Glasses and Amorphous Materials

1 Classical Glass Technology Michael Cable Division of Ceramics, Glasses and Polymers, School of Materials, University o...

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1 Classical Glass Technology Michael Cable Division of Ceramics, Glasses and Polymers, School of Materials, University of Sheffield, Sheffield, U.K.

List of 1.1 1.1.1 1.1.2 1.1.3 1.1.4 1.1.5 1.2 1.2.1 1.2.2 1.2.3 1.2.4 1.2.5 1.2.5.1 1.2.5.2 1.2.5.3 1.2.5.4 1.2.5.5 1.2.6 1.2.7 1.3 1.3.1 1.3.2 1.3.2.1 1.3.2.2 1.3.3 1.3.4 1.3.4.1 1.3.4.2 1.3.4.3 1.3.4.4 1.3.4.5 1.4 1.4.1 1.4.2

Symbols and Abbreviations The Historical Development of Glass Technology Introduction The Beginnings of Glass Technology The Eighteenth Century The Nineteenth Century The Twentieth Century Choice of Glass Compositions Properties Important to the User Properties Important to the Glass Maker Choice of Glass Composition Composition-Property Relations Models for Composition-Property Relations The Viscosity-Temperature Relation Liquidus Temperature Specific Heat Thermal Conductivity Summary The Modern Approach to Choice of Glass Composition Choice of Raw Materials The Melting of Glasses Introduction Energy Requirements Enthalpy of Reaction Sensible Heat Preparations The Stages of Melting Batch Heating The Initial Melting Reactions Refining The Homogenizing of Glass Melts Modern Furnaces Glass Forming Introduction The Manufacture of Containers

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

3 6 6 6 8 11 13 18 18 20 21 22 23 24 25 26 26 29 29 32 32 32 33 33 34 34 35 35 37 45 53 59 62 62 64

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1.4.3 1.4.4 1.4.4.1 1.4.4.2 1.4.4.3 1.4.5 1.4.5.1 1.4.5.2 1.4.6 1.4.6.1 1.4.6.2 1.4.6.3 1.4.6.4 1.4.6.5 1.5 1.5.1 1.5.2 1.6

1 Classical Glass Technology

The Production of Lamp Bulb Envelopes The Manufacture of Flat Glass Introduction Sheet Glass Processes Float Glass Rod and Tubing The Danner Process Vertical Drawing Processes Glass Fibers Introduction The Physics of Fiber Drawing The Technology of Fiber Production Continuous Fibers Non-Circular Rod Tube and Fiber Polishing Mechanical Polishing Acid Polishing References

69 70 70 71 74 78 78 79 80 80 80 81 82 83 83 83 84 85

List of Symbols and Abbreviations

3

List of Symbols and Abbreviations A A Ao a a0 a0 at b b B B Ca Cs C ro CEQ Ct C c ct Ac d D E Ex E2 £* Ft F (a) F(p) g gt G H h h / kB k / L m M

amplitude of wave parameter in Vogel-Tammann-Fulcher equation initial amplitude of wave radius or semi-major axis of elliptical inclusion initial radius of sphere constant term in Eqs. (1-1), (1-2) and (1-4) coefficient for term i in Eqs. (1-1) and (1-2) coefficient in Eq. (1-43) semi-minor axis of elliptical inclusion parameter in Vogel-Tammann-Fulcher equation rate of production of bottles dissolved concentration in liquid at radius a concentration of gas inside bubble uniform dissolved concentration in liquid far from bubble equilibrium concentration of silica in liquid in contact with silica grain concentration of dissolved silica in liquid at time t dimensionless concentration (0 < C < 1) specific heat concentration of component i concentration difference driving dissolution equilibrium thickness of Float glass ribbon diffusivity dimensionless equilibrium shape of deformed inclusion approximate dimensionless equilibrium shape of deformed inclusion parameter used to define approximate dimensionless equilibrium shape of deformed inclusion activation energy for viscous flow dimensionless dissolved concentration of gas i net surface tension force over unit length net force due to pressure over unit length gravitational acceleration mole fraction of gas i in a bubble rate of shear enthalpy height of Float glass ribbon above surface of tin bath depth of glass melt parameter describing initial behaviour of a multi-component bubble Boltzmann constant constant in Eqs. (1-19), (1-20), (1-42) and (1-44) linear dimension length of orifice number of components in system mass rate of flow through orifice

4


n n n n n N p p Ap R R R s sa 5 aH 5 T T{ t U V w X X x y z z

number of degrees of freedom number of moles of a component refractive index number of terms in series number of bubbles of given size per unit volume of melt total number of bubbles per unit volume of melt pressure number of moles of silica in silicate liquid pressure difference or excess pressure due to surface tension gas constant dimensionless radius of sphere radius of atom or molecule natural strain natural strain of a-axis for inclusion differing in viscosity from surrounding liquid natural strain of a-axis when inclusion h a s same viscosity as matrix parameter defining eventual behaviour of multi-component bubble temperature interfacial temperature time velocity vector volume wall thickness value of a property mole fraction of a constituent diameter of bubble thickness of reaction product layer volume of product per unit volume of sphere number of moles of silica

a a a a OL{ P y S X X X X Xo XR rj

angle absorption coefficient mass fraction reacted thermal diffusivity Ostwald solubility coefficient for gas i rate of growth parameter for sphere auxiliary parameter in Appen's property calculations concentration boundary layer thickness wavelength of electromagnetic radiation wavelength of wave on liquid thermal conductivity dimensionless viscosity parameter true thermal conductivity apparent thermal conductivity due to radiant heat transfer viscosity


q> q> 0 ©0 9 90 Q a o \jj s

effective solubility of gas in liquid auxiliary parameter in Appen's property calculations temperature in °C temperature constant in Vogel-Tammann-Fulcher equation angle coefficient in Eq. (1-6) mass density surface tension or interfacial energy Stefan-Boltzmann constant auxiliary parameter in Appen's property calculations eccentricity of ellipse


1.1 The Historical Development of Glass Technology 1.1.1 Introduction

Glass making is an extremely old technology, the history of which has often been recounted, see for example Douglas and Frank (1972), but is constantly in need of revision as archaeological evidence keeps advancing our understanding of various aspects and throwing up new puzzles. Here we consider only how the general advance of science and the evolution of glass making have interacted with each other. Few events earlier than the middle of the seventeenth century deserve detailed discussion; until that time chemistry and physics were too primitive to be able to assist development of high temperature processes like glass or ceramic manufacture or iron making. But before proceeding it is salutary to remind ourselves of the brilliant technical achievements occasionally produced in distant ages: first, skill in glass melting such as the Wilsford bead (Guido et al., 1984) and the sealing-wax red glass from Nimrud (Cable and Smedley, 1987 b) and the glass of the Lycurgus cup (Brill, 1965) required; second, virtuosity in after working of the cold glass such as the Roman diatreta ware (Wiedman, 1954), the Portland or Barberini vase, and the modelling of the Lycurgus cup. These remind us that technological advance has often come about by intuition and intelligent trial and error experimentation rather than by applying scientific methods or knowledge. Even in recent times advances in scientific understanding have often been stimulated by technical advances rather than the converse. Several notable cornerstones of modern science depended on the availability of glass apparatus and from mediaeval times

onwards glass was the pre-eminent choice of alchemists and chemists for their apparatus. Even if borosilicate glass for laboratory apparatus (Pyrex) is a twentieth century invention, the relatively fragile glass apparatus then available was essential to many laboratory operations in earlier times. One of the events having an obvious claim to mark the beginning of modern science was Galileo's work on the motion of the planets which would have been impossible without astronomical telescopes needing glass lenses. Isaac Newton's pioneering work in optics, begun in 1666, also required prisms, lenses and mirrors. Other basic investigations which required glass apparatus were the classic investigations of the properties of gases (Boyle's law and Charles's law), thermometry, barometry and the development of microscopes. 1.1.2 The Beginnings of Glass Technology The earliest written records of glass making are some famous clay tablets, dating from around 650 BC, from the library of Assur-bani-pal, see Douglas and Frank (1972), but these are incompletely understood because we have no dictionary to explain the technical terms. Many centuries passed before written accounts of glass making contained any useful insight besides recipes to be followed by rote. The earliest development in glass making of which we have a reasonably documented description seems to be the invention of glass of lead by Ravenscroft around 1673-1676 (Moody, 1988, 1989). From very distant times it had been common to make much European glass using sand and an alkali flux obtained from plant ash. By mediaeval times it was known that leaching the ash and purifying the alkali by evaporation had several advantages in melting the glass. Unfortunately this also

1.1 The Historical Development of Glass Technology

made glass of simpler compositions richer in alkali, to the serious detriment of chemical durability. When Ravenscroft was called their rescue the holders of the monopoly on glass in England were in danger of losing their privilege because of customer dissatisfaction with the chemical durability of their product. Ravenscroft rescued them by developing a glass of lead (not the same as modern English lead crystal). This is the earliest work that we know where an investigation was deliberately made to find how to modify glass properties by adjusting composition. However, this could not have been done by scientific methods because chemistry was still on a mystical basis and the techniques of analysis needed did not exist. Some of the shortcomings of chemical knowledge of those times are indicated by the many years that Isaac Newton devoted to chemical studies which had a negligible influence, unlike his profound insights into gravitation and light. His Optics (1704) was the first important scientific book to be published in any vernacular language rather than Latin. It was not only directly concerned with the properties of glass but also the first to expound the modern scientific method of proposing hypotheses, devising experiments to test them and reporting the results before theorizing further. It is interesting to speculate how much further he might have developed optics if he had been able to experiment with glasses of distinctly different refractive indices and dispersions. The primitive state of glass technology may have let him down but led him to invent the reflecting astronomical telescope. The most influential of all books on glass was Antonio Neri's L'Arte Vetraria which first appeared in AD 1612 and was soon translated into both Latin and several other vernacular languages (Turner,

1962), generally with a commentary by the translator as exemplified by Merret's Art of Glass (1662) and Kunckel's Glasmacherkunst (1679). Although these give much useful information they are little more than recipe books: insight into the reasons why particular things should be done or avoided is rare. The beginnings of a sound glass science needed a better understanding of both chemistry and physics. Developments in chemistry were needed to permit the analysis of both glasses and raw materials as well as to understand the difference between elements such as sodium and potassium or calcium and magnesium. Science lacked a proper understanding of heat, which was thought of as some kind of chemical element though, as knowledge developed, it had to be treated as one with a negative mass. As a result melting and solidification and also glass formation could not be understood. The only important glass properties that could easily be measured were density and refractive index. This gives an unduly pessimistic a picture of what practitioners of the useful arts could achieve. For example, in those days glass makers did have some simple quality control tools for their ash, probably depending more on taste than anything else because sodium and potassium salts have different tastes as do carbonate, chloride, sulphate and nitrate; there are published comments such as "the bitterest is the best for making glass". Assessment of silica was a bigger problem and it was often assumed that all whitish stones which would neither dissolve in acid nor be affected by heat but struck a spark with steel were chemically equivalent and equally suitable for making glass. The reasons for this situation are clear: no other analytical tools were available. Another century was to pass before much progress was possible with any of


these crucial factors. Given what we now know about the sensitivity of glass properties to changes in composition, it sometimes seems amazing that any good quality glass was regularly made. Few glass makers can have enjoyed placid lives, a situation possibly not very different from today. The other main problems were associated with furnaces. First there was the problem of what to build them from, secondly, how to attain sufficiently high temperatures and, thirdly, how to measure and control temperature; even at the end of the last century it was normal to speak of degrees of heat when talking about high temperature processes. It was realised at an early stage that drying the wood used as fuel had important advantages; the net calorific value of wood decreases almost linearly with moisture content and becomes zero at about 70% H 2 O, so that air dried wood still containing around 20% moisture is much inferior to that which has been thoroughly dried. It is also clear that in those times glasses were regularly made which needed melting temperatures much above the 1200°C which used to be assumed to be the maximum melting temperature attainable (Cable and Smedley, 1987 a). The introduction of coal as the main fuel required significant changes in the design of furnaces to allow for its different combustion characteristics but this was done, as so often, by trial and error without real scientific insight. Up to those times two types of furnace had been developed (Newton, 1985). One was the southern European 'beehive' type exemplified by the famous woodcuts in Agricola's book, Fig. 1-1 (Hoover and Hoover, 1912). The other from northern Europe was a rectangular chamber frequently built with four smaller furnace chambers as wings on the corners, the plan looking like a butterfly, see Fig. 1-2.

Figure 1-1. The traditional southern European beehive type of furnace; from Agricola. The wood fire was central at ground level and charged through the opening shown; the exhaust gases passed over the pots and out of the working holes. Straight sided pots were more common than the vases shown.

Techniques of glass melting and forming processes remained virtually unchanged from the practices of several preceding centuries. 1.1.3 The Eighteenth Century

Several branches of chemistry and physics made very rapid advances towards the end of the eighteenth century. Some of the essential physical properties of gases were already known; Boyle's law was demonstrated in 1660 but Charles's law


0

5m

Figure 1-2. A northern European wood fired furnace showing the four small wing furnaces. Vertical section through the middle and plan view just above the level of the siege. Two fires were made, one at each end of the hearth. After Bosc D'Antic and other French

not until 1787. The experiments that were needed for these investigations would have been impossible without glass apparatus. A clear appreciation and separation of the chemical and physical aspects of heat and combustion came much later. Physicists had the evidence to abandon phlogiston towards the end of the 18th century but a considerably longer time elapsed before all chemists also came to a modern view of heat. There were, however, some notable publications about glass making in the second half of the century. The glass

making sections of the great Diderot and D'Alembert Encyclopedic (1765 -1772) contain more than a hundred beautifully drawn and engraved plates, which are well known, as well as very detailed descriptions of the processes, which are unjustly neglected. The text of the Diderot and D'Alembert Encyclopedic gives the most detailed account of glass making practices ever published and makes clear that much skill and experience was involved but very little science. The plates were republished with a significantly different and obviously more modern text in the Encyclopedic Methodique (1791). Figures 1-3 and 1-4 show examples of these plates which illustrate the two long established methods of making window glass, the crown process and the cylinder process. The crown process used a large gather formed like a shallow bowl which was transferred to a punty then reheated and spun by hand so that centrifugal force made it open up into an almost flat circular disk with excellent fire polished surfaces; the main disadvantages of crown glass were the thickened central bullion where the punty was attached and the fact that the disk was always somewhat saucer shaped. The glass, when homogeneous, was nevertheless of uniform thickness, generally in the range 1 to 2.5 mm (Cable and Swan, 1988). Cylinder glass was made by blowing a cylinder, cutting off the ends, cracking it longitudinally, then reheating it and opening out the cylinder into a flat sheet in a separate furnace. This operation required the use of a kind of wooden rake to open out the cylinder. The effect of this tool on the glass and of contact with the slab on which it lay always produced slightly rippled surfaces, although the sheet could be quite flat overall. Cylinder glass could provide considerably larger panes than

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1 Classical Glass Technology Tig.z

Figure 1-3. Reheating and spinning the gather in making crown glass: from the Diderot Encyclopedia.

crown. Crown glass could make good but slightly convex or concave mirrors but cylinder glass was rarely good enough to make looking glasses. The Collected Works of Paul Bosc D'Antic (1780) cover a range of subjects but glass making is the major part. In a fascinating introduction and a lengthy essay written in 1760 which is supplemented (in the established way) by additional commentaries written in 1780, he writes for the first time about glass making in the modern way referring, where possible, to the latest scientific literature. However, D'Antic was a man of complex personality and some influence at the court of Louis XVI (as physician to the King) but of dubious practical achievement because he was dis-

Figure 1-4. Steps in making cylinder glass; from the Diderot Encyclopedia.

missed from his position as Director at Saint Gobain in 1761 after only two years in that post. A clash of personalities may have contributed to D'Antic's downfall. His vivid style of writing suggests that he may have been vain and opinionated, a view clearly shared by Delaunay Deslandes, his deputy and successor as Director, who may not be an entirely impartial witness but whose distinguished 31 years in that post demonstrates his own technical


expertise and tends to lend credence to his strictures on D'Antic (Barton, 1989). 1.1.4 The Nineteenth Century

Enormous advances were made during the last century. The title of most eminent glass technologist of all time should probably be awarded to Joseph Fraunhofer (1787-1826) who as a more or less self educated orphan was in 1806, at the age of 19, employed at the Optical Institute in Benediktbeuern, where he assisted the elderly Guinand in developing the stirring of glass melts to produce optical glasses capable of making good achromatic doublets. Fraunhofer soon supplanted Guinand and spent the whole of his regrettably short career in this post, making his enormous contributions to astronomical optics, especially spectral analysis and diffraction, whilst engaged in the manufacture of astronomical telescopes. Although none of the telescopes made by Fraunhofer himself still exists, one made to the same design by his immediate successors is still to be seen at the Harvard College Observatory. One of Fraunhofer's (1817) published papers shows that he had developed a test for the chemical durability of glasses using sulphuric acid and also implies that he was the discoverer of the mixed alkali effect, that is to say recognizing that a mixture of alkalis often gives properties quite different from what one would have predicted from measuring properties of glasses containing only each alkali alone. Although chemistry was advancing rapidly, Fraunhofer would have been hindered by lack of pure materials and inability to analyse them or his glasses. These problems were rather less severe for Michael Faraday, the most creative of all scientists to have spent some of his time working as glass technologist, who had better resources close to hand.

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Faraday (1791-1867) was asked by the Board of Longitude and the Royal Society to find how to make good quality optical glasses to enable better instruments to be made and worked on this project from 1825 to 1830 when, having had reasonable success and not seeing how to make much further progress, he asked to be released to continue his work with electricity. Faraday (1830) described his methods but his work failed to have any practical impact on glass manufacture, largely because the system of controlling glass making, to ensure that the taxes were paid, and the way in which taxes were levied made experimentation by glass makers too difficult and expensive for most of them to contemplate. The small scale of his operations may also have failed to impress glass makers (Cable and Smedley, 1989). William Vernon Harcourt (1789-1871) was an important pioneer about whose work we know too little. Vernon Harcourt was a Church of England clergyman who was influential in founding first the Yorkshire Philosophical Society (his father was Archbishop of York at the time) and then the British Association for the Advancement of Science; the early history of the latter has been recounted by Morrell and Thackray (1981). During much of his long life he spent a great deal of time in making unusual glasses using a hydrogen furnace that he had invented (Vernon Harcourt 1844). His interest was to extend the range of optical properties available to allow better optical instruments to be made, latterly in conjunction with Prof. Stokes who undertook the optical measurements (Stokes, 1871). He used at least 29 elements in his glasses and was the first person ever to use at least 13 of them in glasses, see Fig. 1-5. He produced good samples of titanate, borate and phosphate glasses. Unfortunately his work, like Faraday's, led to no practical

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Li

Be

B

Na

Mg

Al

K

Ca

Ti

V

Cr

Sr

Mo

Ba

W

Mn

Fe-

Co

Ni

Cu

Si

Zn

P

F

S

As

Cd Au

0

TI

Sn

Sb

Pb

Bi

II

Figure 1-5. Periodic table of the elements showing those used in his glasses by Vernon Harcourt. Those which he was the first to use are marked by a bold outline; the others shown had previously been used in glasses.

U

applications. The punitive tax on glass had been abolished in 1845 so that was not the reason in this instance. Perhaps glass makers were unwilling to take seriously the results of such small scale laboratory experiments by an amateur or to consider using such unusual ingredients. The real beginnings of glass technology had to wait for the arrival on the scene of Abbe and Schott who began the first really fruitful investigations of property-composition relations in 1881, again with the intention of improving optical instruments, initially microscopes. Their success owed much to the collaboration of Carl Zeiss and his son Roderich in developing methods of large scale high quality lens manufacture which were soon also applied to the production of photographic lenses: Schott and Zeiss remain influential names today. The results of their pioneering investigations were described in detail by Hovestadt (1900) and an English translation by Everett (1902) soon appeared. The basic engineering industries developed rapidly during the nineteenth century, making possible advances in many other fields which required the large scale production of components and machines or high standards of accuracy; the development of electrical machines playing an especially important part. It is an interesting

coincidence that the Siemens Brothers had important roles in both electrical machinery and in glass melting. The tank furnace, which made possible continuous large scale production of molten glass, and machines for mechanized production of containers and flat glass were inventions crucial to the glass industry which together revolutionized it. The earliest patent for a regenerative glass melting furnace appears to have been granted to Robert Stirling in 1816 but this patent was never published, or exploited. Nevertheless it seems that Wilhelm Siemens knew of this work (Maurer and Bischoff, 1930). Attempts to make glass melting continuous had begun as early as 1840 when Joseph Crosfield obtained a patent for a reverberatory furnace in which batch was placed on an inclined surface and ran down into a pot as it melted. Chance Brothers in Smethwick obtained a patent for a tank about this time but, even if tried, there is no record of it being successful. The regenerative tank furnace was brought to success by two of the Siemens Brothers, of whom there were five, Friedrich, Hans, Karl, Werner, and Wilhelm, who between them worked in England and Russia as well as Germany but remained in regular contact. Friedrich had worked on regenerative furnaces in Eng-


land in 1857 and, jointly with Wilhelm, obtained an English patent for a regenerative system of firing a gas furnace in 1861. The regenerator as a means of heat recovery brought both higher temperatures and better fuel economy. The first successful glass tank was built by Friedrich in Dresden in 1867; on examining its plans one is surprised to see how little the main features changed during the ensuing years. The use of the tank for melting glass then spread rapidly. At about the same time Friedrich also devised a three compartment pot which allowed continuous melting and working on a smaller scale but it was never successfully exploited. A fascinating history of these developments has been written by Stein (1958). The introduction of iron mold was an important step forward in the glass industry. Magoun obtained an American patent for their use in 1847 and their usage was soon accepted. The first major development in mechanization occurred in United States where the machine pressing of glass made great progress between about 1820 and 1860. Soon after this the possibilities of the press and blow process for hollow ware were seen. In 1865 Gillinder of Pittsburgh was granted a patent for a combined press plunger and blow pipe with which he could press the top of a water jug and then blow the body. Following this line of thought Arbogast in 1881 developed the pressing of the neck and parison of a bottle in one mold followed by its transfer to another mold for blowing to the final shape, which he patented in 1882. This reversal of the traditional way of making containers in which the mouth was the last part to be shaped and hence called the finish was crucial to the subsequent development of all mechanized processes. The first blow and blow machine for containers was invented by Ashley, in England, in 1886. Although

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Owens began work on bottle manufacture around 1898, his major work took place in the early years of the present century, so his story will be taken up later. 1.1.5 The Twentieth Century

In the early years of the century the possibility of solids reacting together was becoming widely recognized and some of the earliest systems studied were of interest to glass makers. For example, Cobb (1910) published some studies of reactions involving sodium carbonate, calcium carbonate, and alumina with silica. Gustav Tammann (1861-1938) did much to develop scientific studies of glasses, including melting reactions, over an extended period. One of the most notable pioneers was W. E. S. Turner (1881-1963) who, at the beginning of the first World War, was already an ambitious university physical chemist. The early stages of the war showed him how badly the British glass industry needed scientific advice and research for which it had been relying on Germany and this led to him found the Society of Glass Technology in 1915 and the Department of Glass Technology at Sheffield University a year later. This was the first University Department to have glass technology as its special field of teaching and research. For forty years from its foundation the department was organized and financed in a way very unusual for those times but probably now widely thought very commendable, relying heavily on funding coming directly from the glass industry and being run by a joint University-Industry committee. The first successful attempt to produce an approximate theory to describe the kinetics of solid state reactions was by Jander (1927) who used data for systems including carbonates and silica to support his theory. This developed an interest in

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studies of glass making reactions among chemists as well as glass technologists. Science saw rapid advances in all fields. More and more elements became readily available and could be incorporated into glasses to investigate their possible uses. Correspondingly ever wider ranges of applications have called for novel glasses with properties not previously known or studied. Important novel families of glasses have been developed: these include inorganic non-oxide glasses such as the chalcogenides sharing many general structural similarities with oxides; quite unexpected inorganic systems of which the halide, especially fluoride, glasses are the most notable; metallic glasses and organic glasses, the last of which are no longer given only grudging recognition by glass scientists. All of these are discussed in later chapters of this volume. One of the most significant developments for glass technology was the Griffith (1920) theory for the strength of brittle materials which proposed that surface flaws were the controlling factor (see Sec. 13.3). Griffith himself tested his theory on glass bulbs deliberately scratched with a diamond. This at once aroused interest in the strength of glasses and provided a sound theoretical underpinning for previously ill defined and poorly understood studies of glass strength. It thus had an enormous beneficial influence on such work and on attempts to improve the practical strength of glasses. A notable practical result was the elegant demonstration by Thomas (1960) that strength is not necessarily dependent on sample size. The X-ray diffraction analysis of crystal structures was a particularly exciting field which had an enormous impact on glass science in the first quarter of the century. The most influential event in glass science was probably Zachariasen's (1932) publi-

cation of his random network hypothesis of oxide glass structures (see Sec. 5.1.1). This derived from early studies of crystal structures by X-ray diffraction which had led Zachariasen consider how one could build up extended structures in which all bonding requirements were met and nearest neighbor coordination maintained without imposing the exact long range order that a crystal demands. Although this is a static geometrical model of glass structures it has remained useful and fruitful to the present time, although it is now generally thought that models based on rates of cooling required to avoid crystallization are more universally valid (Turnbull and Cohen, 1960); however, they do not yield such a rich harvest of ideas about composition-property relations. The next most exciting development in structural studies probably was the ability to use high magnification electron microscopy to examine sub-liquidus phase separation after about 1960. Developments in technology also saw enormous strides in many fields, some considered to be in the realms of fantasy, if thought about at all in earlier times. An interest in lighting, initially for purely economic reasons, had led Count Rumford to invent photometry two hundred years ago (Brown, 1979) and twentieth century developments in lighting again called for major improvements by glass technologists, for example, in glasses for sealing to wire leads and others resistant to sodium vapour, then more recently glasses suitable for the envelopes of quartz-halogen lamps. An interesting review of the development of lamp manufacture in Germany has recently been published by Tober (1990 a, b). Radio equipment made rather different demands for the development of glasses and television demanded consideration of Xray absorption, the improvement of glass


homogeneity and development of high quality pressing for large face plates. Solid state electronics and microelectronics have had yet other requirements, mainly for electrical and mechanical properties. Some of the ways in which glasses played a part in these advances have been recorded in an impressive history of one of Britain's most successful industrial research laboratories, the General Electric Company's Hirst Research Centre, by Clayton and Algar (1989). The vast expansion of architectural uses and automobile manufacture put flat glass production under great stress and must have played an important part in the decisions to invest very large sums in the development of the Float glass process. The industry's major developments were in flat glass manufacture, automatic production processes for containers and lamp bulbs, and the development of fibers for insulation and for textiles. The first improvement in flat glass production was the Sieverts process which mechanized the blowing of hand gathered cylinders and somewhat increased their size but the Lubbers process of 1903 was more important. This mechanized the blowing of large cylinders, up to about 12 m long and 0.6 to 0.8 m in diameter, but these still had to be split then opened up in a flattening furnace. This increased the size of sheets that could be made and the scale of production but not the quality. Better flatness had to await the success of drawing flat sheet directly from the melt. Patents for sheet glass processes date back to the 1850s but then had no chance of success. Fourcault, who had obtained a Belgian patent for a sheet drawing process in 1902, was the first to succeed but did not manage to produce continuously drawn sheet glass until 1916, during the First World War. Colburn obtained a United States patent in 1903 and a French one in 1905 but likewise did not achieve

15

success until the Libbey Owens company was established in 1916. The 1920s saw advances in other methods of drawing flat glass and in polished plate manufacture. The Pittsburgh sheet process was first operated in the United States in 1928 and brought to Europe in 1930. The Pilkington continuous process for grinding both sides of the cast plate ribbon at the same time was a notable engineering achievement of the 1930s. However, the most important large scale development was the invention of the Float process in the 1950s which made the very expensive plate process redundant. By a remarkable coincidence the Float process was being worked on simultaneously by both Ford in the United States and Pilkington in Britain but Pilkington submitted their patent applications only a few months before Ford and thus won the race which neither of them had consciously been running. Some of the problems encountered and solved by Pilkington Brothers in making the process work have been described by Pilkington (1969). Considerably quicker success attended the inventors of machines for making bottles. Michael J. Owens joined E. D. Libbey when Libbey moved his bottle factory from Boston, Massachusetts, and reopened in Toledo, Ohio, in 1888. By 1894 Owens had developed a paste mold machine which could make lamp chimneys and he began work on a bottle making machine in 1898. By 1903 Owens had produced a successful six arm rotary machine which differed from most others in the way in which it was supplied with glass. Semiautomatic machines which had to be supplied with gobs by a skilled gatherer already existed and persisted until about 1960. Owens solved the gathering problem by using his parison mold for this purpose. The parison mold dipped into a pool of relatively fluid glass

16


and was filled by suction; a second mold was then used for blowing, just as in the press and blow process. Further models followed and by 1920 improved and very effective machines which used six, ten, fifteen, and twenty sets of molds had been been put on the market. However, the Owens machine had important disadvantages, some technical and some commercial. The major technical problem (which was never solved) was the cut-off scar on the base of the container where the hot glass had been severed by a knife as the parison mold was lifted from the pool of glass. The Owens machine was very large and this was a disadvantage. Apart from its actual physical dimensions and weight, hence heavy power consumption (despite its continuous rotation), it also required large number of sets of molds for every article made. It was therefore suitable for long runs producing millions of one type of container but much less suited to producing a range of different products on a less ambitious scale. Commercial disadvantages included the high initial cost, the strict licensing arrangements and the heavy royalty payments required. Many smaller manufacturers therefore were not willing to use the Owens machine. This stimulated work on feeder fed blow and blow machines. The glass industry has been very fortunate in its engineering pioneers. The Owens machine was brought almost to perfection by about 1920: it then remained almost unchanged but was an important bottle producer until about 1960 when it was supplanted by machines supplied by gob feeders; the most successful of these likewise established its main features at an early stage. The most important advance needed by container manufacture was the successful development of forehearths and gob feed-

ers capable of supplying accurately made gobs of good quality glass to the forming machines. This was necessary for any other type of machine to compete with the Owens. The Homer Brooke feeder was first used in 1903 but was not very successful because it used a cup to collect the glass from a steady stream and thermal homogeneity was impossible to maintain. The crucial advance here was made in 1922 by Karl Peiler, a Massachusetts Institute of Technology graduate, when he introduced the first of the modern type of Hartford feeder which used a reciprocating vertical plunger and surrounding tube to control the flow of glass and produce separate gobs one at a time from the orifice. This made possible the successful development of gob-fed machines for container manufacture and took away from the Owens machine the one major advantage that it had enjoyed since its invention. Containers are now almost universally made by the Individual Section, or IS, machine which was invented in 1925 by Henry Ingle of the Hartford Empire Company. Nearly all previous machines had been conceived as using molds on a circular table which rotated, at first only intermittently, to execute the necessary sequence of operations. Most machines, other than the Owens, used two tables, one for parisons and one for blow molds. The major novelties of the IS machine were to have molds which are stationary, apart from opening and closing, only the neck ring holding the glass being moved, which greatly decreased essential operating power consumption, and to make each section essentially independent of the others, which allowed interruption of part of the machine, for example to change a mold, without having to stop the whole operation, a feature unique to the IS. Although numerous improvements have been made to con-


trol methods and mechanisms in recent years, for example the development of the narrow mouth press and blow process for containers in addition to the original blow and blow and wide mouth press and blow methods, the IS remains identifiably the original machine and the most efficient yet widely exploited. None of the numerous alternative machines developed in the last sixty years has long survived direct competition with the IS, one of the important reasons being that having the molds stationary, except for opening and closing, allows much more efficient mold cooling to be installed. The Heye company in Germany has developed a machine of great technical promise but it has yet to become a major competitor of the IS. Although processes were needed for the large scale manufacture of rod and tube, which had long been drawn by hand, their development did not need the same imaginative leap to entirely new methods as had containers. The Danner process, developed in 1912, is remarkably like the traditional hand made process with glass being continuously fed onto the outer surface of an inclined rotating mandrel from which it is drawn off. The Philips process is similar but draws the glass from inside a hollow mandrel. Corning developed both upward and downward drawing processes and the Velio process is also a downward drawing one. The large scale production of glass fiber for insulation and for textiles was another important twentieth century development. One of the puzzling facts of the early days of glass technology was the high strength of fine fibers and this must have influenced attempts to exploit them. Reaumur, who attempted to convert bottles to glass ceramic about 270 years ago, also realized that sufficiently fine glass fibers would be capable of being woven. Some novelty fab-

17

rics of the nineteenth century used glass fibers interwoven with silk. The evolution of a separate branch of the industry devoted to fibers dates from the 1930s when the Owens-Corning company was established and has ever since been the leader in this field. Other important advances which have received little public attention include high quality dimensionally accurate pressing for television screen face plates, car headlight lenses and some optical components. The development of small tank furnaces, partly lined with platinum and using platinum stirrers, for the continuous production of very homogeneous optical glass also played a vital part in satisfying the needs of the optical industries. Optical instruments benefited from vigorous research into expanding the ranges of combinations of optical properties available in glasses. During the last twenty years this has been matched by advances in lens design resulting from use of computers. Previously lens design and the evaluation of aberrations depended on extremely tedious manual ray tracing for every modification envisaged. Computer ray tracing so accelerated the evaluation of lens designs that major improvements in performance have been realized in the recent past. A number of notable developments have come from the Corning research laboratories, the earliest being Pyrex borosilicate glass for laboratory ware and other purposes needing good thermal shock resistance or chemical durability. Some years later the Corning ribbon machine made possible the very large scale production of lamp bulb envelopes and Corning also developed a process for spinning television tube components. On a more scientific level the Corning laboratories saw the invention of optical wave guides (also devel-

18


oped by the STL laboratories in England); photosensitive glasses, the exploitation of which by S. D. Stookey and his colleagues led to glass ceramics (see McMillan, 1979) (see Vol. 11, Chap. 4 of this series); photochromic glasses and more recently polychromatic glass which can have multicoloured images developed in it. Another Corning success was the exploitation of phase separation in borosilicate glasses to make Vycor which is produced by making and forming an easily melted alkali borosilicate glass then heat treating it to cause phase separation. After that it is leached in acid to leave a microporous skeleton of almost pure silica which can be fired again to densify it. This makes possible the manufacture of some articles very difficult to form when working directly with pure silica. It also provides microporous structures for other applications. The last two decades have seen the need for glasses with much smaller transmission losses than previously imagined to be feasible, for use in optical communication systems and this has been one of the most fruitful research and development fields (see Chap. 15). This has led to the development of halide glasses made in systems never before considered capable of producing glasses or worth investigation (see Chap. 8). Subsequent developments have led to studies of other possible optical communication devices including optical switches and amplifiers; this has encouraged detailed studies of glasses with nonlinear optical properties (see Chap. 12). Glasses are usually good electrical insulators but can be made with a very wide range of electrical properties including semi-conduction and fast ion conduction. The most exciting discovery of the past few years in the ceramic field has been 'high temperature' superconductors, meaning those which superconduct at liquid nitro-

gen temperatures. This property depends on a particular type of crystal structure and there is no sign that glasses can show such behavior. However, it has been shown that such superconductors can be made as glasses and then converted to the crystalline superconducting form by the usual glass-ceramic techniques (Zeng et al., 1989). Where this can be done it is much simpler than the usual ceramic techniques of preparation.

1.2 Choice of Glass Compositions Choosing a glass composition is a more complicated exercise than may at first appear. One must first establish the properties important to the final user, next consider those properties important to the glass maker, then achieve a balance between these and lastly determine what choice of batch materials will produce either the best quality or, perhaps, the cheapest glass meeting the quality requirements. Table 1-1 gives some examples of the range of compositions used for various purposes. 1.2.1 Properties Important to the User

Many glass properties vary fairly smoothly with composition across a considerable range. The user of a glass for any particular purpose therefore wishes to choose the glass which will be the best for his application. This requires decisions about the most important properties and a search for the glass coming closest to the desired values. Which properties are important depends very much on the application. From a designer's point of view, strength would nearly always be the first to be considered. However, because the practical strength of glasses is determined more by surface flaws than anything else,

19

1.2 Choice of Glass Compositions

Table 1-1. Typical glass compositions (wt.%). Type of glass Containers Mid 19th C bottle Mid 20th C bottle Late 20th C bottle Pharmaceutical Ampoule Ampoule Flat glass Float (UK) Fourcault sheet Lead crystal English European Laboratory ware Pyrex Kavalier Vycor As melted After leaching Sealing glasses Molybdenum Tungsten Fibers E glass Textile Mineral wool C glass Incandescent lamp Envelope Pinch Pinch Sodium vapor lamp Inner coating Inner coating Inner coating Outer casing

Na 2 O

K2O

CaO

MgO

ZnO

BaO

PbO

4.7 14.5 13.5

0.9 0.3 0.4

20.5 9.9 11.0

5.4 0.3 1.5

0 0 0

0 0 0

0 0 0

4.4 1.0 1.0

0 0 0

62.5 73.7 72.3

9.0 12.8

3.0 0

0 3.9

0 1.1

0 2.3

6.5 0

0 0

9.0 8.1

8.0 1.4

64.5 70.2

13.0 12.3

0.6 0.7

8.4 8.8

3.9 3.6

0 0

0 0

0 0

1.0 1.8

0 0

72.6 72.1

5.1 1.0

7.2 14.9

0 0

0 0

0 0

0 0

30.0 24.0

1.0 0.1

0 0

56.5 60.0

4.1 7.6

0.5 7.7

0.3 7.4

0.2 0.3

0 0

0 0

0 0

2.2 0.6

11.9 0

80.8 76.4

6.6 0.2

0 0

0 0

0 0

0 0

0 0

0 0

3.5 0.8

26.9 4.0

62.7 95.0

4.8 4.0

0.7 1.8

0.9 0

0 0

0 0

4.6 0

0 0

4.8 2.0

8.4 16.9

75.5 75.3

0.5 1.0 3.5 8.5

0 1.1 0

19.0 18.0 10.4 14.0

3.5 4.5 10.3 3.0

0 0 0 0

0 0 0 0

0 0 0 0

15.0 14.6 13.5 4.0

7.0 7.4 0 5.0

55.0 54.3 45.6 65.0

16.3 12.9 5.1

1.0 0.9 7.2

5.5 0.4 0

3.4 0 0

0 0 0

2.0 0 0

0 22.6 30.0

1.4 0.5 1.0

0 0 0

70.3 61.8 56.5

14.0 6.5 0 15.0

0 0 0 1.0

6.0 10.0 5.0 6.4

0 0

0 0

0 0 10.0 2.3

0 0

24.0 23.7 32.5 1.5

48.0 37.0 24.0 0.5

8.0 22.6 0 69.1

0

0

3.7

0

0 0

A12O3 B 2 O 3 SiO2

Other

Fe 2 O 3 SO3 SO 3

SO 3 ,Fe 2 O 3 SO 3 , Fe 2 O 3

F2 15.5Fe 2 O 3

28.5 P 2 O 5

Totals may be less than 100% because of rounding off or omission of some minor constituents (e.g. refining agents or decolorizers).

strength can generally be taken to be weakly dependent on composition and omitted from the specification. So far as strength is concerned commercial glasses can usually be considered as being either pure silica or "the rest" and only two sets of strength data need be considered.

The next most important property, which may not always come immediately to mind, often is resistance to corrosion. Good glasses are generally stable, already being oxides, but can be leached by water or other chemicals, something which is only rarely desirable. Chemical durability

20


is strongly dependent on composition, especially alkali and alumina contents, and thus should always be included. Next we come to the properties essential for the specific application. These may include refractive index, electrical resistivity, thermal expansion, transparency to or absorption of radiation, softening temperature, and so on. These properties fall into two classes, those for which a specific value is needed, like refractive index in an optical glass or thermal expansion for a sealing glass, and those that need to be better than some particular limit, like chemical durability or thermal expansion when thermal shock resistance is important. 1.2.2 Properties Important to the Glass Maker

Apart from the criteria set by the final user, several properties are very important to the glass manufacturer. The viscositytemperature characteristic is crucially important to efficient forming; Fig. 1-6 shows

1

1

I

i

|\

1

\

-\

1

1

1

|

1

1

1

1

1

\

AA

\

\

\2

\3

10

\

A

- y 5

1 500

•

\

^

:

:

k I

1

i

I

1000

I

1

I

i

i

1500

i

i

i

i

2000

Temperature in °C

Figure 1-6. Viscosity-temperature relations for some common types of glasses. 1) vitreous silica, 2) a glass for fibers, 3) a container glass, 4) sodium disilicate, 5) lead crystal.

some typical viscosity curves for different types of glasses and shows that a wide range of working temperatures can be required. Also the liquidus temperature must be below the temperature at which the melt must be held to begin forming operations. The actual devitrification characteristics may be less important but it can be useful to know whether crystal growth may be rapid if it does occur. The glass manufacturer also wants to have a glass as easy as possible to melt, refine, and homogenize but these factors are not capable of being specified in terms of standard properties. Some glasses contain significant proportions of elements which can exist in more than one valence state and these may need their oxidation states to be controlled. The most familiar example is the decolorizing of glass in which iron is oxidized, as far as possible, to the ferric state which gives a paler tint than the same concentration of iron reduced to ferrous. On the other hand, to make a heat absorbing glass one would wish to reduce the iron to ferrous which has a broad absorption peak in the near infrared. Control of oxidation is generally achieved largely by the selection of oxidizing or reducing materials added to the batch but partly by control of furnace atmosphere. In small scale laboratory melting oxidation can be controlled by bringing the melt to equilibrium with a specific atmosphere but this is not necessary and would be difficult to achieve in large scale manufacture. The batch materials can considerably influence ease of melting, degree of segregation during melting, volatilization losses, refining, and homogeneity of the glass. Both control of oxidation and overall melting performance can also be affected by minor constituents, that is to say cations or anions added at levels usually below 1%, which control oxidation through mutual


interactions or have beneficial effects on melting, refining, and homogeneity. The interactions between iron and arsenic, antimony or cerium can play an important part in decolorizing. Sulfate is the most commonly used refining agent: arsenic is often efficient but now rarely used because of legal controls on its use and halides can be effective. The glass maker will usually expect to be allowed to modify slightly the user's composition specification to optimize these factors. 1.2.3 Choice of Glass Composition Taking account of all the properties referred to above can easily produce a list of ten or more factors important to either the user or the glass maker. Finding a glass to satisfy all these requirements may not be easy. However, the task is easier if only some of the properties need to have specific values and the others need only to be within some given limit. The number of constraints to be met is the most important reason for the complexity of most commercial glasses many of which contain at least six major constituents: soda, potash, lime, magnesia, alumina, and silica. It is in fact gratifying that so many different glasses can be made without requiring a much longer list of constituents although most of the elements have some specific use. The most commonly used other oxides include Li 2 O, ZnO, B 2 O 3 , BaO, and PbO. If one tries to select a glass from a binary system only two degrees of freedom are available: 1) which particular system to choose (e.g. Na 2 O-SiO 2 , K 2 O-SiO 2 or Li 2 O-SiO 2 ) and 2) the specific composition. The composition may be chosen so that one property, such as thermal expansion coefficient, has the desired value but all other properties are then already fixed. If a third component is added it becomes

21

possible to keep the same thermal expansion but adjust composition to match one more property. With a four component glass three properties can be matched, and so on, see Fig. 1-7. Looked at formally it may be seen that trying to match a particular set of n properties requires n degrees of freedom or, since every composition must add up to 100%, n + 1 components. If the number of constraints exceeds the degrees of freedom it is impossible to satisfy all the desired requirements. In that case it will be necessary to accept a compromise. Choice of a glass composition used to rely heavily on the glass technologist's experience and intuition, requiring first the selection of a composition, then checking its properties, then making another guess and repeating the process until the desired result was obtained: this could be a tedious process. Any exercise of this

Figure 1-7. Property value surfaces for two different properties (Y and Z) in a four component system (A-B-C-D). All compositions along the line XX have the same values of Yand Z; a third property can also be matched by choosing a particular composition along this line.

22


kind is made much easier if models exist to describe the relations between properties and composition. This can clearly greatly reduce the number of steps needed and the necessity for numerous trial melts and measurement their properties. 1.2.4 Composition-Property Relations

Most research on composition-property relations has been restricted to systems with no more than three components. The major exceptions have been when an investigation was undertaken with the intention of producing a model for predicting properties from composition. Several factors have influenced this; the most important are the scientist's normal wish to work with as simple a system as is worth investigating and the difficulty of representing data for more than three components in a two dimensional diagram, as illustrated just above. The latter was a very serious problem before the ability of computers to work in multi-dimensional space was exploited. This is clearly seen in the invaluable comprehensive collection of composition-property data assembled in six volumes by Mazurin and his colleagues (1973-1981), which is limited to three components. Some of the problems of dealing with more complex glasses can be appreciated by consulting books such as Volf (1961) where much insight into the reasons for the complexity of several types of glass may be obtained but information on the specific effects of various individual components helpful in designing a new glass may be sparse. One of the most familiar examples of developing new compositions to solve manufacturing problems is sheet glass. The upward drawing of sheet glass was first brought into production by Fourcault during the first World War. Because of the

inherent instability of drawing a flat sheet, these processes have very strict requirements for viscosity in the drawing chamber and the rate of cooling of the sheet. As a result the soda-lime glasses originally used had to be held very close to their liquidus temperatures and were subject to devitrification. This remained a serious problem for some years. Eventually it was discovered that partial replacement of lime by magnesia greatly alleviated the problem by somewhat lowering liquidus but also giving much slower crystal growth. The classic work on the subject is by Swift (1947), see Fig. 1-8. Ever since then flat glass compositions have contained about 8% CaO and 3.5% MgO. Another important problem concerned the glass used in electric lamp bulbs through which the wires carrying the current are sealed. This glass must have suitable thermal expansion for sealing to the wires, appropriate softening point and

1000 Temperature in °C

Figure 1-8. Devitrification characteristics of flat glass compositions with 0, 2, and 4% MgO. Full lines are for devitrite and dashed ones for cristobalite; after Swift (1947).


good electrical resistivity up to at least normal lamp operating temperatures. The second requirement implies a glass of fairly high soda content but this clashes with the third. Using a lead glass similar in composition to English lead crystal met those requirements and far more glass of this type is today used in lamps than for making decorative products. 1.2.5 Models for Composition-Property Relations

Most experimental work has obviously led to data allowing the prediction of properties from the composition. Fortunately simple additive equations are quite successful for several important properties over the range of compositions most often used. Much effort was devoted to such work by a number of pioneer glass technologists; one of the oldest such investigations being that of Winkelmann and Schott (1894). Such models are entirely empirical and often of unknown accuracy and limited validity. Properties for which there are widely accepted models of this kind include thermal expansion, room temperature density, refractive index, Young modulus, Poisson ratio, dielectric constant, surface tension, specific heat, and thermal conductivity. One of the most attractive features of Scholze's (1977) well known book is the inclusion of a considerable number of these models and some comparisons of their predictions and ranges of validity. The classic models nearly all assume that a property is a simple linear function of composition and capable of calculation from an equation of the type X = Zaici

(1-1)

or = a0

a, ct

(1-2)

23

where X is the property value, a{ coefficients for each constituent and c{ the concentration of each constituent present. Concentrations are often expressed as weight percentages, which are generally the most convenient to use: in principle molar percentages ought to be better, especially when oxides of very different molar masses are concerned but, with linear approximations, the accuracy is not always improved by converting to moles. Sometimes, because m components give only m — 1 degrees of freedom, compositions are expressed by the ratios of the other constituents to the silica content when Eq. (1-2) must be used; the coefficient a0 then represents the notional property value for pure silica. If the regression analysis fitted the data very closely there would be no point in using more than the necessary number of coefficients; that is to say m — \. Sometimes, when the fit is acceptable but clearly not perfect, using m coefficients and having one more degree of freedom in the curve fitting exercise can yield a slightly better result. Before computers were available, processing the data and obtaining the best set of coefficients was a very tedious task and this clearly made the evaluation of complex models too daunting a task for most investigators. Occasionally the inverse of the property was found to give a better correlation but few other refinements were widely tried. It is unfortunate that present understanding of the structures of glasses still does not provide a more scientific basis for dealing with accurate composition-property relationships. The most important advances of recent years have been in the more sophisticated models and methods of analysis made possible by the development of computer hardware and software. One of the earliest useful attempts to work from

24


Their original measurements and analysis were restricted to a range of compositions including soda, potash, lime, magnesia, alumina, and silica but were later extended to include small proportions of several other oxides. In separate exercises they also dealt with lead crystal glasses (Lakatos et al., 1977, 1978, 1979) and glasses for insulating fibers (Lakatos et al., 1981). Geologists are interested in the viscosities of silicates, though not to the precision 1.2.5.1 The Viscosity-Temperature wanted by glass technologists; two interRelation esting papers on the estimation of viscosity It should be no surprise to find that visin systems of geological interest have been cosity has received more attention than published but, so far as is known, no one most other properties. One of the first athas compared their predictions with those tempts to produce a simple useful method already discussed. Bottinga and Weill was that of Okhotin (1954) whose work is (1972) reviewed viscosity data for a wide discussed by Braginskii (1973). range of compositions and pointed out the One of the most notable exercises has considerable scatter when plotted as In 77 been the work of Lakatos et al. (1972versus mole fraction silica (XSiO2) but 1981). They made their own set of very chose best fit straight lines for several segcareful viscosity measurements on a set of ments with boundaries at XSiO2 = 0.35, carefully selected glasses and then analysed 0.45, 0.55, 0.65, 0.75, and 0.81. They then the results. This work was initially inused a simple linear additive relation to tended only to cover a fairly narrow range estimate In 77 at 50 °C intervals from 1200 of compositions close to those used for to 1700°C for each of these ranges for containers and flat glass (Lakatos et al., 11 oxides (SiO2, TiO 2 , FeO, MnO, MgO, 1972 a) but experience has shown that it CaO, SrO, BaO, Li 2 O, Na 2 O, and K 2 O); can be extrapolated considerably outside alumina was dealt with in terms of six aluthe original field with reasonable accuracy. minate compounds of Na, K, Mg, Ca, Ba, Their particular success was to find that and Mn (e.g. MgAl2O4). They include a the constants A, B, and 67, a (SiO2) = 5.3 + 0.018 c (SiO2). Boric oxide: calculate cp as above and select as follows: l/(nD t)lj2, a2 = a2 + 2D[(C^-Ca)/Cs]t

(1-46)

or l/(7i D 0 1 / 2 M M a = a0 +

(2/T^2)D1/2

[(C*, - Ca)/Cs] t^2

have often been used; the latter can be cast into the same form as Jander's Eq. (1-21). The motion of the boundary changes the area through which mass transfer can occur and also distorts the concentration profile in the liquid around the bubble. A change in composition of the bubble means that concentrations of the various gases at the surface of the bubble also

52


change with time; this further complicates solution of a realistic model of the process. Adding surface tension for small bubbles and the fact that Sieverts' law rather than Henry's law may be needed to describe conditions at the interface for water vapour increases the complexities. These complications mean that numerical methods must be used to obtain valid results and this family of problems in diffusion-controlled bubble growth and dissolution have been studied in detail by Cable and Frade (1987a,b,c,d, 1988) for both one component and multi-component bubbles. Growth of a one component bubble from zero initial size must follow R = 2p(Dt)1/2

(1-48)

as shown by Scriven (1959), where R is the dimensionless radius and the growth rate constant is a function of, but not in general equal to, (CO0 — Ca)/Cs. This also represents the asymptotic behavior of a bubble growing from finite initial size and most bubbles closely follow this regime for R > 5. Dissolving bubbles, on the other hand, are always in a transient regime and the only valid simple approximation for one component dissolving bubbles applies only for very low solubility and is Ri = l-D[(C^-Ca)/Cs]t

(1-49)

Over most of the range of values of solubility the form of JR (t) is sensitive to the values of the parameters. Multi-component bubbles can show several interesting features. Bubbles which continue to grow will always eventually achieve a constant composition which can be estimated from the properties of the particular case. If the bubble initially had this composition it would behave like a one component bubble but one with any other initial composition can show com-

plex transient behavior. It may, according to the deviation from equilibrium bubble composition, initially exhibit either shrinkage or accelerated growth: it seems that only one change in the sign of dR/dt is possible with a given bubble but this is difficult to demonstrate rigorously. Multicomponent bubbles which eventually dissolve can show either positive or negative values of dR/dt at the beginning, for the same reasons as with growing bubbles, but do not generally tend to an asymptotic constant composition because they cannot achieve a pseudo-steady state. Although it is difficult to predict the details of behavior there are simple rules for deciding whether the initial value of dR/dt will be positive or negative and for deciding whether the bubble will in the end grow or dissolve (Cable and Frade, 1987 d). If the dissolved concentration of each gas i is defined in terms of Fi = (C — C (oo))J C s , gt(0) is the mole fraction of each gas initially in the bubble and oct is the Ostwald solubility coefficient for that gas, the initial sign of dR/dt will be the same as that of I = I.(Fo.t-*igi(0))

(1-50)

whilst its final behavior is controlled by S = ItFOti/ai

(1-51)

If S is positive the bubble will grow, if S is negative it will dissolve. The asymptotic composition of a growing bubble could often be determined experimentally but the solubilities, diffusivities and saturations of each of the gases involved will rarely be known with sufficient accuracy to make a theoretical prediction. However, the bubble must have the most mobile species tending to diffuse into the bubble as its major constituent. The observation that seed eventually become rich in nitrogen towards the end of refining cannot be attrib-

1.3 The Melting of Glasses

uted to bubble growth because nitrogen normally behaves like an inert gas of low solubility and diffusivity. Bubbles which become rich in nitrogen late in their lives must be dissolving, the other gases which find it easier to diffuse out leaving the bubble rich in nitrogen. This does not exclude the possibility that other bubbles grew because those may have risen to the surface and burst by that stage of refining. It is interesting that Cable and Frade (1987d) could not match the observed CO 2 ->O 2 -> N 2 composition cycle or any plausible set of values of solubilities, diffusivities and dissolved concentrations. The theory confirms the finding of Greene and his students that a tiny impurity content in the initial gas or a very small residual content of other gases dissolved in the melt can greatly retard complete dissolution of a bubble and shows that it is not easy to tell which of these factors has affected any particular bubble. The standard boundary layer model for freely rising bubbles was applied to bubbles in glass by Onorato et al. (1981), using plausible model values for the properties of the gases but there is again a lack of accurate data for these parameters and also for experimental data to which the model is known to apply. It is difficult to claim that our knowledge of refining glass melts is qualitatively clearly understood and only in need of data for solubilities and diffusivities to resolve all the problems. Why, for example, does it seem to be frequently true that too little refining agent makes refining worse and that too much also makes performance fall off again? This appears to be related to the rate of conversion from carbon dioxide to oxygen; with too little refining agent this is not observed to happen, with too much it is retarded. The usually accepted model, proposed by Otto Schott,

53

assumes a process such as (1-52) and that it tends to go further to the right as temperature falls so that the melt is supersaturated at the maximum melting temperature and less than saturated on cooling to near working temperature. However, this does not explain why refining agents function in isothermal melts. Nor does it account for the more rapid transfer of carbon dioxide out of the bubble than of oxygen in observed by Cable and Haroon (1970). Refining requires that the melt around a bubble can rapidly absorb or desorb a small amount of gas; this may not necessarily require an increased equilibrium solubility, a transient kinetic effect would suffice. 1.3.4.4 The Homogenizing of Glass Melts The discussion of melting reactions has made it clear that a range of liquids which vary considerably in density, viscosity, reactivity, volatility and other properties will be formed at different stages of melting. These must be mixed together to attain the degree of homogeneity required of most glasses. Differences in refractive index lead to optical distortion and, as a result, optical glasses must have higher standards of homogeneity than any other material made on a large scale. Differences in thermal expansion can cause considerable and increasing internal stress as a glass cools from the glass transition range which can make inhomogeneous glasses very fragile at room temperature and this implies high standards of homogeneity in many glasses where optical properties are not the most important. Likewise not all properties are simple additive functions of composition so that accurate and reproducible measurements of many properties need samples of good homogeneity.

