K. C. Mills-Recommended Values of Thermophysical Properties for Selected Commercial Alloys (2002) (2)

Recommended values of

thermophysical properties

for selected

commercial alloys

Kenneth C Mills

National Physical Laboratory

The MaterialsInformation Society

W O O D H E A D P U B L I S H I N G L I M I T E DCambridge England

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FOREWORD

It is incredible to recall that personal computers first saw the light of day not much more than20 years ago, so much now do computers dominate our lives. The growth of cheaper andcheaper but more and more powerful computers has conferred an aura of invincibility uponthe keyboard, the mouse, the screen and the CPU. Nothing seems beyond them. The almostunbelievable 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 thinkingthat 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 thehuman 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. Theenormity of the technical calculations that computers can now undertake and the complexityof the engineer models that can be forged, imbue computers with an illusion of greatauthority. But the true authority of a computer stems, not from the computer itself, but fromthe quality of the data on which the computer model is built, a fact in danger of beingforgotten when engineering decisions are based on computed results.

Materials processing is a complex area linking many aspects of the physical, chemical andmicroscale 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 datathat quantifies wider and wider aspects of material behaviour during processing. Inacknowledgement of this need, the Department of Trade and Industry (DTI) initiated, in1993, a series of programmes as part of its statutory/regulatory Programme in MaterialsMetrology, to fund the development of methods for the measurement of material propertiesthat influence their behaviour during processing - The Processability Programmes. As amajor part of these Programmes, the National Physical Laboratory (NPL) was contracted todevelop methods to measure the fluid flow and heat transfer properties of engineering alloysat high temperatures — up to and beyond their melting points.

This is an area of measurement fraught with experimental difficulty - material reactivity ishigh so that containers and measurement probes are subject to attack, material samples areprone to contamination from the solid surfaces and gaseous atmospheres that they contact andthe controlled and uniform high temperature conditions required are difficult to establish andsustain. Ken Mills played a leading role in the NPL team that carried out the work underthese DTI contracts - work which established NPL as, to quote a Swedish expert, 'one of theleading laboratories in the world in property measurement'.

An important milestone in DTFs contract with NPL required validation of the methods thatwere developed by reviewing the quality of the data they generated for accuracy, forusefulness to industry and for standing against corresponding data measured in other worldwide centres. The review grew and grew, and has now grown further into the present bookby Ken Mills. It is very gratifying that its publication will make important results from theDTI 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 wasKen, with his indefatigable pursuit of literature data and his 'nose' for the most reliable ofmeasurements. 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 mostreliable measured values presented in graphical and tabular form.

The result is an extensive and authoritative survey of the high temperature properties of awide range of real engineering materials. It will constitute a valuable source book for manyyears to come for those developing and using computer models of metallurgical processes, aswell 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 HillsDTI 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.

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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

vi Contents

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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

1 INTRODUCTION

The objective of this work was to provide the best available data for commercial alloys tofacilitate the mathematical modelling of processes, such as casting, primary and secondaryrefining, etc. This study was funded by the Department of Trade and Industry. Most of thework contained in this critical review was carried out as part of the National PhysicalLaboratory's (NPL) MTS Programme on Processability. However, where data are available inthe literature, these have been incorporated into the review.

Mathematical modelling has become an established tool to improve process control andefficiency and product quality. There are several different types of models used which seek topredict, the thermodynamics kinetics, heat transfer, fluid flow etc of various processes. Modelsof heat and fluid flow have proved useful in predicting, defects in castings, the geometry ofweld pool profiles, microstructure etc. These models have been developed to the stage whereone of the prime requirements is for accurate reliable data for the thermophysical propertiesinvolved 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 surfacetension. A recent investigation has shown that predictions of the defects in castings can besignificantly improved by replacing data of unknown origin for relevant thermophysicalproperties of alloys held in commercial software packages by reliable experimental values forthese properties. There are few data available in the literature for the above thermophysicalproperties of commercial alloys, hence the need for a measurement programme and acompendium of critically-assessed data to assist the mathematical modeller.

In practice, reliable thermophysical property data are needed for a much wider range ofcommercial alloys than covered in this review. To facilitate this, two steps have been taken inthis work to allow the reader to assess the viability of using estimated thermophysical propertydata:

(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 thechemical composition and, in some cases, the liquidus temperature of the alloy.

Consequently, recommended values are provided for the parent metals and values estimated byMETALS model are compared with the experimental values to allow the reader to determinewhether 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 metalalphabetical order of the letters used in alloy designation (eg ESf 718)numerical designations given (e.g. 3004), with lowest numbers first, e.g. LM4comes 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 (startingwith 1) for each alloy. A list of symbols and abbreviations is given immediately prior to thesection 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 TemperaturePhysical 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 TaylorNPL: 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) review of published literature [1-8](ii) information supplied by J H Henderson (Netszch), Ivan Egry (DLR) G Pottlacher

(TU Graz), Profs Sato and Yamamura (Tohoku University)(iii) manufacturers data, where available.

For the pure metals, the values were obtained from standard texts [1-8] in addition to the datagenerated in the NPL measurement programme.

The NPL thermodynamic package [9] MTDATA was used to calculate the phase equilibria forcertain alloys. These were used to interpret the phases present and the origin of certain peaks inthe 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 andY 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 inExtraction Metallurgy, Proc. Quebec Conf. for Metallurgists Computer Software inChemical 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 theform of a disc was placed on an alumina disc located at the bottom of a Pt crucible completewith a Pt lid. A matched Pt pan was used as the reference pan. The reference and sample panswere placed in the DSC and heated (or cooled) from a known temperature (T1) to the targettemperature (T2) at a known rate, eg 10 K min"1. When the sample undergoes a transition, eg anendothermic event, the temperature of the sample pan lags behind the reference pan and poweris supplied to the sample cell to maintain it at the same temperature as the reference cell. Thepower required is continuously monitored. Consequently, this instrument is known asdifferential 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 Aratmosphere in all cases. The procedures used to derive Cp are given elsewhere [1,2]. Theresults are obtained in the form of a Cp-T curve between T1 and T2, the experimental uncertaintybeing usually around ± 1%. Enthalpy (HT2-HTl 1) values are derived by integrating Cp valuesbetween T1 and T2.

Measurements for temperatures between 720 and 1500 0C were obtained using a StantonRedcroft DSC (denoted HTDSC) which is effectively a quantitative DTA unit. In this case thedifference between the temperature of the reference and sample cells is measured. Purified Aris flowed through the apparatus throughout the experiment. The procedure and the method ofobtaining Cp and (HT2-HTl2) were similar to that adopted for the DPSC. Experimentaluncertainties of ± 4% were obtained in calibration experiments carried out on pure Ni butuncertainties of ± 2% were frequently recorded.

Fraction solid (fs) values were derived from the enthalpy-temperature curve recorded for thetemperature range covering solidification. The fs for a specific temperature (T) was derivedfrom the ratio of (enthalpy evolved from temperature where solidification started to temperature(T)/(total heat given out during solidification). (See Figure 1).

Temperature (0C) Temperature (0C)

Figure 4-1 Schematic diagram showing derivation of fraction solid at temperature, T.

4.1.2 Density measurements

Density measurements at 20 0C were obtained from the mass and volume of a machinedcylinder 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 sampleof known mass is levitated in an electromagnetic coil and once the temperature has stabilisedphotographs of the drop are taken simultaneously in three directions (Figure 4-2). Since thespecimen has a natural oscillation it is necessary to identify these images where the drop wasspherical. The images taken from above are examined to identify circular drops and then theequivalent images from the side are identified and the volume calculated. The magnificationfactor 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 obtainedwith this technique are thought to be subject to experimental uncertainties of ± 2%.

2 color pyrometer

Area AAreas

Temperature display

Calibration ball

Sample turntable

Pushrod

Synchronizedcameras (3rdremoved forclarity)

RF coil

Figure 4-2 Schematic drawing of the levitated drop method for measuring densities.

Ap

pa

ren

t C

P (

J g-

1 K

~1)

Ent

halp

y, H

j-H

iIq

(Jg

-1)

Density measurements on liquid alloys were also made with the hydrostatic probe method [3] inwhich the apparent mass of an alumina rod suspended from a balance is measured as it ispushed into the molten alloy (Figure 4-3). The apparent mass-immersion depth curve (shown inFigure 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 loweringmechanism

Thermocouple

Bob supportrod

Bob

Sample

Ta heating element

Thermocouple

Figure 4-3 Schematic drawing of the hydrostatic probe method [3].

Gas

Bob

Mass

change

Liquid

Bob touches liquid

Surfacetension

EquilibriumBuoyancy

Distance moved

Figure 4-4 Schematic drawing showing the principle underlying the hydrostatic probemethod.

4.1.3 Viscosity (TJ)

The viscosities of the alloys were measured using an oscillating viscometer (Figure 4-5) wherethe 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 asecond stainless steel crucible (24 id x 65 mm) but subsequent work was carried out with asingle alumina crucible. The crucible was suspended on a Pt-8%W wire (0.2 mm diam) whichwas contained in a water jacket at 30 0C. A mirror sited on the suspension train was used tofollow the oscillations of the crucible using 1 mW laser. The reflected light was detected by anarray of light sensitive diodes arranged in an arc of a circle (± 30°). The output voltages from allbut the central diode were combined and measured using an A/D card and computer; the outputfrom the central diode was logged separately. A waveform was deduced from the results fromwhich 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

Constanttemperaturejacket

Platinumsuspensionwire

Mirror

Crucible

Sample

Furnace

Atmospherecontroljacket

Window

Laser and diodearray

Figure 4-5 Schematic diagram of the oscillating viscometer [3 J.

4.1.4 Surface tension (y) measurements

Surface tensions (y) were obtained using the levitated drop technique [4,5] as shown inFigure 4-6a. The sample was levitated in a silica tube (13 mm od) by applying the powersupplied by a 15 kW, 450 kHz Radyne RF generator to the coil when the specimen was raisedon a BN push rod. A flowing atmosphere of purified Ar, He and Ar + 5% H2 was maintained toprevent oxidation of the sample and the temperature of the specimen was adjusted either byaltering the concentrations of He or H2 in the gas mixture, (since these have higher thermalconductivities than that of Ar), or by varying the power of the generator, eg a reduction inpower 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 oscillationfrequency spectrum was obtained by projecting the image of the drop onto a photodetector andanalysing the resultant electrical signal with a Wavetek dynamic signal analyser.

Figure 4-6 Schematic diagrams of (a) the levitated drop apparatus, (b) typical 5 peakspectra.

The surface tension (y) can be shown by the Rayleigh relation shown in Equation (4-1), wherem 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 thesingle frequency predicted by Rayleigh [6] is found. Recent investigations [7,8] have shownthat oscillations of the drop can arise from translational movements of the drop and the effect ofmagnetic pressure which result in an asymmetric drop. Cummings and Blackburn [9] derivedEquation (4-2) for 5 peak spectra which allows the Rayleigh frequency to be derived from thefrequency spectrum.

col = 7la>? + a>i + a>i + o>5 + a > ? - co2fr 1.9 + 1.2 (^] (4-2)

5 \ a J

where the subscripts 1 to 5 refer to the various peaks, tr to the translational frequency, g thegravitational 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 casesreliable values of y could be obtained [9] by using all 9 peaks in a modified form ofEquation (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 diamwith a thickness of 2-4 mm. However, for the liquid phase it is necessary to contain the liquidin a sapphire cassette, (shown in Figure 4-7b). An energy pulse was directed onto the front faceof the sample and the temperature transient was monitored at the back face. Thetemperature transient goes through a maximum (ATmax) and the time to reach a temperature of

Lens Photocell2 colour

pyrometer

Sampleloading window

PushrodSampleturntable

Signalanalyser

Controllingcomputer

Frequency (Hz)

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

1.37 L2a - -p- * (4-3)Corrections were made for the effect of heat losses [11] and for finite pulse effects [12].

Gas inletExternal trigger

HFgenerator

.Prism

Coil

Nd glass laser

Specimen ThermocoupleLaserpower

unit

Susceptor

LensVacuum/pressurechamber

Temperaturemonitor

InSbdetector

MirrorLens

Vacuum system

Amplifier

Colloidalgraphite

Microcomputer

Figure 4-7 Schematic diagrams of (a) the laser pulse method and (b) the sapphire cassetteused by UMIST to contain the sample.

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

IR sensor

IrisGe lensCaF2 windowTransmittedenergy

Sample

Graphite furnace

Water coolingLaser pulse

Fused silicawindow

Laser shuttle

Power supply

L

(Nd, GGG)1.064 |iim laser

L

PC controland

data acquisition

Cap

Cruciblelid

Crucible

Samplesupport

Samplecarrier

tube

Sampleinstalled

Figure 4-8 Schematic diagrams of (a) laser pulse apparatus and (b) cell used to measurethermal diffusivity of liquid metals by NPL [13].

4.2 Estimation methods

(i) METALS model was used extensively to estimate Cp? (H7-H25), density, thermalexpansion coefficient, viscosity, thermal diffusivity and conductivity. Full details of theprinciples underlying the estimation routines are given in Appendix 1. The followingimprovements to METALS model were incorporated into the estimation of the datapresented 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 conductivityor diffusivity extrapolated to the liquidus temperature and assuming (A,S/A/) was identicalto 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. onContainerless 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, MJD: 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 alloyscontain 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. Itis 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.

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 effecton the fusion range, the enthalpy of fusion value and the fraction solid (fs) results, particularly atthe high fs end.

Temperature (0C) Temperature (0C)(a) (b)

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

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 apparentlyincreases markedly in the fusion range. In fact, this is not a true Cp value since the increase isdue to the latent heat of fusion (or solidification) and is an enthalpy (not a Cp) but which ismanifested as an apparent Cp. Such curves are useful in determining fs but should not beused for, say, the conversion of thermal diffusivity to thermal conductivity; an estimatedCp is recommended for use in this task.

Solid state transitions are usually denoted as 1st Order or 2nd Order type transitions.

Hea

t ca

paci

ty,

Cp

(J g

~1 K~1)

Hea

t ca

paci

ty,

Cp

(J g

~1 K-1)

1st Order- involves an enthalpy change (like fusion) and thus the apparent Cp valuesin this case are not true Cp values,

2nd Order 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 beenconsidered 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 whichhave 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). Inthese cases an estimated Cp for Tsol is recommended. Solid-solid transitions are relativelysluggish and sometimes require time for structural rearrangement of the atoms. DSC is adynamic technique and sometimes does not allow enough time for the atoms in the alloy torearrange themselves. Consequently, the "valley" Cp values tend to vary significantly from runto 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 liquidformation and consequently will not be conducted through the sample. This leads to anerroneous value of the thermal diffusivity (or conductivity) (Figure 5-2). Thus values recordedin the mushy region are subject to error and it is recommended that values should be

derived by using the relation (A, = ̂ ̂ 501 fs + XTH(] (f s) .

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

Temperature (0C)

Figure 5-2 Apparent thermal diffusivity of Ni alloy IN 718 in the "mushy" region.

Th

erm

al

diffu

siv

ity,

106a

(m

2s~

1)

Values of the thermal diffusivity of the liquid phase of the aluminium alloy LM25 have beenreported by four groups and the results split into two groups with lower values in goodagreement and two groups in good agreement with higher values. The differences in the twosets of results was about 30%. This trend in results reported by the various groups for LM25 ismaintained 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 valuescould be prone to error.

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

Temperature (0C)

Figure 5-3 Thermal conductivity of Al-alloy LM25; —o—, • • • -experimental; • frominverse temperature modelling.

5.4 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 as50 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 inthe soluble O and S levels in the alloy [3]. Thus, it is not possible to provide recommended

Th

erm

al conductivity,

K (

W rrr

1 K

~1)

values for the surface tension of specific alloys, say IN 718, since it is dependent upon theconcentrations 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 givenfor 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 surfaceor flotation of inclusions) on the surface of the metal. These films prevent the oscillations of thesample when using the levitated drop method. Some of these oxide films melt, eg those in Ni-based 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 oscillationfrequency spectra eg 9 peaks of 5 peaks normally obtained and this needs special analysis togive 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 constantand the energy required to maintain these balanced temperatures is monitored. In DTSC (DTA-type) the temperature difference between the two pans is monitored and consequently there issome uncertainty in the measured temperature. Thus the temperature scale for fraction soliddeterminations (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

Figure 6-1 shows the fraction solid (fs) of aluminium alloy LM25 as a function of temperatureas determined by DPSC. It can be seen that the fraction solid is to some extent dependent uponthe cooling rate of the metal. The thermophysical properties of the liquid phase are differentfrom those of the solid alloy (e.g. thermal conductivity and diffusivity) thus the value of thethermophysical property in the mushy region will be dependent upon the amount of liquid andsolid (i.e. fraction solid). Since the fraction solid differs with cooling rate then thermophysicalproperties-temperature relations would also differ with cooling rate. This would entailprovision of a series of property-temperature relations for different cooling rates. This has notbeen attempted in this review.

