Recommended Values of Thermophysical Properties for Selected Commercial Alloys

Recommended values of thermophysical

properties

for selected commercial

alloys

Kenneth C Mills

National Physical Laboratory

The Materials Information Society

WOODHEAD PUBLISHING LIMITED Cambridge England

Published by Woodhead Publishing Limited, Abington Hall, Abington Cambridge CBl 6AH, England www.woodhead-publishing.com Published in North America by ASM International, The Materials Information Society, 9639 Kinsman Road, Materials Park, OH 44073, USA First published 2002, Woodhead Publishing Ltd and ASM International © Crown Copyright 2002. Reproduced by permission of the Controller of HMSO. The author has asserted his moral rights. This book contains information obtained from authentic and highly regarded sources. Reprinted material is quoted with permission, and sources are indicated. Reasonable efforts have been made to publish reliable data and information, but the author and the publishers cannot assume responsibility for the validity of all materials. Neither the author nor the publishes, nor anyone else associated with this publication, shall be liable for any loss, damage or liability directly or indirectly caused or alleged to be caused by this book. Neither this book nor any part may be reproduced or transmitted in any form or by any means, electronic or mechanical, including photocopying, microfilming and recording, or by any information storage or retrieval system, without permission in writing from the publishers. The consent of Woodhead Publishing Limited does not extend to copying for general distribution, for promotion, for creating new works, or for resale. Specific permission must be obtained in writing from Woodhead Publishing Limited and ASM International for such copying. Trademark notice: Product or corporate names may be trademarks or registered trademarks, and are used only for identification and explanation, without intent to infringe. British Library Cataloguing-in-Publication Data A catalogue record for this book is available from the British Library. Library of Congress Cataloging in Publication Data A catalog record for this book is available from the Library of Congress Woodhead Publishing Ltd ISBN 1 85573 569 5 ASM International ISBN 0-87170-753-5 Printed by Antony Rowe Ltd, Wiltshire, England

FOREWORD It is incredible to recall that personal computers first saw the light of day not much more than 20 years ago, so much now do computers dominate our lives. The growth of cheaper and cheaper but more and more powerful computers has conferred an aura of invincibility upon the keyboard, the mouse, the screen and the CPU. Nothing seems beyond them. The almost unbelievable speed at which the computer has come to dominate key aspects of our personal, legal, medical and technical activities has dazzled our senses and mesmerised us into thinking that computing power is all that matters - that there is nothing the computer cannot do. In reality, of course, the computer is a mere tool that can extend the speed and reach of the human mind - informing our decisions but not changing the ways in which we make them. The field of engineering is one where this important truth can be easily overlooked. The enormity of the technical calculations that computers can now undertake and the complexity of the engineer models that can be forged, imbue computers with an illusion of great authority. But the true authority of a computer stems, not from the computer itself, but from the quality of the data on which the computer model is built, a fact in danger of being forgotten when engineering decisions are based on computed results. Materials processing is a complex area linking many aspects of the physical, chemical and microscale behaviour of materials. Computer methods are being rapidly developed, however, to encompass this complexity, but as their scope expands, so does the need for accurate data that quantifies wider and wider aspects of material behaviour during processing. In acknowledgement of this need, the Department of Trade and Industry (DTI) initiated, in 1993, a series of programmes as part of its statutory/regulatory Programme in Materials Metrology, to fund the development of methods for the measurement of material properties that influence their behaviour during processing - The Processability Programmes. As a major part of these Programmes, the National Physical Laboratory (NPL) was contracted to develop methods to measure the fluid flow and heat transfer properties of engineering alloys at high temperatures — up to and beyond their melting points. This is an area of measurement fraught with experimental difficulty - material reactivity is high so that containers and measurement probes are subject to attack, material samples are prone to contamination from the solid surfaces and gaseous atmospheres that they contact and the controlled and uniform high temperature conditions required are difficult to establish and sustain. Ken Mills played a leading role in the NPL team that carried out the work under these DTI contracts - work which established NPL as, to quote a Swedish expert, 'one of the leading laboratories in the world in property measurement'. An important milestone in DTFs contract with NPL required validation of the methods that were developed by reviewing the quality of the data they generated for accuracy, for usefulness to industry and for standing against corresponding data measured in other world wide centres. The review grew and grew, and has now grown further into the present book by Ken Mills. It is very gratifying that its publication will make important results from the DTI Processability Programmes widely available. Although all the members of NPL's team, as Ken acknowledges, played important roles in the review, the principal driver behind it was Ken, with his indefatigable pursuit of literature data and his 'nose' for the most reliable of measurements. It is the product of these skills that pervade this book - the key processability

properties of important engineering alloys are subject to detailed scrutiny, and the most reliable measured values presented in graphical and tabular form. The result is an extensive and authoritative survey of the high temperature properties of a wide range of real engineering materials. It will constitute a valuable source book for many years to come for those developing and using computer models of metallurgical processes, as well as for those interested in the study of materials properties in their own right. Authority in the reviews for each alloy stands out from each page - but I leave that for you, the reader, to judge and enjoy. A W D Hills DTI Specialist Technical Advisor for Processability

ACKNOWLEDGEMENTS I wish to thank my colleagues, (members of the High Temperature Physical Property Group at the National Physical Laboratory) for the excellent work used in this review: Peter Quested (Section Leader), Richard Andon, Rob Brooks, Lindsay Chapman, Austin Day, Alan Dinsdale, David Hayes, Amanda McCormick, Brian J Monaghan and Mike Richardson, and Helen Szelagowski and Roy Taylor (UMIST) who participated in NPL's measurement programme. The data provided by Jack Henderson of Netzsch, Prof. G. Pottlacher (TU Graz), Prof I Egry (DLR Cologne) and Prof T Yamamura (Tohoku Univ., Sendai) are also gratefully acknowledged. I would also like to thank those who helped in the production of this review: Barbara Miller and Ly n Nelhams (NPL) for the typing, Michael Waters, Lindsay Chapman (NPL), Alaistair Fox (Imperial College) and my wife Margaret and my daughter Anna, who all helped in the production of the drawings.

Contents

Foreword ..................................................................................................................

vii

Acknowledgements ..................................................................................................

ix

1. Introduction .......................................................................................................

1

2. Arrangement of the Report ..............................................................................

2

3. Sources of Data .................................................................................................

3

4. Methods .............................................................................................................

5

4.1 Experimental Methods ..................................................................................................

5

4.2 Estimation Methods .......................................................................................................

11

5. Some Words of Caution ...................................................................................

13

5.1 Determining the Fusion Range .....................................................................................

13

5.2 Heat Capacities in the Fusion/Solidification and Transition Ranges ...........................

13

5.3 Determining Thermal Diffusivities (Conductivities) in the (Solid + Liquid) and Liquid Ranges ...............................................................................................................

14

5.4 Surface Tension Measurements ...................................................................................

15

5.5 Fraction Solid ................................................................................................................

16

6. Property Values for the Mushy Region ...........................................................

17

7. Symbols, Abbreviations, Units ........................................................................

18

Aluminium ...............................................................................................................

19

Al ...........................................................................................................................................

19

Al-LM4 (A319) .......................................................................................................................

26

Al-LM5 (5182) .......................................................................................................................

32

Al-LM13 (4032) .....................................................................................................................

37

Al-LM25 .................................................................................................................................

43

Al-1100F ................................................................................................................................

50

Al-2024-T4 ............................................................................................................................

54

Al-3004 ..................................................................................................................................

58

Al-6061-T6 ............................................................................................................................

64

Al-7075-T6 ............................................................................................................................

68

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v

vi

Contents

Cobalt ......................................................................................................................

73

Co ..........................................................................................................................................

73

Co-X-45 .................................................................................................................................

80

Copper .....................................................................................................................

89

Cu ..........................................................................................................................................

89

Cu-Al (Al Bronze) ..................................................................................................................

98

Iron .......................................................................................................................... 105 Fe .......................................................................................................................................... 105 Fe-C Ductile Iron ................................................................................................................... 113 Fe-C Grey Cast Iron ............................................................................................................. 119 Fe-304 Stainless Steel .......................................................................................................... 127 Fe-316 Stainless Steel .......................................................................................................... 135

Magnesium .............................................................................................................. 143 Mg ......................................................................................................................................... 143 Mg-Ag-Ce (QE22) ................................................................................................................. 148 Mg-Ce-Zn (EZ33) .................................................................................................................. 153

Nickel ....................................................................................................................... 159 Ni ........................................................................................................................................... 159 Ni-CMSX-4 ............................................................................................................................ 167 Ni-Hastelloy-X ....................................................................................................................... 175 Ni-IN 718 ............................................................................................................................... 181

Silicon ...................................................................................................................... 191 Si ........................................................................................................................................... 191

Titanium .................................................................................................................. 205 Ti ........................................................................................................................................... 205 Ti-6 Al-4 V (IMI 318) .............................................................................................................. 211

Zinc .......................................................................................................................... 219 Zn .......................................................................................................................................... 219 Zn-Al ...................................................................................................................................... 225

Appendix: Details of METALS Model to Calculate the Thermophysical Properties of Alloys .......................................................................................... 233

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1

INTRODUCTION

The objective of this work was to provide the best available data for commercial alloys to facilitate the mathematical modelling of processes, such as casting, primary and secondary refining, etc. This study was funded by the Department of Trade and Industry. Most of the work contained in this critical review was carried out as part of the National Physical Laboratory's (NPL) MTS Programme on Processability. However, where data are available in the literature, these have been incorporated into the review. Mathematical modelling has become an established tool to improve process control and efficiency and product quality. There are several different types of models used which seek to predict, the thermodynamics kinetics, heat transfer, fluid flow etc of various processes. Models of heat and fluid flow have proved useful in predicting, defects in castings, the geometry of weld pool profiles, microstructure etc. These models have been developed to the stage where one of the prime requirements is for accurate reliable data for the thermophysical properties involved in the heat and fluid flow in the process viz fraction solid, melting range, heat capacity, enthalpy, thermal diffusivity and conductivity, emissivity, density, viscosity and surface tension. A recent investigation has shown that predictions of the defects in castings can be significantly improved by replacing data of unknown origin for relevant thermophysical properties of alloys held in commercial software packages by reliable experimental values for these properties. There are few data available in the literature for the above thermophysical properties of commercial alloys, hence the need for a measurement programme and a compendium of critically-assessed data to assist the mathematical modeller. In practice, reliable thermophysical property data are needed for a much wider range of commercial alloys than covered in this review. To facilitate this, two steps have been taken in this work to allow the reader to assess the viability of using estimated thermophysical property data: (i)

by using the relevant data for the parent metal of the alloy and

(ii)

using METALS model (available from NPL) where properties are calculated from the chemical composition and, in some cases, the liquidus temperature of the alloy.

Consequently, recommended values are provided for the parent metals and values estimated by METALS model are compared with the experimental values to allow the reader to determine whether estimated values would suffice for his (or her) application.

2

ARRANGEMENT OF THE REPORT

Alloys have been arranged in alphabetical order of the chemical formulae of the parent (or base) metal eg steels can be found under Fe9 superalloys under Ni. Within any one family of alloys (eg steels) they are arranged in the following order: parent metal alphabetical order of the letters used in alloy designation (eg ESf 718) numerical designations given (e.g. 3004), with lowest numbers first, e.g. LM4 comes before LM5 or Al-11 OOF before Al-3004. The figures, and equations run sequentially as they appear in the text of the data sheet (starting with 1) for each alloy. A list of symbols and abbreviations is given immediately prior to the section giving the assessed data. SI units are used throughout and temperatures are given in °Celsius. References and Tables are given at the end of chapter or the data review for each alloy.

3

SOURCES OF DATA

Much of the work used in this review was supplied by the NPL Section for High Temperature Physical Property Measurement led by Dr P N Quested, viz: Heat capacity, enthalpy, fraction solid: DPSC: Dr M J Richardson. HTDSC: Ms L Chapman, Dr A P Day, D M Hayes. Drop calorimetry: R F Brooks. Density: Levitated drop: Mrs A McCormick, R F Brooks, Dr A P Day. Hydrostatic probe: Dr A P Day. Viscosity: Oscillating viscometer: R J L Andon, Dr A P Day. Surface Tension: R F Brooks. Electrical resistivity/conductivity: Dr B J Monaghan. Thermal diffusivity (under contract to NPL): UMIST: Ms H Szelagowski, Prof Roy Taylor NPL: Dr B J Monaghan, J Neale. Thermodynamic calculations: Dr A T Dinsdale and J Robinson. Other data have been obtained from the following sources: (i) (ii) (iii)

review of published literature [1-8] information supplied by J H Henderson (Netszch), Ivan Egry (DLR) G Pottlacher (TU Graz), Profs Sato and Yamamura (Tohoku University) manufacturers data, where available.

For the pure metals, the values were obtained from standard texts [1-8] in addition to the data generated in the NPL measurement programme. The NPL thermodynamic package [9] MTDATA was used to calculate the phase equilibria for certain alloys. These were used to interpret the phases present and the origin of certain peaks in the DSC results.

References 1.

Touloukian, Y S et al: Thermophysical properties of matter, Volumes 1-12, publ. IFI/ Plenum (1970).

2.

Touloukian, Y S: Thermophysical properties of high temperature solid materials, publ. Macmillan, New York (1967).

3.

Dinsdale, A T: SGTE data for pure elements. CALPHAD 15 (1991) 317/475.

4.

Iida, T and Guthrie, R I L: The physical properties of liquid metals, Clarendon Press (Oxford), 1988.

5.

Handbook of physico-chemical properties at high temperatures, edited Y Kawai and Y Shiraishi, publ. ISI Japan, Tokyo, Special Issue No 41 (1988).

6.

Mills, K C; Monaghan, B J and Keene, B J: Intl. Materials Reviews 41 (1996) 209.

7.

Keene, B J: Intl. Materials Reviews, 38 (1993) 157/192.

8.

Zinovyev V E: Thermophysical properties of metals at high temperatures, publ. Metallurgia, Moscow (1989) (ISBN 5-229-002 60-3).

9.

Gisby, J A; Barry, T I; Dinsdale, A T and Davies, R H: MT DATA Applications in Extraction Metallurgy, Proc. Quebec Conf. for Metallurgists Computer Software in Chemical and Extractive Metallurgy, held Quebec, Sept (1993).

4

METHODS

4.1

Experimental methods

The following methods were used to determine thermophysical properties at the NPL.

4.1.1

Measurements of heat capacity, enthalpy, fraction solid

Measurements up to 730 0C were carried out using a Perkin Elmer DSC. The sample in the form of a disc was placed on an alumina disc located at the bottom of a Pt crucible complete with a Pt lid. A matched Pt pan was used as the reference pan. The reference and sample pans were placed in the DSC and heated (or cooled) from a known temperature (T1) to the target temperature (T2) at a known rate, eg 10 K min"1. When the sample undergoes a transition, eg an endothermic event, the temperature of the sample pan lags behind the reference pan and power is supplied to the sample cell to maintain it at the same temperature as the reference cell. The power required is continuously monitored. Consequently, this instrument is known as differential power scanning calorimeter (DPSC). The sample pan is run from T1 to T2, (i) empty, (ii) filled with a sapphire disc (of known Cp) and (iii) with the sample, using an Ar atmosphere in all cases. The procedures used to derive Cp are given elsewhere [1,2]. The results are obtained in the form of a Cp-T curve between T1 and T2, the experimental uncertainty being usually around ± 1%. Enthalpy (H T 2 -H T l 1) values are derived by integrating Cp values between T1 and T2. Measurements for temperatures between 720 and 1500 0C were obtained using a Stanton Redcroft DSC (denoted HTDSC) which is effectively a quantitative DTA unit. In this case the difference between the temperature of the reference and sample cells is measured. Purified Ar is flowed through the apparatus throughout the experiment. The procedure and the method of obtaining Cp and (H T 2 -H T l 2) were similar to that adopted for the DPSC. Experimental uncertainties of ± 4% were obtained in calibration experiments carried out on pure Ni but uncertainties of ± 2% were frequently recorded. Fraction solid (fs) values were derived from the enthalpy-temperature curve recorded for the temperature range covering solidification. The fs for a specific temperature (T) was derived from the ratio of (enthalpy evolved from temperature where solidification started to temperature (T)/(total heat given out during solidification). (See Figure 1).

Temperature ( 0 C) Figure 4-1

4.1.2

Enthalpy, Hj-HiIq(Jg-1)

Apparent CP (J g-1 K~1)

Area A Areas

Temperature (0C)

Schematic diagram showing derivation of fraction solid at temperature, T.

Density measurements

Density measurements at 20 0C were obtained from the mass and volume of a machined cylinder of the alloy, the dimensions of the cylinder being obtained with a micrometer. The density of liquid alloys was obtained with the levitated drop method [3] in which a sample of known mass is levitated in an electromagnetic coil and once the temperature has stabilised photographs of the drop are taken simultaneously in three directions (Figure 4-2). Since the specimen has a natural oscillation it is necessary to identify these images where the drop was spherical. The images taken from above are examined to identify circular drops and then the equivalent images from the side are identified and the volume calculated. The magnification factor was determined in a previous experiment in which photographs (in all three directions) were taken of a suspended ball bearing of known diameter. Density measurements obtained with this technique are thought to be subject to experimental uncertainties of ± 2%. 2 color pyrometer

RF coil Temperature display Calibration ball

Synchronized cameras (3rd removed for clarity)

Sample turntable Pushrod

Figure 4-2

Schematic drawing of the levitated drop method for measuring densities.

Density measurements on liquid alloys were also made with the hydrostatic probe method [3] in which the apparent mass of an alumina rod suspended from a balance is measured as it is pushed into the molten alloy (Figure 4-3). The apparent mass-immersion depth curve (shown in Figure 4-4) can be used to derive the density from the slope of the linear regions of these curves. Experimental uncertainties are considered to be in the range of ± 1 to 2%. Balance

Balance lowering mechanism Thermocouple Bob support rod Bob

Sample

Ta heating element Thermocouple

Liquid

Schematic drawing of the hydrostatic probe method [3].

Gas

Bob touches liquid Mass change

Bob

Figure 4-3

Surface tension Equilibrium Buoyancy Distance moved

Figure 4-4

Schematic drawing showing the principle underlying the hydrostatic probe method.