54


Diffusive Mixing In the end mass transfer working at an atomic level must make glass composition as uniform as can be achieved. Although the classic Stokes-Einstein relation between viscosity and diffusivity > = kBT/(6nrjR)

(1-53)

applies only to liquids comprised of large spherical molecules of radius JR, not to typical glass melts, it is sufficient to show that mass transfer diffusivities are very low in glass melts even at melting temperatures. Effective diffusivities for mass transfer are strongly dependent on both composition and temperature; values will not often exceed 10~ 1 0 m 2 s~ 1 . Unaided diffusion will require extremely long times to homogenize a viscous liquid. If an inhomogeneity could be represented as a slab of thickness 2 /, with a concentration of solute C o , immersed in a large bulk of material with uniform concentration C^, its centre concentration would decay with time according to

Table 1-6. Dimensionless times for the decay of concentration at the centre of inhomogeneities of thickness or diameter 2 /.

OAAC0 Isolated: Slab Cylinder Sphere Regular array: Alternate layers

-erf(//2(Dr)

)

(1-54)

If it were a cylinder the radial diffusion would proceed rather faster according to C(0) = 1 - e x p ( - l2/(4Dt))

(1-55)

if it were a sphere the result would be 12

C(0) = erf 1/2{Dt) ' - (2/^/n) (1/2 JDt) • •exp(-/ 2 /(4£>£))

(1-56)

All of these involve the dimensionless time Dt/l2 which shows that real time is inversely proportional to diffusivity and directly proportional to square of size. Table 1 -6 shows the predicted times for the maximum concentration to decay to a tenth and a hundredth of its original value for these cases. It can be seen that the geome-

0.05 AC0 0.01 AC0

31.67 2.37 0.854

126.8 4.87 1.42

3185 24.87 4.34

1.031

1.31

1.97

try has a very significant effect; a point which is reinforced by imagining that the flat slab has been stretched and folded numerous times to make a laminar structure with alternate layers of the two compositions. If these layers are assumed to be of equal thickness the dimensionless concentration is given by (-i)n (1-57) exp

1/2

2

Time (Dt/l ) to decay to:

Type of inhomogeneity

Dt

-

Jf2

cos

2/

and the concentration on the centre line of a layer by C(0)=^ exp

Dt

Jl2

(1-58)

This series converges rapidly for (Dt)/l2 >0.2; for short times the following is more convenient, ,. ^_Q.

Figure 1-22 compares the rates of decay of the central concentrations in an isolated layer and in one in a regular array: the


advantage of the latter is clear. The decay of the latter is much quicker for two reasons: 1) the maximum distance over which diffusion must occur is greatly reduced and 2) stretching and folding that layer p times to make one layer of thickness 2 / into a series of layers each of thickness only 2 l/p brings an extra advantage. These relations make clear that there are only three ways in which homogenizing by diffusion can be accelerated: 1) by increasing diffusivity by raising temperature, 2) by decreasing duffusion distances and 3) by decreasing the initial concentration difference which must be reduced. The first of these can only be achieved by raising temperature, which is only possible within specific limits; the second is the most attractive and achieved by stirring; the third is very important but often forgotten in general discussions; choice of batch materials and melting schedules can be very influential here. Preventing the development of inhomogeneity is better than trying to cure it afterwards.

1

102

10

10 3

2

Dimensionless time, Dt/I

Figure 1-22. Predicted decay by diffusion of the centre concentration for a single slab of inhomogeneity of thickness 2 / embedded in a melt and for a layer in a regular array of alternate layers and glass matrix each of the same thickness.

Convective Mixing Glass melts are sufficiently viscous for flow to nearly always be governed by viscous drag and so in the laminar flow regime. This is very convenient when wishing to describe and calculate flow patterns but the predictability of the flows implies that the degree of randomness required for good mixing is difficult to achieve. However, as is shown below, simple shear can assist homogenizing of viscous liquids. It can redistribute inhomogeneities on a large scale by convective flow so that diffusion distances are decreased and in doing so individual inhomogeneities can be dispersed, stretched and made thinner. Three cases need to be examined. The Deformation of Homogeneous Inclusions A homogeneous inclusion is one which is assumed to have the same viscosity as its surroundings although differing in other properties. Its deformation is thus a relatively simple exercise in analysis of flow patterns. The most useful model to consider is steady laminar flow with a constant velocity along a straight flow path but a velocity gradient at right angles, such as will occur in flow along a rectangular open channel. The inhomogeneities that concern us are generally much thinner than the overall body of fluid and it is reasonable to assume that the local velocity distribution is represented by a straight line although, in many cases, this will be part of a parabola. Consider a rectangular element of length / lying at an angle a0 to the direction of flow. Its two ends will be moving at different velocities so that it is stretched out and rotated, see Fig. 1-23. This model has been evaluated by several authors including Mohr (1960), McKelvey (1962) and Cooper (1966a,b).

56

1 Classical Glass Technology h cot a.

Ght

Figure 1-23. The geometry of deformation by simple shear of a layer initially lying at an angle <x0 to the velocity vector U.

The most important facts are that the layers are rotated to become almost parallel to the direction of flow but that the rate of stretching approaches zero as this occurs. For the two dimensional case where the velocity vector U lies along the x axis and dU/dx = 0 but dU/dy = G and the liquid is assumed incompressible, this leads to

large amounts of shear may be required merely to make these the same thickness as they were to start with. However much shear is applied there will always be a narrow range of angles for which matters will be made worse but sufficient shear means that these will occur infrequently. Of course, with almost perfect laminar flow, acceleration of the flow will attenuate inhomogeneities in an easily predictable way. The simplest way of achieving this is to make the melt flow through a reduced cross section, such as the throat of a furnace or the orifice of a gob feeder, when all the constituent parts of stream will be reduced in the same proportions as the cross section of the whole flow. However, if the stream expands again, as on exit from the throat, little may have been achieved. Unfortunately this is not likely to assist diffusive mixing very much because of the short

(1-60) b _ 1 Yo ~ [1 + G t sin 2 a 0 + G2t2 sin2 a o ] 1 / 2 Note that only the product Gt, the total shear, appears and neither of these variables is itself important. Some of the predictions of this equation are shown in Fig. 1-24. The decrease in thickness with amount of shear is roughly a double exponential of G t for favorably oriented layers and a factor of ten reduction in thickness is easily achieved but a factor of a hundred is hardly possible. If attenuation by a factor of more than about twenty is required, it is necessary to change the flow pattern and the orientation of the layers relative to the velocity vector. Note particularly that some layers in a randomly oriented array will be compressed rather than attenuated;

0.01 0

20

40

Total shear, Gt

Figure 1-24. Predicted changes in layers of initial thickness b0 by simple shear for a range of initial orientations according to Eq. (1-60) which ignores differences in viscosity.

57


Deformation of Inhomogeneous Inclusions Here this term means inclusions which differ in viscosity from their surrounding matrix. Most inclusions in glass will fall into this category. A rigid inclusion would not deform at all although it would rotate, so intuition rightly suggests that a more viscous inclusion should deform less than one of low viscosity subject to the same stresses. This problem can be elegantly treated by a method devised by Eshelby (1957, 1959) to deal with elastic inclusions which he kindly demonstrated to the author in 1968. By this method a simple relation can be deduced to describe the difference in deformation of a homogeneous two dimensional inclusion and an inhomogeneous one when both have been subjected to the same (but unspecified) amount of shear. Since deformation may be large it is defined in terms of the natural strain 5 f

d a

1

a = In s= J—

(1-61)

flo

The other parameter introduced is the relation between the two viscosities defined by * = (*1i-*iM)/tiM

(1-62)

where the subscripts refer to the inclusion (i) and the matrix (M). The relation between the deformation of the inclusions in the two cases is given by s a +(A/2) tanhs a = :

(1-63)

where sa is the elongation of the longer axis of, for example, the cross section of a long cylinder being deformed at right angles to its major axis, and saH is the deformation in the homogeneous case (k = 0). For the two

dimensional case and an incompressible liquid, the minor axis of the inclusion must decrease by the same factor as the major axis increases. Figure 1-25 shows how viscosity affects deformation according to this model; it can be seen that an inclusion of lower viscosity deforms rather more than a homogeneous one but increasing viscosity soon causes a considerable decrease in the deformation. This analysis is best used in two steps; the model in the previous section is used to obtain an explicit relation between shear and deformation for the homogeneous case and Eq. (1-63) used to determine the difference in deformation between the homogeneous and inhomogeneous cases. One important inference to be drawn from this is that any furnace will be unable to deal with inclusions significantly more viscous than those that usually occur; feasible changes in furnace operating conditions are likely to have very little effect: only removing the source of the viscous inclusions will cure the problem, Three dimensional inclusions were studied by Bilby et al. (1975) and Howard and Brierley (1976); the general features of these are very similar to Eshelby's original analysis. 1

fB '

J

I -J

I

I

^° w

8

£ o

x

\ \ \

0.1

1

1

-

X

\2 0

0.01 -

6

\

^

\

wNX

S\

\

\

\

0.002

1

1

i

0.1

l

l

'

20

\

X

CD O>

|

1

•

- — — .

in th

residence time in the narrow part of the system. The combined effects of shear and reduction in cross section were discussed by Rhiel (1976).

1

1

10" 2

\k

\

\ \ \

I 10" 3

i ^X

i

10~ 4

b/bQ for homogeneous case

Figure 1-25. Results of Eshelby's analysis of the difference in deformation of homogeneous and inhomogeneous (in the sense of viscosity) elliptical inclusions subject to simple shear; values on the diagram are viscosity ratios, see text.

58


Deformation Limited by Surface Tension Both of the above models assume that inclusions are, in principle, infinitely deformable and that only the total shear G t affects the result. This is not true when an interfacial tension exists, as is the case with gas bubbles. Here there is a discontinuity in pressure and normal stress at the interface because of the additional pressure which is given by Ap = - S i - O - S i + ROH The escape of residual products from closed pores may constitute a problem; the organic residues are finally carbonized at a higher temperature which brings about a coloration of the gel and leaves carbonaceous particles in the glass. It is therefore important to favor the escape of residues

2.7 Solution Methods; "Sol-Gel" Processing of Glasses

before complete closure of the pores, and oxidation treatments are often necessary to eliminate certain organic groups. For pure SiO2 gels this oxidation treatment is carried out at 300-400 °C. It is important to define the heating schedule in each particular case in order to eliminate the unwanted residues without impairing monolithicity before the onset of viscous flow. Occluded OH groups and H 2 O may cause bloating on heating at high temperatures - even if the specimen has remained monolithic up to this stage. Residual OH groups may be eliminated by chlorination treatments if very low OH levels are required in the final glass (e.g., for optical fibers applications). On the other hand, occluded water may be used in foaming processes, e.g., in blowing gel particles into microspheres (see Sec. 2.7.5.4). 2.7.4.1 Viscous Flow Sintering

Densification is essentially a sintering process by which the pores of a dry gel are eliminated, and the initially opaque material progressively converted into clear bulk glass. After elimination of residues, the driving force in this process is supplied by the surface energy of the porous gel. This tends to reduce the interface, thus eliminating the pores, the collapse being governed, in the case of glasses, by Newtonian viscous flow. Extra pressure, as in hot-pressing techniques, may be applied externally to speed up the process (Decottignies et al., 1978). The theoretica aspects of sintering are presented in Chapter 3 of this Volume.

111

tween phenomena which lead to densification and those which promote crystallization. The TTT (time-temperature-transformation) diagrams are a convenient way of studying the problem of devitrification versus compaction in order to define the appropriate thermal treatment (Zarzycki, 1982 b). The TTT diagrams show the time ty required to obtain a determined crystallized fraction y as a function of the temperature T. Treating y as a parameter, a set of Cy curves is obtained which represent the kinetic behavior of the system. In particular, if y0 corresponds to the smallest crystallized fraction detectable by analytical techniques, the curve Cyo represents a frontier not to be crossed during a thermaltreatment schedule if crystallization is to be avoided (generally y0 = 10 ~6 is adopted, see Chapter 3). The relative positions of the thermaltreatment path during densification and the Cyo curve of the gel determine the possibility of obtaining glassy or crystallized materials at the end of the compaction program. For example, (Fig. 2-21) if there is no danger of devitrification using path (a) for

2.7.4.2 Devitrification Kinetics Use of TTT Diagrams

During densification crystallize (devitrify) at successful conversion therefore depends on

the gel will tend to the same time. The of gel into glass a competition be-

Time Figure 2-21. Use of TTT diagrams for determining sintering heat treatment without crystallization (from Zarzycki, 1982 b. Reprinted by permission of the American Ceramic Society).

112

2 Special Methods of Obtaining Glasses and Amorphous Materials

a gel corresponding to Cl9 this will no longer be true for the curve of C 2 , the same path would lead to crystallized material. The solution would then be either to shorten the sintering time, e. g., by applying a suitable external pressure (path (b)), or to increase the temperature for a short time using the technique of "flash-pressing" (path (c)). In the case of gels the position of the curves C strongly depends on the impurities of the material and, in the first instance, of water content which influences the viscosity, as well as the surface energy of the material. 2.7.5 Forming Processes In the classical process, the resulting melt is generally immediately formed into the desired end products: sheet glass, hollow ware, or fibers. In sol-gel technology the various forming operations have to occur before or during the gelling stage (e.g., molding an object, forming a thin coating, or spinning a fiber); the drying-curing and sintering stages simply consolidate the original shape produced at low temperatures (Fig. 2-11). The nature of the processes during gelling and subsequent drying, which are of a diffusional nature, favors, however, those configurations in which at least one of the dimensions is small: Thin films, fibers, and small particles (or shells) are current examples, and it is significant that the first established industrial applications of the sol-gel route were precisely in the field of thin coatings. 2.7.5.1 Bulk Glass It is possible to produce bulk pieces of glass if cracking of gels during drying is avoided. This problem of obtaining monolithic gels has been extensively studied in

recent years - hypercritical solvent evacuation and drying chemical control additives (DCCA) have proved effective against cracking. In the laboratory, pure SiO2 glasses, as well as those combining SiO2 with other oxides (e.g., B 2 O 3 , TiO 2 , GeO 2 , P 2 O 5 , ZrO 2 , etc.) were successfully prepared. Glasses containing oxides of alkali and alkaline-metals sometimes prove more difficult to obtain because of the tendency of gels to devitrify during the sintering stages. The difficulty linked with monolithicity can be avoided if hot-pressing techniques are used to compact gels in a granular form; this, however, limits the size of the specimens. In industrial practice the early attempt in 1970 by Owens-Illinois (USA) at commercializing bulk gel-made glass was discontinued because of the high cost. However, the manufacture of sizeable glass pieces of pure SiO2 for optical applications has been reported (Hench, 1986). Advanced glasses for optical-fiber preforms (SiO2 doped by GeO 2 , P 2 O 5 , or B 2 O 5 ) have been successfully made, but the corresponding industrial applications have not yet followed. 2.7.5.2 Thin Films At the present time, the main industrial applications recognized for sol-gel methods are in the production of thin glass coatings by Schott Glass (FRG). They use the alkoxide method to modify the spectral transmission of flat glass for architectural applications (Schroeder, 1969; Dislich, 1971, 1988). In the method of dip coating (Fig. 2-22), a sheet of glass is first immersed in a tank containing a dilute solution of suitable alkoxide precursors and then slowly withdrawn at a constant rate. This leaves a superficial film of equal thickness which is then reacted with water vapor from the

2.7 Solution Methods; "Sol-Gel" Processing of Glasses

surrounding atmosphere to induce hydrolysis and polymerization. The glass is then dried and baked in an oven at ^500°C; successive layers of several hundred angstroms may be applied up to a total thickness of « 3000 A, Thicker films tend to craze or peel away. Other methods consist in applying an even initial liquid film by spinning (e.g., for optical components of circular shape) or spraying. Solar reflective TiO 2 coatings containing Pd or Au are manufactured by these methods. Antireflective coatings, contrast-enhancing coatings and protective coatings for optical surfaces against laser damage as well as electrically conductive layers have also been produced in this manner (Mukherjee and Lowdermilk, 1982; Dislich, 1988; Pettit et al., 1988). An interesting application of thicker solgel films of about one micron, which may be superficially patterned by pressing, is reported for the production of supports for recording disks for audio-visual purposes (Fig. 2-23), (Tohge et al, 1988).

7"~5OO°C

Glass sheet Film -=

H20 Vap. ROH Vap.

(a)

W////////////////M*--Gel

113

film

2 (t) is a function that can be represented by a sum of exponential terms or the KWW function. Corsaro (1976 a) showed that the dilatational relaxation of B 2 O 3 could be described by using the KWW function for (j)2 (t) with j8 = 0.60. The final strain was about three times greater than the instantaneous elastic strain, J2(ty/ j 2 (oo) = 0.30. He further showed (Corsaro, 1976 b) that, because of the nonexponential nature of the relaxation, the crossover effect (discussed in Section 3.4.1.5) could be produced by subjecting a sample to a series of pressure jumps. Since the dilatational modulus relaxes to a substantial fraction (typically ~ l / 3 ) of its original value, while the shear modulus goes to zero, it is not surprising that the relaxation of uniaxial or biaxial stresses is dominated by the shear behavior. For example, for a material whose shear response is given by Eq. (3-88) and which exhibits no dilatational relaxation at all (J 2 = 1/3K), the response to a constant uniaxial strain &z is (Scherer and Rekhson, 1982 a) (3-96)

Thus, shear deformation allows the uniaxial stress to relax to zero even though the stress is partially hydrostatic. The uniaxial relaxation time, TU , exceeds the shear relax-

159

(3-97) where x is an average relaxation time. If Gx is given by Eq. (3-92) (3-98) k =1

and if Gx is given by Eq. (3-93) (DeBast and Gilard, 1963), (3-99) where F is the gamma function. Comparing Eqs. (3-86) and (3-97) we see that the Maxwell relaxation time is the average relaxation time for the glass. Indeed, experimental studies confirm that the viscosity obtained from direct measurements (i.e., in creep experiments) agrees with the values found by integrating stress relaxation data, according to Eq. (3-97). Comparing Eqs. (3-38) and (3-97) we see that the structural relaxation time and the stress relaxation time are proportional to one another, but experiment (Rekhson, 1975) indicates that Kp is about an order of magnitude smaller than G, so stress relaxation is a much faster process. This is what makes it possible to measure the isostructural viscosity (Mazurin et al., 1979): a measurable amount of creep occurs before structural relaxation produces a significant change in 7^.

160

3 Glass Formation and Relaxation

From Eqs. (3-84) and (3-94) it can seen that the shear strain rate in a creep experiment approaches the limit (3-100) If the applied stress is uniaxial (as is typically the case) rather than pure shear, the corresponding relation is At

3rj

(3-101)

Thus, the viscosity can be measured from the slope of a plot of strain versus time; it is only necessary to wait until the delayed elastic strain is fully developed. Oxide liquids exhibit Newtonian viscosity, which means that the viscosity does not depend on the magnitude of the stress that is applied. This also means that the relaxation time governing stress relaxation and creep is independent of the applied stress, so oxides are linearly viscoelastic. This is in contrast to the nature of structural relaxation in the same materials: the rate of structural relaxation depends on the size and direction of the temperature jump; the stress relaxation rate is the same for tensile or compressive stresses. Actually, this is only approximately true: if the stress is large enough to affect the structure of the liquid significantly, nonlinear effects appear. However, the stresses required to produce nonlinearity are large: for a soda-lime-silicate glass it can be shown (Scherer, 1986 b) that a pressure of 12MPa is thermodynamically equivalent to a temperature change of 1 °C. Nonlinearity is evident following temperature jumps of ~ 5 °C, so the same should be expected under applied pressures >60MPa. Indeed, Simmons et al. (1982) found non-Newtonian behavior under tensile stresses of that magnitude. Li and Uhlmann (1970) showed that alkali silicate

glasses exhibited non-Newtonian behavior under shear stresses exceeding ~ 100 MPa. In both cases, the viscosity decreased by an order of magnitude or more. This is consistent with molecular dynamics calculations which indicate that catastrophic changes in the structure of liquids occur under high stresses: the atoms arrange into layers that slide relatively easily. Particularly interesting effects are observed under purely hydrostatic loads. It is expected (intuitively, and particularly where the free volume model applies) that hydrostatic compression will increase the viscosity. However, Sharma et al. (1979) found that the viscosity of GeO 2 decreases under high compressive loads. It is known (Mysen et al., 1980) that network silicates exhibit this behavior when the average silicon atom has less than one nonbridging bond. Thus, highly modified networks, such as Na 2 O • SiO2 (with two nonbridging bonds per Si), show "normal" behavior (viz., rj increasing with pressure), but germania (with no nonbridging bonds) does not. This experimental result is supported by molecular dynamics calculations (Angell et al, 1982). 3.5.2 Temperature Dependence

The rates of relaxation and creep are strongly temperature-dependent. We first examine how the VE response varies in isothermal experiments at various temperatures, when the liquid remains in thermodynamic equilibrium during the experiment. Then we consider cases in which structural relaxation and stress relaxation occur simultaneously. 3.5.2.1 Equilibrium Liquid

Since the relaxation time is proportional to the viscosity, the rate of stress relaxation increases rapidly with temperature. For ex-

3.5 Viscoelasticity

161

and plot the data for T3 against log [t a (T3)], those data coincide with the other sets. In this way the shift function, a(T\ can be used to create a single master curve from all the data. This is possible for any materials whose relaxation function retains the same shape at all temperatures when plotted against \ogt. A material that exhibits this behavior is said to be thermorheologically simple (TRS). In terms of Eq. (3-92), TRS behavior is obtained when all of the relaxation times have the same temperature dependence (xk oc t] for all h) and the weighting factors

ample, if a constant shear strain is applied to a glass, the shear relaxation function varies with temperature as shown in Fig. 3-27. If the data are plotted against log £, as in Fig. 3-27 b, curves for different temperatures are identical in shape, but shifted along the abscissa. The distance, which we shall call log [#(71)], between points A and B is the same as that between points D and E. If the data for temperature 7\ are plotted against log t + log [a (T±)] = log [t a {T±)]9 they coincide with the data for temperature T2. Similarly, if we call the (negative) distance between points C and B log[a(T 3 )],

0.8

a)

25

1 0.8 0.6 2G

0.4 0.2 0

b)

0.001

0.01

1

i

i

0.1

1

10

log t

100

Figure 3-27. Shear stress relaxation function of thermorheologically simple material at several temperatures: a) relaxation rate increases with temperature; b) when plotted versus log t, the curves have the same shape, but are shifted along the abscissa.

162

3 Glass Formation and Relaxation

are constant [w k ^w k (T)]t. If the relaxation function is represented by Eq. (3-93), TRS requires that the exponent /? be independent of temperature. In either case, the shift function represents the temperature dependence of the average relaxation time, (3-102) where, Tr is the reference temperature, the temperature of the data set onto which all of the others are shifted. In relaxation studies it is conventional to introduce the reduced time, (3-103) When T= TT, then £ = t; in general, £ is the time that would be required at Tr to relax to the same extent that occurs in time t at temperature T. Thermorheological simplicity was first noted by Leaderman (1943) in a study of organic polymers, and has been widely observed in oxides (see discussion in Scherer, 1986 b). It must be recognized that TRS is only approximately true: the distribution of relaxation times seems to become narrower at temperatures well above Tg. However, for oxides, TRS provides an excellent approximation at least within + 50°C of Tg, and this proves to be very helpful in analysis of thermal stresses, as we shall see in Section 3.5.3. 3.5.2.2 Nonequilibrium Liquid Hopkins (1958) pointed out that nonisothermal stress relaxation in a TRS mate-

t In principle, each of the relaxation times could have different temperature dependence and the weighting factors could change in such a way that the relaxation function retains the same shape. This seems improbable.

rial could analyzed by writing the reduced time in the form At1

= \a[T(t')]dt' (3-104) o

and replacing t with I; in the stress relaxation functions. During an isothermal test, £/T (Tr) = t/z; if T= Tr, then £ = t. This is an inescapable consequence of TRS of equilibrium liquids; however, it is not obvious that TRS will hold if the changing temperature causes the liquid to drift out of equilibrium. That is, the form of the relaxation function might change under nonequilibrium conditions. This proposition was tested in an ingenious experiment by DeBast and Gilard (1963), in which they measured structural relaxation and uniaxial stress relaxation simultaneously on the same sample. The equilibrium relaxation was found to obey a At)

MO)

- 650 °C, the parabolic temperature gradient is established without significant stress, and the maximum tempering stress is achieved; no tempering is possible if T 0 W{ ( 0 Wap za Z

neutron scattering length concentration of atomic species a distance between crystal planes with Miller indices hkl rc-dimensional energy atomic scattering factor reduced interference function pair distribution function vibrational density of states function reduced radial distribution function interference function intensity, nuclear spin radial distribution function photon or photoelectron wave vector Boltzmann constant modification function atomic fraction of species a coordination number, number of atoms number of constraints number of degrees of freedom running coordination number coordination number of j ' t h atomic shell P a i f correlation function between atomic species a and /? peak shape function phonon scattering vector scattering vector, modulus Q number of bridging oxygens (n) (around Si in this case) interatomic distance between atoms of species a and /? mean bond length of i'th shell radius o f / t h shell of atoms structure factor glass transition temperature melting temperature mean square displacement of atomic species i Debye-Waller factor for atomic species i weighting factor for atoms of species a and p electronic charge on atoms of species a atomic number

5 e X (k) , and standard deviation, a(r£), (and higher moments if necessary) of bond length, bond angle distributions and the number of neighbours - the coordination number. An ordered arrangement implies a narrow distribution of first neighbour distances and, ideally, an identifiable coordination number, Nc - rather than a continuous increase in N(r) with increasing r. Comparison with a compositionallyequivalent crystalline phase may show some correspondence between values for crystals and glasses and this can be taken as further evidence for ordering - although not necessarily for a crystallographic model of ordering. If the parameters for higher order neighbour shells can be extracted - and usually they can, with more difficulty, to second neighbours - then

•

i

1

Figure 4-15. a) Contrast transfer functions, T(Q), for 100 kV microscopes (dashed line) and 500 kV (full line) corresponding to a generalised defocus value of 3 1/2 . b) Structure factors for a-Pd4Si taken from neutron scattering data (full line) and X-ray data for a-Ge (dashed line) (Gaskell et al., 1979).

specimen potential and electron density. In terms of the interference function, i(Q), high resolution images contain information limited to the first peak in i{Q) for amorphous semiconductors and only the best microscopes have resolution extending to the first peak for amorphous metals, which have smaller d-spacings. With modern high resolution microscopes, the problems are no longer severe for the majority of amorphous solids with relatively large d-spacings. However, much of the older work in the literature needs to be treated with caution due to neglect of the effects of the aberrations in 100 keV microscopes operated at or beyond their limits of resolution.

212

4 Models for the Structure of Amorphous Solids

The second problem arises as a result of the effects of projection. Since the electron wave-function immediately after the specimen is a projection of the specimen potential over a column which is the thickness of the specimen, it becomes impossible to distinguish atoms that are, say, nearest neighbours, from those that appear to be at the same projected distance but in fact lie at the upper and lower edge of the foil and are thus separated by about 4 nm in the z direction. Moreover, ordered regions giving coherent Bragg diffraction, are unlikely to be larger than 2 nm in size so that there is at least as much material contributing information to the image which is either ordered but not Bragg orientated, or from a random matrix. The non-Bragg oriented material therefore contributes noise which significantly degrades the image. In practice, there is a third problem due to inelastic scattering which is especially prominent at low scattering angles and can submerge the coherently scattered electron intensity and thus further degrade the image. As a result of these problems, HRTEM has proved to be of only limited use in establishing the short-range structure of amorphous solids. It is important to recognise, though, that when the technique is used to complement diffraction studies, the information gained concerns the medium-range structure in the range 1 to 2 nm where diffraction methods are relatively powerless. Examples of the use of HRTEM will be discussed in Sec. 4.5.

4.3.8 Nuclear Magnetic Resonance In a strong applied magnetic field, Ho, the degeneracy of nuclear spin states is removed (Zeeman interaction). For nuclei with spin, /, the difference between the en-

ergy levels is given by:

E(m) = yhmH0

(4-27)

where, y is the gyromagnetic ratio characteristic of the nucleus and m is the magnetic quantum number. Application of exciting radiation results in a transitions between states with quantum numbers that differ by Am= ± 1, and the frequency at which this transition occurs depends, through y, on the excited nucleus. NMR is thus an element-specific structural technique. Sensitivity to the local environment of the nucleus comes from electrons near the nucleus which, by their motion, create small magnetic fields that add vectorially to // 0 , so modifying the local magnetic field at the nucleus. The nucleus can be said to be partially shielded from the external field by the electron distribution of the atom which, in turn, is determined by bonding interactions with neighbouring atoms. Since the electron distribution is, in general, non-spherical, the interaction is orientation-dependent, represented by a shielding tensor, a; the isotropic component being represented by the "trace" of the tensor: a{ = 1/3Tr(d) = 1/3(tT±1 +rik~r20 cos 90)2

(4-35)

where a and p are stretching and bending force constants, r0 and rtj are the equilibrium and actual internuclear distances between atoms / and j and 90 is the equilibrium angle jik. Lapiccirella et al. (1984) have introduced a more sophisticated version of the valence force-field - the LipsonWarshel PE function, in calculations of the structure and properties of a-Si and a-Ge (Tomassini et al., 1987).

4.4 Modelling Techniques

Molecular dynamics simulations using empirical potential energy functions have the drawbacks noted above. A method for removing this difficulty has been proposed and applied by Car and Parrinello (1985) and coworkers. In this approach, the interatomic potential is derived from the electronic ground state of the system calculated with accurate density-functional techniques. Specifically, the sets of atomic coordinates and electronic wavefunctions of the occupied states are both considered as dynamical variables, governed by equations of motion for electron and nuclei. The minimum energy state is obtained by following the "motion", as the temperature is reduced, by a process described as "Dynamical simulated annealing" to compare with the "simulated annealing" method of Kirkpatrick et al. (1983) (using MC formalism). The method is effectively parameter-free so that such ab-initio calculations can describe the "true" structure of an amorphous material given only the electronic properties of its atoms. Applications to aSi and a-C are considered in Sec. 4.5.

4.4.4 Energy Minimisation Models constructed by hand or by various computer algorithms lack realism in that bonds are strained, broken, or the coordination numbers are unrealistic. By calculating the potential energy - essentially the elastic strain energy of the structure and the gradient, atoms can be moved in directions that minimise the energy. After a relatively small number of iterations the model settles into the potential energy minimum in the local region of configurational space corresponding to the starting structure: the model becomes "relaxed", implying an increase in geometrical order.

219

The extent of topological ordering depends on the detailed algorithm. The method embraces a number of minimisation algorithms. A popular and easy method is the steepest-gradients method which involves calculation of the energy and the force on each atom. Each atom is then moved either a distance proportional to the force or to an estimated position of minimum energy (Steinhardt et al., 1974). Another method is the so-called "conjugate gradient" method which attempts to find the minimum in configuration space by searching in orthogonal directions at each iteration. Like MC calculations, the potential energy functions and derivatives are reasonably simple to compute so that with the Keating potential energy function the method is computationally cheap. Various sophisticated potentials have been devised for silicon, and carbon compounds and are only marginally more difficult to deal with.

4.4.5 Monte Carlo Calculations Models may also be generated and refined using variations of the Metropolis Monte Carlo method. An initial, essentially arbitrary starting structure is chosen usually with periodic boundaries. An atom is selected at random and given a randomly chosen displacement. The state of the system, as characterised by the energy or the fit to an experimental variable such as the structure factor, is then tested. The move is accepted if the goodness of fit is improved, rejected if not. A variant is that the move may be accepted according to a Boltzmann probability, exp(— AE/kBT) where AE is a measure of the goodness of fit - the decrease in energy, say, and kBTis a suitable scaling factor. Thus the algorithm allows the system to explore con-

220


figurations that initially may be unfavourable, so that the procedure helps to prevent the model becoming trapped in a local minimum of configuration space. The process is repeated until the fit to experiment is judged to have converged. The method has been used extensively in constructing models for amorphous metals, chalcogenides, amorphous semiconductors and oxides. It has the advantage that a relatively large number of configurations can be explored quickly and cheaply in computer time. Moreover, it is generally possible to use more realistic potentials so that difficulties introduced by pairwise potentials have not been so prominent in MC as in MD simulations. McGreevy and Putztai (1988) have revised a method similar to that used by Renninger et al. (1974) in which the criterion for guiding the approach of the MC computation is the quality of the fit to experimental scattering measurements alone. The energy is not considered. The authors point out that the amount of information normally extracted from experimental diffraction data is generally small and that a fitting procedure offers a more detailed idea of the real 3-D geometric structure. The authors are clear that while it appears that a 3-D structure has been extracted from 1-D S(Q) or G(r) information, this is strictly impossible and that the final structure is only one (of many, perhaps) that is consistent with the data. Evans (1990) has commented on the apparent contradiction that higher order functions such as the three-body distribution should be obtainable from structural knowledge that contains no more than pairwise information (see Sec. 4.3). Evans points out that a simulation could succeed for an amorphous solid for which the atomic forces are describeable solely by a pairwise potential. For materials with sig-

nificant three-body terms in the PE function, such as the covalently-bonded amorphous semiconductors, this need not be so. Although the pair distribution function, g(r), depends on three-body terms, this dependence is insufficient to determine, uniquely, any higher order correlations. If two- and three-body terms are present in the PE function then experimental g (r) and triplet correlation functions would be necessary. 4.4.6 Validation of the Model: Calculation of Microscopic and Macroscopic Properties

Given a complete set of atomic coordinates, it is then possible to calculate microscopic properties such as G(r), S(Q), or S(Q), even S(Q, co). With further assumptions, vibrational and electronic densities of states functions can also be computed as described below. Macroscopic physical properties are also accessible - density, enthalpy of crystallisation, free energy, entropy, elastic moduli, gas solubility, diffusivity etc. These are often neglected or deemphasized when checking the validity of a model, which is generally a mistake. It comes as a surprise to find that a simple property like density is sensitive to structural details that appear to evade comparisons with microscopic properties - particularly when the latter are used in a qualitative or semi-quantitative fashion. An accurate fit to the experimental density should be seen as an essential prerequisite for further consideration of the model, and failure to agree should lead to its demise. Density values may be built into a simulation as a constraint. When this is done, it follows from the foregoing that it is a rather strong constraint. The most useful properties are probably G(r) and S{Q\ combined with density and heat of crystallisation data. For reasons

221

4.4 Modelling Techniques

discussed earlier, the information content of partial pair correlation functions and partial structure factors is so much greater than that contained in the total functions, that the former provide the most discriminating test of a structure model. For polyatomic materials, even models that are radically different produce adequate fits to S(Q) or G(r) - especially when experimental data is measured to low values of Q. Only by examination of the detail of these functions can differences be discriminated.

pulsed neutron sources), multiple scattering introduces low Q limitations also. The result of terminating S(Q) at g max leads to convolution of G{r) with a peak shape function so that a ^-function in G(r) is transformed into a broadened peak with side lobes - so-called termination broadening and termination ripple (see Fig. 4-20). Thus a

^ || 2 V y a *

is replaced with: 4.4.6.1 Bond Length Distributions

Successful models must reproduce the details of each of the bond length distributions, that is, not only the interatomic distance corresponding to the peak and the integrated area leading to the coordination number, but the shape of the distribution as expressed through higher moments: standard deviation and (possibly) asymmetry (kurtosis). Such parameters are important structurally and represent valuable diagnostic information. Microscopic parameters computed from models and those derived by experiment must be compared in detail, as indicated above, and using equivalent data. Early models were relatively crude and thus the two data sets were compared only superficially without proper regard for equivalence. However, the efforts of a number of authors such as Wright and Leadbetter (1976) have emphasized the proper treatment. A major problem arises from the fact that experimental data are generally limited in reciprocal space. X-ray and neutron diffraction S(Q) data are often limited to values of Qmax in the region of 200 nm" 1 and whilst EXAFS data can routinely be extended to higher values (as can X-ray and neutron data with synchrotron and

a

p

0

(4-36)

where P*p(r-r') is a peak shape function given by: Pa%(x) = M(Q)cos(Qx)dQ (4-37)

E GO

o

-0.2 1

Figure 4-20. Experimental difference distribution function GCa (r) for a calcium silicate glass (bold line) and a fit to the data to about 0.5 nm (upper dashed line). The latter has been convoluted with a SINC function to compare with experimental data. The underlying (unconvoluted) sum of gaussian functions is shown by the lower dashed line. This function has more information, since the termination smearing is absent but is only one of the possible fits to the experimental data (Eckersley et al., 1988).

222


Here M(Q) is a modification function (see Sec. 4.3.3). For X-ray and neutron diffraction this could be a step function, M ( 0 = 1, for Q < Q m a x , and M(Q) = 0 thereafter, or some smoother function such as the exponential function. For neutron scattering where the atomic scattering lengths are Q-independent, or for X-ray scattering in those cases where the ratios fa{Q)ffi(Q)/Kf>\2 are essentially g-independent for all a and /?, then: P«%(x) = c*°^2 K\\U/\

TM(Q)cos(Qx)dQ o

(4-38) If M (Q) is a smooth function, it may be possible to replace P*p (x) with a gaussian,

(2nr1/2exp(-x2/2a2)

with a = l.6/Qmax

for approximate work. For accurate comparison, a convolution of the model G (r) is necessary before comparison is made with experimental realspace data. Even analysis of the experimental data to obtain parameters such as the first, second and higher coordination numbers and associated mean bond lengths and G values requires care. Although the coordination number can be obtained approximately from an integral: jG aj3 (r) n

where r1? and r2 represent the "limits" of the peak, such limits cannot be defined accurately - especially if termination ripple is present and peaks overlap. A better method involves fitting the experimental data with a series of gaussian peaks (say) convoluted by P*p (x). Once this has been done, the set of gaussians (unsmeared by the peak shape function) is narrower and may be more representative of the structure. Thus where available, this function should be quoted. An example is shown in Fig. 4-20 from recent investigations of Eckersley et al. (1988) on a-CaSiO 3 . Convolution by a peak shape function and the resulting smearing thus represents

some degradation of the structural information and efforts have been made to minimise the impact. One solution is to compare computed and experimental data in reciprocal space so that problems of termination broadening of the g-space data are circumvented. However, unless the model is large, with a radius greater than about 1.5 nm, truncation of the r-space data leads to a convolution of computed reciprocal space data with another peak-shape function. Ideally comparison of models with experiments should be made in both Q- and r-space since although they both contain the same information, certain features such as the first sharp diffraction peak, may be more evident in one than the other. Konnert, Karle and coworkers and others have attempted to devise methods to reduce the impact of termination at Qmax. Their treatment is based on the fact that if Qmax is reasonably large - say 150 nm" 1 for oxide glasses - then only the first one or two interatomic correlations are sufficiently sharp in r-space to contribute to S(Q) near Qmax. If the contribution from these peaks to S(Q) is removed, then Qmax c a n be set to infinity for the remainder with no loss in accuracy. Since the result is obtainable only by fitting the experimental data for the first few peaks, it represents a nonunique solution and lacks some of the objectivity of the Fourier transform. The choice of the fitting algorithm clearly biases the results and a question arises as to the most appropriate choice of function. Recently, the claims of maximum entropy techniques in this field have been enhanced by several workers. If experimental data is fitted by a procedure that maximises the (information) entropy, then this set of choices represents the least biased (maximally non-committal) choice. Wei (1986) has shown that experimental neutron scat-

4.5 Elemental Tetrahedral Semiconductors

tering data for a-Ni 64 B 36 (Cowlam et al., 1984), analysed using a maximum entropy technique provides more informative data in real space than the fourier transform technique (Fig. 4-21). This would be expected for most fitting algorithms - the advantage of the Maximum Entropy technique is that it allows an objective (unbiased) choice of one of the manifold of possible solutions that could fit experimental data. The use of ME techniques in extraction of partial distribution functions in a ternary Ag-Ge-Se alloy has been demonstrated by Westwood and Georgopoulos

223

(1989). In this case the data was from Xray anomalous scattering measurements at two energies at each of the K-edges of all the elements. 4.4.7 Calculation of Dynamical Properties

From the coordinates of an atomic model and an assumed PE function, the vibrational density of states function can be calculated. Description of the various computational techniques lies beyond the scope of this review and a brief list of references giving an entree into the subject must suffice. Vibrational frequencies are obtainable directly in a MD simulation - see for example Hockney and Eastwood (1981). A popular and efficient method for calculating the phonon states of a cluster is the "recursion method" reviewed in Heine et al. (1980). A similar method is the "equation of motion" method (Beeman and Alben, 1977). Electron states can also be calculated by the use of these techniques (Heine et al., 1980).


Figure 4-21. Reduced radial distribution function, G (r) for 58 Ni 64 B 36 obtained from the neutron scattering data of Cowlam et al., 1984 by fourier transform (FT) (a, c) and maximum entropy (ME) methods (c? d). Km is the maximum value of 4 n sin djX in the dataset (Wei et al., 1986).

Of all amorphous solids, silicon and germanium are perhaps the most extensively investigated. Recently, interest has mounted in a a third element - carbon - although this is not strictly a tetrahedral material the extent of tetrahedral bonding is variable and as yet, inadequately defined. The three materials have important properties - Si and Ge are semiconductors and, like the crystalline elements, can be doped to provide a range of useful electronic properties. Carbon, in its diamond-like form, can be very hard and has useful properties

224


as a damage-resistant coating and as a dielectric. Each can be prepared as an alloy with other elements - notably hydrogen. Indeed, some contamination with H is difficult to avoid but, more importantly, deliberate alloying with H decreases the number of energetic defects such as 'dangling bonds' thus improving optical and electronic properties. In this section, we concentrate on the structure of the essentially pure elements, recognising that H may be an almost unavoidable impurity. A recent review by Elliott (1989) extends the subject to alloys of Si containing large amounts of H and other elements. With the exception of amorphous carbon, there is no paucity of good experimental, data for amorphous semiconductors. The most complete data is for a-Ge and, since there are strong qualitative similarities between the results for all the Group IV elements (and their alloys) we concentrate on data for a-Ge and introduce deviant behaviour as appropriate amorphous carbon being the most important case. 4.5.1 Amorphous Ge and Si 4.5.1.1 Local Structure - Diffraction Data X-ray data for several specimens of aGe has been reported by Temkin et al. (1974) (see Fig. 4-4) and Kinney (1976). Neutron scattering data was obtained by Etherington et al. (1982) from the specimen of evaporated Ge used by Kinney. A small amount of H was observed (indirectly). Results of this work are shown in Fig. 4-22 as the experimentally-derived correlation function f (r) and the authors' best estimate of the true correlation functions t(r). The latter function was obtained by subtracting the contribution of the first peak (in r-space) to the reciprocal space data, Q(S(Q) — 1). This gives a reciprocal

Figure 4-22. Experimental correlation function (full line) t'(r) = 4n rg{r) for a-Ge, together with Etherington et al.'s (1962) estimate of the true correlation function t(r) (dashed line) obtained as a fit to the experimental scattering data.

space function that has effectively reached an asymptotic value below Qmax, so that fourier transformation is possible without any truncation effects. The overall tetrahedral nature of the material is confirmed, with = 0.246 3 nm (0.2450 nm for c-Ge) although the first shell coordination number, 3.68, is less than the expected value. Second shell coordination numbers depend on the assumptions made in fitting the second peak around 0.395 nm but a figure below the value of 12 expected for a fully-coordinated network is likely. Deviation from fourfold coordination is ascribed to broken bonds associated with voids etc. A notable feature of the structure of a-Ge and a-Si is the small disorder-induced broadening of the first neighbour distance. For a-Ge, the static broadening parameter o\ amounts to 0.0074 nm. By contrast, the static breadth of the second peak is much larger, as2 = 0.026 nm, indicating that the disorder chiefly introduces variations in the bond angle of about a (6) = 10° from the mean tetrahedral angle. Current data

225


for a-Si is less accurate but results from X-ray and electron diffraction techniques on a-Si: H alloys suggest values of the first coordination number less than four and that the second coordination number is less than 12. For instance, Schulke (1981) finds = 0.2363 nm, Si = O groups is also dropped in favour of = S i - O - O - S i = groups. Hosemann et al. (1984, 1986) have produced a remarkable but little-understood model for a-SiO2. A pair of SiO4 tetrahedra, Fig. 4-48 a, form the basis for a f.c.c. lattice with a lattice constant of 0.715 nm, Fig. 4-48 b. In order to fit the density, tetrahedra are given correlated twists of + 22° parallel to the cell axes. The spacing of the {111} planes of this lattice are allowed to vary according to Eq. (4-2). A good fit to experimental X-ray data is found with the interplanar variation constant, g = 0.12, corresponding to an octa-

245

Figure 4-47. Phillips' (1982) sketch of the {100} interface in cristobalite formed by removing a "molecular plane" of thickness 0.37 nm and allowing the interface to relax.

hedral microparacrystal comprising 3 or 4 {111} planes, with an edge length of 1.25 nm. The glass is pictured as being composed of microparacrystals with "parallel oriented twists of SiO 4/2 tetrahedra" separated by grain boundaries where the distortions are larger due to different orientations of the rotation axes in adjoining domains. The fit to experimental data is impressive, Fig. 4-48 c - the authors claim that their model fits experimental data to "within the thickness of the drawn line". The domain structure is compared with several of the crystalline modifications of SiO2 but is identical to none of them with cristobalite being the closest approximant. 4.6.6 Simulation of Dynamical Properties As mentioned earlier, a number of features of the vibrational spectra of silica particularly the polarised Raman Spectrum - have no obvious counterparts in spectra for crystalline forms of SiO 2 . Two of the Raman bands at 495 and 605 cm" 1 are sharp (see Fig. 4-41) and, since they are sensitive to preparation conditions and to radiation damage, they have been termed "defect" bands.