Temperature (0C)

Figure 6-1 Fraction solid of Al-alloy LM25 as a function of temperature for differentcooling rates.

Where information is required for the mushy region the reader is advised to calculate therequired property (P) at temperature T from Equation 6-1 where fs(T) is the fraction solid at T andP1 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 ) )PT l i q (6-D

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

Fra

ctio

n s

olid

, fs

7 SYMBOLS, ABBREVIATIONS, UNITS

a Thermal diffusivity mV1

Cp Heat capacity J K'1 g'1

fs Fraction solidfL Fraction liquidH Enthalpy J g'1

(H1-H25) Enthalpy relative to 25 0C (298 K) J g1

AHfos Enthalpy of fusion J g1

AHtrans Enthalpy of transition J g'1

T Temperature 0C or KTliq Liquidus temperatureTsol Solidus temperatureTfr Transition temperature

a Thermal expansion coefficient K"1

y Surface tension mN m"1

8 EmissivityA, Thermal conductivity Wm"1 K"1

r| Viscosity Pas

subscripts and superscriptss SolidI Liquidm Value at melting point or Tliq

N NormalT TotalA, Spectral (wavelength dependent)

DSC Differential scanning calorimetryDTA Differential thermal analysisDPSC Differential power scanning calorimetryDTSC Differential thermal scanning calorimetryHTDSC High temperature differential scanning calorimetryNPL National Physical LaboratoryUMIST University of Manchester Institute of Science and TechnologyWFL Wiedemann-Franz-Lorenz Rule

AlPure Aluminium

1 Transitions, melting point

mp = 660.20C[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 beenreported for liquid Al9 at the melting point the following density pm values have beenrecommended, 2380 kgm'3 [4] and 2390 kgrn3 [5]. Recently a value of pm = 2375 kgm"3 wasobtained by the y-attenuation method [6]. Equation 2 has been adopted and used in derivingthe 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)

The density change on melting is ca 7%.

Temperature (0C)

Figure 1 Density of pure Al as a function of temperature.

Den

sity

, p

(Kg

nrf3)

3 Heat capacity (Cp) enthalpy (HT-H25)

The values shown in Figures 2 and 3 and Table 1 are derived from the data reported byDinsdale [I].

CP25 (S)=O^OSJK-1S-1 [1] :CP (*)=!. 1 SJR-'g-1 [1]

AH6" = 397 Jg'1 [1]

Temperature (0C)

Figure 2 Heat capacity of pure Al as a function of temperature.

Temperature (0C)

Figure 3 Enthalpy (H1-H25) of pure Al as a function of temperature.

Hea

t C

apac

ity,

C9

(J g

'1 J

C1)E

ntha

lpy,

H1-H

25 (

Jg'1)

4 Thermal diffusivity (a) and conductivity (A,)

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

X(f)=91+3.4xl(T2 (T -66O0C) WnT1K'1 (3)

Temperature (0C)

Figure 4 Thermal conductivity of pure Al as a function of temperature.

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.

The

rmal

Con

duct

ivity

, ̂

(Wm

-1K

'1)

The

rmal

diff

usiv

ity,

106a

<m

V)

5 Viscosity

Viscosity data reported in the literature show a wide range of divergence which is presumablyassociated 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 theselie at the lower limit of the published values (Figure 6). Equation 4 was derived from thesemeasurements

Iog10 TI (mPas) = - 0.562 + 567T'1 (4)

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

Figure 6 Viscosity of pure Al as a function of temperature - Andon et al [9].

6 Surface tension

Keene [10] reviewed the surface tension for pure Al and Equation 5 is based on the mean ofthese 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 whereasEquation 5 refers to oxygen-saturated liquid Al.

Temperature (0C)

Vis

cosi

ty,r

\ (m

Pa

s)

Temperature (0C)

Figure 7 Surface tension of pure Al as a function of temperature; o? — Equation 5which may relate to oxygen saturated liquid A1[10];A[11]; D [12], x [13],values reported for Al with very low oxygen levels.

7 Emissivity, s

Shiraishi [14] reports the following values of total normal emissivity S1 .̂

Polished: 480-630 0C STO = 0.057-0.065 [14]Oxidised: 400 0C STO = 0.393 [14]

60O0C eTO = 0.414

The following spectral emissivity Sx values are given by Touloukian [2] for the range1.5-15 urn.

Polished: Sx = 0.1 to 0.05Rougher surface: Sx = 0.25Beyond 10 |um = s depends upon surface oxidation.

Sur

face

Ten

sion

, y

(mN

nrf1)

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 hightemperatures, 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 propertiesof 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)

25100200300400500600660.2660.27008009001000

Densitykg in3

2702268526622640261725942571255823802366233122962261

Cp(Jg-1K-1)0.9050.9450.991.031.071.101.151.181.181.181.181.181.18

(H1-H25)(Jg1)O6916626737248159366310601107122513431461

X(Wm-1K-')

23724023823322822221521191929699103

106amV

979590868178737132333536.538.5

n(mPas)

1.111.0490.930.83(b)

0.76W

YmNrrT1

871(a)

865ta)

849(a)

834(a)

818(a)

(SL]v ; = may relate to oxygen - saturated pure Al

^ ' = extrapolated value

A1-LM4 (A319)

1 Chemical composition (wt%)

Al89.4

Cu3.0

Mg0.1

Mn0.4

Ni0.35

Si5.0

Zn1.0

Others0.5

2 Transitions

T801 = 525 0C [I]; Tliq = 625 0C [1]Measured by DPSC [2]Tsol = 518 0C; Tliq (peak temperature) - 621 0C [2]

3 Density

P25 (s) = 2750 kg m'3 [1] Estimated p25 (s) = 2774 [3]a (20-100 0C) = 21 x 10'6 IC1 [1] 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 andconsequently, values for the liquid phase calculated by METALS model have been adopted.

ps (kg.m~3) ~ 2753 - 0.223(T-25 0C) (1)

p, (kg.m~3) - 2492 - 0.27 (T - 6210C) (2)

Temperature (0C)

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

Den

sity

, p

(Kg

m"3)

4 Heat capacity, enthalpy

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

Cn = 0.83 J K'1 g'1 : estimated Cn = 0.87 J K'1 g'1P25 P25

AH*18 = 400 Jg1 : AHfos = 393 Jg1

Cp(f) =1.17 Jg-1 K'1 : estimated Cn(^) = 1.13 J K'1 g 1

Temperature (0C)

Figure 2 Heat capacity of LM4 as a function of temperature; over entire temperaturerange o? , experimental; A5 , estimated values. (Use Equn6.1 tocalculate properties in the 'mushy' region.)

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.)

Hea

t C

apac

ity,

Cp (J

g'1

K'1)

Ent

halp

y, H

1-H

25 (

Jg'1)

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 itsequivalent A319, respectively, by the laser flash method. Thermal conductivities (X) werecalculated using the values of Cp, and density recommended in Table 1.

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

Temperature (0C)

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

Temperature (0C)

Figure 5 Thermal conductivity of Al alloy LM4 as a function of temperature. (UseEqun 6.1 to calculate properties in the 'mushy' region.)

The

rmal

diff

usiv

ity,

10 6a

(mV

)

The

rmal

Con

duct

ivity

, A,

(W m

'1 IC

1)

6 Viscosity (r|)

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

7 Fraction solid

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

Temperature (0C)

Figure 6 Fraction solid for LM4 as a function of temperature for a cooling rate of10 K min'1, ; heating 10 K min'1, - - -.

Fra

ctio

n S

olid

, f s

References

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

2. MJ Richardson, D Hayes, A P Day and K C Mills: NPL Report "MTS Programme onProcessability: 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 ofcommercial alloys. Proc. of Nottingham Univ-Osaka Univ. Joint Symp. heldNottingham, 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

T0C

25100200300400500518621*621*7008009001000

Densitykgm'3

2750273727172693266826462640261924922470244224152388

CpJg-1 K-1

0.830.900.950.981.12[1.2]a

[1.09]a

[1.13]a

1.171.171.171.171.17

(H1-H25)Jg-'O6515725435947549560810081100121713341451

106aHi2S-1

60636362605552

242452525526

XWm'1 K-'

137155163164179175150

7071717273

T]mPas

[1.3]«[1.2]a

[i.ir

[ ]a estimated values * melting range

Table 2

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

HeatingCooling

Fraction solid, fs

1.0513504

0.95537532

0.9550544

0.8562553

0.7567557

0.6571563

0.5583582

0.4595592

0.3605600

0.2611606

0.1616

608.5

O624610

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

Al - LM5 (5182)

1 Chemical composition (mass %)

Al94

Cu0.15

Cr0.1

Fe0.35

Mg4.5

Mn0.3

Si0.2

Zn0.25

2 Transitions

T801-575 0C[I] Tliq = 640 0C[I]DPSC measurements: Tsol = 542 0C [2] Tliq = 633 0C [2]

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

3 Density

P25 = 2650 kgm'3 [I]: Estimated (METALS) p25 = [2660] kgm3 [3]a (25-T 0C) = (23 + 1.1 x 10"2 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]

p^ (kg.nT3) = 2354-0.27 (T-633°C) (1)

ps (kg.m"3) - 2650 - 0.231 (T - 25 0C) (2)

Temperature (0C)


Den

sity

, P

(K

g m

'3)

4 Heat capacity (Cp) enthalpy (Hx-H25)

Richardson [2] measured Cp and enthalpy values using DPSC. The results are given inTable 1 and Figures 1 and 2, respectively.

Cp25 = 0.91 JKV: Estimated (METALS)Cp25 = [0.92] JK'1 g 1 [3]Cp(O = 1-22 JKV Cp(O = [1.18] JKV [3]AH^ = 358 JKV AH*18 = [375] JK'V [3]

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

Temperature (0C)

Figure 2 Heat capacity of Al alloy LM5 as a function of temperature. (Use Equn 6.1 tocalculate properties in the 'mushy' region.)

Temperature (0C)

Figure 3 Enthalpy of Al alloy LM5 as a function of temperature. (Use Equn 6.1 tocalculate properties in the 'mushy' region.)

Hea

t C

apac

ity,

Cp

(Jg

"1 K'1)

Ent

halp

y, H

7-H

25 (

Jg'1)

5 Thermal diffusivity (a) thermal conductivity (X)

Values for the thermal diffusivity of the solid alloy have been obtained using the laser pulsemethod, these are given in Table 1 and Figure 4. Thermal diffusivities of the solid did notvary very much with temperature. Values for the thermal conductivity shown in Table 1 andFigure 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 forpure Al.

Temperature (0C)

Figure 4 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.)

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.)

The

rmal

diff

usi

vity

, lfi

a

(mV

1)

The

rmal

Conduct

ivity

^

(Wm

'1 K

"1)

6 Viscosity

The viscosity values given in Table 1 were estimated by comparison with the viscosities ofpureAlandLM25.

7 Fraction solid

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

Temperature (0C)

Figure 6 Fraction solid as a function of temperature; , O heating 10 Kmin"1; , o,cooling at 10 Kmin"1 (estimated).

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 ofcommercial alloys. Proc of Nottingham Univ - Osaka University Joint Symposiumheld Nottingham, Sept (1995).

Fra

ctio

n S

olid

, fs

Table 1

The recommended thermophysical properties for Al alloy LM5

Temp(0C)25100200300400500542C

633°633700800

Density, p(kgm-3)[2650]a

[2636]a

[2615]a

[2592]a

[2568]a

[2540]a

[2526]a

[2354]a

[2336]a

[2309]a

Cp(JK-1E1)

0.920.980.991.06

1.1051.191.19

1.221.221.22

(H7-H25)(Jg-1)

O72170273381497550655101310951217

X(Wm-1K'1)

85103116128133139

[63]b

[65]b

[68]b

106aCm2S-1)[35]"4045

46.5474645

[22]b

[23]b

[24]b

*1(mPas)

[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

Temperature for fraction solid (fs)O

636640

0.05633637

0.1631635

0.2630634

0.3627631

0.4623627

0.5620624

0.6615620

0.7608613

0.8600607

0.9585596

0.95568585

1.0527542

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

Al - LM13 (4032)


Al84.3

Cu0.9

Fe0.8

Mg1.2

Ni0.8

Si12

2 Transitions

DPSC: Tsol = 532 0C [IJ Tliq = 5710C [1]T801 = 542 0C [2] Tliq = 573°C[2]

The Cp-T curve showed a bump followed by a sharp increase in Cp above 480 0C; this maybe 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 Figure1. 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)

pe (kg.nT3) = 2482-0.27 (T-573 0C) (2)

Temperature (0C)


Den

sity

, P

(K

gm

'3)


Richardson [2] measured, Cp and (H1-H25) values using DPSC. These are given in Figures 2and 3, respectively.

Cp25 = 0.86 JK'V1 [2]: Estimated (METALS) Cp25 = [0.87] JK"1^1 [3]Cp(I) =1.19 JKV [2]: Cp = [1.14] [3]AHftls = 489 Jg"1 (excluding small amount of premelting): AHfus = [413] Jg'1 [3]

Values for the solid calculated by METALS model were in good agreement but the estimatedAHftls is appreciably lower than measured values. It can be seen from Figure 2 that Cp valuesincrease from the smooth Cp-T curve above 300 0C, this may be due to a solid/solid transitionand, consequently, possibly may contain enthalpy contributions to Cp. Hence estimated Cpvalues have been used to convert thermal diffusivity data. It can also be seen that there is ashoulder on the melting peak which could be associated with molecular arrangements in thesolid or with premelting. The latter was assumed and the AHftls was derived assuming theenhanced 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. (UseEqun 6.1 to calculate properties in the 'mushy' region.)

Hea

t C

apac

ity,

Cp (J

g-1

K'1

)

Temperature (0C)

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

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

Values OfX25 = 141 to 155 Wm-1K"1 have been reported for the alloy [4] the values dependingon the thermal treatment. Thermal diffusivity values have been measured for the solid phaseusing the laser pulse method. The results are given in Table 1 and Figure 4. Thermalconductivity values shown in Figure 5 were calculated from recommended values of thermaldiffusivity, density and Cp. Values for the liquid alloy were estimated by (i) extrapolating Ato 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 calculateproperties in the 'mushy' region.)

Ent

halp

y, H

7-H

25 (

Jg'1)

The

rmal

diff

usi

vity

, l6

a

(mV

)

Temperature (0C)

Figure 5 Thermal conductivity of Al-alloy LM13 as a function of temperature; , o,recommended values; A, , estimated values. (Use Equn6.1 to calculateproperties in the 'mushy' region.)

6 Viscosity

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

7 Fraction solid

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

Temperature (0C)

Figure 6 Fraction solid, fs, as a function of temperature; , o, cooling 10 K min"1;,O 9 heating 10 K min"1.

The

rmal

Con

duct

ivity

, ^

(Wm

-1K

'1)

Fra

ctio

n S

olid

, f s

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 ofcommercial alloys. Proc of Joint Symp. Nottingham Univ - Osaka University heldNottingham, Sept (1995).

Table 1

Recommended thermophysical properties of Al alloy LM13

T(0C)25100200300400500542°573C

573600700800

Density, p(kgm-3)2690267926622643262226002592°

[2482]a

[2473]a

[2445]a

[2417]a

Cp(JK-'g-1)

0.860.910.960.981.1-

1.191.191.191.19

(H1-H25)(Jg-')

O66160257359472

-5511040107211911310

X(Wm-1K'1)

139152164169161d

[147]b

[64]"[64.5]b

[66.5]b

[68.5]b

106a(Hi2S-1)

6062646559

[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 forheating and cooling rates of 10 K min"1

CoolingHeating

Fraction solid, fs

O568578

0.05566576

0.1564575

0.2562574

0.3560572

0.4559570

0.5557568

0.6554564

0.7550561

0.8544557

0.9537552

0.95532549

1.0517542

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

Al - LM25

1 Chemical composition

Al

91.1

Co

-

Cr

-

Cu

0.2

Fe

0.5

Mg

0.4

Mn

0.3

Ni

0.1

Si

7.0

Ti

0.2

Others

0.2 [1]

2 Transitions, melting range

T501 = 550 0C: Tliq = 615 0C[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 xIQ-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 inexcellent agreement with experimental values. The values given in Table 1 for the solid phasewere derived using the experimental density value and the estimated volume thermal expansioncoefficient.

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 theresults of these two studies for the heating curve and with values estimated by METALS modelor both solid and liquid phases. Results obtained by Day [6] using Archimedean andHydrostatic probe method are ca. 2% lower and higher respectively. Brooks [7] has obtainedpreliminary results with the maximum bubble pressure method which are 3-4% lower. Thepressure of oxide films in contact with the probe, bob or the capillary may have been affected bythe results of these studies. The values shown in Table 1 are based on the dilatometricmeasurements [2,3].

