresis behavior (Cullity, 1972 a; Smit and Wijn, 1959 b; Heck, 1974 b). The major difference between these two classes of materials, one primarily metals and the other ceramics, is that the resistivity of ferrites, depending on composition, is at least six to twelve orders of magnitude higher than that of ferromagnetic materials such as permalloys and silicon irons. This has given ferrites a distinct advantage as magnetic materials of choice in high frequency applications, although their saturation magnetization is approximately one fifth to one eighth that of silicon irons (Table 13-1). In addition, the crystal structures of ferrites are tolerant to numerous variations in their chemical compositions, giving the technologist access to a wide range of properties.

Table 13-1. Saturation flux density Bs, resistivity Q and Curie temperature Tc for several magnetic materials'1. Material

Iron (100% Fe) Silicon-Iron (4% Si) Cobalt (99.95% Co) Nickel (99.6% Ni) FeO • Fe 2 O 3 MnO • Fe 2 O 3 NiO • Fe 2 O 3 CuO • Fe 2 O 3 MgO • Fe 2 O 3 MnZn Ferrite NiZn Ferrite MgMn Ferrite MgZn Ferrite Zn Ferrite BaO-6Fe 2 O 3 5Fe 2 O 3 -3Y 2 O 3 (YIG)

Q

(T)

(Ocm)

(°Q

2.158 2.00 1.9 0.608 0.60 0.52 0.35 0.17 0.14 0.4-0.63 0.3-0.4 0.06-0.22 0.24-0.27 0 0.41 0.17

9.6 xlO" 6 60xl0"6 6.3 x l 0 ~ 6 8.7xlO~ 6 4xlO~ 3 104 8xl05 105 107 0.1-10 106 10 4 -10 6 10 7 -10 8 (4.5-8) xlO 3 10 4 -10 5 10 10 -10 12

770 730 1121 358 563-590 295-303 575-597 410-490 325-440 90-300 100-500 120-350 150-160 — 450 275

a Data from various sources including Heck (1974 b), Landolt-Bornstein (1970). The high value of Bs for MnZn ferrites is quoted from Kugimiya and Hirota (1989).

684

13 Ferrimagnetic Ceramics

Ceramic processing techniques allow the economic fabrication of devices in various shapes and sizes. Depending on their coercivity (Hc), ferrites are said to be either soft (Hc< 10 A/ cm) or hard (Hc > 100 A/cm) (for an explanation of Hc refer to Sec. 13.3.5). Soft ferrites may be subdivided further into two categories, one suitable for nonmicrowave applications (f< 100 MHz), and the other suitable for microwave applications (/MOOMHz). In this chapter, we will focus primarily on soft ferrites used in devices typically operating in the frequency range of 4 kHz (voice frequency) to 50 MHz. A few basic concepts necessary to understand the behavior of magnetic materials and their applications will be described, followed by an examination of the relation between composition, processing and microstructure, and resulting properties of ferrites. We will then elaborate on processing of three major product families of the technologically important MnZn spinel ferrites. The reader is also referred to Chap. 8 by Guillot (Magnetic Properties of Spinel Ferrite), Chap. 14 by Boll (Soft Magnetic Materials and Alloys), and Chap. 15 by Buschow (Permanent Magnet Materials) in Vol. 3 B of this Series. They cover the basic physics of ferro- and ferrimagnetism and materials science of garnets in particular, and some aspects of hexaferrite magnetic ceramics.

13.2 Historical Ferrites came into prominence at the end of the Second World War. The early work on ferrimagnetic materials was done in Japan by Kato and Takei (1933), and Kawai (1934), and in the Netherlands by Snoek (1936). It was Snoek and his coworker, Six, who realized that the most

important property of an inductor core material is not tan £g, is exceeded. As shown in Fig. 14-10, the hot electrons can collide with valence band electrons to impact ionize them into the conduction band. More important for the conduction process is the positively charged hole created in the valence band. The hole is strongly attracted to the electrons trapped at the boundary, and rapidly moves there. This process reduces the net trapped charge which reduces the potential barrier. The value of B decreases until the

Figure 14-10. Hole creation near a grain boundary. This energy diagram schematically illustrates the mechanism of impact ionization by hot electrons. Most electrons crossing the potential barrier thermalize quickly by emission of optical phonons; these are shown as e th . A few electrons escape this process and become "hot", or high energy. When their kinetic energy becomes larger than the bandgap, they can lose energy by impact ionizing electrons from the valance band. The remaining positively charged hole moves rapidly to the electrons trapped at the boundary, and reduces the net charge there (from Pike et al., 1985).