246


Figure 4-48. a) The building block, consisting of two silicon-oxygen tetrahedra, proposed by Hosemann et al. (1984, 1986) which is then connected to form the structure shown in b). Circles are oxygens and squares, silicons. The fit to experimental data (Mozzi and Warren, 1969) is shown in c) with component partials indicated. The agreement with experimental data is "within the thickness of the drawn line". The insert shows the peak shape function with a full width at half height of 0.19 A compared to the computed width of the first peak of 0.21 A.

4.6 Amorphous Silica

Interpretation of the defect bands by Galeener (see for example Galeener, 1983), Galeener et al. (1983) and by Phillips (1982) starts from the assumption that calculated vibrational spectra, based on coupled SiO4 tetrahedra and for random network models such as Bell and Dean's, do not agree either with the number or the frequency of those modes observed experimentally. Phillips (1982) then proposes that the two defect bands are assigned to localised vibrations of point defects or surface oxygens associated with the postulated 'broken chemical order' at the bonding surface of (3-cristobalite microparacrystallites and involving a double Si = O bond. Galeener (1983) takes the view that the additional features in the spectrum reflect the presence of three-membered rings (Si3O9) by analogy with vibrations near 600 cm" 1 in hexa methylcyclotrisiloxane, and four-membered rings corresponding to octamethyl cyclotetrasiloxane which has a Raman active mode at about 480 cm" 1 . These explanations fit uncomfortably with the findings of Bell (1983) and Evans et al. (1983). These authors calculated the vibrational densities of states, g(co), for several cluster models of a-SiO2, none of which contain 3-membered rings but give results that are in reasonable agreement with the experimental data of Leadbetter and Stringfellow (1974). Bell (1982) also calculated the IR, polarised and unpolarised Raman spectrum and observed Raman and IR-active modes near 600 cm" 1 . Evans et al. (1983) also found IR activity in the energy-minimised Bell-Dean structures at 600 cm" 1 and peaks in g((o) for all models considered in the region near 600 cm" 1 . The problem therefore, as Bell says, is not what type of network defect could be responsible for the vibrations but to understand why, in conflict with experi-

247

ment, the cluster-based calculations predict a measure of IR and depolarised Raman activity at 600 cm" 1 . The matter is still controversial, therefore. 4.6.7 Molecular Dynamics Models Similation of the static structural properties of a-SiO2 using molecular dynamics was pioneered by Woodcock et al. (1976). A modified Born-Mayer-Huggins potential was used and the resulting distribution functions are shown in Fig. 4-49. Soules (1979, 1982) and Mitra et al. (1982) have also produced fits to experimental X-ray data for SiO2 using larger models than that used by Woodcock et al. (54 molecular units in the periodic box). Mitra, for example, used 375 ions in a

Figure 4-49. Pair correlation functions, G(r), for aSiO2 obtained from the MD simulations of Woodcock et al., 1976 (full line). Experimental data of Mozzi and Warren (1969) is also shown (dashed line). N (r) is the running coordination number centred on Si.

248


cubic box with dimensions adjusted to provide agreement with the experimental room temperature density. The results of the MD simulation were compared with experimental data without any attempt to reproduce termination broadening or to match thermal broadening. Good agreement with experiment is reported, although there are discrepancies in the detail. For instance, the authors draw attention to the spread of ±7° in the Si bond angle compared with a = 0.6° from ESR data and (7 = 4.5° from neutron and X-ray data. The oxygen bond angle distribution agrees with that proposed by Da Silva with a peak value of 151°. A few of the atoms are abnormally coordinated as 3- or 5-coordinated Si or singly- or triply-bonded oxygens. Kubicki and Lasaga (1988) have simulated a-SiO2 using ionic and covalent potentials parameterised by fitting ab initio quantum mechanical potential energy surfaces for H 4 SiO 4 and H 6 Si 2 O 7 molecules. Again the authors claim a good fit to experimental X-ray data but the secondneighbour coordination numbers are in error by factors of 2 in some cases, and there are also significant errors in nearest neighbour bond lengths and in the breadth of bond angle distributions (apart from questionable values of the mean oxygen angle). A recent MD simulation of Feuston and Garofalini (1988) has used Stillinger-Weber three body potentials adapted for aSiO 2 . The results, Fig. 4-50, are a great improvement on earlier calculations based on two- body terms - the bond angle distributions and the numbers of over- and under-coordinated atoms are more realistic. MD simulations of a-SiO2 have thus far failed to match the potential of the technique (or the claims of their adherents) - at least in so far as realism is concerned. None of the simulations matches experi-

Figure 4-50. Structure factor, S (Q\ for a-SiO2 calculated by Feuston and Garofalini (1988) using Stillinger-Weber potentials including three-body interactions, compared with experimental data (Misawa et al., 1980).

mental data to the accuracy of that data few authors have even tried to make meaningful comparisons. Unphysical potential energy functions are probably the cause of the mismatch in early work, but the recent efforts of Feuston and Garofalini using Stillinger-Weber type three-body interactions shows that the challenge of matching experimental data to within statistical error still exists (see Fig. 4-50). 4.6.8 Monte Carlo Simulations Guttman and Rahman (1988) have produced a number of models for a-SiO2 by methods in which the central step involves randomly-chosen exchanges of neighbours followed by energy minimisation and acceptance or rejection of the move based on an assessment of the changes in energy. Variations in the number of n-membered rings in the starting structures were tried, as well as changes in the relative magnitude of the terms in the modified Keating PE function. Once the energy had ef-

4.6 Amorphous Silica

fectively converged, the reality of the models was tested by the fit to experimental values of the density, elastic moduli and Q(S(Q) — 1) data - particular attention being paid to the position and intensity of the first sharp diffraction peak at about 15 nm" 1 . The most successful models (324 atoms) were generated and energy-minimised in the form of models for a-Si (with the density fixed at values appropriate to a-Si) and oxygens only inserted at the final stage. (Models based on SiO2 throughout were less successful.) Agreement with g-space data is (again) said to be "excellent", but the best models fail to reproduce experimental data to within experimental statistics. Models with 3-membered Si-O rings were observed to reproduce inadequately the low Q features in the experimental results and with more than one 4-membered ring per 10 Si atoms, errors are again noticeable at low Q. Keen and McGreevy (1990) have presented a simulation of the structure of aSiO2 using a "Reverse Monte-Carlo" algorithm. The procedure, outlined in Sec. 4.4.5, takes an arbitrary starting structure - in this case 2596 atoms in a periodic cubic box of length 3.4 nm. Atoms are randomly chosen and moved to minimise the weighted difference between the structure factors for the model and those obtained from X-ray and neutron scattering measurements for the same sample. At no stage are energetic terms involved. Results are shown in Fig. 4-51 and are clearly impressive. The structural parameters derived from the model are similar to those derived "directly". However, the authors draw attention to the low value of the Si-0 coordination number of 3.7. The average oxygen bond angle is 141° in good agreement with Mozzi and Warren's (1969) value, although the distribution is found to

249

0.2-

,0.0:

-0.2:

0.2:

,0.0:

-0.2tt.O

Figure 4-51. Calculated neutron and X-ray structure factors for a-SiO2 (solid line) using the Reverse Monte Carlo method. The dashed line shows experimental neutron and X-ray data (Keen and McGreevy, 1990),

be significantly broader, as is the Si bond angle distribution. The Si-Si-Si angle distribution shows a significant peak at 60° corresponding to three-membered rings, which are also observed in projections of the structure. Such rings are thus not inconsistent with the diffraction data and it remains to be seen just how the additional constraints employed in many other construction algorithms - particularly that of Gladden (1990) - have lead to radically different models. This work certainly concentrates the mind on the limited amount of information available in diffraction data for amorphous solids and the extent to which other prior knowledge - or prejudice - has been incorporated in less objective constructs.

250


4.7 Binary Alkali and Alkaline Earth Silicates, Borates and Phosphates 4.7.1 Apologia These glasses may not be the most popular materials with academic scientists. Their compositional complexity leads to structural investigations that are necessarily difficult and inconclusive. But it would be artificial to exclude them from this chapter. Silicates, borosilicates, aluminosilicates and (less usually) phosphates, form the basis of the modern glass industry. Moreover, the class of ionic oxide glasses represented here is of central importance in the earth sciences. There is every reason, therefore, to establish what we now know about these materials - since it is far from insubstantial - and how it may be incorporated into our understanding of structure of glasses in general. Section 4.1.4 outlined the various ways in which the structure of glasses can be discussed - positional and compositional ordering, local symmetry and coordination, network topology, speciation etc. Each aspect merits attention in the case of the binary oxide glasses. But in this section we focus on two interwoven aspects - firstly, the local structure around an alkali (or alkaline earth) element and especially on the consequences this may have at the level of medium-range structure. The reasons for emphasising this topic were set out in Sec. 4.2.3. If local order is observed in close-packed regions, so that local structural units are highly interconnected and if the bonds to nearest-neighbours are not strongly directional, then the arguments of Sec. 4.2.3 suggest that the perceived local order is a consequence of medium-range ordering. Local ordering around cationic "network modifiers" like Li, Na, Mg, Ca,

and (possibly) the trivalent elements thus gives very important clues to the degree of ordering over distance scales much larger than nearest-neighbour bond lengths. Secondly, we consider several determinations, chiefly by NMR, of the distribution of anionic species present in a glass speciation. These questions focus attention on the extent to which randomness inherent in the Warren-Zachariasen model, actually represents the structure of real amorphous materials. I am not aware of a modern restatement of the Warren-Zachariasen model for oxide glasses but the consensus view seems to be the following. Elements such as Si, B, P etc., bonded to oxygen, constitute an extended network: such elements are thus the "network-formers". Alkali, alkaline earth and similar elements denoted here by M - "modify" the connectivity and thus determine the dimensionality of the network. The B-, P- and Si-0 bonds are regarded as the strongest and most directional interactions - largely covalent, perhaps - whereas network modifier, M-O links are considered to be weak mostly ionic and with isotropic, pairwise forces. The Si environment should thus be well-defined in contrast to M-0 correlations, where variable coordination is possible (or probable). Moreover, the M-M distribution in the Warren-Zachariasen picture is viewed as being random - determined largely by composition; although it is a common over-simplification to regard the M ions as fitting into suitable cavities in a silicate framework "formed" to satisfy the coordination and bonding requirements of Si and O, as Zachariasen pointed out in his original paper (1932).

4.7 Binary Alkali and Alkaline Earth Silicates, Borates and Phosphates

4.7.2 Local Structure Around "Network Modifiers" in Oxide Glasses 4.7.2.1 Diffraction and EXAFS Data A major difficulty in establishing the structure around atoms such as Li, Na, Mg, Ca in oxide glasses stems from the fact that M-O, M-Si and particularly M-M correlations generally give only weak contributions to the total scattered X-ray or neutron intensity. This follows from the dependence of the weighting factors in Eq. (4-19) on the concentration and atomic scattering factors, so that for light elements, M-M correlations can be virtually invisible in X-ray scattering. Moreover, M-0 first- and higher-neighbour peaks often lie at similar distances to the more intense 0 - 0 correlations. Some insight was gained in early work by taking differences between scattering data for specimens containing ions of two chemically similar species which are assumed to substitute isomorphously. Urnes and coworkers (see for example, Hanssen and Urnes, 1978) have used Si/Ge replacement to identify features in K 2 O-SiO 2 and Cs2O-SiO2 glasses and differences between X-ray and neutron atomic scattering factors to identify features in silicates (Urnes et al, 1978). An exceptionally thorough survey of the structure of silicate glasses and melts was conducted by Waseda and Suito (1976, 1977) - work that probably did not receive due attention until the results were later republished (Waseda, 1980). X-ray and neutron scattering data were collected to Qmax = 170 nm" 1 from about eight compositions in each series of Li, Na, and K silicate glasses both as the room temperature glass and the melt. In addition, melts in the CaO-, MgO- and FeO-SiO2 series were also examined by X-ray scattering (Waseda, 1980). Structural parameters were estimat-

251

ed by fitting the reciprocal space data with a modified Debye equation. Coordination numbers were found to vary slightly with concentration - at the metasilicate composition approximate values are Li-O 4, NaO 6, K-0 8, Mg-O 5 and Ca-O 7 (see also Table 4-1). Misawa et al. (1980) used pulsed neutron scattering techniques to study SiO 2 , Li 2 O-2SiO 2 and Na 2 O-2SiO 2 and a mixed Li/Na glass to Qmax = 4$Q nm" 1 . No real attempts were made, however, to analyse the M-O contributions in detail apart from indicating peak positions, 0.20 and 0.24 nm for Li-O and Na-O, respectively. A further paper by Ueno and Suzuki (1981) ona-Na 2 Si 2 O 5 to 0 max = 3OO nm" 1 , reported the position of the Na-O peak at 0.241 nm with a coordination number of 5, in good agreement with values for cNa 2 Si 2 0 5 (0.241 nm and 5.0). Also in 1981, Greaves et al. reported studies on a-Na 2 Si 2 O 5 and other Na-containing glasses using EXAFS. This represented the first use of a soft X-ray monochromator on a synchrotron to obtain "element-specific" local structural information for a light-element in oxide glasses, Fig. 4-52. The Na-O mean bond length was established to be 0.23 nm with a = 0.004 nm and a coordination number of 5 + 0.5. This paper marked the beginning of an impressive series of measurements by Greaves and coworkers on the local structure around modifying elements in oxide glasses of scientific, commercial and geological importance (see also Greaves (1990)). Similar EXAFS investigations by Brown and coworkers relate principally to glasses relevant to the earth sciences. A number of EXAFS results are collected in Table 4-1. There are some clear discrepancies between the results of Greaves and coworkers and Brown et al. (1986), over the local

N> Ol I\D

Table 4-1. Local structural parameters for silicate and phosphate glasses. Bond

M-O/nm

cr/nm

Li-O Li-O Li-O Na-O Na-O Na-O Na-O Na-O Na-O Na-O Na-O Na-O Na-O Na-O Na-O K-O K-O K-O K-O K-O K-O K-O Cs-O Cs-O Cs-O Ca-O Ca-O Ca-O Ca-O

0.207 ±0.001 0.20 0.212 0.240 0.235 + 0.001 0.24 0.23(0) ±0.003 0.24(3) ±0.003 0.241 0.240 0.247 0.261 0.262 0.257 0.260 0.25(6) 0.300 ±0.002 0.303 ±0.002 0.306 ±0.002 0.302 ±0.002 0.278 0.288 0.308 0.318 0.30(0) 0.243 ±0.001 0.241 ±0.001 0.241 0.237

0.010 0.009 0.012 0.010 0.007 0.012 0.02 0.004 0.015 0.010 0.015 0.019 0.015 0.013 0.015 0.015 0.013 0.0035 0.023 0.015 0.028 0.016 0.013 0.01 0.012

3.9 ±0.3 4 5 6.0 5 ±0.5 2 ±0.5 5.0 4.0 5 6.4 5.1 5.5 7.6 5 8.9 ±0.9 9.6 + 1.0 10.4 ±1.0 9.5 ±1.0 5 6 5 6 5 6.8 ±0.3 6.9 ±0.3 6 6.15 + 0.17

Ca-O Ca-O Ca-O Mg-O

0.237 0.264 0.263 0.214 ±0.001

0.022 0.023 0.011

5.40 ±0.18 7 8 4.5

CN

Composition

Reference

Tech

Comments

Li2SiO5 Li 2 Si 2 O 5 Li2SiO3 a-Na 2 Si 2 O 5 Na 2 Si 2 O 5 Na 2 Si 2 O 5 Na 2 Si 2 O 5 Na 2 CaSi 5 O 12 Na 2 Si 2 O 5 Na 2 SiO 3

Wasedaetal.(1977) Misawa et al. (1980) Yasui et al. (1983) Waseda et al. (1977) Misawa et al. (1980) Greaves et al. (1981) Greaves et al. (1981) Ueno etal.(1981) Yasui et al. (1983) Yasui et al. (1983) McKeown et al. (1985) McKeown et al. (1985) McKeown et al. (1985) McKeown et al. (1985) Greaves (1989) Jackson et al. Jackson et al. Jackson et al. Jackson et al. Yasui et al. (1983) Yasui et al. (1983) Yasui etal.(1983) Yasui et al. (1983) Greaves (1989) Waseda (1980) Waseda (1980) Yin et al. (1983, 1986) Eckersley et al. (1988)

X,N N X X X,N N E E N X

6 other glasses and melts e max = 480nm- 1 Fitted data Crystal data 6 other glasses and melts

E X N X N

Fitting with a crystal model Isotope substitution

Matsubara et al. (1988) Binsted et al. (1985) Binsted et al. (1985) Waseda (1980)

X E E X

Other compositions reported Asymmetric peak Asymmetric peak - mean value quoted Data for melt also

Na 2 Si 2 O 5 KNa3(AlSiO4)4 KNa3(AlSiO4)4 Na 2 Si 3 O 7 KCsSi2O5 KAlSi3O8 Na 0 . 3 K 0 . 7 AlSi 3 O 8 Na 0 . 5 K 0 . 5 AlSi 3 O 8 Na 0 . 3 K 0-7 AlSi 3 O 8 K 2 SiO 3 K 2 SiO 3 Cs2SiO3 Cs2SiO3 KCsSi2O5 (CaO)0.45(SiO2)0.55 (CaO)0-45(SiO2)0.55 CaSiO3 (CaO)0.48(SiO2)0.49 (Al2O3)0.03 Ca(PO 3 ) 2 CaAl2Si2O8 CaMgSi 2 O 6 MgSiO3

1 CD_ (/>

o* E-%r CD CO

a value estimated by Gaskell Two estimates of a from fitting

c Q

c" CD

E E

E E E E E X

o Nepheline glass Nepheline crystal Nepheline crystal Orthoclase glass

o -t ZT •D O

c (/)

CO

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Data for melt also

4.7 Binary Alkali and Alkaline Earth Silicates, Borates and Phosphates

60

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" 120
2 eV, which are inorganic and on which ion implantation experiments have been performed are a subset and consequently, much smaller in number. It is this subset which will be discussed in this review. The purview of this review will be: i. Optical properties of ion-implanted glasses, including first, second and third order terms in the susceptibility of the glass to electromagnetic radiation within the band-gap of the material and ranging from band-gap energies to the infrared vibrational bands. ii. Magnetic properties of implanted ions and of the substrate modified by implantation. iii. Optical and magnetic properties of amorphous materials produced by implanting insulating crystalline substrates. iv. Structures in the implanted materials.

v. Most of the glasses with which this review will be concerned will be wide bandgap materials. The review will not be comprehensive, that is, it will not note, neither in the citations nor in the text, all papers published on these topics. The selection of papers is idiosyncratic and, of course, biased to the author's interests. The selection has also been guided by our perception of good experiments and those which may have technical applications at some time in the future. A review of the literature clearly shows that this topic of research is being diligently pursued in only a few laboratories. These laboratories are best identified by reference to the names of a few individuals in these laboratories whose names appear, almost consistently, with many coauthors. The research of these individuals, M. Antonini, G. W. Arnold, P. Mazzoldi, A. Perez, P. D. Townsend and their collaborators, will be frequently cited in this review.

6.2 Distributions of Implanted Ions in Wide Band-Gap Materials 6.2.1 Atomic Collisions and Ionization Processes

Implanting ions (+1 or + 2 charges) into metals (see Vol.15, Chapter 6) or semiconductors does not have the problem of substrate charging which occurs in insulating materials, i.e., wide band-gap materials. In the case of metals and semiconductors attaching ground to a substrate provides a route through which a charge to compensate the charge introduced by implantation can move into the implanted material. In the case of wide band-gap materials which may have resistivities >10 1 8 Qcm at room temperature, the

6.2 Distributions of Implanted Ions in Wide Band-Gap Materials

source of compensating charge and the process of compensation is not evident. Before briefly reviewing the process of implantation we will discuss briefly some aspects of the charging phenomenon when implanting wide band-gap materials. Charging of insulating materials when irradiated with charged particles frequently results in electrostatic discharges within the material. Another consequence is the growth of an electric field which repels subsequent charges. Irradiation of some insulating materials with a y-ray beam also will produce catastrophic discharges if there are trapping sites for the Compton electrons, predominantly scattered in the direction of the y-ray photons, which are stable at the ambient temperature of the material (Gross, 1964; Hilczer and Malecki, 1986; Weeks et al., 1977). These effects may be ameliorated if there are ions in the material with sufficient mobility to redistribute in the electric field produced by the added charge. This redistribution reduces the field generated by the additional charge. The field due to the irradiating particles may be compensated by injection of charge of the opposite sign. In the case of irradiating with positively charged particles the injected charge would be electrons. If the material is in contact with an electron source, if the potential barrier to injection is small and if the mobility of the injected charge is not too small then the charge added by irradiation may be compensated. Both of these processes appear to be active, depending upon the material, when insulating materials are implanted with positively charged ions. It is possible to implant insulating glasses with a range of compositions without catastrophic electrostatic discharges. Some of the compositions which have been implanted are silica, alkali silicates (Arnold and Mazzoldi, 1987) and fluoro-zirconates

337

(ZBLAN) (cf. Chapter 8; Mazzoldi, 1990). All of these glasses have resistivities at room temperature, the usual temperature of implantation, >10 1 2 ficm. Samples used for these investigations have usually been either discs with a thickness of ~ 1 mm or parallelpipeds with one dimension of the order of 1 mm. During implantation, samples have been mounted on grounded metal supports. Thus the support has provided a source of electrons to compensate the positive implanted charge. Zuhr and Weeks (1988) observed that a discharge could be induced in silica disc samples of 0.2 cm thickness mounted on a grounded metal sample support when the current was >20jiAcm~ 2 . The discharge was between the planar faces of the sample. The current in this case was more than an order of magnitude greater than that used to implant SiO2 in the experiments of Whichard (1989). Beam currents used in experiments are often not reported in published papers. In view of the potential for charging effects during implantation of insulting materials, it is essential that experimentalists report the conditions, average (ions c m ~ 2 s - 1 ) and instantaneous currents, sample mounting geometries, and grounding circuits for their experiments. For ions with energies greater than a few keV, the initial loss of energy after impinging on a target is primarily through excitation of substrate electrons (Biersack, 1987). An implanted particle slows with this loss of energy, elastic collisions with substrate ions absorb the remainder of energy of the implanted particle (Biersack, 1987). These elastic collisions displace substrate ions creating disorder in the substrate, or in the case of glass substrates changing the already disordered structure to a different type of disorder (Wittels and Sherill, 1954). In the last part of the loss of energy by an implanted ion, in the case of wide band-

338

6 Optical and Magnetic Properties of Ion Implanted Glasses

gap materials, the implanted ion changes its charge state and reacts with substrate ions to form an implanted phase (Perez etal., 1987). 6.2.2 Distributions of Implanted Ions

The experimental and theoretical bases for calculating the distribution of ions implanted in a solid material through the use of a probe ion elastically scattered from the substrate and implanted ion is thoroughly described in many papers and books (see also Vol. 15, Chapter 6). Only one reference will be given here. It cites many of the most pertinent references and it also provides a table of ion ranges in many materials. It is the first chapter in "Ion Beam Modification of Insulators", written by Biersack (1987). Calculations based on the TRIM model (Biersack and Eckstein, 1984) give a distribution of the implanted ion that is approximately Gaussian about the mean range projected on the velocity vector of the ion beam. Implanting a planar surface then results in a distribution of ions which is shown in Figure 6-1 (Whichard, 1989). In the case of a material in the glass phase there is no channeling effect (Kelly, 1987). Implanting ions with large mass, greater than the mass of substrate ions, and with energies of the order of a few keV, sputters ions and atoms from the substrate (Kelly, 1987; Wang et al., 1987). Hence, there is a loss of substrate material and implanted ions. In some cases the loss of material by sputtering has a significant effect on the distribution as a function of distance from the surface into which ions are implanted. The range of an implanted ion is a function of ion energy and density of the substrate. For low-density substrates the range is larger than for high-density substrates for identical ion energies. Implanting an ion with an atomic mass greater

than that of substrate ions produces a back scattering spectrum shown in Figure 6-1 (Whichard, 1989). The distribution of ions as a function of distance from a surface on which the implanted ions were incident can be calculated. An example of such is the TRIM 17 calculation. The distribution shown in Figure 6-2 (Whichard, 1989) is typical of the profile observed for many ions with atomic masses >Si when implanted in a silicate glass at a single energy. The partition of energy of implanted + H , He + , O + , Ar + , Kr + , and Xe + between electronic and nuclear interactions is given in Table 6-1 (Arnold, 1973). This table shows that, for an energy of 250 keV, the fraction of energy dissipated in nuclear interactions increases with increasing atom mass. Although the relative fractions of energy will change with changing implant energies, these partitions will be representative for most of the ion energies used in experiments which will be reviewed here. There are two reports, to our knowledge, that describe implantations at a single energy for which distributions do not have Gaussian shapes. Arnold and Borders (1977) observed a bimodal distribution of Ag ions implanted in alkali silicate glasses. In the other case (Whichard, 1989), a bimodal distribution is observed for Cu-implanted samples of SiO2 glass in as-implanted samples when the implanted dose Table 6-1. Partition of 250 keV accelerating energy into electronic (s) and nuclear (u) interaction processes for various ions. Ions

ji(keV)

e (keV)

H+ He + O+ A+ Kr + Xe +

0.6 6.5

249.4 243.5 182.4 91.6 41.7 28.3

67.6 158.4 208.3 221.7

6.2 Distributions of Implanted Ions in Wide Band-Gap Materials

339

Mn implantation profile in SiO2 a Weeks C 0.014 A Weeks C 0.015 ° Weeks C 0.016

6***www«rt^Don^

0.4

0.6

0.8

1.0 1.2 Energy in MeV

1.4

1.6

Figure 6-1. Energy spectrum of He + ions back-scattered from SiO2 glass implanted with Mn + .

Fe implantation profiles in SiO2 + -0.95 E16 Fe-cm" 2 Weeks I 0.035 A -2.77 E16 Fe-cm" 2 Weeks I 0.036 x -5.43 E16 Fe-cm" 2 Weeks I 0,040

Figure 6-2. Depth profiles of Fe implanted in SiO2 glass samples. Energy of the ions was 160 keV, at a current of 4 uA cm" 2 . Ion backscattering data were used to calculate the implanted ion distributions. 0.00

0.05 0.10 0.15 Depth in pm

0.20

0.25

Cu implanted in SiO2

#68 #67 #66

-

E16/cm2 E16/cm2 E16/cm2

5.4 2.8 1.0

)

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o °0

o

o

o OgA

A

A

*

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v

o
ooo w. °°O0 >§

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0.20

Figure 6-3. Depth profiles of Cu ions implanted in SiO2 glass samples. The energy of the ions was 160 keV at a current of 4 uA cm" 2 . The TRIM calculation was used to calculate the distribution.

340


was 10 16 ions/cm 2 and the ion energy was 160 keV. The distribution for three doses is shown in Figure 6-3 (Magruder et al., 1989). The bimodal distribution was observed for substrate temperatures during implantation which ranged from 100 to 673 K (Magruder et al., 1989). Implantation of an ion at a single energy, with the exceptions noted above, produces a Gaussian distribution, the peak of the distribution being determined by the projected range of the ion in the material implanted. By implanting ions at two or more energies, distributions approaching a step function can be produced. By choosing energies with a sufficient difference, two well resolved Gaussian distributions can be produced. Accelerators which can produce ions with energies > 1 MeV can implant, in many materials, ions to depths of several microns. After one ion has been implanted, another ion or ions can be implanted with the same energy to produce a layer in which the ions may interact with each other and the substrate ions. Thus the number of possible combinations of substrate/ions/energies is quite large.

6.3 First-Order Optical Properties of Implanted Wide Band-Gap Glasses Optical properties of wide band-gap glasses have usually been described in terms of the first order approximation of the electric susceptibility of glass materials. With the development of coherent and intense light sources it is now necessary to consider higher order terms in the susceptibility of a material to interaction with photons (see Chapter 12). In wide band-gap materials it is usually assumed that interaction with photons whose energies fall within the band-gap can be described in

terms of a linear function of refractive index and absorptivity. It has been demonstrated that for very high fluxes of photons this linear relation is insufficient to describe the interaction (Taylor et al., 1988). The higher order terms are usually small when compared with the first order terms. Consequently, before laser sources were available, the higher order terms were of little consequence. The polarization due to photon-material interaction can be expressed in terms of the susceptibility of the material, a property of the elements comprising the material and their structure. The susceptibility can be written as an expansion (Bloembergen, 1965): + X(3)E1-E2-E3...)

(6-1)

in which e0 is the dielectric constant of vacuum, x(l) is the fth term in the expansion, and Et is the electric field of the photons. Each of the x are complex and experiments have been developed to measure the first 3 terms (Milonni and Elerly, 1988). The first order term can be written, using the Lorentz-Lorenz model: w X

=FZNiXi(co)

(6-2)

i

in which F is the local field correction, Nt is the number density of the fth constituent ion, and Xi *s the polarizability of this ion. (The hypothesis that the ion polarizabilities are independent of each other and their surroundings and that the total polarizability of a material is a linear sum of these ion polarizabilities has been questioned (Lines, 1990). Then (Joos, 1934): n2-l = 4nZNixi(co)

(6-3)

i

where n is the complex refractive index, and n=

(6-4)

6.3 First-Order Optical Properties of Implanted Wide Band-Gap Glasses

341

2U

I20 o 16

Figure 6-4. Optical density (arbitrary units) vs. wavelength in nm for Corning silica 7940 which has first been implanted with 5 • 1015 400 keV Xe+ ions cm" 2 and then with 6 • 1014 400 keV H + ions cm""2. Bottom curve is for a similar sample with 1 • 1014 400 keV H + ions cm" 2 only.

5x1015 400 keV XeVcm 2 Xenon implant plus 1x 10 u 400 keV HVcm 2 1x10 u 400 keV HVcm 2

150

200

350

where n0 is the refractive index and k is the absorptivity. The absorption coefficient, A, of a material is (Frohlich, 1958):

A = 2kco/c

(6-5)

where co is the photon frequency and c is the speed of light. In Section 6.3.1 we will review the effects of ion implantation on n and k for some glasses. In the following section (Sec. 6.4) the effects on # (2) and %(3) will be reviewed.

the E' center (Weeks and Nelson, 1960). Also evident in the spectrum of the Heimplanted sample is a band emerging at 250 nm. With increasing mass of the implanted ion this band becomes well resolved. It has been labeled the B 2 band (Arnold, 1973) and attributed to the E" center (Arnold, 1973; Weeks and Nelson, 1960).

Xe\

i1

6.3.1.1 Optical Absorption Spectra of Glasses Implanted with H, He, Ne, Ar, Kr, Xe

The absorption of silica implanted with H, with Xe, and with H and Xe sequentially, as a function of photon wavelengths, in the range 350 to 190 nm, is shown in Figure 6-4 (Arnold, 1973). The absorption in silica samples each implanted with one of the following ions: H, He, A, Kr, and Xe, at various energies and integrated fluxes, is shown in Figure 6-5 (Arnold, 1973). The most intense band produced by implanting H or He is at 210 nm. This band is due to

JQ

O C

Absorpition

6.3.1 Optical Absorption Spectra and the Imaginary Part of the Refractive Index

trar>' units

\

\

A\\

\X \ \ He \ \ \ \ ^

B2

-A

\\

\

\

H—'""Y

i

200

250 A in nm

i

300

350

Figure 6-5. Optical density (arbitrary units) vs. wavelength in nm for Corning silica 7940 implanted with H, He, Ar, Kr, and Xe ions at various energies and fluences. Individual curves have been displaced vertically for clarity. Relative values of absorption can be obtained by normalizing all curves to zero optical density at 350 nm.

342


The assignment of this band to the E" center is based on deductions based on the relative intensities of the band in the spectra of samples irradiated with energetic ions of differing elements. This model for this band is placed into question by the absorption spectrum of samples implanted with O + . The optical absorption spectrum of a sample, so implanted, is shown in Figure 6-6 (Arnold, 1973). In this spectrum the intensity of the 250 nm band is much greater relative to the intensities of the 210 nm bands shown in Figure 6-5. It has been suggested that the peroxy molecule ion has an absorption band at ~ 250 nm (Friebele et al., 1987; Hosono and Weeks, 1990 a). In a sample implanted with O + it would be expected that the oxygen molecule ion would be produced. The EPR spectra of Derryberry et al. (1990) clearly show that there is a relatively high concentration of such molecule ions and very small concentrations of E' centers compared with concentrations in silica samples implanted with other ions. We suggest that in the spectra of oxygen-implanted samples the absorption at ~ 245 nm is due to oxygen molecule ions. The paper by Derryberry et al. is discussed below in Section 6.5.1. Antonini et al. (1982) have also implanted silica with these ions and others. Figure 6-7 (Antonini et al., 1982) shows the spectra of one of their samples. The range of wavelength over which these measurements were made extends into the vacuum ultra-violet, to 120 nm. These data show that well-resolved bands are produced near the band edge at ~120 nm. It is evident from these data that the variety of bands and their production rate is dependent upon the element implanted. That there should be such a dependence on a particular noble gas ion may be indicative of chemical reactions between the noble

18 16

Corning 79£0 1 x 1016 250 keV OVcm 2

"12 •e 10

a

o. 6 o in

•9

4

200

250

300

350

A in nm

Figure 6-6. Optical density (arbitrary units) vs. wavelength in nm for Corning silica 7940 implanted with 1 -1016250keVOionscnr2.

gas ions and the substrate ions. Even though these data may be interpreted as showing noble gas ion-substrate interactions, such interactions are very small when compared with implanted cationsubstrate ion interactions. This disparity of effect is demonstrated in Figure 6-8 (Ar-

E-Band A

5 ooo Experimental points Computer fitted components in vacuum UV

A \i\ 1!

3 -

2 -

10.5 eV ft

/

B2

E-

Al

6 Energy in eV

7

v

J i

Figure 6-7. Absorption spectrum of v-SiO2 after R.T. irradiation with 46.5 MeV Ni + 6 ions (~ 1014 particles cm" 2 ). Solid line, bestfit spectrum; dotted lines, computer resolved structures in the vacuum u. v. (low energy details omitted).

343

6.3 First-Order Optical Properties of Implanted Wide Band-Gap Glasses 1017 B, Si and N/Ar implants in Si 0 2 0.500 0.400 .2 0.300 ! 0.200 0.100 0.000

200

220 240 260 Wavelength in nm

280

300

Figure 6-8. Optical absorbance vs. wavelength (nm) for samples implanted with 50 keV B, 95 keV Si and 50 keV N. The 50 keV N implant yield somewhat less absorbance than a 250 keV Ar implant, but on this scale the differences are not visible. All implants were at the 1 10 17 fluence level. The B 2 absorbance is at 245 nm.

nold etal, 1990). The absorption bands due to E', B 2 and a background absorption which increases with decreasing wavelength are more than an order of magnitude greater for implants of B and Si than for N or Ar. We suggest, as did Arnold (1978) in a comparison of the optical absorption spectra of Al (200 keV, 1016 ions cm" 2 ) and Ne (180 keV, 1.1-10" 16 ions cm" 2 ), that this difference is, in large part, due to chemical reactions between B, Al, Si and other cations with substrate Si and O. The noble metal cations and Cu are an exception which will be discussed below. 6.3.1.2 Ions from the First Transition Series of Elements

The group in the Departement de Physique des Materiaux, Universite Claude Bernard has been investigating the properties of ion-implanted glasses for several years. This group has implanted the iron ion in a variety of materials (Perez, 1984). High purity silica was their choice of a glass for implantations of iron. Their beam energies were 100 and 200 keV at a beam

current of ~ 1 JIA cm 2. Conversion electron Mossbauer, optical absorption and electron magnetic resonance spectroscopies, among other techniques, were used to determine some of the properties of the implanted glass (Perez et al., 1983 a, b, 1985, 1987; Griscom et al., 1988). On the basis of their Mossbauer and TEM (transmission electron microscopy) data, they identify several chemical states for Fe after implantation, and a major fraction of the implanted ions are found in separate phases. The relative fractions of Fe in differing charge states and sites are given in Table 6-2 in as-implanted samples as a function of dose and in Table 6-3 as a function of annealing temperature for one Table 6-2. An abstract of Table 1 in the paper of Perez et al. (1987). The numbers are relative areas of Mossbauer components in the conversion electron Mossbauer spectra of implanted silica samples. Doses (ions cm 2)

Components

Fe° Fe 3 O 4 single line Fe + 2 Fe + 2 Fe° (sextet)

4-10 1 6

6-10 1 6

14 10 16

13 29 35 23

20 40 21 19

2 12 8 13 65

Table 6-3. An abstract from Table 2 in the paper of Perez et al. (1987) implanted with a dose of 1.4 * 10 17 250 keV Fe ions cm ~ 2 and subsequently annealed in air at 600 and 800 °C. The values are percentages of each species of Fe ion. Components

Single line Fe 3 O 4 Doublet Fe + 2 Doublet Fe 2 O 3 Sextet Fe° Sextet Fe 2 O 3

Annealing temperature (°C) 600

800

10 10 37 33 10

13 21 66

344


dose. The various types of Fe in the as implanted samples are Fe° in colloid particles, and Fe + 2 in two distinct environments one of which is Fe 3 O 4 particles. The fraction of ions in these various states was a function of the dose in the range 4 • 1016 to 14 • 1016 ions cm" 2 for 25°C substrate temperature during implantations. The precipitates were crystalline and ranged from 2 to 50 nm in size. a) Cr, Mn, and Fe The optical absorption of the implanted samples, shown in Figure 6-9 (Perez, 1987) as a function of dose, was reasonably explained by the Mie theory (Mie, 1908) for absorption and scattering by small particles (dimensions ^ the wavelength of the incident light) suspended in a material whose refractive index differs from that of the particles. The optical absorption was due primarily to absorption by the precipitated particles of iron and iron oxides. The absorption spectrum of samples implanted to a dose of 12 • 10 16 cm ~ 2 and annealed at 800 °C in air contained three peaks at 220, 400 and 550 nm (curve e in Figure 6-9, indicated by arrows), which were attributed to Fe + 3 charge transfer bands. Stark et al. (1987) have described the optical absorption spectra of high-purity silica implanted with Cr, Mn and Fe to doses ranging from 10 16 to 6 10 16 cm~ 2 at a substrate temperature of ~ 25 °C during implantation. Beam currents were ~ 4 JIA cm" 2 and beam energy was 160 keV. The spectra observed, shown in Figure 6-10 (Stark et al., 1987) for the three ions after implanting a dose of 1016 cm" 2 consisted of two bands with peaks at ~ 5 and 5.8 eV and the tail of a band with a peak at higher energy. Their measurements were limited to energies less than or equal to 6 eV. They attributed these bands to defects of the sil-

300


700

Figure 6-9. Optical absorption of Fe-implanted SiO2 glass samples, a) 1016 ions cm" 2 , b) 3 • 1016 ions 20- 1016 ions cm" 2 , cm 2, c) 6 16 ions cm" 2 heated for 20 h at d) sample with 20 • 10 ^ 800 K in air.

ica substrate produced by the implanted ions. The defects were the B 2 band (Antonini et al., 1982) and the E' center (Weeks and Sonder, 1963). In this regime of doses, and for the same dose, the absorptivity was a function of the ion implanted, as shown in Figure 6-10 b. Iron was the most absorbing and Mn the least. This ion-dependent absorptivity is attributed to the differing absorptivities, i.e., differing complex refractive indices, of particles of Cr, Mn and Fe oxides. The absorption spectra in samples implanted with 0.5 • 1016, 2 • 1016, and 6 • 1016 160 keV Fe ions cm" 2 have been measured in the range from 5.5 to ~ 8 eV (Hosono et al., 1990). The spectra of the three samples have a single very intense peak at ~ 7.6 eV whose peak absorption increases with increasing dose. The peak is attributed to a transition from the ground state


1 x 1016 ions/cm 2 3x 1016 ions/cm 2 6x 1016 ions/cm 2

15 10 -

Cr

5 -

(/) 0

4.0 5.0 Energy in eV

3.0

(a)

6.0

15

Cr* 3x1016 ions/cm2/side Mn+ 3 x 1016 ions/cmVside Fe+ 3 x 1016 ions/cmVside £ 10

o 5

2.5

(b)

3.0

3.5

4.0 Lb 5.0 Energy in eV

5.5

6.0

6.5

Figure 6-10. Optical absorption of SiO2 glass samples implanted with ions from the first transition series of elements, Cr, Mn, Fe ions each implanted to three doses, (b) comparison of optical absorption of samples implanted with Cr, Mn, Fe with the same dose of 3-10 1 6 ions c m ' 2 (160 keV, 4uAcm~ 2 , substrate temperature ~30°C).

345

of a neutrally charged Si-Si bond, labeled homo-bond (Imai et al., 1988). The model proposed for the homo-bond is indistinguishable from that of the E" center. For doses < 3 • 1016 ions c m ' 2 the amplitude of the absorption peak is the same for either Cr, Mn, or Fe. It is much larger for Ti. For larger doses the amplitude for Cr and Mn are almost the same and larger than for the Fe-implanted sample. The amplitude in the case of the Ti implanted sample is almost twice larger. Assuming an implantation layer thickness =140 nm and an absorption cross-section for the transition of 8 • 10~~17 cm" 2 , the calculated concentration of the homo-bond as a function of dose is approximately equal to the dose in the case of the Cr-, Mn-, and Fe-implanted samples. The concentration of homo-bonds in the sample with the largest dose of Ti ions is approximately 1.5 times larger than the dose. At higher doses, spectra for Cr, Mn, Fe implanted samples in the range 2 eV (700 nm) to 6 eV (190 nm) were similar in that the absorptivity increased approximately linearly with increasing photon energy from ~ 2 to 6 eV. This linear increase with increasing energy is similar to that reported by Perez et al. (1987) and attributed to absorption by particles with diameters much less than the wavelength of the light, i.e., Mie absorption. For particles with radii smaller than the incident photon wavelength the extinction coefficient, for both absorption and scattering, is given approximately by (Arnold and Borders, 1977): (6-6) where Kahs is the absorption by small particles and Kscat is the scattering by small particles. These two terms are given by: Kabs = - (6 TI/A) / Im ((n2 - n20)/(n2 + 2 n2) (6-7)

346

and Kscai


(6-8) 3 2 2 2 = (24 7i VN/X*) ((n - n 0)/(n + 2 n2))

where n is the complex refractive index of the particles, n0 is the real part of the refractive index of the material in which the particles are imbedded, V is the volume per particle, / is the volume fraction of the particles, X is the wavelength of the incident photons, and N is the particle concentration. The spectrum will be approximately a linear function of photon energy for particles with R < X and with small conductivities. For metallic particles of Ag, Cu, and Au and for J^ < 20 nm, an absorption maximum will be observed at photon energies < 5 eV (Arnold and Borders, 1977). In the case of Cr, Mn, and Fe ions implanted at energies of the order of 200 keV, the distribution, as typically in Figure 6-2, has a width at half maximum amplitude of ~ 140 nm. Hence most (~ 80%) of the particles which form will have radii < 70 nm. For wavelengths > 200 nm both the absorption and scattering equations will be applicable. Absorption-plus-scattering spectra would be expexted to have a dependence on photon energy which falls somewhere between being proportional to photon energy and photon energy to the fourth power. Since the absorption spectra of Cr- and Mn-implanted samples are similar to those of the Fe-implanted samples and this Fe spectrum is similar to that reported by Perez et al. (1987), it is reasonable to attribute a major fraction of the absorption spectra of the Cr- and Mn-implanted samples to Mie absorption of precipitates containing Cr and Mn and with sizes that are small compared to the wavelength of the incident photons. It is interesting to note that the absorption spectra shown in Figure 6-5, although

containing well resolved components due to the E' center and the B 2 band, have a background component which is approximately linear with photon energy. The rather featureless spectra, without well resolved bands, are surprising since Perez et al. (1987) have identified several charge states for implanted Fe, given in Table 6-2, from conversion electron Mossbauer spectra. Although for a dose of 6 • 1016 ions cm" 2 the fraction of ions in the + 3 state is ~ 27% no bands attributable to charge transfer bands are resolved. Given the similar oxygen activities of Fe, Cr, and Mn (Table 6-4) we expect that the fraction of ions in the 0, + 2 and + 3 charge states of implanted Cr and Mn to be similar to those of Fe. After an anneal at 800 °C, bands are resolved in Fe-implanted samples which are attributed to charge-transfer bonds of Fe 3 + (see Figure 6-9). The absorption spectra of Cu implanted SiO2 glass differ from the spectra observed for ions of the other transition series of elements. Only at doses 1016 ions cm~ 2 and for several substrate temperatures the refractive index as a function of the optical absorption at 2.2 eV is well fitted by a linear function. Weeks et al. (1989) attribute 2000

1.00


zoo

Figure 6-11. Optical absorption of SiO2 glass samples implanted with Cu ions, (a) 6-10 16 ionscm~ 2 , (b) 3 • 1016 ions cm" 2 , (c) 1016 ions cm" 2 , (d) 0,5 • 1016 ions cm' 2 , (e) 0.3 • 1016 ions cm" 2 (160 keV, 4 A cm" 2 , ~30°C).

1.5

1.6 Refractive index

Figure 6-12. The optical density measured at 2.2 eV (the peak of the first resolved band in the spectra shown in Figure 6.6) is plotted as a function of the refractive index, measured at 1.9 eV (633 nm) by an ellipsometric technique. The numbers and symbols have the following meanings: A, dose = 1016 ions cm" 2 ; n, dose = 3 • 1016 ions cm" 2 ; o, dose = 6 • 1016 ions cm" 2 : 1, substrate temperature ~ 100 K; 2, substrate temperature — 300 K; 3, substrate temperature ~ 700 K.

347

this linear relation to the case in which the imaginary part of the refractive index is much larger than the real part. Magruder et al. (1989,1991) have attributed the absorption band in the region of 4.2 and 2.2 eV to spherical particles of Cu° and oblate or prolate colloidal spheroids of Cu with an axial ratio of ~ 2, respectively. The 4.2 eV band is attributed to spheroidal colloids of Cu with diameters ranging from a few nm to ~ 10 nm. Calculations have shown (Arnold and Borders, 1977) that for Ag particles with radii > 10 nm the peak absorption shifts to lower energies. In the spectra of samples implanted with doses > 3 • 1016 Cu ions cm" 2 there is a shift to lower energies of the shoulder at ~ 4.2 eV observed in the spectra of samples implanted with smaller doses (1016 Cu ions cm ). Spectra calculated for Ag particles shows that for particle radii > 25 nm the absorption splits into two maxima, one at the wavelength of the absorption for particles with radii < 14 nm and one with a wavelength that shifts to longer wavelengths with increasing particle radii and whose width at half maximum amplitude also increases. With the bimodal distribution of Cu shown in Figure 6-3 for doses > 1 • 10 16 ions cm" 2 the fraction of Cu particles with radii > 200 nm must be very small. Most of the spheroidal Cu particles have radii < 50 nm, assessed on the basis of the shift of the 4.2 eV shoulder. Another property of colloidal particles which produces a splitting of the absorption is deviation of particle shape from spherical (Trotter et al., 1982). Thus, an absorption band at 2.2 eV, observed by Magruder et al. (1989) was attributed to oblate or prolate spheroids with a major-to-minor axis ratio of ~ 2 . Optical absorption of Cu + 1 in silicate glasses has been observed at ~ 5.2 eV (Parke and Webb, 1972). The absorption

348


spectra of implanted silica samples have a shoulder at ~ 5.2 eV which may be due to Cu + 1. Weeks et al. (1989) report that no spectral component attributable to Cu + 2 was detected in the EPR spectra of implanted samples. Thus it appears that in the case of Cu implanted into silica a major fraction, perhaps as high as 99%, is in the Cu° and C u + 1 states. Weeks et al. (1989) did not detect any EPR spectral component attributable to Cu + 2 in Cu implanted borosilicate and aluminosilicate commercial glasses. They also note that neither is an optical absorption band detected at 2.2 eV nor at ~ 4 eV. They tentatively conclude that most of the Cu in these glasses is in the + 1 state. They comment that optical absorption measurements could not be made at energies > 4 eV because of very intense absorption at these energies in their samples. We noted above that the chemical reactivity between implant ions and substrate ions will, in part, determine the optical absorption spectra directly attributable to implanted ions and also, as we will discuss below, the paramagnetic states of defect states in the substrate structure. Magruder etal. (1989) have discussed these reactivities in terms of the relative oxygen activities of some implant cations and the substrate cation, Si. These relative activities are given in Table 6-4. From this table we note that Ti has a higher free energy of Table 6-4. Gibbs free energy, G*, of formation at 298 K (Kcal/mol) (per mol oxygen). Reduced oxide a-SiO2 TiO MnO Cr 2 O 3 FeO Cu 2 O

G*

Oxidized oxide

G*

-189.9 -233.8 -173.5 -168.8 -117.3 - 35.5

TiO 2 Fe 2 O 3 MnO 2 CrO 3 CuO

-212.4 -118.3 -111.3 - 80.6 - 61.7

formation with oxygen than does Si. Hence we expect that displaced oxygen ions will react with implanted Ti ions to form oxides and that these reactions will result in higher concentrations of E' centers, E" centers, and smaller concentrations of oxygen related paramagnetic centers such as peroxy molecule ions. The lowest free energy of formation is between Cu and O. In this case the reactions between Si and O will dominate. The result will be smaller numbers of E' and E" centers, higher numbers of oxygen related centers as compared with those for Ti implanted samples. We expect that the numbers of these centers in Cr, Mn, and Fe implanted samples will be intermediate between those for Ti and Cu. The optical absorption spectra of lithiaalumina-silica glasses implanted with Ag and Au will be described below in Section 6.3.3.1. Colloidal particles also form in these glasses during implantation and in some glasses after thermal treatments. c) Titanium There is little to report on the absorption of Ti-implanted silica. For doses < 5 - 1 0 1 5 Cu ions the optical spectra shown in Figure 6-13 is due primarily to the bands of B 2 and E' centers. With increase in dose the absorption at energies > 5.5 eV increases three-fold while there is little change at energies < 5 eV. Becker et al. (1990) note that the absorption of Ti implanted samples increase by a factor of two with an increase in dose from 1 • 10 16 to 6 • 1016 ions cm" 2 . Their measurements of the absorptivities of samples implanted with Ti have values of a ~ 5 • 103 cm" 1 for a dose of 1016 ions cm" 2 , assuming that the thickness of the absorbing layer is equal to the width at half maximum amplitude of the distribution as a function of depth, i.e., 2-130 nm = 260 nm, since both


0 4.00


7.00

Figure 6-13. Optical absorption as a function of photon energy of Ti implanted samples with (a) 1 • 1015 ions cm" 2 and (b) 3 • 1015 ions cm" 2 .

sides of their samples were implanted with the same dose. The non-linear properties of the absorption spectra of Cu and Ti implanted samples will be discussed below.