Temperature (0C)

Figure 1 Density of LM25 as a function of temperature; , O5 recommended values,—, Henderson [4], •••, Morrell [5]; A, estimated using METALS model. (UseEqun 6.1 to calculate properties in the 'mushy' region.)


Heat capacity and enthalpy have been measured by DSC [2]. The Cp results are shownin Figure 2 and this was followed by Cp peaks corresponding to the fusion region. A departurefrom Cp-T curve indicated that a solid state transition occured around 380 0C and between567 0C and 607 0C (Figure 3). The values Cp(f) = 1.19 J K'1 g1 for the liquid phase and AHftls =425 ± 5 Jg"1 were obtained. Values for the apparent Cp in the fusion region (Figure 3) are nottrue Cp values and estimated Cp values should be used for the (solid + liquid) region. Enthalpyvalues are given in Figure 4.

Temperature (0C)

Figure 2 Heat capacity of LM25 as a function of temperature; , o, recommendedvalues; x, estimated using METALS model; —, measured Cp app values. (UseEqun 6.1 to calculate properties in the 'mushy' region.)

Den

sity

, P

(K

g m

"3)H

eat C

apac

ity,

Cp

(Jg

-1K

"1)

Values of Cp have been estimated by MTDATA [8] and METALS models [3]; estimated valuesare 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)

Figure 3 Apparent Cp-T curves for the fusion region of LM25 obtained with variouscooling rates; ; 10 K min"1; -—, -20 K min"1; , 4 O K min"1; , -80 K min"1.

Temperature (0C)

Figure 4 Enthalpy (Hx-H25) of LM25 as a function of temperature. (Use Equn6.1 tocalculate properties in the 'mushy' region.)

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

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

Heat

capaci

ty,

Cp (

J g-1

Kr1)

EnW

IaIP

y 1H

1-H

25 (J

g'1)

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 showingtwo sets of data in good agreement with each other. The higher values [3,10] were obtainedwith 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 affectedthe thickness of the sample. Preston [9] used a similar cell to Szelagowski. It is not possible todifferentiate 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)

Figure 5 Thermal diffusivity of LM25 as a function of temperature, , Henderson; •••;Preston [9]; Szelagowski [1O]; A Monaghan [U]. (Use Equn6.1 tocalculate properties in the 'mushy' region.)

Temperature (0C)

Figure 6 Thermal conductivity of LM25 as a function of temperature; , o,recommended values; *; values calculated from the WFL Rule; A, estimatedfrom (X /^) for pure Al; - - -, Henderson [4]; •••, Szelagowski [1O]. (UseEqun 6.1 to calculate properties in the 'mushy' region.)

The

rmal

diff

usiv

ity,

106a

(mV

)

Th

erm

al

conductivity,

K (

W rrr

1 K

~1)

Estimated values of the thermal conductivity of the solid were derived by calculating theelectronic and lattice contributions to the thermal conductivity at 25 0C and applying atemperature dependence [3]. These values refer to a fully annealed state. As can be seen fromFigure 6 the estimated values are in good agreement with the measured values. Values for theliquid were estimated [3] by (i) estimating the electrical conductivities of the liquid alloy andapplying 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 butvalues obtained with the second method were in good agreement with experimental values.

6 Viscosity (r\)

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

Temperature (0C)

Figure 7 Viscosity of LM25 as a function of temperature; , o recommended valuesfor LM 25; A, —; measured values for Al.

7 Fraction solid (fs)

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

Vis

cosi

ty,

rj (m

Pa

s)

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 DifferentialScanning Calorimetry, PMP, CMMT, NPL, (1996).

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

4. Henderson, J B; Blumm, J; Hageman, L: "Measurement of the properties of analuminium-silicon casting alloy in solid and molten regions", Netzsch-GeratebauGmbH, 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. NPLReport, CMMT(D) 196, (1999).

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

Fra

ctio

n S

olid

, f s

Table 1

Recommended thermophysical properties for LM25

Temp(0Q

25

100

200

300

Transition 380

400

500

567"

614a

700

800

900

1000

Densitykgm'3

2680

2662

2641

2620

2602

2600

2578

2567

2406

2379

2352

2325

2300

±3%

Cp(Jg-1 K-1)

0.880

0.921

0.967

1.011

1.046

1.055

1.098

1.127

1.19

1.19

1.19

1.19

1.19

±3%

AHfo = 425Jg-1

(H7-H25)(Jg-')

O

68

162

261

343

364

472

547

1025

1144

1263

1382

1401

±3%

X(a)

Wm'1 K'1

163

165

162

155

153

153

145

134

65.8

67.9

70

71.9

73.9

± 10%

P3 = SOxIO-6K-'

106amV

69

67

63

60

56

55

50

45

23

24

25

26

27

± 10%

t|(mPas)

-

1.38

1.2

1.1

1.0"

0.9b

± 10%

p, = 116 x IQ-6K-1

(a' melting range extrapolated value

Table 2

Fraction solid for LM25 as a function of temperaturefor a cooling rate of -10 K min"1

fsTOG

O611

0.05609

0.1607

0.2600

0.3590

0.4577

0.5571

0.6570

0.7569

0.8568

0.9567

0.95565

1.0550

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

Al-IlOOF

1 Composition (mass %)

Al98.8

Cr Cu0.10

Fe0.1

Mg Mn0.05

Si0.85

Ti Zn0.10

2 Transitions

DSC measurements: Tsol = 643 0C [I]: Tliq = 648 0C

3 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 ingood agreement with the measured value pm = 2410 kg m"3. The density as a function oftemperature [1] is given in Figure 1 and Table 1.

ps (kg.nT3) = 2710-0.242 (T-25°C) (1)

p, (kg.nT3) - 2410-0.27 (T-6480C) (2)

Temperature (0C)

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


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

Den

sity

, P

(K

g m

'3)

CP25 =0.91 JK-1B1 [1] Estimated [Metals] C^ =0.90 JK"1 g1

AHfos = 367 Jg1 [1] AHfos = [389] Jg1

Cptf) = [LlT]Jg-1

Estimated Cp values for the solid using METALS model were in excellent agreement andnever deviated by more than 3% from the measured values. The estimated enthalpy of fusionwas about 6% higher than the measured value. The adopted values for Cp for the liquid alloywere derived from the estimated Cp values since the measured values (ca 1.1 JK'1 g"1) due toTaylor 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 6.1to calculate properties in the 'mushy' region.)

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. (UseEqun 6.1 to calculate properties in the 'mushy' region.)

Ent

halp

y, H

T-H

25 (

Jg'1

)H

eat

Cap

acity

, Q

(J

K"1 g

'1)

5 Thermal diffusivity (a) thermal conductivity (̂ )

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

Temperature (0C)

Figure 4 Thermal diffusivity of Al alloy HOOF as a function of temperature. (UseEqun 6.1 to calculate properties in the 'mushy' region.)

Thermal conductivity values were calculated by Taylor et al [1] from the measured values ofthe 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 liquidphase, respectively. (Use Equn 6.1 to calculate properties in the 'mushy'region.)

Ther

mal

Con

duct

ivity

^

(Wm

-1 K1)

Ther

mal

Diff

usiv

ity,

I6a

(m2*1

)

Taylor et al [1] also measured the electrical resistivity of the alloy. Values of the thermalconductivity for the fusion region were calculated using the WFL Rule. It can be seen fromFigure 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 andLM25.

References

1. Taylor, R E; Groot, H; Goerz, T; Ferrier, J; Taylor, D L: High Temp.-High Pressure30(1998)269/275.

Table 1

Recommended values for the thermophysical properties of Al alloy - HOOF

T0C

25100200300400500600643a

648a

648"700800

Densitykgm'3

271027002660264026152595257525672565241023962369

J K-1V0.910.93

0.9751.001.031.081.14

[1.15]"[1.15]"

1.171.171.17

H7-H25

Jg1

O6916426336547057662563199810591176

106aHl2S

908887

85.5838074--

34.53535b

XWm'1 K-'

219221226226224224217

--

979897

T|mPas

[1.15]'[1.05]°[0.9]c

n |»» p= melting range = extrapolated value [ ] = estimated value

A1-2024-T4


Al92.0

Cr Cu0.10 4.4

Fe0.50

Mg1.5

Mn0.6

Si Ti Zn0.50 0.15 0.25

2 Transitions

DSC measurements: Tsol - 538 0C [I]: Tliq = 632 0C [1]

The as-received material exhibited an exothermic transition on heating which was absent inthe cooling cycle.

3 Density

P25 = 2785 kg m'3 [I]: Estimated (Metals) = 2795 kg in3

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.

ps (kg.nT3) = 2785-0.213 (T-25°C) (1)

P^ (kg.m~3) = 2500-0.28 (T-632 0C) (2)

Temperature (0C)

Figure 1 Density of Al alloy 2024 as a function of temperature [I]. (Use Equn 6.1 tocalculate properties in the 'mushy' region.)

Den

sity

, P

(K

gm"3)


Taylor et al [1] measured Cp on the heating and cooling cycle using DSC. The results for the as-received 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, thesmooth Cp-T values obtained on the cooling curve have been adopted in Figure 2 and Table 1.

CP25 = 0.85 JK'1 g'1 [1] Estimated [Metals] C = [0.87] JK'1 g 1

AHfUS = 297Jg1 [1] AH*8 - [366JJg-1

Cptf) = [1.H]Jg1K-1

Temperature (0C)

Figure 2 Heat capacity of Al alloy 2024 as a function of temperature [I]. (UseEqun 6.1 to calculate properties in the 'mushy' region.)

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 valuewas appreciably higher (> 20%) than the measured value. The enthalpy (H1-H25) values shown inFigure 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 veryinsensitive scale.

Temperature (0C)

Figure 3 Enthalpy (H1-H25) of Al alloy 2024 as a function of temperature [I]. (UseEqun 6.1 to calculate properties in the 'mushy' region.)

Ent

halp

y, H

T -

H25

(Jg

"1)

Hea

t C

apac

ity,

Cp

(J K

'1 g

'1)


Taylor et al [1] measured the thermal diffusivity using the laser pulse method. It was foundthat values obtained on the cooling cycle were significantly higher than those derived on theheating cycle. Several sets of values were recorded for different cooling cycles. Thisbehaviour was attributed to strain in the specimens resulting from the thermal and mechanicaltreatment. 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. (UseEqun 6.1 to calculate properties in the 'mushy' region.)

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

Temperature (0C)

Figure 5 Thermal conductivity of Al alloy 2024 as a function of temperature; , ofrom thermal diffusivity values; G£, ^9 calculated using WFL Rule. (UseEqun 6.1 to calculate properties in the 'mushy' region.)

The

rmal

Con

duct

ivity

, A.

(Wm

-1 K

'1)T

herm

al D

iffus

ivity

, 10

6a

(m2s-

1)

Thermal conductivity values for the fusion region were calculated from the electricalresistivity values reported by Taylor et al [1] using the WFL Rule. It can be seen fromFigure 5 that the calculated values are in agreement with the measured values although theestimated 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 valuesfor pure Al and LM25.

References

1. Taylor, R E; Groot, H; Goerz, T; Ferrier, J; Taylor, D L: High Temp-High Pressures30(1998)269-275.

Table 1

Recommended values for the thermophysical properties of Al alloy - 2024

T0C

25100200300400500538a

632a

632700800

Densitykgm"3

2785277027502730270726832674

-250024802452

J K-1V0.850.90

[0.95]c

0.971.001.081.10

-1.14°1.14°1.14C

H7-H25

Jg1

O6615925535345756667397010481162

106aHi2S-1

74b

747473706564-

303030b

XWin'1 K-1

175185193193190188188

85.58584

*\mPas

[1.3]c

[l-2]c

[1.1]"

n K Q

= melting range = extrapolated value [ ] = estimated value

Al-3004


Al97.2

Cu0.2

Fe0.43

Mg1.0

Mn1.0

Si0.14

Zn0.25

2 Transitions

T801-629 0C[I] Tliq = 654 0C[I]DPSC: T801 = 617 0C [2] Tliq = 656 0C [2]

MTDATA predicts T801 = 589 0C Tliq - 644 0C

The latter values [2] have been adopted. Two bumps in the Cp-T curve were observed withmaximum 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)

ps (kg.m~3) - 2720-0.234 (T-25°C) (1)

p^ (kg.m"3) - 2400-0.27 (T-6560C) (2)

Temperature (0C)

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

Den

sity

, P

(K

g m

"3)

Density values are given in Table 1 and Figure 1. Values calculated using METALS modelare 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 1and Figure 2. Two "bumps" at ca 400 and 550 0C were observed in the Cp-T curve on thefirst heating cycle. However, after cooling at -10 Kmin"1 the second heating curve moved to420 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]: Estimated (METALS) Cp25 - [0.90] JK^g1 [2]Cp(O = 1.22 JKV: Cp(O = [1-17] JKV P]AHfos = 382 JKV-' AHftls =383 Jg1 [2]

The Cp and (H1-H25) values are given in Table 1 and Figures 2 and 3, respectively. Values ofCp in the temperature range (300-617 0C) (Figure 2) probably contain contributions fromenthalpies of solid state transitions and consequently estimated Cp values should be used forthe 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 aftercooling at -10 Kmin"1. (Use Equn6.1 to calculate properties in the 'mushy'region.)

Heat

Capaci

ty,

Cp (J

g'1

K"1)

Temperature (0C)

Figure 3 Enthalpy (H1-H25) of Al alloy 3004 as a function of temperature based onrecommended values. (Use Equn6.1 to calculate properties in the 'mushy'region.)

5 Thermal diffusivity (a) thermal conductivity (A)

A value OfA25 =165 Wm-1K"1 has been reported for the solid [I].

The thermal diffusivity of 3004 was measured by Szelagowski [4] using the laser flashmethod, the results are given in Figure 3. Thermal conductivities shown in Figure 4 werecalculated from these values using the heat capacity and density values given in Table 1. Thediscrepancy in the thermal conductivity values at 25 0C could be a result of differences inthermal and mechanical histories of the samples. The thermal diffusivity of the solid is fairlyconstant over the temperature range studied. The thermal diffusivity values show a rapiddecrease at 600 0C5 this would be expected to occur at 630 0C which suggests temperaturemeasurements 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.

Ent

halp

y, H

7-H

25 (

Jg'1)

Temperature (0C)


Temperature (0C)

Figure 5 Thermal conductivity of Al alloy 3004 as a function of temperature. (UseEqun 6.1 to calculate properties in the 'mushy' region.)

6 Viscosity

The viscosity of alloy 3004 was estimated by comparison with the experimental values forLM25 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 inFigure 6 and in Table 2. Values of fs calculated by MTDATA which relate to equilibriumconditions agree well with fs values obtained in the heating cycle for most of the temperaturerange.

The

rmal

Con

duct

ivity

, A,

(Wm

-1K

"1)

The

rmal

diff

usiv

ity,

106a

(Hl2S

-1)

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 ParkOH5 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 ofcommercial alloys, Proc. Nottingham Univ - Osaka Univ, Joint Symp heldNottingham, Sept (1995).

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

Fra

ctio

n S

olid

, fs

Table 1

Recommended thermophysical properties of Al alloy 3004

T(0C)25100200300400500600617"656"656700800900

Density(kgm-3)2720270626852662263826112587258325722400238823612334

Cp(Jg-1K-1)0.900.940.991.004(1.066)3

(1.11)"(1.16)a

1.221.221.221.22

(H1-H25)(Jg1)O691652653724866056256701052110512271349

X(Wm-1K'1)

141148156158167174182183

61616160

106

(Hi2S-1)57.55858.55959.56060.5"61b

21212121

T!(mPas)

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

a • (c)( ) = estimated using METALS model [ ] estimated value

= melting range

Table 2

Fraction solid as a function of temperature for Al-3004 using heatingand cooling rates of 10 Kmin '

Temp CCoolingHeating

Fraction solidO

654658*

0.05• 649657*

0.1649

656*

0.2647655

0.3646653

0.4645652

0.5644650

0.6643648

0.7641645

0.8638643

0.9634637

0.95629634

1.0597617


A1-6061-T6


Al96.45

Cr0.4

Cu0.3

Fe0.7

Mg1.0

Mn0.15

Si0.6

Ti0.15

Zn0.25

2 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 usingdilatometry. The estimated density at the liquidus temperature pm = [2408] kgm"3 is in goodagreement with the measured value, pm = 2415 kgm"3.

ps (kg.m"3) - 2705-0.201 (T-25°C) (1)

p^ (kg.m~3) = 2415-0.28 (T-642°C) (2)

Temperature (0C)

Figure 1 Density as a function of temperature [I]. (Use Equn 6.1 to calculate propertiesin the 'mushy' region.)


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

Den

sity

, p

(Kg m

'3)

CP25 = 0.87JK-Ig-I [i] Estimated [Metals] C = [0.89] JK'l g-1

AHfos = 336Jg-I [i] AHftls = [38O]Jg-I

CpW = [1.17] Jg-I K-I

Estimated Cp values were in good agreement with the measured values, never deviating bymore 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 valuesare reported [1] on a very insensitive scale.