4.1.3

Viscosity (TJ)

The viscosities of the alloys were measured using an oscillating viscometer (Figure 4-5) where the viscosities are determined from the decay of the oscillations of a twisting sample [3]. Initially, the sample was placed inside a crucible OfAl2O3 (or BN) which was then inserted in a second stainless steel crucible (24 id x 65 mm) but subsequent work was carried out with a single alumina crucible. The crucible was suspended on a Pt-8%W wire (0.2 mm diam) which was contained in a water jacket at 30 0C. A mirror sited on the suspension train was used to follow the oscillations of the crucible using 1 mW laser. The reflected light was detected by an array of light sensitive diodes arranged in an arc of a circle (± 30°). The output voltages from all but the central diode were combined and measured using an A/D card and computer; the output from the central diode was logged separately. A waveform was deduced from the results from which the logarithmic decrement of the decaying sine wave was obtained over a period of ca. 200 s. An atmosphere of Ar was maintained in the 3-zone furnace used in the measurements. Solenoid Constant temperature jacket Platinum suspension wire Mirror

Window Laser and diode array

Crucible Sample Furnace Atmosphere control jacket

Figure 4-5

4.1.4

Schematic diagram of the oscillating viscometer [3 J.

Surface tension (y) measurements

Surface tensions (y) were obtained using the levitated drop technique [4,5] as shown in Figure 4-6a. The sample was levitated in a silica tube (13 mm od) by applying the power supplied by a 15 kW, 450 kHz Radyne RF generator to the coil when the specimen was raised on a BN push rod. A flowing atmosphere of purified Ar, He and Ar + 5% H2 was maintained to prevent oxidation of the sample and the temperature of the specimen was adjusted either by altering the concentrations of He or H2 in the gas mixture, (since these have higher thermal conductivities than that of Ar), or by varying the power of the generator, eg a reduction in power causes the drop to move lower in the coil which results in an increase in temperature. The temperatures of the droplets were measured with a 2 colour pyrometer. The oscillation frequency spectrum was obtained by projecting the image of the drop onto a photodetector and analysing the resultant electrical signal with a Wavetek dynamic signal analyser.

Photo cell

Lens

2 colour pyrometer Sample loading window

Sample turntable

Pushrod

Frequency (Hz)

Signal analyser Controlling computer

Figure 4-6

Schematic diagrams of (a) the levitated drop apparatus, (b) typical 5 peak spectra.

The surface tension (y) can be shown by the Rayleigh relation shown in Equation (4-1), where m is the mass of the drop and COR the Rayleigh frequency of oscillation. Y

=

STC mcoi/ 8

(4-1)

However, in practice, a frequency spectrum containing 3 or 5 peaks (Figure 4-6b) and not the single frequency predicted by Rayleigh [6] is found. Recent investigations [7,8] have shown that oscillations of the drop can arise from translational movements of the drop and the effect of magnetic pressure which result in an asymmetric drop. Cummings and Blackburn [9] derived Equation (4-2) for 5 peak spectra which allows the Rayleigh frequency to be derived from the frequency spectrum. col

= 7la>? + a>i + a>i + o>5 + a > ? - co2fr 1.9 + 1.2 (^] 5 \ aJ

(4-2)

where the subscripts 1 to 5 refer to the various peaks, tr to the translational frequency, g the gravitational constant, a the radius of the drop and z = (g/20^2). In some cases spectra with up to 9 peaks were obtained for commercial alloys, in these cases reliable values of y could be obtained [9] by using all 9 peaks in a modified form of Equation (2).

4.1.5

Thermal diffusivity (a), thermal conductivity (k)

Thermal diffosivities were measured at UMIST using the laser flash method (Figure 4-7a) [1O]. For measurement in the solid state, a disc-shaped sample was used, typically, 10 to 15 mm diam with a thickness of 2-4 mm. However, for the liquid phase it is necessary to contain the liquid in a sapphire cassette, (shown in Figure 4-7b). An energy pulse was directed onto the front face of the sample and the temperature transient was monitored at the back face. The temperature transient goes through a maximum (ATmax) and the time to reach a temperature of

0.50 ATmax5 (denoted I0 5) was derived. Measurements of thermal diffusivity (a) were derived using Equation (4-3) where L is the thickness.

a

(4 3)

- -p- * 1.37

L2

Corrections were made for the effect of heat losses [11] and for finite pulse effects [12].

-

Gas inlet

External trigger

HF generator

.Prism

Nd glass laser

Coil Laser power unit

Specimen

Thermocouple Temperature monitor

Susceptor Vacuum/pressure chamber

InSb detector

Lens

Mirror

Colloidal graphite

Lens Vacuum system Amplifier

Microcomputer

Figure 4-7

Schematic diagrams of (a) the laser pulse method and (b) the sapphire cassette used by UMIST to contain the sample.

The NPL laser pulse apparatus [13] and the cell used to hold the liquid sample are shown in Figure 4-8. IR sensor

Cap

Iris Ge lens CaF2 window Transmitted energy

Crucible lid

Sample Graphite furnace

L

PC control and data acquisition

Water cooling Laser pulse Power supply

Crucible

Sample support

Fused silica window Laser shuttle (Nd, GGG) 1.064 |iim laser

Sample installed Sample carrier tube

L

Figure 4-8

Schematic diagrams of (a) laser pulse apparatus and (b) cell used to measure thermal diffusivity of liquid metals by NPL [13].

4.2

Estimation methods

(i)

METALS model was used extensively to estimate Cp? (H7-H25), density, thermal expansion coefficient, viscosity, thermal diffusivity and conductivity. Full details of the principles underlying the estimation routines are given in Appendix 1. The following improvements to METALS model were incorporated into the estimation of the data presented here: (a) the program to correct errors in density of the solid and the viscosity were used. (b) the program to improve density predictions of Ni-based superalloys by accounting for the Al held interstitially was used. (c) METALS model suggests that values estimated in thermal conductivity (diffusivity) of the liquid will be high by at least 10% - the 10% correction has been applied to all alloys - a 20% correction was used where the liquid metal contains a large concentration of alloying elements eg Ni-based superalloys.

(ii)

Thermal conductivities QC) have been estimated by using values of thermal conductivity or diffusivity extrapolated to the liquidus temperature and assuming (A,S/A/) was identical to that of the pure metal.

References 1.

Richardson, M J: Compendium of Thermophysical Measurement Techniques: VoI 2, edited K G Maglic, A Cezairliyan and V E Peletsky

2.

Mills, K C and Richardson M J: Thermochimica Acta, 6 (1973) 427/438.

3.

Brooks, R F; Day, A P; Mills, K C and Quested, P N: Intl. J. Thermophys. 18 (1997) 471/480.

4.

Mills, K C; Brooks, R F: Mater. ScL Eng. A178 (1994) 77/81.

5.

Sauerland, S; Brooks, R F; Egry, I; Mills, K C: Proc. TMS Conf. Ann. Conf. on Containerless Processing (1993) 65/69.

6.

Lord Rayleigh, Proc. Royal Soc. 147 (1879) 71.

7.

Cummings, D and Blackburn, D: J. FluidMech 224 (1991) 395.

8.

Suryanarayana, P and Bayazitoglu, H: Phys. Fluids A3 (1991) 967/977.

9.

Brooks, R F; Monaghan, B J; Barnicoat, A J; McCabe, A; Mills, K C; Quested, P N: Intl. J. Thermophys, 17 (1996) 1151.

10.

Szelagowski, H; Taylor, R: High Temp.-High Pressure 30 (1990) 343/350.

11.

Cowan, R D: J. Appl Phys. 34(1) (1962) 926/927.

12.

Taylor, R E and Clark, L M: High Temp.-High Pressure 6( 1974) 65/72.

13.

Monaghan, B J and Waters, M J D : Laser flash metal thermal diffusivity measurements, NPL Report CMMT(D)196, April (1999).

5

SOME WORDS OF CAUTION

5.1

Determining the fusion range

Differential scanning calorimetry (DSC) traces indicate that a significant number of alloys contain an endothermic peak on heating (or exothermic peak on cooling) near the melting range. Typical examples are the Ni-based alloy IN 718 and the Co-alloy X45 shown in Figure 5-1. It is not easy to determine whether peaks on the low temperature side are a consequence of (a) eutectic melting of the alloy or (b) a solid/solid state transformation.

Heat capacity, Cp (J g~1 K~1)

Heat capacity, Cp (J g~1 K-1)

In some cases MTDATA calculations have been carried out to help in the allocation of the Cp peak, but it has not been possible to do this in every case. Obviously the decision has an effect on the fusion range, the enthalpy of fusion value and the fraction solid (fs) results, particularly at the high fs end.

Temperature ( 0 C) (a)

Temperature (0C) (b)

Figure 5-1 The heat capacity of (a) Ni-alloy IN 718 and (b) Co-alloy X-45 as functions of temperature.

5.2

Heat capacities in the fusion/solidification and transition ranges

Figure 5-1 (a) shows a Cp-T plot for a nickel based superalloy. It can be seen that Cp apparently increases markedly in the fusion range. In fact, this is not a true Cp value since the increase is due to the latent heat of fusion (or solidification) and is an enthalpy (not a Cp) but which is manifested as an apparent Cp. Such curves are useful in determining fs but should not be used for, say, the conversion of thermal diffusivity to thermal conductivity; an estimated Cp is recommended for use in this task. Solid state transitions are usually denoted as 1st Order or 2nd Order type transitions.

1st Order2nd Order

involves an enthalpy change (like fusion) and thus the apparent Cp values in this case are not true Cp values, involve a Cp change.

It has not been possible to determine the nature of the transitions observed in this review. Consequently, the following procedure has been adopted, all solid state transitions have been considered as First Order except in those cases where the Cp change is relatively minor, eg the transitions around 600-700 0C in Ni based superalloys (marked A) in Figure 5-1 which have been designated Second Order. Inspection of Figure 5-Ia shows a "valley" in the Cp-T immediately below the melting range. Consequently, it is difficult to assign a true Cp for the solid at the solidus temperature (T801). In these cases an estimated Cp for Tsol is recommended. Solid-solid transitions are relatively sluggish and sometimes require time for structural rearrangement of the atoms. DSC is a dynamic technique and sometimes does not allow enough time for the atoms in the alloy to rearrange themselves. Consequently, the "valley" Cp values tend to vary significantly from run to run.

5.3

Determining thermal diffush itics (conductivities) in the (solid + liquid) and liquid ranges

In the laser pulse method (and other methods) when a sample in the (solid + liquid) or 'mushy1 region is subjected to a pulse of energy some of this energy may be converted into further liquid formation and consequently will not be conducted through the sample. This leads to an erroneous value of the thermal diffusivity (or conductivity) (Figure 5-2). Thus values recorded in the mushy region are subject to error and it is recommended that values should be derived by using the relation (A, = ^ ^501 f s + XTH(] (f s ).

Thermal diffusivity, 106a (m2s~1)

This would also apply to solid/solid transitions involving large enthalpy changes.

Temperature ( 0 C) Figure 5-2 Apparent thermal diffusivity of Ni alloy IN 718 in the "mushy" region.

Values of the thermal diffusivity of the liquid phase of the aluminium alloy LM25 have been reported by four groups and the results split into two groups with lower values in good agreement and two groups in good agreement with higher values. The differences in the two sets of results was about 30%. This trend in results reported by the various groups for LM25 is maintained in results for other alloys. Some possible reasons are: (i) Convective contributions could have affected the higher results (ii) non-wetting of the cassette by the metal could lead to non-cylindrical geometry and an error in thickness L (iii) reflection from the surface of the metal (iv) the presence of an oxide film which produces an interfacial resistance. These causes of the discrepancies have not been resolved yet and thus recommended values could be prone to error.

Thermal conductivity, K (W rrr1 K~1)

Thermal conductivity values for the liquid phase are for a static liquid. It is therefore important to account for convective heat flow when modelling heat transfer during solidification. The differences between the experimental thermal conductivity and that obtained by inverse temperature modelling [2] can be clearly seen in Figure 5-3, these differences increasing with increasing temperature where convective contributions would be expected to rise sharply.

Temperature (0C)

Figure 5-3

5.4

Thermal conductivity of Al-alloy LM25; —o—, • • • -experimental; • from inverse temperature modelling.

Surface tension measurements

Surface tension (y) values and the sign and magnitude of the temperature dependency (dy/dT) are very dependent upon the concentrations of soluble O and S present in the metal (as little as 50 ppm O can cause a decrease of 30% in y and change (dy/dT) from negative to positive [3]. Small concentrations of elements such as Ca, Ce5 Al and Mg can cause a marked reduction in the soluble O and S levels in the alloy [3]. Thus, it is not possible to provide recommended

values for the surface tension of specific alloys, say IN 718, since it is dependent upon the concentrations of trace elements (eg O, S, Ca, Al etc) present in each batch of the alloy. Values will tend to vary on a batch to batch basis. In this review some general values are given for alloys with low concentrations of O and S. A second problem is the presence of oxide skins or films (formed by the oxidation of the surface or flotation of inclusions) on the surface of the metal. These films prevent the oscillations of the sample when using the levitated drop method. Some of these oxide films melt, eg those in Nibased superalloys melt 1700-175O0C and allow surface tensions to be measured. However, they can result in (i) a short range of measurement temperature, (ii) a more complex oscillation frequency spectra eg 9 peaks of 5 peaks normally obtained and this needs special analysis to give reliable surface tension values [4]. 5.5

Fraction solid

Fraction solid can be determined from DSC measurements (see Section 4.1.1). With DPSC, used for determinations on aluminium alloys the temperature of the two pans are kept constant and the energy required to maintain these balanced temperatures is monitored. In DTSC (DTAtype) the temperature difference between the two pans is monitored and consequently there is some uncertainty in the measured temperature. Thus the temperature scale for fraction solid determinations (on alloys with melting ranges > 730 0C) may be prone to error. References 1.

Szelagowski, H and Taylor, R: High Temp.-High Pressure 30 (1998) 343/350.

2.

Oxley, S; Quested, P N and Mills, K C: Proc. of AVS Conf. 1999 held Santa Fe, NM, Feb 1999.

3.

Mills, K C and Keene, B J: Intl. Materials Reviews 35 (1990) 185.

4.

Brooks, R F; Monaghan, B J; Barnicoat, A J; McCabe, A; Mills, K C; Quested, P N: Intl. J. Thermophys. 17 (1996) 1151.

6

PROPERTY VALUES FOR THE MUSHYREGION

Fraction solid, fs

Figure 6-1 shows the fraction solid (fs) of aluminium alloy LM25 as a function of temperature as determined by DPSC. It can be seen that the fraction solid is to some extent dependent upon the cooling rate of the metal. The thermophysical properties of the liquid phase are different from those of the solid alloy (e.g. thermal conductivity and diffusivity) thus the value of the thermophysical property in the mushy region will be dependent upon the amount of liquid and solid (i.e. fraction solid). Since the fraction solid differs with cooling rate then thermophysical properties-temperature relations would also differ with cooling rate. This would entail provision of a series of property-temperature relations for different cooling rates. This has not been attempted in this review.

Temperature (0C)

Figure 6-1

Fraction solid of Al-alloy LM25 as a function of temperature for different cooling rates.

Where information is required for the mushy region the reader is advised to calculate the required property (P) at temperature T from Equation 6-1 where fs(T) is the fraction solid at T and P1 oi and P1 are values of the property at the solidus temperature and the liquid at the liquidus temperature, respectively. PT =fs ( T ) Pr501 + ( l - f s ( T ) ) P T l i q

(6-D

Values of the following properties, (P), can be calculated in this manner; density (p); heat capacities (Cp) enthalpy of fusion (AH*18), thermal conductivity (X) and diffusivity (a) and emissivity (s). For systems where there is a solid/solid transition just below the melting peak in DSC results an estimated Cp should be used for Cp at Tsol (see Section 5.2).

7

SYMBOLS, ABBREVIATIONS, UNITS mV1 J K'1 g'1

a Cp fs fL H (H1-H25) AHfos AHtrans

Thermal diffusivity Heat capacity Fraction solid Fraction liquid Enthalpy Enthalpy relative to 25 0C (298 K) Enthalpy of fusion Enthalpy of transition

T Tliq Tsol Tfr

Temperature Liquidus temperature Solidus temperature Transition temperature

0

a y 8 A, r|

Thermal expansion coefficient Surface tension Emissivity Thermal conductivity Viscosity

K"1 mN m"1

J g'1 J g1 J g1 J g'1 C or K

Wm"1 K"1 Pas

subscripts and superscripts s Solid I Liquid m Value at melting point or Tliq N Normal T Total A, Spectral (wavelength dependent) DSC DTA DPSC DTSC HTDSC NPL UMIST WFL

Differential scanning calorimetry Differential thermal analysis Differential power scanning calorimetry Differential thermal scanning calorimetry High temperature differential scanning calorimetry National Physical Laboratory University of Manchester Institute of Science and Technology Wiedemann-Franz-Lorenz Rule

Al Pure Aluminium 1

Transitions, melting point

mp = 660.2 0 C[I]

2

Density, thermal expansion coefficient (a)

P25 (solid) = 2702 kgin3 [2]

a = 28 x 10'6 K'1 [3]

Values given in Table 1 and Figure 1 are based on these values. Density values have been reported for liquid Al9 at the melting point the following density pm values have been recommended, 2380 kgm'3 [4] and 2390 kgrn 3 [5]. Recently a value of pm = 2375 kgm"3 was obtained by the y-attenuation method [6]. Equation 2 has been adopted and used in deriving the values given in Table 1 and Figure 1. ps (kg.m"3) - 2702 - 0.228 (T-25 0C)

(1)

p^ (kg.m~3) = 2380-0.35 (T-660 0C)

(2)

Density, p (Kg nrf3)

The density change on melting is ca 7%.

Temperature (0C) Figure 1

Density of pure Al as a function of temperature.

3

Heat capacity (Cp) enthalpy (HT-H25)

The values shown in Figures 2 and 3 and Table 1 are derived from the data reported by Dinsdale [I]. CP25 (S)=O^OSJK-1S-1 [1] :CP (*)=!. 1 SJR-'g-1 [1]

Heat Capacity, C9 (J g'1 JC1)

AH6" = 397 Jg'1 [1]

Temperature (0C) Heat capacity of pure Al as a function of temperature.