349

ellipsometric technique. The variation in the index near the implant surface of the as-received sample may be due to surface contaminants and polishing defects. The heat treatment appears to have removed these. In the treated sample there does appear to be a small maximum in the index at a depth of ~200nm and at a depth of ~ 600 nm the effects of implantation disappear. The increase in index over the entire range in the heat treated sample is An/n -0.005. The refractive index changes produced by various ions are shown in Figure 6-15 (Webb and Townsend, 1976). The data in this figure illustrates, in our opinion, the effects of chemical reactions between substrate ions and implanted ions. For example a dose of 1015 20keVH + or B + ions cm" 2 increases the index of the implant surface as much as 10 16 20 keV He + ions cm" 2 . The much greater range of the H + ions produces an increase in the index

63.1.3 Refractive Index, Real Part Neutron irradiation of silica increases the density by 2.5% (Wittels and Sherill, 1954). Implantation of noble gas ions, for which chemical reactions with substrate ions would be expected to be negligible, produce increases in refractive index An/n ~ 1.5% (Bayly and Townsend, 1973). The refractive index as a function of distance from the implant surface is shown in Figure 6-14 (Boyly and Townsend, 1973) after implanting 1016 Ar ions cm" 2 at 300 keV. Although no information about substrate temperature is given, the lack of information is probably indicative of nominal room temperature. Shown in the figure are profiles for two samples, one as received and one thermally treated for 90 min at 425 °C. Samples were sectioned by three techniques and the index measured by an

After"! 90minat425°C 0.010 An n

0.005

=n LJ

0.010 nK 0.005 0

—>

L..J

i i

r

J 1

•—I

j—'

b n_

1 r__.j

2

3

4

1

5

H

Range in nm

Figure 6-14. Refractive index profiles of samples implanted with 300 kV Ar, 1016 ions cm" 2 , with and without prior annealing for 90 min at 425 °C in air.

350


800

Figure 6-15. Refractive index profiles for implantations of silica with (a) 20 keV B + to a dose of 1 • 1015 ions cm" 2 , (b) 20keV He + to 1 • 1016 ions cm" 2 , (c) 20 keV H + for 1 • 1015 ions cm" 2 , and (d) 2000 keV Bi + for 1 -10 ionscm~ 2 .

that extends to a depth > 400 nm. The maximum change in the index in the three cases is An/n ~ 0.017. A high energy (2000 keV) implant of Bi increased the index to a depth of ~ 800 nm, with the maximum at a depth of ~ 600 nm. The increase was slightly larger than in the case of the H ions. Reactions between Bi and substrate ions may be a factor in this increase, also. Some data on the effects of Cr, Mn, and Fe implanted in silica on refractive index have been reported (Whichard et al, 1988). These data show that the index, measured by an ellipsometric technique at ~ 633 nm, increases with in-

creasing dose when the dose is 1016 ions cm" 2 or greater and the increases are similar for the three ions. The values for the refractive indices were calculated for a "single layer" model. In this model it was assumed that the change in index was uniform throughout the implanted layer. For the highest dose, 6 • 1016 ions cm" 2 , the indices increased ~ 5%, with the largest increase in the Fe implanted sample (Whichard and Weeks, 1989). One of the interesting features of the changes in refractive index produced by heavy ions is that the variation in the index with depth from the implanted surface is not large until the end of the range of the implanted ions. A comparison of the index change, together with vacancy and implanted ion distributions calculated with the TRIM program, are shown in Figure 6-16 (Faik et al., 1986). Before annealing the index is almost constant to a depth at which the distribution of the implanted ion is a maximum. After annealing it varies in the same way as the calculated vacancy concentration and not as the implant ion distribution. The temperature of the anneal (450 °C) was sufficient to remove most of the electronic states which were paramagnetic

- U6 0.3 Depth in jjm

Figure 6-16. A comparison of the experimentally determined refractive index profiles (a) before and (b) after annealing at 450 °C with TRIM calculations of (c) vacancy and (d) impurity distributions. The N + ion energy was 0.18 MeV for a


states of intrinsic defects (Perez et al., 1983 b). It was not sufficient to remove the chemical disorder introduced by the implantation. At the dose used for these measurements and calculations, 1016 180keV N + ions cm = 2, all of the substrate ions will have been displaced a least once. Weeks and Sonder (1963) and Stevens et al. (1958) showed that for a neutron dose sufficient to displace all silica ions at least once the concentration of intrinsic paramagnetic states begins to decrease. At neutron doses much higher (1021 n cm" 2 ) than this dose (3 • 1019 n cm" 2 ) the decrease is almost a factor of two. For implant doses >10 1 4 ions cm" 2 most substrate ions have been displaced at least once. Thus for all of the implant doses, discussed thus far, we expect that the vacancy concentration as measured by intrinsic paramagnetic states is less than the maximum concentration observed in the case of neutron irradiation. It is difficult to interpret the TRIM calculation of vacancies per ion when the vacancies per ion exceeds the concentration of ions. It may be that the agreement between the index after thermal treatment and the number of vacancies per ion is fortuitous. In Section 6.5.1 we review the data of Hosono and Weeks (1990 b) in which it is shown that E' centers, i.e., singly charged vacancies, have a higher concentration near the implant surface and peroxy radical centers, i.e., interstitial oxygen, has a higher concentration at the peak of the implanted ion distribution. Thus the distribution of defects is a function of the type of defect and is not uniform. 6.3.1.4 Infrared Spectra One of the problems in measuring the effects of ion implantation on the vibrational bands of silica is the measurement of a very thin layer on a thick substrate, both

351

of which are principally SiO 2 . The usual technique is to measure the reflectivity of implanted samples. This technique, for wavelengths > 5 jim, samples a layer that is less than ten times thicker than the implanted layer (Magruder et al., 1990 a) if that layer is < 300 nm thick. Quantitative measurement of relative amplitudes of bands is difficult whereas relative measurement of peak positions of bands is more accurate by this method. In our review of the literature reports of bands due to implanted ion-substrate ion vibration bands have not been detected. The effects reported are due to changes in the bands observed in silica before implantation (Arnold and Borders, 1977; Arnold, 1978,1980,1981). These changes are attributed to changes in the SiO2 structure. 6.3.2 Alkali Silicate Glasses Glasses with alkali silicate compositions are an extensive group with many uses. For most applications, additional elements are added to design a glass with particular properties. In most of the research on effects of ion implantation on properties, three-component (alkali, silicon, oxygen) glass compositions have been chosen for investigation. The vast literature on properties of these glasses provides an excellent basis for interpreting effects produced by ion implantation. 6.3.2.1 Noble Gas Ions During implantation of Xe a depletion of Li and Na in Li 2 O:SiO 2 (Arnold and Peercy, 1980) and Na 2 O:nSiO 2 (Bach, 1975) glasses, respectively, in the implanted layers has been observed. In the case of the Li 2 O:SiO 2 glass samples, Arnold and Peercy (1980) observed that H, already present in their samples, diffused into the Li-depleted region. In the case of the

352


Na 2 O: n SiO2 glass samples, this effect was not reported (Arnold, 1978). In either case the optical absorption spectra produced by the implantation of Xe ions would be affected. In the paper of Bach (1975) the absorption spectra of the Xe implanted Li 2 O:SiO 2 glass samples are only given after the samples have been annealed at 500 °C. In these spectra an intense band with a peak at 470 nm is present. The spectra of samples of silica implanted with Li have a band with a peak at ~ 500 nm (Arnold and Peercy, 1980). The peak position shifts to smaller wavelengths after annealing. In both cases the band in annealed samples is attributed to colloidal Li. We note that bands in the region of 500 nm in silica and in alkali silicate glasses have been attributed to non-bridging oxygen hole centers (Friebele and Griscom, 1986). The band, produced by radiation with energetic photons, electrons, protons, or noble gas particles in either glass system, disappears after an anneal at temperatures above 300 °C. The absence of a decrease and the presence of an increase with annealing at temperatures above 500 °C is strong evidence that the ~ 500 nm band in both systems implanted with Xe or Li is not due to non-bridging oxygen hole centers. The stability and increase in intensities is certainly consistent with the formation and growth of colloidal Li particles. The specular reflectances of samples of a soda-lime glass implanted with Ar ions has been reported (Geotti-Bianchini et al., 1984). The samples had a composition 73.4 wt.% SiO2,13.6 wt.% Na 2 O, 6.8 wt.% CaO, 3.8 wt.% MgO and 2.4wt.% of other oxides. Measurements were made over a range of wavelengths from 300 to ~ 2000 nm. The reflectance decreased with increasing doses of Ar (2 JIA cm~ 2 , 50 keV) with a minima in the range of 700 nm and

with no measurable change at ~ 380 nm for doses less than or equal to 5 • 1016 ions cm" 2 . At higher ion energies the wavelength dependence of the reflectivity was more complex. The maxima and minima shifted to longer wavelengths with increasing ion energy. 6.3.3 Multi-Component Glasses Four-component glasses such as alkalialkaline earth-silica compositions have many applications and, consequently, there is considerable research on the modification of the properties of these glasses by ion implantation. The alkali aluminosilicate compositions are used in many applications and glasses with these elements have been frequently chosen for ion implantation experiments. 6.3.3.1 Noble Metals In Section 6.2 we noted that Ag implanted in samples with those compositions have a distribution similar to that of Cu in silica. This ion also forms colloids as implanted and after implantation and subsequent thermal treatments. Figure 6-17 (Arnold and Border, 1977) shows the absorption spectra of samples implanted with 1016 Ag ions cm" 2 at an energy of 275 keV. Arnold (1975) and Arnold and Borders (1977) attribute this spectrum to colloidal Ag particles with radii of the order of 2 nm. The spectrum has only one well resolved peak at a wavelength of ~410nm. The spectrum for Cu in silica is much more complex (see Section 6.3.1.2, above). The peak, in the spectrum of samples given isochromal (30min) anneals, shifts to longer wavelengths until a 400 °C anneal. After an anneal at 500 °C the peak shifts to a shorter wavelength. These shifts are due to an increase in particle radii from 15 to

6.4 Non-Linear Optical Properties 1016 275 keV Ag+ ions/cm 2

6.3.3.2 Halide Glasses

(no annealing) this experiment MIE theory. R = fl = 1.75nm ) Kreibic and /9 = 2.75nml v - Fragstein data

340

380

420

460 500 A in nm

540

353

580

620

Figure 6-17. Measured optical extinction K (arbitrary units) as a function of wavelength A (nm) for 1 • 1016 275 keV Ag ions cm ~ 2 as implanted into a lithia-alumina-silica glass compared with Equation (6-1) evaluated for R ~ 20 A, contamination factor C ~ 1, and d = 2.2.

~ 40 nm and then a decrease to 10 nm after the 500 °C anneal. The formation of colloidal particles in as implanted samples is attributed to beam heating by Arnold and Borders (1977). In the Cu implanted silica colloids formed at substrate temperatures ~100K. We suggest that colloid formation may be due to other processes. In the case of Au implantation into the lithia-alumina-silica glass samples, colloids did not form until samples were annealed (Arnold and Borders, 1976). Implanting Ag into crystalline LiNbO 3 , A12O3, and a-quartz caused colloids to form upon implantation (Rahmani and Townsend, 1989). At implant doses > 5 • 1016 ions cm" 2 , the implanted layers were amorphous in the three crystals.

Halide glasses composed of Zr, Ba, Al, and other cations have been considered as potential fiber optic glasses for applications in the 2 to 10 jim wavelength range (cf. Chapters 8 and 15). They have the potential for attenuations that are one to two orders of magnitude lower than silica fibers. The effects of implanting samples of various compositions have not been extensively reported. Most of the research has been in the laboratories of P. Mazzoldi (1990). One of the effects of implanting Ar is an increase in the relative amounts of Zr and Ba in the implanted layer. The reflectance of the surface increased in the range 350 to 2500 nm. The absorptivity of the samples also increased in the range from 250 to 2000 nm. The wavelength dependence of the absorptivity was observed to be a function of the implanted ion species, e.g., N produced the largest increases compared with H and Ar. The data reported were for differing doses of these ions and hence a comparison for the same dose is not possible.

6.4 Non-Linear Optical Properties It was noted above that the polarization of a wide band-gap material can be expressed as a power series of electric fields interacting with the material. The third order term, expressed as the refractive index, is n = no + n2E3

(6-9)

in which n0 is the first order term of the refractive index, n2 is the non-linear index, and E is the electric field. In the case of photons, E is the field of the photons. Thus to measure the value of n7 the E-field of


500 1000 Laser power in mW

Figure 6-18. Absorption of Ti implanted samples as a function of incident photon power, X = 532 nm. Doses (1015 ions cm" 2 ): o = 60, A = 60, + =10, x = 3, * =1.

550

600


800

Figure 6-19. Laser induced fluorescence of Ti implanted fused silica. The structure in the region of 5500 nm is stray light from the laser.

1 uni

en

Cu h

i arbit

(JDJ

incident photons must be varied. One technique for this measurement is called the z-scan method (Sheik-Behae et al., 1989). Becker et al. (1990) have made such measurements on Ti and Cu implanted silica. They used a frequency-doubled Nd-YAG laser (532 nm, 100 ps FWHM pulse width, 76 MHz pulse repetition rate, and 1.8 W average power). Both samples absorbed strongly at this wavelength. Absorption at 532 nm in samples implanted with Ti to doses of 1015, 3 • 1015, 10 • 1015, 60 • 1015 and 60 • 10 15 ions cm~ 2 is shown in Figure 6-18 (Beeker et al., 1990) as a function of photon power in mW. Interesting features of this absorption are: the similar absorptivity of samples with 1 to 10 • 1015 ions cm" 2 and the two samples with a dose of 60 • 1015 ions cm" 2 , absorptivity in the low dose samples saturates and absorption decreases from 17% to 12% with increase of power from 100 to 1300 mW, absorptivity in the high dose samples was independent of power in the same range, and the increase in absorptivity with increase of dose from 10 to 60 • 10 16 ions cm" 2 is from 17% to 30%. A 17% decrease in transmission represents a very large change in absorption coefficient since the thickness of the absorbing layer is only 120 nm. The absorption coefficient is of the order of H^cm" 1 . Luminescence stimulated by the 532 nm photons is shown for one Ti-implanted sample in Figure 6-19 (Beeker et al., 1990). Luminescence in Cu-implanted sample was similar, with the peak occurring at a wavelength ~ 30 nm greater than that for the Ti samples. The z-scan data are shown in Figure 6-20 (Beeker et al., 1990) for Ti- and Cuimplanted samples. The z-scan spectrum for an unimplanted silica sample is also shown in both parts of the figure. The shape and amplitude of the two spectra are

(NJ

\ pure FS l_Lirm

*

•tLIULJiTl-lWW.-MiP'*

->>

Q

detector

354

c o >^

pure FS

U)

3 • 1016 ions cm" 2 . A major fraction, - 9 0 % for a dose of 6 • 1016 ions cm" 2 , is not detected in the EPR spectrum. Whichard et al. (1990) have found that the magnitude of the exchange integral for the paramagnetic fraction of the Ti 3 + ions ranges from 10 to 1.6 • 10 ~6 eV. They assume that the paramagnetic fraction is that fraction in the tails of the ion distribution measured by ion back scattering, as shown in Figure 6-32 (Whichard et al., 1990) by the triangles. The temperature dependence from 5 to 300 K of line width, resonance field and intensity for all doses was that expected for a paramagnetic state. The chemical states of the large fraction of Ti ions not detected in the EPR spectra were not identified. It is plausible to assume that some fraction of those undetected Ti ions are in + 2 and + 3 states. On the basis of this assumption we then suggest that these Ti ions have large exchange Table 6-8. The g-value, line width, and relative intensity of the Ti EPR signal for three implantation doses. g

AH (G)

Relative intensitiy (arbitrary units)

1.936 + 0.007 1.931 ±0.007 1.941 ± 0.005

145 + 15 180 ± 15 205 + 15

6 3 4

Nominal dose (1016 ions/cm2 )

Ti 6 3 1

RBS of Ti ion implanted silica Ti dose in ions/cm2 A

1 x10,16

0.15 E

° 3 0.10 -2

0.05 £ a

1°o A.2 °A

^ '

0.0

0.1 0.2 Depth in |jm

0.3

0.00

Figure 6-32. The backscattering depth profiles for titanium implanted samples. The outlined regions in the tails at depths > 150 nm account for half of the implanted ions detected by EPR in that sample. The other half of the detected ions are assumed to be located in the tail near the sample surface.

interactions which are either anti-ferrimagnetic or speri-magnetic. Whichard (1989) reports some experiments in which he detected transient signals that were at least two orders of magnitude more intense than the paramagnetic component. He does not describe an experimental procedure which ensured reproducible data. He did note that the transient signal was detected again when a sample was removed from the EPR spectrometer and magnetic field for more than three days. e) Cu Ions The only EMR or EPR components detected in Cu implanted samples were those due to silica defects. Weeks et al. (1989) implanted silica and two other types of glass samples. The other two samples were a standard Corning borosilicate and alumino-silicate glasses. In none of these glasses did they detect any compoent attributable to Cu + 2. They suggest that implanted Cu is either in a colloidal state, i.e. Cu°, or Cu + 1 . They note that in the case of silica implanted with Cu, the optical absorption spectra of samples, with a range of doses

368


>10 1 6 ions cm 2, contained no resolved band at 5.2 eV, the energy of a band attributed to Cu + 1 in silicate glasses. They note that in the case of the samples of the other glasses the optical absorption at energies > 4 e V were too intense to observe this band. By comparison with the absorption spectra of Cu in silica samples in which the absorption bands in the 2 to 4 eV range are attributed to Cu colloids, the absence of these bands in implanted samples of the other glasses leads to the conclusion that in these glasses a major fraction of the Cu is in the + 1 state.

6.6 Glasses Produced by Implantation of Crystalline Substrates Irradiation of one of the crystalline forms of silica, a-quartz, with neutrons transforms the crystal to a glass with a density that is ~ 2 . 5 % greater than the density of a silica glass formed by thermal processing (Lines and Arndt, 1960; Primak et al, 1955). The increase in the refractive index of silica implanted with noble gas ions is ~ 2%. This is the increase expected from the increase in density which results from the modification of the structure of thermally processed silica by atomic displacements. In addition to the changes in structure which produce the increase in density, optical absorption bands and paramagnetic states due to defects are introduced by the irradiation. Among other wide band-gap crystals which have been observed to transform to the amorphous state under some conditions of ion implantation are A12O3 (McHargue et al., 1990a, b), SiC (McHargue et al., 1990 c), Si^N* (Arnold and Borders, 1976), CaTiO 3 (White et al.,

1989), KTaO 3 (Arnold and Borders, 1976), and many naturally occurring silicates (Wangetal., 1990). Townsend et al. (1990) have fabricated optical waveguides in A12O3 by implanting group IV elements. The amorphous state is produced by elements of the group IV column at doses and substrate temperatures during implantation, less than for the elements in other columns of the periodic table. The dose is < 10% of the dose and the substrate temperature during implantation may be 300 K compared with a temperature of ~ 80 K required for other elements (McHargue et al., 1985). Figure 6-33 (Townsend et al., 1990) shows the refractive index of A12O3 implanted with 5 • 1016 carbon ions cm" 2 . The data show that larger decreases in the refractive index are produced when the implanted face of an A12O3 crystal is the Z face. The damage profile and the carbon ion profile have substantial differences as shown in Figure 6-34 (Antonini et al., 1982; Arnold, 1980). The chemical state of the C ion has not yet been investigated. Townsend et al. (1990) suggest that the column IV ions act as catalysts in the process of forming a glass network: "The distortions associated I./D

Z

Y

/77 = 2

m=1 1.77

n

h

Z

1.76

-

m-\

\ 1.78

i

i

1

Depth in nm

Figure 6-33. Waveguide refractive index profiles (for an implanted dose of 5 • 1016 carbon ions cm" 2 ): 6MeV.

6.6 Glasses Produced by Implantation of Crystalline Substrates

Figure 6-34. Comparison of ion range and damage distributions (for 6 MeV carbon implants in A12O3).

with the tetravalent bonding are not localized at a single site but influence some tens of neighboring lattice atoms." This quotation clearly indicates that Townsend et al. have assumed that the C ions are multivalent. The chemical reactions between implanted ions and substrate ions affect the structure of substrate ions far beyond the nearest neighbor range. The mechanism for such a long range interaction is not obvious, as is indicated by the use of the term "catalyst". In this case C ions cannot react directly with each of the "tens of neighboring ions" as is the case for those chemical reactions usually labeled "catalytic". Conversion electron Mossbauer spectroscopy (CEMS) has been used to determine the chemical states of Fe and Sn implanted in A12O3 (McHargue et al., 1987, 1990 b). The chemical states of Fe, as a function of dose implanted at ~ 300 K, are shown in Figure 6-35 (Perez, 1984). The implanted layers for these doses implanted at ~ 300 K are still crystalline. A substrate temperature ~ 80 K is necessary for the formation of an amorphous layer. The chemical states of Fe in this case are shown in Figure 6-35 (Perez, 1984). The data show that there are differences in the chemical states which form at the two temperatures.

369

The major differences are the production of Fe + 4 which increases with increasing dose in two different sites and the absence of Fe + 3 in samples implanted at 77 K. A decrease in Fe + 2 in two differing sites with increasing dose occurs in both cases. The fraction of Fe in the Fe° state is invariant with dose for implantation at 77 K but increases with dose for implantation at 300 K. The optical absorption of the implanted layer, implanted at ~ 300 K, has a dependence on photon energy that is similar to that of Fe implanted silica (Stark et al., 1987). Optical absorption of A12O3 implanted at 77 K has not yet been reported. Based on this similarity, the explantation proposed by Perez et al. (1987) for the photon energy dependence of the absorption in Fe: SiO2 is also applicable to the Fe: A12O3 case. In the case of implanted C ions in A12O3, Townsend et al. (1990) suggested that column IV elements were much more effective in producing an amorphous state in A12O3 than were other elements. McHargue et al. (1990) have determined the chemical states and their fractions of implanted Sn ions in the amorphous layer of A12O3 produced by implantation at - 3 0 0 K of 4 • 1016 ions cm" 2 . The final charge states of the Sn ions were + 2 and + 4. The possibility that some small (< 2%) fraction of the Sn was in the 0 state could not be resolved. Neither refractive index nor optical absorption of Sn implanted samples have been reported, to our knowledge. If the Sn ions interact with the substrate ions to form the amorphous state does this interaction also affect the defect states of the substrate? McHargue et al. (1990 b) have used CEMS to determine the chemical states of Fe implanted in single crystal SiC. Their samples were implanted with doses ranging from 1 to 6 • 1016 ions c m ' 2 at - 3 0 0 K .

370

6 Optical and Magnetic Properties of Ion Implanted Glasses (b)

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to broaden about an average value of 4> ~ 105° and to allow some randomness in the phase relationship between neighbouring dihedral angles. The fit of this model to the X-ray data is shown in Fig. 7-20, for which 60% of configurations were trans-like and 40% cis-like. A model of freely-rotating chains does not seem to give as good a fit. TRANS With increasing temperature, above the melting point (493 K) in the liquid domain, it is expected that the ring-chain equilibrium should shift in favour of chain-like molecules, the average chain length decreasing rapidly with increasing temperaCIS Figure 7-19. Definition of dihedral angle <j> for the ture. This picture has been supported by neutron diffraction measurements (Edeling case of a Se chain, and the atomic configurations of the cis and trans conformers. and Freyland, 1981; Bellisent and Tourand,

neutron-scattering study of glassy sulfur, prepared by quenching the melt in liquid nitrogen. They find that the structure of the melt and of the quenched glass are rather similar with a bond length of 2.06 A, although the experimental RDF of the glass differs in significant details from that of the molecular dynamics S 8 model of Stillinger et al. (1986), indicating that, as expected, the structure of the glass comprises an appreciable fraction of chains. The structure of amorphous (and liquid) Se has been much more extensively studied than is the case for S, and reviews have been given by Andonov (1982) and Corb et al. (1982). Four crystalline forms exist: the most stable trigonal (or hexagonal) form consists of helical chains packed in a parallel fashion, whereas the a- and /?-monoclinic forms are composed of S8 rings but packed differently; in all cases the bond length is ^2.32 A and the bond angle is 0^105°. What distinguishes the various polymorphs is the dihedral angle, or more specifically the correlation between neighbouring dihedral angles. Fig. 7-19 shows how x>0.6) and liquid alloys (l>x>0.3) could be well fitted by a chain-like model, in which Te substitutes for Se atoms whilst maintaining two-fold coordination. In the more Te-rich liquid alloys, however, the influence of three-fold coordinated Te atoms could not be neglected. Finally, an interesting feature of Se-Te alloys is that if the metallic crystalline phase (of Se67Te33), produced by the application of high pressure to the amorphous form, is quenched to atmospheric pressure and 223 K, the semiconducting trigonal form results but, when heated up to 300 K, the material becomes amorphous again (Mushiage et al., 1983). 7.3,3.2 Structure of V-VI Materials The most commonly studied materials in this system are the As chalcogenides, based on the stoichiometric compositions As 2 S 3 , As2Se3 and As2Te3. The structure of amorphous As 2 S 3 , in both bulk glassy and amorphous thin-film forms has been studied by Daniel et al. (1979), and the experimental data are

7 Chalcogenide Glasses

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300 400 500 Raman shift/cm"1 b) Figure 7-24. (a) Vibrational density of states (VDOS) for glassy P2Se measured by inelastic neutron scattering (Verrall and Elliott, 1988). (b) Raman spectra of a-PxSe1_x alloys (0.67 < x < 1.0) (Phillips et al., 1989). In both cases, the cage-like vibrational modes of the P4Se3 molecule are indicated, together with an assignment of features in the VDOS and Raman spectrum in terms of these modes.

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ments on P-Se glasses also provide evidence for the existence of P4Sen clusters in the structure (Lathrop and Eckert, 1988; Eckert, 1989). In particular, the proportion of tetrahedral P sites (with a doubly-bonded Se terminator atom, viz. Se = PSe3/2) progressively increases with decreasing P content (see Fig. 7-25); this is evidence for the existence of say P 4 Se 10 clusters (see Fig. 7-23) at low P contents. In the case of glassy P2Se, evidence that the structure consists almost entirely of P4Se3 molecules (with a small excess of P) is overwhelming. The static structure factor S(Q) for g-P2Se can be fitted almost exactly for Q 2> 6 A" 1 by the form factor calculated for the P4Se3 molecule (Verrall and Elliott, 1989). Inelastic neutron scattering studies of the vibrational excitations of g-P2Se reveal a highly structured density of states (see Fig. 7-24 a), the peaks in which can be assigned to the vibrational excitations of a P4Se3 molecule (Verrall and Elliott, 1988 a, 1989); Raman measurements by Phillips et al. (1989) support this finding, and the higher resolution of this technique allows more of the vibrational modes to be distinguished (Fig. 7-24 b). Finally, quasi-elastic neutron scattering mea-

409

7.3 Structure

surements have been performed on g-P2Se, and a quasi-elastic broadening of the elastic line was observed at elevated temperatures (300-450 K), indicative of the presence of atomic motion (Verrall and Elliott, 1989). These findings have been interpreted in terms of a rotational diffusion of P4Se3 molecules in the glassy structure, similar to that which occurs in the plastic phase (T > 355 K) of crystalline P 4 Se 3 .

Se=PSe3/2

PSe3/2

5.0

7.3.3.3 Structure of I V - V I Materials

The Ge and Si chalcogenides also exhibit a rich variety of structural features, particularly related to MRO, as a result of the propensity for the formation of edgesharing tetrahedra compared with their oxide counterparts. A survey of the structural features of amorphous IV-VI materials determined by diffraction methods has been given by Wright et al. (1982). It is significant that in the AX2 materials (A = Si, Ge; X = O, S, Se), oxides have an A-X-A bond angle greater than the tetrahedral angle of 109.47°, where the corresponding chalcogenide materials have an angle 6 (A-X-A) which is smaller than this. The structure of amorphous GeS 2 has been relatively little studied, perhaps because of the difficulty of preparing exactly stoichiometric material in a glassy form (Voigt etal, 1978). Feltz et al. (1985) and Cervinka etal. (1987) have performed X-ray diffraction studies on glassy GeS 2 , finding the Ge-S bond length to be 2.23 A or 2.26 A, respectively and the Ge-S-Ge bond-angle distribution to be centred at 115°. From a ball-and-stick structural modelling study, Feltz etal. (1985) infer that the structure consists mainly of corner-sharing GeS 4/2 tetrahedra, but that about 25% of the tetrahedra form edgesharing connections. The structure of (the

400

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0 ppm

-100

-200

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Figure 7-25. 31 P magic-angle spinning NMR spectra of various P^Se^^ glasses (Eckert, 1989). Assignments of the two principal features in the spectra in terms of trigonal PSe3/2 and tetrahedrally-coordinated Se = PSe 3/2 units are indicated.

high-temperature form of) crystalline GeS 2 (and GeSe2) consists of two types of structural configuration, one which contains corner-sharing tetrahedra in a chain-like configuration, and the other containing edge-sharing units bridging two chains (see Fig. 7-26). Cervinka (1988) has discussed the MRO in glassy GeS 2 , particularly as-

410


C-Configuration

E-Configuration Figure 7-26. Chain (C) and edge (E) sharing configurations in GeX2 (X = S, Se) (Cervinka, 1988).

sociated with the FSDP at Qx«1 A \ in terms of correlations between such structural configurations; a reasonable fit to the first two peaks in the X-ray scattering pattern was achieved in terms of a parallel packing of chain-like clusters separated by about 7-8 A. The structure of glassy Ge 2 S 3 has been studied by X-ray diffraction by Pohle et al. (1985); the structure could be well described in terms of the structural unit being the ethane-like grouping [Ge2S6], with all chalcogens being two-fold coordinated in corner-sharing links. 4: 2 coordination of Ge and S, respectively, was found for the case of a-GeS by Drahokoupil et al. (1986) using X-ray emission and EXAFS, despite the fact that in the structure of crystalline GeS the Ge (and S) atoms have a 3 : 3 coordination. Drchal and Malek (1988) have constructed two structural models for a-GeS, one a 3D structure containing Ge(Ge 4 _ n SJ tetrahedra of all types, and the other a layered model in which Ge(Ge 2 S 2 ) units were predominant, the former giving the best fit with experimental scattering data.

There have been many more structural investigations of glassy GeSe 2 . An X-ray diffraction study has been performed by Feltz et al. (1985), an anomalous X-ray scattering study by Fuoss et al. (1981) and neutron scattering measurements made by Uemura et al. (1978), Nemanich et al. (1983), Wright et al. (1987), and Susman et al. (1988); a Ge-Se bond length of 2.37 A is found. As for the case of g-GeS2, the presence of a significant proportion (—15%, c.f. 25% for the crystal) of edge-sharing connections between GeSe 4/2 tetrahedra in the structure of g-GeSe2 has been suggested on the basis of diffraction data (Nemanich etal., 1983), Raman scattering (Bridenbaugh et al, 1979; Sugai, 1987) and a molecular dynamics (MD) structure simulation involving two-body interaction potentials only (Vashishta et al, 1989). MRO in glassy GeSe2 has been the subject of much controversy, and two experimental features have been the centre of discussion, namely the FSDP at Q ^ l A " 1 and the so-called companion line to the main Ge-Se stretch mode in the Raman spectrum. From neutron scattering measurements the FSDP found in the glassy phase remains with the same intensity (Susman etal, 1988), or even enhanced (Uemura et al, 1978) in the liquid state see Fig. 7-15. (This behaviour is also reproduced by the MD simulation of Vashishta et al, 1989). This observation makes it unlikely that any microcrystalline-like structural ordering is responsible for the FSDP. The anomalous X-ray scattering results of Fuoss et al. (1981) indicate that Ge-centred (Ge-Ge, Ge-Se) correlations contribute primarily to the FSDP; this conclusion is supported by X-ray diffraction measurements on GeSe 2 -GeTe 2 glassy alloys, in which the FSDP grows in intensity as Te is replaced by Se, thereby enhancing the Ge contribution (Moss, 1974). The MD simu-

7.3 Structure

lation study by Vashishta et al. (1989) also found that Ge-based correlations were mainly responsible (although for the simulated structure the FSDP appears at a larger value, Q 1 ^1.35A"" 1 , than observed experimentally), and they ascribed this to Ge-Ge correlations at separations of 9-10 A (since the FSDP disappeared if only atomic correlations less than 8.8 A were included in the calculation of S (Q)). The companion line at ^220 cm" 1 (26.5 meV) to the main At symmetricstretch breathing mode of GeSe 4/2 tetrahedra at ^200 cm" 1 (25 meV) observed in the Raman spectrum of g-GeSe2 has also been taken to be a signature of MRO in this material. The band is unusally narrow and strongly polarized; moreover it exhibits an unusually strong compositional dependence (Nemanich et al., 1977), varying as ~x5 in the alloys Ge^Se^,,, whereas the intensity of the Ax mode varies linearly with x as expected from a progressive break-up of GeSe 4/2 tetrahedra with increasingly off-stoichiometric composition (see Fig. 7-27). Nemanich et al. (1983) and Sugai (1987) have ascribed the anomalous companion line to the vibration of the four-membered (Ge2Se2) rings associated with edge-sharing tetrahedra (Fig. 7-26), whereas Bridenbaugh et al. (1979) have ascribed it to the vibrations of Se-Se bonds (dimers) bordering what they have termed a raft, namely a 2D section of the crystalline structure containing edge-sharing units cross-linking parallel chains of cornersharing tetrahedra (see Fig. 7-17 a). (Wright et al. (1987), however, have indicated that the structural correlations associated with such rafts are incompatible with the measured RDF; in particular, the third peak at ~4.7A is much too pronounced in raftlike structures). However, matrix-element enhancement of Raman bands can occur in the case of symmetric vibrational modes

300

411

200 100 0 Raman shift Icrrf1)

Figure 7-27. Raman (solid line) and depolarization (dashed line) spectra of a-GexSe1 _x. Note the anomalous composition dependence of the companion line at ^220 c m ' 1 compared with the symmetric-stretch At breathing modes of GeSe4/2 tetrahedra at %;200 cncT1 (Nemanich et al., 1977).

(Elliott, 1990), and thus it is not clear whether the anomalous compositional changes in the Raman intensity of the 220 cm" 1 band are due entirely to a systematic change in the structure (e.g. in the proportion of edge-sharing tetrahedra), or from a change in the Raman matrix element. An experiment probing the vibrational density of states which is less sensitive to matrix-element effects is inelastic neutron scattering, and two such experiments have been reported for g-GeSe2 (Gladden et al., 1988; Walter et al., 1988). The dynamic structure factor S (Q, co) is shown in Fig. 7-28 a and the vibrational density of states (VDOS) G(E) in Fig. 7-28 b (Walter et al., 1988). The four modes labelled v1-vA, in

412


6O

a)

O.O

GeSe 2 DOS13K

Figure 7-28. (a) Dynamical neutron structure factor, S(Q, w), of glassy GeSe2 with the elastic contribution removed (Walter et al., 1988). (b) Vibrational density of states of glassy GeSe2 obtained from inelastic neutron scattering (Walter et al., 1988).

10 b)

20 25 E(meV)

Fig. 7-28 b correspond to the vibrational modes of GeSe 4/2 tetrahedra which, in the central-force-field model of Sen and Thorpe (1977) where bond-bending forces are neglected, are vibrationally decoupled as long as the chalcogen bond angle is near 90°. The origin of the other features in the VDOS is less clear, although Bridenbaugh et al. (1979) and Kumagai et al. (1977) have

assigned a (Raman) peak at 265 cm 1 (and 175 cm""1) to vibrations of Ge-Ge bonds in ethane-like (Ge2Se6/2) structural groupings. Unfortunately, even the highest-resolution inelastic neutron scattering spectrometers available have a considerably worse energy resolution than is routinely attained in Raman scattering experiments; as a result, the companion line has not yet

7.3 Structure

been unambiguously resolved from the A± mode in inelastic neutron scattering measurements (Gladden et al., 1988). There has been some controversy concerning the atomic coordination in the material a-GeSe (see Fowler and Elliott, 1982, for a review), although the anomalous X-ray scattering data of Fuoss et al. (1981) seem to favour 3 : 3 coordination, with a Ge-Se bond length of 2.4 A and an average bond angle of ^106° (Uemura et al., 1974). A modelling study by Fowler and Elliott (1982), in which 3 : 3 coordination was assumed, gave good agreement with the neutron scattering results of Uemura et al. (1974) and also the anomalous X-ray scattering results of Fuoss et al. (1981). Pohle et al. (1985) have investigated the structure of amorphous Ge 2 Se 3 using X-ray diffraction, and found that the structure can be understood in terms of cornersharing (Ge2Se6/2) structural units, i.e. containing a Ge-Ge homopolar bond. The macrostructure of obliquely-evaporated a-GeSe2 (and GeS 2 and GeSe3) films exhibiting a columnar microstructure has been investigated by Rayment and Elliott (1983), Spence and Elliott (1987) and Verrall etal. (1988 b) using small-angle neutron and X-ray scattering. The Si chalcogenide glasses SiS2 and SiSe2 also exhibit extremely interesting structural features. The crystalline modifications of these materials are chain-like structures consisting entirely of edgeshared SiX4/2 tetrahedra (X = S, Se), and there is much experimental evidence that this form of MRO persists in the glassy phase as well. Neutron diffraction measurements have been carried out on the glassy Si x Se!_ x system (Johnson etal., 1986; Johnson, 1986), and many Raman scattering studies have been performed on both SiS2 and SiSe2 glasses (Tenhover etal., 1983a, 1983b; Griffiths etal., 1984;

413

Malyj etal. 1985; Tenhover etal., 1984, 1985; Susman et al, 1986; Sugai, 1987). In addition, 29Si MASNMR experiments have been performed on these materials (Tenhover et al, 1988; Eckert, 1989) as well as inelastic neutron scattering measurements (Arai et al, 1988). Although there is no consensus concerning the detailed assignment in terms of vibrational modes of the various bands observed in the Raman spectra of these glasses (Arai etal, 1988), nevertheless it is generally agreed that the structure of the glasses cannot be understood in terms of either being completely chain-like (i.e. 100% edge-shared units) or completely corner-sharing (as in SiO2), but that both types of connection are present with edge-sharing being dominant. 29Si MASNMR results (Tenhover etal, 1988; Eckert, 1989) provide evidence for three distinct types of Si environment in the glass compared with the single site in the crystal (Fig. 7-29); these have been ascribed to SiX4/2 units (X = S, Se) having zero, one and two edge-sharing connections (labelled E°, E 1 , E 2 , respectively). Tenhover et al. (1988) find that in glassy SiS2 and SiSe2 the proportions of these sites are approximately 25% E°, 50% E \ and 25% E2. An extensive structural modelling study of glassy SiSe2 (SiS2) has been undertaken by Gladden and Elliott (1987, 1989) in which the neutron diffraction data of Johnson et al. (1986) is best fitted by a mixture of structural groupings, including about 15% of the cross-linked chain cluster (essentially a 12-membered ring consisting of four E 1 and two E° units) proposed by Griffiths etal. (1984) (see also Griffiths, 1986) with the rest of the structure in the form of random chains containing an average of seven E 2 units, of which approximately 15% show some degree of local parallelism between two chains extending for two or three E 2 units. Fig. 7-30 shows

414


+50

-150 29

Si (ppm)

Figure 7-29. 29Si magic-angle spinning NMR of glassy and crystalline SiS2 (Tenhover et al., 1988). The assignment of the peaks in the spectrum of the glass in terms of En (n = 0-2) configurations, where n is the number of edge-sharing connections per SiS4/2 tetrahedron, is shown.

the fit of the model to the experimental structure factor and RDF with, in the latter case, an indication of which MRO features contribute to particular regions of the RDF. 7.3.3.4 Structure of III-VI Materials

Relatively little structural work has been undertaken on the boron chalcogenide glasses, mainly because of their great sensitivity to hydrolysis; moreover, neutron scattering measurements are not possible

with the naturally occurring isotopic mixture of boron due to the very high absorption cross-section of the 10B nucleus. Nevertheless, there have been a number of X1 B c.w. (broad-line) NMR studies of the structure of boron chalcogenides (Hendrickson and Bishop, 1975; Rubinstein, 1976; Hintenlang and Bray, 1985; Hiirter et al., 1985). For the case of the stoichiometric B 2 X 3 materials (X = S, Se), the NMR spectra exhibit clear evidence for second-order quadrupolar splitting due to the presence of an appreciable quadrupole coupling constant associated with trigonal planar BX 3/2 units. These triangular units are presumably connected by corner-sharing at the apical chalcogen atoms, as in the corresponding oxide glass, B 2 O 3 . The addition of the modifiers Li2S (Hintenlang and Bray, 1985) and T12S (Eckert et al., 1984) to B 2 S 3 converts the coordination of the B from trigonal to tetrahedral; the proportion of tetrahedrally-coordinated B is a maximum at about 40mol.% modifier, as for the analogous behaviour found in the alkali borates, and at higher modifier contents trigonal B units are created with non-bridging (singly-coordinated) sulfur atoms. 7.3.3.5 Metal Chalcogenide Materials

In many cases, metals are present in amorphous chalcogenide materials as ternary (or higher) constituents, acting as network modifiers. In such cases, a major structural influence of the modifier is to alter in some way the structure of the network-forming matrix, either by a change in coordination of the network-forming cation (e.g. from 3 to 4 for B as evidenced by NMR studies (Eckert et al., 1984) - see Sec. 7.3.3.4) or of the network-forming anion, usually a reduction in coordination, resulting in a network depolymerisation

7.3 Structure

b) Figure 7-30. (a) Experimental neutron scattering intensity function, i(Q) (dashed line) for glassy SiSe2 (Johnson et al., 1986) compared with that calculated for the model of Gladden and Elliott (1987, 1989) (solid line), (b) Experimental RDF for glassy SiSe2 (points) (Johnson et al., 1986) compared with that calculated for the model of Gladden and Elliott (1987, 1989) (solid line). The contributions of various structural groupings to the RDF are also indicated.

415

and the creation of non-bridging chalcogen atoms (e.g. in Tl 2 S-As 2 S 3 studied by XPS by Heo et al. (1988)). However, the structural environment of the metal (modifier) atom is often difficult to investigate in such multicomponent materials and atomspecific structural probes must be used. Thus, as examples, the technique of EXAFS has been applied to the Ag-As-S system (Steel etal, 1989), anomalous X-ray scattering to the Ag-Ge-Se system (Westwood and Georgopoulos, 1989) and isotopic substitution neutron scattering to the Ag-As-S system (Penfold and Salmon, 1989). From such studies, it is found that the Ag atoms are generally coordinated by ~ 3 chalcogen atoms. Less common are (binary) metal chalcogenide systems in which the metal atoms play a significant structural role. The structure of a-MoS 3 has been extensively studied by X-ray diffraction and EXAFS measurements (Liang etal., 1980a, 1980b; Chien etal., 1984) and Raman scattering (Bhattacharya et al., 1987). Octahedral coordination of Mo atoms by S atoms was found with a bond length of 2.47 A, and evidence was also found for Mo-Mo dimers with a bond length of ~ 2.9 A, considerably shorter than the normal Mo-Mo

416


bond length of 3.4 A (Chien et al., 1984). The structure proposed by Chien et al. (1984), based on modelling studies, is of a chain-like structure built from Mo atoms with an alternating sequence of long and short bonds and with disulphide (S-S) bonds between two S atoms in alternate octahedra. It is interesting that the X-ray scattering intensity shows a sharp intense FSDP at Q i - l A " 1 (Chien et al., 1984) which, because of the relative weightings of the scattering factors involved, must be due almost entirely to Mo-Mo correlations. Chien et al. (1984) account for this feature in terms of a local parallel coupling of chains, much as in the case of g-SiSe2 or SiS2 (Gladden and Elliott, 1989). 7.3.3.6 Structure of Halogen Chalcogenides

The structural and other properties of a wide range of halogen-containing chalcogenide glasses have recently been extensively reviewed by Sanghera et al. (1988). In general, the structural effect of the inclusion of halogens is for the atoms to act as network terminators, i.e. singly-coordinated halogen atoms substitute for two-fold coordinated chalcogens, and as a result the structure is depolymerised and the viscosity is concomitantly dramatically lowered (Rawson, 1967). Although direct structural techniques (e.g. diffraction) appear to have been seldom used for these materials, with the exception of the (GeS2)JCBr1__x and (GeS^Ji _x systems (Wagner et al., 1988), Raman spectroscopy has been widely applied, e.g. for the As-S-I system (Koudelka and Pisarcik, 1982, 1984), As-S-Br (Koudelka et al., 1979; Koudelka and Pisarcik, 1983), Ge-S-Br (Koudelka et al., 1984), and G e - S - I (Sanghera et al., 1988). In all cases it appears that the halogens (H) replace the chalcogens (C) in the structure, i.e. As-H or, Ge-H bonds form preferen-

tially with respect to C-H bonds. As a result, in some cases there appears to be evidence, from the Raman spectra, for a type of microphase separation in which discrete molecular species, e.g. AsBr3 (Koudelka et al., 1979) and S8 rings (presumably formed from the chalcogens displaced by the halogens) are dissolved in the remaining glassy matrix. In the case of the binary halogenchalcogen Te-X (X = Cl, Br) materials discovered recently (Zhang et al., 1988; Lucas and Zhang, 1990), bonds between halogens and chalcogens must occur. Zhang et al. (1988) suggest that the structure of glassy Te3Cl2 or Te3Br2 is similar to that of the corresponding crystal (Kniep et al., 1973), which is based on helical Te chains, in which every third Te atom is bonded axially to two additional halogen atoms, making such Te atoms tetrahedrally coordinated (see Fig. 7-31 a), and the structure of glassy Te2Cl and Te2Br is also proposed to be similar to that of the crystalline modification (see Fig. 7-31 b), which consists of a ladder-like structure of two interconnected Te chains, with bridging halogen atoms. However, there does not yet appear to be any direct structural evidence for these proposed structures.

7.4 Defects 7.4.1 Introduction

Defects can only be discussed sensibly in the context of some reference structure which is non-defective. In the case of crystalline materials, this requirement is readily satisfied, in terms of a perfect single crystal, but in the case of amorphous materials the situation is not as clear-cut: what is to be taken as the reference, non-defective (i.e. ideal), non-crystalline structure?

7.4 Defects

417

Figure 7-31. Structure of crystalline Te3Cl2 (a) and Te2Cl (b) (Kniep et al, 1973), b)

In the case of covalently-bonded systems, at stoichiometric compositions, the ideal reference structure may be taken to be a chemically-ordered continuous random network (COCRN) (Elliott, 1984, 1990). Thus, defects in such a structure can be wrong (homopolar) bonds and coordination defects, e.g. over-coordinated atoms or under-coordinated atoms (dangling bonds). However, in certain cases for amorphous materials it is difficult to decide whether or not a particular structural feature is a defect under the above definition. For instance, should the negativelycharged non-bridging (NB) chalcogen sites, denoted by the symbol C^~ (where C stands for chalcogen, and the superscript and subscript are the charge state and atomic coordination, respectively), resulting from the introduction into chalcogenide glasses of network-modifier cations (e.g. alkalis, Ag + , Tl + ) and which compensate the positively charged cations (see e.g.

Heo etal., 1988), be regarded as defects? We will take the viewpoint that if the structure intentionally and necessarily contains say modifier cations, the concomitant changes in the structure (e.g. over-coordinated boron atoms - Sec. 7.3.3.4) or NB chalcogens (see Sec. 7.3.3.6) should not be regarded as constituting defects, but instead they are a natural feature of the (modified) structure. However, any such structural entities which are present with a concentration in excess of that otherwise normally expected should be regarded as defects. 7.4.2 Wrong Bonds

If the COCRN is taken as the ideal structure for a compound chalcogenide material with stoichiometric composition, wrong or homopolar bonds occurring in a real material are obviously defects in the structure since they represent broken

418


chemical order. However, for the case of off-stoichiometric compositions, wrong bonds can naturally occur as the response of the structure in accommodating the element in excess. In this case, such wrong bonds should not be regarded as defects. (Wrong bonds also obviously have no meaning in the case of elemental chalcogen materials.) It is often difficult to detect the presence of wrong bonds, and there are several reasons for this. Often, they are present in very low concentrations ( 1070 K (Tanaka et al, 1985). Vanderbilt and Joannopoulos (1981) have calculated the electronic properties of wrong bonds in the case of glassy As 2 Se 3 , and find that such defects give rise to electron states lying in the bandgap between valence and conduction bands (see Fig. 7-34). The Se—Se wrong bond, denoted by C 2 (CXP) where the symbols in parentheses refer to the type of nearest neighbours (C = chalcogen, P = pnictogen), gives rise to a deep-lying gap state due to an anti-

As 2 Se 3

C 2 (C.P)

P 3 (P.2C)

Figure 7-34. Electronic density of states for arsenic chalcogenides with heteropolar (a) and homopolar bonds (b, chalcogen-chalcogen; c, pnictogen-pnictogen) (Vanderbilt and Joannopoulos, 1981).

bonding a| e state associated with the abonded pair of p Se orbitals of the Se-Se bond; the defect is neutral when the afe state is unoccupied. Similarly the As-As bond also gives rise to a deep gap state, now due to the TI* combination resulting from a ^-interaction between the aAs bond orbital of the homopolar bond and two neighbouring pSe orbitals; the defect is neutral when this gap state is fully occupied. 7.4.3 Coordination Defects Much discussion has also been devoted to coordination defects in chalcogenide glasses, i.e. those defects arising from broken bonds where, if atomic reconstruction does not subsequently take place, the defects will be under-coordinated, and if local reconstructions can occur, the defects may be over-coordinated with respect to the normal bonding configurations in a chemically-ordered network. Such reconstructions are favourable in chalcogenide mate-

7.4 Defects

rials owing to the presence of the nonbonding p-like lone-pair orbitals of the chaleogens, forming the top of the valence band in the electronic density of states (Kastner, 1972; see Sec. 7.5.1), and which can take part in dative-bonding reactions. In Fig. 7-35 is shown the hypothetical transformation of two neutrally-charged chain-end dangling bonds (C?) to a negatively-charged under-coordinated defect (Cf) and a positively-charged overcoordinated (Cj) site, viz.