Temperature (0C)

Figure 2 Heat capacity of Al alloy 6061 as a function of temperature [I]. (UseEqun 6.1 to calculate properties in the 'mushy' region.)

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

Temperature (0C)

Figure 3 Enthalpy (H7-H25) of Al alloy 6061 as a function of temperature [I]. (UseEqun 6.1 to calculate properties in the 'mushy' region.)

Ent

halp

y, H

7-H

25 (

Jg'1)

Hea

t C

apac

ity,

Cp

(J K

"1 g"1)


Taylor et al [1] measured the thermal diffusivity for both heating and cooling cycles using thelaser pulse method. The results for the solid were obtained for both free-standing samplesand specimens held in sapphire cells. Differences of up to 12% were recorded whichprobably 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 annealedsamples.

Temperature (0C)


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 forsolid and liquid states, respectively. (Use Equn 6.1 to calculate properties inthe 'mushy' region.)

The

rmal

Con

duct

ivity

, K

(Wm

-1IC

1)

The

rmal

Diff

usiv

ity,

106a

(m

2 s

'1)

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

6 Viscosity


References


Table 1

Recommended values for the thermophysical properties of Al alloy - 6061-T6

T0C

25100200300400500600a

642a

642a

700800

Densitykgm"3

27052695267526552635261025902580241524002372

J K-'V1

0.870.950.981.021.061.151.16

[1.16]b

1.17C

1.17°1.17C

H1-H25

Jg1

O69166266370480596

[645]b

98110491166

106aHi2S-1

-76

77.5787675

66.5

3232.533b

XWm'1 K-1

-195203211212225200

909192

1mPas

[1.15]'[1.05]c

[1.O]"

n V\ p= melting range = extrapolated value = estimated value

A1-7075-T6


Al88.7

Cr Cu0.2 1.6

Fe0.50

Mg2.5

Mn0.30

Si0.4

Ti0.2

Zn5.6

2 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 andliquid states using dilatometry. The estimated density of the liquid at the liquidus temperaturepm = [2493] kgm"3 is in good agreement with the measured value, pm = 2500 kgm"3.

ps (kg.m"3) - 2805-0.224 (T-25°C) (1)

pe (kg.nT3) = 2500-0.28 (T-628 0C) (2)

Temperature (0C)

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


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

Den

sity

, p

(Kg

m"3)

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 resultsobtained during the heating cycle have been adopted and are given in Figure 2 and Table 1.

CP25 = 0.85 JK-1 g'1 [1] Estimated [METALS] CP25 = [0.86] JK'1 g1

AHfus = 332jg-i tl] AHfuS = [358] jg-i

CpW = [LH]Jg1K"1

The estimated Cp values obtained with METALS model were in good agreement with themeasured values, never deviating by more than 3%. The estimated enthalpy of fusion was7% higher than the measured value. The Cp values for the liquid alloy were based onestimated 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 tocalculate properties in the 'mushy' region.)

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

Temperature (0C)

Figure 3 Enthalpy (H1-H25) of Al alloy 7075 as a function of temperature. (UseEqun 6.1 to calculate properties in the 'mushy' region.)

Ent

halp

y, H

T-H

25

(Jg

1)

Hea

t Cap

acity

, C

p (J

IC1Q

'1)


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

Temperature (0C)


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 fusionregion were calculated from the electrical resistivity values reported by Taylor et al using theWFL Rule. It can be seen from Figure 5 that the calculated values are in good agreementwith the measured values for the liquid phase but are about 10% low for the solid at thesolidus 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 forsolid and liquid phases, respectively. (Use Equn 6.1 to calculate properties in the'mushy' region.)

The

rmal

Con

duct

ivity

, A,

(Wm

-1IC

1)

The

rmal

Diff

usiv

ity,

106a

(m2s

1)

6 Viscosity


References


Table 1

Recommended values for the thermophysical properties of Al alloy - 7075

T0C

25100200300400500532a

628a

628a

700800

Densitykgm"3

2805279527702750272527002692

250024802452

J K-1V0.850.910.960.981.041.101.11

[1.13]"1.13°1.13°1.13°

Hx-H25

Jg1

O66160257358465501

[608]b

100010811194

106aHi2S-1

7374726966

64.5

303030b

A.Wm-' K'1

-186197194196196193

858483

T!mPas

[l-3]c

[l-2]c

[1.1]«

a = melting range [ ] = extrapolated value [ ]c = estimated value

CoPure Cobalt


(Cph) -» (fee) T; = 422 0C [1] Curie temperature = 1123 0C [1]mp= 1495 0C [1]

2 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 tothat recommended by Watanabe et al [5]. The density decrease at the melting point is 5.5%.

ps (kg.m~3) - 8862 - 0.443 (T-25°C) (1)

p^ (kg.nT3) = 7750-1.1 (T-1495°C) (2)

Temperature (0C)Figure 1 Density of pure cobalt as a function of temperature.


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 at1123 0C which corresponds to the Curie Temperature.

Dinsdale [1] reported:

AHS- = 7.25Jg-1Il]

AHfos= 275 Jg-![l]

Cp(I) = 0.667Jg-1K-Ml]

Densi

ty,

p (

Kg rrr

3)

Temperature (0C)

Figure 2 Heat capacity of pure Co as a function of temperature.

Temperature (0C)

Figure 3 Enthalpy of pure Co as a function of temperature.

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

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

EH

tHa

IPy

7H

i-H

25(J

g-"

1)

Heat

capaci

ty,

CP (

J g'1

K"1)

Temperature (0C)

Figure 4 Thermal conductivity of Co as function of temperature; , o, recommended[ ]; - -, Zinovyev [4]; A5 Ostrovskii [5], <*, *, WFL values for solid andliquid, respectively.

Thermal conductivity values for liquid Co (Figure 4) have been reviewed by Mills et al [3]. Itcan be seen from Figure 4 that values reported by Zinovyev et al [4] are ca 43 Wm-1K"1

whereas Ostrovskii [5] has reported a value of 35 Wm-1K"1 for A,™. Values for A,™ and A,™ canbe derived from electrical resistivity measurements using the WFL Rule [2]. Calculations

gave values for A£ (Wm-1K"1), of 55, [6] 50 [7] 50 [8] and 42 [4] Win1 K"1 and A/J1 (Wm-1K"1)values of 42 [6] 34 [7] 36 [8] and 30 [4] Wm"1 K"1. The following values have been adoptedbut are subject to uncertainties of about +5 Wm-1K"1 and further work is needed to resolvediscrepancies.

A,™ =48WnT1 K'1; X* =40WnT] K"1

Thermal diffusivity (a) values derived from the adopted data are given in Table 1 andFigure 5.

Temperature (0C)Figure 5 Thermal diffusivity of pure Co as a function of temperature, after Zinovyev et

al [4].

The

rmal

diff

usi

vity

, 10

6a (m

2s~1)

Th

erm

al

conduct

ivity

, A

(W

m~1 K

~1)

5 Viscosity (r|)

Viscosity measurements [10] for liquid Co have been reported several investigators (Figure 6)and it can be seen that there is 20% discrepancy between the lower values [11,12] and thehigher values [13,14,15]. Recently, Sato and Yamamura [22] have reported values, thesehave been adopted.

2514Iog10 r|(mPas) = - 0.690 + —— (3)

where T is in K.

Temperature (0C)Figure 6 Viscosity on a logarithmic scale as a function of temperature; , o

recommended values [22], +, [U]; O [12]; D [13]; x [14]; A [15].

6 Surface tension (y)

Keene [16] reviewed the surface tension measurements and proposed the following relation:

y (mNm-1)=1882-0.34(T-1495°C) (4)

Brooks and Mills [17] obtained Equation 5 by applying a correction for the effect ofelectromagnetic pressure on values derived previously with the levitated drop method.

y(mNm-1)=1936-0.43(T-1495°C) (5)

Egry et al [18] obtained Equation 6 using the levitated drop method and was able to apply thecorrection directly to the results.

y (mNnT1 )= 1874-0.28(T -1495 0C) (6)

The values given in Equation 6 are in excellent agreement with Keene's recommendedequation and are preferred because of the nature of the corrections was more certain, in thisspecific case, than for those applied to data reported by Brooks [17].

Vis

cosi

ty, t|

(M

Pa

s)

Temperature (0C)Figure 7 Surface tension as a function of temperature; —, o[16]; — [18]; • • • • [17].

The effect of oxygen on the surface tension has been determined by Ogino et al [19]. Theresults are shown in Figure 8.

In (mass% O)Figure 8 Surface tension as a function of logarithm of mass % oxygen [19].

7 Emissivity (s)

Values of Sx at 0.65 ^m of 0.38 [20] and 0.21 [16] have been cited for the solid and ex = 0.37at 0.65 jim for the liquid.

References

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

2. Iida, T and Guthrie, R I L . The physical properties of liquid metals. Oxford ClarendonPress, Oxford (1988).

Surface

tensi

on,

y (m

N m

"1)S

urf

ace

tensio

n,

y (m

N m

""1)

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

4. Zinovyev, V Y; Polev, V E; Taluts, S G; Zinovyeva, G P and Ilinykh, S A. Phys. MetMetallog 61 (1986) 85/92.

5. Ostrovskii, O I; Ermachenko, V A; Popov, V M; Grigoryan, T A and Kogtan, L E:Russ. J. Phys. Chem. 54 (1980) (5) 739/741.

6. Regeli, cited in reference 2.

7. Ono, Y; Yagi, T. Trans. ISIJ12 (1972) 314.

8. Kite, V; Oguchi, S; Morita, Z. Tetsu to Hagane 64 (1978) 711.

9. Pottlacher, G; Jager, H; Negev, T. High Temp - High Pressures 19 (1987) 19/27.

10. Iida, T and Shiraishi, Y. Handbook of Physico-chemical properties at hightemperatures publ. ISIJ, Tokyo, edited Y Kawai and Y Shiraishi, (1988) Special IssueNo !,Chapter4.

11. Cavalier, G: Compt. Rendus 256 (1963) 1308.

12. Vertman, A A and Sumarin A M: DoId. Akad. NaukSSSR, 132 (1960) 572.

13. Frohberg, M G and Weber, R: Archiv. Eisenhuttenw. 35 (1964) 885.

14. Cavalier, G: (1959) cited in reference 10.

15. Kaplun A B and Avaliani, MI Teplofiz. Vysoh.Temp. 15 (1977) (2) 305.

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

17. Brooks, R F and Mills, K C. High Temp-High Pressure 25 (1993) 657/664.

18. Egry, I and Eichel, M. Z Metallkunde 90(1999).

19. Ogino, K; Taimatsu, H and Nakatani, F. J. Jap. Inst Metals 46 (1982) 957.

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

21. Smithells, C J. Metals Reference Book, Butterworths, London, 4th edition (1967) vol 3732.

22. Sato, Y and Yamamura, T: Private communication, Tohoku Univ., Sendai, Japan,Aug(l 999).

Table 1

Recommended values for thermophysical properties of pure Co

T0C25100200300400500(a)

600700800900100011001123(b)

1200130014001495149515001600

PTkgm'3

88628827878487408696865486088563851984748429838583748341829782538208775077447634

CpJg1 K-1

0.4240.4520.4620.4960.5140.5420.5760.6160.6620.7250.8080.9300.9610.7070.6710.6670.6670.6670.6670.667

(Hx-H25)Jg1

O3379126177237293353416485562649669720789853916119111941261

106aIn2S-1

26.322.319.515.914.011.710.59.78.98.17.05.55.07.38.38.48.27.0

XWm'1 K-'

9989796962.55552.5515049.54843404346474840

T]mPas

5.45.34.5

YmNm'1

188218801812

SXat 0.65 fj,m

0.36

0.370.370.37

/a\v ' = after phase transition (cph -> fee)

^ ' = Curie Temperature

Date: March 1999

Co - X-45


C

0.25

Co

52.6

Cr

25.5

Fe

2.0

Mn

0.7

Ni

10.5

P

0.04

S

0.04

Si

0.8

W

7.5

2 Transitions

DSC experiments suggested that a transition occurs between 600 and 620 0C and results in anincrease in Cp. A second transition occurs around 1160 0C was also observed. The meltingrange has been reported [1] as

T801 = 13330C Tliq = 13810C [1]

Preliminary MTDATA calculations [2] indicate that the eutectic melting commences at 1200 0Cand the Tliq occurs at 1377 0C.

Values obtained by DSC on the heating cycle for a small sample of X45 (Figure 2) indicatedeutectic melting started at 1214 0C and fusion was completed at 1435 0C [3] with peaktemperature around 1425 0C.

T801 = 12140C and Tliq = 1425 ±5 0C

3 Density (p) thermal expansion coefficient (a)

A value of p = 8610 kg m"3 has been reported for the density of solid X45 at 25 0C and thermalexpansion coefficients given by of (25-T 0C) = (11.7 + 5.8 x 1O-3T) x 10"6 K'1 have beenadopted. The linear thermal expansion coefficient (a) values reported previously for X40(which is of similar composition to X45) are in good agreement. Density data listed in Table 1and Figure 1 are derived from these values, the density of the liquid was derived by assumingthe decrease in density at the liquidus temperature was identical (4%) with that for pure cobalt.

ps (kg.m~3) = 8610-0.401 (T-25°C) (1)

Pe (kg.nT3) - 7720-1.05 (T-1425 0C) (2)

Temperature (0C)

Figure 1 Density of Co alloy X45 as a function of temperature. (Use Equn6.1 tocalculate properties in the 'mushy' region.)

4 Heat capacity (Cp) enthalpy

The temperature dependencies of Cp and enthalpy (H1 - H25) given in Figures 2 and 3,respectively, were obtained [3] by differential scanning calorimetry (DSC). Inspection ofFigure 2 shows that there is evidence for a transition around 620 0C. There is also a peak in therange 1050-130O0C, where there are two peaks around 1160 and 1250-130O0C which isprobably associated with eutectic melting. It was noted that the enthalpy associated with thelatter transition was much higher (ca 35 Jg"1) in the as-received material than in samples cooledfrom 1500 to 95O0C where the peaks tended to be smudged out. The phase diagramcalculations carried out using MTDATA [2] indicate that this transition corresponds to theeutectic melting in the alloy. The property values reported in Table 1 are based on theassumption that the fusion range was 1214 to 1405 0C. The following recommended values arecompared with estimated values below. It can be seen from Figure 2 that the estimatedenthalpies are in very good agreement with the measured values. The estimated Cp valuesshould be used for Cp values in the transition ranges around 1160 0C and (1214-1405 0C) sincemeasured values are apparent Cpapp values containing enthalpy contributions.

Measured values:

Cp25

CPW

AH*5

= 0.435 Jg1 K'1

= 0.75 ± 0.03 Jg-1 K-'

= 245 ± 10 Jg'1

(Estimated values)

Cp25 =(0.4 13) Jg-' K-'

Cp(f) -0.675Jg-1K-1

AHfos =275 Jg-'

Densi

ty,

p (

Kg n

rr3)

Temperature (0C)Figure 2 Heat capacity of Co alloy X45 as a function of temperature; , o

recommended values [3]; —, ••••, C0 in transition ranges for small (48 mg)Fapp

and large (247 mg) specimens, respectively; x, values estimated with METALSmodel. (Use Equn 6.1 to calculate properties in the 'mushy' region.)

Temperature (0C)

Figure 3 Enthalpy (H7-H25) as a function of temperature for Co alloy X45; , o,recommended values; x? estimated by METALS model.

Enth

alp

y, H

T-H

25 (

Jg

-1)

Heat

capaci

ty,

CP (

J g~

1 K"1)

Temperature (0C)

Figure 4 Thermal diffusivity for Co alloy, X45, as a function of temperature ASzelakowski [4]; , Monaghan [5]; , o, recommended (values for theliquid were derived from estimated thermal conductivity data). (Use Equn 6.1 tocalculate properties in the 'mushy' region.)


Thermal diffusivity (a) values (Figure 4) were obtained up to 1100 0C by Szelakovskii [4] andMonaghan [5] using the laser flash method. The values of Szelakowskii [4] are about 10%higher than those due to Monaghan, which may be due to differences in thermal and mechanicalhistories of the samples. Mean values have been adopted. Thermal conductivity values derivedfrom the relationship, A,= aCp.p are given in Figure 5. No values were derived at highertemperatures, this was attributed to reaction between the sample and the sapphire cassetteholding it [4]. An electrical resistivity of 1.3 mQm has been reported at 1200 0C [1] whichyields a value of about 28 Wm"1 K"1 using the Lorenz relationship A = 2445 Ta where a = thereciprocal resistivity. The thermal conductivity value A, = 30 Wm"1 K"1 was estimated for theliquid phase by (i) comparison with equivalent measurements for nickel-based alloys and (ii)extrapolating the a-T curve to Tliq and assuming a 20% decrease in a for the liquid and (iii)values based on estimated electrical conductivities of the liquid.