Enthalpy, H1-H25 (Jg'1)

Figure 2

Temperature (0C) Figure 3

Enthalpy (H1-H25) of pure Al as a function of temperature.

4

Thermal diffusivity (a) and conductivity (A,)

The thermal conductivity (X) values for the solid phase shown in Figure 4 and Table 1 are based on those reported by Touloukian [7]. Thermal conductivity values for liquid Al were taken from the review of Mills et al [8] using the recommended Equation 3. (3)

(Wm-1K'1)

Thermal Conductivity, ^

X(f)=91+3.4xl(T2 (T -66O0C) WnT1K'1

Temperature (0C)

Figure 4

Thermal conductivity of pure Al as a function of temperature.

<mV)

Thermal diffusivity, 106a

Thermal diffusivity values were calculated from selected values of thermal conductivity, density and Cp shown in Table 1 (A/Cpp). These data are given in Table 1 and Figure 5.

Temperature (0C) Figure 5

Thermal diffusivity of pure Al as a function of temperature.

5

Viscosity

Viscosity data reported in the literature show a wide range of divergence which is presumably associated with the formation of a strong oxide film on the surface. The recent measurements reported recently by Andon et al [9] have been adopted and these lie at the lower limit of the published values (Figure 6). Equation 4 was derived from these measurements Iog10 TI (mPas) = - 0.562 + 567T'1

(4)

Viscosity,r\ (mPas)

where T is in K. These data are given in Table 1 and Figure 6.

Temperature (0C)

Figure 6

6

Viscosity of pure Al as a function of temperature - Andon et al [9].

Surface tension

Keene [10] reviewed the surface tension for pure Al and Equation 5 is based on the mean of these values Y (mNm'1) = 871 - 0.155 (T - 660 0C)

(5)

However, Keene [10] points out that several values for y (Al) in the range 1050-1100 mNm"1 have been obtained [11-13] and it has been suggested that these relate to pure Al whereas Equation 5 refers to oxygen-saturated liquid Al.

Surface Tension, y (mN nrf1)

Temperature (0C)

Figure 7

7

Surface tension of pure Al as a function of temperature; o? — Equation 5 which may relate to oxygen saturated liquid A1[10];A[11]; D [12], x [13], values reported for Al with very low oxygen levels.

Emissivity, s

Shiraishi [14] reports the following values of total normal emissivity S1^. Polished: Oxidised:

480-630 0C 400 0C 60O 0 C

STO = 0.057-0.065 [14] STO = 0.393 [14] eTO = 0.414

The following spectral emissivity Sx values are given by Touloukian [2] for the range 1.5-15 urn. Polished: Sx = 0.1 to 0.05 Rougher surface: Sx = 0.25 Beyond 10 |um = s depends upon surface oxidation.

References 1.

Dinsdale, A T. SGTE data for pure elements. CALPHAD 15 (1991) 317/325.

2.

CRC Handbook, Handbook of Chemistry and Physics edited D R Lide, 74th edition, publ CRC Press, Ann Arbor (1993/4).

3.

Touloukian, Y S. Thermophysical properties of high temperature solid materials, Volume 1, Elements, publ. McMillan, New York (1967).

4.

Iida, T; Guthrie, R I L . The physical properties of liquid metals, Clarendon Press, Oxford (1988).

5.

Watanabe, S; Ogino, K; Tsu, Y. Handbook of Physico-chemical properties at high temperatures, publ. ISIJ, Tokyo edited Y Kawai and Y Shiraishi. Special Issue No 1 (1988) Chapter 1.

6.

Nasch, P M; Steinemann, S G. Phys. Chem. Liq. 29 (1995) 43/58.

7.

Touloukian, Y S; Powell, R W; Ho, C Y; Klemens, P G. Thermophysical properties of matter: Volume 1, Thermal conductivity, Publ. IFI/Plenum, New York (1970).

8.

Mills, K C; Monaghan, B J; Keene, B J. Intl. Materials Review, 41 (1996) 209/242.

9.

Andon, R J L ; Chapman, L; Day, A P; Mills, K C. NPL Report CMMT(A), 167 (1999).

10.

Keene, B J. Intl. Materials Review, 38 (1993) 157/192.

11.

Garcia-Cordovilla, C; Louis, E; Pamies, A. J. Mater. Sd, 21 (1986) 2787.

12.

Goumiri, L; Joud, J C. Acta Metl, 30 (1982) 1397.

13.

Pamies, A; Garcia-Cordovilla, C; Louis, E. Scr. Met, 18 (1984) 869.

14.

Shiraishi, Y. asinrefS. Chapter 10

Table 1 Recommended thermophysical properties for pure AI Temp (0C) 25 100 200 300 400 500 600 660.2 660.2 700 800 900 1000 (SL] v;

Density kg in3 2702 2685 2662 2640 2617 2594 2571 2558 2380 2366 2331 2296 2261

Cp (Jg-1K-1) 0.905 0.945 0.99 1.03 1.07 1.10 1.15 1.18 1.18 1.18 1.18 1.18 1.18

(H1-H25) (Jg1) O 69 166 267 372 481 593 663 1060 1107 1225 1343 1461

= may relate to oxygen - saturated pure Al ^ ' = extrapolated value

X (Wm-1K-') 237 240 238 233 228 222 215 211 91 92 96 99 103

106a mV 97 95 90 86 81 78 73 71 32 33 35 36.5 38.5

n (mPas)

Y mNrrT1

1.11 1.049 0.93 0.83(b) 0.76W

871(a) 865ta) 849(a) 834(a) 818(a)

A1-LM4 (A319) 1

Chemical composition (wt%)

Al 89.4 2

Cu 3.0

Mg 0.1

Mn 0.4

Ni 0.35

Si 5.0

Zn 1.0

Others 0.5

Transitions T801 = 525 0C [I]; Measured by DPSC [2] Tsol = 518 0C;

3

Tliq = 625 0C [1] Tliq (peak temperature) - 621 0C [2]

Density P25 (s) = 2750 kg m'3 [1] a (20-100 0C) = 21 x 10'6 IC1 [1]

Estimated p25 (s) = 2774 [3] Estimated of (20-500 0C) = 27.6 x 10'6 [3]

These data were used to calculate the density data given in Table 1 and Figure 1. Values estimated for the solid phase by METALS model [2] are in excellent agreement and consequently, values for the liquid phase calculated by METALS model have been adopted. (1)

p, (kg.m~3) - 2492 - 0.27 (T - 6210C)

(2)

Density, p (Kg m"3)

ps (kg.m~3) ~ 2753 - 0.223(T-25 0C)

Temperature (0C)

Figure 1

Density of Al alloy LM4 as a function of temperature. (Use Equn6.1 to calculate properties in the 'mushy' region.)

4

Heat capacity, enthalpy

Richardson et al [2] reported Cp and (H1-H25) values for LM4, these are given in Figures 2 and 3, respectively, and Table 1. Estimated values obtained by METALS model were found to be in excellent agreement with experimental values except in the transition range. The following values were obtained: Cn P

25 18

= 0.83 J K'1 g'1 1

: :

estimated C n = 0.87 J K'1 g'1 P

25

fos

AH = 393 Jg 1 estimated Cn(^) = 1.13 J K'1 g 1

Heat Capacity, Cp (Jg'1 K'1)

AH* = 400 Jg Cp(f) =1.17 Jg-1 K'1

:

Temperature (0C)

Heat capacity of LM4 as a function of temperature; over entire temperature range o? , experimental; A5 , estimated values. (Use Equn6.1 to calculate properties in the 'mushy' region.)

Enthalpy, H1-H25 (Jg'1)

Figure 2

Temperature (0C)

Figure 3

Enthalpy of LM4 as a function of temperature; , o, experimental; A, - -, estimated values. (Use Equn 6.1 to calculate properties in the 'mushy' region.)

5

Thermal diffusivity (a), thermal conductivity (X)

A value of A, = 121 Wm"1 K"1 has been reported for the thermal conductivity at 25 0C [I]. Szelagowski [4] and Henderson [5] measured the thermal diffusivity of LM4 and its equivalent A319, respectively, by the laser flash method. Thermal conductivities (X) were calculated using the values of Cp, and density recommended in Table 1.

(mV)

Thermal diffusivity, 10 6a

The thermal diffusivity values for the solid state, especially at lower temperatures, tend to be affected by the thermal and mechanical histories of the samples, which could account for the much lower value reported at 25 0C [I]. The thermal and conductivity values are shown in Figures 4 and 5, respectively. Mean values of the results obtained from laser flash studies have been adopted except in the (25-300 0C) where the higher values [5] have been taken.

Temperature (0C)

Thermal diffusivities of LM4 as a function of temperature, o, selected values •••, Henderson [5]; , Szelagowski [4]. (Use Equn 6.1 to calculate properties in the 'mushy' region.)

(W m'1 IC1)

Thermal Conductivity, A,

Figure 4

Temperature (0C)

Figure 5

Thermal conductivity of Al alloy LM4 as a function of temperature. (Use Equn 6.1 to calculate properties in the 'mushy' region.)

6

Viscosity (r|)

The viscosity values given in Table 1 were estimated by comparison with the measured viscosities for pure Al and LM25.

7

Fraction solid

Fraction Solid, fs

Fraction solid values given in Figure 6 were derived from the results obtained by DPSC for a cooling rate of-10 K min"1.

Temperature (0C)

Figure 6

Fraction solid for LM4 as a function of temperature for a cooling rate of 10 K min'1, ; heating 10 K min'1, - - -.

References 1.

British and European aluminium casting alloys, their properties and characteristics, compiled R Hartley, publ. Assoc. Light Metal Refiners, Birmingham (1992).

2.

M J Richardson, D Hayes, A P Day and K C Mills: NPL Report "MTS Programme on Processability: Thermophysical Property data for commercial alloys 4/93-3/96.

3.

K C Mills, A P Day and P N Quested: Estimating the thermophysical properties of commercial alloys. Proc. of Nottingham Univ-Osaka Univ. Joint Symp. held Nottingham, Sept (1995).

4.

H Szelagowski: PhD Thesis, Department of Materials Science, UMIST, Manchester (1999).

5.

J Henderson: data cited in reference 4.

Table 1 Recommended thermophysical properties of LM4

T C

0

25 100 200 300 400 500 518 621* 621* 700 800 900 1000

Density kgm'3 2750 2737

2717 2693 2668 2646 2640

Cp Jg-1 K-1 0.83 0.90 0.95 0.98 1.12 [1.2]a [1.09]a [1.13]a

2619

1.17 1.17 1.17 1.17 1.17

2492 2470 2442

2415 2388

[ ]a estimated values

(H1-H25)

Jg-' O 65 157 254 359 475 495 608 1008 1100 1217 1334 1451

106a 2

1

Hi S-

60 63 63 62 60 55 52 24

245 25 255 26

X Wm'1 K-' 137 155 163 164 179 175 150 70 71 71 72 73

T]

mPas

[1.3]« [1.2]a

[i.ir

* melting range

Table 2 Fraction solid (fs) as a function of temperature of LM4 for heating and cooling at 10 K mm"1

Heating Cooling

1.0 513 504

0.95 537 532

0.9 550 544

0.8 562 553

0.7 567 557

Fraction solid, fs 0.4 0.6 0.5 571 583 595 582 592 563

0.3 605 600

0.2 611 606

0.1 616 608.5

O 624 610

The difference in T1 values shown in Tables 1 and 2 is associated with the fact that Tliq is usually taken as the peak temperature whereas the temperature where the endotherm on heating returns to the baseline is used when calculating fs. Supercooling results in a decrease in T^ for the cooling cycle.

Al - LM5 (5182) 1

Chemical composition (mass %) Cu 0.15

Al 94

2

Cr 0.1

Fe 0.35

Mg 4.5

Mn 0.3

Si 0.2

Zn 0.25

Transitions

T801-575 0 C[I] DPSC measurements: Tsol = 542 0C [2]

Tliq = 6400 C[I] Tliq = 633 0C [2]

The latter values have been adopted. Two small bulges (at 90 0C and 490 0C) were observed in the Cp-T curve which could be the result of solid state transitions. 3

Density

P25 = 2650 kgm'3 [I]: Estimated (METALS) p25 = [2660] kgm 3 [3] 2 0 a (25-T C) = (23 + 1.1 x 10" T 0C) x 10"6 K'1. Density values given in Table 1 and Figure 1 were calculated from the measured values. Liquid alloy densities were calculated from METALS model [3] (1)

ps (kg.m"3) - 2650 - 0.231 (T - 25 0C)

(2)

Density, P (Kg m'3)

p^ (kg.nT3) = 2354-0.27 (T-633°C)

Temperature (0C)

Figure 1

Density of Al alloy LM5 as a function of temperature. (Use Equn6.1 to calculate properties in the 'mushy' region.)

4

Heat capacity (Cp) enthalpy (Hx-H25)

Richardson [2] measured Cp and enthalpy values using DPSC. The results are given in Table 1 and Figures 1 and 2, respectively. Cp25 = 0.91 JKV: Cp(O = 1-22 JKV AH^ = 358 JKV

Estimated (METALS)Cp25 = [0.92] JK'1 g 1 [3] Cp(O = [1.18] JKV [3] AH*18 = [375] JK'V [3]

Heat Capacity, Cp (Jg"1 K'1)

METALS model provided very good estimates of Cp and (H1-H25).

Temperature (0C)

Heat capacity of Al alloy LM5 as a function of temperature. (Use Equn 6.1 to calculate properties in the 'mushy' region.)

Enthalpy, H 7 -H 25 (Jg'1)

Figure 2

Temperature (0C)

Figure 3

Enthalpy of Al alloy LM5 as a function of temperature. (Use Equn 6.1 to calculate properties in the 'mushy' region.)

5

Thermal diffusivity (a) thermal conductivity (X)

(mV1)

Thermal diffusivity, lfia

Values for the thermal diffusivity of the solid alloy have been obtained using the laser pulse method, these are given in Table 1 and Figure 4. Thermal diffusivities of the solid did not vary very much with temperature. Values for the thermal conductivity shown in Table 1 and Figure 5 were calculated from these data. Thermal conductivities of the liquid alloy shown in Table 1 were estimated by assuming that (X™ /X1J1) for the alloy was identical to that for pure Al.

Temperature (0C)

1

(Wm' K" )

Thermal diffusivity of Al alloy LM5 as a function of temperature, A, •••, indicates estimated values. (Use Equn6.1 to calculate properties in the 'mushy' region.)

1

Thermal Conductivity^

Figure 4

Temperature (0C)

Figure 5

Thermal conductivity of Al alloy LM5 as a function of temperature, A, •••, indicates estimated values. (Use Equn 6.1 to calculate properties in the 'mushy' region.)

6

Viscosity

The viscosity values given in Table 1 were estimated by comparison with the viscosities of pureAlandLM25. 7

Fraction solid

Fraction Solid, fs

Richardson [2] only reported values (derived from DPSC measurements) for the heating cycle, these are given in Figure 6 and Table 2. Values for fraction solid, fs, obtained from the cooling curve were estimated by assuming that the cooling curve was displaced 10 0C from the heating curve.

Temperature (0C)

Figure 6

Fraction solid as a function of temperature; cooling at 10 Kmin"1 (estimated).

, O heating 10 Kmin"1;

, o,

References 1.

British and European aluminium casting alloys: their properties and characteristics, compiled R Hartley, publ. Assoc. of Light Alloy Refiners, Birmingham UK (1992).

2.

Richardson, M J. Private communication, NPL, Teddington (1999).

3.

Mills, K C; Day, A P; Quested, P N. Estimating the thermophysical properties of commercial alloys. Proc of Nottingham Univ - Osaka University Joint Symposium held Nottingham, Sept (1995).

Table 1 The recommended thermophysical properties for Al alloy LM5 Temp (0C) 25 100 200 300 400 500 542C 633° 633 700 800

Density, p (kgm-3) [2650]a [2636]a [2615]a [2592]a [2568]a [2540]a [2526]a

Cp (JK-1E1) 0.92 0.98 0.99 1.06 1.105 1.19 1.19

[2354]a [2336]a [2309]a

1.22 1.22 1.22

(H7-H25) (Jg-1) O 72 170 273 381 497 550 655 1013 1095 1217

X (Wm-1K'1) 85 103 116 128 133 139

106a Cm2S-1) [35]" 40 45 46.5 47 46 45

*1 (mPas)

[63]b [65]b [68]b

[22]b [23]b [24]b

[1.2]b [l.l] b [1.0]b

[ ]a = estimated by METALS model [ ] = estimated = melting range 0C [ ] = extrapolated value Date: March 1999

Table 2 Fraction solid (fs) as a function of temperature

Cooling, 10 Kmin"1 Heating, 10 Kmin'1

O 636 640

0.05 633 637

0.1 631 635

0.2 630 634

Temperature for fraction solid (fs) 0.4 0.3 0.5 0.6 0.7 627 623 620 615 608 631 627 624 620 613

0.8 600 607

0.9 585 596

0.95 568 585

1.0 527 542

The difference in T^ values shown in Tables 1 and 2 is associated with the fact that Tliq is usually taken as the peak temperature whereas the temperature where the endotherm on heating returns to the baseline is used when calculating fs. Supercooling results in a decrease in T^ for the cooling cycle.

Al - LM13 (4032) 1

Chemical composition (mass %)

Cu 0.9

Al 84.3

2

Fe 0.8

Mg 1.2

Ni 0.8

Si 12

Transitions Tsol = 532 0C [IJ T801 = 542 0C [2]

DPSC:

Tliq = 571 0 C [1] Tliq = 573°C[2]

The Cp-T curve showed a bump followed by a sharp increase in Cp above 480 0C; this may be due to premelting or alternatively to some structural transition in the solid.