2c?^c 3 + + e r

(7-i8)

The transfer of an electron from one Cj centre to another in Fig. 7-35 involves a change in energy U, the effective correlation (or Hubbard) energy, with C/R

(7-19)

where Uc is the positive coulombic energy cost involved in placing a second electron at a site (i.e. in forming a Cj~), and UR are the energy changes involved in any subsequent reconstructions at the defects, e.g. in the formation of the dative bond between the empty p-orbital of a Ct+ centre (after the removal of an electron from Cf) and the occupied lone-pair p-orbital of a neighbouring normally-bonded chalcogen, viz.

421

Anderson (1975), in a general discussion of defects in chalcogenide materials, argued that the effective correlation energy U should be negative, i.e. reaction (7-18) should be exothermic, essentially because the structure of an amorphous material will minimise its energy by ensuring that electron pairing always occurs, either in covalent bonds or lone-pair (non-bonding) orbitals. Subsequently, Mott et al. (1975) and Kastner et al. (1976) applied the general spin-pairing picture of Anderson (1975) to the specific case of point (dangling-bond) defects in chalcogenide glasses, as in Fig. 7-35, where it was assumed from simple chemical-bonding arguments that U was negative, so that the spin-paired, oppositely charged valence-alternation pairs (VAPs; Kastner et al., 1976) would be energetically favourable. Realistic total-energy calculations for aSe by Vanderbilt and Joannopoulos (1980) have indicated that the neutral undercoordinated C° centre is lower in energy, i.e. more stable, than the overcoordinated C° centre and that the C° defect produces a deep-lying gap state due to a 71-bonding interaction between the unpaired spin and a lone-pair orbital on the neighbouring chalcogen atom. However, subsequent calculations by Vanderbilt and Joannopoulos

Figure 7-35. Schematic illustration of the formation of valence alternation pair coordination defects (D + , D~) from neutral dangling bonds in a-Se (Elliott, 1990).

422


(1983 a, 1983 b) have shown that for the case of a-Se, in fact the effective correlation energy is positive, U«0.4 eV, since although the relaxation UR in Eq. (7-19) associated with the process C^ -»C J is negative (^ — 0.5 eV), the intra-site couloumb repulsion energy for the process C?->C^ is much larger in magnitude {Uc~ +0.9eV). Hence, diamagnetic spin pairing in a-Se is predicted to be energetically unfavourable. The situation is considerably more complicated for compound chalcogenide materials, e.g. V-VI materials, where both pnictogen- and chalcogen-based defects could occur in principle (e.g. C j , C^, P 2 , P4, PJ, and the neutral centres C°, P 2 and possibly P^); furthermore the type of atoms (P or C) which are nearest neighbours of the coordination defect should also be specified since they affect the energy levels of the associated gap states. In summary, the theoretical calculations of Vanderbilt and Joannopoulos (1981) indicate that for V-VI materials, deep gap states associated with neutral paramagnetic defect centres only occur when homopolar bonds are immediately adjacent to the defect (e.g. C° (C), P°(2P),P°(P,C)). Dangling-bond defects at which the local bonding is chemically ordered (viz. CX(P) and P2(2C)) give rise to electron states which prefer to be charged and diamagnetic, i.e. Cj~, P j ; the empty nonbonding orbital (NBO) associated with the P^ centre can, in principle, take part in further dative-bonding reactions with a nearby Se p-like NBO, thereby forming a C3 centre, or even with the s-like NBO of a nearby As atom, thereby resulting in an overcoordinated P4 centre at which sp 3 hybridization has occurred. Although realistic total-energy calculations have not been performed for amorphous compound chalcogenides, e.g. As2Se3, nevertheless it is likely that the

effective correlation energy U for such systems would be negative (Vanderbilt and Joannopoulos, 1981). The concentration of such coordination defects will be determined by the VAP creation energy EVAP associated with the defect creation reaction 2C°2

(7-20)

£y AP might be expected to be relatively low (^0.5 eV) since reaction (7-20) involves essentially just a bond flip. The concentration of randomly-distributed VAP centres frozen-in on quenching through Tg will then be given by (Vanderbilt and Joannopoulos, 1981): nR « n0 exp(-£ VAP /2/e T)

(7-21)

where n0 is the total atomic density. Experimental evidence for the existence of such thermally-generated defects in As2Se3 has come from transient photoconductivity (TPC) measurements in the glassy state below Tg and in the liquid state above Tg (Thio et al., 1984). If neutral defects (C?) are the dominant recombination centres, measurement of the recombination time from TPC measurements yields an estimate for the concentration n of such defects. Thio et al. (1984) found that n was thermally activated, with an activation energy 0.35 eV and a pre-exponential factor of ^ 4 x 1017 cm" 3 for T < Tg, whereas for T > Tg, the activation energy was 0.8 eV and the pre-factor ^ 6 x 1022 cm" 3 . Above Tg, defects are created thermally from normally-bonded atoms (C2) with a number density of —1022 cm" 3 ; the activation energy involved in the creation of (C°) recombination centres from C^ or C^~ centres will be therefore (\U\ + EyAP)/2, which is identified with the value of 0.8 eV found experimentally. However, for temperatures below Tg, the total defect concentration is frozen-in, but the conversion of C? centres

7.4 Defects

from C^ or Cx centres (the reverse of reaction (7-18)) continues to be thermally activated with an activation energy \U\/2; experimentally this value is 0.35 eV. Thus, these results indicate that for a-As2Se3, £ VAP ^0.9eV and E/«-0.7eV. 7.4.4 Experimental Probes for Defects

In this section we will review some experimental techniques which are sensitive to the presence of small concentrations of defects, particularly coordination defects, utilising their opto-electronic properties. Those techniques which are sensitive to homopolar bond defects, i.e. Raman and Mossbauer spectroscopies, have been discussed in Sec. 7.4.2 (see also Chap. 6). 7.4.4.1 Electron Spin Resonance

Electron spin resonance (ESR), or equivalently paramagnetic resonance (EPR), is a probe for unpaired electron spins associated, say, with neutral (paramagnetic) dangling-bond defects, e.g. C° or P°; the method has the advantage of having a high sensitivity (^10 1 5 spins cm" 3 ). ESR signals in pure chalcogenide glasses are generally observed only after optical excitation (see Bishop et al.91977), the materials being diamagnetic in cold, dark conditions (Agarwal, 1973). (It was this observation that prompted Anderson (1975) to propose the negative effective correlation model.) An exception to this rule concerns glassy G e ^ S i ^ materials which, exceptionally, do exhibit an ESR signal in the absence of optical excitation (Cerny and Frumar, 1979; Kordas et al., 1985; T. Shimizu, 1985; Watanabe et al., 1988). The nature of the spin centres in a-Ge^S^^ has been the subject of some disagreement: Cerny and Frumar (1979), Gaczi (1982), and T. Shimizu (1985) have ascribed them to Ge or S dangling bonds depending on

423

the stoichiometry (x>0.33 and xC?; the remaining carrier was then supposed to recombine radiatively with the trapped carrier, viz. C? -+- e -»C[" -h h vPL. The luminescence and excitation photon energies differ (by a Stokes shift) if a structural relaxation occurs upon charge trapping.

5 10 Photon energy (eV) Figure 7-38. Comparison of spectra for steady-state (c.w.) photoluminescence (PL), photoluminescence excitation (PLE), optical absorption (a) and photo-induced absorption (dashed line) for two chalcogenide and an oxide glass (Elliott, 1990).

However, this simple model for the PL process has had to be revised in the light of time-resolved (transient) PL studies (e.g. Murayama, 1983; Higashi and Kastner, 1983; Robins and Kastner, 1984). For both amorphous and crystalline chalcogenides, the PL decay exhibits a knee in a doublelogarithmic plot (see Fig. 7-39). Thus the PL decay behaviour can be divided into two regimes, one being dominated by processes characterised by short times (t^ 10" 6 s) and the other by longer times (t^lO~ 4 s); the long-time processes account for most of the PL quantum efficiency and therefore they dominate the steady-state (c.w.) behaviour. The origin of these two decay processes is still not entirely clear but probably is as follows.

426


J Ditrar>f uni

if)

105 2.15 eV

104

bio- 7 a

103 intensit

= 2.56eV

To 10"6 c

1.78 eV

^ icr

2

10

£ 10" c

i

10 1

_L 10"

6

_L

I

10' 10"* Time delay (s)

10" 10-2

10-6

10"*

10-2

Time (s)

ta)

(b)

Figure 7-39. Photoluminescence time decays in chalcogenide materials: (a) amorphous As2Se3 (Higashi and Kastner, 1983), (b) crystalline As2Se3 (Robins and Kastner, 1984).

The short-time behaviour seems to be consistent with a mechanism of donoracceptor pair recombination (Higashi and Kastner, 1981; Depinna et al., 1983), in which radiative recombination occurs when an electron of a neutralized donor is transferred to a neutralized acceptor; the centres are equally and oppositely charged in the ground state (e.g. CJ, C^ pairs) and neutral in the excited state. There is an extra coulombic contribution Ec to the PL recombination energy, resulting from the interaction between ionized donor and acceptor, given by = e2/4nss0R"

(7-22)

with the PL energy therefore being Ep = E» + Ec

(7-23)

where E™ is the energy corresponding to infinite separation. Since the rate of radiative recombination is governed by the rate at which the electron tunnels between sites, given by v = v0 exp(—2aJR)

(7-24)

where a describes the spatial extent of the wavefunction, varying the distances R between the donor and acceptor sites produces a correlation between the PL energy and the time at which the PL is measured. From Eqs. (7-23) and (7-24), the mean PL energy is predicted to shift to lower photon energies with increasing delay time according to (Higashi and Kastner, 1981) = £» +

2cce2

47tee0 ln(vot)

(7-25)

and the width A(t) of the PL peak is also predicted to narrow with increasing time delay. I" 2 a e2 1 (7-26) 2 L47i££ o ln (i? o 0j where a is the width of an assumed Gaussian homogeneous line shape. The time dependence embodied in Eqs. (7-25) and (7-26) appears to have been observed experimentally (Higashi and Kastner, 1981). For the case of PL decays at long times, Higashi and Kastner (1983) have suggested

7.5 Opto-Electronic Properties

that such slow rates (long times) are determined by a forbidden quantum-mechanical selection rule involving spin, in particular resulting from the (formally forbidden) transition between a spin triplet excitedstate configuration and a singlet (i.e. spinpaired) ground state. Further evidence in support of the triplet excited state has come from optically-detected magnetic resonance (ODMR) measurements (see e.g. Cavenett, 1981). Two possible candidates for PL centres involving triplet excited states are a self-trapped exciton (STE), where the initially free photo-created exciton can subsequently lower its energy by forming self-trapped (localised) states in which the lattice is locally distorted (see Fig. 7-40) (Emin, 1980; Murayama et al., 1980); Street (1977) has suggested that a metastable version of such an STE state could arise from a photo-induced bond switch, resulting in an intimate valence al-

Energy Configuration coordinate

Figure 7-40. Schematic illustration of the model for self-trapping of excitons in chalcogenide glasses. Optical excitation (I) to an exciton state can be followed by two non-radiative decay channels (Street, 1977), either directly back to the ground state (III) or to the metastable self-trapped exciton (STE) state (IV), which can be regarded as a D + - D ~ pair (IVAP). Alternatively, STE states can form where the lattice distortion is less severe, and may then act as the (triplet) radiative recombination PL centre (II) (Elliott, 1990).

427

ternation pair (IVAP) (see Fig. 7-40). Alternatively, previously existing IVAP defects could act as sites for triplet excitation (Higashi and Kastner, 1981).

7.5 Opto-Electronic Properties 7.5.1 Electronic Structure The electronic density of states (DOS) in chalcogenide materials comprises a valence band, composed principally of p-like bonding (a) orbitals, and a conduction band formed from antibonding (a*) orbitals, with the top of the valence band being composed of chalcogen-derived plike non-bonding orbitals and the nonbonding s-states lying at the bottom of the band (see Fig. 7-41 for a schematic representation for the case of As2Se3 and Fig. 7-34 a for a calculated DOS (Vanderbilt and Joannopoulos, 1981)). Numerous calculations of the DOS for various chalcogenides have confirmed this general picture, although it appears that the lone-pair band is less distinct, i.e. there is more mixing of p - a and p-7i states, in the As chalcogenides (Bullett, 1976; Althaus et al., 1978) than for either the pure chalcogens (Joannopoulos et al., 1975) or the Ge chalcogenides (Louie, 1982). The electronic DOS can be probed experimentally using photoemission techniques and this has been done, for example, for the case of Se (Takahashi, 1982), As 2 X 3 (X = S, Se, Te) (Bishop and Shevchik, 1975) and GeX2 (X = S, Se) (Takahashi and Harada, 1980; Hindo et al., 1980); the lone-pair band at the top of the valence band can be seen clearly (see Fig. 7-42). The changes in XPS and UPS spectra have also been used to demonstrate that a-GeSe films deposited onto cooled substrates have 3 : 3 coordination, but this changes to 4 : 2 after thermal annealing (Takahashi and Sagawa, 1982).

428


BULK \

AS

\ / \

/ /

•

v

v

V

>

2.

O cc 0 ui z UJ

c* Se

/

p

/

/

|

\

.1...

/

/\ \ / /

/

Y

/ \ y

, ' '

Pc Se

.N

/

^

\

t 5 i.

\

''

\ N

/

v

/

/

Amorphous chalcogenide materials are invariably semiconductors, with the size of the bandgap varying in the range ~ 1 3 eV. Several factors influence the magnitude of the gap: the gap generally increases as chalcogen atoms are substituted at fixed composition by other chalcogens in the series Te-*Se->S; furthermore, the gap for chalcogenide alloys varies with composition and often exhibits extrema at stoichiometric compositions, for example, minima in the case of A s ^ S ^ (Fisher et al., 1976) and As^Se^^ (Kosek et al., 1976), and a maximum in the case of GexSe1_JC (Tronc etal, 1973). Shimakawa (1981) has accounted for such compositional variations in terms of a simple alloying model in which the energy gap, Eg of a chalcogenide alloy AXC±_X (e.g. ,4 = Ge, As; C - S , Se) can be represented as the sum of two contributions, one associated with the gap of aji ordered (stoichiometric) composition, and the other associated with the element in excess, both weighted by the appropriate atomic fractions, e.g.

Eg = yEg(A) + (l-y)Eg(AmC^m)

Q 2

\

/

b

b

\

\ V

a

i a.

/

.

V

ft. Se

p *s

, \

i -2

'

/ N

a.1

\

a

/

V

BAI

cr# BAND

r—"i

DEFECTS

BASIS

(7-27)

Se

b

Figure 7-41. Schematic origin of the electronic density of states in As2Se3 in terms of atomic and molecular orbital states (Vanderbilt and Joannopoulos, 1981). The positions of various defect states are also marked.

where AmC1_m is the stoichiometric composition. 7.5.2 Optical Properties

In this section, we will consider only those optical properties of amorphous chalcogenide materials resulting from optical transitions across the bandgap, between electron states at the top of the valence band (i.e. the p-n lone-pair band) and the bottom of the conduction band, neglecting, therefore, the transitions occurring at higher energies (in the UV and Xray regions) from states deeper in the valence band or from the core states. In the case of the semiconducting amorphous chalcogenides, the optical absorption coefficient, a, changes rapidly for photon energies comparable to that of the bandgap, Eg9 giving rise to an absorption edge. Three regions can be distinguished: I - at the largest photon energies where a is concomitantly also the highest (^10 4 cm" 1 ), and tends to a saturated value, interband transitions occur between valence and conduction bands; II - in the


429

region I exhibits a power-law dependence on photon energy hco if the densities of states in the valence and conduction bands also have a power-law energy dependence in the vicinity of the gap, viz. 0 c (E-E o )ocE«

(7-28 a) (7-28 b)

whence (DOL{(D) GC (hco — Eo)

5

and where Eo is some measure of the bandgap. In the special case, where both valence and conduction band edges have a parabolic shape (p = q = \\ Eq. (7-29) becomes

20

10 15 Binding energy (eV)

a)

cooc(co) oc (hco — E 0 ) 2

uni

larb. ;ity V) C CD

XPS ii

a

Monochromatized XPS (hv = U86.6eV)

s.

V)

\

\r\

J

J\

n\ \

As2S3 glass (bulk)

\

^ ^

\

>v \ J

/

f

**—""* * \ III

>v

As2S3 crystal

\ I ! 5 10 Binding energy (eV)

^V

(orpirnent)

(7-29)

^

i 15

b)

Figure 7-42. (a) X-ray photoemission spectra (XPS) of amorphous, trigonal (t) and monoclinic (m) Se taken using Mg Ka radiation (Takahashi, 1982). The upper and lower 4 p bonding bands are indicated by bars in the spectra of t- and m-Se, and the approximate 4 s bandwidths are indicated by dashed lines, (b) XPS of glassy and crystalline As2S3 (Bishop and Shevchick, 1975).

region of the edge itself (10 < a < 104 cm 1); and III - at the lowest photon energies and at low values of a ^ 10 cm" 1 where transitions between (defect) states in the gap and the bands take place. Under certain conditions (in the random-phase model, where the k-selection rule breaks down - see Elliott, 1990), the absorption coefficient in

(7-30)

Thus, Tauc plots of (ahco)112 versus hco should be linear and extrapolate to values of the (optical) gap, Eo. Fig. 7-43 shows this quadratic dependence for chalcogenide glasses (and a-Si). However, not all chalcogenide materials exhibit this behaviour for coa(co): a-Se exhibits a linear energy dependence, and multicomponent chalcogenide alloys (e.g. Ge-As-Te-Si) show a cubic energy dependence. It should be noted that Eo, obtained in this way, is not necessarily exactly equal to the true gap £ g between mobility edges in the valence and conduction bands. Part of the uncertainty arises from a breakdown of the random-phase approximation for photon energies hco& Eg (Dersch et al., 1987; Abe and Toyozawa, 1981); as a result, the optical absorption is not just determined by the joint density of states, as in Eq. (7-29), but also depends on energy-dependent matrix-element terms. The optical absorption edge in amorphous semiconductors is not as sharp as predicted from Eqs. (7-29) or (7-30), but exhibits a long tail into the gap region, and which almost invariably depends exponen-

430


Figure 7-43. Tauc plots of optical absorption coefficient ([ahco]112 vs. hco) for

various chalcogenide glasses (Mott and Davis, 1979). 1.0

U

1.8

2.2

2.6

3.0

Photon energy (eV)

tially on the photon energy: a((o) = oc0 exp[— r(Ef0 — hco)]

(7-31)

where E'o is an energy comparable to the threshold energy Eo involved in interband transitions (see Eq. (7-30)), and F is a temperature-dependent constant, typically having values in the range 10-25 eV" 1 . This Urbach-edge behaviour is also exhibited by chalcogenide materials (Fig. 7-44). The origin of the Urbach edge is still unclear, but two general mechanisms may be responsible: either the exponential en-

ergy dependence of a arises from an exponential energy dependence of the valence and conduction band densities of states at the band edges (neglecting matrix-element effects), or a particular universal absorption mechanism exists which gives rise to the exponential behaviour of a, e.g. the field-broadened exciton model of Dow and Redfield (1970). In the former case, Abe and Toyozawa (1981) and Soukoulis et al. (1984) have shown theoretically that exponential band tails can result from potential fluctuations associated with structural dis-

10-

0)

S 103

_Q
48 Si 0 . 12 Ge 0A glass for a) d.c. electrical conductivity; b) thermopower; c) Hall mobility (Nagels, 1979).

(

K"1 )


cases, conduction takes place by variablerange hopping between (paramagnetic) defect states lying at EF in mid-gap. In chalcogenide bulk glasses, or well-annealed thin films, variable-range hopping conduction is not normally observed because the negative effective correlation energy associated with the coordination defects in chalcogenides results in the formation of spin-paired, charged defects lying away from EF (see Sec. 7.4.3), and for which the electron-phonon coupling is so large that the hopping rates become unobservably slow (Phillips, 1976). In common with other amorphous semiconductors, chalcogenides also exhibit a frequency-dependent (a.c.) conductivity which, in the frequency range 10< 1 0 9 s ~ \ exhibits a power-law frequency dependence, viz. a(co) = Acos

(7-36)

where s < l and both A and s can be (weakly) temperature dependent. At high temperatures and/or low frequencies, the d.c. conductivity becomes dominant since it has a much larger temperature dependence than that of o{co\ so that the total measured conductivity can be written formally as: ^totM = crdc + ^ M

(7-37)

(Eq. (7-37), as written, implies that the d.c. and a.c. conductivities arise from different mechanisms; if they arise from the same mechanism, adc is just the co-+0 limit of a{co).) Elliott (1987 a) has given an extensive review of the a.c. conductivity behaviour of amorphous chalcogenide materials. The mechanism which seems best able to account for the experimentally observed a.c. behaviour is the correlated barrier hopping (CBH) model proposed by Elliott (1977, 1987 a). In this, two electrons (a bipolaron) are assumed to hop under the

Se-

-Se

Se

-Se

Se-

:Sei

D+) Se

a)

Se

437

Se

Se

Se

-Se

Se

Se

Se

Conduction band

Figure 7-51. The correlated barrier hopping (CBH) model for a.c. conductivity in chalcogenide glasses (Elliott, 1987). a) Schematic illustration of two-electron transport in a-Se causing the interconversion of D + , D~ (C3, Cf) defect centres, b) Schematic illustration of the lowering of the activation energy barrier from WM to W for two-electron hopping for two oppositely charged defect centres separated by a distance R due to a coulomb interaction. A site disorder energy A is also shown.

influence of the applied a.c. field between oppositely-charged coordination defect sites (e.g. C^, C^ - see Fig. 7-51 a), or possibly single polarons are assumed to hop between C^, C? or Cf, C° pairs of sites. The hopping rate involved in such processes involves an activation energy W which is correlated with the intersite separation R through a coulombic interaction between charge carrier and defect (see Fig. 7-51 b); for the case of a bipolaron W=WM-2e2/n880R

(7-38)

where WM is the maximum barrier height (for R = 00) and which has a value comparable to the (optical) bandgap (Elliott,

438


1987 a). The a.c. conductivity can then be calculated to be (Elliott, 1977, 1987 a) a(co)=7^N28sowRi

(7-39)

where N is the concentration of defects and the hopping distance R^ at a frequency co is given by

100

200

300

400

500 600

(a)

(7-41)

The success of this model in accounting for the experimental a.c. data for, say, amorphous As2Se3 (Hirata et al., 1983; Giuntini etal., 1981) is demonstrated in Fig. 7-52. However, in certain cases, the temperature dependence of a(co) at elevated temperatures (^300K) in chalcogenides, particularly those with smaller bandgaps, is considerably stronger than is predicted for bipolaron CBH (Eqs. (7-39), (7-40)). Shimakawa (1982) has explained this behaviour in terms of the thermal creation of neutral, paramagnetic centres (C?) from pre-existing charged spin-paired centres (the reverse reaction of (7-18)), which is an activated process; single polaron transport involving such defects is then assumed to be dominant. It can be seen from Fig. 7-53 that, with this modification, the CBH model can account for the a.c. conductivity of amorphous chalcogenides over a wide range of temperatures and frequencies. 7.5.4 Photo-Induced Changes

A wide variety of changes can be induced in amorphous chalcogenide materials by the absorption of photons of energy

h nduc t i v i t y

6kT [W M -fcrin(l/eoT o )]

'E 100 kHz

Â in

10

10

v.

id" o o

A.c.

where T0 is a characteristic relaxation time. The frequency exponent s of the a.c. conductivity can then be evaluated to be

10 kHz *•—*

N ^

•

1 kHz

10 12 (by

6 8 10 1000/T (K"1)

Figure 7-52. Application of the CBH model to experimental data for glassy As2Se3 (Elliott, 1987). a) Temperature dependence of the frequency exponent s. b) Temperature dependence of the a.c. conductivity at three frequencies.

comparable to the optical bandgap (or by irradiation by electrons or ions). Such changes may conveniently be divided into two categories, namely transient and metastable changes. Transient changes occur only whilst the sample is illuminated: examples include photoluminescence (see Sec. 7.4.4.2) and photoconductivity (see Sec. 7.4.3), and these will not be considered further here. By contrast, metastable changes remain after being induced, and these can be sub-divided into two further categories, namely irreversible and reversible, i.e. the latter of which can be annealed out by heating the samples to the glass-transition temperature, T . Some reversible changes


Figure 7-53. Prediction of the CBH model for glassy Se with both single (S) and bipolaron (B) hopping contributions (Shimakawa, 1982).

are associated with the photo-excitation of pre-existing (coordination) defects, e.g. light-induced ESR (see Sec. 7.4.4.1) and optically-induced mid-gap absorption (see Sec. 7.5.2), and these also will not be discussed further. Reviews of photo-induced phenomena have been given by Ka. Tanaka (1982), Owen et al. (1985), Elliott (1986), and Ke. Tanaka (1990). Amongst the class of irreversible photoinduced changes are a variety of chemical changes, including the phenomena of metal photo-dissolution, photo-crystallization and giant photo-densification of films. In the photo-dissolution process, a layer of metal (e.g. Ag, Cu or Zn) in contact

439

with an amorphous chalcogenide film dissolves into the chalcogenide upon irradiation with light having an energy comparable to the bandgap of the chalcogenide (Kostyshin et al., 1966; Ka, Tanaka, 1982; Doane and Heller, 1982; Owen et al., 1985; Lyubin, 1987). The actinic radiation appears to be absorbed at the interface between the metal-doped and undoped chalcogenide (Owen et al., 1985; Rennie and Elliott, 1985, 1987), and the speed of the reaction, as well as the formation of a sharp boundary between doped and undoped layers, appears to be a consequence of the fact that the doped chalcogenide material acts as a superionic conducting matrix for the dissolving metal ions. Another irreversible photo-induced chemical change observed in chalcogenides is photo-vaporization (Janai, 1981), in which an amorphous thin film (e.g. As2S3) is first photooxidised (Kolobov et al., 1989), and the resulting volatile surface oxide subsequently evaporates. Many amorphous chalcogenide materials, particularly those with low values of Tg, crystallize upon optical irradiation (e.g. Se (Dresner and Stringfellow, 1968) and As-Te-Ge (Weiser et al., 1973)). Finally, obliquely evaporated thin films of amorphous Ge chalcogenides, exhibiting a columnar morphology, undergo giant (~20%) changes in thickness (density) after optical excitation (Singh et al., 1980); this effect has been found to be due to a photo-induced collapse of the void structure comprising the columnar microstructure (Spence and Elliott, 1989). Another type of irreversible photo-structural change involves the photo-polymerization of As 4 S 4 molecules in as-deposited amorphous As-S films (Nemanich et al., 1978; Treacy et al., 1980; Lowe et al., 1986) to form a more nearly continuously bonded random network; the same process occurs in the photo-decomposition of realgar (c-

440


As4S4) to give orpiment (c-As2S3) (Porter and Sheldrick, 1972). Reversible photo-induced charges in chalcogenides are less well understood than their irreversible counterparts; reviews of the subject have been given by Elliott (1986) and Ke. Tanaka (1990). Perhaps the most studied reversible change is photo-darkening, whereby an increase in the optical absorption at a particular wavelength, resulting from a parallel shift of the Urbach edge to lower energies, occurs on illumination (see Fig. 7-54 a). The

magnitude of the shift A£ in the optical edge is largest for illumination at low temperatures (see Fig. 7-54 b), and A£ decreases to zero at Tg, where the change is annealed as fast as it is induced. It is interesting to note that A£ in chalcogenide alloys appears to exhibit a maximum at an average atomic coordination m^2.67 (see Fig. 7-54 c), the optimum value for satisfaction of mechanical constraints if a 2D-like MRO exists in the glass (Tanaka, 1989 b) (see Sec. 7.2.1). A very interesting variant of this is the photo-induced anisotropy (e.g.

104

I

0.15 -

•

I

i

A

c

a Ge-Se

0.10 -

i

i

o Q

w w

* As-S

o

1

oo

Ge-As-S Ge-S

o

0)

1

nF T Tf T

wR

material parameters extrinsic scattering total intrinsic attenuation coefficient Rayleigh factor Racah parameter constant dependent on source of scattering A independent scattering crystal field parameter band gap energy gap force constant mass refractive index non-linear refractive index indices at X\ d = 0.589 mm, F = 0.486 mm, c = 0.656 mm glass softening point freezing temperature glass transition temperature energy transfer rate multiphonon emission rate radiative rate

Qt

attenuation coefficient quantum efficiency Curie-Weiss temperature wavelength reduced mass vibrational frequency indicator of the covalent character bonding phenomenological parameters with t — 2, 4, 6

CN F.L.N. RAP R.E.-R.E. T.M.-R.E.

coordination number fluorescence line narrowing reactive atmosphere processing rare earth-rare earth transition metal-rare earth

n

9 X Vv0 Q2

Composition of glasses BATY 20BaF 2 , 29A1F3, 22ThF 4 , 29YF 3 BiGaZYT Ba 3 0 In 1 8 Ga 1 2 Zn 2 0 Y 1 0 Th 1 0 BIZYT Ba 3 0 In 3 0 Zn 2 0 Y 1 0 Th 1 0 BTYbZ 16 BaF 2 , 28 ThF 4 , 28 YbF 3 , 28 ZnF 2 ZBL 60ZrF 4 , 33BaF 2 , 7LaF 3 ZBLA 55ZrF 4 , 35BaF 2 , 6LaF 3 , 4A1F3 ZBLAN Zr 5 3 Ba 2 0 La 4 Al 3 Na 2 0

457

458

8 Halide Glasses

8.1 Introduction Halide materials are usually reputed to exist in the crystalline state when cooling down from a molten halide salt; they also form easily volatile molecular species when the halogen is associated with small, highly charged cations. Only a limited number of halide systems lead to glass formation and usually the glass to crystal or glass to molecule competition is very severe. Considerable progress has been made during the last two decades both in the discovery of new halide glass-forming compositions based on the anions F, Cl, Br, I, the elements of group VII of the periodic chart, and in knowledge of the optical properties of these exotic glasses. The main justification for research in this field is the possibility of extending the infrared transparency domain towards long wavelengths and of consequently achieving mid-infrared ultratransparency. There are at least three intrinsic factors which limit the technological and scientific development of such vitreous materials and in which they are inferior to oxide based glasses, especially silicates. The first factor, typical of almost all halide compounds, vitreous or otherwise, is their susceptibility to corrosion by water or moisture, which can strongly affect their optical properties. This poor chemical durability can be explained by the fact that the M - O H 2 , M - O H , or M O bonds are usually stronger than the M - X bond (M = metal; X = F, Cl, Br, I). The second factor is also associated with the weakness of the M - X bond compared with the M - O bond: halide-based materials have low characteristic temperatures. For example, glass transition temperatures, Tg, are low and range from room temperature to a maximum of 400 °C. As a direct consequence, the thermal expansion

coefficients of halide glasses are usually high, and these materials are sensitive to thermal shock. Their mechanical strength is also poor compared with traditional oxide glasses. The last factor impeding the development of these glasses is that they are formed from the most electronegative elements of the periodic chart, especially in the case of fluorine F, which has a strong tendency to form ionic crystalline materials. A direct consequence is that the glasscrystal competition in halide systems when crossing the strategic liquidus-solidus line often favors microcrystallite formations. Hence, the optical properties, especially the scattering losses, suffer from the tendency to devitrify. Thus it is not surprising that only a limited number of halide glasses among the numerous compositions which have been described in the literature may be suitable for practical applications. The study of optical properties requires the samples to be of reasonable size and optical quality and to have a strong resistance to corrosion from atmospheric moisture. This explains why only a few halide glasses have been thoroughly investigated. This chapter will briefly review the halide compositions which have been proven to be glass formers, even if the glasses have little chance of becoming optical materials because of their poor stability. Particular attention will be paid to the limited number of stable glasses and to their specific optical properties. Among them, the fluoride glasses occupy a dominant position, especially those based on ZrF4 or other multicomponent compositions. These are usually termed heavy metal fluoride glasses. Most of the investigations on fluoride glasses have been motivated by the potential to develop ultralow-loss optical fibers operating in the mid I.R. Several general

8.2 Glass Formation in Halide Systems

articles reviewing the optical properties of these materials have been published (Baldwin etal., 1981; Tran et al., 1984; Drexhage, 1985; France etal., 1987; Lucas, 1986) as well as four international conference proceedings (Almeida, 1987; Lucas and Moynihan, 1985; Drexhage etal., 1987). This fast growing field of glass science has a short history, only about twelve years, since the only halide materials previously known to give glasses were beryllium fluoride, BeF2, and zinc chloride, ZnCl 2 . Because of the toxicity of the former and the hygroscopicity of both, investigations of their optical properties have been very limited, despite the interest expected in them (Weber, 1986; Van Uitert and Wemple, 1978). The goal of this review is to try to set up for these special glasses relations between the chemical composition, which determines the structure and nature of the bonds, and their optical properties. In addition to the development of very large optics often difficult to realize with crystalline materials, an important property of vitreous materials is the potential to develop very transparent optical waveguides or optical fibers. The formation of fibers from crystalline materials is a very difficult operation, while the glassy state, with its unique viscosity-temperature dependence, represents the ideal situation for transforming a bulk material into a very long waveguide. Among the different objectives for developing these optical waveguides are the possibility of repeaterless long distance telecommunication links and analytical applications such as remote I. R. spectrometry, pyrometry and thermal imaging, and energy transfer of the output of powerful lasers for welding, cutting, and surgical operations (see Chap. 15).

459

8.2 Glass Formation in Halide Systems As indicated already, the term halide glass refers to any vitreous material in which the anions come from the group VIIA elements of the periodic table, namely F, Cl, Br, and I. Because of its size and electronegativity, fluorine is often considered a special halogen which has to be treated separately. In this article, we shall also discuss the fluoride glasses as a special family owing to the very large research effort devoted to this group during the last ten years, and we shall examine the socalled "heavy halide glasses", namely chlorides, bromides, and iodides, together as a separate family. 8.2.1 The Fluoride Glasses

Fluoride glasses can be classified according to structural considerations, and, although glass formation has been observed in many fluoride systems, the vitreous materials obtained cannot be considered of equal interest because of the high tendency for most of them to devitrify. 8.2.1.1 The MF 2 -Based Glasses

The MF2-based glasses are represented only by the BeF2 glass family which shows a strong resistance to devitrification. According to Baldwin et al. (1981) it is generally agreed that these vitreous materials are isotypic with SiO2-based glasses. X-ray and molecular dynamics studies clearly indicate that the aperiodic framework is based on the BeF4 tetrahedron. BeF2 is the only fluoride giving a viscous melt which easily vitrifies on cooling. BeF2-based glasses are of special interest for some optical applications for high power lasers owing to their low linear and non-linear refractive indices (see Chap. 12). However,

460

8 Halide Glasses

because of their toxicity, they have received only limited attention. 8.2.1.2 The MF3-Based Glasses These glasses are represented by the A1F3 or transition metal fluoride groups and result from the formation of an aperiodic 3-D framework based on MF6 octahedra. The MF 3 materials, which have been proven to give glasses when combined appropriately with other fluorides, are A1F3, FeF 3 , CrF 3 , and GaF 3 (Sun, 1947; Jacoboni et al., 1983). The other fluoride components are usually ZnF2 or MnF2 and PbF2 which seems to play the important role of modifier. In the typical glass forming ternary system, FeF 3 -MnF 2 -PbF 2 , the glass composition PbFeMnF 7 , which falls in the vitreous domain, corresponds to a glassy material extremely rich in magnetic cations which exhibits interesting spinglass properties at low temperatures (Renard et al., 1981). The glass-crystal competition is also very severe in this family, and the aperiodicity introduced in the ReO 3 structure by rotating or tilting the octahedra can be easily destroyed, with the formation of ordered crystalline materials. A significant improvement in the stability of A1F3-based glasses has been obtained by incorporating ZrF4 to this glass.

tions. As indicated in Fig. 8-1 the stability of the glasses towards devitrification is strongly improved by using a third fluoride such as ThF4 or LaF3. The glass called ZBL, corresponding to the composition 60 ZrF 4 , 33 BaF2, 7 LaF3 and located in the middle of the vitreous area of Fig. 8-1, is a rather stable glass. The rate of crystallization can also be significantly decreased by using a small amount of A1F3. For instance, an optimized composition giving a good technical glass called ZBLA is 55ZrF 4 , 35BaF2, 6LaF 3 , 4A1F3. Many others compositions have been developed in order to decrease the nucleation rate and avoid scattering losses in optical fibers. It appears that the so-called confusion principle can be also applied in this domain of glass science and, for instance, one of the best candidates for fiber drawing is the multicomponent fluoride ZBLAN, with the molar cation composition Zr 53 Ba 20 La 4 Al 3 Na 20 . In this glass, 60ZrF4 33BaF 2 7LaF 3

8.2.1.3 The ZrF4-Based Glasses These glasses were the first of the socalled "heavy metal fluoride glasses". Their discovery in the author's laboratory in 1974 (Poulain et al., 1975) attracted considerable interest because the glasses had very promising properties for mid I.R. applications. Although ZrF 4 by itself cannot be vitrified, if it is combined with an appropriate modifier such as BaF2 it leads, by fast quenching, to simple binary glasses which are useful for structural investiga-

LaF3

ZBLA

BaF2

Glass :

ZBLAN Glass Figure 8-1. Glass forming domain in the ternary diagram ZrF 4 -BaF 2 -LaF 3 . Some compositions are given in molar percentage, for example, for the binary unstable glass ZB, the ternary ZBL and the four and five-component glasses ZBLA and ZBLAN, which are the most resistant to devitrification.


461

These new stable fluoride glasses have been widely investigated, and abundant literature on them exists, as discussed by Drexhage (1985). In the field of structural modelling, relationships have been established between the structure of BaZr 2 F 10 in its crystalline and vitreous states (Phifer etal., 1987). Figure 8-2 presents the 3-D aperiodic framework built up by the connection of Zr 2 F 13 bipolyhedra originating from ZrF7 and ZrF8 edge-sharing polyhedra. The Ba 2+ cations playing the role of modifier elements are inserted in the framework and interact mainly with the nonbridging ions. This model has been obtained from X-ray and neutron diffraction studies, molecular dynamics simulations, and local probe spectroscopies.

Zr

OF

Ba

Figure 8-2. A structural model for the binary glass 2 ZrF 4 -l BaF2. Elementary polyhedra ZrF7 and ZrF8 sharing corners and edges form a 3-D aperiodic framework. The large Ba 2+ cations play the role of lattice modifiers.

where the modifier Ba2 + has been partially replaced by Na + , an interdiffusion barrier to crystallization has been introduced because of the competition between Na and Ba in crystalline fluorozirconate formation. The usual way to prepare these fluorozirconate glasses is by melting the different starting fluorides in vitreous carbon or platinum crucibles in a dry atmosphere. In order to convert some materials starting as oxides to fluorides or to prevent any pyrohydrolysis during heating, it is convenient to add NH 4 HF 2 to the mixture to avoid the presence of O 2 ~ in the melt.

8.2.1.4 Multicomponent Zr-Free Heavy Metal Fluoride Glasses Research into new Zr-free fluoride glasses has been motivated by the need to synthesize glasses having the widest optical windows. The transmission range for the fluorozirconate family is limited in the multiphonon region to about 7 jim because of Zr-F, especially by Al-F vibrational modes. It has been demonstrated that heavy metal fluoride glasses not containing Zr 4 + exist but they are more difficult to prepare (Lucas, 1987), and at least three fluorides need to be incorporated to realize the conditions of glass formation. Three-Component Fluoride Glasses Depending on the quenching rate, small glassy chips can be obtained from ternary liquids. For instance, glasses have been prepared by fast quenching from the following ternary melts: BaF 2 -ZnF 2 -LnF 3 , BaF 2 -ZnF 2 -ThF 4 , BaF 2 -ZnF 2 -CdF 2 or YF 3 -ZnF 2 -ThF 4 .

462

8 Halide Glasses

Four-Component Glasses

8.2.2 Glasses Based on Heavy Halides

Systematic investigations of the quaternary diagram YbF 3 -ThF 4 -ZnF 2 -BaF 2 show that, when BaF2 is added to the glass forming composition YnThZnF9, the tendency to devitrify decreases significantly. For instance, the fluoride glass Ba 16 Th 28 Yb 28 Zn 28 , called BTYbZ, can be obtained in about a 10 mm thickness. The same kind of observation has been made in the system BaF 2 -InF 3 -ZnF 2 -ThF 4 , where the stable composition is Ba 3 0 In 3 0 Zn 3 0 Th 1 0 .

This terminology refers to glasses in which the electronegative part is a heavy halogen such as Cl, Br, I. Most of these materials suffer, in terms of their technological development, from their hygroscopicity, low softening temperature, and the tendency to devitrify. Research activity in this field (Mackenzie, 1987) has been largely motivated by the fact that, from a simple consideration of masses of anions associated with cations, chloride, bromide, and iodide glasses would be expected to be more transparent in the I.R. than the fluoride glasses.

Five-Component Glasses To demonstrate that the multiplication of cations having a flexible coordination was a suitable factor for retarding the crystallization, a systematic investigation has been done of the fluoride system Ba 30 In 20 Zn 30 _ x Y c Th 10 . For x = 10, the melt has a maximum viscosity, and samples of 20 mm thickness can be obtained. This so-called BIZYT glass, with the composition Ba 30 In 30 Zn 20 Y 10 Th 10 , is the most stable Zr-free fluoride glass and has been proven suitable for fiber drawing (Bouaggad et al., 1987). The partial substitution of In by Ga, for example, in the glass BiGaZYT with the composition Ba 30 In 18 Ga 12 Zn 20 Y 10 Th 10 allows us to decrease the critical cooling rate Rc from about 120°C/min to 10°C/min. The structure of these multicomponent glasses is obviously a subject of speculation because of the great number of pair interactions. Nevertheless, an analogy exists between these glasses and the fluorozirconate glasses in the sense that the variety of ZrFn polyhedra in these glasses are replaced by a variety of other equivalent MFn building elements.

8.2.2.1 Glasses Based on Divalent Metal Halides MX2 Vitreous materials have been prepared with M = Zn 2 + , Cd 2 + and X = C1", Br~, I~. ZnCl 2 is the best and most widely known glass former. With an I.R. edge in the 12-13 jim region, it is of interest for optics operating in the 8-12 jim atmospheric window and has a potential for ultratransparency (Van Uitert and Wemple, 1978). Many attempts have been made to increase its resistance to water corrosion and to devitrification by the addition of other halides such as KBr or PbBr 2 (Yamane et al., 1985). Nevertheless, hygroscopicity remains very high and severely affects the optical properties in the I.R. region. The glass transition temperature of such mixed halide glasses is also low, about 50 °C. The glass forming ability is explained by the formation of a 3-D aperiodic framework based on ZnCl 2 tetrahedra. The isotypic ZnBr2 is also known to be a glass former with an expected I.R. cut-off in the 20|im region (Hu et al., 1983), but vitreous ZnBr2 exhibits very poor chemical durability and a weak resistance to de-


vitrification. Addition of a glass modifier such as KBr (Kadono etal.? 1987) improves these two properties. Cadmium chloride CdCl 2 has also been proven to lead to vitreous materials, when associated with other halides such as Pbl 2 or PbCl 2 (Angell et al., 1987). In this case, the I.R. transmission extends to 20jLim. When CdCl2 glasses are stabilized by a mixture of chloride and fluoride such as CdF 2 -BaF 2 -NaCl (Matecki et al., 1987), the multiphonon edge is determined by the metal-fluoride bond and shifts back to the 8-12 jim region. Although they appear less sensitive to humidity than the zinc chloride-based glasses, these CdCl2 glasses cannot be kept in an ambient atmosphere without surface corrosion occurring. A large glass forming domain has been discovered by Cooper and Angell (1983) in the CdI2-based system when Cdl 2 is associated with KI and Csl as modifiers. With an I.R. edge shifted towards the 30 |im region, those glasses have the largest optical window of any known vitreous material. Unfortunately, but as expected, the mechanical properties are very poor and the hygroscopicity is high, essentially owing to a Tg ranging from 10 to 35 °C. One can speculate that these glasses contain a Cdl 4 tetrahedron as a structural module. 8.2.2.2 Glasses Based on Trivalent and Quadrivalent Metal Halides

Angell and Ziegler (1981) reported several glasses based on BiCl3 with I.R. edges located in the 14 jam region. These glasses also suffer from low glass temperatures, around 30 to 50 °C, and the rapid attack of atmospheric moisture. Hu and Mackenzie (1982) succeeded in preparing vitreous chlorides based on ThCl 4 associated with NaCl and KC1. The I.R. edge is located near 14 |im, but strong

463

corrosion due to a high sensitivity to moisture affects the optical transmission severely. In this kind of glass, the structure can be reasonably described as a 3-D framework of connected MC1 6 , MC1 7 , and MC18 polyhedra. 8.2.2.3 Miscellaneous Non-Conventional Vitreous Halides

The concept of the aperiodic framework can be applied to the previous glasses, but fails to explain the existence of some multicomponent monovalent cation halide glasses. It has been demonstrated (Angell et al., 1985, for instance), that large vitreous areas exist in the middle of the AgCl-Agl-CsCl and CuCl-PbCl 2 -RbCl systems. Even in binary systems such as AgX-CsX (X=Br, I) glasses can be obtained by rapidly quenching the melt. The addition of 2% of PbX 2 improves glass formation and allows for the preparation of samples 10 mm thick (Nishii et al., 1985). I.R. transmission occurs out to 15 |im, but the glass temperature is rather low (T g =21°C) for the stabilized glass 59AgX-39CsX-2PbX 2 . Some attack by atmospheric moisture is observed after several hours. One explanation for glass formation in multicomponent systems involving halides such as AgCl, CuCl, Agl, and CsCl can be based on the observation that the eutectic points in these systems are at relatively low temperatures, giving melts where the ionic diffusional processes are slow. Also, the nucleation and crystal growth mechanisms are highly impeded by the fact that the four halides AgCl, CuCl, Agl, and CsCl belonging to four different non-miscible structural types have to compete in forming individual crystallites.

464

8 Halide Glasses

8.2.2.4 The Tellurium Halide Glasses

The author's group recently discovered a new family (Lucas and Zhang, 1986; Lucas et al., 1987) of halide glasses based on the combination of tellurium Te with chlorine, bromine or iodine. These tellurium halide glasses, called "TeX glasses", have been obtained in the following binary or ternary systems: Te-Cl, Te-Br, Te-Cl-S, Te-Br-S, Te-Br-Se, T e - I - S , Te-I-Se. Addition of S or Se to the binary TeX glasses decreases the devitrification rate, and some of these ternary compositions are very resistant to crystallization. In Fig. 8-3 the large vitreous domains in the six different systems are shown. The glass Te3Cl2 with Tg=82°C crystallizes at 189 °C on heating, but the glass Te3Cl2S with T g =81°C shows no devitrification. Most of these TeX glasses are not corroded by atmospheric water, except for those having a high halogen content. As dis-

Q\

Q

20

20

40

40

60

60

80

80

20

B r

20

40

40

cussed in Sec. 8.3.1.2 which is devoted to the multiphonon edge, the TeX glasses can be divided into two groups: a) the light TeX glasses containing light elements such as S or Cl and having an I.R. cut-off at 13 |im, and b) the heavy TeX glasses with a multiphonon edge near 20 jim. The very large glass-forming domain in the Se-containing ternary system is due to the fact that the binary glass, Te3Cl2 for instance, has the same structure as the Se glasses. The chain-like structure of crystalline Te3Cl2 is represented in Fig. 8-4 and is obviously isotypic with the spiral-type structure of crystalline Se giving a broad domain of solid or liquid solution between the two components. Densities and molar volume measurements indicate that all the Te-Br-Se glasses are very homogeneous consisting of infinite mixed Te and Se chains and no phase separation has been observed.

60

60

j

80

80

Se

j

20

40

60

80

20

40

60

80

Figure 8-3. Glass formation in tellurium halides systems. The TeX glasses are stabilized against devitrification by S or Se addition. A large domain of glass formation is shown between the TeX glasses and the selenium due to the similarity in their chain-like structure.

8.3 Halide Glasses as Optical Materials: Passive Properties

OTe •

Cl

Figure 8-4. The chain-like structure of the crystalline form of Te3Cl2. After melting and a moderate quenching rate, Te3Cl2 easily vitrifies. The spiral structure is induced by the steric effect of the lone pair of electrons represented on one Te atom.