A(liq) = [30] Wm"1 K'1

Th

erm

al d

iffu

sivi

ty,

106a

(mV

)

Temperature (0C)

Figure 5 Thermal conductivity of X45 as a function of temperature; O, values obtainedfrom recommended thermal diffusivity values, * derived from electricalresistivity value and Wiedemann-Franz-Lorenz relation.

6 Emissivity (s)

Normal emissivity values have been reported [1] at 35 and 629 0C and are shown in Figure 6.

Wavelength, X (nm)

Figure 6 Normal spectral emissivity as a function of wavelength [I]; , A9 at 35 0C; oat 629 0C.

Spec

tral

emis

sivi

ty, e

xT

her

mal

co

nd

uct

ivity

, X

(W m

'1 K

"1)

7 Viscosity (r|)

The viscosity of X45 has been determined by oscillation viscometry [6] and the results arecompared with those reported for pure cobalt in Figure 7. The viscosity of the alloy is about20-30% higher than that reported for pure cobalt.

r|i44o = 7.8 mPas

Temperature (0C)

Figure 7 Viscosity of liquid X45 as a function of temperature [5] compared withrecommended values for pure Co , O, experimental values for X45; x, pureCo.


The surface tension of the alloy will be dependent upon the concentration of soluble surfactantssuch as O and S; the values listed in Table 1 were derived by comparisons with pure Co andwith Ni alloy IN718 and pure Ni and represent value for an alloy with low S and O contents.


The fraction solid (fs) values obtained by DSC when heating a small specimen at 10 Kmin"1 areshown in Figure 8. No values are available for the cooling cycle, typically there is a gap of1O0C between the heating and cooling curves. The values are compared with those for fs

reported for alloy X-40 [1] in Figure 8.

Vis

cosi

ty,

TI (

mP

a s)

Temperature (0C)

Figure 8 Comparison of fraction solid as a function of temperature for alloy X45 ( )[3] with those reported for X40 ( ), [I]; MTDATA calculation(equilibrium). (Note temperature scale in DTSC experiments may be in error,see Section 5.5).

References

1. Alloy Digest publ. Eng. Alloy Digest Inc., Upper Montclair, NJ9 USA, Dec 1985.

2. Dinsdale, A: Unpublished results NPL, 1998.

3. Hayes, D; Day, A P; Richardson, M P; Chapman L: Unpublished results NPL, 1998.

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

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

6. Andon, RJL; Day, A P: unpublished results, National Physical Laboratory (1999).

Fra

ctio

n s

olid

, f s

Table 1

Thermophysical properties for Co - X-45 alloy

T0C

25

100

200

300

400

500

600

700

800

900

1000

1100

1200

1425(1)

1500

1600

Pkgm'3

8610

8580

8541

8500

8460

8436

8412

8247

8307

8265

8223

8186

8145

7732

7640

7535

Jg1 K-1

cooling

0.429

0.450

0.475

0.496

0.514

0.552

0.562

0.613

0.605

0.605

0.61

0.64

0.66

0.75

0.75

0.75

heating

0.429

0.450

0.475

0.496

0.514

0.532

0.562

0.613

0.605

0.60

0.61

0.63

0.61

0.75

0.75

0.75

HT - H25

J g 1

heating

O

33

79

128

178

231

285

346

407

467

528

591

660

1043

1098

1173

106amV

-

3.5

3.9

4.2

4.6

4.9

5.3

5.5

5.6

5.7

6.0

6.1

[5.2]

[5.2]

[5.2]

XWm'1 K-'

-

13.5

15.8

17.7

20.0

22.8

25.1

27.8

28.1

28.5

30.1

32.0

[30]

[30]

[30]

Tl

mPas

8.0

6.8

5.6

YmNm'1

[1900]

[1900]

[1900]

[ ] estimated values.

Table 2Fraction solid, fs as a function of temperature when

heating at 10 K min"1 (see Section 5.5)

fs 1.01214

0.951280

0.91330

0.81390

0.71404

0.61412

0.51415

0.41417

0.31420

0.21422.5

0.11424

O1430

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

CuPure Copper


mp = 1084.60C [I].


P25 (solid) - 8930 kg in3: a - 1.9 x 10'5 K"1 [2]

VoI TEC9 p = [5.0 + 10'3 (T - 25 0C) ] x 10'5 K'1 [2,1].

The recommended density of the solid and liquid phases as functions of temperature [2] aregiven in Figure 1. There have been a large number of determinations of the density of liquid Cu[3,4], and these have been reviewed by Iida and Guthrie [3] and Watanabe et al [4]. The p-Trelations recommended by Iida and Guthrie [3] and Watanabe et al [4] along with recent workreported by McCormick and Brooks [5] using the levitated drop method, and by Nasch andSteinemann [6] using the y-ray attenuation technique and Henderson [2] using dilatometry areshown in Figure 2. It should be noted that the levitated drop results were affected by someuncertainty in the mass resulting from vaporisation. The difference in the p-T relations is about1.5 to 2% which is of similar magnitude to the experimental uncertainties (1-2%) of the variousmethods. The following p-T relation is a weighted mean of these relations

p, (kg m'3) = 7960 - 0.76 (T-1084 0C) (1)

The temperature dependence of the density (dp/dT) reported by Nasch and Steinemann [6] islower than that obtained in other studies; this was attributed to the fact that the value refers toconstant volume cf. constant mass in other studies.

The recommended p-T relation is shown in Figures 1 and 2. The change in volume on melting is about 4%.

Temperature (0C)

Figure 1 Recommended values for density of pure Cu as a function of temperature.

Den

sity

, p

(Kg

m"3)

Temperature (0C)

Figure 2 Density of liquid Cu as a function of temperature showing results of differentinvestigations [4]; —, o, recommended values; - - Iida [3], •••• Watanabe [4]-•-, McCormick [5]; A, Nasch [6], x Henderson [2].


Heat capacity and enthalpy values for pure copper as a function of temperature are given inFigures 3 and 4, respectively, and Table 1. Dinsdale [1] reported the following values:

AHfos = 208.7 Jg1

CpCO = 0.495 Jg1 K-1

Temperature (0C)

Figure 3 Heat capacity of liquid Cu as a function of temperature.

Hea

t Cap

acity

, Cp

(J

g'1

K"1)

Den

sity

, p

(Kg

m"3)

Temperature (0C)

Figure 4 Enthalpy of pure Cu as a function of temperature.

4 Thermal conductivity (X) thermal diffiisivity (a)

Thermal conductivity calculated from recent measurements of thermal diffusivity for thesolid phase [7,8,9,2] are shown in Figure 5 and recommended values are given in Figure 5and Table 1.

Temperature (0C)

Figure 5 Thermal conductivity of pure Cu as a function of temperature; , o, •••Touloukian [7]; conductivity values calculated from thermal diffusivity data,-•-, Monaghan [8], , Henderson [2].

Thermal conductivity values for the liquid metal, given in Figure 6, were reviewed by Millset al [9], it can be seen that there is good agreement between the values reported by Tye andHay den [10], Filippov [11], Zinovyev et al [12] and those calculated from electricalresistivity data using the WFL Rule. The following values were recommended:

X™ = 330Wm'1; X? -163Wm'1 K'1 [9]

The

rmal

Con

duct

ivity

, A,

(Wm

-1K

"1)

Ent

halp

y, H

1-H

25 (

Jg'1)

X1 = 163 + 2.67 x 10~2 (T - 1085) Wm"1 K"1 [9] (2)

Temperature (0C)

Figure 6 Thermal conductivity of Cu as function of temperature, for the liquid and thesolid near the melting point, after ref 9; - - , Touloukian [7]; - - - ,Szelagowski [13] A, Zinoviev [12]; Filippov [U]; D, Tye [1O]. ®, *, WFLvalues

More recently Henderson et al [2], Monaghan et al [8] and Szelagowski [13] have measuredthe thermal diffusivity of liquid Cu using the laser flash method, these are shown in Figures5, 6 and 7. The results of the three studies are in excellent agreement with (i) each other and(ii) the results for the solid recommended by Touloukian [7].

Temperature (0C)

Figure 7 Thermal diffusivity of pure Cu as a function of temperature; ••• Henderson etal [2]; A, Monaghan [8]; , Touloukian [7]; - • -, Szelagowski [13].

The recommended thermal conductivity and diffusivity values given in Table 1 are based onthe thermal diffusivity values obtained for thermal diffusivity values reported byHenderson [2] and Monaghan [7], and by Szelagowski [13].

The

rmal

diff

usiv

ity,

106a

(mV

)

The

rmal

Con

duct

ivity

, k

(Wm

-1K

'1)

5 Viscosity (r|)

Iida and Shiraishi [14] recommended Equation 3 for the viscosity-temperature relationshipfor pure copper.

2870In T] = -0.638 + -— mPas (3)

where T is in K. Recent viscosity values obtained by Andon and Day [15] using oscillatingviscometry are in excellent agreement (Figure 8) with values predicted by Equation 3.

Temperature (0C)

Figure 8 Viscosity of pure Cu as a function of temperature [14]; , o, Andon [15],- -, x? Iida and Shiraishi [14] .


Keene [16] has reviewed the extensive literature on the surface tension of pure Cu andrecommended the relation

Y(InNnT1) -1330-0.23(T-1085 0C) (4)

More recent measurements by Brooks et al [17] covering measurements on Cu in fivedifferent laboratories resulted in Equation 5.

Y(InNnT1) = 1304-0.286(T-1085°C) (5)

The results are shown in Figure 9. Values given in Table 4 are based on Equation 5.

Vis

cosi

ty,T

I (m

Pa

s)

Temperature (0C)

Figure 9 Surface tension of pure Cu as a function of temperature; , Brooks etal[17];---,Keene[16].

Oxygen is surface active and reduces the surface tension. Figure 10 shows the dependency ofsurface tension of oxygen content of copper [18].

log (Pressure of O2) (atm)

Figure 10 Surface tension of copper as a function of log partial pressure of O2 inexperiments as reported by different investigators.

7 Emissivity (s)

Several investigators have reported the spectral emissivity of copper (Sx) in the solid andliquid states. Recently, Watanabe et al [19] have reported spectral emissivities using coldcrucible levitation, these values have been adopted. A comparison of the data reported byother investigators with those reported by Watanabe et al [19] are shown in Figure 11, it canbe seen that Sx is wavelength dependent. It can also be seen from Figure 12 (sx liquid/sx solid)is also a function of wavelength.

Sur

face

Ten

sion

, y

(mN

m"1)

Sur

face

Ten

sion

, y

(mN

m"1)

Wavelength, X (nm)

Figure 11 The spectral emissivity as a function of wavelength for solid , o andliquid---,A Cu [19].

Wavelength, A, (nm)

Figure 12 The ratio (sx liquid/sx solid) as a function of wavelength for pure copper [19].

8X (l

iqui

d) 1

8X

(sol

id)

Spe

ctra

l E

mis

sivi

ty,

e x

References

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

2. Henderson, J B; Hagemann, L and Blumm, J: Thermophysical properties of copper:Netzsch Report 820.030/96 TPS No 4; Netzsch GmbH SeIb9 Germany, March 1996.

3. Iida, T and Guthrie, R L: The physical properties of liquid metals. Oxford SciencePublication, Oxford (1988), Chapter 3.

4. Watanabe, S; Ogino, K and Tsu, Y: Handbook of Physics - Chemical properties athigh temperatures edited by Y Kawai and Y Shiraishi, publ. ISI Japan, Special IssueNo 41 (1988), Chapter 1.

5. McCormick, A and Brooks, R F: MTS Programme on Processability:Thermophysical property data for commercial alloys measured in PMPl, 2 and 3(April '93 - March '96) National Physical Laboratory, Teddington.

6. Nasch, P M and Steinemann, S G: Phys. Chem. Liquids 29 (1995) 43/58.

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

8. Monaghan, B J; Neale, J and Chapman, L: Intl. J. Thermophys. (1999) in press.

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

10. Tye, P R and Hayden, R W: High Temp - High Pressure 11 (1979) 597/605.

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

12. Zinovyev, V E; Taluts, S G, Kamashev, M G, Vlasov, B V, Polyakova, V P, Korenovskii, NI; Chipina, LI and Zagrebin, L D: Phys. Met. Metallogr. 77 (1994) 492/497.

13. Szelagowski, H: PhD Thesis, UMIST, Manchester (1999).

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

15. Andon, R J; Chapman, L; Day, A P and Mills, K C: Viscosities of metals and alloys,NPL Report A (1999).

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

17. Brooks, R F; Mills, K C; Egry, I; Grant, D; Seetharaman, S and Vinet B: Reference data forhigh temperature viscosity and surface tension data: NPL Report CMMT(D) 136 (1998).

18. Brooks, R F: Transfer Examination Report, Imperial College (1993).

19. Watanabe, H; Susa, M and Nagata, K: Metall Trans. A 28A, (1997) 255.

Table 1

Recommended thermophysical properties for pure Cu

T0C

2510020030040050060070080090010001084.51084.511001200130014001500

PTkgm-3

893088908850880087408690863085708500843083608295796079497873779777217645

Jg1 K-1

0.3850.3970.4080.4190.4270.4340.4410.4470.4530.4600.4640.4690.4950.4950.4950.4950.4950.495

(H1-H25)Jg1

O2969111153196240284329375421461670677727776826875

106aHi2S-1

1161121071041019895939189878337375385---

XWm'1 K-'400395388382376370363356350343337330146147150---

1mPas

4.374.273.73.28b

2.93b

2.66b

YmNm'1

130413001271124212141186

£(a)

650 (am

0.100.100.100.100.160.160.160.16

a at 650 jam

extrapolation

Date: March 1999

Cu-Al(Al bronze)


Al9.7

Cu80.5

Fe4.6

Mn0.64

Ni4.6

2 Transitions

The DPSC results showed 'bumps' in the Cp-T relation at ca 320 0C and 520 0C which maybe related to solid-solid transitions [I]. Inspection of the Cu-Al phase diagram [2] suggeststhat the 520 0C endotherm may be associated with transformation into the (3 and aCu phases.It was also observed that there were 2 peaks in the Cp-T curve at 850 0C and 970 0C beforethe main fusion peak starting at 1040 0C. The peak temperature corresponded to Tliq = 10770C. The Cu-Al phase diagram indicates a short melting range so the two peaks have beenattributed to ocCu-»p transition.

Recommended: Tsol - 104O0C: Tliq = 10770C

3 Densities

The densities of Al-bronze have been estimated by the METALS model [3].

P25 = 7262 kg m'3 [3]: a = 22.2 x 10"6 K'1 [3]

The values are given in Table 1 and Figure 1.

ps (kg.m"3) - 7262 - 0.486 (T-25°C) (1)

pc (kg.m"3) = 6425-0.65 (T-1077 0C) (2)

Temperature (0C)

Figure 1 Densities of Cu-Al (Al bronze) alloy as a function of temperature.

4 Heat capacities, enthalpies

Richardson et al [1] measured the heat capacities and enthalpies, the results are given inFigures 2 and 3 and Table 1. Estimated values are shown on these figures and it can be seenthat they lie within 2% of the experimental curves except when in regions where transitionsare occurring; the experimental Cp values in these regions may not be true Cp values in theseregions since they may contain enthalpy contributions.

Cp25 = 0.44 JKV^ Estimated Cp25 = 0.442 JKV [3]

Cp(liq) = 0.65 J KV: Estimated Cp(liq) = 0.582 J KV [3]

Temperature (0C)

Figure 2 Heat capacities of aluminium bronze as a function of temperature; , o,obtained with DPSC and HTDSC [I]; x, estimated values. Estimated Cpvalues should be used in the transition regions. (Use Equn6.1 to calculateproperties in the 'mushy' region.)

Hea

t C

apac

ity,

Cp

(J(C

1Q"1)

Den

sity

, P

(K

g m

"3)

The experimental value of Cp for the liquid is only an upper limit and consequently theestimated Cp has been adopted.

Experimental values:

AHtrans (for 85() ̂ QJQ oQ transitions) = 50 + 5 Jg1

AHfos = 195 ± 8 Jg1: Estimated AHfos = 240 Jg'1

The enthalpy of fusion is a disordering process as is the enthalpy of transition (at 850 and950 0C); the experimental values of AHfos + AH1™8 = 245 Jg"1 are in good agreement with theestimated value of AHfos = 240 Jg'1. Since the Cp in the transition range (840-1000 0C) maybe enhanced by enthalpy contributions, the Cp values in this range are based on the valuesestimated by METALS model.

Temperature (0C)

Figure 3 Enthalpies of aluminium bronze as a function of temperature [I]; —, orecommended values.