3

Density

P25 = 2700 kgm"3: Estimated (METALS model) p25 = [2685] kgm"3 [4] P25 2680 kgm'3 [2] a (25-T 0C) = (16.5 + 1.5 x 10'2 T 0C) x 10'6 K'1 The recommended density values (based on p25 = 2690 kgm"3) are given in Table 1 and Figure 1. The values reported for the liquid alloy are based on the METALS model estimates (Equation 2). ps (kg.m~ 3 ) ^ 2690-0.19 (T-25°C) (1) (2)

Density, P (Kgm'3)

p e (kg.nT3) = 2482-0.27 (T-5730C)

Temperature (0C)

Figure 1

Density of Al alloy LM13 as a function of temperature. (Use Equn6.1 to calculate properties in the 'mushy' region.)

4

Heat capacity (Cp) enthalpy (Hx-H25)

Richardson [2] measured, Cp and (H1-H25) values using DPSC. These are given in Figures 2 and 3, respectively. Cp25 = 0.86 JK'V1 [2]: Estimated (METALS) Cp(I) =1.19 JKV [2]: AHftls = 489 Jg"1 (excluding small amount of premelting):

Cp25 = [0.87] JK"1^1 [3] Cp = [1.14] [3] AHfus = [413] Jg'1 [3]

Heat Capacity, Cp (Jg-1K'1)

Values for the solid calculated by METALS model were in good agreement but the estimated AHftls is appreciably lower than measured values. It can be seen from Figure 2 that Cp values increase from the smooth Cp-T curve above 300 0C, this may be due to a solid/solid transition and, consequently, possibly may contain enthalpy contributions to Cp. Hence estimated Cp values have been used to convert thermal diffusivity data. It can also be seen that there is a shoulder on the melting peak which could be associated with molecular arrangements in the solid or with premelting. The latter was assumed and the AHftls was derived assuming the enhanced Cp values above 480 0C were part of the fusion process.

Temperature (0C)

Figure 2

Heat capacity of Al alloy LM13 as a function of temperature, , o, recommended values; , apparent Cp values in transition range. (Use Equn 6.1 to calculate properties in the 'mushy' region.)

Enthalpy, H 7 -H 25 (Jg'1)

Temperature (0C)

FigureS

5

Enthalpy of Al alloy LM13 as a function of temperature, , o, recommended values; x, estimated values (METALS model). (Use Equn 6.1 to calculate properties in the 'mushy' region.)

Thermal diffusivity (a) thermal conductivity (A,)

(mV)

Thermal diffusivity, l6a

Values OfX 25 = 141 to 155 Wm-1K"1 have been reported for the alloy [4] the values depending on the thermal treatment. Thermal diffusivity values have been measured for the solid phase using the laser pulse method. The results are given in Table 1 and Figure 4. Thermal conductivity values shown in Figure 5 were calculated from recommended values of thermal diffusivity, density and Cp. Values for the liquid alloy were estimated by (i) extrapolating A to Tliq and (ii) assuming (A,™ /A1J1) was identical to that of pure Al.

Temperature (0C)

Figure 4

Thermal diffusivity of Al-alloy LM13 as a function of temperature; , o, recommended values; A9 , estimated values. (Use Equn 6.1 to calculate properties in the 'mushy' region.)

(Wm-1K'1)

Thermal Conductivity, ^

Temperature (0C)

Figure 5

6

Thermal conductivity of Al-alloy LM13 as a function of temperature; , o, recommended values; A, , estimated values. (Use Equn6.1 to calculate properties in the 'mushy' region.)

Viscosity

The values shown in Table 1 were estimated by comparison with Al and Al alloy LM25. 7

Fraction solid

Fraction Solid, fs

The fraction solid at various temperatures in the fusion range are given in Figure 6 and Table 2 for heating and cooling rates of 10 Kmin"1.

Temperature (0C)

Figure 6

Fraction solid, fs, as a function of temperature; ,O 9 heating 10 K min"1.

, o, cooling 10 K min"1;

References 1.

Aluminium and aluminium alloys, edited J R Davis, publ ASM, Materials Park, OH (1999).

2.

Richardson, M J. Private communication, NPL, Teddington (1999).

3.

British and European aluminium casting alloys, their properties and characterisation, compiled by R Bartley, publ. Assoc. Light Alloy Refiners, Birmingham (1992).

4.

Mills, K C; Day, A P; Quested, P N. Estimating the thermophysical properties of commercial alloys. Proc of Joint Symp. Nottingham Univ - Osaka University held Nottingham, Sept (1995).

Table 1 Recommended thermophysical properties of Al alloy LM13 T 0 ( C) 25 100 200 300 400 500 542° 573C 573 600 700 800

Density, p (kgm-3) 2690 2679 2662 2643 2622 2600 2592° a

[2482] [2473]a [2445]a [2417]a

Cp (JK-'g-1) 0.86 0.91 0.96 0.98 1.1 -

1.19 1.19 1.19 1.19

(H1-H25) (Jg-') O 66 160 257 359 472 551 1040 1072 1191 1310

X (Wm-1K'1) 139 152 164 169 161d

106a (Hi2S-1) 60 62 64 65 59

[147]b [64]" [64.5]b [66.5]b [68.5]b

[50]b [21.7]" [22]b [23]b [24]b

T! (mPas)

[1.5]b [1.45]b [1.35]b [1.25]b

[ ]a = estimated by METALS model [ ] = estimated = melting range = using estimated Cp

Table 2 Fraction solid values as a function of temperature for heating and cooling rates of 10 K min"1

Cooling Heating

O 568 578

0.05 566 576

0.1 564 575

0.2 562 574

0.3 560 572

Fraction solid, fs 0.4 0.5 0.6 559 557 554 570 568 564

0.7 550 561

0.8 544 557

0.9 537 552

0.95 532 549

1.0 517 542

The difference in T, values shown in Tables 1 and 2 is associated with the fact that Tliq is usually taken as the peak temperature whereas the temperature where the endotherm on heating returns to the baseline is used when calculating fs. Supercooling results in a decrease in T^ for the cooling cycle.

Al - LM25 1

2

Chemical composition

Al

Co

Cr

Cu

Fe

Mg

Mn

Ni

Si

Ti

Others

91.1

-

-

0.2

0.5

0.4

0.3

0.1

7.0

0.2

0.2

[1]

Transitions, melting range

T501 = 550 0C: Tliq = 615 0 C[I] Tsol - 567 0C: Tliq = 614 0C [2] and a transition, Ttr = 380 0C [2] were obtained by DSC. The latter values have been adopted.

3

Density (p), thermal expansion coefficient (a)

Solid: p25 = 2680 kg m-3 [I]: p25 = 2650 kg m'3 [2,3] Liquid: p= 2410 kg in3 [2,3] Linear thermal expansion coefficient a (20-100 0C) = 22 x IQ'6 K"1 [1] a (20-500 0C) = 26 x IQ-6 K-1 [3] for the solid and a = 3.6 x IQ'3 IC1 for the liquid. ps (kg.m~ 3 ) - 2680-0.212 (T-25°C)

(1)

p^ (kg.m~ 3 ) = 2401-0.264 (T-614 0C)

(2)

Volume expansion coefficient ((3) can be taken as 3 a . Estimated values [3] for the density (p25 = 2694 kg m"3) obtained with METALS model were in excellent agreement with experimental values. The values given in Table 1 for the solid phase were derived using the experimental density value and the estimated volume thermal expansion coefficient. Density measurements have recently been obtained using dilatometry by Henderson et al [4] and Morrell [5] and it can be seen from Figure 1 that there is good agreement between the results of these two studies for the heating curve and with values estimated by METALS model or both solid and liquid phases. Results obtained by Day [6] using Archimedean and Hydrostatic probe method are ca. 2% lower and higher respectively. Brooks [7] has obtained preliminary results with the maximum bubble pressure method which are 3-4% lower. The pressure of oxide films in contact with the probe, bob or the capillary may have been affected by the results of these studies. The values shown in Table 1 are based on the dilatometric measurements [2,3].

Density, P (Kg m"3)

Temperature (0C)

Figure 1

4

Density of LM25 as a function of temperature; , O5 recommended values, —, Henderson [4], •••, Morrell [5]; A, estimated using METALS model. (Use Equn 6.1 to calculate properties in the 'mushy' region.)

Heat capacity, enthalpy

Heat Capacity, Cp (Jg-1K"1)

Heat capacity and enthalpy have been measured by DSC [2]. The Cp results are shown in Figure 2 and this was followed by Cp peaks corresponding to the fusion region. A departure from Cp-T curve indicated that a solid state transition occured around 380 0C and between 567 0C and 607 0C (Figure 3). The values Cp(f) = 1.19 J K'1 g 1 for the liquid phase and AHftls = 425 ± 5 Jg"1 were obtained. Values for the apparent Cp in the fusion region (Figure 3) are not true Cp values and estimated Cp values should be used for the (solid + liquid) region. Enthalpy values are given in Figure 4.

Temperature (0C)

Figure 2

Heat capacity of LM25 as a function of temperature; , o, recommended values; x, estimated using METALS model; —, measured Cp app values. (Use Equn 6.1 to calculate properties in the 'mushy' region.)

Heat capacity, Cp (J g-1 Kr1)

Values of Cp have been estimated by MTDATA [8] and METALS models [3]; estimated values are in excellent agreement in the non-transitional range and the liquid phase (Cpl) =1.16 JK"1 g"1 and AHfos = 425 Jg"1 The values for Cp given in Table 1 are based on estimated values since Cp values recorded by DSC in the transition contain enthalpy contributions.

Temperature (0C)

Apparent Cp-T curves for the fusion region of LM25 obtained with various cooling rates; ; 10 K min"1; -—, -20 K min"1; , 4 O K min"1; ,80 K min"1.

EnWIaIPy1H1-H25 (Jg'1)

Figure 3

Temperature (0C)

Figure 4

5

Enthalpy (Hx-H25) of LM25 as a function of temperature. (Use Equn6.1 to calculate properties in the 'mushy' region.)

Thermal conductivity (A,), thermal diffusivity (a)

Thermal diffusivity measurements have been carried out by four laboratories [4,9,10,11], using the laser flash method. The measurements for the liquid phase were carried out holding the specimen in sapphire cassettes. The results of these studies are shown in Figure 5. Thermal conductivity values were calculated using estimated density and Cp values and are given in Figure 6. A value of A, = 150.6 Wm"1 has been reported [1] slightly lower than that derived from

Thermal diffusivity, 106a (mV)

laser flash measurements. This divergence in the solid state may reflect differences in (i) impurity levels, (ii) thermal and mechanical histories of the different specimens. However, the values for the liquid at 620 0C vary between a = 2.0 and 2.6 x 10"5 mV1, the results showing two sets of data in good agreement with each other. The higher values [3,10] were obtained with the same make of instrument and sample cells. For the lower values, Szelagowski [10] experienced problems with 'balling up' in the cells on other systems which may have affected the thickness of the sample. Preston [9] used a similar cell to Szelagowski. It is not possible to differentiate between the various results at this stage and so mean values have been adopted. Further work to resolve the source of this discrepancy is recommended.

Temperature (0C)

Thermal diffusivity of LM25 as a function of temperature, , Henderson; •••; Preston [9]; Szelagowski [1O]; A Monaghan [U]. (Use Equn6.1 to calculate properties in the 'mushy' region.)

Thermal conductivity, K (W rrr1 K~1)

Figure 5

Temperature ( 0 C)

Figure 6

Thermal conductivity of LM25 as a function of temperature; , o, recommended values; *; values calculated from the WFL Rule; A, estimated from (X /^) for pure Al; - - -, Henderson [4]; •••, Szelagowski [1O]. (Use Equn 6.1 to calculate properties in the 'mushy' region.)

Estimated values of the thermal conductivity of the solid were derived by calculating the electronic and lattice contributions to the thermal conductivity at 25 0C and applying a temperature dependence [3]. These values refer to a fully annealed state. As can be seen from Figure 6 the estimated values are in good agreement with the measured values. Values for the liquid were estimated [3] by (i) estimating the electrical conductivities of the liquid alloy and applying the Wiedemann-Franz Rule and (ii) extrapolating the A, for the solid phase A,m = 130 W mK"1 to Tliq and assuming that (A,™/X^) at the melting point was identical to that of Al. As can be seen from Figure 6, the values obtained by the first method were about 10% high but values obtained with the second method were in good agreement with experimental values.

6

Viscosity (r\)

Viscosity, rj (mPa s)

The viscosity of LM25 was measured using the oscillating viscometer [12] and the results are shown in Figure 7 and in Table 1. Estimated values [3] are in reasonable agreement with those obtained experimentally (r|m = 1.75 mPas compared with 1.38 mPas) especially when the fact that the scatter of experimental values for Al in the literature is ± 100% is taken into account.

Temperature (0C)

Figure 7

7

Viscosity of LM25 as a function of temperature; for LM 25; A, —; measured values for Al.

, o recommended values

Fraction solid (fs)

Values of the fraction solid (Figure 8 and Table 2) were determined from the temperature dependence of the evaluation of enthalpy of fusion; values were derived for different cooling rates. Fraction solid was also calculated using the MTDATA model to derive fs from Scheil equation and for equilibrium conditions shown in Figure 7.

Fraction Solid, fs

Temperature (0C)

Figure 8

Fraction solid as a function of temperature for alloy LM25; experimental results; o predicted by MTDATA [8].

,

, • • •,

References 1.

British and European aluminium casting alloys: their properties and characteristics, edited R Hartley, publ. Assoc. Light alloy refiners, Birmingham (1992).

2.

Richardson, M J; Hayes, D; Day, A P; Mills, K C: Final Report on Differential Scanning Calorimetry, PMP, CMMT, NPL, (1996).

3.

Mills, K C; Day, A P; Quested, P N: Estimating the thermophysical properties of commercial alloys. Proc. of Nottingham Univ. - Osaka Univ. Joint Symp. held Nottingham, Sept (1995).

4.

Henderson, J B; Blumm, J; Hageman, L: "Measurement of the properties of an aluminium-silicon casting alloy in solid and molten regions", Netzsch-Geratebau GmbH, Rept. TPS No 1-4E (1996) June.

5.

Morrell, R; Quested, P N: NPL Report CMMT(A)106 (1998).

6.

Day, A P: Results published in R F Brooks et al: Intl. J. Thermphys. 18 (1997) 471/480.

7.

Brooks, R F: Unpublished results, National Physical Laboratory (1998).

8.

Dinsdale, A T: Results obtained for PMPl programme.

9.

Preston, S D: Results obtained for PMP3 programme.

10.

Szelagowski, H; Taylor, R: to be published ISIJIntl. (1997).

11.

Monaghan, B J; Waters, M:, Laser liquid metal thermal diffusivity measurements. NPL Report, CMMT(D) 196, (1999).

12.

Andon, R J L ; Day, A P; Quested, P N; Mills, K C: Measurements of the viscosities of metals and alloys. Final Report PMP2 programme. CMMT, NPL (1996).

Table 1 Recommended thermophysical properties for LM25 Density kgm'3

Cp (Jg-1 K-1)

(H7-H25) (Jg-')

X(a) Wm'1 K'1

106a mV

t|(mPas)

25

2680

0.880

O

163

69

-

100

2662

0.921

68

165

67

200

2641

0.967

162

162

63

300

2620

1.011

261

155

60

380

2602

1.046

343

153

56

400

2600

1.055

364

153

55

500

2578

1.098

472

145

50

567"

2567

1.127

547

134

45

614a

2406

1.19

1025

65.8

23

1.38

700

2379

1.19

1144

67.9

24

1.2

800

2352

1.19

1263

70

25

1.1

900

2325

1.19

1382

71.9

26

1.0"

1000

2300

1.19

1401

73.9

27

0.9b

±3%

±3%

±3%

± 10%

± 10%

± 10%

Temp 0

(Q

Transition

AHfo = 425Jg-1 (a

' melting range

P3 = SOxIO- 6 K-'

p, = 116 x IQ-6K-1

extrapolated value

Table 2 Fraction solid for LM25 as a function of temperature for a cooling rate of -10 K min"1 fs

T

OG

O 611

0.05 609

0.1 607

0.2 600

0.3 590

0.4 577

0.5 571

0.6 570

0.7 569

0.8 568

0.9 567

0.95 565

1.0 550

The difference in T, values shown in Tables 1 and 2 is associated with the fact that Tliq is usually taken as the peak temperature whereas the temperature where the endotherm on heating returns to the baseline is used when calculating fs. Supercooling results in a decrease in T^ for the cooling cycle.

Al-IlOOF 1

Composition (mass %)

Cr

Al 98.8 2

Cu 0.10

Fe 0.1

Mg

Mn 0.05

Si 0.85

Ti

Zn 0.10

Transitions

DSC measurements: Tsol = 643 0C [I]: 3

Tliq = 648 0C

Density (p) P25 = 2710 kg m-3 [I]:

Estimated [Metals] = [2711] kg m'3

Taylor et al [1] measured mean thermal expansion coefficients by dilatometry for the solid, mushy and liquid phases. The estimated value for the liquid pm = 2395 kg m"3 at Tliq was in good agreement with the measured value pm = 2410 kg m"3. The density as a function of temperature [1] is given in Figure 1 and Table 1. (1)

p, (kg.nT3) - 2410-0.27 (T-648 0 C)

(2)

Density, P (Kg m'3)

ps (kg.nT3) = 2710-0.242 (T-25°C)

Temperature (0C)

Figure 1

4

Density of Al alloy HOOF as a function of temperature. (Use Equn6.1 to calculate properties in the 'mushy' region.)

Heat capacity (Cp) enthalpy (Hx-H25)

Taylor et al [1] measured Cp values for both heating and cooling cycles using DSC. The results are shown in Figure 2 and Table 1.

C P25 =0.91 JK- 1 B 1 [1] AHfos = 367 Jg 1 [1]

Estimated [Metals]

C^ =0.90 JK"1 g 1 AHfos = [389] Jg 1 Cptf) = [LlT]Jg- 1

Heat Capacity, Q (J K"1 g'1)

Estimated Cp values for the solid using METALS model were in excellent agreement and never deviated by more than 3% from the measured values. The estimated enthalpy of fusion was about 6% higher than the measured value. The adopted values for Cp for the liquid alloy were derived from the estimated Cp values since the measured values (ca 1.1 JK'1 g"1) due to Taylor et al [1] are reported on an insensitive scale.