746

14 Semiconducting Polycrystalline Ceramics

boundary can capture enough additional electron current to equal the hole current, and thus establish a new steady state condition. The change of B with applied voltage, with and without the hole mechanism, has been calculated for typical ZnO parameters and is shown in Fig. 14-11. Since by Eq. (14-8) the current density is exponentially dependent on ^ B , the increase of nonlinearity with the onset of the hole mechanism is apparent. A direct confirmation that holes are indeed created in the highly nonlinear conduction region has been accomplished by measurement of characteristic energy, bandgap photons created by the recombination of the holes with the thermalized electrons, eth (Pike et al., 1985). Another manifestation of the presence of holes is the so called negative capacitance discussed in the next section. The unusual steady state conduction behavior described above was due to changes in applied voltage. If the semiconducting ceramic is also ferroelectric, then another unusual conduction phenomenon occurs due to changes in temperature. Again the key parameter is the barrier height, B. Equation (14-1) shows that the barrier height is inversely proportional to the rela-

0.6

(U-

0.2-• Effect of minority carriers produced by impact ionization

2 3 Voltage in V

tive permittivity, s. Above the Curie temperature of a ferroelectric £ decreases substantially with increasing temperature according to the Curie-Weiss law. This causes 4>B to increase, and by Eq. (14-8) the conductivity decreases exponentially (Heywang, 1971; Mader et al., 1984). An example of the temperature dependence of resistivity is given in Fig. 14-12 for BaTiO 3 and a series of related compounds containing Sr or Pb (Andrich, 1969). This effect has been widely utilized to produce "positive temperature coefficient" (PTC) resistors for temperature sensors (thermistors) and selfcontrolled heating elements (Hill and Tuller, 1986). For the latter applications the PTC element is placed in series with the heater. Regulation is achieved by Joule heating within the element; an increase in current raises the temperature and the resistance which tends to reduce the current again. 14.3.3 Harmonic Response

When a ceramic grain boundary with an electrostatic potential barrier formed by trapped carriers is subjected to a harmonic voltage in addition to any steady state Figure 14-11. Effect of hole generation on barrier height. This graph plots calculated curves of barrier height versus voltage for a bicrystal with grain boundary trap states all at one energy. The solid curve considers the effect of majority carriers alone; cj)B decreases slowly towards zero above five volts. When the effect of impact ionization above the bandgap energy threshold is added, the dashed curve is generated; <j)B decreases more rapidly with applied voltage which yields a much higher nonlinearity in the current-voltage relationship (from Pike et al., 1985).

14.3 Electrostatic Barriers and Transport Properties

747

io 7 y=o.7.

o

_

C3 I O 3

IO1

10"

-100

100 200 TEMPERATURE (°C)

300

400

Figure 14-12. Resistivity versus temperature for polycrystalline, ferroelectric semiconductors. These are the measured variations of resistivity with temperature for sintered ceramics of n-type BaTiO 3 and related compounds in which Sr or Pb is substituted for the Ba. These substitutions cause the Curie temperature to change relative to that of BaTiO 3 which is at 120°C. The inclusion of 0.3 mol.% of LaTiO3 makes these mixed titanates semiconducting. Above the Curie temperature of each compound the effect of the decreasing dielectric constant on increasing the barrier height, B, and the resistivity is seen. [Fr6m Andrich (1969); courtesy of D. Clarke; published with permission of Philips Technical Review.]

voltage, several interesting phenomena are observed. For simplicity this section will consider ceramic grains with only one, shallow donor species. However, effects for multiple donor species have been observed, and their explanation has been treated extensively (Blatter and Greuter, 1986; Greuter et al., 1986). In particular deep donors, additional to the shallow donors, are a source of dispersion in single bicrystals even at equilibrium in contradistinction to the simple example presented below. The general response of a charge trapping grain boundary to an applied dc plus harmonic voltage of frequency co, V(t) = Vdc + Fac sin co t

(14-9)

laxation forms: (14-10)

l+C0 2 T 2

(14-11)

where in the absence of deep donors Gdc is the dc conductance, C^ is the high frequency capacitance, i is a time constant associated with the bulk/boundary exchange of charge, and CD is a complex function of the barrier parameters which vanishes for Vdc = 0; i.e., at equilibrium. This case will be treated first, then followed by the response in the presence of a nonzero steady state voltage.

has been studied by several groups for the 14.3.3.1 Harmonic Response case of e Vac < k T (Seager and Pike, 1980; at Equilibrium Pike, 1984; Blatter and Greuter, 1986). The conductance and capacitance per unit area Even without a detailed solution it can of boundary are found to have Debye rebe shown from symmetry arguments that

748

14 Semiconducting Polycrystalline Ceramics

the conductance and capacitance of a simple, and symmetric, grain boundary barrier as depicted in Fig. 14-6b are independent of the harmonic frequency. A simple model of the grain boundary electrical admittance, which will also be useful in a later section, may be used to demonstrate this frequency independence. In Fig. 14-13 the grain boundary is schematically illustrated as the center node connected to the conductive bulk of each adjacent crystallite by a parallel conductance-capacitance network representing the depletion region. The admittance of the left (right) depletion region is given by: *I (U\ — ^T (R\ + 1 CO C i /m

(14-12)

By the assumed symmetry at equilibrium, G L =G R = 2G and C L = C R = 2C. As in a metal-semiconductor contact, neither G nor C has a frequency dependence. The series combination of the two depletion layer networks has an admittance of Y=G + icoC