Thermal diffusivity values given in Figure 4 and Table 1 have been determined bySzelakowski [4] using the laser pulse method. Thermal conductivities were calculated fromthe recommended density (p) and Cp values and are given in Figure 5 and Table 1. It shouldbe noted estimated values of Cp were used in the transition ranges since Cp values for thetransition ranges are only apparent Cpapp values and may contain enthalpy contributions. Onthe basis of these results the Al additions cause a 5-fold reduction in conductivity.

Ent

halp

y, H

7-H

25 (

Jg'1)

Temperature (0C)

Figure 4 Thermal diffusivity (a) [4] of aluminium bronze as a function of temperature.(Use Equn 6.1 to calculate properties in the c mushy' region.)

Temperature (0C)

Figure 5 Thermal conductivity of aluminium bronze as a function of temperature. (UseEqun 6 to calculate properties in the 'mushy' region.)

6 Viscosity (r|)

The viscosity values recorded by Andon et al [5] for aluminium bronze are given in Figure 4and Equation 3. It can be seen that values for pure Cu are 25% lower than those foraluminium bronze.

3218In TI (mPas) = -0.536 + —— (3)

where T is in K.

The

rmal

Con

duct

ivity

, ̂

(Wm

-1K

'1)

The

rmal

Diff

usiv

ity,

106a

(m2s

1)

Temperature (0C)

Figure 6 Viscosity of aluminium bronze as a function of temperature —, o, Al bronze,, pure Cu [5].

7 Surface tension

The estimated values given in Table 1 were calculated by analogy with values for pure copperand refer to a sample with low oxygen and sulphur contents.

8 Fraction solid

Fraction solid-temperature data given in Figure 5 and Table 2 were obtained from HTDSC [1]measurements of enthalpy evolution in the solidification range.

Temperature (0C)

Figure 7 Fraction solid (fs) as a function of temperature in the solidification range; O,heating and O9 cooling at 10 K min"1. (Note temperature scale in HTDSC maybe in error, see Section 5.5.)

Fra

ctio

n S

olid

, f s

Vis

cosi

ty,

TI (m

Pa

s)

References

1. Richardson, M J; Hayes, D; Day, A P; Mills, K C. MTS Programme onProcessability: Thermophysical property data for commercial alloys measured inPMP 1, 2 and 3, April 93 - Mar 96. Final Report NPL. Chapter 3.

2. Hansen, M; Anderko, K. Constitution of Binary Alloys ̂ publ McGraw-Hill, New York(1958) p86.

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

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

Table 1

Recommended thermophysical properties for Cu-Al (Al-bronze) alloy

Temp(0C)25100200300400500600700(b)

800(b)

900(b)

10001040*1077*107711001200130014001500

Densitykgm'3

[7262fJ

[7225](a)

[7177](a)

[7128](a)

[7080](a)

[7031](a)

[6982](a)

[6934](a)

[6885](a)

[6836](a)

[6788](a)

[6760]la)

[6750](a)

[6425]w

[6410](a)

[6343](a)

[6277](a)

[6213](a)

[6150](a)

Cp(Jg1K-1)0.440.450.4650.490.510.540.545

[0.535](a)

[0.545](a)

[0.555](a)

[0.563](a)

[0.567](a)

[0.57]{a)

[0.582](a)

[0.582](a)

[0.582](a)

[0.582](a)

[0.582](a)

[0.582](a)

(H7-H25)(Jg1)O33791261772292843424094815595876088038168749329901048

X(Wm-1K'1)

5161677580776955464342--2730303029

106aHi2S-1

14(0

15.818.220.220.921.020.318.514.612.011.211.0--7.28.08.28.2[8.2](a)

T|(mPas)

6.36.15.24.5W

4.0(c)

3.6(c)

Y(mNm-1)

[1240](a)

[1235](a)

[1215](a)

[ f a' = estimated value = transition range = extrapolated value* melting range

Date: March 1999

Table 2

Fraction solid of Cu-al (Al-bronze) for heating and cooling ratesof 10 K'1 (see Section 5.5)

fsTOC

(Cooling)TOC

(Heating)

O1070

108Ka)

0.051066

1078

0.11063

1076

0.21058

1073

0.31054

1070

0.41051

1068

0.51047

1066

0.61044

1064

L 0.71042

1062

0.81039

1060

0.91035

1057

0.951033

1054

0.981031

1052

1.01024

1046

(a) Tliq given in Section 1 is based on peak temperature

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

FePure Iron

1 Transition, melting point

cc(bcc) -»y(fcc) T^5 = 9110C [1]Y (fee) -> 8 (bee) Ttrans = 13940C [1]Melting point mp = 15380C [1]Curie temperature = 77O0C [1]

2 Density

P25 (s) = 7874 kg in'3 [1] a (20-900 0C) = 14.5 x 10'6 K'1 [2]

(P^p0 = ) at 9110C = 1.012 [2]

(p/pa) - 1.010 [3] : ps (kg m'3) (900-1394 0C) ~ 7650-0.51 (T - 9110C) [3] (1)

(p5/PY)i394°c = 0-995 [3] : ps(kgm-3) (1394-1538) ~ 7355 - 0.42 (T-1394 0C) (2)

There have been a number of density determinations carried out on liquid iron, reviews ofthese data by Iida and Guthrie [4] and Watanabe et al [5] resulted in identical relations(Equation 3).

P^ (kg.nT3) = 7030-0.86 (T-1538°C) (3)

Recently, Sharan et al [18] reported p = 7050 kgm'3 at 155O0C and Nasch and

Steinemann [6] reported a value of p™ = 6980 kg m"3 using the y-ray attenuation method.The recommended values, given in Table 1 and Figure 1, are based on Equation 1 and thevalues given above for the solid phase. The change in density at the melting pointcorresponds to 4.3% in agreement with the results of Watanabe et al [3].

Temperature (0C)

Figure 1 Density of pure Fe as a function of temperature.

Den

sity

, P

(K

g nV

3)


The recommended Cp and (H7-H25) values as functions of temperature given in Figures 2 and3, respectively, and in Table 1 are based on the values recommended by Dinsdale [I].

CP25 - 0.45 JKV [1]AH^8 (a->y) = 16Jg1 [1]AH*3118 (y-> 5) = 15Jg1 [1]AHfus = 247Jg1 [1]

Temperature (0C)

Figure 2 Heat capacity of pure iron as a function of temperature.

Temperature (0C)

Figure 3 Enthalpy (H1-H25) of pure Fe as a function of temperature.

Ent

halp

y, H

1-H

25 (

Jg'1)

Hea

t C

apac

ity,

Cp

(J K

'1 g

"1)

4 Thermal diffusivity (a) conductivity (A,)

Values for solid Fe have been reported by Touloukian [2]. Published values for solid andliquid phases in the temperature range (600-1600 0C) have been reviewed by Mills et al [7].Recently, Monaghan [8] and Szelgowski [9] have reported thermal diffusivity values obtainedusing the laser pulse method. These values [8,9] are in excellent agreement with thoserecommended by Touloukian [2] for the a phase (Figures 4 and 5). The thermal diffusivitymeasurements due to Monaghan [7] have been adopted for the y, 5 and liquid phase values. Itshould be noted that thermal diffusivity values for the 8 phase [2] showed considerable scatter(± 1 m2 s"1) and a constant value of 7 x 10"6 m2 s"1 was adopted. Consequently, errors for thethermal conductivity of the 8 phase could be of the order ±15%. The values of the thermalconductivity obtained with the WFL Rule are about 10% lower than the recommended values.

Temperature (0C)

Figure 4 Thermal conductivity of pure Fe as a function of temperature; o, —,recommended values; D, Touloukian [2]; +, Monaghan [7]; A, Szelagowski[8]; - - -, Zinovyev [9]; $, * WFL Rule.

The thermal diffusivity (a) values calculated from the thermal conductivity measurementsgiven by Touloukian [2] are given in Table 1 and Figure 5. They are compared in Figure 5with those given by other investigators including the recent laser pulse measurementsreported by Monaghan et al [8] and Szelagowski [9]. The results of the three studies for thesolid state data are in excellent agreement.

The

rmal

Con

duct

ivity

, X

(Wm

-1KT

1)

Temperature (0C)

Figure 5 Thermal diffusivity of pure Fe as a function of temperature; o, calculated fromrecommended thermal conductivity values; x, Monaghan [8]; A Szelagowski[9]; •••, Zinovyev [1O]; D, Touloukian (from thermal conductivity data)..

5 Viscosity (r|)

Iida and Guthrie [14], reviewed viscosity data in the literature and found that the variationaround the mean was about ±50%. There have been two recent investigations [11,12]utilising oscillating viscometry and the results (Figure 6) are in excellent agreement. Thesedata have been adopted and can be represented by Equation 4.

Iog10 T| (mPas) = - 0.622 H- 2478/T (4)

where T is in K.

Temperature (0C)

Figure 6 Viscosity of pure Fe as a function of temperature o, Andon et al [11]; x, Satoet al [12]; . . . limits of results of previous investigations [4].

Vis

cosi

ty,

TI (m

Pa

s)T

herm

al D

iffus

ivity

, 10

6a

(HI2

*1)


Keene [13] correlated the surface tension data in the literature and Equation 5 represents thetemperature dependence of the mean values for the surface tension of pure Fe.

Y (mNm-1) = 1909 - 0.52 (T - 1538 0C) (5)

Recently, an interlaboratory study [14] was carried out to measure the surface tension of pureFe. The results are given by Equation 6.

Y (mNm-1) = 1870 - 0.43 (T - 1538 0C) (6)

The recommended values shown in Figure 7 and Table 1 are based on Equation 6 and thevalues given by Keene [13] are in very good agreement.

Temperature (0C)

Figure 7 Surface tension of pure Fe as a function of temperature, —, Brooks et al [14];A - - - , Keene [13].

Oxygen is very surface active in molten Fe. Several investigators have carried outmeasurements on this system [15] (Figure 8). Although there is significant variation in theactual surface tension values the trend is clear. Cramb [16] proposed the relationship given inEquation 7.

Y mNm-1 = 1913 - 279 In [1 + 140 aj (7)

where a0 = activity of oxygen (which can be taken as the weight % O).

Sur

face

Ten

sion

, y

(mN

m"1)

Oxygen Content (at%)

Figure 8 Surface tension of Fe-O system as a function of O content as reported byvarious investigators [15]; , values derived from Equn 5; other symbolsrefer to other investigators.

7 Emissivity (s)

Shiraishi [17] reported the following normal emissivity values for a wavelength of 0.65 |iim.

Smooth sample; T 0C (s,); 830 (0.376); 1230 (0.34); 1430 (0.32)Liquid Fe; T 0C (sj; 1600 (0.28); 1800 (0.105)Total normal (C1^) values were also given:Polished Fe; T 0C (S11,); 400-600 0C (0.186-0.248)Oxidised Fe; T 0C (STO); 430 (0.54) 630 (0.58) 830 (0.63).

References


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

3. Watanabe, S; Tsu, Y; Takano, K; Shiraishi, Y: J. Jap. Inst. Metals 45 (1980) 242/249.

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

5. Watanabe, S; Ogino, K and Tsu, Y: Handbook of physico-chemical properties at hightemperatures edited Y Kawai and Y Shiraishi, publ. ISI Japan, Tokyo, Special IssueNo 41 (1988), Chapter 1.

Sur

face

Ten

sion

, -y

(mN

m"1)

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

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

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

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

10. Zinovyev, V Y; Polev, V F; Taluts, S G; Zinovyeva, G P; Ilinkha, S A: Phys. Met.Metallog. 61 (6) (1986) 85/92. See also V Y Zinovyev, Thermophysicalproperties ofmetals at high temperatures, publ Metallurgica, Moscow (1989) ISBN5-229-002-60-3

11. Andon, R S L ; Chapman, L; Day, A P; Mills, K C: Viscosities of liquid metals andcommercial alloys. NPL Report A CMMT167 (1999).

12. Sato, Y; Moriguchi, S; Yamamura, T; Proc. 18th Japan Symp. Thermophysical.Properties held Nara, Japan (1997) 147.

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

14. Brooks, R F; Mills, K C; Egry, I; Seetharaman, S; Grant, D; Vinet, B: Reference datafor high temperature viscosity and surface tension data: NPL Report CMMT(D) 136.

15. Brooks, R F: Transfer Examination Report, Imperial College (1994). See alsoB J Keene, Intl. Materials Reviews, 33 (1988) 20.

16. Cramb, A; Jimbo, I: Proc. of Turkdogan Conf. held Pittsburgh, PA, May (1994),publ. TMS, 195/206.

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

18. Sharan, A; Nagasaka, T and Cramb, A W: Met. Trans. B, 25B (1994) 939/942.

Table 1

Recommended thermophysical properties for pure Fe

T0C

25100200300400500600700(770)c

800900911a

911"10001100120013001394a

1394a

140015001538"1538"160017001800

DensityKgm-3

78747849781577817747771376797646762276127578757476507605755475037452744874117408736673507030697768916805

Jg1 k-'0.450.4790.5200.5620.6010.6600.7450.9051.0550.9450.750.7410.6070.620.6350.650.6650.680.7350.7380.7550.7620.8240.8240.8240.824

(H7-H25)Jg-'

O34.884.71391972603304114790.5130.593602618672735799865927942948102310501297135014321515

10" aHi2S-1

20.518.115.012.610.58.56.74.3

4.1

6.356.656.97.157.47.657.07.07.07.06.26.36.556.8

XWm-' K-'72.76861554943.538.533.6

29.329.6

29.531.533.335.237.039.038.638.739.439.73636.237.238

T!Pas

5.65.O24.303.74

TmNm"1

1870184318001757

e

0.28

0.105

transition temperature

fusion temperature

Curie temperature

Fe-CDuctile Iron


C3.61

Cr0.08

Fe92.4

MgO.002

Mn0.65

Mo0.02

Ni0.13

P0.12

S0.076

Si2.91

2 Transitions

DPSC results [1] indicated:Curie temperature: ca 740 0C [1]OC-»Y transition: onset 805 0C peak 850 0CT801 =1140 0C [1] TIiq (peak) = 1178 0C [1]TUq=1235°C[2].

3 Density (p)

P25 = 7300 kgm'3 [2]

a (T-25 0C) = (11.9 + (0.42 x 10'2 T0C)) 10'6 K'1 [3]

Reported values for the change in density (Ap) for the (cc-»y) transition [3] vary widely; a 1%change, identical to that for pure Fe has been adopted. Values for the density of the liquidalloy were calculated from Equation 3 proposed by Jimbo and Cramb [4] for Fe-3.6%Cwhich was subsequently modified to account for the Si content

Ps(25-8o5°c) (kg-nT3) = 7300 - 0.288 (T-25°C) (1)

P£(805-ii90°C) (kg-ni'3) = 7150-0.30 (T-SOS0C) (2)

p, (kg m-3) = 6836 - 0.513 (T-1550 0C) -130 (%Si) (3)

Recommended density values at various temperatures are given in Table 1 and Figure 1.

Temperature (0C)

Figure 1 Density of ductile iron as a function of temperature. (Use Equn 6.1 to calculateproperties in the 'mushy' region.)


Richardson et al [1] reported Cp and (H7-H25) values for temperatures up to 700 0C and Chapman [5]between 700 and 1300 0C. These values are given in Table 1 and in Figures 2 and 3, respectively

Cp25 = 0.48 Jg1 Cp(^) = 0.83 JKV AHftls - 220 ± 10 Jg1

The following values were estimated by analogy with the values obtained for grey iron

AH* (a-»y) = [36] Jg1 AHftls = [240] Jg1

METALS model [6] gave a value of AHftls = [262] Jg'1 and Cp(^) = 0.755 JK'V when thecarbon content was ignored.

Temperature (0C)

Figure 2 Heat capacity of ductile iron as a function of temperature; , o,experimental values; x, estimated values (Metals model); —, apparent Cp intransition regions. (Use Equn 6.1 to calculate properties in the 'mushy' region.)

Hea

t Cap

acity

,Cp

(Jg

'1 K

'1)D

ensi

ty,

P

(Kg

m'3)

Temperature (0C)

Figure 3 Enthalpy of ductile iron as a function of temperature; , o, recommendedvalue; x, Metals model. (Use Equn 6.1 to calculate properties in the 'mushy'region.)

5 Thermal diffusivity (a) thermal conductivity (k)

Szelagowski [7] reported thermal diffusivity values for the solid state. The values are givenin Table 1 and Figure 4. Thermal conductivity values were calculated from the thermaldiffusivities using the selected Cp and density values (Figure 5). The values for ductile ironare compared with those for pure Fe and grey cast iron, it can be seen that for temperaturesabove 200 0C there is little difference in thermal conductivity and diffusivity values. Theliquid alloy was found to "ball up" so no values could be obtained for the liquid alloy.

Temperature (0C)

Figure 4 Thermal diffusivity for ductile iron as a function of temperature, (—, o) arecompared with those for pure Fe (• • •) and grey cast iron ( ). (UseEqun 6.1 to calculate properties in the 'mushy9 region.)