Temperature (0C)

Figure 2

Heat capacity of Al alloy HOOF as a function of temperature. (Use Equn 6.1 to calculate properties in the 'mushy' region.)

Enthalpy, H T -H 25 (Jg'1)

Enthalpy (H1-H25) values given in Figure 3 and Table 1 were calculated from the adopted Cp values.

Temperature (0C)

Figure 3

Enthalpy (H7-H25) of Al alloy HOOF as a function of temperature. Equn 6.1 to calculate properties in the 'mushy' region.)

(Use

5

Thermal diffusivity (a) thermal conductivity (^)

(m2*1)

Thermal Diffusivity, I6a

Taylor et al [1] measured the thermal diffusivity using the laser flash method for both heating and cooling cycles. Results were obtained for both free-standing specimens and samples enclosed in sapphire cells. Differences in the results of about 12% were recorded which is probably caused by differences in the thermal and mechanical histories of the specimens. The results given in Figure 4 and Table 1 represent the higher values obtained with annealed samples.

Temperature (0C)

Figure 4

Thermal diffusivity of Al alloy HOOF as a function of temperature. (Use Equn 6.1 to calculate properties in the 'mushy' region.)

(Wm- K )

1

1

Thermal Conductivity^

Thermal conductivity values were calculated by Taylor et al [1] from the measured values of the thermal diffusivity, Cp and density, the results are shown in Figure 5 and Table 1.

Temperature (0C)

Figure 5

Thermal conductivity of Al alloy HOOF as a function of temperature, o, measured values; ®, *, values calculated by WFL Rule for solid and liquid phase, respectively. (Use Equn 6.1 to calculate properties in the 'mushy' region.)

Taylor et al [1] also measured the electrical resistivity of the alloy. Values of the thermal conductivity for the fusion region were calculated using the WFL Rule. It can be seen from Figure 5 that these calculated values were in agreement with the measured values. 6

Viscosity (t|)

The values given in Table 1 were estimated by comparison with the values for pure Al and LM25. References 1.

Taylor, R E; Groot, H; Goerz, T; Ferrier, J; Taylor, D L: High Temp.-High Pressure 30(1998)269/275.

Table 1 Recommended values for the thermophysical properties of Al alloy - HOOF T0C 25 100 200 300 400 500 600 643a 648a 648" 700 800 n

Density kgm' 3 2710 2700 2660 2640 2615 2595 2575 2567 2565 2410 2396 2369

= melting range

1

J K- V 0.91 0.93 0.975 1.00 1.03 1.08 1.14 [1.15]" [1.15]" 1.17 1.17 1.17 |»»

H7-H25 Jg 1 O 69 164 263 365 470 576 625 631 998 1059 1176

= extrapolated value

106a 2

Hl S

90 88 87 85.5 83 80 74 34.5 35 35b

X Wm'1 K-' 219 221 226 226 224 224 217 97 98 97 p

T| mPas

[1.15]' [1.05]° [0.9]c

[ ] = estimated value

A1-2024-T4 1

Composition (mass %) Al 92.0

2

Cr 0.10

Cu 4.4

Fe 0.50

Mg 1.5

Mn 0.6

Si 0.50

Ti 0.15

Zn 0.25

Transitions

DSC measurements: Tsol - 5380C [I]: Tliq = 632 0C [1] The as-received material exhibited an exothermic transition on heating which was absent in the cooling cycle. 3

Density P25 = 2785 kg m'3 [I]:

Estimated (Metals) = 2795 kg in 3

Taylor et al [1] measured the thermal expansion of the alloy using dilatometry for the solid, mushy and liquid alloys. The estimated density of the liquid at the liquidus temperature pm = 2476 kgm"3 is in good agreement with the measured value, pm = 2500 kgm"3. (1)

P^ (kg.m~ 3 ) = 2500-0.28 (T-6320C)

(2)

Density, P (Kgm"3)

ps (kg.nT3) = 2785-0.213 (T-25°C)

Temperature (0C)

Figure 1

Density of Al alloy 2024 as a function of temperature [I]. (Use Equn 6.1 to calculate properties in the 'mushy' region.)

4

Heat capacity (Cp) enthalpy (Hx-H25)

Taylor et al [1] measured Cp on the heating and cooling cycle using DSC. The results for the asreceived material showed a small exothermic peak on heating which was absent in the cooling curve. Since it was not known whether these enhanced Cp values contained enthalpy contributions, the smooth Cp-T values obtained on the cooling curve have been adopted in Figure 2 and Table 1. C P25 = 0.85 JK'1 g'1 [1] 297Jg 1 [1]

C

= [0.87] JK'1 g 1

AH*8 - [366JJg-1 Cptf) = [1.H]Jg 1 K- 1

Heat Capacity, Cp (J K'1 g'1)

AHfUS =

Estimated [Metals]

Temperature (0C)

Figure 2

Heat capacity of Al alloy 2024 as a function of temperature [I]. Equn 6.1 to calculate properties in the 'mushy' region.)

(Use

Enthalpy, HT - H25 (Jg"1)

The estimated Cp values obtained with METALS model were found to be in excellent agreement, never departing by more than 3% from the measured values. The estimated enthalpy of fusion value was appreciably higher (> 20%) than the measured value. The enthalpy (H1-H25) values shown in Figure 3 and Table 1 were obtained from integration of the recommended Cp-T relation. The Cp values for the liquid alloy are estimated values since the experimental values [1] are given on a very insensitive scale.

Temperature (0C)

Figure 3

Enthalpy (H1-H25) of Al alloy 2024 as a function of temperature [I]. (Use Equn 6.1 to calculate properties in the 'mushy' region.)

5

Thermal diffusivity (a) thermal conductivity (A,)

Thermal Diffusivity, 106a (m2s-1)

Taylor et al [1] measured the thermal diffusivity using the laser pulse method. It was found that values obtained on the cooling cycle were significantly higher than those derived on the heating cycle. Several sets of values were recorded for different cooling cycles. This behaviour was attributed to strain in the specimens resulting from the thermal and mechanical treatment. The values shown in Figure 4 represent the higher values obtained on cooling.

Temperature (0C)

Figure 4

Thermal diffusivity of Al alloy 2024 as a function of temperature. Equn 6.1 to calculate properties in the 'mushy' region.)

(Use

(Wm-1 K'1)

Thermal Conductivity, A.

Thermal conductivity values given in Figure 5 for the alloy were calculated from the measured values [1] for thermal diffusivity, Cp? and density.

Temperature (0C)

Figure 5

Thermal conductivity of Al alloy 2024 as a function of temperature; ,o from thermal diffusivity values; G£, ^9 calculated using WFL Rule. (Use Equn 6.1 to calculate properties in the 'mushy' region.)

Thermal conductivity values for the fusion region were calculated from the electrical resistivity values reported by Taylor et al [1] using the WFL Rule. It can be seen from Figure 5 that the calculated values are in agreement with the measured values although the estimated thermal conductivity for the solid at Tsol is about 8% low. 6

Viscosity

The viscosity values given in Table 1 were estimated by comparison with measured values for pure Al and LM25. References 1.

Taylor, R E; Groot, H; Goerz, T; Ferrier, J; Taylor, D L: High Temp-High Pressures 30(1998)269-275.

Table 1 Recommended values for the thermophysical properties of Al alloy - 2024 T0C 25 100 200 300 400 500 538a 632a 632 700 800

Density kgm"3 2785 2770 2750 2730 2707 2683 2674 2500 2480 2452

n

J K-1V 0.85 0.90 [0.95]c 0.97 1.00 1.08 1.10 1.14° 1.14° 1.14C

H7-H25 Jg 1 O 66 159 255 353 457 566 673 970 1048 1162

K

= melting range

106a Hi2S-1 74b 74 74 73 70 65 64 30 30 30b

X Win'1 K-1 175 185 193 193 190 188 188

*\ mPas

85.5 85 84

[1.3]c [l-2]c [1.1]"

Q

= extrapolated value

[ ] = estimated value

Al-3004 1

Chemical composition (wt%)

Al 97.2 2

Cu 0.2

Fe 0.43

Mg 1.0

Mn 1.0

Si 0.14

Zn 0.25

Transitions T801-629 0 C[I] T801 = 617 0C [2] MTDATA predicts

DPSC:

Tliq = 6540 C[I] Tliq = 656 0C [2] T801 = 5890C Tliq - 6440C

The latter values [2] have been adopted. Two bumps in the Cp-T curve were observed with maximum Cp values at 400 0C and 550 0C, which may be related to phase transitions.

3

Density

P25 = 2720 kgm'3 [1] Estimated [METALS] p25 = 2726 kgm"3 [3] a (25-T 0C) = 22.5 + 0.011 (T 0C) (1)

p^ (kg.m"3) - 2400-0.27 (T-6560C)

(2)

Density, P (Kg m"3)

ps (kg.m~ 3 ) - 2720-0.234 (T-25°C)

Temperature (0C)

Figure 1

Density of Al alloy 3004 as a function of temperature. (Use Equn6.1 to calculate properties in the 'mushy' region.)

Density values are given in Table 1 and Figure 1. Values calculated using METALS model are in good agreement and have been used to calculate the values for the liquid alloy (p™ .= 2400 kgm"3) at the liquidus temperature.

4

Heat capacity (Cp) enthalpy (H7-H25)

Richardson [2] determined Cp and enthalpy using DPSC. The results are given in Table 1 and Figure 2. Two "bumps" at ca 400 and 550 0C were observed in the Cp-T curve on the first heating cycle. However, after cooling at -10 Kmin"1 the second heating curve moved to 420 and 500 0C and a sharp peak occurred at ca 600 0C which could be due to either a solid/ solid transition or premelting. The results of the first run have been used for calculation. Cp25 = 0.90 JK'V1 [2]: Cp(O = 1.22 JKV: AHfos = 382 JKV-'

Estimated (METALS)

Cp25 - [0.90] JK^g 1 [2] Cp(O = [1-17] JKV P] AHftls =383 Jg 1 [2]

Heat Capacity, Cp (Jg'1 K"1)

The Cp and (H1-H25) values are given in Table 1 and Figures 2 and 3, respectively. Values of Cp in the temperature range (300-617 0C) (Figure 2) probably contain contributions from enthalpies of solid state transitions and consequently estimated Cp values should be used for the conversion of thermal diffusivity to conductivity.

Temperature (0C)

Figure 2

Heat capacity of Al alloy 3004 as a function of temperature; , o, recommended values; , run 1 on as-received material; ••• run 2 after cooling at -10 Kmin"1. (Use Equn6.1 to calculate properties in the 'mushy' region.)

Enthalpy, H 7 -H 25 (Jg'1)

Temperature (0C)

Figure 3

5

Enthalpy (H1-H25) of Al alloy 3004 as a function of temperature based on recommended values. (Use Equn6.1 to calculate properties in the 'mushy' region.)

Thermal diffusivity (a) thermal conductivity (A)

A value OfA 25 =165 Wm-1K"1 has been reported for the solid [I]. The thermal diffusivity of 3004 was measured by Szelagowski [4] using the laser flash method, the results are given in Figure 3. Thermal conductivities shown in Figure 4 were calculated from these values using the heat capacity and density values given in Table 1. The discrepancy in the thermal conductivity values at 25 0C could be a result of differences in thermal and mechanical histories of the samples. The thermal diffusivity of the solid is fairly constant over the temperature range studied. The thermal diffusivity values show a rapid decrease at 600 0C5 this would be expected to occur at 630 0C which suggests temperature measurements may be in error by 30 0C. Values were estimated by assuming (A™ /A™) was identical with that for pure Al, the estimated value for the liquid A™ = 80 Wm-1K"1 is 20% higher than the measured value.

(Hl2S-1)

Thermal diffusivity, 106a

Temperature (0C)

Thermal diffusivity of Al alloy 3004 as a function of temperature. (Use Equn 6.1 to calculate properties in the 'mushy' region.)

(Wm-1K"1)

Thermal Conductivity, A,

Figure 4

Temperature (0C)

Figure 5 6

Thermal conductivity of Al alloy 3004 as a function of temperature. (Use Equn 6.1 to calculate properties in the 'mushy' region.)

Viscosity

The viscosity of alloy 3004 was estimated by comparison with the experimental values for LM25 and pure Al and the results are given in Table 1. 7

Fraction solid

Values for the fraction solid, fs for both heating and cooling rates of 10 Kmin"1 are given in Figure 6 and in Table 2. Values of fs calculated by MTDATA which relate to equilibrium conditions agree well with fs values obtained in the heating cycle for most of the temperature range.

Fraction Solid, fs

Temperature (0C)

Figure 6

Fraction solid of Al alloy 3004 as a function of temperature; DPSC —, O9 cooling -10 Kmin"1; —, O heating +10 Kmin"1.

References 1.

Aluminium and aluminium alloys edited J R Davis publ ASTM Intl Materials Park OH5 USA (1993).

2.

Richardson, M J. Private communication, National Physical Laboratory, March 1999.

3.

Mills, K C; Day, A P; Quested, P N. Estimating the thermophysical properties of commercial alloys, Proc. Nottingham Univ - Osaka Univ, Joint Symp held Nottingham, Sept (1995).

4.

Szelakowski, H. PhD Thesis, Dept Materials Science, UMIST, Manchester (1999).

Table 1 Recommended thermophysical properties of Al alloy 3004

T (0C) 25 100 200 300 400 500 600 617" 656" 656 700 800 900 a

Density (kgm-3) 2720 2706 2685 2662 2638

2611 2587 2583 2572 2400 2388

Cp 1

0.90 0.94 0.99 1.004 (1.066)3 (1.11)" (1.16)a

1.22 1.22 1.22 1.22

2361 2334

1

(Jg1) O 69 165 265 372 486 605 625 670 1052 1105 1227 1349

(Jg- K- )

•

[ ]

1

(Wm- K' )

(Hi2S-1)

141 148 156 158 167 174 182 183

57.5 58 58.5 59 59.5 60 60.5" 61b

61 61 61 60

21 21 21 21

(c)

( ) = estimated using METALS model = melting range

106

X

(H1-H25) 1

T! (mPas)

[1.15]' [1.05]" [1.O]" [0.9]c

estimated value

Table 2 Fraction solid as a function of temperature for Al-3004 using heating and cooling rates of 10 Kmin ' Temp C Cooling Heating

O 0.05 654 • 649 658* 657*

0.1 649 656*

0.2 647 655

0.3 646 653

Fraction solid 0.4 0.5 0.6 645 644 643 652 650 648

0.7 641 645

0.8 638 643

0.9 634 637

0.95 629 634

1.0 597 617

The difference in T^ values shown in Tables 1 and 2 is associated with the fact that Tliq is usually taken as the peak temperature whereas the temperature where the endotherm on heating returns to the baseline is used when calculating fs. Supercooling results in a decrease in T^ for the cooling cycle.

A1-6061-T6 1

Composition (mass %) Cr 0.4

Al 96.45

2

Cu 0.3

Fe 0.7

Mg 1.0

Mn 0.15

Si 0.6

Ti 0.15

Zn 0.25

Transitions

DSC measurements: Tsol = 600 0C [I]: Tliq = 642 0C [1] 3

Density P25 = 2705 kg m'3 [I]:

Estimated (METALS) = [2725] kg m'3

Taylor et al [1] measured the thermal expansion of the solid, mushy and liquid alloys using dilatometry. The estimated density at the liquidus temperature pm = [2408] kgm"3 is in good agreement with the measured value, pm = 2415 kgm"3. (1)

p^ (kg.m~ 3 ) = 2415-0.28 (T-642°C)

(2)

Density, p (Kg m'3)

ps (kg.m"3) - 2705-0.201 (T-25°C)

Temperature (0C)

Figure 1 4

Density as a function of temperature [I]. (Use Equn 6.1 to calculate properties in the 'mushy' region.)

Heat capacity (Cp) enthalpy (Hx-H25)

Taylor et al [1] measured the Cp by DSC for the solid and liquid alloy for both heating and cooling cycles. Small Cp peaks were observed during the heating cycle which were absent in the cooling cycle. It is not known whether these enhanced Cp values contained enthalpy contributions, the smooth Cp-T values obtained on the cooling curve have been adopted and are given in Figure 2 and Table 1.

C P25 = 0.87JK-Ig-I [i] AHfos = 336Jg-I [i]

Estimated [Metals]

C

= [0.89] JK'l g-1 = [38O]Jg-I AH CpW = [1.17] Jg-I K-I ftls

Heat Capacity, Cp (J K"1 g"1)

Estimated Cp values were in good agreement with the measured values, never deviating by more than 3%. The estimated enthalpy of fusion was 15% higher than the measured value. The Cp values for the liquid alloy were based on estimated values since the measured values are reported [1] on a very insensitive scale.

Temperature (0C)

Figure 2

Heat capacity of Al alloy 6061 as a function of temperature [I]. (Use Equn 6.1 to calculate properties in the 'mushy' region.)

Enthalpy, H 7 -H 25 (Jg'1)

Enthalpy (Hx-H25) values shown in Figure 3 and Table 1 were derived from the recommended Cp values and the measured enthalpy of fusion.

Temperature (0C)

Figure 3

Enthalpy (H7-H25) of Al alloy 6061 as a function of temperature [I]. (Use Equn 6.1 to calculate properties in the 'mushy' region.)

5

Thermal diffusivity (a) thermal conductivity (A,)

Thermal Diffusivity, 106a (m2 s'1)

Taylor et al [1] measured the thermal diffusivity for both heating and cooling cycles using the laser pulse method. The results for the solid were obtained for both free-standing samples and specimens held in sapphire cells. Differences of up to 12% were recorded which probably reflect the differences in the thermal and mechanical histories of the specimens. The results shown in Figure 4 and Table 1 represent the higher values obtained with annealed samples.

Temperature (0C)

Figure 4

Thermal diffusivity of Al alloy 6061 as a function of temperature. Equn 6.1 to calculate properties in the 'mushy' region.)

(Use

(Wm- IC )

1 1

Thermal Conductivity, K

Thermal conductivity values given in Figure 5 were calculated from the measured values [1] for thermal diffusivity, Cp, and density.