8.3 Halide Glasses as Optical Materials: Passive Properties 8.3.1 Optical Properties of Bulk Glasses

For definitions, see Chap. 12. 8.3.1.1 The Bandgap Absorption

The U.V. edge in halide glasses MxXy is associated with the excitation of electrons from lower to higher energy states on the molecular orbital diagram of the M - X bond. It is obvious, because of the great polarizing ability of cations such as Be2 + , Al 3+ , and Zr 4 + and the high value of the corresponding ionization energy, that the M - F bond in fluoride glasses has a strongly covalent character. Consequently, the energy gap between the bonding level and the first unoccupied antibonding level

465

is estimated to be rather high unless impurities such as cations with partly filled d or f levels or heavy halogens such Cl~, Br~, or I~ introduce parasitic levels which can strongly modify the absorption mechanisms in the U.V. A study by Brown (1982) shows that for most of the ZrF4- and HfF4-based glasses the U.V. edge is in the region E = 5 eV, corresponding to X = 0.25 jim, according to the relation /I (jam). £(eV) = 1.24. Compared to very pure vitreous SiO2 where £ = 8.0eV (vl = 0.16 jim), the fluorozirconate glasses are less interesting in terms of U.V. transmission. The U.V cut-off, of course, depends on other M - F bonds if additional metallic fluorides are added to the melt. The cut-off is also governed by the M-Cl molecular orbital diagram if Cl~ anions (Adam and Poulain, 1983) are present in the glass due to Reactive Atmosphere Processing using CC14, for example. It is often observed that CC14 treatment leads to a yellowish coloration of the glass due to a shift of the U.V edge into the visible region. Although no thorough investigation has been done in this area, it is expected that for most heavy halide glasses the U.V. edge will shift towards the visible region progressively, from Cl to I, due to the increasing size and decreasing electronegativity of the corresponding halogen. Visual observation of TeX glasses shows clearly that these "black glasses" have their band gaps in the near I.R. lying typically between 1.40 eV (0.9 \im) in TeSe6Br3 and 0.7 eV (1.8 jim) in the binary glass Te 3 Cl 2 . These glasses have a chain-like structure in which the lone pair of 5 s2 electrons associated with the Te have an important stereochemical effect. The low band gap in these glasses is due essentially to the excitation of these electrons located in non-bonding orbitals.

466

8 Halide Glasses

8.3.1.2 The Multiphonon Absorption Edges

Infrared Edge in Fluoride Glasses

The possibility of shifting the I.R. edge in halide glasses to longer wavelengths has served as a catalyst for much of the research activity on these materials. The synthesis of a glass having multispectral capabilities is of interest to many infrared technologies, especially if a potential for ultratransparency exists. It is well known that the multiphonon absorption mechanisms are among the most important for explaining the optical losses in a material (see Chap. 12). The I.R. or multiphonon edge in a transparent solid results from combinations and overtones of the far-infrared fundamental vibrational frequencies of the bonds between anions and cations. The position of the fundamental frequencies is governed by the Szigeti equation (Szigeti, 1950), which shows the dependence of the vibrational frequency v0 on the reduced mass \i of the atoms A and B and the force constant / for the bond between them: VO = (1/2TT) (//AO 1 / 2 - The reduced mass is given by fi = mAmB/(mA + mB). It is obvious that heavier atoms and weaker bonding are preferable for extended I.R. transmission. As discussed by Lines (1986) and Bendow et al. (1981 b), at the far infrared end of the optical spectrum, the attenuation is dominated by absorption from polar modes of lattice vibrations. This absorption extends as an exponential tail to shorter wavelengths from the intense single phonon band. This tail is the result of absorptions involving the simultaneous excitation of more than one phonon. The dependence of this so-called "multiphonon loss" on wavelength is expressed by the general equation a = A exp (— a/A), in which A and a are material parameters and a is the attenuation coefficient.

The fundamental vibrational modes of the fluoride glass matrix occur in the far infrared at wavelengths between 15 and 50|im. Bendow et al. (1983a, 1983b) and Drexhage (1985) have measured and discussed the reflectivity spectra of several fluoride glasses, which show the compositional variation of the I.R. edge absorption. Figure 8-5 shows the percentage of reflectivity directly related to the absorption coefficient versus the wavelength for different kind of glasses: a) a ZBL glass in the system ZrF 7 4 BaF 2 -LaF 3 ; b) a multicomponent Zr-free heavy metal fluoride glass BTYbZ having the composition 16BaF2, 28ThF 4 , 28YbF3, 28ZnF 2 ; c) the same BTYbZ glass doped with about ten percent A1F3, which often plays the role of stabilizing the glass; and d) a "BATY" glass, in which A1F3 plays the important role of glass former, with the composition 20BaF 2 , 29A1F3, 22ThF 4 , 29YF3. The interpretation of these spectra is as follows: The absorption in the region 250 cm" 1 is attributed to the B a - F bond, the bands in the range 400-450 cm" 1 are due to T h - F or Y b - F bonds, and the large absorption near 550 cm" x in the fluorozirconate is attributed to the Z r - F vibration. The Al-F vibrational mode, which corresponds to a strong M - F bond involving a small and highly charged cation Al3 + is located in the 600-650 cm" 1 region and shows the detrimental effect of A1F3 in fluoride glasses in shifting the multiphonon absorption towards shorter wavelengths. These results, obtained in the far I.R. part of the spectra, are also verified when examining the evolution of the I.R. edge in different kinds of fluoride glasses.

8.3 Halide Glasses as Optical Materials: Passive Properties

50

467

WAVELENGTH (pm) 25 20 15

Figure 8-5. Reflectivity spectra in the single phonon band for several fluoride glasses: a) a ZrF4-based glass; b) a heavy metal Zr-free fluoride glass; c) the same glass as b) but doped with A1F3, and d) an AlF3-based glass. 100

300 500 700 FREQUENCY (cm"1)

900

Figure 8-6 shows the position of the I.R. cut-off for different fluoride glasses having a thickness of about 3 mm. Spectrum 1 corresponds to a BeF2-based fluoride glass in which the strong Be-F bond between two light elements places the I.R. cut-off almost in the same region as the Si-O vibration of the silica glass (Baldwin, 1979). Spectrum 2 corresponds to fluorozirconate of Zr-free fluoride glasses doped with a few percent of A1F3, for example ZBLA glass (4% A1F3). Spectrum 3 is that of a pure fluorozirconate glass such as ZBL in which the I.R. cut-off is governed by the vibrational modes of Z r - F bonds. Finally, spectrum 4 corresponds to the so-called Zr-free multicomponent heavy metal fluoride glasses such as BTYbZ or BIZYT (see the previous

section for an explanation of the acronym). In these glasses, the multiphonon edge is governed by the T h - F or I n - F bonds, and the corresponding atomic weights and force constants are such that the I.R. cutoff is in the 8 jim region, leading to glasses having the widest optical window for stable fluoride glasses. Chung et al. (1987) have recently measured the multiphonon edges of single crystal specimens obtained from the different fluoride used for glass preparation. They also concluded that AIF3 or LiF addition to the glass shifts the I.R. edge to a higher frequency. Figure 8-7, which uses data taken from Chung et al. (1987) and from France et al. (1987) and Takahashi (1987), provides an indication of the wavelength dependence of

100

.BIZYT Glass z o

" \ ||SiO2 Glass\ 1 \ 50 .

I

ZBL Glass^ \ \ 1

I

CO

z

BeF2 Glass 1

2

3

\

3

\ V

ZBLA Glas

\ 1

\ 2

4

, 5

: 6

7

WAVELENGTH (jim)

8

9

Figure 8-6. Infrared absorption edges of several fluoride glasses compared to SiO2 glass. Spectrum 1 corresponds to BeF2-based glasses, spectrum 2 to the ZrF4based glass ZBLA stabilized by AIF3, spectrum 3 is a pure ZrF4based glass ZBL, and spectrum 4 corresponds to a heavy metal Zr-free fluoride glass such as the

468

8 Halide Glasses

the absorption coefficient or loss in dB/km for a fluorozirconate glass from the far I.R. region (50 to 15 |im), corresponding to the high absorption region of the stretching vibration, to the potential ultralow loss region in the mid I.R. region (2-4 |im). The data were obtained in the far I.R. region by reflectivity measurements, in the 5 to 10 jim region by absorption measurements on bulk samples, and in the 2 to 5 jim from optical losses in fibers ranging from a few meters to one hundred meters in length. Figure 8-7 also shows the intrinsic minimum loss expected in the 2 - 4 |im region, which is estimated to be in the range of 10" 2 dB/km. The Infrared Edge in Heavy Halide Glasses As discussed before, the metal heavy halide glasses have the general formula MxXyKz, where M = Zn 2 + , Cd 2 + , Bi3 + , Th 4 + , X = Cl, Br, I, and A is a large cation

WAVELENGTH (Mm) 3 5

2 i

From reflectivity spectra

108

i/Km)

From bulk sample

Y

104

m

From fiber

TJ

479

8.4 Fluoride Glasses: A new Host for Rare-Earth and Transition Metals 4 and 1.52 {im 13/2" • I15/2), 4 e have previ2.78 pm ( I 1 1 / 2 ously reported that the minimum loss of fluoride glass fibers could be reasonably expected at 2.55 jim. At the moment, the 4 111/2 ->4113/2 emission of Er 3 + is the only one available in that region, for use with solid state lasers. That wavelength would of course be better matched by using U 3 + ions whose 4 I 11/2" I 9/2 transition peaks at nearly 2.5 jim. L

8.4.3.2 Non-Radiative Processes in Rare-Earth Doped Glasses Another important parameter for evaluating the lasing potentiality of a given transition is the quantum efficiency rj: n

= WK/{W^Wu^W^)

(8-2)

where WR is the radiative rate and WMJ> and WET are the multiphonon emission and energy transfer rates, respectively. The last two quantities correspond to non-radiative processes and have to be as small as possible in order to have a quantum coefficient equal to or near unity. The multiphonon emission rate varies exponentially according to the following empirical law: WMP = Ce-«*E

(8-3)

where C and a are constants for a given host and AE is the energy gap between the emitting level and the next lower-lying level. The evolution of WMP as a function of AE is portrayed in Fig. 8-14 for ZrF4-based glass (Adam and Sibley, 1985; Tanimura et al., 1984; Shinn et al, 1983), BeF2-based glasses (Layne and Weber, 1977), and various oxide glasses (Yeh et al., 1987; Layne et al., 1977; Reisfeld and Eyal, 1985). As far as the quantum efficiency is concerned, the superiority of fluorozirconate glass is obvious with multiphonon emission rates lower

by one to four orders of magnitude when compared with other glasses. In consequence, fluorescence is more intense and occurs from a greater number of levels in heavy-metal fluoride glasses. This special feature is directly related to the fundamental vibration mode of the host. In fluorozirconate glasses, phonon energies are as low as 500 cm" 1 , compared to 1000 cm" 1 in silicates. For a given energy gap, a greater number of phonons is then required, leading to lower non-radiative probabilities. The WMP=f(AE) curve for YAG crystals (Krupke, 1974) is also shown in Fig. 8-14. It should be noted that WMP is even lower for the ZrF4-based glass in the 2500-5000 cm" 1 region. Energy transfer between ions of the same nature causes a well-known phenomenon: 1OC

H\\\ *\ \ *\ \ \\\ \

LU

7

8

9

1 0 1 1 1 2

13

W a v e l e n g t h (jLim) Figure 8-17. Transmission spectra of a TeX glass optical fiber.

The attenuation spectrum shows that the low loss region is, as expected, in the 8 12|im region and that the loss is dominated by X independent scattering due to the imperfections of the fibers. Bubbles and fluctuations in diameter are the main reasons of loss and explain the difference between expected and experimental values. Due to the extreme hygroscopicity of the other chloride, bromide and iodide glasses, it has never been possible to draw fibers from those materials and TeX glasses are the only vitreous heavy halide materials drawn into optical fibers. These new waveguides are very promising materials for carrying the CO 2 laser light to targets for laser surgery and industrial operations such as cutting, welding, surface treatment, etc.

485

8.6 Stability of Halide Glasses against Chemical Attack and Devitrification

solution of the matrix with a very fast migration of certain species such as Li + , Na + , Al 3+ into the solution. The direct consequence is that the ZrF4-based glasses have chemical durability in non-basic solutions comparable to the poorest silicates. The direct result of these chemical modifications is the devitrification of the corroded surface which crystallizes and forms an opaque film on the surface. In basic solutions, the stability of the glass is much higher and some compositions could stay in these conditions for a few weeks without apparent corrosion. The corrosion by H 2 O vapour is quite different (Loehr et al., 1987); depending on the composition, it usually starts just below the glass temperature around 300 °C. The mechanism of corrosion is illustrated by the following reaction: ME, (glass) 4- y H 2 O (vapour) ->

/g_^

-> MF,_ y OH^ (glass) + y HF (vapour) This attack becomes significant when the temperature increases and is visually easy to detect when a fluoride glass melt is treated in a normal atmosphere due to the formation of white fumes. The result of this corrosion is the presence of a strong OH absorption peak at 2.9 jim in the glass and the potential formation of oxides playing the role of nucleation agents according to the reaction: 2OH

O2

+H.O/'

8.6.2 Devitrification of Fluoride Glasses As discussed by Moynihan and coworkers (Moynihan, 1987; Chrichton et al., 1987), one of the major problems encountered in the development of heavy metal fluoride glass has been the tendency for the glasses to devitrify above the glass transition temperature. Also, during the cooling process of the melt, a critical cooling rate is necessary to avoid nucleation (EsnaultGrosdemouge et al., 1985) and then growth of the crystallites (Bonsai et al., 1985). The main feature illustrating the special thermal behaviour of fluoride glasses is the temperature dependence of the viscosity which is represented in Fig. 8-18. It is clear that there is a large gap between the hightemperature viscosity data collected in the melt (Hu and Mackenzie, 1983) and the highly viscous zone just above Tg. This situation is due in part to the tendency of these melts to crystallize mainly because the viscosity is only a few dPa s at temperatures significantly below the liquidus allowing relatively high mobility of the

900 700

T(° C) 500 400

300

(8-5)

The practical effect of this corrosion phenomenon leading to hydroxyl and then oxide formation, is the risk of nucleation and crystallization originating from the surface; consequently the only way to prepare good optical glasses is to operate in a dry glove box.

0.001

0.0014

0.0018

Figure 8-18. Viscosity versus temperature for two different fluoride glasses ZBLA and ZBLAN. Experimental points are missing in the middle of the diagram due to crystallization on cooling TXC or heating TXH.

486

8 Halide Glasses

ions for nucleation and crystallization processes. Figure 8-18 is a comparison of two good technical glasses: 1) ZBLA with the composition Zr 55 Ba 35 La 6 Al 4 and 2) ZBLAN with the composition Zr 55 Ba 17 La 6 Al 4 Na 18 . The second has been proven to be more resistant to devitrification and is one of the best candidates for fibre drawing. This interesting behaviour is explained by an interdiffusion barrier to crystallization due to the competition between two crystalline forms. Indeed, it has been noticed that a partial substitution of the modifier cation Ba2 + by Na + cations introduces a competition between sodium fluorozirconate and barium fluorozirconate formation during the crystallization process and consequently delays the devitrification phenomena. This observation appears to be a kind of illustration of the so-called "confusion principle" and could show that one route to finding fluoride glasses compositions more stable against crystallization may be to incorporate into the melt additional components which will inhibit the first crystalline species formation.

8.7 Preparation of Fluoride Glasses and some Physical Properties The interest in fluoride glasses is mainly related to their passive or active optical properties and in both cases the search for materials having excellent optical quality is essential. The preparation route then becomes a key factor especially when ultra pure glass is the ultimate goal. This constraint is less critical for some physical investigations, such as electrical and magnetic properties.

8.7.1 Preparation of Fluoride Glasses

The conventional route for preparing fluoride glasses is the melting of the starting fluorides into an inert atmosphere using vitreous carbon, gold, or platinum crucibles. The liquidus temperature for heavy metal fluoride glasses is around 550 to 650 °C, and then heating until 800 to 950 °C is needed to obtain an homogeneous melt. Another convenient way to prepare the melt is the ammonium fluoride route using NH 4 FHF which easily converts oxides in fluorides. The conversion reaction takes place at temperatures around 300 to 400 °C and an excess of ammonium fluoride is needed to completely transform the oxides in a mixture of metallic ammonium fluorides which are then decomposed by heating at 800 °C. This treatment eliminates the excess of NH 4 FHF and produces a melt which is poured in preheated brass moulds. The glasses are then annealed at a temperature close to Tg. As mentioned before, the development of high optical quality optics or optical fibres is governed by the production of highpurity materials where one must avoid the presence of transition metal, rare-earth, complex anions such as OH, SO 4 ~, P O | ~ , ... which absorb in the optical window of fluoride glasses. Sublimation of volatile fluoride, such as ZrF 4 , as well as solvent extractions are the most common techniques used for purifying the starting fluorides from the most poisonous absorbing cations such as Fe 2 + , Cu 2 + , Co 2 + , Ni 2 + , Nd 3 + , Ce 3 + , Pr 3 + . It must be noted that 1 ppm of these impurities leads to parasitic absorption in the range of 10 to 100 dB/km and that the tolerated level of contamination for reaching the ultimate transparency values will have to be at the part per billions level.

8.7 Preparation of Fluoride Glasses and some Physical Properties

Purification based on chemical vapour deposition also seems to be a solution for separating transition metals. The vapour pressure of ZrCl 4 and ZrBr 4 is, for instance, a few orders of magnitude higher than the transition metal equivalents. Their conversion in ZrF 4 through the vapour state via a fluorinating agent is an elegant way of producing very pure starting materials (Folweiller and Guenther, 1985). The natural impurity of the fluoride material is OH~ due to hydrolysis with HF formation. In order to decrease the level of OH" which introduces a large absorption band in the middle of the optical window, a "reactive atmosphere processing" (RAP) technique has been developed, initially by Robinson (1985). A gaseous atmosphere, such as CC14, SF6, NF 3 , CS 2 used above the melt helps the substitution of OH ~ and O 2 ~ impurities by Cl~, S 2 ~, etc. An NF 3 atmosphere also maintains an oxidizing situation above the melt which allows iron impurities to be retained in the trivalent non-infrared absorbing Fe 3 + state. It must be noted that an O2~ impurity in fluoride glasses has two effects: it modifies the multiphonon absorption mechanisms by the formation of M - O vibrational modes which introduce shoulders in the multiphonon region; depending on the degree of contamination, O 2 ~ could contribute to the formation of ZrO 2 crystallite particles having a high lattice energy and producing a very poor effect on the Rayleigh scattering factor even if the particles are of the 0.2 jam range size (Takahashi, 1987). Using the RAP technique for decreasing the oxygen content in glasses is consequently justified especially for lowering the scattering loss mechanism in longdistance repeaterless optical fiber for telecommunication.

487

8.7.2 Magnetic Properties of Fluoride Glasses Fluoride glasses offer unique opportunities to study the magnetic properties of amorphous disordered systems because they exhibit a large range of glass compositions, high atomic concentrations, and various associations of magnetic ions belonging either to the 3d or 4f series. These properties have been essentially investigated by Dupas and co-workers (Dupas et al., 1981) on many FG compositions containing either high concentrations of magnetic lanthanides or 3d metals such as iron or a combination of both species. As an example, we shall select the glass PbMnFeF 7 belonging to the 3d metal system PbF 2 /MnF 2 /FeF 3 and a rare-earth rich material with the composition 20 BaF2, 30 H0F3, 45 ZnF 2 . Most of these magnetic glasses are usually not resistant to devitrification and need to be obtained by quenching. The magnetic susceptibility of doped fluoride glasses follows a Curie-Weiss law over a wide range of temperature. These systems exhibit very low values of the Curie-Weiss temperature (0 ~ 100 K) and thus evidence of antiferromagnetic interactions. At low temperatures, a cusp occurs in the thermal variation of the a.c. susceptibility, indicating the onset of spin-glass ordering. The spin-freezing temperature, Tf = 10 K is remarkably high for the glass PbFeMnF 7 which contains large amounts of 3d 5 cations Fe 3 + and Mn 2 + , compared to the Ho 3+ -containing glass where Tf ^ 1 K. Many investigations have been conducted on this type of magnetic material in order to see the effect of metallic substitutions on the properties and to clarify the nature of the spin-glass interactions in these insulating materials (see also Chap. 6).

488

8 Halide Glasses

8.7.3 Electrical Properties of Fluoride Glasses Electrical investigations on fluoride glasses have been initiated by Ravaine (1985). They concluded that the main features of the electrical behaviour of this new vitreous materials were that: (a) as expected, they are very poor electronic conductors taking into account the very electronegative character of the fluorine atoms; (b) the conductivity measured on many samples and compositions is in the range of 1 0 " 6 Q - 1 c m " 1 at200°C; (c) the conductivity mechanism is only due to F~ ion mobility which gives to these glasses solid electrolyte properties and makes them candidates for a solid-state battery involving F2 or derivatives at one electrode;

T(°C) 250

150

100

(d) the activation energy is very dependent on the composition and is in the range E = 0.66 to 0.89 eV. Kawamoto and Nohara (1985) confirmed these results and Inoue and Yasui (1987) have proposed a conductivity mechanism from molecular dynamics simulations which shows that the dominant factor of the conduction is due to the migration of the non-bridging fluorine ions. The fluorine mobility can be explained by the plurality of the ZrFn polyhedra (n = 6, 7, 8) in the glass, as discussed in the section on structure. This situation can be compared to the mixed valence effect in electronic semiconductors (see Chap. 7). Figure 8-19 shows the conductivity-temperature diagram for different crystalline and vitreous fluoride conductors. It appears that the conductivities of all fluoride glass compositions are located in the same order of magnitude, approximately between the very good fluorine conductors such as PbSnF4 and the poor fluorine conductors such as CaF 2 .

50

8.8 References

-8 1.5

Figure 8-19. Anionic F conduction in fluoride glasses based on ZrF4 or Zr-free BTYZ glass for example, versus temperature. For comparison the best F conductors, such as PbSnF4 are given.

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Ofelt, G.S. (1962), /. Chem. Phys. 37, 511. Ohishi, Y, Hattori, H. (1986), Jap. J. Appl. Phys. 25, L844. Ohishi, Y, Takahashi, S. (1985), J. Non-Cryst. Solids 74, 407. Ohishi, Y, Takahashi, S. (1986), Appl. Opt. 25, 720. Ohishi, Y, Mitachi, S., Shibata, S., Manabe, T. (1981), Jap. J Appl. Phys. 20, L191. Ohishi, Y, Mitachi, S., Kanamori, T, Manabe, T. (1983), Phys. Chem. Glasses 14, 135. Okada, K., Miura, K., Masuda, I., Yamashita, T. (1988), Mater. Science Forum 19-20, 557. Orera, V.M., Alonso, P.X, Cases, R., Alcala, R. (1988), Phys. Chem. Glasses 29, 59. Perry, P. B., Shafer, M. W, Chang, I. F (1981), / Lumin 23, 261. Phifer, C.C., Angell, C.A., Laval, J.P., Lucas, X (1987), J Non-Cryst. Solids 94, 315. Pinnow, D. A., Gentille, A. L., Standlee, A. G., Timper, A. X, Hobrock, L. M. (1978), Appl. Phys. Lett. 33, 28. Poignant, H. (1981), Electron. Lett. 17, 973. Pollack, S.A., Robinson, M. (1988), Electron. Lett. 24, 320. Poulain, M., Lucas, X (1978), Verres Refract. 32, 505. Poulain, M., Poulain, M., Lucas, X, Brun, P. (1975), Mat. Res. Bull. 10, 242. Poulain, M., Lucas, X, Brun, P., Drifford, M. (1977), in: Colloques Internationaux du C.N.R.S. 255; Paris: C.N.R.S., pp. 257-263. Quimby, R. S. (1988), Mater. Science Forum 32, 551. Quimby, R. S., Drexhage, M. G., Suscavage, M. X (1987), Electron. Lett. 23, 32. Ravaine, D. (1985), Mater. Science Forum 6, 761. Reisfeld, R., Eyal, M. (1985), /. Phys. 436, 349. Reisfeld, R., Jorgensen, C.K. (1987), in: Handbook on the Physics and Chemistry of Rare-Earth, Chap. 58. Amsterdam: Elsevier Sci. Publ., pp. 1-90. Reisfeld, R., Greenberg, E., Brown, R. N., Drexhage, M.G., Jorgensen, C.K. (1983), Chem. Phys. Lett. 95, 91. Reisfeld, R., Eyal, M., Greenberg, E., Jorgensen, C.K. (1985), Chem. Phys. Lett. 118, 25. Reisfeld, R., Eyal, M., Jorgensen, C. K., Guenther, A.H., Bendow, B. (1986 a), Chimia 40, 403. Reisfeld, R., Eyal, M., Jorgensen, C.K. (1986b), /. Less. Common. Met. 126, 187. Reisfeld, R., Eyal, M., Jorgensen, C.K. (1986c), Chem. Phys. Lett. 132, 252. Reisfeld, R., Eyal, M., Jorgensen, C. K., Jacoboni, C. (1986 d), Chem. Phys. Lett. 129, 392. Renard, J.P., Dupas, C , Velu, E., Jacoboni, C , Fonteneau, G., Lucas, X (1981), Physica 108 B, 1291. Robinson, M. (1985), Mater. Science Forum 5, 19. Robinson, M., Pastor, R. C , Harrington, X A. (1982), SPIE 320, 37. Rubin, X, Brenier, A., Moncorge, R., Pedrini, C , Moine, B., Boulon, G., Adam, J. L., Lucas, X, Henry, X Y (1987), J. Phys. C48, 367.

8.8 References

Sakagouchi, S., Takahashi, S. (1987), /. Lightw. Technol. 5, 1219. Sanz, X, Cases, R., Alcala, R. (1987), /. Non-Cryst. Solids 93, 311. Schneider, H. W., Schoberth, A., Staudt, A., Gerndt, C.H. (1987), SPIE799, 112. Shafer, M.W, Perry, P. (1979), Mat. Res. Bull. 14, 899. Shinn, M. D., Sibley, W. A., Drexhage, M. G., Brown, R.N. (1983), Phys. Rev. B27, 6635. Simmons, C.J., Simmons, J. H. (1986), /. Amer. Ceram. Soc. 69, 661. Sun, K.H. (1947), J. Amer. Ceram. Soc. 30, 277. Suzuki, Y, Sibley, W. A., El Bayoumi, O. H., Roberts, T.M., Bendow, B. (1987), Phys. Rev. B35, 4412. Szigeti, B. (1950), Proc. Roy. Soc. A 204, 51. Takahashi, S. (1987), /. Non-Cryst. Solids 95-96, 95. Tanabe, Y, Sugano, S. (1954 a), /. Phys. Soc. Jap. 9, 753. Tanabe, Y, Sugano, S. (1954 b), J. Phys. Soc. Jap. 9, 166. Tanimura, K., Shinn, M. D., Sibley, W. A., Drexhage, M.G., Brown, R.N. (1984), Phys. Rev. B30, 2429. Tran, D. C , Sigel, G. H., Levin, K. H., Ginther, R. J. (1982), Electron. Lett. 18, 1046. Tran, D. C , Sigel, G. H., Bendow, B. (1984), /. Lightwave Technol. LT2 # 5 , 566. Tsoukala, V. G., Schroeder, I, Floudes, G. A., Thomson, D.A. (1987), Mater. Science Forum 19-20, 637. Weber, M. J. (1986), in: Critical Materials Problems in Energy Production. New York: Academic Press, pp. 261-279. Weber, M.J., Brawer, S.A. (1982), /. Non-Cryst. Solids 52, 321. Weber, M. X, Cline, C.E, Smith, W.L., Milan, D., Heiman, D., Hellwarth, R.W. (1978), Appl. Phys. Lett. 32, 403. Van Uitert, L.G., Wemple, S.H. (1978), Appl. Phys. Lett. 33, 57.

491

Yamane, M.Y, Moynihan, C.T. (1988), in: Mater. Science Forum 32-33, Vth International Symposium on Halide Glasses. Japan. Yamane, M., Kawazoe, H., Inoue, S., Maeda, K. (1985), Mat. Res. Bull. 20, 905. Yeh, D.C., Sibley, W.A., Suscavage, M., Drexhage, M.G. (1986), J. Non-Cryst. Solids 88, 66. Yeh, D.C., Sibley, W.A., Suscavage, M., Drexhage, M.G. (1987), J. Appl. Phys. 62, 266. Yeh, D.C., Sibley, W.A., Suscavage, M.J. (1988), J. Appl. Phys. 63, 4644. Yeh, D. C , Petrin, R. R., Sibley, W. A., Madigou, V., Adam, XL., Suscavage, M.X (1989), Phys. Rev. B39 [1], 80-90. Zheng, H., Gan, F. (1986), Chin. Phys. 6, 978.

General Reading Baldwin, C M . , Almeida, R.M., Mackenzie, XD. (1981), Halide Glasses, Journal of Non-Crystalline Solids 43, 309. Comyns, A.E. (Ed.) (1989), Fluoride Glasses, Critical Reports on Applied Chemistry, Vol. 27, New York: John Wiley. Drexhage, M.G. (1985), "Heavy-metal fluoride glasses", Treatise on Materials Science and Technology, Vol. 26, Glass IV: Tomozawa, M., Doremus, R.N. (Eds.). London: Academic Press. Drexhage, M.G., Moynihan, C.T. (1988), "Infrared Optical Fibers", Scientific American 256, no. 11. France, P. W, Carter, S.F., Moore, M. W, Day, C.R. (1987), "Progress in Fluoride Fibres for Optical Telecommunications", British Telecom. Technol. J 5, no. 2. Lucas, X (1989), "Review on Fluoride Glasses", Journal of Materials Science 24, 1-13. Tran, D.C., Sigel, G.X, Bendow, B. (1984), "Heavy Metal Fluoride Glasses and Fibers", Journal of Lightwave Technol., Vol. LT2, no. 5.

9 Metallic Glasses Robert W. Cahn Department of Materials Science and Metallurgy, University of Cambridge, Cambridge, U.K.

List of 9.1 9.1.1 9.1.2 9.1.3 9.2 9.2.1 9.2.2 9.2.3 9.2.4 9.2.5 9.2.6 9.2.7 9.2.8 9.2.9 9.3 9.3.1 9.3.2 9.3.3 9.3.4 9.4 9.4.1 9.4.2 9.4.3 9.4.4 9.4.5 9.5 9.5.1 9.5.2 9.6 9.6.1 9.6.2 9.6.3 9.6.4

Symbols and Abbreviations Introduction Quenching from the Vapor The Origins of Quenching from the Liquid State Treatment of Metallic Glasses in the Series Methods of Making Metallic Glasses and Amorphous Alloys Melt-Quenching Vapor-Quenching Electrolytic Deposition Ion Implantation and Ion Mixing Amorphization by Irradiation Amorphization by Interdiffusion and Reaction Mechanically Aided or Induced Amorphization Amorphization at High Pressure Composition Ranges of Glass Formation and Glass Structures for Different Preparation Techniques Amorphizable Alloy Systems Favorable Combinations of Metals Composition Ranges for Glass Formation Criteria for Glass Formation The Special Case of Silicon Diffusion, Relaxation and Crystallization Diffusion Relaxation Thermal Embrittlement Relaxation of Magnetic and Elastic Properties Crystallization Chemical Properties Corrosion Resistance Heterogeneous Catalysis and Electrocatalysis Applications Magnetic Applications Brazing Foils Mechanical Properties Chemical Properties

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

495 496 496 497 498 499 499 500 501 502 502 503 506 507 507 508 508 510 510 517 518 518 521 526 528 530 535 535 536 536 537 538 539 540

494

9.6.5 9.6.6 9.7 9.8

9 Metallic Glasses

Diffusion Barriers Metallic Precursors for Devitrification Acknowledgement References

542 542 543 543


495

List of Symbols and Abbreviations B b c#m D E G(r) H HLY Hsy KP k kF Rc r T To

magnetic flux density characteristic distance minimum solute concentration of element B diffusion constant Young's modulus total reduced atomic pair radial distribution magnetic field strength large-atom hole-formation enthalpy small-atom hole-formation enthalpy first peak of the X-ray scattering curve Boltzmann constant fc-vector of the Fermi energy critical quenching rate interatomic distance temperature temperature at which two phases of identical composition have equal free energies TBD ductile-to-brittle transition temperature Tf thermodynamic freezing temperature Tg glass transition temperature 7^° ideal freezing temperature Ts limiting glass transition temperature from entropy crisis models Tx, Tcryst crystallization temperature 7^ limiting glass transition temperature from free volume models t time vA, vB atomic volumes g rj a

strain rate viscosity stress

CALPHAD CSRO DSC GFA SRO SSAR TEM TSRO

calculation of phase diagrams chemical short-range order differential scanning calorimeter or calorimetry glass forming ability short-range order solid-state amorphization reaction transmission electron microscopy topological short-range order

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9 Metallic Glasses

9.1 Introduction A solid alloy with a liquid-like atomic arrangement is called a metallic glass, or alternatively an amorphous (metallic) alloy. A glass is, strictly speaking, a liquid which has been cooled into a state of rigidity without crystallizing, while a material with a similar structure made by some process other than cooling is properly called "amorphous" rather than "glassy". This fine distinction, which is not always observed, will be retained here. Very few pure metals can be made amorphous, so the use of the word "alloy" is mostly appropriate in this context. Unlike the production of, say, an oxide glass, which can be accomplished by very slow cooling of a siliceous melt, the making of a metallic glass by simple cooling requires very rapid quenching of an alloy melt: with two known exceptions, a minimum cooling rate of about 103 K~ x is required, and minimum rates of 104 to 106 K " 1 are common (see Chap. 2). 9.1.1 Quenching from the Vapor

The earliest observations of amorphous alloys did not involve starting with a liquid alloy, but were made by physicists who used thermal evaporation to prepare metal films intended for the study of superconducting properties. The condensation of a metallic vapor on a cold substrate is functionally equivalent to an ultrarapid quench from the melt. In the 1930s, a German physicist, Kramer (1934, 1937) claimed to have generated amorphous Sb by this approach; he was one of the early users of electron diffraction in support of this research. Much later, Buckel and Hilsch in Gottingen evaporated metals such as Bi, Ga and Sn and Sn-Cu alloys on to substrates held at 4 K (because they were preparing their films for superconductivity

measurements). Their papers (Buckel, 1954; Buckel and Hilsch, 1952,1954,1956) have become classics. They believed, from electron diffraction findings, that their films were ultrafine-grained, and they also found that the normal, very slight solubility of Cu in Sn could be extended beyond 20 at.%, and that of Bi in Sn to 45 at.%. A little later, it had become clear that several of the films originally believed to be ultrafine-grained were in fact amorphous: this was true of Bi, Ga and Sn-Cu. Buckel and Hilsch had thus discovered, before the first researches on rapid quenching from the melt were performed, two of the key features of rapid quenching: the extension of solid solubility and vitrification. Curiously, there is still today disagreement whether the Bi films made by Buckel and Hilsch's method were truly amorphous or only microcrystalline. Thus Comberg et al. (1975) claimed, on the basis of Hall effect measurements in particular, that vapor-quenched bismuth is in fact microcrystalline, and the issue was further discussed in a review, by Bergmann (1976), of amorphous superconductivity. Bergmann also describes experiments which showed that other metals besides Sn, including Pb, In and Tl, could be forced into the amorphous state by co-depositing them with 10-20 at.% of a second component. Ge (Haug et al., 1975) and Sb (Muller et al., 1975) were made amorphous only by coevaporating them with a high concentration of solute (e.g., 50 at.% Au); this suggests that Kramer's prewar claim to have amorphized pure Sb should be regarded as suspect. - The special case of amorphous Si will be discussed later in this chapter. The continuing debate between those who believe that Bi films made by the Buckel method are amorphous and those who regard them as microcrystalline is an echo of a long-standing disagreement of

9.1 Introduction

this kind, most vigorous in the 1970s, concerning a number of supposed metallic glasses. A good discussion of this type is to be found in a paper by Dixmier and Guinier (1970): these authors examined two alloys, P t - C and N i - P , the former made by evaporation, the latter by electrolysis. Examination of the X-ray scattering pattern proved to be an uncertain basis for deciding between the amorphous and microcrystalline options, but Dixmier and Guinier discovered that the two alloys behaved quite differently on annealing. In Pt-C, the scale of the structure gradually coarsened, with a progressive sharpening of the diffraction lines, whereas in N i - P , diffraction lines due to Ni and Ni 3 P appeared and gradually strengthened while the pattern due to the N i - P itself remained unaltered. - This, they held, implied that the P t - C was microcrystalline and underwent progressive grain growth, a quasi-homogeneous process (see Vol. 15, Chap. 9) whereas the N i - P t was truly amorphous and crystalline phases were nucleated from it and grew heterogeneously. - A technique has however now been perfected which should obviate arguments as to the amorphousness/microcrystallinity of any specific phase. Chen and Spaepen (1988,1991) have used a scanning differential calorimeter (see Vol. 2, Chap. 4) in isothermal mode, to establish the form of the heat release of the contentious alloy: the "fingerprint" of the heat release of an alloy undergoing normal (i.e., uniform) grain growth is quite different from that of an alloy undergoing nucleation and growth of one or more crystalline phases from a true glass. 9.1.2 The Origins of Quenching from the Liquid State

Pol Duwez, a highly original metallurgist at the California Institute of Technol-

497

ogy, is universally regarded as the father of rapid quenching from the liquid state. He was not the first to use such methods, but earlier innovators were interested only in using rapid quenching as a production method for cheaply making the relevant shapes, whereas Duwez explicitly investigated the metallurgical consequences of rapid quenching from the melt, that is, he was using the technique from a researcher's viewpoint while his predecessors were seeing it from a production engineer's viewpoint. - The various experimental techniques of rapid quenching from the melt, alias rapid solidification processing, are

fully explained in Vol. 15, Chap. 2, and will not be further described here. - In his own account of his early researches in the field, Duwez (1967 a, b) describes his concern to resolve the paradox of the failure of the Ag-Cu system to generate a continuous series of solid solutions while the Ag-Au and Cu-Au systems did have such a series. He wrote later that "the possibility of removing this rather exceptional case from the list of binary alloys which did not follow the Hume-Rothery criteria was the main incentive for finding an experimental technique capable of achieving extreme rates of cooling from the liquid state". He concluded that quenching from the melt might force concentrated Ag-Cu alloys into a state of solid solution which was only just unfavorable from a free-energy viewpoint, if it were done fast enough, and he understood the quenching process well enough from his earlier attempts to accelerate cooling in the solid state (Duwez, 1951) to recognize the need to bring a thin layer of liquid rapidly into contact with a cold solid chill-block: thus the Duwez gun, a device for atomizing a metallic melt and impelling the small droplets against a copper sheet, was born; at about the same time Duwez also developed the piston-and-

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9 Metallic Glasses

anvil apparatus. Duwez and his colleagues used this new equipment to show that melt-quenched Cu-Ag alloys did indeed form a seamless series of solid solutions (Duwez et al., 1960). It would be difficult to find a clearer example of the truth that the exercise of curiosity concerning fundamental scientific issues can launch an experimental programme leading to momentous technological consequences. Very soon after the first publication just cited, the same group of investigators decided to look for the formation of a metallic glass in a melt-quenched alloy and promptly found it in the Au-Si system (Klement et al., 1960). Thereupon Cohen and Turnbull, who happened to be sharing the same room at the Cavendish Laboratory at the time, wrote a key paper (Turnbull and Cohen, 1961) in which they suggested that the ready formation of a metallic glass in the Au-Si system near 25 at.% Si was connected with the existence of a deep eutectic in equilibrium near this composition: this gave the melt the opportunity to cool stably to a temperature at which its viscosity had become quite high and therefore diffusion in the melt had become sluggish. This immediately provided a logical basis for finding other glass-forming systems, and led, inter alia, to the discovery of the important glass in the Pd-Si system (Duwez et al., 1965) on which much of the early systematic work on metallic glass properties was done. Duwez began this process by examining the Pd-Si glass by transmission electron microscopy and studying its crystallization in situ. - Turnbull has analyzed the many stages in the recognition and characterization of the metallic glass state (Turnbull, 1985).

9.1.3 Treatment of Metallic Glasses in the Series

Different aspects of metallic glasses are treated in several Volumes of the Series. The structure of both molten and amorphous binary alloys is treated in Vol. 1, Chap. 4, together with a discussion of the requisite instrumental methods, including not only wide-angle X-ray diffraction but also small-angle X-ray scattering and Xray absorption methods. A more extensive treatment of models of glass structure and the problems encountered in deriving such models from diffraction and spectroscopic data is to be found in Vol. 9, Chap. 4; this treatment covers all kinds of glasses, including metallic ones. Physical properties of metallic glasses (as well as metallic melts), including particularly magnetic and electrical properties, are treated in Vol. 3, Chap. 9. A chapter on the deformation and fracture of glassy materials in Vol. 6, Chap. 11 includes some discussion of deformation and fracture mechanisms in metallic glasses. The formation of amorphous alloys by ion implantation and ionmixing is treated in Vol. 15, Chap. 6. Because of this varied coverage, and to avoid needless duplication, the remainder of this chapter will be restricted essentially to the following topics: (1) Methods of making metallic glasses and amorphous alloys; (2) the systematics of the alloy systems and composition ranges in which it has been possible to make such materials, and, more generally, criteria for glass formation in alloy systems; (3) diffusion and crystallization in metallic glasses; (4) structural relaxation of metallic glasses and its consequences for properties, including embrittlement; (5) corrosion resistance and catalytic activity of metallic glasses; and (6) applications.

9.2 Methods of Making Metallic Glasses and Amorphous Alloys

9.2 Methods of Making Metallic Glasses and Amorphous Alloys 9.2.1 Melt-Quenching The various methods currently used for rapidly abstracting heat from thin sections of molten alloys are fully described in Vol.15, Chap. 2. (See also this Volume, Chap. 2.) They include melt-spinning (in which a jet of melt is projected against a spinning polished copper wheel), to make narrow ribbons; planar flow-casting, in which a slit through which the melt flows is held within a fraction of a millimeter of the surface of the copper wheel, to make wide sheet up to about 25 cm in width; melt extraction, itself available in several variants, in which a sharp-edged wheel barely touches a molten surface and extracts a ribbon of D-shaped cross-section from it; the piston-and-anvil method, in which a free-falling melt droplet is caught between rapidly colliding metal plates to make a disc; free jet melt-extrusion, in which a jet is spun under conditions which discourage break-up into discrete droplets, so that the wire cools freely in contact with the surrounding cold gas; the twin-roller technique, in which a flat melt-jet is pinched between counter-rotating rollers; the in-rotating-water spinnning process, in which a fine jet of melt is injected into a rotating annulus of water, to make an amorphous wire; laser treatment, in which a laser beam focused to a small area is traversed across a solid surface so as to melt it in a transient fashion, the underlying solid acting as a chill-block, or else nanosecond or picosecond pulses are applied to a spot on a stationary substrate (see also Vol. 15, Chap. 3); atomization, in which an alloy melt jet is broken up by a cold, transverse liquid or gaseous jet into alloy droplets which solidify by depositing

499

their heat in the atomizing fluid, to make a melt-quenched powder; the Taylor wire method, which creates a fine alloy wire encapsulated in an oxide glass sleeve through which heat is abstracted; and several other methods such as spark erosion which are curiosities rather than mainline techniques. Four of the mainline methods are shown schematically in Fig. 9-1. In all these methods, the melt is given a geometrical shape in which one or more dimensions are small, so that heat can be removed fast. In melt-spinning or planar flow-casting, ribbon or sheet thickness is typically in the range 20-50 jam, wires made by the in-rotating-water method are typically 50-100 jim in diameter, powders have a size distribution typically 20-100 jam diameter. The cooling rate in these various methods varies with the dimensions of the melt and the experimental variables such as wheel speed or piston-and-anvil speed, and it also varies as the sample cools, being fastest when the sample is hottest. The common practice of citing a single figure for the cooling rate during a melt-quenching operation thus has little physical meaning without further information. - Fig. 9-2a shows a series of measurements on free-falling drops of pure molten iron, quenched in an electromagnetically operated piston-and-anvil apparatus; the temperature versus time plots were obtained by means of microthermocouples built into the anvil (Duflos and Cantor, 1982). It is clear that cooling rates decline greatly during the solid-state phase of cooling. - Cantor subsequently used ingenious pyrometric methods to map the cooling-rate history of glass ribbons during melt-spinning (Fig. 9.2 b) (Hayzelden et al., 1983; Gillen and Cantor, 1985); it is to be noted that none of the methods for estimating cooling rates which depend upon measurement of microstructural features such as

500

9 Metallic Glasses LEVITATION COIL

MELT

PRESSURE

/ OPTICAL SENSOR

/INDUCTION COIL

MELT DROPLET

SUBSTRATE PISTONS

(b)

(a) PRESSURE

MELT

FEED

INGOT ROD MELT DROPLET

INDUCTION COIL

\

RIBBON

SUBSTRATE WHEEL

(c) (d) Figure 9-1. Principal methods of quenching alloys from the melt: (a) Drop-smasher or piston-and-anvil method, (b) Melt-spinning, (c) Pendant-drop melt extraction, (d) Twin-roller quenching device.

dendrite arm spacing (Vol. 15, Chap. 2) can be used with metallic glasses. With regard to atomization as used to make powders, only computational methods are available for assessing cooling rates. Systematic studies (Clemens et al., 1987) have shown that metallic multilayer films (here Ni and Zr) can be converted to glass by microsecond current pulses which take the film above the glass transition temperature but not above the melting-point of the constituent metals; the effective quenching rate is I O ^ I O ^ S " 1 .

9.2.2 Vapor-Quenching

The early work of Buckel and Hilsch on vapor-quenching of a number of metals and alloys has, rather surprisingly, not had a great deal of follow-up. Dahlgren (1983) has reported on the method of highrate vapor-quenching, based on sputtering rather than thermal evaporation (Vol. 15, Chaps. 7, 8), to make glassy objects of substantial thickness. Others (Bickerdike etal., 1986; Gardiner and McConnell, 1987) developed high-rate thermal evapo-


107

ration methods on to cold substrates to make objects up to ingot size, but these techniques appear to have been used only to manufacture crystalline, not amorphous alloys. Dahlgren's approach appears to be too expensive to have found large scale application, but vapor-quenching has been used in connection with electronic and magnetic amorphous films, as will be seen below.

7in 106 c

E io 5 c "o o o

900 V

A

A

750 V • 500 V •

D

0.5g

500

(a)

o 1g

1000 1500 Temperature, T in K

1600

1200 (b)

501

9.2.3 Electrolytic Deposition Many years ago (Brenner et al., 1950) it was discovered that N i - P alloys, containing more than about 10at.%P, can be electrodeposited in amorphous form to give an ultrahard surface coating. Much further research has been done on this family of electrodeposits (see Brenner, 1963), more recently in relation to electroplating variables such as steady or pulsed current (Lashmore and Weinroth, 1982). Indeed, it seems that N i - P amorphous layers electrodeposited by steady and pulsed currents are structurally distinct (Lashmore et al., 1982). Electrodeposition allows good control of glass production. Some account of this method will be found in Vol. 15, Chap. 11, including the generation of amorphous alloy multilayers by electrodeposition. Not much search for other amorphous alloys that can be made by electrodeposition has been reported, though apparently C o - W - B is one other candidate. Also, it has been established that bright amorphous chromium of very high hardness can be electrodeposited

t in ms

Figure 9-2. (a) Data from many cooling curves obtained from a microthermocouple built into the anvil of a piston-and-anvil quenching apparatus, during drop-smashing of pure iron. The voltages are accelerating voltages: higher values imply faster quenching. Larger specimens had greater superheat. (After Du-

flos and Cantor, 1982.) - (b) Cooling Curves for Ni5 wt.% Al ribbons melt-spun on a copper wheel, using temperature-calibrated color photography, at a superheat of 200 K, ejection pressure of 42 kPa, and circumferential wheel speeds of 12 (A), 24(B) and 36 (•) m s" 1 . (After Gillen and Cantor, 1985.)

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9 Metallic Glasses

from a chromic acid solution with additives (e.g., formic acid or iron) (Hoshino et al., 1986; Tsai and Wu, 1990). It is also possible to deposit a few glasses by electroless deposition, and this method has been particularly used to produce glasses for magnetic investigations, N i - P in particular (Dietz, 1977). Recently, it has been shown that certain organic materials, for instance polyacetylene, can be used as catalysts to aid the deposition of glasses such as N i - C o - B and N i - C o - P (Kamrava and Soderholm, 1990). 9.2.4 Ion Implantation and Ion Mixing

A number of amorphous phases have been prepared by implanting high-energy solute ions into metallic surfaces, or by mixing successively vapor-deposited layers of different elements by means of the thermal energy of injected rare-gas ions. The most thoroughly researched such phase is the wear-resistant amorphous layer obtained by injecting Ti and C into a Fe surface. This, and other instances, are discussed in detail in Vol. 15, Chap. 6, Sec. 3.4. 9.2.5 Amorphization by Irradiation

A number of intermetallic compounds have been amorphized by irradiation with high-energy electrons, heavy ions such as Ni + or fission fragments. This was first discovered when the compound U 6 Fe was bombarded with fission fragments (Bloch, 1962); much research was then done with more familiar compounds, notably NiTi, Zr3Al and the nickel aluminides. The last of these remained crystalline, whichever irradiation projectiles were used, while the first two are instances of compounds which became amorphous, the former with electrons, the latter only with heavy ions. Primary solid solutions can never be amorphized by this approach.