The

rmal

diff

usiv

ity,

106a

(mV

)E

ntha

lpy,

H1 -

H25

(Jg

'1)

Temperature (0C)

Figure 5 Thermal conductivity for grey cast iron as a function of temperature, (—, o)are compared with those for pure Fe (• • • ) and grey cast iron (- -). (UseEqun 6.1 to calculate properties in the 'mushy' region.)

6 Viscosity (r|)

In the absence of reliable measurements the viscosity values given in Table 1 were estimatedby analogy with those for grey cast iron.


Jimbo and Cramb [8] noted that the surface tension of Fe-C alloys increased slightly withincreasing C content (by +30 mNm (%C)"1) in contrast to the results of other workers whorecorded a decrease in y with increasing C content. The surface tension will be determined bythe Soluble S and O levels. Jimbo and Cramb [8] point out that C increases the activity of Sand thus the value of y will be controlled by the S content.

Estimates of y at 1550 0C can be obtained using the following Equation derived by Cramb[12] for Fe-S and modified for the effect of C on y [11].

y1550 (mNm"1) = 1913-195 In [1 + 365 aj + 30 (%C) (4)

where as = activity of S and can be taken as wt % S. The temperature dependence will bepositive for alloys containing >10 ppm S.

8 Fraction solid

Fraction solid values calculated from DTSC measurements are given in Figure 6 and Table 2.It should be noted that there is a wide gap between heating and cooling curves which mayhave been affected by (i) large specimen mass (> 100 mg), (ii) uncertainties in temperaturescale for DTSC measurements and (iii) low thermal conductivity of specimen.

The

rmal

Con

duct

ivity

, A,

(Wm

-1K

'1)

Temperature (0C)

Figure 6 Fraction solid in ductile iron as a function of temperature for heating (- -, D)and cooling rates ( , o) rates of 10 K min"1. (Note temperature scale inDTSC studies may be in error, see Section 5.5).

References

1. Richardson, M J; Hayes, D; Day, A P; Mills, K C. Final report on differentialscanning chlorimetry. Final Report on Processability: Thermophysical property datafor commercial alloys measured in PMP 1, 2 and 3 (1.4.93-31.3.96). NationalPhysical Laboratory (1996).

2. CRS Handbook of Chemistry and Physics edited D R Lide, publ CRC Press 74th

edition (1993/4).

3. Touloukian, Y S; Powell, R W; Ho, C Y; Klemens, P G. Thermophysical propertiesof matter: Thermal expansion, publ IFI/Plenum, New York (1970).

4. Jimbo, I; Cramb, A W. Met. Trans B 24B (1993) 5/10.

5. Chapman, L. Unpublished results National Physical Laboratory, Teddington (1999).

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

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

8. Jimbo, I; Cramb, A W. ISIJMl 32 (1992) 26/36.

9. Cramb, A W; Jimbo, A W. Proc Turkdogan Conf held Pittsburg, PA, May 1994, publTMS, pp 195/206.

Fra

ctio

n S

olid

, f s

Table 1

Recommended thermophysical properties for ductile iron

Temp(0Q25100200300400500600700740800

805 (cc-»y)900100011001140a

1178a

130014001500

Densitykgm'3

73007280725072217192716371347106709570787150712070907060

6620658665356484

Cp(Jg-1K-1)

0.480.5150.560.600.650.720.821.041.170.680.680.720.760.80

0.830.830.830.83

(Hx-H25)(Jg1)

O3790148210279356447491532571638712790

1073117512581341

X(Wm-1K'1)

3941423939353124

18.8

25.629.631.0

[28]b

[28]b

[29]b

[3Of

106amV1

10.310.09.88.47.55.94.22.93.9

5.05.55.5

[5.Of[5.1]°[5.4]b

[5.6]"

T!(mPas)

[14. ]b

[11.5]b

[9.]b

[7]b

a b= fusion range = estimated model

Table 2

Fraction solid of ductile iron as a function of temperaturefor heating and cooling rates of 10 K min"1. (See Section 5.5)

HeatingCooling

Fraction solid, fsO

11901165

0.0511851151

0.111831143

0.211801140

0.311781137

0.411761134

0.511741132

0.611721130

0.711691128

0.811661126

0.911601122

0.9511531119

1.011401106


Date: March 1999

Fe-CGrey Cast Iron


C3.72

Cr0.95

Fe91.9

Mg<0.002

Mn0.66

Mo0.59

Ni0.19

P0.09

S0.032

Si1.89

2 Transitions

DTSC [1] revealed several endotherms (shown below); their origin was attributed throughinspection of the Fe-C phase diagram:

(i) Peak at 740 0C = Curie point(ii) a -^ Y transition: onset 790 0C: peak 805 0C: (displaced from 723 0C by presence of

Si, Cr5 Mn and Mo).(iii) 945 0C - not known,(iv) Melting range: 1080 - 1190 0C.

3 Density

P25 (s) = 7200 kg rn3 [2] of (T-25 0C) = 11.9 + (0.42 x 10'2 0C) x 1(T6 K'1 [3]

Density values given in Table 1 and Figure 1 were derived using these data. The change indensity for the a -> y transition was assumed to be +2.7% [3] and 0% for the a -> 8transition

Ps(25-805°o (kg.m-3) - 7200 - 0.289 (T-25°C) (1)

P*(805-i08o°c) (kg.nT3) = 7047-0.280 (T-SOS0C) (2)

Values for the liquid alloy were calculated by interpolating the equations reported by Oginoet al [4] and Jimbo and Cramb [5] shown in Equations 3 and 4, respectively for Fe-3.7% C.

p, (kg m-3) = 7560 - 0.542 (T 0C) (3)

p, (kg mf3) = 6829 - 0.50 (T - 1550 0C) (4)

Values for 1550 0C calculated with Equations 3 and 4 were within 1% of each other.However, Si has the effect of decreasing the density and consequently 130 (% Si) wassubtracted from the density calculated with Equations 3 and 4. The modified version ofEquation 4 is shown in Equation 5, this was used to calculate the values shown in Table 1.

p, (kg m-3) = 6829 - 0.50 (T -1550 0C) - 130 (%Si) (5)

Temperature (0C)

Figure 1 Density of grey cast iron as a function of temperature. (Use Equn6.1 tocalculate properties in the 'mushy' region.)


Richardson et al [1] measured Cp and (H1-H25) for the solid and liquid states using DPSC andDTSC. The Cp and (H1-H25) results are given in Figures 2 and 3, respectively and in Table 1.The following values were obtained:

CP25 = 0.49 JK-1 g l : CpCO = 0.95 JK'1 g1

AH805 (a -» y) = 36 Jg1 K"1 AH945 = 1 Jg1

AHfos =240 Jg1.

METALS model (Kubamelt) yields values in reasonable agreement except in both thetransition regions and liquid phases.

Den

sity

, P

(K

g m

"3)

Temperature (0C)

Figure 2 Heat capacity of grey cast iron as a function of temperature; o, ,experimental values; x, Metals model estimates (ignoring C content); - -,apparent Cp in transition ranges. (Use Equn 6.1 to calculate properties in the'mushy' region.)

Temperature (0C)

Figure 3 Enthalpy of grey cast iron as a function of temperature; , o experimentalvalues; x, estimated values Metals (Kubamelt) model. (Use Equn 6.1 tocalculate properties in the 'mushy' region.)


Values of thermal conductivity have been reported for a sample with 3%C and Si = 0.6% [7].Szelakowski [8] reported thermal diffusivity values for solid and liquid states using the laserpulse method. The values obtained are shown in Figure 4 and Table 1. Thermal conductivityvalues were calculated using the selected Cp and density values and these are given inFigure 5 and Table 1. The thermal diffusivity of grey cast iron is very similar to (a) that of(i) Fe + 3%C + 0.6% Si and (ii) pure iron for temperatures above 400 0C. The valley in the

Ent

halp

y, H

1-H

25 (

Jg'1)

Hea

t Cap

acity

,Cp

(Jg

-1K

'1)

a-T curve is associated with the Curie temperature (ca 740 0C). The liquid sample tended to"ball up" so the values obtained for the liquid phase may be prone to error since the specimenwould lose its disc-shaped geometry. Values for the liquid were estimated by assuming

(A,™ /Ttf } = 1.1, the value obtained for pure Fe.

Temperature (0C)

Figure 4 Thermal diffusivity of grey cast iron as a function of temperature; , orecommended values; •••, Fe+3%C +0.6% Si; - -; pure Fe. (Use Equn 6.1 tocalculate properties in the 'mushy' region.)

Temperature (0C)

Figure 5 Thermal conductivity of grey cast iron as a function of temperature. (UseEqun 6.1 to calculate properties in the 'mushy' region.)

6 Viscosity

Andon et al [9] measured the viscosity of grey cast iron from 1170 to 130O0C usingoscillating viscometry. The results are shown in Figure 6 and Table 1 and the temperature

The

rmal

Con

duct

ivity

, A,

(Wm

'1 K

'1)T

herm

al d

iffus

ivity

, 10

6a

(HfI2S'

1)

dependence is given in Equation 6.

log,0 T| (mPas) = -0.721 + (2747 / T) (6)

where T is in K. These values are in reasonable accord with those cited by Avaliani et al [10]for the Fe-3.7%C system.

Temperature (0C)

Figure 6 Viscosity of grey cast iron as a function of temperature. O , Andon etal [9]; x, Avaliani et al [10] for Fe -3.7%C. (Use Equn 6.1 to calculateproperties in the 'mushy' region.)


Jimbo and Cramb [11], observed that the surface tension of Fe-C alloys increased withincreasing C content by +30 mNm"1 (0XoC)"1. This is in contrast to the results of mostinvestigators who reported a decrease in y with increasing C content. The surface tension ofthe alloy will be controlled by the soluble S and O contents. Jimbo and Cramb [11] notedthat C tends to increase the activity of sulphur (as). Furthermore, only Mg of the elementspresent would have any effect on the soluble S concentrations. Consequently, it would beexpected that the surface tension would be largely determined by the S content of the alloy.

Cramb [12] proposed Equn 7 for Fe-S melts at 1550 0C.

Y1550 (mN m'1) = 1913 - 195 In [1 + 365aJ (7)

This can be modified to account for the effect of C on y (Equation 8).

y(mN m-1) = 1913 - 195 In [1 + 365 aj + 30 (%C) (8)

The temperature dependence (dy/dT) will be positive for all alloys with S > 10 ppm.

Vis

cosi

ty,

TI (m

Pa

s)


Fraction solid values as a function of temperature are given in Table 2 and Figure 7 and werederived from DTSC measurements.

Temperature (0C)

Figure 7 Fraction solid of grey cast iron as a function of temperature for heating(—,0) and cooling ( , o) rates of 10 K min"1 (Temperature scale may bein error, see Section 5.5)

References

1. Richardson, M J; Hayes, D; Day, A P; Mills, K C: Final report on differentialscanning calorimetry. Final Report on Processability: Thermophysical property datafor commercial alloys measured in PMPl, 2 and 3 (1.4.93-31.3.96). National PhysicalLaboratory (1996).

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

3. Touloukian, Y S; Powell, R W; Ho C Y; Klemens, P G: Thermophysical properties ofmatter: Thermal expansion, publ. IFI/Plenum, New York (1970).

4. Ogino, K; Nishiwaki, A; Hosotani, Y: J. Japan Inst. Metals, 40 (1984), 1004/1010.

5. Jimbo, I; Cramb, A W: Met. Trans. B, 24B (1993) 5/10.

6. Mills, K C; Day, A P; Quested, P N: Proc. Osaka Univ.-Nottingham Univ. JointSymp. held Nottingham, Sept 1995.

7. Reference cited in ref. 8.


Fra

ctio

n S

olid

, f s

9. Andon, R J L ; Day, A P; Quested, P N; Mills, K C: Measurements of the viscositiesof metals and alloys using an oscillation viscometer - as in ref 1.

10. Avaliani, M I; Kaplun, A B; Krutko, M F; Vashukov, I A: Izv. VVZ Chern. Met.(1977)2,123.

11. Jimbo, K; Cramb, A W: ISIJIntl., 32, (1992) 26/36.

12. Cramb, A W; Jimbo, I: Proc. ET Turkdogan Conf. held Pittsburgh, PA, May 1994,publ. By TMS, pp 195/206.

Table 1

Recommended thermophysical properties for grey cast iron

T0C

25100200300400500600700740°800805(coc-»y)90010001080"1190"1200130014001500

Densitykgm'3

7200718071507121709270637034700669956977704770206992696467646759670966596609

Jg1 k-1

0.490.510.5550.600.640.70

0.7851.001.17C

--

0.660.610.660.950.950.950.950.95

(H1-H25)Jg-'

O37.591149211278352441484

-58264871276310801090118512801375

106aHi2S-1

14d

1311.510.19.28.36.95

4.35.4-7

6.76.2

[4.0]a

[4.0]a

[4.2]a

[4.4]a

[4.6]a

XWm'1 K'1

49d

4846434241383535

332929

[26]a

[26]a

[27]a

[28]a

[29]a

^lmPas

14.314

10.58.3d

6.7d

a b[ ] estimated values melting range

phase transition assuming a + 1% increase in density extrapolated values

Table 2

Fraction solid as a function of temperature at heatingand cooling rates of 10 K min"1 (see Section 5.5)

HeatingCooling

O12091198

0.0511751185

0.111621174

0.211581142

0.311551127

0.411521125

0.511491122.5

0.611451120

0.711411117

0.811341114

0.911231101

0.9511151084

1.010801070

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

Fe-304 Stainless Steel


C0.08

Cr19.0

Cu0.3

Fe69

Mn2

Ni9.5


T501 = 140O0C [1] TU, = 14540C [1]

3 Density, thermal expansion coefficient

P20 = 8020 kg m'3 [2] Estimated (METALS) p20 = 7790 kg m'3 [3]a = 14.2XlO-6K'1

The values of a reported by Bogaard et al [4] for the linear thermal expansion coefficient aregiven in Equation 1. The estimated density (7790 kg m"3) is about 3% lower than the valuecited by Touloukian [2]. Density values given in Figure 1 and Table 1 were estimated fromthe experimental values of p and a for the solid and for the liquid (i) by assuming thedecrease in density at TUq was identical to that for pure Fe and (ii) by comparing values withthe experimental values for 316 stainless steel.

a(T-25°C)-(16+6x!0-3 (T0C))XlQ-6K-3 (1)

ps (kg.nT3) ^ 8020 - 0.501 (T-25 0C) (2)

p, (kg.nT3) = 6900-0.80 (T-14540C) (3)

Temperature (0C)

Figure 1 Density of stainless steel 304 as a function of temperature. (Use Equn 6.1 tocalculate properties in the 'mushy' region.)

Den

sity

, P

(K

g m

'3)


Bogaard et al [4] reviewed Cp data for solid and liquid 304 alloy. More recently, Richardsonet al [5] measured Cp values up to 700 0C using DPSC. The results of the two studies are ingood agreement. Henderson et al [6] have recently reported Cp values for an unspecifiedstainless steel which are also in good agreement. Estimates based on METALS model areabout 3% lower at ambient temperatures but are in good agreement at higher temperatures.Recommended values for Cp and (H1-H25) of the solid alloy are given in Figures 2 and 3,respectively, and in Table 1. No experimental Cp data are available for the liquid alloy,estimated Cp values of 0.82 and 0.75 Jg"1 K"1, respectively, were reported by Bogaard et al [4]and by METALS model calculations. A value Cp = 0.80 JK"1 g"1 has been adopted.

Temperature (0C)

Figure 2 Heat capacity of 304 stainless steel as a function of temperature •, Bogaard[4]; o, Richardson, A, Henderson, x, METALS model estimates. (Use Equn 6.1to calculate properties in the 'mushy' region.)

Hea

t C

apac

ity,

Cp (

Jg-1

K'1

)

Temperature (0C)

Figure 3 Enthalpy of 304 stainless steel as a function of temperature. (Use Equn 6.1 tocalculate properties in the 'mushy' region.)

No experimental values have been reported for the enthalpy of fusion, consequently the valueestimated with METALS model AHfus = 261 Jg"1 has been adopted. Enthalpy values are givenin Table 1 and Figure 3.


Thermal conductivity (A,) data for solid 304 have been reviewed by Chu and Ho [7] and byBogaard [8] and thermal diffusivity data by Bogaard et al [4]. More recently, Szelakowski etal [1] have reported thermal diffusivity data for solid and liquid 304 stainless steel. Theresults for the solid phase are in close agreement as can be seen from Figure 4. The thermalvalues reported by Szelakowski for the liquid alloy lie between 0.32 and 0.34 x 10"6 m2 s"1

which involves a decrease in (a ™ /a ™) of almost 50% at Tliq which is much larger than thatrecorded for pure Fe. Thermal conductivity values calculated from the thermal diffusivitywith the recommended values of Cp and p are compared with thermal conductivity valuesreported by Chu and Ho [7] and Bogaard [8] in Figure 5. It can be seen that the conductivityvalues derived from thermal diffusivity measurements are in excellent agreement with thevalues recommended by Chu and Ho [7] and Bogaard.