Temperature (0C)

Figure 5

Thermal conductivity of Al alloy 6061 as a function of temperature; o, , derived from thermal diffusivity values; ^9 ^, calculated using WFL Rule for solid and liquid states, respectively. (Use Equn 6.1 to calculate properties in the 'mushy' region.)

Thermal conductivity values were calculated for the fusion region using the electrical resistivity data reported by Taylor et al [1] and the WFL Rule. It can seen from Figure 5 that the calculated values are in agreement with the measured values. 6

Viscosity

The viscosity values given in Table 1 were estimated by comparison with measured values for pure Al and LM25. References 1.

Taylor, R E; Groot, H; Goerz, T; Ferrier, J; Taylor, D L: High Temp-High Pressures 30(1998)269-275.

Table 1 Recommended values for the thermophysical properties of Al alloy - 6061-T6 T0C 25 100 200 300 400 500 600a 642a 642a 700 800 n

Density kgm"3 2705 2695 2675 2655 2635 2610 2590 2580 2415 2400 2372

= melting range

1

J K-'V 0.87 0.95 0.98 1.02 1.06 1.15 1.16 [1.16]b 1.17C 1.17° 1.17C V\

H1-H25 Jg 1 O 69 166 266 370 480 596 [645]b 981 1049 1166

= extrapolated value

106a Hi2S-1 76 77.5 78 76 75 66.5

X Wm'1 K-1 195 203 211 212 225 200

1 mPas

32 32.5 33b

90 91 92

[1.15]' [1.05]c [1.O]"

p

= estimated value

A1-7075-T6 1

Composition (mass %) Cr 0.2

Al 88.7

2

Cu 1.6

Fe 0.50

Mg 2.5

Mn 0.30

Si 0.4

Ti 0.2

Zn 5.6

Transitions

DSC measurements: T50, = 532 0C [I]: Tliq = 628 0C [1] 3

Density P25 = 2805 kg m'3 [I]:

Estimated (METALS) p25 = [2815] kg m"3

Taylor et al [1] measured the thermal expansion of the of the alloy in the solid, mushy and liquid states using dilatometry. The estimated density of the liquid at the liquidus temperature pm = [2493] kgm"3 is in good agreement with the measured value, pm = 2500 kgm"3. (1)

pe (kg.nT3) = 2500-0.28 (T-6280C)

(2)

Density, p (Kg m"3)

ps (kg.m"3) - 2805-0.224 (T-25°C)

Temperature (0C)

Figure 1

4

Density of Al alloy 7075 as a function of temperature. (Use Equn6.1 to calculate properties in the 'mushy' region.)

Heat capacity (Cp) enthalpy (Hx-H25)

Taylor et al [1] measured the Cp by DSC for both heating and cooling cycles. Small Cp peaks

were observed on the heating cycle which were absent in the results obtained on the cooling cycle. Since it was not known whether the Cp values contained small enthalpy contributions, the results obtained during the heating cycle have been adopted and are given in Figure 2 and Table 1. C P25 = 0.85 JK-1 g'1 [1] AHfus = 332j g -i t l ]

Estimated [METALS] C P25 = [0.86] JK'1 g 1 AHfuS = [358] jg-i CpW = [LH]Jg 1 K" 1

Heat Capacity, Cp (JIC1Q'1)

The estimated Cp values obtained with METALS model were in good agreement with the measured values, never deviating by more than 3%. The estimated enthalpy of fusion was 7% higher than the measured value. The Cp values for the liquid alloy were based on estimated values since the measured values [1] are presented on a very insensitive scale [I].

Temperature (0C)

Figure 2

Heat capacity of Al alloy 7075 as a function of temperature. (Use Equn 6.1 to calculate properties in the 'mushy' region.)

Enthalpy, HT-H 25 (Jg 1 )

Enthalpy (H1-H25) values shown in Figure 3 and Table 1 were derived from the recommended Cp values and the measured enthalpy of fusion.

Temperature (0C)

Figure 3

Enthalpy (H1-H25) of Al alloy 7075 as a function of temperature. Equn 6.1 to calculate properties in the 'mushy' region.)

(Use

5

Thermal diffusivity (a) thermal conductivity (X)

Thermal Diffusivity, 106a (m 2 s 1 )

Taylor et al [1] measured the thermal diffusivity using the laser pulse method. The results obtained on the cooling cycle were significantly higher than the results obtained on heating the as-received sample. This was attributed to differences in the strain of the specimen resulting from differences in mechanical and thermal treatment of the specimen. The results shown in Figure 5 and Table 1 represent the higher values obtained with annealed specimens.

Temperature (0C)

Figure 4

Thermal diffusivity of Al alloy 7075 as a function of temperature. Equn 6.1 to calculate properties in the 'mushy' region.)

(Use

(Wm-1IC1)

Thermal Conductivity, A,

Thermal conductivity values given in Figure 5 were calculated from the measured values [1] for thermal diffusivity, Cp? and density. Values of the thermal conductivity around the fusion region were calculated from the electrical resistivity values reported by Taylor et al using the WFL Rule. It can be seen from Figure 5 that the calculated values are in good agreement with the measured values for the liquid phase but are about 10% low for the solid at the solidus temperature.

Temperature (0C)

Figure 5

Thermal conductivity of Al alloy 7075 as a function of temperature; , o; derived from thermal diffusivity values; ^, ^, calculated using WFL Rule for solid and liquid phases, respectively. (Use Equn 6.1 to calculate properties in the 'mushy' region.)

6

Viscosity

The viscosity values given in Table 1 were estimated by comparison with measured values for pure Al and LM25. References 1.

Taylor, R E; Groot, H; Goerz, T; Ferrier, J; Taylor, D L: High Temp-High Pressures 30(1998)269-275.

Table 1 Recommended values for the thermophysical properties of Al alloy - 7075 T0C 25 100 200 300 400 500 532a 628a 628a 700 800 a

Density kgm"3 2805 2795 2770 2750 2725 2700 2692 2500 2480 2452

= melting range

1

J K- V 0.85 0.91 0.96 0.98 1.04 1.10 1.11 [1.13]" 1.13° 1.13° 1.13°

Hx-H25 Jg 1 O 66 160 257 358 465 501 [608]b 1000 1081 1194

[ ] = extrapolated value

106a Hi2S-1

T! mPas

73 74 72 69 66 64.5

A. Wm-' K'1 186 197 194 196 196 193

30 30 30b

85 84 83

[l-3]c [l-2]c [1.1]«

[ ]c = estimated value

Co Pure Cobalt 1

Transitions, melting point

(Cph) -» (fee) mp= 1495 0C [1] 2

T; = 422 0C

[1]

Curie temperature = 1123 0C [1]

Density (p) thermal expansion coefficient

P25 (solid) = 8862 kg m'3 [15]

a (25-900 0C) = 16.7 x 10'6 K'1 [15]

The density as a function of temperature is given in Figure 1 and Table 1. The density temperature relationship for the liquid recommended by Iida and Guthrie [2] is very similar to that recommended by Watanabe et al [5]. The density decrease at the melting point is 5.5%. (1)

p^ (kg.nT3) = 7750-1.1 (T-1495°C)

(2)

Density, p (Kg rrr3)

ps (kg.m~3) - 8862 - 0.443 (T-25°C)

Figure 1 3

Temperature (0C) Density of pure cobalt as a function of temperature.

Heat capacity (Cp) enthalpy (H7-H25)

The heat capacity and enthalpy data are given as functions of temperature in Figures 2 and 3, respectively and in Table 1. There is a sharp increase in Cp culminating in a maximum at 1123 0C which corresponds to the Curie Temperature. Dinsdale [1] reported: AHS- = 7.25Jg-1Il] AH fos = 275 Jg-![l] Cp(I) = 0.667Jg-1K-Ml]

Heat capacity, CP (J g'1 K"1)

Temperature (0C) Heat capacity of pure Co as a function of temperature.

EHtHaIPy 7 Hi-H 25 (Jg-" 1 )

Figure 2

Temperature ( 0 C) Figure 3

4

Enthalpy of pure Co as a function of temperature.

Thermal conductivity (A,) thermal diffusivity (a)

Thermal conductivity data reported for the solid and liquid phase are given in Figure 4 and Table 1.

Thermal conductivity, A (W m~1 K~1)

Temperature (0C)

Figure 4

Thermal conductivity of Co as function of temperature; , o, recommended [ ]; - -, Zinovyev [4]; A5 Ostrovskii [5], 1%) [15]. Recommended values for the liquid: pe = 2560 - 0.30 (T-Tm) kgm"3

(1)

Density (kg/m3) Density (kg/m3)

Temperature (0C)

(b)

Figure 1

Temperature (0C)

Density of a) Solid [15] and b) Liquid silicon as a function of temperature (a)—, Rhim [3,12,13] Recommended; (b) [4,5], — Recommended.

3

Heat capacity (Cp) enthalpy (H1-H25)

The heat capacity (Cp) and enthalpy values reported by Dinsdale [1] have been adopted and are given in Figures 2(a) and (b) respectively. Cp25(s) = 0.712 JKV C p (*) = 0.968 JKV AH615 - 1787Jg-1: ASft's = 1.06 JKV

103 Heat Capacity (JK~1 g~1)

Rhim et al [12,13] reported a value of Cpm = 0.911 JK'V from Cp/s values obtained by an analysis of cooling curves and using a value of eTO = 0.18 (which is 6% lower than the recommended value).

Enthalpy (HT-H25) J g~1

Temperature (0C)

Temperature (0C)

(b)

Figure 2

(a) Heat capacity and (b) enthalpy (H1-H25) as functions of temperature for silicon.

4

Thermal diffusivity (a) conductivity (A,)

Thermal Conductivity (Wrrr1 K~1}

Touloukian [2] reported values for the thermal conductivity of solid silicon and values have been derived by Yamasue et al [16], Glassbrenner et al [17] and Fulkerson et al [18]. The results for the solid state are shown in Figure 3.

Temperature (0C)

Figure 3

Thermal conductivity of solid silicon as a function of temperature; •, Yamasue [16]; D Glassbrenner [17]; O 9 Fulkerson [18]; A, Beers [19]; •, Yamamoto [2O]; A Kimura [7,8,21].

Details of the measurements carried out on molten silicon are given in Table 2 and Figure 4. It can be seen that the results of the various investigations are in good agreement and with the values calculated from electrical conductivity using the WFL Rule. Recommended values for the liquid: A,, = 58.2 - 2.5 x 10'2 (T-1414 0C):

(2)

a, = 2.33 x IQ-5 + 1.5 x IO"8 (T-1414 0C) m2 s'1

(3)

Thermal Conductivity (Wrrr1 K~1) Thermal Diffusivity (x104 m2/s)

Temperature (0C)

(b)

Figure 4

Kimura(21) Solid,Yamamoto (20) Liquid,Yamamoto (20)

Temperature (0C)

(a) Thermal conductivity and (b) thermal diffusivity; liquid silicon as a function of temperature.

5

Electrical conductivity (a)

Resistivity (p, ohm cm)

Electrical resistivity (I/a) values have been reported by Glazov [22], Kimura [7,8,23], Schnyders and van Zytfeld [24]; the results are reported in Figure 5.

Temperature (0C)

Figure 5

6

Electrical resistivities (1/cr) of liquid silicon as a function of temperature; +, Kimura [7,8,23]; •, Schnyders [24]; •, Glazov [22]. (Note: 100 ju ohm cm = 1 ohmm)

Viscosity (r|)

Viscosities have been reported for liquid silicon by several investigators [5,25,26,27]. The results, shown in Figure 6, show an appreciable amount of scatter. This can be attributed to two factors [28]; (1) the type of analysis used to obtain the viscosity from the damping data recorded with the oscillating viscometer; the modified Roscoe equation has been reported [28] to be superior to the Shvidovski and Knappwost equations; (2) if the crucible is non-wetting to the liquid metal there will be slip at the crucible wall which would lead to an erroneously low value for the apparent viscosity.Kimura et al [7,8,26] reported that viscosity values obtained using 'wetting' SiC crucibles were 20% higher than those recorded with a 'non-wetting BN crucible. Kimura, Sasaki and Tereshima [8,26] have reported that changing from the Shvidovski approach to the Roscoe equation resulted in an increase in viscosity of 0.2 mPas or 35%. The crucible used by Kimura et al [8,26] had a relatively small (height/radius) ratio and it was not stated whether these workers applied corrections for end effects. Sato et al [27] carried out viscosity measurements using crucibles fabricated from a variety of materials. Their results (i) showed some variation and (ii) were lower than those reported by other workers. The average of these values has been tentatively adopted.

Viscosity (mPas)

Average viscosity (mPas) Sato Glazov Kakimoto Sasaki SiC Sasaki PBN Linear (average viscosity (mPas))

100OT (0C)

Figure 6

7

The viscosity (on a logarithmic scale) as a function of the reciprocal temperature (0C"1); •, average viscosity Sato [27]; D, Glazov [5]; ••••••• Kakimoto [25]; O 9 Sasaki, Kimura [8,26] with SiC crucible; A, with PBN crucible.

Surface tension (y)

The surface tension (y) and its temperature dependence (dy/dT) have been measured by a large number of workers [29-38]. Keene [38] noted that the values tended to fall into two bands and he suggested that (i) high values of y and (dy/dT) pertained to the pure element with a low p 02 and (ii) the lower values pertained to oxygen-saturated silicon. There have been a considerable number of investigations since Keene's review [7,8,39-46] and the results are in agreement (Figure 7) with Keene's proposal since most of the values of (i) y are around 825 mNm"1 or (ii) y are around 730-740 mNm"1 i.e. close to those attributed to oxygen-saturated silicon.

Surface Tension (mN/m)

Temperature (0C)

Figure 7

Recently reported values of the surface tension of liquid silicon as a function of temperature; +, Kimura [7,8]; •, Przborowski [39];» Kawasaki [43]; A, Chung [42]; -, Niu [44]; •. Huang [41]; •, Rhim [12].

The effect of p 02 on y and (dy/dT) was investigated by Niu et al [43,44] the results are shown in Figure 8a and 8b, respectively. The recommended values are ym = 825 mNm'1

Surface Tension (mN/K)

oxygen-saturated Si:

calculated calculated

yT = 730 - 0.104 (T-1414 0C) mNm'1

(4)

Temperature coefficient of Surface Tension (mN/mK)

pure Si:

log P02 (MPa) log P02 (MPa)

Figure 8

(a) Surface tension y and (b) (dy/dT) as functions of partial pressure of oxygen [44,45].

9

Emissivity (s)

Normal Spectral Emissivity

Spectral emissivities (sx) have been reported for both the solid and liquid [47-54] phases. The results are given in Figure 9. The lower values due to Watanabe et al [47] have been adopted since reflections from radiation shields will tend to increase the apparent emissivity. The total hemispherical emissivity (s^) values reported by Rhim et al [12,13] are consistent with these selected values of 8^.

Normal Spectral Emissivity

Wavelength (nm)

(b)

Figure 9

Wavelength (nm)

The normal spectral emissivity of silicon as a function of wavelength for (a) solid silicon D, Aoyama [54] —•—, Watanabe [47]; •, Lampert [5O]; A9 Takasuka [53] ---o-- , Drude model and (b) liquid silicon; +, Watanabe [47], •, Jellison [51]; •, Krishnan [52]; A, Takasuka [53]; D, Shvarev [48]; O Aoyama [54].

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Touloukian, Y S. Thermophysical Properties of High Temperature Solid Materials, Macmillan, New York, NY, USA (1967) VoI 1.

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Ohsaka, K; Chung, S K; Rhim, W K. Appl. Phys. Lett. 70 (1997) 423.

4.

Lucas, A D. Mem. Sd. Rev. Met. 61 1964 1.

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Glazov, V; Chizhevskaya, S; Glagoleva, N. Liquid Semiconductors, Plenum New York, NY US A 1969.

6.

Sasaki, H; Tokizaki, E; Terashima, K; Kimura, S. Jpn J. Appl. Phys. 33 (1994) 6078.

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Kimura, S; Terashima, K et al; Proc. 4tn Asian Thermophys. Prop. Conf., Tokyo, Sept 1995 Paper AIaI.

8.

Kimura, S; Terashima, K. J. Cryst. Growth 180 (1997).

9.

Sasaki, H; Tokizaki, E; Terashima, K; Kimura, S. J. Cryst. Growth 139 (1994) 225.

10.

Sasaki, H; Tokizaki, E; Terashima, K; Kimura, S. Jpn. J. Appl. Phys. 33 (1994) 3803.

11.

Langen, M; Hibiya, T; Eguchi, M; Egry, I. J. Cryst. Growth 186 (1988) 550.

12.

Rhim, W K; Chung, S K; Rulison, A J; Spjut, R E. Thermophys. Prop. Tokyo, Sept 1995 Paper C2al.

13.

Rhim, W K; Chung, S K; Rulison, A J; Spjut, R E. Intl. J. Thermophys. 18 (1997) 459.

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Niu , Z et al. J. Jpn. Cryst. Growth 24 (1997) 369.

15.

Mills, K C; Courtney, L. ISIJIntl. 40 (2000) S130.

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Yamasue, E; Susa, M; Hayashi, M; Fukuyama, H; Nagata, K. High Temp. High Press. In press.

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22.

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Niu, Z; Mukai, K; Shiraishi, Y; Hibiya, T; Kakimoto, K. Proc. 4th Asian Conf. Thermophys. Prop. Tokyo, Sept 1995 PaperBlcS.

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51.

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52.

Krishnan, S; Weber, J K; Nordine, P C; Schiffman, R A; Hauge, R H; Margrave, J L. High Temp. ScL 30 (1991) 137.

53.

Takasuka, E; Tokizaki, E; Terashima, K; Kimura, S. Jpn. J. Appl Phys. 34 (1995) 3426.

54.

Aoyama, T; Takamura, Y; Kuribayashi, K. Jpn. J. Appl. Phys. 37 (1998) L687.