There has been much dispute over the criteria which determine the ability to amorphize such compounds. The principal earlier overview was by Russell (1985): low temperature, high doses and high dose rates were generally found necessary. There is still some disagreement about the principal criterion, viz., that compounds with a narrow or vanishing homogeneity range amorphize most readily; the difficulty is that for many intermetallic compounds, the homogeneity range is not known with precision. This criterion may well prove to be generally valid: since irradiation knocks a proportion of atoms off their proper crystal sites, wrong atom pairs are generated, and compounds with a narrow homogeneity range necessarily have free energies which rise very steeply with departure from stoichiometry such compounds therefore rapidly gain free energy as they are irradiated, which would favor amorphization. Such compounds also necessarily have high ordering energies, which by implication therefore is one of the criteria for amorphizability by irradiation. Luzzi and Meshii (1986) propose as one criterion that an amorphizable compound is ordered up to its melting-point; again, this is another way of saying that its ordering energy is high. They also suggest that compounds with constituents separated by more than two groups in the periodic table and those with a relatively complex structure are favored for amorphization. None of these criteria, in the light of later evidence, appears to be watertight ... except possibly the one calling for a high ordering energy. More recently, Luzzi and Meshii (1988), concentrating on 2 MeV electron irradiation, have accumulated evidence that destruction, not necessarily complete, of longrange crystallographic order (i.e., of the superlattice) is a precondition of amor-


phization by irradiation. Others interpret such disordering as implying a mechanical destabilization of the lattice, such as has been proposed by some as a precondition of melting also. The evidence for this is well assembled by Okamoto et al. (1988), who examined Zr3Al. It is not quite clear at present whether the crucial feature is disordering per se, or the lattice expansion which accompanies it, but the most recent analysis prefers the second alternative. - A recent, illuminating comparison of melting with amorphization in the solid state, which includes irradiation as one variant (Wolf etal, 1990), makes the point that there are two forms of melting, and two of amorphization: one involves heterogeneous nucleation at interfaces or defects, one is homogeneous. Wolf et al. conclude that the destruction of a superlattice "merely drives the crystal to a critical combination of volume and temperature at which the amorphous phase can form heterogeneously or homogeneously". These fundamental issues have also been analyzed by Fecht and Johnson (1990). - In this connection, it has been suggested (Vepfek etal., 1982) that a microcrystalline-to-amorphous transition in silicon is driven by lattice expansion. 9.2.6 Amorphization by Interdiffusion and Reaction

An extraordinary phenomenon was discovered by Schwarz and Johnson in 1983 the formation of an amorphous alloy by the interdiffusion of two pure polycrystalline metals. They deposited successive thin films of Au and La, 10-50 nm in thickness, in a multilayer configuration, and annealed the multilayers at a low temperature (50-100°C). The final composition of the mixed phase was controlled by adjusting the relative thickness of the two

503

films. This study followed an earlier, accidental discovery of a related phenomenon: the compound Zr 3 Rh, in a metastable crystalline form, could be amorphized by reacting it with hydrogen to form a metastable amorphous hydride (Yeh et al., 1983). The very fast diffusion of hydrogen was thought to be a crucial aspect of this process, named a solid-state amorphization reaction (SSAR). For the second study, the somewhat exotic combination of La and Au was chosen because Au was known to be a "fast diffuser" in crystalline La (in the technical sense that Au diffusion in La is many orders of magnitude faster than selfdiffusion in La), and it was assumed that a similar disparity in diffusion rates would extend into the amorphous phase, if one was formed. (A discussion of fast diffusion can be found in Warburton and Turnbull, 1975). The 1983 discovery that a compound (Zr3Rh) could be amorphized by hydrogen absorption has now been generalized (Aoki et al., 1991). 'Hydrogen-induced amorphization' has been found to be possible in many binary metal compounds of which one constituent is a hydride former. Examples include R2A1, R3In, R 3 Ga, RFe 2 (where R is a rare-earth metal), Zr3Al, and others. The apparent thermodynamic paradox that two stable phases can generate a metastable phase was dealt with by means of two hypotheses: (a) The amorphous phase has a lower free energy than the initial mixture of elements; this arises from entropy terms, due to the fact that the amorphous phase has a large negative heat of mixing, whereas the crystalline elements have a large positive heat of mixing, (b) There are indeed intermetallic crystalline compounds with a still lower free energy than the amorphous phase, but they cannot form because one constituent diffuses

504

9 Metallic Glasses

(relatively) very sluggishly, and apparently both constituents must diffuse reasonably fast if crystalline nuclei of an intermetallic phase are to form. The intermetallic phase cannot be prevented from nucleating if the annealing temperature is chosen too high. The essentials of the situation are shown in Fig. 9-3. In the seven years since this discovery, a very great deal of research has been done on the SSAR and hundreds of papers published. Reviews (Johnson et al., 1985; Johnson, 1986) and a conference devoted to SSAR (including amorphization by irradiation, which is now generally included in the SSAR designation) (Schwarz and Johnson, 1988) have marked this burgeoning of

-90 E o "a

L

r=373K ' •#

- u

i \

S -ioo Am+ La

Au + \ Am

c

-110 To; what this means is that the melt rigidifies before reaching the temperature at which freezing without composition change (and thus without long-range diffusion), also known as solute-trapping, becomes possible. The implications of this are clearly set out in the review by Massalski (1986) and applied to a detailed analysis of GFA across the Cu-Ti system in a paper published about the same time (Massalski and Woychik, 1985). The problem is that, before a glass has actually been made, its Tg is not known. Here, Hafner's (1983, 1986) ability to calculate glass transition temperatures comes into its own. In Fig. 9-11, for the Ca-Mg system, the calculated To values are shown, and also two estimates for Tg, an upper limit based on the "entropy-crisis" or Kauzmann model, and a lower limit based on a free-volume model. (For a fuller explanation, see Hafner (1983).) Theoretical composition ranges for glass formation are shown for two cooling rates; here the criterion Tg > To is the central consideration; agreement with experiment is quite good. - Another detailed thermodynamic analysis of metallic glass formation near eutectic troughs was published by Highmore and Greer (1989). Another set of theories is based on the postulate that metallic melts are not homogeneous in composition but contain compositional clusters. Such clusters are held to aid crystal nucleation, and their absence or weak development to aid glass formation. Contrariwise, short range order (the

9.3 Amorphizable Alloy Systems

converse of clustering), which is believed (though there is a singular absence of experimental evidence on this point) to increase with falling temperature of a glass, just as it does in a crystalline solid solution, should enhance GFA. (See, for instance, Wagner's survey of SRO in metallic glasses, 1986; at least, it has been established for Cu-Ti that a glass has higher SRO than the melt from which it is quenched (Sakata et al., 1981).) Indeed, there is some evidence that some Cu-Ti alloys show clustering in the melt whereas the glass has SRO. This field of research, which has a large literature, is at present somewhat beset by controversy: for further details, the reader is referred to Ramachandrarao (1980, 1984). A further development is the application of CALPHAD (CALculation of PHAse Diagrams) methods to calculate from first principles the part of a phase diagram in which the free energy of a supercooled melt (i.e., a glass) is particularly low relative to that of the competing terminal phases, and only slightly higher than that of a competing intermetallic phase. A successful beginning with this approach has been published by Saunders and Miodownik (1986). The method has been applied in detail to one particular system, Ni-Ti, by Nash and Schwarz (1988). NiTi has also been studied by Zollzer and Bormann (1988) who have made E.M.F. measurements on a-NiTi at 613 K to complement purely theoretical estimates of free energy. - The free energies of a-Cu/Zr phases have also been calculated by a least-squares fitting program from available thermodynamic data (Bormann et al., 1988). Finally, we return to a less sophisticated "figure-of-merit" approach which has been quite successful in rationalizing GFA. Donald and Davies (1978) long ago recognized the awkwardness of theories which

515

Figure 9-11. Calculated phase diagram, To values and upper and lower limits (Ts, 7^) for Tg for the Ca-Mg system, with theoretical and observed glass-forming ranges. (After Hafner, 1983, 1986.)

related GFA to quantities (such as TJT{) which involve Tg, when normally this is unknown unil a glass has been made and examined. They proposed that a good test of GFA is the extent to which the equilibrium freezing temperature of an alloy melt is depressed below the ideal value, which they calculated simply by linear interpolation between the freezing points of the constituent metals. This simple method was then developed by Whang (1983), who took into account the modification required to allow for possibly extensive solid

516

9 Metallic Glasses

solution of one metal in the other, in the solid state. This is necessary because solid solubility reduces the slope of the To versus composition curves (like those shown in Fig. 9-11). Whang generated figure-ofmerit maps in which one axis gave TLR, defined as TLR = AT/T£, where AT is the difference between the ideal freezing temperature for an alloy (Tj°), defined as above, while along the other axis is C er , a simple measure of the amount of the solubility of the minor constituent in the major at the eutectic temperature. - A large value of TTR implies a severely depressed liquidus, while a small Cer implies a steeply sloping To versus composition curve ... both factors favouring easy glass formation. In fact, the maps so generated show a clear boundary between glass-forming and non-glass-forming alloys. - Dubey and Ramachandrarao (1990) have developed Whang's model to show that most eutectic phase diagrams can be expected to show an asymmetry of GFA, in the sense that glass formation is easier just to one side of the eutectic composition than on the other; the melt-spinning range indicated in Fig. 9-8 shows an example of this. Whang's theory was then adapted by Tendler (1986) to show, for a series of Zrbased alloys, that alloys which according to Whang's criterion should be good glassformers are also those in which there is fast diffusion, in the special sense used before (Warburton and Turnbull, 1975). Fig. 9-12 shows one of Tendler's figures for a series of Z r - M alloys. All the alloys showing fast diffusion (Zr-Cr, Mn, Fe, Co, Ni, Cu and Be) are also glass-formers. For fast diffusion, the solute atom must be much smaller than the solvent (for details see Tendler's paper) and this clearly also favors GFA. In fact, some years ago Turnbull (Turnbull, 1974) had predicted an association between good GFA and fast diffusion.

\J.\J

o Ga Al o

Bi o

0.1 c oB

NON-GFA oRe

0.2 GFA

\ Cr Mn

*• v \

0.3 -

Pt.

iBe Co kI . Ni • • Cu» i

1.0

oAg

\

i

0.8

#

\Ru

Os • \

Rh

#

• Fe i

i

0.6

'

\ 0.4

0.2

Figure 9-12. A number of Z r - M alloys plotted on a Whang graph, separating glass-formers (GFA) from non-glass-formers. (After Tendler, 1986).

This by no means exhaustive overview of the models and theories that have been advanced to make sense of glass-forming systems and ranges might well seem discouraging, because at first sight they are mutually exclusive. In fact, hidden crossconnections undoubtedly exist: the linkage between Whang's thermodynamic approach (related to terminal solid solubilities) and Tendler's association between fast diffusion and GFA clearly comes from a correlation of both solid solubilities and fast diffusion with atomic size ratios. Perhaps in due course even the electronic criteria studied by Nagel and Tauc and by Hafner may prove to be linked with some of the other ideas, e.g., the free volume approach due to Ramachandrarao and Yavari. My own view is that simple geometry ... atomic sizes ... will prove to be the main criterion that in various subtle ways incorporates the others.

9.3 Amorphizable Alloy Systems

9.3.4 The Special Case of Silicon Metallic glasses resemble oxide glasses in that the transition from the liquid to the glassy state is a continuous, seamless one. The atomic configuration changes with temperature during cooling, fast or slow according to the type of material, until a temperature range is reached in which diffusion cannot keep up and a non-equilibrium configuration is "frozen in"; this is of course the glass transition range. "Frozen in" has been put in quotes because the glass transition is not at all like real freezing, which is a first-order phase transition with a well defined equilibrium temperature, at which the Gibbs free energies of the liquid and crystalline phases are equal. In contrast, the glass transition temperature (temperature range is a more suitable phrase) is a function of cooling rate and is kinetically, not thermodynamically, determined (see Chap. 3). Correspondingly, of course, on heating a glass, the glass transition (softening) temperature is again variable, whereas the melting of a crystal happens at a well defined equilibrium temperature. We briefly discuss silicon here because it breaks this simple, clear distinction between freezing and vitrification, between melting and softening. It is true that crystalline silicon is not metallic and so does not strictly belong to this chapter, but molten silicon does have a metallic character. Amorphous silicon is quite distinct from the liquid form, and resembles the crystalline form in having covalently bonded character. Amorphous silicon can be made, with difficulty, by quenching liquid silicon with ultrafast, picosecond laser pulses (Liu et al, 1979). The more common way, however, of making a-silicon is by ion implantation, especially by self-ion bombardment. (This process has some peculiar

517

features, such as a dependence on the orientation of the initial crystalline silicon: Yater and Thompson, 1989.) On the basis of microcalorimetric measurements of such a-silicon layers, Spaepen and Turnbull (1979), and Bagley and Chen (1979), independently proposed that a-Si (and also a-Ge) undergo first-order melting to the metallic liquid on heating. This bold hypothesis, implying a latent heat of melting for an amorphous solid, could only be tested some years later, when it became feasible (e.g., Thompson etal., 1984) to measure transient electrical conductance and reflectance of silicon films: since a-Si and 1-Si have drastically different bond character, their electrical and optical properties are also quite different. In this way, the prediction made in 1978, that a-Si melts at a well defined temperature more than 200 K below the melting temperature of c-Si, was confirmed: the a-Si melting temperature was experimentally found to be 225 + 50 K. These experiments and theoretical calculations are excellently reviewed by Poate et al. (1987). It would, however, be a mistake to assume that the melting temperature of a-Si is well defined thermodynamically, because the structure of a-Si is itself not well defined and can be altered by a relaxation anneal. Fig. 9-13 (Sinke etal., 1988 a) shows a series of estimated free energy curves, which show clearly that the intersections between the a-Si and 1-Si curves come at quite different temperatures for different degrees of relaxation; accordingly, the melting temperature should vary in the same way. Indeed, if a-Si could relax to the theoretical limit at each temperature (curve 5 in the figure) it should intersect the c-Si curve before it intersects the 1-Si curve, and thus in that hypothetical case, a-Si should not melt at all, but crystallize directly. Thus, a-Si resembles a conventional

9 Metallic Glasses

Figure 9-13. Calculation of the isobaric Gibbs free energy of a-Si (curves 1 to 5) and of /-Si relative to that of c-Si, using strain energies deduced from Raman spectra. Curves 1 to 4 represent increasing degrees of thermal relaxation of the a-Si. Curve 5 is an estimated curve for a-Si prepared in a wholly unrelaxed form, but allowing it to relax to an equilibrium degree at each temperature. (After Sinke et al, 1988 a.)

glass in having a variable melting (transition) temperature. - More will be said about relaxation of a-Si in Section 9.4.2.

9.4 Diffusion, Relaxation and Crystallization When a metallic glass of amorphous solid is heated to a sufficiently high temperature, the constituent atoms begin to diffuse. This permits the amorphous structure to relax towards the state corresponding to the ideal congealed liquid. If diffusion is fast enough, the amorphous structure begins to crystallize. These three linked phenomena are treated in this Section. 9.4.1 Diffusion The first experimental study of atomic diffusion in a metallic glass was made as

recently as 1978 (Chen et al., 1978). The reason for this tardy start was the experimental difficulty of such measurements. The duration of a diffusion anneal of a metallic glass is limited by the need to ensure that no crystallization takes place, and this in practice means that penetration of the diffusing species is limited to a few tenths of a micrometer. Normal methods depending on mechanical sectioning and chemical analysis are therefore not applicable, and investigators have mostly used Rutherford back-scattering (used in Chen et al.'s initial study), ion erosion combined with radioactivity measurements, secondary ion mass spectrometry, nuclear reaction analysis and X-ray diffraction from multilayer films. These methods can measure diffusion coefficients as small as 10~ 20 -10~ 2 6 m 2 s" 1 . In the last few years, over a hundred publications have appeared on this theme and there is room here only for a brief account of the principal generalizations that can be made with confidence. More detailed information can be found in reviews by Cantor (1986), Cahn (1986), Mehrer and Dorner (1989) and Cahn (1990). Fig. 9-14 shows a characteristic set of measured diffusion coefficients for B diffusing in a Ni-Nb glass (Kijek et al., 1986). The xl B(p,a) 8 Be nuclear reaction was exploited; this has a strong resonance for a particular proton energy and by varying the energy of the probing beam, B concentrations at different small depths below the surface could be determined. It is clear that (as first discovered by Chen et al. 1978) a relaxation anneal reduces the diffusivity. Other studies have determined the kinetics of this reduction and shown that it saturates, and have also shown that the diffusivity falls as the atomic volume reduces during an anneal ... i.e., as the amount of free volume diminishes (Chason and Mi-

9.4 Diffusion, Relaxation and Crystallization

•

Fe

519

82 B 18

A Zr 61 Ni 39

10"19 =-\ \r

:

Uu

in

C

io- 2 T

CO

\

\

:

• Sb

\

:

"5

v

Q

s,.\ \ \«Au\ \

10-,21

\

S b

10 0.12

(a) 1.2

U 1.6 1 0 0 0 / T i n K"1

0.U 0.16 Atomic radius in nm

0.18

1.8

Figure 9-14. Diffusion coefficients of X1B in Ni 6 0 Nb 4 0 glass. O unrelaxed; x relaxed 420 s at 878 K. (After Kijek et al., 1986.)

zoguchi, 1987; see also discussion by Cahn, 1990). Fig. 9-14 also shows that, after relaxation, the diffusivity obeys an Arrhenius-type temperature variation, a fact which has occasioned much surprise, because a well defined activation energy would seem to imply that all atomic jumps go over similar energy barriers, which clearly is not true in a glass. The rather unsatisfactory present situation with regard to the theory of diffusion in metallic glasses is reviewed by Frank et al. (1988) and by Mehrer and Dorner (1989). The best established generalization concerning diffusion in metallic glasses is its great sensitivity to the relative sizes of the diffusing and host atoms. Sharma has done much to establish this (see Sharma et al., 1989) and the previously cited study by Greer et al. (1990) on the asymmetry of diffusivity of Zr and Ni in a-Ni-Zr has neatly confirmed it. Fig. 9-15 shows graphs

Ni Co Fe Cu

Au Ti

Zr

10"19

10-27 20 10 12 U 16 18 (b) Atomic vol. in 10"30m3 Figure 9-15. (a) The dependence of diffusivity of different metals in two metallic glasses on atomic radius of the diffusing species. (After Sharma et al., 1989.) (b) Diffusivities of various metals in amorphous N i Zr, with a Ni content in the range 50-65 at.%, as a function of the atomic volume of the diffusion species. (After Greer et al., 1990.)

520

9 Metallic Glasses

from these two studies. This is reminiscent of the behavior of diffusing species in crystalline metals, but is particularly pronounced here. This size sensitivity of diffusivity in metallic glasses still does not tell us for sure whether the diffusing process should be regarded as being mediated by vacancy-like holes or whether it is to be regarded as primarily interstitial. A recent study, via indirect diffusion measurements under hydrostatic pressure, of the activation volume for diffusion in a metallic glass (Limoge, 1990) suggests a vacancy-like mechanism. Further, the reduction of diffusivity as a result of relaxation has been closely correlated with the loss of free volume, and this indicates that "holes" play an essential part in diffusion. It is clear that the ultrafast diffusion of H in metallic glasses is of an interstitial nature, but it is also to be noted that the small number of interstitial spaces of large sizes act as traps for hydrogen, so that (e.g., Kirchheim etal., 1982; Kirchheim 1988, Kirchheim et al., 1991) the diffusivity of H in metallic glasses becomes extremely sensitive to concentration (which has not been established for any other diffusant). Whether such large units of free volume are to be regarded as holes or interstitial spaces is really a matter of lexicography; it may turn out that the vigorous debate as to whether, in general, diffusion in metallic glasses is to be perceived as an interstitial or as a vacancy-type mechanism is a matter of shadow-boxing. The one thing which is unambiguously clear is that free volume plays a vital role in determining diffusivity. A very recent study (Faupel et al., 1990) has shown, for a Co-rich glass, that there is no pressure dependence at all of cobalt diffusivity and a very small isotope effect. The conclusion is that diffusion is not mediated through quasivacancies in thermal equilibrium, but rather takes place by a 'direct'

mechanism involving about 10 atoms cooperatively. One well-known theoretical approach to diffusion in metallic glasses is firmly predicated on the notion of diffusion via atom-sized holes. Buschow (1984) was able to estimate the heats of formation of holes in various metallic glasses, using a method introduced by Miedema, and was able to show that the crystallization temperature scales as does this heat of formation. (He assumed that the diffusion of holes of the same size as the smaller constituent atoms was the important variable.) A larger heat of formation, as with crystal vacancies, implies a smaller concentration of holes, thus a smaller diffusivity at a given temperature and, in consequence, more sluggish crystallization. Barbour et al. (1987) have developed this approach by computing also the heats of formation for holes of the same size as the larger constituent atoms of each glass, and concluded that the readiness of a particular amorphous alloy to be formed by the interdiffusion SSAR mechanism depends on a large difference between the heats of formation for the larger and smaller holes, and this of course relates to the size difference of the constituent atoms. A large size difference implies a large diffusivity difference, as we have seen. Fig. 9-16 shows the results of the calculations by Barbour et al. As we saw above, diffusion is an essential process in some of the solid-state amorphization mechanisms. It is not known what the state of relaxation of an amorphous alloy made by interdiffusion of layers is, but it is no doubt significant that the diffusivity calculated from measured growth kinetics (Rubin and Schwarz, 1989) of such an alloy layer in Ni/Zr and the directly measured diffusivity of Ni in a Ni/Zr glass made by melt-quenching, have quite different activation energies (1.01 eV/


521

1500 .9

11000

Figure 9-16. Crystallization temperatures for various transition metal amorphous alloys plotted against the calculated heats of formation of holes equivalent in size to the larger constituent atoms (HLV) or the smaller constituent atoms (HSY). (After Barbour et al., 1984.)

CD C

o N

5

500

o

50

100

150

200

250

HSw (A) or HLy ( • ) in kJ mole

atom in the first case, 1.45 eV/atom in the second). It will be interesting to see more critical comparisons of diffusivities in meltquenched and SSAR amorphous alloys. Relaxation does not always depress the diffusivity in an amorphous solid. a-Si is a notable exception. A recent study (Polman et al, 1990) has established that the diffusivity of Cu in a-Si made by ion implantation increases by a factor of 2 to 5 when the silicon is relaxation-annealed. The explanation is that as-implanted a-Si contains a large concentration of defects (point defects and agglomerates) which act to trap Cu atoms; relaxation destroys many of these defects and thus enhances mobility of the Cu. Free volume seems to be of secondary importance here. 9.4.2 Relaxation

As we have already seen in connection with diffusion, annealing a metallic glass below its crystallization temperature reduces the free volume and thereby decreases the self-diffusivity. (a-Si behaves differently.) The reduction in free volume

also affects many other physical and mechanical properties: changes of physical properties are briefly discussed in this section, relaxation-induced embrittlement in the next. Oxide glasses behave similarly: for instance, when an optical glass is annealed close to its glass transition, the refractive index changes steadily. Relaxation in oxide glasses is treated in Chap. 3 of this Volume. Table 9-2, modified by Cahn (1983) from a compilation by Egami, lists the properties the changes of which on thermal relaxation have been most frequently studied. A distinction is made between those phenomena which change in a primarily irreversible way and others which change in a primarily reversible way as the annealing temperature is cycled; recent research has however made it clear that no property changes in a wholly irreversible or a wholly reversible way. Thus, length changes, which are most directly tied to free volume changes, while almost wholly irreversible have nevertheless recently been shown to have a small reversible component (Huizer and van den Beukel, 1987). The principal

522

9 Metallic Glasses

Table 9-2. Changes in physical and mechanical properties during structural relaxation. (After Egami et al. (1982), slightly modified.) Properties

Volume Specific heat Young's modulus Internal friction b ' c Electrical resistivity Diffusivityb Viscosity15 Embrittlementb Thermal resistivity Curie temperature Coercive field Magnetic anisotropy, field-induced Superconductive transition temperature

Direction of Reversible (R) change during or irreversible (I) below Tg relaxationa D I I/D I I/D D I/D I/D D I I D I/D I/D

I I R I R I I R I I I I I/R I/R

I/D

R

D

I

a

I denotes increase, D decrease. These properties are conventionally (for crystalline solids) considered to be structure-sensitive, and indeed do show large changes in amorphous solids upon annealing. c This property is itself a reversible relaxation phenomenon. b

difference between these two fundamentally distinct types of relaxation-induced change was first recognized by Egami (1981). He proposed a distinction between topological short-range order, or TSRO (which in effect describes the density of packing of atoms) and chemical short-range order, or CSRO, which defines the extent to which atoms have unlike nearest neighbours. On relaxation annealing, TSRO changes through the progressive, irreversible removal of free volume, and this causes irreversible property changes. Chemical SRO, by analogy with crystalline alloys (see Cahn, 1982) is assumed to vary with tem-

perature in metallic glasses only, although no direct diffraction evidence of this has ever been reported (it would be more difficult to obtain in glasses than in crystals). Because of this postulated reversible variation of chemical SRO with temperature, changes in properties that are particularly sensitive to it, such as elastic properties or Curie temperature, have a large reversible component to their changes on relaxation. Very recently Haruyama and Asahi (1991) claim to have found calorimetric and resistometric evidence of reversible SRO in N i - C r - B glasses. One test of Egami's rationalization of the two types of relaxation effect would be to test whether the incidence of reversible changes of property are correlated with the magnitude of chemical SRO present in different glasses: thus, Cu-Ti glasses are known to order strongly, Fe-Ti glasses have recently been found to have no chemical SRO, and comparative measurements, for instance of Young's modulus, between them might serve as a test of what is still, after 9 years, no more than a very reasonable hypothesis: the association between reversibility of property changes and chemical SRO. - An excellent overview of known facts concerning relaxation of metallic glasses in the light of Egami's hypothesis was published more recently (Egami, 1986). Fig. 9-17 shows some characteristic examples of relaxation-induced property changes. The kinetics of such processes, especially reversible ones, became an interesting problem when the so-called crossover effect was discovered in metallic glasses, with respect to properties such as the Curie temperature and elastic moduli (Greer and Spaepen, 1981; Scott and Kursumovic, 1982). This effect is most easily understood by reference to Fig. 9-18, which actually refers to earlier work done with respect to

523

9.4 Diffusion, Relaxation and Crystallization jL0*?0'{5)

p Relaxed at 623 K {Pre-relaxed 30 m'm at 5/3 K)

-

;

•

Fe

40 Nl40

B

20

179-

-3623 time (s)

-4

1000

60

10

12

U tjh]

Figure 9-17. Manifestations of relaxation of metallic glasses: (a) irreversible length change of a Fe 40 Ni 40 B 20 glass; (b) short-term reversible changes of Young's modulus of Co 58 Fe 5 Ni 10 B 16 Si 11 glass cycled between 623 K and 723 K; (c) longterm change of Young's modulus in the same glass at various temperatures, from the as-quenched state; (d) changes of Curie temperature of Fe 80 B 20 glass as a function of holding time at various temperatures above the Curie temperature, substantially reversible; dashed lines indicate incipient crystallization; (e) reversible changes of coercive field of the above-mentioned Co-rich glass, a composition of low magnetorestriction, during cyclic annealing. (After Cahn, 1983.)

524

9 Metallic Glasses

1.5U60 Equilibrium line

1.51430

200 300 Time in minutes

400

Figure 9-18. Refractive index vs. time in a crossover experiment on a borosilicate glass. The glass was held at temperature Tx until the index reached the value characteristic of equilibrium at a second, higher temperature T2. The temperature was then changed abruptly to T2: instead of remaining steady, the index followed the curve shown, returning eventually to the T2 equilibrium value. (After Macedo and Napolitano, 1967.)

the refractive index of a borosilicate glass (Macedo and Napolitano, 1967). The caption indicates the treatment used. - Such behavior can only mean that two or more distinct atomistic processes, with different activation energies and different kinetics, operate simultaneously: it also implies that there is not a one-to-one relationship between measurable properties and the internal state of the glass, in the sense that the same value of a property can be associated with distinct states generated by different heat-treatment programs. A thorough analysis showed that, in fact, not two but a spectrum of activation energies has to be operative (Gibbs et al., 1983; Leake et al., 1988), and this idea has had a major effect on subsequent theories of relaxation phenomena. The idea has been used to particularly good effect in a long series of papers by van den Beukel and colleagues, in which the relaxation of a number of properties, including viscosity, length changes, resistivity, Young's modulus and Curie temperature, mostly in Fe 4 0 Ni 4 0 B 2 0 glass, was analyzed experimentally and theoretically in great detail. Their entire programme of research has been summarized (van den

Beukel, 1986). This work is too complex and extensive to treat here. Most commonly, relaxation kinetics of various properties follow a In t law, which has been shown to be consistent with the existence of a spectrum of activation energies. Not only melt-quenched glasses relax. Thus Riveiro and Hernando (1985) measured the relaxation of coercive field in an electrodeposited Co 91 P 9 glass, and found a drop by two orders of magnitude. They were able to analyze this change in terms of the spectrum of activation energies and decided that at least 4 distinct processes were in play; they also concluded that the diffusion of P atoms from "unstable" to "stable" holes was the main relaxation process. When a metallic glass is stressed at a high temperature, it undergoes homogenous flow by a purely viscous process. (At room temperature, flow proceeds inhomogeneously, along shear bands - see Vol. 6, Chap. 11). As creep proceeds, free volume is progressively annealed out and since the viscosity is directly linked to free volume (see Chap. 3, this Volume), the creep rate under constant stress progressively diminishes. The relation between viscosity, rj, stress, 10 1 0 -a Tensile creep

/

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360

400

Figure 9-22. (a) Strain at fracture in a bending test as a function of temperature for a Fe 79 3 Be 16 4 Si 4 0 C 0 3 glass, annealed for 2 h at 350°C after melt-spinning. TBD is the ductile-brittle transition temperature, (b) Change of TBD with isochromal anneals at progressively increasing temperature: same glass. (After Spaepen et al., 1986.)

528

9 Metallic Glasses

The theories to explain thermal embrittlement fall into two categories: (1) the hypothesis that annealing removes excess free volume and (2) the hypothesis that the homogeneous glass structure separates into two distinct amorphous phases. The basis of the first hypothesis is clear from the foregoing: further, Wu and Spaepen (1986) have assembled detailed evidence on thermal embrittlement consistent with this model. The second hypothesis leans on observations such as that due to Walter et al. (1976), who by Auger electron spectroscopy established an enrichment of P at fracture surfaces of a Fe 40 Ni 40 P 14 B 6 glass, and Piller and Haasen (1982) who used field ion microscopy to demonstrate the formation, during relaxation annealing of Fe 4 0 Ni 4 0 B 2 0 , of minute zones enriched in boron to 25 at.%. However, tests by Xray small-angle scattering of some other glasses have failed to demonstrate phase separation of this kind, whereas other experiments have given contrary results. The literature is quite extensive. A possible marriage between the two types of hypothesis has been proposed in an interesting paper by Yavari (1986). By analyzing the volume per metal atom in Fe-B glasses of different compositions, he shows that a local enrichment of B will need to "suck" free volume from the adjacent matrix, reducing the free volume concentration there. He suggests, therefore, that the phase separation hypothesis resolves itself, indirectly, into the free volume hypothesis. According to Yavari, the fact that some additives (e.g., Ce) delay embrittlement to higher temperatures, whereas others such as Sb promote it, can also be interpreted on the basis of his model. Another observation (Yamasaki et al., 1985) to the effect that Fe-based glasses whose compositions fall close to an equilibrium eutectic composition embrittle

much more sluggishly, if at all, is attributed to a reduced tendency to phase separation for such compositions. The clearest demonstration to date of the central role of free volume in determining the incidence of thermal embrittlement comes from an important series of publications by Gerling et al. (1985, 1988, 1989, 1990) relating to Fe 4 0 Ni 4 0 B 2 0 glass. Briefly, they have established in circumstantial detail how this glass is embrittled by the loss of free volume on annealing; for instance, the embrittlement behavior varies with ribbon thickness, because the quenched-in free volume varies also. They have further shown that a glass which has been thermally embrittled can be reductilized by neutron irradiation, which creates fresh free volume. The new ductility can in turn be removed by a second relaxation anneal. 9.4.4 Relaxation of Magnetic and Elastic Properties Changes in the Curie temperature, which is particularly affected by CSRO, and of the coercive field, have already been discussed. A number of other magnetic properties have also been studied in relation to relaxation. The magnetic and mechanical properties of soft ferromagnetic metallic glass sheets, which are now widely used for transformer laminations (see Sec. 9.6.1) are considerably affected by relaxation anneals. Because of the role of magnetostriction in enhancing core losses, it is important to remove residual stresses without changing glass structure appreciably. Taub (1984) has shown that a short pulsed anneal at high temperature is much more effective in achieving this than a long anneal at a lower temperature. A comprehensive study of the effect of annealing on a range of properties,


with special emphasis on magnetic ones (Liebermann et al, 1989) of Fe 78 B 13 Si 9 glass has reached the conclusion that embrittlement is associated with clusters as small as 0.3 nm in size. The authors also established that stress relief was complete at annealing temperatures lower than those at which embrittlement began; it is thus possible to achieve the desirable objective of stress relief without embrittling the laminations. Another form of magnetic relaxation which is of practical importance is the generation of magnetically induced uniaxial (ferromagnetic) anisotropy. This is a form of "magnetic annealing" well known in ferromagnetic crystalline solid solutions (Graham, 1959) but less familiar in glasses. The relevant theory is well established. The phenomenon is of practical concern because an induced uniaxial anisotropy affects the response of magnetic components to applied fields. - An alloy is annealed in a magnetic field at a temperature high enough to permit exchange of places between neighboring atoms, and pairs of unlike atoms tend to line up preferentially parallel to the field, inducing a magnetic anisotropy. The statistical tendency for this to happen is very weak, but magnetic measurements are ultrasensitive even to minute amounts of directional short-range order which would be too weak to measure by X-ray diffraction. The phenomenon is best defined where two distinct kinds of metal atom are present (usually, Fe and Ni) and is most pronounced for concentrated solid solutions, since it depends on the presence of numerous pairs of unlike nearest neighbor atoms. The kinetics of reorientation of the preferred magnetic direction when the field direction is changed depends on self-diffusivities in the alloy concerned, although no attempts have been made to measure diffusivities in this

529

way. The establishment of directional SRO (which can exist at the same time as normal isotropic SRO) is reversible, in the sense that a change in direction of the applied field, or its removal, will redirect or destroy the directional SRO. The phenomenon, which deserves more exploitation than it has had as a useful way of measuring structure change kinetics in metallic glasses, is described in detail by Luborsky (1980). Evetts and Hodson (1985) have in fact analyzed the kinetics of the process (which they term 'polarization') in terms of the concept of a spectrum of activation energies, mentioned in Sec. 9.4.2. A closely related process is stress-induced ordering; here the external influence is a stress instead of a magnetic field, and the measured property is anelastic strain instead of a magnetic anisotropy. In an experimental tour de force, Suzuki et al. (1987) were able to show directly, by energy-dispersive X-ray diffraction from a stress-annealed Fe 40 Ni 40 Mo 3 Si 12 B 5 glass done successively with two orthogonal diffraction vectors, that directional order (they called it 'bond-orientational anisotropy') was induced by stress-annealing and decayed on subsequent stress-free annealing. The ordering kinetics followed In t kinetics, characteristic of a material with a spectrum of relaxational activation energies. According to their model, bond-orientational anisotropy involves a directional variation in the number of all kinds of bonds, whereas the accepted theory as applied to crystalline alloys involves, as we have seen, anisotropies in different kinds of bonds. In fact, a more recent study from the same laboratory (Tomida and Egami, 1991) recognizes that chemical as well as topological anisotropy is involved in bondorientational anisotropy. A recent study of stress-induced ordering in Fe 4 0 Ni 4 0 B 2 0 glass, by Leusink and

530

9 Metallic Glasses

van den Beukel (1988), has proved that the ordering kinetics is determined by the amount of free volume present. As these authors point out, this is a good way of estimating the kinetics of establishment of CSRO in a metallic glass; the fact that the state of order here is anisotropic rather than isotropic is of no consequence. Other special forms of relaxation, particularly magnetoelastic and thermoelastic relaxation in metallic glasses, and internal friction, are reviewed by Kiinzi (1983). Internal friction can be used to monitor structural changes; this was done, for instance, in a study by Sinning et al. (1991) on crystallization of a C o - Z r - H glass, to be cited in the next Section. 9.4.5 Crystallization

When a metallic glass is heated, it will crystallize to form some combination of intermetallic compounds and metallic solid solutions, just as an oxide glass crystallizes to form a glass-ceramic. The nomenclature of the product poses a problem: "Glass-alloy" has not found favor, "Pyromet" by analogy with "pyroceram" is excluded because the word is a registered trademark; there is a family of engineering alloys made by crystallizing, or "devitrifying" metallic glasses with the trade name "Devitrium"; probably "devitrified alloy" is the best available generic term. Crystallization mechanisms of metallic glasses are generally divided into three categories - polymorphous, eutectic and primary crystallization (Koster and Herold, 1981) - to which a fourth, crystallization with phase separation, can usefully be added: - In polymorphous crystallization (e.g., of Fe 7 5 B 2 5 glass), a single intermetallic compound crystallizes without change of composition.

- In eutectic crystallization (e.g., of Fe 8 0 B 2 0 glass), the glass transforms to two phases growing in a closely coupled form. In the example cited, the constituent phases are a-iron and Fe 3 B. There is no change in overall composition between the glass and the eutectic colony. - In primary crystallization (e.g., of Fe 8 6 B 1 4 glass), a primary phase, here airon, crystallizes out first, which involves a change in composition of the residual glass; later, a compound, here Fe 3 B, crystallizes separately (i.e., not in closely coupled form). - In crystallization with phase separation, the glass itself phase-separates into two distinct amorphous phases with different compositions and glass transition temperatures, and these then crystallize at different temperatures during further heating. A good example of a glass behaving like this is Zr 3 6 Ti 2 4 B 4 0 (Tanner and Ray, 1980). Early studies of crystallization of metallic glasses largely depended on the use of a differential scanning calorimeter (DSC), which generates curves such as that shown in Fig. 9-23. In this particular instance, it is not certain whether the double peak is due to amorphous phase separation (there is a faint indication of a second glass transition) or to primary crystallization followed by crystallization of a small amount of residual glass at a higher temperature. This uncertainty indicates that micrographic examination is really necessary as well to determine crystallization mechanisms for certain, and this has been widely done for a variety of glasses (see reviews by Koster and Herold, 1981; Scott, 1983; Koster and Schunemann, 1992). A very large literature exists on the results of such investigations, which it would not be profitable to review. Many studies have examined the effect on crystallization mechanisms and kinetics of


I

230

I

I

270

I

I

310 350 390 430 Temperature in °C

470

510

Figure 9-23. Differential scanning calorimeter record during heating, at 20Kmin~ 1 , of Pd 77 5 Cu 6 Si 16 5 glass. The ordinate represents power released (exotherm upwards) or absorbed (endotherm downwards). Tg is clearly differentiated from the first crystallization peak, Txl.

changing the proportion of the constituent elements. A good, very recent specimen of this literature is a paper by Sprengel et al. (1990) on the crystallization of a range of Co-Zr glasses. Other investigations, which are increasing in frequency, have examined the effect of systematically varying ternary additions to a fixed binary composition (e.g., Bhatnagar et al., 1990, with respect to NiZr 2 plus Al or Ga; Ghosh et al., 1991, with respect to "micro-additions" to Ni 24 Zr 76 ). - For detailed information the reader is referred to the cited overview articles. The crystallization temperature not only depends on the alloy system but also varies somewhat with the composition of the glass within a given system. This is exemplified by Fig. 9-24, for the Fe-B system: this shows that the same system can show single or double crystallization peaks, according as the type of crystallization

531

changes between the various categories listed above. The activation energy for the crystallization process as a whole, which is usually well defined, is obtained by varying the heating rate in the DSC and applying a theory developed by Kissinger (1957) to the measured peak values of crystallization temperature. However, as often in physical metallurgy, little useful has been done with the activation energies once they have been determined! They could be compared with activation energies for the self-diffusion of the constituent species, where known, to help define rate-determining process in crystal growth, but this does not appear to have been widely done. (However, Koster and Herold (1981) have used crystallization kinetics as an indirect way to estimate diffusion rates, without being able to determine which diffusing species is rate-determining.) DSC studies can only encompass a limited range of heating rates, approximately 5-100 K/min, and until recently no methods were available to study crystallization kinetics and mechanisms at very high heating rates or isothermally at high temperatures. This has been altered by the intro-

350,

Figure 9-24. Crystallization temperatures Tcryst (peak in DSC continuous-heating records for different heating rates) of Fe-B metallic glasses. The various symbols refer to different investigators. (After Koster and Herold, 1981.)

532

9 Metallic Glasses

duction of time-resolved X-ray diffraction, in which extremely intense monochromated X-ray beams from a synchrotron source are combined with very rapid («10 4 K s ~x) electrical self-heating of glass ribbons to constant high temperature (Sutton et al, 1989). With the aid of positionsensitive X-ray detectors, an entire diffraction pattern can be determined in as little as 3 ms. In this first study by the new technique, polymorphous crystallization of NiZr 2 was studied up to 680 K (at which temperature, 50% crystallization is achieved in 4 s) and it was established that at these high temperatures, a transient precursor phase is formed initially. From a practical viewpoint, plots like that shown in Fig. 9-25 are useful. These are obtained by isothermal anneals (less often used than continuous heating ones) at a range of temperatures. Metal-metal glasses are of particular interest because some of them have very high crystallization temperatures. Notable among these are W 65 Ru 35 , W 50 Re 50 (both with T x ^800°C, and Ta 55 lr 45 , with T x ^ ^900°C (Denier van der Gon et al., 1987). Such glasses have found an unexpected ap-

450

Temperature. T in °C 400 350

plication because of their resistance to crystallization (Sec. 9.6.5). These high crystallization temperatures have been successfully rationalized on the basis of Buschow's hole model of diffusivities (Sec. 9.4.1). Attention has recently moved from the simple determination of crystallization temperatures to the investigation of nucleation mechanisms, in particular, whether nucleation in particular case is homogeneous or heterogeneous, and to a study of the role of heterogeneous nucleation at the free surface of a glass. The leading investigator in recent years into nucleation mechanisms and kinetics has been Greer. His series of papers began with an important study of the crystallization of Fe 8 0 B 2 0 glass (Greer, 1982). His approach combines DSC and micrographic observation with modelling. Isothermal DSC runs (with elaborate corrections for various sources of error) were used to fit the parameters of the standard Johnson-Mehl-Avrami equation, x (t) = l - e x p ( - K t " ) , where x{t) is the fraction crystallized in time t and K = Ko • Qxp( — E/kT). Special steps are taken to make allowance for the mutual impinge-

300

Figure 9-25. Time for the start of crystallization of a range of metallic glasses as a function of temperature. (After Luborsky, 1980.)

Fe*oN'*opuB6

1.4

1.5 1.6 1000/7" in K"1

17

1.8

533


ment of growing grains. TEM established the growth rate of crystals at specific temperatures. These correspond to an exponent, n = 3 in the above kinetic equation. Putting all this information together allowed a computer model to be set up for the crystallization kinetics during continuous heating in a DSC, which permits the highest precision, and the experimental output was compared with the predictions from the model. Fig. 9-26 shows the results in the form of a dx/dt plot derived both from the DSC output and from the fitted model, both for the as-quenched glass and for a sample preannealed at a constant temperature (which initiates crystallization on preexisting nuclei). One adjustable parameter, Ko, is adjusted to give the best fit for both curves and it can be seen that a very exact fit was obtainable for experimental peaks, except for a small unfitted subsidiary peak at high temperatures. (This was shown to be due to a thin surface skin on the ribbons which was known to contain no preexisting nuclei, so that crystallization of this skin was delayed until new nuclei could form.) Greer showed that Ko is directly proportional to the nucleus density for a fixed growth rate, and was able to deduce a nucleus density (not affected by the preanneal) of3.5xl0 1 8 m~ 3 . This was checked against the grain concentration in partly crystallized specimens as determined by TEM, and fitted well. At this stage, he could not be certain as to the nucleation mechanism, but because of the very high nucleus density he deduced that it was very probably a homogeneous mechanism. - He found that the nucleus density was very sensitive to the thickness of the ribbon and thus to the quench rate. The next stage was to study both theoretically and experimentally the phenomenon of transient homogeneous nucleation; this term is applied to a nucleation

as-quenched

3

0.4

0.0

680

700 TEMPERATURE(K)

720

Figure 9-26. Crystallization kinetics, dx/dt, deduced from continuous DSC heating data, for Fe 80 B 20 glass 32 urn thick (solid curves), compared with fitted curves derived from a model. The lower peak corresponds to a preannealed sample. (After Greer, 1982.)

rate increasing from zero to a steady state value as the material is undercooled. (In the case of Fe 8 0 B 2 0 Just discussed, the observations fit the hypothesis of transient nucleation during the quench itself.) Fig. 9-27, taken from a review of nucleation mechanisms (Greer, 1988) shows schematically the different forms of nucleation

Time

Figure 9-27. Schematic variation in the number of nuclei with time in an isothermal anneal for the following nucleation types: (a) steady-state homogeneous; (b) transient homogeneous; (c) steadystate heterogeneous; (d) transient heterogeneous; (e) quenched-in active nuclei. (After Greer, 1988.)

534

9 Metallic Glasses

which can arise during crystallization of a glass (and beforehand, during the quench). Kelton and Greer (1986) published a detailed analysis of the role of transient homogeneous nucleation in glass formation and showed that a glass can sometimes form only because nucleation was of the transient rather than the steady-state type. This is exemplified by Fig. 9-28, which shows calculations, based on known material parameters, for both types of nucleation for Au 81 Si 19 . The dashed line in the lower figure indicates the low level of volume fraction transformed which has usually been taken as the condition for forming a metallic glass successfully; it can be seen that this level is achieved with transient nucleation for a quench rate of 105 K s" 1 , whereas for steady-state nucleation the unrealistic rate of 10 8 Ks~ 1 would be needed.

Au 81 Si 19

10 5

10 6

10 7

108

Quench r a t e in K / s

Figure 9-28. (a) The number of nuclei and (b) the transformed crystal fraction calculated for quenching molten Au 81 Si 19 at various rates, assuming either steady-state or transient homogeneous nucleation. (After Kelton and Greer, 1986.)

Homogeneous nucleation has been firmly established in the much-studied Fe 40 Ni 40 P 14 B 6 glass, by appeal to crystallite counting (Morris, 1982) and a few other metal-metalloid glasses. Other glasses in which homogeneous nucleation is much slower, notably Pd 4 0 Ni 4 0 B 2 0 (Drehman and Greer, 1984) crystallize predominantly heterogeneously, both from internal defects and from defects at free surfaces. Even for such alloys, homogeneous nucleation with the concomitant fine grain size can be achieved by first annealing close to the temperature of maximum nucleation frequency and then raising the temperature to allow the nuclei thus formed to grow. Contrariwise, this same alloy can be formed into large glassy volumes, « 1 cm3, by cooling at a rate as low as 1 K s ~ 1 , if the surface is cleared of local defects by immersing it in a molten flux (Kui et al, 1984). At the opposite extreme, it has recently been shown (Sinning et al., 1991) that a Co 33 Zr 67 glass containing a small amount of hydrogen can be crystallized by fairly fast heating to give a nanocrystalline structure (see Vol.15, Chap. 13). This is most simply interpreted in terms of a very copious homogeneous nucleation, with a crystal growth rate that slows down sharply at higher temperatures. Generally, heterogeneous nucleation is most clearly demonstrated at free surfaces. In some instances, the process is so dominant that columnar grains grow in from the surface while none grow in the interior - i.e., the exact converse of what is observed in Fe 8 0 B 2 0 , as we have seen above. However, a glass of this type can crystallize preferentially at the surface if the surface is chemically or otherwise modified before or during annealing. Thus, if Fe 8 0 B 2 0 is differentially oxidized so that the boron content is reduced at the surface (Koster, 1984), preferential surface nucleation is found.

9.5 Chemical Properties

The related composition Fe 4 0 Ni 4 0 B 2 0 behaves similarly; here, iron is preferentially removed. Recently, Wei and Cantor (1989) made a detailed study of surface crystallization of Fe 4 0 Ni 4 0 B 2 0 and found that it is enhanced if the alloy is first phase-separated by relaxation and then abraded at the surface, or else the surface is enriched in Ni by electroplating Ni and then annealing the glass. Sometimes, surface oxidation can have the opposite effect of inhibiting surface crystallization; with Pd 4 0 Ni 4 0 P 2 0 , a thin NiO layer protects the glass from local loss of P; such loss is the prime cause of preferential surface nucleation. - Removal of the original surface can drastically modify crystallization behavior: thus, Ni 6 6 B 3 4 glass (which normally crystallizes from the surface with a strong accompanying [100] fiber texture, loses the quenched-in nuclei responsible for this if the surface is etched off (Koster and Schiinemann, 1991). According to the same authors, another way of inhibiting surface crystallization is to remelt the original surface by means of laser pulses; the self-quenching resulting from this seems to be fast enough to obviate quenched-in nuclei. Clearly, the variegated phenomena surrounding surface nucleation during the crystallization of metallic glasses as yet defy generalization, and it must be left to future research to systematize and interpret them, as homogeneous nucleation has recently been interpreted. Certainly, there is a practical interest in gaining such understanding, because preferential surface nucleation can produce undesirable sideeffects, such as increased magnetic eddy current losses in surface-crystallized soft magnetic glass ribbons for high-frequency applications (Datta et al., 1982).

535

9.5 Chemical Properties A good deal of research has been done, mostly in Japan, on the corrosion resistance of metallic glasses, which can be spectacularly good. Much more recently, such research has extended also to the catalytic and electrocatalytic properties of suitable treated metallic glasses. A combined overview of these fields of research can be found in a recent conference proceedings (Diegle and Hashimoto, 1988) and in review papers (Hashimoto, 1985, 1992). Here we have space only for a summary.

9.5.1 Corrosion Resistance

The wet corrosion resistance of metallic glasses is greatly affected by their structural and chemical homogeneity. In particular, there are no grain boundaries with their frequent forms of chemical heterogeneity; accordingly, no electrolytic microcircuits are set up with their bad effects on corrosion resistance. Most of the research which has been done on iron-base glasses containing metalloid addition, in various acids and sodium chloride solutions, although very recently, work has been extended to some metal-metal glasses, for instance in the Ni-Ta series. With respect to Fe-based glasses, the following have been thoroughly established: 1) Most metallic solutes increase corrosion resistance; Cr and Mo are particularly effective, most so in combination. By way of example, a-Fe 72 Cr 8 P 13 C 7 passivates spontaneously in 2 N HC1 (a very powerful corrodant) at ambient temperature, while some glasses containing both Cr and Mo will passivate spontaneously even in hot concentrated HC1.