(14-13)

which shows that the net double layer structure, at equilibrium, does not intro-

n/WHi Figure 14-13. Schematic diagram of grain boundary admittance. The depletion layers at semiconductor grain boundaries are represented by parallel conductance, G, and capacitance, C, networks. The grain boundary, shaded region, acts as an electrical node between the two depletion layers. The outer edges of the depletion layers are the highly conductive bulks of the crystallites, and represent the input to each network.

duce a frequency dependence for either the capacitance or conductance. At equilibrium the conductance and capacitance, per unit area of grain boundary, are given by (Seager and Pike, 1980; Pike, 1984): / c\eA ( kT (14-14) (14-15)

Thus the capacitance is essentially that of a parallel plate capacitor whose electrodes are separated by the width of the depletion region, 2d. A practical application of this result is that a thin capacitor dielectric can be obtained in a strong mechanical structure. If the ceramic grain size is D^>2d, then the apparent, or effective, dielectric constant for the ceramic body is e e0 D/(2 d). This is a geometric enhancement of the dielectric constant which is commonly the basis of the so called ceramic boundary layer capacitors (Goodman, 1986). Notice that the enhancement is greater when the grain conductivity is high [large Nd and thus small d by Eq. (14-2)], and when an intergrain second phase is absent (smaller effective d). Practical ceramic capacitors with large capacitance can be made with semiconducting ceramics which are also ferroelectric (see Chap. 9 of this Volume). For ferroelectrics the local value of & within the material depends on the local dc electric field. However, since there is a variable electric field F(x) within the depletion layer near the grain boundary, the effective value of a for the ceramic body is not easily calculated. Also the local value of e depends strongly on the temperature, and thus these types of capacitors are used where an enhanced, effective & is needed only over a small temperature range (Goodman, 1986).

14.3 Electrostatic Barriers and Transport Properties

14.3.3.2 Harmonic Response in Steady State

Application of a steady state voltage, F dc , in addition to the harmonic voltage causes the potential barrier to become asymmetric (see Fig. 14-7). This broken symmetry permits several interesting, and qualitatively unusual, harmonic phenomena to occur. Figure 14-14 illustrates several of these phenomena observed in a

Ge, low field

40

10*1 \ -

T=296K

-

10 Hz

UL

0 .

phase separation technique • • HP-4270 Bridge

(

-20 •

-40

i

i

i

100 F in V/cm

polycrystalline ZnO varistor material. The capacitance of this material is plotted as a function of the dc voltage. At low voltages it decreases slightly, followed by a region of substantial increase, and finally a maximum and a plunge to negative values. The increase and negative value of capacitance has been documented on well characterized bicrystals as well (Seager and Pike, 1980; Pike et al., 1983). To understand this behavior it is first necessary to understand how the capacitance is measured. A harmonic voltage is impressed across the sample, and the resultant harmonic current flow is measured. For the voltage of Eq. (14-9), the current is generally of the form: J =J

+ J^coscot

(14-16)

dc

20

c

749

i

200

Figure 14-14 Capacitance versus eleptric field for a commercially available low field (General Electric, Type V22ZA3) ceramic ZnO varistor. This graph shows the small signal capacitance of a ZnO varistor measured as a function of the dc electric field across the sample. The frequency range of 10 to 104 Hz was spanned using two techniques (points and solid curves) which overlapped at 103 Hz. All curves decrease slightly from their value at zero bias. At low frequencies, less than 104 Hz, the curves then increase in the range of 100 to 200 V/cm. At 102 and 103 Hz the measured capacitance reaches a maximum value significantly above C (F = 0), and then plunges to large, negative values. The curve at 104 Hz also becomes negative (from Pike, 1982).

where subscripts i and q denote in-phase and quadrature currents. The capacitance per unit area is defined as Jq/(co Vac\ where J q is generally a function of co, Vdc, and T. Reference to Fig. 14-15 will help understand the response of a charge-trapping grain boundary to the applied voltage. As for equilibrium, one component of the capacitance results from displacement currents at the edge of the depletion regions. It is this component which represents stored charge and is expected. As Vdc is increased, the combined thickness (dx -h dr) of the depletion layer grows (see Fig. 14-7) and this component, C^, decreases slightly. This is the effect seen at low voltages in Fig. 14-14. The anomalous capacitance results from the modulation of real current, J over , crossing the boundary. Because there is a time constant T governing the exchange of charge between bulk and boundary, the charge in the boundary cannot achieve its equilibrium value corresponding to the instantaneous value of applied voltage. This causes (j)B (t) to be slightly out of phase with V(t), and since Jocexp[-(/> B (£)/(& T)], the

750

14 Semiconducting Polycrystalline Ceramics

£=-=0

==qB

Figure 14-15. Schematic diagram for anomalous capacitance. The anomalous capacitance is due entirely to self-modulation of the current passing over the potential barrier in a bicrystal. Under steady state conditions this current would be the dc current; but when V(t) contains a harmonic variation, Jover does also. The trapped charge in the grain boundary obeys a rate equation with a time constant T. The finite value of T causes