Table 1 Experimental details of density determinations of molten silicon Reference

Method

Lucas 141 Glazov [5] Kimura [6101 Langen [11]

AM

Rhim [3,12,13]

LD

Niu [14]

Container/ Probe

Temp range 0 C

Al7O1

1410-1650 1450-1640 1415-1650

2526 2530 2570

0.352 0.35 0.20

1160-1500

2520

0.35

300-1530

2580

0.171

0.161 x 10'J

2530 2560 2520

0.168 0.169

0.174 x 10-j 0.175 x ID'3

AM

SiC

LD

None (EML) None (ESL)

SD

Results (kgm"3) = pm - bAT* - CAr

pTm

P-

BN

b

C

*A - (T-Tm): Methods: AM = Archimedean; LD = levitated drop; SD = sessile drop EML = electromagnetic levitation; ESL = electrostatic levitation

Table 2 Experimental details of the measurement of thermal diffusivity (a) and thermal conductivity (X) of liquid silicon Reference

Yamamoto F201 Kimura [7,8,21]

Method

Container material

Temp range OC

Analysis method

LP

SiC

25-1456

tO.5

LP

SiO2 Quartz

1320-1500

(i) tQ.5 for radiation (ii) Curve

Results aj = am + b(Tm-T)m 105am (m^s- 1 ) 2.28

10 5 b (m2 s -l) 0.06 x 10-2

2.38

0.15 XlO' 2

fitting

Yamasue [16]

Methods:

HW

Al2O3 (Pt coated SiO7.)

1427-1351

Ar, ^surface > 1 base

LP = laser pulse; HW = hot wire method

Wn = 56.5 Wm-I K-1

Table 3 Recommended values for thermophysical properties of silicon 1 Temperature P (kgm"3) Cp (Jg- K-) 0 C 2330 0.712 25 0.770 2328 100 2325 0.820 200 2323 0.860 300 2320 0.877 400 2317 0.897 500 2314 0.916 600 2313 0.932 700 2309 0.949 800 0.964 2306 900 2304 0.980 1000 2302 0.995 1100 2299 1.010 1200 1.024 2296 1300 2294 1.037 1400 2293 1.040 1414 2560 0.968 1414 2534 0.968 1500 2504 0.968 1600

H1-H25 (Jg-1) O 56 136 220 306 395 485 578 672 768 865 964 1064 1165 1268 1283 3070 3153 3251

Jl (Wm-1K-') 105a(m2s-') TI (mPas) 141 108 82 66 50 42 38 32 28 24 22 21 20 19 18

8.5 6.0 4.3 3.3 2.45 2.02 1.8 1.48 1.28 1.08 0.97 0.91 0.86 0.81 0.76

58.2 60.4 62.9

2.33 2.46 2.60

0.58 0.52 0.51

Ti Pure Titanium 1

Transitions, melting range (cph) -» (bcc) - Ttr - 882 0 C [1] mp = 16680C [1]

2

Density (p) thermal expansion coefficient (a) P25(SOHd)

=

4540 kg m-3 [2]

a = 11 x 1(T6

K'1 [2]

The density-temperature relation is given in Figure 1. Density temperature relations for liquid Ti have been recommended by Iida and Guthrie [2] (p - 4130 - 0.223(T - 1668 0C) kg m'3) and by Watanabe et al [3] (p = 4140 - 0.226 (T 1668 0C) kg m"3) by Vinet [13] (p = 4150 kg m"3 at the melting point). Mean values were used to derive the following equations: ps (kg.nT3) - 4540 - 0.150 (T-25°C)

(1)

pc (kg.m~ 3 ) - 4140-0.225 (T-1668°C)

(2)

Density, P (Kg m"3)

There is a 3.6% decrease in density at the melting point on the basis of the data given in Table 1.

Temperature (0C) Figure 1

Density of pure Ti as a function of temperature.

3

Heat capacity (Cp) enthalpy (Hx-H25)

The heat capacity and enthalpy values are given in Figures 2 and 3 respectively, and in Table 1. Dinsdale [1] reported the following values: AH* 2 = 87Jg-' AHJT68 = 295Jg-1 = 0.965Jg 1 K- 1

Heat Capacity, Cp (J g'1 KT1)

CpCO

Temperature (0C) Heat capacity of pure Ti as a function of temperature [I].

Enthalpy, H 7 -H 25 (Jg'1)

Figure 2

Temperature (0C) Figure 3

Enthalpy of pure Ti as a function of temperature [I].

(Wm-1K'1)

Thermal conductivity (A,) thermal diffusivity (a)

Thermal Conductivity, A

4

Temperature (0C)

Figure 4

Thermal conductivity of solid Ti as a function of temperature; - - Filippov [8]; -•-, Zinovyev [6]; ••••, Zinovyev [7]; ^9 value calculated from WFL Rule.

Thermal conductivity values for (3-phase solid Ti and liquid Ti [5-8] are given in Figure 4. The most recent investigation indicated a slight increase in conductivity on melting. Values calculated from electrical resistivity data and the WFL Rule are slightly lower and showed a small increase in A, on melting. The values suggested by Mills et al [5] are adopted. A,™ =31 Wm-1K"1 :A,7 - 31 WnT1K'1

Thermal Diffusivity, 106a (mV)

Thermal diffusivity values shown in Figure 5 were calculated from recommended values of A, Cp and p.

Temperature (0C) Figure 5

Thermal diffusivity of Ti as a function of temperature.

5

Viscosity (TI)

Iida and Shiraishi [10] recommend a value of r|m = 2.2 mPas based on the measurements of Agaevetal [U]. 6

Surface tension (y)

Keene [12] collated the surface tension values for pure titanium and did not recommend a value of y"1 at the melting point since values varied between 1650 to 1390 mNm"1. Vinet [13] reported a value 1525 mNm"1 using the drop weight method in a vacuum with a residual pressure of 10"7 mbar. Eustapopoulos et al [14] estimated a temperature coefficient of -0.28 mNm"1 K"1. The principal problem is that titanium has a large solubility for oxygen and it is difficult to remove the oxygen from the metal. Consequently, it is difficult to recommend a value of y and (dy/dT) unless the soluble oxygen concentration is stated. The value given by Vinet [13] is adopted but may be subject to significant error as a result of oxygen solubility. yc (mNm"1) = 1525 - 0.28 (T-1668° C)

7

(3)

Emissivity

Shiraishi [15] reported the following values for the spectral emissivity, B^ at 0.65 |tim for a smooth surface of Ti: T 0C (sj: 750 (0.505): 1000 (0.485): 1200 (0.47): 1550 (0.45). Shiraishi [15] also reported the following values for the total normal emissivity S1^ Polished surface: Oxidised surface:

T 0C (eTO): 500 (0.20): 1000 (0.36) T 0C (STO): 1000 (0.60)

and Touloukian cites for a polished surface T 0C (STN): 1300 to 1500 0C (0.42). References 1.

Dinsdale, A T: SGTE data for pure elements. CALPHAD 15 (1991) 317/425.

2.

Touloukian, Y S: Thermophysical properties of high temperature solid materials: VoI 1 Elements, publ. Macmillan, New York (1967).

3.

Iida, T and Gurthrie, R I L : The physical properties of liquid metals. Clarendon Press, Oxford (1988).

4.

Watanabe, S; Ogino, K and Tsu, Y: Handbook of physico-chemical properties at high temperatures, edited by Y Kawai and Y Shiraishi, publ. ISIJ, Tokyo (1988): Chapter 1.

5.

Mills, K C; Monaghan, B J and Keene, B J: Intl. Materials Review 41 (1996) 209/242.

6.

Zinovyev, V E: High temperature transport properties of metals, publ. Metallurgiya, Moscow (1984).

7.

Zinovyev, V E; Polev, V F; Taluts, S G; Zinovyeva, G P and Ilinykh, S A: Phys. Met. Metallog. 61 (6) (1986) 85/92.

8.

Filippov, L P: Intl. J. Heat Mass Transfer, 16 (1973) 865/885.

9.

Seydel, U and Fucke, W: J. Phys. F., Met. Phys. 10 (1980) L203/L206.

10.

Iida, T and Shiraishi, Y: as in ref 4, Chapter 4.

11.

Agaev, A D; Kostikov, V I and Bobkovski, Y N: Izv. Akad. Nauk SSSR, METALLY (1980) (3) 43.

12.

Keene, B J: Intl. Materials Review 38 (1993) 157/192.

13.

Vinet, B and Garandet, J P: Proc. Intl. Conf. on High Temperature Capillary held Smolenice Castle, May 1994, edited N Eustathopoulos, publ. Reproprint, Bratislava, 1995, pp 223-227.

14.

Eustapopoulos, N; Drevet, B and Ricci, E: J. Crystal Growth, 191 (1998) 268/274.

15.

Shiraishi, Y: as in ref 4, Chapter 10.

Table 1 Recommended thermophysical properties for pure Ti

T 0 C 25 100 200 300 400 500 600 700 800 882b 882" 900 1000 1100 1200 1300 1400 1500 1600 1668C 1668° 1700 1800

PT kgm'3 4540 4529 4514 4499 4484 4469 4454 4439 4424 4412 4412 4409 4394 4379 4364 4349 4334 4319 4304 4294 4140 4133 4110

CP Jg1 K-1 0.522 0.549 0.580 0.601 0.622 0.643 0.661 0.685 0.703 0.718 0.612 0.614 0.626 0.641 0.662 0.689 0.708 0732 0.760 0.783 0.965 0.965 0.965

(H1-H25) Jg1 O 40 97 156 217 280 346 413 483 540 627 638 700 763 828 895 965 1037 1112 1189 1484 1515 1611

10" a mV 8.65 8.7 7.3 7.1 6.7 6.5 6.3 6.0 5.9 6.6 7.7 7.8 8.1 8.4 8.6 8.7 9.0 9.1 9.2 9.2 7.8 7.8 7.8

X Wm'1 K-' 20.5 20 19.2 19 18.8 18.8 18.4 18.2 18.4 20.8 20.8 21 22.3 23.6 24.9 26.2 27.5 28.8 30.1 31 31 31 31

polished surface and X = 0.65 |tim phase transition - density change assumed to be zero melting temperature

Tl

mPas

Y mNm"1

£P (a)

x

0.50 0.50 0.49 0.49 0.49 0.48 0.47 0.46 0.46 0.46 0.45 2.2

1525 1516 1488

Ti: Ti-6 Al-4 V (IMI318) 1

2

Chemical composition (wt%)

Al

Fe

Ti

V

H

02+N2

Ref

5.5-6.7

0.03

90

3.5-4.5

0.0125

0.25

[1]

Transitions

T (oc->p Transition) = 995 ± 15 0C

3

Tliq = 1650 0C

Density, thermal expansion coefficient

P20 = 4420 kg m"3 [1]

Estimated value p25 - 43 74kg m'3

Mean linear thermal expansion coefficient.

T0C

25-200

25-300

25-400

25-500

Estimated

a.106

9

9.5

9.8

16

a = 11. 0 x 10'6K-'

The density values in Table 1 were derived from the measured p20 value and the estimated values of a for the solid. McCormick and Brooks [2] measured density values for the liquid alloy over the temperature range (1600-1880 0C) using the levitated drop technique. The results shown in Figure 1 indicate that the density is very close to the values estimated using additivity rules (METALS model) and can be expressed by Equation (2). ps (kg in 3 ) = 4420 - 0.154 (T- 25 0C)

(1)

p^ (kg m'3) = 3920 - 0.68 (T-1650 0C)

(2)

Density, P (Kg m"3)

Temperature (0C)

Figure 1

4

The density of TI/6A1/4V as a function of temperature; values [2]; x, Metals model estimates.

, o, recommended

Heat capacity, enthalpy

Values for Cp and (H1-H25) have been measured by Bros [3] and Richardson [4] for temperatures up to 600 0C; it can be seen from Figure 2 that estimated values are in excellent agreement with the measured values. Heat capacity values were obtained to 1100 0C by Hayes [4] using a high temperature DSC and the a -> P transition was found to occur around 950 0C; a value of AH*3"8 of around 48 J K^g"1 was obtained. Values of (H1-H25) were obtained [5] for the liquid using levitated drop calorimetry (Figure 3). A long extrapolation from (1100 to 1649 0C) was used [5] to derive a value for the enthalpy of fusion, AH^8 = 282 Jg"1, which is in very good agreement with the value AHfos = 286 Jg"1 recorded by Cezairliyan and McClure [6] using the exploding wire technique Very recently, Brooks [11] has obtained drop calorimetry results for solid Ti6A1-4V, as can be seen from Figure 3, these results are in excellent agreement with the extrapolated values, with the one exception of the (H1-H25) at 1650 0C. This could be due to either partial melting of the sample or the electronic contribution to Cp of the solids. METALS model predicts a value of 306 Jg"1 and the (H1-H298) values estimated by METALS model are within 1% of the experimental values. The Cp obtained from the drop calorimetry [11] work yields Cp = 0.67 Jg-1K"1, significantly lower than the estimated value (Cp = 0.9 Jg-1K"1). The recommended values are

AH 9 T =

48 ± 10 Jg 1 ,

AHp 6 SO = 286 Jg 1 ,

C p (liq) = 0.83 Jg 1 K'1 [5]

Heat Capacity, Cp (J g"1 K'1)

Temperature (0C)

Heat capacity of T1/6A1/4V as a function of temperature; values; A5 Bros [3]; •, Richardson [4].

, o, recommended

Enthalpy, H1-H25 (Jg 1 )

Figure 2

Temperature (0C)

FigureS

Enthalpy (H7-H25) as a function of temperature for Ti/6Al/4V; A, drop calorimetry [S]5 •, Brooks [11].

5

Thermal conductivity (A,) thermal diffusivity

Thermal conductivity values up to 600 0C have been reported in several publications [7-9]. These are shown in Figure 4; the scatter in the results is typical of results reported for solid metals which can be affected by thermal and mechanical history and any minor differences in impurity levels and chemical composition. Polev et al [10] used the plane temperature wave method to measure the thermal diffusivity of a Ti/Al/1 V/2 Zr/1 Mo from (700-1700 0C). The thermal diffusivity value calculated from the thermal conductivity results (Figure 4) are compared with the thermal diffusivity data reported by Polev et al in Figure 5. In addition, the latter data have been converted to thermal conductivities using the recommended values of Cp and p given in Table 1. Recommended values are plotted as a solid line in Figures 4 and 5. The thermal diffusivities and conductivities apparently increase on melting; this may be due to convectional contributions to the conductivity and diffusivity results. Estimated values, which are usually high by ca 10%, were obtained: X11650 = 30.6 Wm-1K'1 : X11800 = 32.5 Wm-1K"1 a!650 = 0.80 mV : a!800 = 0.866 mV The

(Wm-1K'1)

Thermal Conductivity, A.

Thus a value at 1650 0C X1 = 27.5 Wm-1K'1 and a = 0.7 mV might be expected. experimental values for the liquid phase are tentatively adopted.

Temperature (0C)

Figure 4

Thermal conductivity values for Ti-6Al-4V as a function of temperature; , o, recommended values based on experimental diffusivity results due to Polev [1O]; - -, Deem [8]; ••••; and Filoni [7].

<mV)

Thermal Diffusivity, 106a

Temperature (0C)

Figure 5

6

Thermal diffusivity values for Ti-6Al-4V as a function of temperature; , o, recommended values based on results due to Polev [1O]; values calculated from conductivity measurements due to Touloukian [9], ••••; and Filoni [7],. A; x, estimated values.

Viscosity

No data have been reported for this alloy. The estimated values are given in Table 1.

References 1.

Donachi, M J9 Jr: Titanium-A Technical Guide, publ. ASM Intl, Metals Park Ohio, (1989).

2.

McCormick, A; Brooks, R F: MTS Programme on processability: Thermophysical property data for commercial alloys measured in PMPl 9 2 and 3 (Apr 93-Mar 96), NPL (1996) Chapter 1.

3.

Bros, H; Michel, M L; Castanet, R: J. Thermal Analysis 41 (1994) 7/24.

4.

Richardson, M J; Hayes, D L; Day, A P; Mills, K C: as in ref 2, Chapter 3.

5.

Corkery, D; Brooks, R F; Mills, K C: as in ref 2, Chapter 4.

6.

McClure, L; Cezairliyan, A: Intl. J. Thermophys. 13 (1992) 75/81.

7.

Filoni, L; Rocchini, G: High Temp-High Pressure 21 (1989) 373/376.

8.

Deem, H V; Wood, W D; Lucks, C F: AIME Trans. 212 (1958) 520/523.

9.

Touloukian, Y S; Powell, R W; Ho, CY; Klemens, P G: Thermophysical Properties of Matter, VoI 1: Thermal conductivity, publ. IFI Plenum, New York (1970).

10.

Polev, V F; Zinovyev, V E; Korshunov, IG: High Temperatures, 23 (1985) 704/706.

11.

Brooks, R F: Unpublished results, National Physical Laboratory, May (1999).

Table 1 Recommended values for thermophysical properties of 90 Ti/6 A1/4V; estimated uncertainties are given at the foot of the table

1 Wm-1K'1

106a mV

4420

JK-1V1 0.546

(H1-H25) Jg1 O

7.0

2.9

100

4406

0.562

42

7.45

3.0

200

4395

0.584

99

8.75

3.4

300

4381

0.606

158

10.15

3.8

400

4366

0.629

220

11.35

4.1

500

4350

0.651

284

12.6

4.4

600

4336

0.673

350

14.2

4.8

700

4324

0.694

419

15.5

5.1

800

4309

0.714

489

17.8

5.7

900

4294

0.734

561

20.2

6.3

995

4282

0.753

636

22.7

6.9

995

4282

0.641

684

19.3

6.9

1100

4267

0.660

749

21.0

7.3

1200

4252

0.678

816

22.9

7.65

1300

4240

0.696

885

23.7

7.8

1400

4225

0.714

956

24.6

7.9

1500

4205

0.732

1028

25.8

8.1

1600

4198

0.750

1102

27.0

8.3

1650

4189

0.759

1184

28.4

8.6

1650"

3920

0.831

1466

33.4

8.6

[3.25]a

1700

3886

0.831

1508

34.6

9.0

[3.03]a

1800

3818

0.831

1591

-

-

[2.66]a

1900

3750

0.831

1674

-

-

[2.36]a

Uncertainty

±3%

±3%

±3%

± 10%

± 10%

± 30%

0

Density kgm"3

25

Temperature

C

n

estimated value Date: May 1999

K

melting point

*1 Pa.s

Zn Pure Zinc 1

Transitions, melting point mp = 419.40C [1]

2

Density (p) thermal expansion coefficient P25 (solid) = 7140 kg mf3 [2];

a = 30 x 10'6 K'1 [2]

The recommended p-T relation for solid Zn is shown in Figure 1. Recommended density-temperature relations for liquid Zn reported by Iida and Guthrie [3] and Watanabe et al [4] are identical: ps (kg.m~ 3 ) - 7140 - 0.641 (T-25°C)

(1)

p £ (kg.m"3) = 6756 -0.98 (T-4190C)

(2)

Density, p (Kg m"3)

There is 1.9% decrease in density at the melting point on the basis of the data given in Table 1.