536

9 Metallic Glasses

2) Metalloids accelerate passivation by aiding the dissolution of all constituents other than the passivating one from a thin surface layer; P has been found to be particularly effective. Accordingly, even small amounts of Cr, « 3 at.%, can lead to much higher surface concentrations of Cr ion than is found on crystalline stainless steels. On Ni-Ta and N i - N b glasses, the cations in the highly effective passive films are almost pure Ta 5+ or N b 5 + . Ni-Ta glass is more resistant to hot phosphoric acid than pure Ta. 9.5.2 Heterogeneous Catalysis and Electrocatalysis Research has been concentrated on catalysts for gas-phase reactions such as the hydrogenation of CO or methanol synthesis, and on electrocatalysts for electrodes used in fuel cells and for electrowinning of metals (see Sec. 9.6.4). The recent literature makes one thing quite clear: while metalmetal glasses often make excellent catalysts, they do so only after treatments which wholly or partly crystallize the surface; unmodified glasses are not effective catalysts. One must therefore think of metallic glasses as precursors for catalysts, although according to a quite recent review (Schlogl, 1985) this was not yet clear at that time. The most comprehensive review, written more with emphasis on the chemical reactions which can be catalysed than on the state of the catalysts, is by a Hungarian group (Molnar et al, 1989); this cites 177 references. Selective oxidation of, or the absorption of hydrogen in, glasses such as Ni-Zr, Cu-Zr or P d - Z r modifies their surface (e.g., the early study by Spit et al., 1981). A recent study by Vanini (1990), using Auger electrons and X-ray diffraction, shows that

hydrogen absorption in various Cu-Zr glasses generates a Cu-enriched surface layers containing Cu microcrystals. A P d Zr glass, activated in CO, O 2 , CO 2 or H 2 , crumbles to a powder consisting of fine Pd and ZrO 2 particles. The catalytic effectiveness of such catalysts depends entirely on the fineness of the crystalline metal particles produced during activation. In both Cu-Zr (Vanini, 1990) and Ni-Zr (Spit et al., 1981) the activity is enhanced because the Cu or Ni can diffuse to the surface along the surface of cracks opened up by the hydrogen activation. Selective oxidation operates in much the same way to provide an activation mechanism as does hydrogen absorption (Schlapbach et al., 1980). Some experiments have also been done with metal-metalloid glassy precursors. Guczi and his coworkers (e.g., Kisfaludi et al., 1987), who sought to catalyze the hydrogenation of CO with Fe-B and F e - N i - B glassy catalysts, found that partially crystallized alloys were more effective than wholly crystalline ones, primarily because in that state, very small iron particles are stabilized. The important Japanese work on activated electrode alloys is outlined in Section 9.6.4.

9.6 Applications Up to the present, the only bulk use of metallic glasses has exploited the soft magnetic properties of certain Fe-based glasses in the form of transformer laminations. However, other magnetic uses, and to a lesser degree electrocatalytic uses, are in the process of developing. The exploitation of the great strength and good toughness of some metallic glasses has, somewhat surprisingly, lagged badly behind other categories of uses.

537

9.6 Applications

Since there is room here only for an outline of what has been done, especially with regard to transformer applications (which is a complex topic in its own right), we cite three important overviews of applications of metallic glasses. Luborsky (1983) has an important overview chapter on applications-oriented magnetic properties, the Proceedings of the Fifth Conference on Rapidly Quenched Metals (Steeb and Warlimont, 1985) have over 200 pages of papers specifically devoted to various types of application, mostly of metallic glasses, and a book on metallic glasses (Anantharaman, 1984) has 4 chapters on applications. 9.6.1 Magnetic Applications

The growing use of wide sheets of Febased metallic glass, made by planar flowcasting, as transformer laminations, is based essentially on two properties of the best of such glasses: a more slender magnetization (hysteresis) loop than grain-oriented Fe-Si sheet, the excellent material used for over half a century for this purpose, can achieve (Fig. 9-29); and a higher electrical resistivity, which reduces induced eddy currents in comparison to the crystalline Fe-Si alloy. The slenderer hysteresis loop is associated with a lower saturation magnetization: this is an inescapable price, because intrinsically, no glass can achieve as good a magnetization as almost pure iron. The gradual recognition that a metallic glass could outperform crystalline alloys which had been gradually perfected over many years led to a progressive improvement of glass compositions as well as technical improvements in the economic production of wide sheets, culminating in the glass composition Metglas® 2605 SC, Fe 81 B 13>5 Si 3 . 5 C 2 ("Metglas" is a trademark of Allied-Signal Corporation); an improved alternative is 2605 S2,

-1.0

-0.5

0 H in A/cm

0.5

Figure 9-29. Comparison of the hysteresis loops at mains frequency for Metglas 2605 SC (0.4 mm thick) and crystalline Fe-3 wt.% Si sheet (0.3 mm thick). (After Hilzinger, reproduced by Anantharaman, 1984.)

Fe 78 B 13 Si 9 . In a classical episode of challenge-and-response, the steel community has set about improving crystalline Fe-Si alloys by increasing the Si content from « 3 to « 6 at.% (with concomitant enhanced resistivity and reduced magnetostriction) by using rapid quenching methods to obviate extreme brittleness, but they have not caught up with the best metallic glasses yet, except for the fact that Fe-Si is still cheaper than metallic glass. Fig. 9-30 shows, on a logarithmic scale, comparative values for the core loss (hysteretic and eddy currents) and the exciting power in watts per kg of core, for oriented and unoriented Fe-Si and for the best metallic glass. The superiority of the glass is very clear. Once the problems of cutting, coating and winding metallic glass sheet on an industrial scale had been solved, a large number of experimental distribution transformers (used in the U.S.A. and Japan to transform supplies down to the domestic voltage of 110 V) were successfully made and evaluated (Natasingh and Liebermann, 1987). Competing designs have also been described (e.g., Schulz et al., 1988). The economics of glass-wound transformers well as a critical comparison with those

538

9 Metallic Glasses 10

M-19 (non-oriented) (0.36mm thick) />'

10" ;

10r 20 -

0.1 urn ~

\ Diffusion of Au in NiNb

\

"

1.0

100 A \ \ ,

1.2 U 1000/ T in K

, - 10 A

1.6

Figure 9-32. Diffusivity of gold in amorphous and polycrystalline Ni 5 5 Nb 4 5 . The righthand ordinate shows the diffusion distance in a period of one year. (After Doyle et al., 1982.)

The use of highly alloyed metal glasses as precursors for the production of finegrained crystalline alloys has received some attention, although very little by comparison with the effort which has gone into the design of glass-ceramics. The first serious research was by Ray (1981): his alloys were based on Fe, Ni, Al, Cr, Mo, Co and W in multiple combinations, with 5 12 at.% of B or other metalloids as glassforming aids. This interesting work has not received any follow-up until very recently, when Arnberg et al. have developed a range of tool steels by devitrification of glassy F e - C r - M o - C - B or F e - C r - M o -

543

9.8 References

C-V glasses (Arnberg, 1991). Subsequent to Ray's work, alloy developments along similar lines were by Das et al. (1985 b) and by Vineberg et al. (1985). Das et al. developed N i - M o - B and N i - A l - T i - X - B alloys, and later other N i - M o - B alloys with added Cr. These alloys were made by meltquenching, comminution and consolidation by extrusion or HIPping (Vol. 15, Chap. 4). During the processing, ordered phases including Ni 4 Mo, Ni 3 Mo, Ni 2 Mo and Ni3(Al,Ti) are precipitated from the crystallized matrix, together with stable boride precipitates. This family of alloys is now manufactured commercially under the trade name Devitrium® (Vineberg, 1985). The best of these alloys have very impressive high-temperature properties, exceeding high-grade tool steels. By far the most industrially important development of this kind is connected with rare-earth permanent magnets. The modern family of magnets based on the highcoercivity phase Nd 2 Fe 14 B can be made either by sintering an alloy powder or by melt-spinning the alloy to form a glass which is then devitrified (or, alternatively, quenching direct to a microcrystalline structure). The melt-quenching method was introduced by Croat et al. (1984) and culminated in a full-scale industrial process for making magnets. The various complications and improvements along the way are surveyed in a major review by Buschow (1986). Fig. 9-33 shows diagrammatically why there is an optimum quenching rate for this process, whether by direct quenching to a microcrystalline phase or by formation of a glass followed by reheating. The hard magnetic phase is desired, the alternative soft magnetic phase must be completely avoided, and a fine grain size is desirable for high coercivity. The process of devitrifying glass precursors in the N d - F e - B system is still receiving exten-

continuous cooling quenching and annealing onset of crystallization soft magnetic phase O \ —

hard magnetic phase I decreasing Tgrain size

W Time

Figure 9-33. Schematic time-temperature-transformation diagram to rationalize optimum conditions for producing N d - F e - B permanent magnets. (After Warlimont, 1985.)

sive attention: thus Jha et al. (1991) have established the formation of a metastable intermediate phase during the devitrification; the nature of the Nd 2 Fe 14 B phase itself was found to change progressively during the anneal, as indicated by a gradual change in the Curie temperature. A beginning has now also been made in using the devitrification approach for making nanocrystalline soft magnetic alloys, for instance a series of Fe-Cu-Nb-Si-B compositions (Herzer, 1991). Nanocrystallinity in such alloys presumably derives from exceedingly copious homogeneous nucleation during crystallization.

9.7 Acknowledgement I am greatly indebted to Dr. A. L. Greer for a critical reading of this chapter.

9.8 References Anantharaman, T. R. (Ed.) (1984), Metallic Glasses Production, Properties and Applications. Aedermannsdorf: Trans. Tech., pp. 203-292.

544

9 Metallic Glasses

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Spaepen, R, Tsao, S. S., Wu, T. W. (1986), in: Amorphous Metals and Semicondutors: Haasen, P., Jaffee, R.I. (Eds.). Oxford: Pergamon, pp. 365-378. Spit, E, Blok, K., Hendriks, E., Winkels, G., Turkenburg, W, Drijver, J.W., Radelaar, S. (1981), in: Proc. 4th Int. Conf on Rapidly Quenched Metals: Masumoto, T.5 Suzuki, K. (Eds.). Sendai: Japan Inst. of Metals, pp. 1635-1640. Sprengel, W, Dorner, W, Mehrer, H. (1990), Z. Metallkde. 81, 467. Steeb, S., Warlimont, H. (Eds.) (1985), Rapidly Quenched Metals (Proc. 5th Int. Conf.). Amsterdam: North-Holland, pp. 1589-1802. Suslick, K. S., Choe, S.-B., Cichowlas, A. A., Grinstoff, M. W (1991), Nature 352, in press. Sutton, M., Yang, Y S., Mainville, J., Jordan-Sweet, XL., Ludwig, Jr., K.F., Stephenson, G.B. (1989), Phys. Rev. Lett. 62, 288. Suzuki, Y, Haimovich, I, Egami, T. (1987), Phys. Rev. B 35, 2162. Tanner, L., Ray, R. (1980), Scripta Metall. 28, 633. Taub, A.I. (1984), IEEE Trans, on Magnetics 20, 564. Tendler, R.H. de (1986), J. Mater. Sci. 21, 64. Thakoor, A.P., Lamb, XL., Khanna, S.K., Mehra, M., Johnson, W. L. (1985), J. Appl. Phys. 58, 3409. Thompson, M.O., Galvin, G.J., Mayer, J.W., Peercy, P.S., Poate, J.M., Jacobson, D.C., Cullis, A.G., Chew, N. G. (1984), Phys. Rev. Lett. 52, 2360. Tomida, T, Egami, T. (1991), Mater. Sci. Eng. A133, 931. Tsai, R.-Y, Wu, S.-T. (1990), J. Electrochem. Soc. 137, 2803. Turnbull, D. (1974), /. de Physique 35, C 4 - 1 . Turnbull, D. (1985), in: Amorphous Metals and Semiconductors: Haasen, P., Jaffee, R.I. (Eds.). Oxford: Pergamon Press, 9-23. Turnbull, D., Cohen, M.H. (1961), Nature 189, 131. Vaidya, R.U., Subramanian, K.N. (1990), /. Mater. Sci. 25, 3291. van den Beukel, A. (1986), in: Rapidly Quenched Materials: Lee, P.W., Carbonara, S. (Eds.). Metals Park: Amer. Soc. Metals, p. 193. van den Beukel, A., Sietsma, J. (1990), Acta Metall. 38, 383. Vanini, F. (1990), Doctoral dissertation, Swiss Federal Inst. of Techn., Zurich. Vepfek, S., Iqbal, Z., Sarott, F.-A. (1982), Phil. Mag. B45, 137. Vineberg, E. X, Ohriner, E. K., Whelan, E. P., Stapleton, G. E. (1985), in: Rapidly Solidified Crystalline Alloys: Das, S.K., Kear, B. H., Adam, C M . (Eds.). Warrendale: The Metallurgical Society, 306. Volkert, C. A., Spaepen, F. (1990), Scripta Metall. 24, 463. Vredenburg, A. M., Westendorp, J. F. M., Saris, F. W, van der Pers, N. M., Keijser, Th. D. (1986), /. Mater. Res. 1, 775.

Wagner, C.N.J. (1986), in: Amorphous Metals and Semiconductors: Haase, P., Jaffee, R. I. (Eds.). Oxford: Pergamon, pp. 54-69. Walter, XL., Bacon, F , Luborsky, F.E. (1976), Mater. Sci. Eng. 24, 239. Warburton, W.K., Turnbull, D. (1975), Diffusion in Solids: Recent Developments. Nowick, A. S., Burton, X X (Eds.). New York: Academic Press, p. 171. Warlimont, H. (1980), Physics in Technology 11, 28. Warlimont, H. (1985), in: Rapidly Quenched Metals (Proc. 5th Conf.): Steeb, S., Warlimont, H. (Eds.). Amsterdam: North-Holland, pp. 1599-1609. Warlimont, H. (1988), Mater. Sci. Eng. 99, 1. Weeber, A.W., Bakker, H. (1988), X Phys. F: Met. Phys. 18, 1359. Weeber, A.W, Haag, W.X, Wester, A.J.H., Bakker, H. (1988), J. Less-Common Metals 140, 119. Wei, Gao, Cantor, B. (1989), Acta Metall. 37, 3409. Whang, S.H. (1983), Mater. Sci. Eng. 57, 87. Wolf, D., Okamoto, P. R., Yip, S., Lutsko, J.F., Kluge, M. (1990), J. Mater. Res. 5, 286. Wu, T. W, Spaepen, F. (1986), in: Mechanical Behavior of Rapidly Solidified Materials: Sastry, S. M. L., MacDonald, B.A. (Eds.). Warrendale: TMSAIME, p. 293. Yamasaki, T, Takahashi, M., Ogino, Y. (1985), in: Rapidly Quenched Metals (V): Steeb, S., Warlimont, H. (Eds.). Amsterdam: North-Holland, pp. 1381-1384. Yater, J.A., Thompson, M.O. (1989), Phys. Rev. Lett. 63, 2088. Yavari, A.R. (1986), J. Mater. Res. 1, 746. Yavari, A.R., Hicter, P., Desre, P. (1983), J. Chim. Physique 79, 572. Yeh, X.L., Samwer, K., Johnson, WL. (1983), Appl. Phys. Lett. 42, 242. Yermakov, A. Ye., Barinov, V.A., Yurchikov, Ye. Ye. (1981), Phys. Met. Metall. 54, 935. Yermakov, A. Ye., Yurchikov, Ye. Ye., Barinov, V.A. (1982), Phys. Met. Metall. 52, 50. Yoshioka, H., Asami, K., Kawashima, A., Hashimoto, K. (1987), Corros. Sci. 27, 981. Zollzer, K., Bormann, R. (1988), J. Less-Common Metals 140, 335.

General Reading Anantharaman, T. R. (Ed.) (1984) Metallic Glasses Production, Properties and Applications. Aedermannsdorf: Trans. Tech. Cahn, R. W. (1980), Metallic Glasses. Contemp. Phys. 21, 43. Giintherodt, H.-X, Beck, H. (Eds.) (1981, 1983), Glassy Metals I and II. Berlin: Springer. Haasen, P., Jaffee, R.I. (Eds.) (1986), Amorphous Metals and Semiconductors. Oxford: Pergamon. Luborsky, F. E. (Ed.) (1983), Amorphous Metallic Alloys. London: Butterworth.

10 Glass-Like Carbons Sugio Otani and Asao Oya Department of Materials Science, Gunma University, Gunma, Japan

List of Symbols and Abbreviations 550 10.1 Introduction 551 10.2 A Short History of Glass-Like Carbon 551 10.3 Preparation Procedures of Glass-Like Carbon 553 10.3.1 Preparation from Cellulose 553 10.3.2 Preparation from Thermosetting Resin 554 10.3.3 Preparation by Use of Filler Material 555 10.3.4 Porous Glass-Like Carbon 555 10.3.5 Fine Glass-Like Carbon Particles 556 10.3.6 Glass-Like Carbon Coating and Film 556 10.3.7 Glass-Like Carbon Fiber 556 10.4 Structure of Glass-Like Carbon 557 10.4.1 Structural Models of Glass-Like Carbon 557 10.4.2 Structural Change on Hardening and Initial Carbonization Processes .. . 558 10.4.2.1 Cellulose 558 10.4.2.2 Phenol-Formaldehyde Resin 559 10.4.2.3 Furfuryl-Alcohol Resin 562 10.4.3 Structural Change During the Carbonization Process 562 10.5 Properties of Glass-Like Carbon 563 10.5.1 Normal Glass-Like Carbon 563 10.5.1.1 Density, Porosity and Gas Permeability 564 10.5.1.2 Mechanical Properties 564 10.5.1.3 Electrical Properties 565 10.5.1.4 Thermal Properties 565 10.5.1.5 Chemical Properties 565 10.5.1.6 Purity 565 10.5.1.7 Comparison with other Materials 566 10.5.2 Properties of Composite Glass-Like Carbon and Porous Glass-Like Carbon 566 10.6 Applications of Glass-Like Carbon 566 10.6.1 Electronic and Magnetic Applications 566 10.6.2 Applications in Analytical Chemistry 569 10.6.3 Metallurgical Applications 569 10.6.4 Applications to Biomaterials 569 10.6.5 Applications to Fuel Cells 569 10.6.6 Other Applications 571 10.7 Acknowledgements . 571 10.8 References 571 Materials Science and Technology Copyright © WILEY-VCH Verlag GmbH & Co KGaA. All rights reserved.

550

10 Glass-Like Carbons

List of Symbols and Abbreviations d002 Lc La

interlayer distance crystallite thickness parallel to the c axis crystallite size normal to the c axis

CVD HHT PAN RVC

chemical vapor deposition heat-treatment temperature polyacrylonitrile Reticulated Vitreous Carbon

10.2 A Short History of Glass-Like Carbon

10.1 Introduction Carbon atoms have three valence states, sp, sp 2 and sp3, from which three allotropic forms are derived: carbyne (Sladkov et al., 1968; Heimann et al., 1983), graphite and diamond. Carbon materials such as coke, carbon black and graphite electrodes, however, have complex structures of sp 2 and sp 3 as well as small amounts of sp carbon atoms. Despite containing only one element, carbon materials therefore have a wide range of structures and properties. Glass-like carbon is a unique carbon material because it consists of an amorphous-like and isotropic structure including a large amount of tetrahedral sp 3 carbon. It has several characteristic properties resulting from its structure in addition to its glass-like appearance. When glasslike carbon was developed around 1960, many practical applications were expected, but were not realized because of some disadvantages described at a later date. Instead, this material served to increase fundamental and academic knowledge of carbon materials and just recently some potential applications have appeared. For successful applications, the preparation procedure as well as the structure and properties of glass-like carbon have been diversified remarkably, once again stimulating interest in this material and raising expectations of future development. Since many of the preparations and applications are described in patents, many are cited, especially from Japan where the most active development is now in progress.

10.2 A Short History of Glass-Like Carbon A short history of this material is shown in Table 10-1. The initial purpose of the

551

Table 10-1. A short history of glass-like carbon. Year 1957 1961 1962 1964

19641965 1966 1967 1969 1969 1971

1974

1975 1980

1981 1983

1983 1984

Event First glass-like carbon Cellulose Carbon by General Electric Company (UK). Vitreous Carbon derived from phenolaldehyde resin by Plessey Company (UK). Glassy Carbon derived from furfuryl alcohol by Tokai Carbon Company. Microporous glass-like carbon by Societe le Carbone-Lorraine (Development year of Carbone Vitreux is not clear). Proposal of some structural models of glasslike carbon using X-ray diffraction technique by Noda et al. Vitro Carbon derived from acetonefurfuryl resin by Nippon Carbon Company. Glass-like carbon fiber by Tokai Carbon Company. Composite glass-like carbon using filler by Lockheed. Formation mechanism of glass-like carbon by Fitzer's group. Structural model of "network of ribbon stacking" for glass-like carbon by Jenkins and Kawamura. Glass-like carbon containing the finely dispersed iron particles by Walker et al. and Yajima et al. Fine porous glass-like carbon by Hucke. Reticulated Vitreous Carbon by Chemotronics International. Glass-like carbon coating by The Aerospace Corp. Activation of study on the fuel cell. A high quality glass-like carbon (Glahard) derived from a hydrophilic resin by Kao Company. Composite glass-like carbon by Showa Denko. Development of a large-sized composite glass-like carbon by Showa Denko. New model of glass-like carbon by Shiraishi.

glass-like carbon was to develop a component of nuclear fuel. For this application, the carbon material must be gas-impermeable and of high purity. Davidson (1957) of the General Electric Company (UK) succeeded in developing the first glass-like carbon, Cellulose Carbon, from cellulose slurry. The products were small pipes. This

552


company developed the preparation procedure of glass-like carbon from thermosetting resins in 1960 (Rivington, 1960). With this as a trigger, the race for the development of glass-like carbon had begun. Plessey in England (Redfern, 1961; Redfern and Floyd, 1962; Cowlard and Lewis, 1967) developed Vitreous Carbon from phenol-aldehyde resin. A glass-like carbon boat, disc and rod in addition to pipes were prepared. The glass-like carbon was gradually shown to have some additional attractive properties, e.g. high chemical durability, and was expected to have practical applications in the use of chemical vessels and electrodes for electroanalysis (Zittel and Miller, 1965; Yoshimori et al., 1965). These applications were later industrialized but their production quantities were quite small. At almost the same time, Tokai Electrode (at present Tokai Carbon) derived Glassy Carbon from furfuryl-alcohol resin (Yamada and Sato, 1962; Yamada and Takada, 1963 a, 1963 b). Here new techniques were developed, e.g., using a powder filler and making a mold by repeatedly coating the resin on a substrate. In 1964, the Societe Carbone-Lorraine developed porous glass-like carbon. This company also distributed a catalog for a dense glass-like carbon called Carbone Vitreux but the preparation procedure has not been published as far as we know. Nippon Carbon subsequently developed Vitro Carbon by using an acetone-furfural resin (Honda et al., 1966; Teranishi et al., 1967). In addition, Sigri GmbH (FRG) developed Sigradur (the preparation procedure is not clear, however). A unique glass-like appearance and some attractive properties of this material led to active interest in its structure, beginning around 1964. Some structural models for glass-like carbon were proposed on the basis of X-ray diffraction analysis as de-

scribed in Sec. 10.4.1. In 1971, Jenkins and Kawamura proposed a novel "network of ribbon stacking" model (sometimes called the "Jenkins nightmare" model) on the basis of high-resolution electron microscopic observations in 1971. Such fundamental work contributed favorably to the understanding of the structure of not only glasslike carbon but also other carbon materials. The pitch-based carbon fiber developed by Otani (1965, 1966) had a similar structure. Stimulated by this invention, a glasslike carbon fiber was developed by Yamada et al. (Yamada and Nakamura, 1966; Yamada and Yamamoto, 1968). However, the resulting fiber was mechanically weak compared with fibers derived from pitch material and polyacrylonitrile (PAN). It was not until around 1980 that carbon fiber from phenol resin was industrialized on the basis of its high flexibility (Kawamura and Jenkins, 1970) or because of the large specific surface area achieved through activation treatment (Miyashita, 1983). Research and development on new applications of glass-like carbon were continued. Walker's group endeavored to apply the glass-like carbon, with or without fine metals, as a catalyst (Jung et al., 1979) and as a catalyst support and molecular sieve (Walker et al., 1977). Its potential use as biomaterial was examined by Fitzer's group (1978). None of these results, however, were industrialized. The uniform dispersion of fine iron metals in glass-like carbon has been achieved by some researchers (Yajima and Omori, 1972; Kammereck et al., 1974). Recently, fine glass-like carbon particles containing dispersed fine metals have again attracted much attention as electromagnetic material, catalyst, etc. (Hirano et al., 1983; Yogo et al., 1986). However, practical applications for glass-like carbon were not developed as ex-

10.3 Preparation Procedures of Glass-Like Carbon

tensively as expected initially because of the low productivity and high price. But then again, in those days there were no high technology application fields in which the unique properties of this material would be required. Around 1980, some potential applications appeared, among which the most attractive ones were as parts of fuel cells and magnetic recording equipment. Both applications required a low priced, large and thin glass-like carbon plate; however, somewhat lower gas impermeability and structural homogeneity were needed in the first case and a high quality glass-like carbon was required in the second. Some companies entered the field of glass-like carbon and made extensive contributions to accomplish these requirements. The first was achieved successfully by the use of filler material (Saura et al, 1987; Fukuda et al., 1988). In connection with the second application, on the other hand, the chemical structure of the starting thermosetting resin itself was reconsidered, and a hydrophilic resin was developed by a structural modification technique or blending technique of the resins to result in a high quality glass-like carbon (Yamauchi et al., 1985). These materials are now undergoing extensive trials for practical uses. Also, the conventional glass-like carbon has penetrated somewhat into the semiconductor as well as other industries (Yasuda and Nakamura, 1975).

10.3 Preparation Procedures of Glass-Like Carbon 10.3.1 Preparation from Cellulose

There are three typical carbonization processes, called the liquid-phase, gasphase and solid-phase carbonizations. The

553

typical carbon materials resulting from these processes are coke, pyrolytic graphite and charcoal (or carbon fiber), respectively. Glass-like carbon is prepared through the solid-carbonization process. As seen in the case of charcoal, the carbon resulting from solid-phase carbonization tends to become porous in nature. In the preparation of glass-like carbon, therefore, the key point is the removal of the pores from the material. Many preparation procedures are disclosed in patents but expert knowledge is essential for practical production. Cellulose Carbon is prepared according to the processes shown in Fig. 10-1 a (Davidson, 1957, 1959). The fibrous structure of the cellulose is mechanically and/or chemically beaten in an aqueous medium to prepare the cellulose slurry. It is important to prepare a fine and homogeneous dispersion of the cellulose because the state of the cellulose slurry is intimately related to the cross-linking reaction in the subsequent heating process and to the properties of the final product. The close cross-linkages result in a dense and homogeneous glass-like carbon. The addition of a dispersion agent such as zinc chloride is effective in forming the homogeneous slurry. The slurry is fed into the bowl of a centrifuge, and, while the water is continuously removed, the beaten cellulose is automatically pressed against the centrifuge wall to form a long hollow tube. The moist cellulose tube is carefully and slowly dried at room temperature and, if necessary, under controlled humidity. The tube undergoes a 50% volume shrinkage. After machining to the desired size and shape, the regenerated cellulose tube is slowly carbonized under an inert atmosphere for several days and then graphitized above 2500 °C. The carbonized tube is microporous in nature, the pore size being approximately 2 nm. Graphitization results in clo-

554

10 Glass-Like Carbons (a)

Cellulose slurry

(c)

(b)

Thermosetting resin

Thermosetting resin

I Molding

Molding

Kneading

I Molding Drying

Hardening

Hardening

Machining

Machining

Machining

Carbonization

Carbonization

I

I

Graphitization

Graphitization

Graphitization

Carbonization

sure of the ends of the pores, achieving gas impermeability. The products are small tubes, as suggested by the preparation method. Glass-like carbon formation from lignin was later attempted by Tormala and Romppanen (1981) using a different procedure from that of Cellulose Carbon, but the resulting product did not exhibit high mechanical strength. 10.3.2 Preparation from Thermosetting Resin

Many kinds of thermosetting resins such as phenol resin and furfuryl-alcohol resin are used as raw materials for glass-like carbon (Rivington, 1960; Redfern, 1961), but the fundamental preparation procedure is almost the same. As shown in Fig. 10-1 b, a thermosetting resin is first shaped. Here the resin is usually poured into a mold and thereafter hardened through polymerization. In practical operations, an organic hardener such as benzoic peroxide or aniline sulfate is sometimes used (Yamada and Takada, 1963 a, 1963 b). When a tube is desired, the resin is poured into a cylindri-

Figure 10-1. Preparation procedures for glass-like carbons from (a) cellulose, (b) thermosetting resin, and (c) thermosetting resin/ filler particle.

cal mold and rotated at high speed (in order to form the resin into a tubular shape by centrifugal force), followed by hardening treatment. The product after hardening is dehydrated slowly by heating under pressure or at a very low heating rate (1 °C h~ x ) under reduced pressure (Redfern, 1961); the resulting product breaks easily since the moisture evolved is not easily released from the mold, which shrinks extensively. This is the most substantial cause of low productivity of this material. A glass-like carbon product of >10mm in thickness is difficult to prepare. According to the patents applied for by Tokai Carbon Company (Yamada and Takada, 1963 a, 1963 b), a shaped substrate is repeatedly coated with resin and then hardened, to form the product. The moisture is easily released from the mold and the resulting product is strong because of the layered structure. The product is carbonized to 10001500°C with a heating rate of about 5°C min" 1 and subsequently graphitized. The largest products attained by this method were a rod of 6.25 mm diameter x 300 mm length and a tube of 23 mm diameter

10.3 Preparation Procedures of Glass-Like Carbon

(thickness 6 mm) x 165 mm length, etc. (Redfern, 1961). 10.3.3 Preparation by Use of Filler Material Attention has concentrated recently on glass-like carbon containing filler material (here, this type of glass-like carbon is referred to as composite glass-like carbon). The addition of filler is effective in decreasing the weight loss and the shrinkage of the product, and in facilitating the release of the evolving gas during the hardening and carbonization processes. This method is used to prepare a large-sized inexpensive glass-like carbon with a lowering of gas impermeability and structural homogeneity. In the initial patent describing this method, the thermosetting resin powder after hardening was used as a filler to prepare the final product consisting of the same glass-like carbon component. Natural graphite has also been used (Bradshaw et al., 1969); and fine graphite powder of less than several microns has again attracted much attention recently (Saura et al., 1987; Fukuda et al., 1988). As shown in Fig. 10-1 c, the thermosetting resin and the filler particles are first kneaded under a vacuum to remove trapped gas. Several effective shaping techniques such as extrusion, pressing and roller forming can be used. The productivity of these methods is far higher compared with the methods without the filler (Saura et al., 1987). A plate as large as 100 x 100 cm and several millimeters in thickness is prepared commercially by using graphite powder filler. In the preparation of the glass-like carbon Strux by the Fudow Chemical Company, a woven fabric of the thermosetting resin fiber is used as a filler. The filler is first impregnated with the resin and stacked,

555

then pressed. The resulting product consists completely of the glass-like carbon component. According to a patent by Sakaguchi (1988), some kinds of ceramic powder (A12O3, SiC, etc.) are used to improve the abrasion resistance of the product. It is well known that the thermosetting resin is used as a matrix for fiber-reinforced carbon composites, further details of which can be found elsewhere (Fitzer, 1987). 10.3.4 Porous Glass-Like Carbon Porous glass-like carbon can be prepared more easily without damage than the products described in 10.3.2 and 10.3.3. In some cases, therefore, porous glass-like carbon is first prepared and then subjected to impregnation by the resin (Johnson et al., 1979) or chemical vapor deposition (CVD) (Nagle and Walker, 1973) to obtain a dense glass-like carbon. There are four fundamental methods for preparing porous glass-like carbon: (i) Polyurethane foam or non-woven fabric of carbon fiber, cellulose, etc., is impregnated with thermosetting resin, followed by removal of the excess resin which then remains on the fiber surface alone. Subsequently, the resulting skeleton is subjected to the usual preparation procedures of glass-like carbon (Franklin, 1980). (ii) The pore former, such as water or polyethyleneglycol, is added to the raw thermosetting resin (Hucke, 1975; Walker Jr. etal., 1977; Yata et al., 1986). It is released from the resin after hardening, leaving the pores, because it is not a component forming the glass-like carbon. The pore size is controlled by additional amounts of both the surface-active agent and the pore former. The procedure involving the replication of a porous sacrificial substrate, i.e., sodium chloride, is used for glass-like foam (Pekala and Hopper,

556


1987). This technique is suitable for preparing glass-like carbons with relatively large pores. (iii) Glass-like carbon particles are shaped with a binder by pressing. The pore remains at the particle boundary. It is difficult, using this method, to prepare porous material with a large pore volume without lowering the mechanical strength. (iv) A chemical foaming agent such as a halogenated hydrocarbon is used (Murakami etal., 1985; Katsura and Shiraki, 1987). The graphite powder is added to prepare the composite glass-like carbon as stated in Sec. 10.3.3. However, when the exfoliated graphite is used instead of the graphite powder, a unique, porous glass-like carbon is obtained (Kikuchi et al., 1985). 10.3.5 Fine Glass-Like Carbon Particles

Fine glass-like carbon particles have several specific applications. So far, particles have been prepared by crushing massive glass-like carbon. Recently, some new practical preparation procedures have been developed: (i) The polymer precursor is subjected to controlled atomization, followed by hardening and heat treatment (Levendis and Flagan, 1989). (ii) A suitable viscous thermosetting resin with a hardener is added dropwise into sulfuric acid and hardened in situ. The fine particles obtained after washing are carbonized and then graphitized. (iii) An aqueous solution of phenol is dropped into a hydrochloric acid/formaldehyde mixture, stirred to convert the mixture into a slurry or resinous state and then hardened by heating. The resulting fine spheres of several tens of microns in diameter are subjected to the subsequent heat treatments (Koyama et al., 1988).

10.3.6 Glass-Like Carbon Coating and Film

To avoid the difficulties involved in preparing a large-sized glass-like carbon product, the conventional artificial graphite products can be coated with glass-like carbon. Initially, a diluted thermosetting resin was used for the coating but the technique developed recently (Murata et al., 1988) is as follows: After initial carbonization, the resin is subjected to extraction with an organic solvent. The solution is concentrated to about 20 wt.%, then used to coat the conventional graphite product - mainly high-density isotropic graphite followed by hardening, carbonization and graphitization. The resulting product is substantially gas-impermeable. When the glass-like carbon is coated on a quartz glass plate coated with a release agent, a glass-like carbon film is obtained by peeling (Ogata et al., 1987).

10.3.7 Glass-Like Carbon Fiber

The thermosetting resin is subjected to continuous melt-spinning, hardening, carbonization and then graphitization, just as the usual pitch-based carbon fiber. The preparation using Kynol-type phenol resin has already been industrialized (Miyashita, 1983). The carbon fiber has low mechanical strength on the one hand, reflecting its amorphous-like structure, but high flexibility on the other. These inherent properties of the fiber are suitable for several applications as explained later. The mechanical properties can be improved by hot stretching carbonization but this technique is not practical (Economy and Lin, 1971). The carbon fiber can be converted into an excellent active carbon fiber through activation treatment (Miyashita, 1983).

10.4 Structure of Glass-Like Carbon

10.4 Structure of Glass-Like Carbon

80 70

10.4.1 Structural Models of Glass-Like Carbon

Figure 10-2 shows changes in the X-ray parameters of two typical kinds of carbons with heat-treatment temperature. Normal pitch coke shows a decrease of interlayer distance (d002) anH 2
Tg (Birge and Nagel, 1985). Here, the temperature can be modulated at frequencies up to the kHz region, with small amplitudes (~0.1K) around some temperature T where the system is in quasi-equilibrium. C* (co) has a frequency and temperature dependence which is similar to the complex viscosity rj*(co) and dielectric constant s* (co) (see below). However, whereas the latter may only couple to part of the glass process, C* (co) depends on all motional degrees of freedom. This has important consequences for analyzing the dependence of the a process on time and temperature (Angell, 1988). 11.2.3.2 Viscosity, Mechanical and Dielectric Relaxation The shear viscosity of supercooled liquids varies over a dynamic range of about 15 decades between the liquid region and the glass transition temperature. Whereas

capillary techniques are only applicable to normal liquids, rotation viscosimetry can be used in the viscous range up to about 10 3 Pas, and sphere drag methods are applicable up to ~ 1 0 8 P a s . Since supercooled liquids and molten polymers are viscoelastic, a frequency-dependent complex shear viscosity (Ferry, 1980) is defined as

= co

-l

[G"(co)-iGf(co)]

where Gf(co) is the storage modulus, and G" (co) the loss modules. The real viscosity is then obtained as the zero frequency limit of Gff(co)/co. Since G(co) is perhaps the most important quantity for characterizing the internal dynamics of polymeric materials and rubbers, rather sophisticated techniques have been developed for its measurement and analysis, mostly by applying small oscillations in plate-plate or coneplate geometry. It is clear that the Fourier transform of G(co) is the shear relaxation function G (t) which is related to the shear compliance J(t). Other mechanical relaxation functions are related to extension and compression experiments yielding the bulk viscosity in the zero frequency limit. We refer the reader to the monograph of Ferry (1980) for a detailed description of these techniques. Recent applications to polymer glass formers have been reviewed by Pearson (1987) and to low-molecularweight glass formers by Angell (1988). Dielectric relaxation is one of the most important observables for studying the a and /? processes in glass formers (McCrum etal., 1967; Johari, 1970, 1971). Although the relation between the complex dielectric constant 8 (co) and the motion of molecular dipoles is complex due to interdipole crosscorrelations, one can often obtain approximate correlation functions for molecular reorientation over a wide time and temper-

11.2 General Considerations

ature range extending from the liquid state, through the glass transition, to the solid glass. Recent technical advances have made it possible to build measuring systems from mostly commercial components, where a frequency range from 10 4 -10 9 Hz can be scanned in 3 stages essentially automatically as a function of frequency and temperature (Kremer etal, 1989). An excellent monograph on dielectric relaxation, which includes IR and optical frequencies as well as the dynamic Kerr effect, was published by Bottcher and Bordewijk (1978). Applications to supercooled liquids and glasses have been reviewed by Johari (1976 and 1987). 11.23.3 Optical Methods Dynamic light-scattering techniques have recently been applied very successfully to the dynamics in polymers and glass-forming liquids. At high frequencies (~ 10 * ° Hz), Rayleigh-Brillouin spectra (RBS) can be analyzed in terms of the frequency-dependent bulk viscosity rjv (co) and adiabatic compressibility Ks (co) which can be related with the dynamics of density fluctuations (Berne and Pecora, 1976). In a temperature range of up to 150 K above Tg, one observes excess scattering in the central Rayleigh line which has been attributed to clusters. These clusters are also detected in static light scattering, which becomes wave vector dependent in the glass transition region, and in photon correlation spectroscopy (PCS). A first account of these findings was given by Fischer (1989) and Gerharz et al. (1990), where references to literature on the applied light-scattering techniques can also be found. PCS has mostly been used for studying the slow dynamics of density fluctuations at the glass transition (Patterson, 1983). However, the Fischer group has also analyzed the dy-

587

namics of concentration fluctuations in mixed systems where a slow mode has been detected in addition to the expected interdiffusion mode. The former can be related to a diffusional motion of clusters of approximately 100 nm in size, which must be related to the structure of the supercooled liquid close to the glass transition (Gerharz et al., 1990). These interesting new results will probably stimulate further applications of dynamic light scattering to glassforming systems. Translational diffusion at the glass transition was previously restricted to relatively rapid motions of small molecules permeating through polymer films. Recently, the application of forced Rayleigh scattering (FRS) has extended the dynamic range to diffusion coefficients D > 1 0 ~ 1 7 cm2 s" 1 (Sillescu and Ehlich, 1990). In this technique, photoreactive dye molecules serve as diffusional tracers. A holographic grating is formed in the sample exposed to two interfering laser beams, and the diffusive decay of this hologram is subsequently monitored by forced Rayleigh scattering. An example is discussed in Section 11.3.1.1 (Fig. 11-10). Photochemical hole burning has been successfully applied to the slow dynamics in glasses at low temperatures. Here, the photoreactive probe molecule is irradiated by a laser in a narrow band of the optical spectrum. Subsequently, the spectrum is recorded and the broadening of the hole is measured as a function of observation time. Eventually, the sample is annealed at higher temperatures, and the dynamics is studied as a function of temperature (Kohler and Friedrich, 1987). A review of the hole-burning technique has been given by Friedrich and Haarer (1984). Recent applications of optical spectroscopy to glasses can be found in a book edited by Zschogge (1986).

588

11 Organic Glasses and Polymers

11.2.3.4 Neutron Scattering

Neutron-scattering methods have become of particular interest recently, since they appear to be most appropriate for testing the predictions of mode-coupling theories of the glass transition (see Sec. 11.2.4.3). Whereas the structure of a supercooled liquid shows no significant change at the transition to a solid glass, the dynamics freezes in a very complex way, and dynamic neutron scattering provides information on the short-time behavior. The techniques available cover a q range of ~10~2__l nm" 1 a n c j a time range of ~10~ 8 -10~ 1 2 s. Neutron backscattering, time of flight, and spin-echo techniques are used to provide optimum conditions in the different q and t ranges. In organic glasses, neutron scattering by the protons of the organic molecules yields an incoherent dynamic structure factor Sinc (k #f chemical-shift spectrum is found for tri10 - 2 cresyl phosphate at low temperatures, o-terphenyl whereas at higher temperatures the spec10 - 3 trum collapses to a narrow single line. Similar behavior is found for HMB in PDB; -4 o 10 =o o however, the characteristic Pake spectrum : °o 5 Tg"1 is found at low temperatures correspond10 — @ ing to the two transitions of a nucleus with I * 11 , 1 , 1 , 1 , " > 1 ! 1 , 1-. spin 1 = 1. 2.5 3.0 3.5 4.0 4.5 5.0 5.5 1/T in 1O'3K"1 •

%

^

f

f

l

:

31

P NMR

222

4K 40

20

0

241 243 -20

-40

kHz 2

HNMR 188

0

kHz

Figure 11-5. NMR line shapes in the supercooled region: neat tricresyl phosphate (top); 2.9% HMB-d18 in phthalic acid di-n-butyl ester (bottom).

Figure 11-6. 2 H NMR spin-lattice relaxation times (7^) and spin-spin relaxation times (T2) of o-terphenyl: T; at 2n 15 MHz (El); Tx at 2TT 33 MHz (x); T, (#) and T 2 (O)at 2n 55 MHz.

At temperatures higher than those of the line-shape changes, measurements of Tt and T2 provide information on the dynamics, whereas at lower temperatures mainly three pulse techniques in connection with measurements of Tt may be applied. 2 H spin-lattice relaxation times (T±) and spinspin relaxation times (T2) as a function of reciprocal temperature are given in Fig. 11-6 for the system o-terphenyl (Dries etal., 1988). Tx passes through an asymmetric minimum, whereas T2 decreases continuously. At temperatures below the Tx minimum, a shoulder appears for the Tx data. At even lower temperatures (i.e., below jTg) another relaxation process with a much weaker temperature dependence takes over, indicating almost rigid molecules in the glassy state. In order to extract correlation times from T± and T2 data, the spectral density is approximated by a Cole-Davidson (CD)

600

11 Organic Glasses and Polymers

distribution function yielding J(co) = sin (/?CD arctan (co TO) • (11-44)

where TO characterizes the cut-off time of the CD distribution. The distribution parameter PCD is the only free-fit parameter because the coupling constant C in Eq. 11-8 is determined from the low temperature width of the powder spectrum. The mean correlation times for o-terphenyl are drawn in Fig. 11-7. Below 10 ~ 6 s, T± and T2 yield the same correlation time, and a temperature-independent width parameter j8CD = 0.50 is found. This corresponds to /? = 0.63 of a Kohlrausch-WilliamsWatts (KWW) distribution if the relation - 0.97 jSCD + 0.144, for

(11-45)

0.2 S £CD ^ 0-6

Igd in s) 0 oc process ; a' n

e*ir B process

o-terphenyl -12

2.4

2.8

3.2 3.6 4.0 4.4 1/T in 1O"3K"1

4.8

Figure 11-7. Correlation times of o-terphenyl from 7^ ( • ) , T2 (O), spin alignment (2H NMR) ( • ) , dielectric relaxation (+), dynamic Kerr effect ( x ) (Beevers etal., 1976), light scattering (©) (Fytas et al., 1981) and dielectric relaxation, /? process (#) (Johari and Goldstein, 1970), dashed line: guide for the eye.

obtained by Lindsey and Patterson (1980) in a numerical comparison of both distributions is used. For > 1 0 ~ 7 S , there is no straightforward analysis of T2 (Dries et al., 1988), and T± yields correlation times considerably below the values obtained for the a process from other experiments. This indicates the influence of a )S process, discussed further in Section 11.3.1.2. The analysis of the spin-alignment data yields the correct correlation times for the a process (Fig. 11-7) and in addition provides information on the type of slow molecular reorientation close to Tg. Although the analysis of the spin-alignment results by Eq. 11-15 is rather complex (Dries etal., 1988; Erratum, 1989; Diehl etal., 1990), reorientations by only small angular step rotational diffusion can clearly be excluded, and some distribution of larger jump angles is in concordance with the experimental results. For tricresyl phosphate the condition cocs TX n\ 62 n, at a critical angle determined by sin 6C = n/ri, light is totally reflected. Light becomes polarized due to reflection, refraction, absorption, and scattering. At Brewster angle 9V, given by ri/n = tan 6p,

only the component of light polarized perpendicular to the plane of incidence is reflected and the intensity is plane polarized; at other angles of incidence the reflected light has mixed polarization. If the glass surface is oriented at Brewster's angle with respect to the direction of propagation of a plane-polarized beam, light is propagated through the glass with no reflective losses. The dependence of the reflectivity on wavelength and angle of incidence (Fresnel

laws) is complex, especially near an absorption band (Born and Wolf, 1980). The index of refraction and the absorption coefficient of a material can be derived from reflectivity data integrated over a broad range of wavelengths beyond the IR and UV absorption edges using a KramersKronig analysis (Powell and Spicer, 1970). The fraction of light reflected by a glass in air (nf«1) for normal incidence is given by the Fresnel reflectivity

In the transparent region where k w 0, this reduces to r = 4% for a glass of refractive index 7? = 1.5. The fraction of light transmitted when multiple reflections at both entrance and exit surfaces are considered is

12.2 Fundamental Optical Phenomena

given by the reflection factor R-

2n

(12-15)

For high-index glasses, Fresnel reflective losses become very large. In addition to spectral reflection depicted by Fig. 12-3, the transmitted flux may also be reduced by diffuse reflection from rough or irregular entrance and exit surfaces and imperfections in the interior of the glass. 12.2.4 Scattering

The flux transmitted in Fig. 12-3 is reduced from the incident flux by a combination of losses due to absorption, reflection, and scattering. Scattering of light in glass may be due to extrinsic causes or it may be intrinsic in nature. The former include discrete scattering centers such as bubbles, inclusions, impurities or flaws introduced during production. The latter includes Rayleigh scattering caused by stationary density, temperature, and compositional fluctuations, and Brillouin scattering caused by propagating fluctuations in the dielectric constant. Spontaneous and stimulated Raman and Brillouin scattering involve optic and acoustic phonons and nonlinear optical processes (Shen, 1984). Scattering processes may also be distinguished by the size and absorptivity of the active centers (Van de Hulst, 1957). Rayleigh scattering is caused by scattering centers that are small compared to the wavelength of light and exhibits a characteristic A~4 dependence on wavelength. As the particle size increases, scattering occurs increasingly in the forward direction and exhibits a l " 2 dependence (Rayleigh-Gan scattering). Mie scattering occurs when the scattering centers have a size comparable to the wavelength of light. Scattering in

629

glass begins to be visible for centers > lOnm in size. For large numbers of centers of dimensions ~100nm, glass appears cloudy. For high densities of centers having dimensions >1000nm, glass is usually opaque. Colloidal particles (crystals) that diffract light - the Tyndall effect - also contribute to light scattering. The color of the scattered light changes with the size of the colloidal particles. This particle size property is used to obtain optimum color characteristics, for example, in gold ruby glass. The spectrum of intrinsically scattered light consists of an unshifted central Rayleigh line and frequency-shifted Brillouin lines, the theoretical and experimental aspects of which are reviewed by Schroeder (1977). The ratio of the intensities of the central component to the total Brillouin components is given by the LandauPlaczek ratio RhP. The scattering loss coefficient as at wavelength X and temperature T is given by (12-16) where 8TI 3 kBT

n8p212

(12-17)

QV\

In Eq. (12-17), p12 is the longitudinal elastooptic constant (see Sec. 12.2.5), and vl is the longitudinal sound velocity (Pinnow et al., 1973). A similar expression applies to Rayleigh scattering where the temperature T is now the fictive temperature Tf at which density fluctuations are frozen in (near the glass transition temperature Tg). Light scattering losses in single-component glasses such as SiO2 are small and limited by microscopic density fluctuations associated with the random molecular structure. Losses in multi-component glasses and mixtures are generally larger because of additional concentration fluctu-

630

12 Optical Properties of Glasses

ations. Compositional studies of scattering losses show, for example, that for simple binary alkali silicate glasses, density fluctuations decrease with decreasing molecular weight of the alkali oxide. Thus glasses composed of low-atomic-number cations have reduced scattering losses. Since Tf > T, Rayleigh scattering is greater than Brillouin scattering. For single-component glasses, RLP~ 20. Scattering losses in optical fibers (Chap. 15), where ultralow losses are important, have been investigated extensively. For these materials, scattering is the major loss mechanism when absorption is successfully reduced. For most bulk optical and laser glasses, losses due to extrinsic imperfections and impurity absorptions are usually larger than intrinsic scattering losses. 12.2.5 Photoelastic Properties While glass is normally considered to be an isotropic material, it becomes birefringent under stress. Photoelastic properties describe the effects of elastic deformation on the refractive index; these result in distortions of the optical wavefront. The piezo-optic and elasto-optic coefficients determine the effects of stress and strain, respectively. In general a material may possess 36 independent piezo-optic or elasto-optic constants, but because glass is isotropic, there are only two independent coefficients for each. The change in refractive index An caused by a change in stress o for light polarized parallel or perpendicular to the line of stress is given by n3 An = Anl]-An1= — (q11-q12)a (12-18) where the g's are the piezo-optic constants and ^44 = îi — î2- The change in refractive index for uniform hydrostatic pressure P i s An = n3(q11+q12)P/2.

Corresponding relations involving elastic-optic constants p (Pockels coefficients) describe changes in refractive index and the state of strain in the glass. The p's and g's are related by (12-19 a)

Pn = and P12 = Cn «i2 + cii(«n

+«i2>

(12-19b)

where the c's are elastic stiffness constants. Also, p 4 4 = (p 11 ~p 12 )/2. Photoelastic constants have been measured for many optical glasses (Schaefer, 1953; Waxier, 1971) and studied as a function of glass composition. The dependence of the elastic-optic coefficients (measured from Brillouin line shifts) on composition for binary and ternary silicate glasses have been correlated with the degree of ion overlap and covalent bonding as the amount of alkali oxide in the base glass was varied (Schroeder, 1980). Stress-Optical Coefficient Mechanical stress, either developed internally during production, applied externally, or as a consequence of fluctuating temperature, changes the refractive index. The resulting change in optical path length S for a sample of length / caused by stress birefringence is AS = Anl = Kla

(12-20)

where, from Eq. (12-18), the stress-optical coefficient K is defined by K = Y(

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