Temperature (0C) Figure 1

Density of pure Zn as a function of temperature.

3

Heat capacity (Cp) enthalpy (Hx-H25)

The values of Cp and enthalpy given in Table 1 and Figures 2 and 3 were derived from the recommended data reported by Dinsdale [I].

Heat Capacity, Cp (Jg-1K'1)

Dinsdale [1] also reported values of AHfos = 1 1 2 Jg'1 and for the liquid phase Cp(£) = 0.480 Jg 1 .

Temperature (0C) Heat capacity of pure Zn as a function of temperature.

Enthalpy, H1-H25 (Jg'1)

Figure 2

Temperature (0C) Figure 3

Enthalpy (HfH25) for pure Zn as a function of temperature [1]

4

Thermal conductivity (A,) thermal diffusivity (a)

Thermal conductivity values recorded for solid and liquid Zn have been reviewed by Touloukian et al [5] and by Mills et al [6], respectively. The thermal conductivity data are given in Figure 4 and Table 1 and it can be seen that values reported by Magmedov [7] are about 10 Wm"1 K"1 lower than values recommended by Touloukian [5] for the solid state but are in good agreement for the liquid metal. Values based on electrical resistivity and the WFL Rule are in good agreement with recommended values;

X m (S) - 100 Wm*1 K-1 :

A,™ = 50 Wm'1 K'1 (3)

2

0

WnT

1

K'

(Wm'1 K'1)

Thermal Conductivity, A,

U= 50 + 6 x 10' (T-419 C)

1

Temperature (0C)

Thermal conductivity (A,) as a function of temperature for pure Zn, , o, recommended values; - - Touloukian [5]; ••• Magmedov [7]; ^ •#• calculated from WFL Rule for solid and liquid respectively.

Thermal Diffusivity, 106a (mV)

Figure 4

Temperature (0C)

Figure 5

Thermal diffusivity derived from the recommended thermal conductivity (A,), Cp and p values (a = X/Cp. p) as a function of temperature.

5

Viscosity (r|)

Viscosity measurements have been reported by several investigators; the measurements vary by ca± 15% around the mean; Iida and Guthrie [3] have reviewed these data. Iida and Shiraishi [8] recommend r|m = 3.58 mPas and the following relationship.

1310 In TI (mPas) - -0.614 + —-

(4)

Viscosity, TI (mPas)

where T is in K. Values given in Figure 6 and Table 1 are based on Equation 4.

Temperature (0C) Figure 6

6

Viscosity of pure Zn as a function of temperature [3].

Surface tension (y)

Keene [9] reviewed surface tension data reported for pure Zn and recommended the following equation: Y(InNnT1) - 789-0.21 (T-420 0C) (5) but suggested that y111 may be as high as 817 mNm"1.

7

Emissivity (s)

Shiraishi [10] cites values of total normal emissivity, S1^ of 0.04 - 0.05 for a polished surface of zinc and S1^ = 0.5 for an oxidised liquid surface at 1000 0C.

References 1.

Dinsdale, A T: SGTE data for pure elements. CALPHAD 15 (1991) 317/325.

2.

CRS Handbook of Chemistry and Physics, edited D R Lide, publ. CRC Press, 74th edition (1993/4).

3.

Iida, T and R I L Guthrie: The physical properties of liquid metals. Clarendon Press, Oxford (1988).

4.

Watanabe, S, K Ogino and Y Tsu: Handbook of physico-chemical properties at high temperatures, edited Y Kawai and Y Shiraishi, publ. JISI, Tokyo, Chapter 1.

5.

Touloukian, Y S: Thermophysical properties of high temperature solid materials: VoI 1 Elements, publ. Macmillan, New York (1967).

6.

Mills, K C, B J Monaghan and B J Keene: Intl. Materials Review, 41 (1996) 209/242.

7.

Magmedov, A M: Tezisy Nauch. Soobn. Vses Konf. Str. Suoistvan Met. Shlak. Rasp. 3rd (1978) VoI 2, 21/24.

8.

Iida, T and Y Shiraishi: Handbook of physico-chemical properties at high temperatures, edited Y Kawai and Y Shiraishi, publ. ISIJ, Tokyo, Special Issue No 41 (1988), Chapter 4.

9.

Keene, B J: Intl. Materials Review, 38 (1993) 157/192.

10.

Shiraishi, Y: as in ref 8: Chapter 10.

Table 1 Recommended values for thermophysical properties of pure Zn

T C 25 100 200 300 400 419.4 419.4 500 600 700 800 900 1000 0

PT kgm'3 7140 7090 7028 6963 6899 6886 6756 6678 6580 6482 6384 6286 6188

1

Jg k0.388 0.398 0.413 0.431 0.451 0.454 0.479 0.479 0.479 0.479 0.479 0.479 0.479

/ \

v aJ

1

polished surface

(H1-H25) Jg1 O 29 70 112 156 165 277 315 363 411 459 507 555

106a Hi2S-1 44 41 39 36 33 32.0 15.4 17.2 19.3 21.5 23.8 26.2 28.2

X Wm'1 K-1 121 117 113 107 101 100 50 55 61 67 73 79 85

n mPas

Y mNm"1

P (a) fc TN

0.045 0.045

3.5 2.9 2.4 2.1 1.8 -

789 111 751 730 709

Zn-Al 1

2

Chemical composition (wt%) Al

Mg

Zn

4.5

0.05

94.45

Transitions

The following transitions were observed in DPSC studies [I]: solid state transition fusion region

: :

273 0C T801 = 357 0C

Tliq = 387°C

A value of Tliq = 387 0C has been reported.

3

Density

Value of p20 = 6700 kg m'3 and a =27x IV6 K'1 [2]. METALS model estimates (p25 = 6643 kg m'3 and a = 31.7 x 10"6 K"1) thus values are in good agreement. Density measurements for the liquid phase reported by Day et al [2], resulted in a value of 6455 ± 100 kg m"3 for 545 0C using the hydrostatic probe method. This is 8% higher than the value estimated by METALS model [2] and would correspond to a very low density change on melting. Consequently, METALS model density values have been adopted and are given in Figure 1 and Table 1 ps (kg.nT3) = 6700 - 0.603 (T-25°C)

(1)

p^ (kg.m~ 3 ) - 6142-0.977 (T-387°C)

(2)

Density, P (Kg m'3)

Temperature (0C)

Figure 1

4

Density of Zn-Al alloy as a function of temperature. (Use Equn 6.1 to calculate properties in the 'mushy' region.)

Heat capacity, enthalpy

Heat Capacity, Cp (Jg-1K'1)

The heat capacity, and enthalpy (H7-H25) have been determined by Richardson et al [1] using DPSC. The results are compared with values estimated by the METALS model in Figures 2 and 3 and it can be seen that the estimated values are in good agreement except in the transition region.

Temperature (0C)

Figure 2

Heat capacity as a function of temperature for Zn-Al alloy; —, o, experimental values; x, estimated by METALS model. (Use Equn 6.1 to calculate properties in the 'mushy' region.)

Enthalpy, H1-H25 (Jg'1)

Temperature (0C)

Figure 3

Enthalpy (H1-H25) of Zn-Al alloy as a function of temperature; —, o, experimental values; x, estimated by METALS model. (Use Equn6.1 to calculate properties in the 'mushy' region.)

The following data were obtained [1] Cp25 = 0.41 Jg-1 K- 1 : AH^5C

=

8 Jg'1

Estimated C p25 = 0.411 Jg'1 K'1 [2] AH f u s - 114 Jg'1: Estimated A Hftls - 114 Jg~' [2]

Cp(liquid)-0.52-6xlO" 5 (T-387 0 C) JKV 1 !Estimated C p CO - 0.51 Jg- 1 KT 1 P] (3)

5

Thermal diffusivity (a) thermal conductivity (A,)

The thermal diffusivity has been measured by Szelagowski [4] and subsequently by Monaghan [5], both using the laser flash method. The results are shown in Figure 4. It can be seen that the values for the solid state are in good agreement but for the liquid there are differences of around 30%. Mean values have been adopted for the liquid phase and these are shown in Table 1. Thermal conductivity values based on recommended values (Table 1) are given in Figure 5.

Thermal Diffusivity, 106a (mV)

Temperature (0C)

Thermal diffusivity (a) of Zn-4%Al as a function of temperature; , o, recommended values; A, Szelagowski [4]; x, Monaghan [5]. (Use Equn 6.1 to calculate properties in the 'mushy' region.)

(Wm-1K'1)

Thermal Conductivity, k

Figure 4

Temperature (0C)

Figure 5

Thermal conductivity (A,) of Zn-4% Al as a function of temperature (Use Equn 6.1 to calculate properties in the 'mushy' region.)

6

Viscosity

Viscosity, TI (mPas)

The viscosity values given in Table 1 and Figure 6 are obtained by Andon et al [6] using oscillating viscometry.

Temperature (0C) Figure 6

7

Viscosities of Zn-Al alloy as a function of temperature [6].

Surface tension (y)

A value of y"1 = 830-0.2 (T-387) mNm"1 was estimated by analogy with surface tension of pure Zn [7]. The surface tension values refer to a sample with low oxygen and sulphur contents.

8

Fraction solid

Fraction Solid, fs

The fraction solid as a function of temperature for a cooling rate of -10 Kmin"1 is shown in Figure 7.

Temperature (0C) Figure 7

Fraction solid (fs) of Zn-4%Al as a function of temperature in the fusion range.

References 1.

Richardson, M J; Hayes, D; Day, A P; Mills, K C: Final Report MTS Programme on Processability: Thermophysical property data for commercial alloys measured in PMPl, 2 and 3, (Apr 93-Mar 96).

2.

Mills, K C; Day, A P; Quested, P N: Estimating the thermophysical properties of commercial alloys. Proc. Joint Symp. Nottingham Univ.-Osaka Univ. held Nottingham, Sept (1995).

3.

Technical Notes on Zinc: Zinc alloy die casting published Zinc Development Assoc., London (1988), Chapter 3.

4.

Szelagowski, H: PhD Thesis, Dept Materials Science, UMIST, Manchester, 1999.

5.

Monaghan, B J; Waters, M J D : Laser flash liquid metal thermal diffusivity measurements. NPL Report CMMT(D) 196.

6.

Andon, R J L ; Day, A P; Quested, P N; Mills, KC: as in reference 1, Chapter 4.

7.

Keene, B J: Intl. Materials Reviews 38 (1993) 157.

Table 1 Recommended thermophysical properties for Zn-4%Al alloy

T C 25 100 200 300 357* 387* 387* 400 500 600 700 800 0

Density kgm'3 Jg1 k-1 0.41 6700 0.42 6655 0.475 6595 0.50 6534 0.50 6500 L[0.51]a 6482 0.520 6142 0.518 6129 0.512 6026 0.506 5927 0.50 5831 0.494 5738

(H1-H25) Jg 1 O 31 76 133 161 177 291 298 349 399 449 499

10" a Hi2S-1 40 L_39

36 32 30 12.5 13 16 20

X Wm'1 K-' 110 109 113 105 98 40 41 49 60

T! mPas

3.5 2.6 2.05

Y mNm"1

g(a)

[830]a [827]a [807]a [787]a

[ ]a = estimated value

* melting range

Table 2 Fraction solid of Zn-4% Al as a function of temperature Temperature 0C 387 Fraction solid, fs O

385 0.08

382 0.18

377 0.46

376 0.82

375 0.96

372 0.98

362 1.0

The difference in T^ values shown in Tables 1 and 2 is associated with the fact that Tliq is usually taken as the peak temperature whereas the temperature where the endotherm on heating returns to the baseline is used when calculating fs. Supercooling results in a decrease in T, for the cooling cycle. Date: March 1999

APPENDIX Details of METALS model to calculate the thermophysical properties of alloys Paper presented at Joint Symposium Nottingham Univ.-Osaka Univ. held Nottingham Sept (1995). ESTIMATING THE THERMOPHYSICAL PROPERTIES OF COMMERCIAL ALLOYS K C Mills, A P Day, P N Quested Division of Materials Metrology, National Physical Laboratory, Teddington, Middx

Abstract Models have been developed to estimate the enthalpies, heat capacities, densities, viscosities thermal and electrical conductivities of multi-component, commercial alloys in the solid and liquid states. The estimated values are compared with measured values for the properties of various commercial alloys.

1

Introduction

Over the last two decades mathematical modelling has become an established tool for improving both process control and product quality. These models have been applied to a wide variety of processes and industries such as the casting and foundry production, steelmaking, secondary refining of non-ferrous metals, welding, spray forming, dip coating, metallic powder and ribbon production. Model development has evolved to the point where one of the prime requirements at the present time is for accurate physical property data for the commercial alloys involved in these processes. Data are required for the factors affecting the fluid flow and heat transfer in the process viz density, viscosity, surface tension, enthalpy, heat capacity, thermal conductivity, thermal diffusivity. The absence of reliable data for commercial alloys reflects the difficulties encountered in obtaining accurate values for these properties at high temperatures; for instance Iida and Guthrie [1] have shown that the reported viscosities of pure iron and aluminium vary by ±50% and ±100% around the mean. Even greater uncertainties would be expected with commercial alloys which are subject to segregation, and the presence of nonmetallic inclusions, etc. The Department of Trade and Industry has recognised this need for accurate thermophysical property data for commercial materials and has funded a research programme to develop methods necessary to provide this information [2]. Industry frequently needs to react quickly to combat specific problems in process control or product quality. Even when experimental methods are available the production of accurate data is frequently time-consuming. Consequently, there is a need for the development of mathematical models to predict the thermophysical properties of alloys from their chemical

composition and melting range, since frequently these are the only information available. However, accurate values may only be estimated if the data used in the model are based on reliable, traceable values for the material. Consequently we have always adopted a threepronged approach which includes: (i)

accurate measurement of thermophysical properties

(ii)

critical evaluation of literature data and

(iii)

the development of estimation routines based on accurate property data from (i) and (ii).

Since many process models involve the solidification of liquid metals, it is necessary to estimate values for the solid, liquid and 'mushy1 phases. It would also be advantageous if such a model had universal application ie it could be applied to a wide range of alloys spanning from aluminium alloys to steels. This paper describes the various models which have been developed to estimate heat capacities, enthalpies, densities, viscosities and thermal and electrical conductivities and these have been incorporated into a software package known as METALS model.

2

Experimental

The thermodynamic temperature (K) has been used throughout this paper. 2.1

Data sources

In order to obtain accurate estimated values it is necessary to use accurate information for the thermophysical properties of alloys in the development of the model. Consequently, property values obtained in the parallel measurement programme have been used for this purpose [2,3]. In addition, the following reference sources in Table 1 have also been used in this development of models. Table 1 Data sources used in model development Property Heat capacity, enthalpy Density Viscosity Thermal and electrical conductivity

Pure elements

Commercial alloys

[4] [5] [6] [1] [1] [7] [1] [8]

[3] [3] [9] [3] [10-17]

2.2

Models

Models based on partial molar quantities (denoted by a bar, egV for partial molar volume) have been widely used in this work ie Equn (1) V = XiVi + X 2 V 2 + X 3 V 3 + X 4 V 4 +

(1)

where x is the mole fraction and subscripts 1,2,3.... denote the various elements present in the alloy. Both the temperature dependence of the properties and the other models used are described below in the text devoted to that property.

3

Estimation of heat, capacities, enthalpies

3.1

Model

The temperature dependence of heat capacities of most elements can usually be satisfactorily expressed in the form shown in Equn 2, where a, b and c are constants, T is the thermodynamic temperature, K. CP = a + bT + ^

(2)

Values a, b and c for a multi-component alloy can be obtained from Equns 3-5 a = aixi + a 2 x 2 + a 3 x 3 b = bixi + b 2 x 2 + b3x3 c = CiXi + C 2 X 2 + C 3 X 3

(3) (4) (5)

The enthalpy (Hx-H298) can be calculated using Equn 6 H x - H 2 9 S = {CpdT = a(T-298) + ^(T 2 -298 2 )-c(^--M

v-i ^y*)

298

(6)

The enthalpy of fusion (AHftls) is calculated from the entropy of fusion (ASftls) as shown in Equns 7 and 8 where Tliq is the liquidus temperature AS fus = x,As?'s + x2As!r + X3As*'5 + ..AH fils = TiiqAS*15

(7)

(8)

Values for the enthalpy of liquid alloys are calculated by Equn 9 where sol and 1 denote the solid and liquid phases, respectively. (Hr-H 298 ) = C P l y (T liq -298) + T liq AS^ y + C P l lloy (T-T,i q )

(9)

3.2

Validity of model

It has been found that the predicted values of Cp and (H7-H298) are typically within 2% of measured values for a wide variety of alloys. However, the model predicts neither the occurrence of phase transitions nor the enthalpies associated with these transitions. It can be seen from Figure 1 that predicted values are in excellent agreement with measured values. Overall enthalpy (H1-H298) values for liquid aluminium bronze were also in excellent agreement with measured values.

Temperature, K

Figure 1

Heat capacity of Al + si alloy as function of temperature; values, • estimated values.

4

Estimation of densities

4.1

Model

, measured

Molar volumes (V) and densities (p) for liquid and solid alloys can be derived using Equns 10-13 where M is the molecular weight (= X1M1 + X2M2 + X3M3 +...) and p is the volume expansion coefficient (p = X1P1 + x2p2 + x3p3) V = XiVi + X 2 V 2 + X 3 V 3

(10)

p = (MAV)

(11)

+

solid: V = V 298 (I P501 (T-298)) HqUIdIV = VTHqO + P1(T-T11,))

(12)