Ent

halp

y, H

7-H

25 (

Jg'1)

Temperature (0C)

Figure 4 Thermal diffusivity of stainless steel 304 as a function of temperature, o, ,recommended values; A Szelagowski, •, Bogaard [8]. (Use Equn6.1 tocalculate properties in the 'mushy' region.)

Temperature (0C)

Figure 5 Thermal conductivity of stainless steel 304 as a function of temperature; -•-,Bogaard; - - - , Chu and Ho; , o, derived from thermal diffusivitymeasurements; ®-, * calculated by WFL Rule. (Use Equn6.1 to calculateproperties in the 'mushy' region.)

It can be seen from Figure 5 that values of the thermal conductivity derived from the thermaldiffusivity value reported by Szelagowski [1] are significantly lower than the values derivedfrom the electrical resistivity values using the WFL Rule. This rule has been found toprovide reliable values for the thermal conductivity of liquid metallic elements but has not yet

been shown to be valid for alloys. Nevertheless, it would be expected that ( A , ™ / T t f ) would besimilar to that for the parent metal (Fe) and would thus be in the region 1.1 to 1.2. The

The

rmal

Con

duct

ivity

, A.

(Wm

-1K

'1)

The

rmal

diff

usiv

ity,

106a

(H2S

-1)

(X™/X7) ratio derived from the measurements of Szelagowski would yield a value close to 2.This suggests that the experimental results are prone to some error. Consequently the valuesderived from WFL Rule calculations have been tentatively adopted and are given in Figure 5and Table 1.

6 Viscosity (r|)

The viscosity values given in Table 1 were estimated by analogy with the values for Fe andthose for Ni and IN 718.


The surface tension (y) of stainless steel (304 and 316) and the temperature coefficients(dy/dT) have been found to be functions of the S content (Figures 6(a) and (b), respectively[9]. The surface tension, as a function of temperature y(T) can be calculated by use ofEquations 4, 5 and 6 where T is in 0C.

y1700(mNm-1) = 1150 - 90.9 ln(% Stotal) (4)

(dy/dT)1700 (mNm-1 K-1) = 1 . 5 1 + 0.268 ln(% Stotal) (5)

Y(TMmNm-1K-1) = y1700 + (dy/dT) 1700 (T-1700°C) (6)

(b)Figure 6 (a) Surface tension (y) and (b) temperature dependence (dy/dT) of 304 stainless steel

as functions of S content in ppm; , (17230C); - -, (145O0C) calculated, [1O].

Surfa

ce T

ensio

n,y

(mN

nrf1)

Tem

pera

ture

Dep

ende

nce

dy/d

T (m

N m

1 K"1)

Sulphur con tent (ppm)

Sulphur conten t ( p p m )

8 Emissivity (s)

The values shown in Figure 7 were taken from the total normal emissivity (e^) reported byBogaard et al [4], It can be seen that for a stable oxide film s™ « 0.7 whereas for polishedsurfaces in vacuum S1N = 0.1 - 0.2.

Temperature (0C)

Figure 7 Total normal emissivity of 304 stainless steel as a function of temperature [4];- - , oxidised at 980 0C; •••, highly polished in vacuum; -•-, mechanicallypolished.

References

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

2. Touloukian, Y S: Thermophysical properties of high temperature solid material,Volume 3. Ferrous alloys publ. Macmillan, New York (1967).

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

4. Bogaard, R H; Desai, P D; Li, H H; Ho, C Y: Thermochim. Acta, 218 (1993) 373/393.

5. Richardson, M J; Hayes, D; Day, A P; Mills, K C: MTS Programme on processibility.Thermophysical property data for commercial alloys measured in PMPl, 2 and 3,

April 93-Mar 96.

6. Henderson, J B; Hagemann, L; Blumm, J; Kaiser, R: High Temp-High Pressure, 30(1998) 147/152.

7. Chu, T K; Ho, C Y: Thermal conductivity, 15, edited V V Mirkovich, Plenum Press,(1978)79/104.

Tot

al N

orm

al E

mis

sivi

ty,

STN

8. Bogaard, C H: Thermal Conductivity 18, edited T Ashworth, D R Smith, PlenumPress, New York (1985) 175-185.

9. Brooks, R F; Mills, K C: High Temp-High Pressure, 25 (1993) 657/664.

10. McNallan, M J; Debroy, T: Met. Trans., 22B (1991) 557/560.

Table 1

Recommended thermophysical properties of 304 stainless steel

T0C

25100200300400500600700800900100011001200130013601454145415001600Uncertainty

Densitykgm"3

8020800079507903785578057751769876457590753274817431738173517302690068606780±3%

Jg1 k-10.480.500.530.540.560.570.5950.600.620.6300.6420.6560.6750.6950.7200.730.800.800.80±3%

(H7-H25)Jg1

O3688141196253311371432495558623690758801869112911661246±3%

XWm'1 K-1

14.815.817.718.820.721.423.524.525.827.528.829.931.632.833.5

28b

29"30

± 10%

106aIn2S-1

3.853.954.24.44.7a

4.85.15.35.455.755.956.16.36.4

5.65.3b

5.5b

± 10%

T!mPas

[8]c

UT

± 30%

derived from WFL Rule c estimated values

Fe - 316 Stainless Steel


C0.08

Cr17

Cu0.3

Fe65

Mn2.0

Mo2.5

Ni12

Si1

2 Transitions melting range

DPSC: Tsol = 13850C[I]: Tliq (peak) = 145O0C[I]

T801 - 1360 0C [2]: Tliq = 1410 0C [2]

The former values [1] have been adopted.


A value of p20 = 7950 kg m"3 [3] has been reported. The values, p25 = 7690 kg m"3 anda = 14.1 x 10"6 K"1 were estimated by METALS model [4]. The estimated density values are3% lower than the measured value. The mean linear thermal expansion coefficients given inEquation 1 were derived from those reported by Bogaard et al [5] for 321 stainless steel

a (T-25°C) = (16 + 6 x 10'3 (T 0C)) x 10'6 K'1 (1)

Values for the liquid alloy have been measured by McCormick and Brooks [6] using thelevitated drop method and are given in Figure 1 and Equation 3. Values for the liquid wereestimated (i)by assuming values estimated by METALS model are 3% lower thanexperimental values and (ii) assuming (p™ / p f ) is identical to the recommended values forFe

Temperature (0C)

Figure 1 The density of stainless steel 316 as a function of temperature; O,experimental data; X estimated by Metals and by D assuming (p™ / pf) isidentical to pure Fe; ••••, McCormick and Brooks [6], (Use Equn6.1 tocalculate properties in the 'mushy' region.)

Den

sity

, p

(Kg

m"3)

ps (kg.nT3) - 7950 - 0.501 (T-25°C) (2)

p^ (kg.m~3) = 6881-0.77 (T-1450 0C) (3)

The values given in Table 1 are based on the experimental values.


Bogaard et al [5] reviewed Cp data for 316 steel and these are given in Figure 2. Morerecently, Richardson et al [1] measured Cp and (H1-H25) using DPSC and DTSC. Hendersonet al [7] measured Cp for an unspecified stainless steel using HTDSC. The results of thevarious experimental studies are in excellent agreement.

DPSC: Cp25 = 0.48 JKV [1] Estimated (METALS)Cp25 = 0.445 Jg1K'1

Cp25 = 0.45 JKV [5]Cp25 = 0.45 JKV [7]AH*15 = 26OJg'1 Estimated (METALS) AHfus = 275 Jg"1

Values for Cp^ [1] were subject to a considerable amount of noise. Values ofCp^ =0.83 JKV were obtained compared with values calculated by METALS model;Cp, = 0.74 JK-y and 0.79 JK^g'1 by MTDATA. Enthalpy values are given in Table 1 andFigure 3, the recommended values are based on measurements of Richardson et al [1], but thevalues for the liquid may be subject to error.

Temperature (0C)

Figure 2 Heat capacity of 316 stainless steel as a function of temperature; o, -Richardson [I]; • Bogaard et al [5]; , Henderson et al [7]; X METALSmodel.

Hea

t C

apac

ity,

Cp (J

g'1

K-1)

Temperature (0C)

Figure 3 Enthalpy (H7-H25) of 316 stainless steel as a function of temperature. (UseEqun 6.1 to calculate properties in the 'mushy' region.)

5 Thermal diffusivity (a) thermal conductivity (A)

Chu and Ho [8] reviewed thermal conductivity data reported in the literature. More recentlySzelagowski [2] and Monaghan [9] have reported thermal diffusivity data for 316 using thelaser flash method. The results of these two studies for the solid state are in excellentagreement (deviation <2%) but are 5-10% higher than values reported by Chu and Ho [8].

Thermal diffusivity values for the liquid have been reported by Szelagowski [2]. As can beseen by the results shown in Figure 4, there is an apparent drop in thermal diffusivity of 50%at Tliq. Chu and Ho [8] reported electrical resistivity data for liquid 316 stainless steel andthermal conductivities were calculated using the Wiedemann-Franz-Lorenz (WFL) Rulewhich has been found to be valid for molten metallic elements. It can be seen from Figures 4and 5 that thermal conductivities calculated in this manner are much higher. Values of thethermal conductivity of the liquid were calculated assuming (p™ / p™) for 316 was identicalto that for pure Fe; these were found to be in reasonable agreement with WFL calculations.Although there is no guarantee that the WFL Rule is valid for alloy systems, the WFL rulecalculated values have been adopted until further data become available for the liquid alloy.

Recommended values of thermal diffusivity and thermal conductivity are given in Table 1and Figures 4 and 5, respectively.

Ent

halp

y, H

7-H

25 (

Jg'1)

Temperature (0C)

Figure 4 Thermal diffusivity of 316 stainless steel as a function of temperature; , o,recommended values; X5 Chu [8]; •, Szelagowski [2]; A, Monaghan [9]. (UseEqun 6.1 to calculate properties in the 'mushy5 region.)

Temperature (0C)

Figure 5 Thermal conductivity of 316 stainless steel as a function of temperature; —, o,calculated from recommended values of a; X, Chu and Ho [8]. Szelagowski;• [2]; * (*) WFL estimates, A, estimates based on (A£ / X1J1) is identical tothat for pure Fe. (Use Equn 6.1 to calculate properties in the 'mushy' region.)

The

rmal

Con

duct

ivity

, ^

(Wm

-1K

'1)

The

rmal

diff

usiv

ity,

106a

(mV

)

6 Viscosity (rj)

The viscosity values given in Table 1 were estimated by analogy with measured viscositiesfor pure iron and Ni and IN718.


Brooks [10] has reported surface tension (y) values for 316 and found them to be very close tothose for 304. The values of y and (dy/dT) were both found to be dependent upon the total Scontent of the steel (Figure 6(a) and (b)). The surface tension can be calculated fromEquations (4) to (6).

y1700 (mNm-1) = 1150 - 90.9 In (% Stotal) (4)

(dy/dT)1700 CmNm-1K-1) =1 .51+ 0.268 In (% Stotal) (5)

Y(T) - y17oo + (dy/dT)1700 (T - 1700 0C) (6)

Figure 6 (a) Surface tension (y) at 1700 0C and (b) temperature dependence (dy/dT) of304 and 316 stainless steels as functions of S content; , - -, calculatedvalues [11] at 1700 and 1450 0C, respectively. (Note: 100 ppm - 10'2 wt%).

Sulphur content (ppm)

Sulphur content (ppm)

Sur

face

Ten

sion

,y (

mN

rrr1)

Tem

pera

ture

Dep

ende

nce

dy/d

T (m

Nm

1 K1)

8 Emissivity (s)

Bogaard et al [5] reported total normal emissivity (s^) values for stainless steel which aregiven in Figure 7. It can be seen that samples with a stable oxide film have a value of S1N ofabout 0.7 whereas mechanically-polished surfaces in high vacuum have S1̂ values of 0.1 to0.2.

Temperature (0C)

Figure 7 Values of total normal emissivity of 316 stainless steel as a function oftemperature [5]; , oxidised at 980 0C; •••• highly polished in vacuum' -•-mechanically polished.


Richardson et al [1] reported fs values derived from DTSC studies which are given in Figure 8and Table 2.

Temperature (0C)

FigureS Fraction solid as a function of temperature for 316 stainless steel. (Notetemperature scale may be in error, see Section 5.5).

Fra

ctio

n S

olid

, f s

Tot

al N

orm

al E

mis

sivi

ty, e^

References

1. Richardson, M J; Hayes, D; Day, A P; Mills, K C. MTS Programme on processabilitythermophysical property data for commercial alloys measured in PMPl, 2 and 3,April 23 - Mar 96, Final Report, NPL, Chapter 3.

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

3. Touloukian, Y S. Thermophysical properties of high temperature solid materials.Volume 3, Ferrous alloys, publ McMillan, New York (1967).

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

5. Bogaard, R H; Desai, P D; Li, H H; Ho, C Y. Thermochim Ada, 218 (1993) 373/393.

6. McCormick, A. and Brooks, R F; as in reference 1, Chapter .

7. Henderson, J B; Hagemann, L; Blumm, J; Kaiser, R. High Temp - High Pressure, 30(1998) 147/152.

8. Chu, T K; Ho, C Y. Thermal conductivity 15 edited V V Mirkovich, Plenum press,(1978)79/104.

9. Monaghan, B J; Waters, M J D . Laser flash liquid metal thermal conductivitymeasurements. NPL Report CMMT(D)196 (1999).

10. Brooks, R F; Mills, K C. High Temp - High Pressure, 25 (1993) 657/664.

11. McNallan, M J; Debroy, T. Met. Trans. B. 22B (1991) 557/560.

Table 1

Recommended values for thermophysical properties of316 stainless steel

Temp0C2510020030040050060070080090010001100120013001385tc)

1450(c)

145015001600

Uncertainty

Densitykgm'3

7950792178807833778577357681762875757520746274117361731172697236(a)

688168426765±3%

CpJK-'g-1

0.470.490.520.540.560.570.590.600.630.640.660.670.70(0.71)(a)

(0.72)(a)

0.73(a)

0.830.830.83±5%

(Hx-H25)Jg1

O3685138193250308367429492557624692763821868ta)

112811701253±5%

XWm-1K'1

13.415.517.619.421.823.424.525.127.227.929.129.330.931.1--

28.529.530.5(a)

±10%

106amV1

3.64.04.34.65.05.35.45.55.75.85.95.96.06.06.0(a)

6.0la)

5.0(a)

5.2(a)

5.4±10%

T!mPa.s

[sr[7](b)

±30%

(a)v ' extrapolated value

' estimated value(c) melting range

Table 2

Fraction solid (fs) for 316 stainless steel in the solidificationrange when cooling at 1OK min"1 (see Section 5.5)

fsT°C

O1424

0.11423

0.21422.5

0.31422

0.41421

0.51420

0.61419

0.71418

0.81417

0.91416

0.951413

11401


MgPure Magnesium


mp - 65O0C [I].


P25 (solid) = 1740 kg m'3 [2] of - 30 x 10'6 K'1 [2].

The density as a function of temperature is given in Figure 1 and Table 1.

The density-temperature relation for liquid Mg recommended by Iida and Guthrie [3] isidentical to that recommended by Watanabe et al [4] viz

ps (kg.m"3) ^174O - 0.156 (T-25°C) (1)

pe (kg.m~3) = 1590-0.26 (T-650 0C) (2)

The density decrease at the melting point from the data shown in Table 1 is 3.1%.

Temperature (0C)

Figure 1 Density of liquid Mg as a function of temperature [3,4].


Heat capacity and enthalpy as functions of temperature are given in Figures 2 and 3,respectively and Table 1.

Dinsdale [1] reported the following values.

AHf«s = 349 jg-i

Cptf) = 1.32Jg1K-1

Den

sity

, P

(K

g m

"3)

Temperature (0C)

Figure 2 Heat capacity of pure Mg as a function of temperature.

Temperature (0C)

Figure 3 Enthalpy (Hx-H25) of pure Mg as a function of temperature.


Thermal conductivity values have been reported by Touloukian et al [5]. These values aregiven in Table 1 and have been converted to thermal diffusivity values using therecommended values of Cp and density values (Table 1). Mills et al [6] recommended thefollowing values:

^sm = 145Wm-1K"1: X™ = 79WnT1K'1

^1 = 79+7xl(T2 (T -65O)Wm-1K'1 (3)

These are shown in Figure 4.

Ent

halp

y, H

7-H

25 (

Jg"1)

Hea

t C

apac

ity,

Cp (J

g-1

K'1

)

Temperature (0C)

Figure 4 Thermal conductivity of Mg as a function of temperature [6].

5 Viscosity (TJ)

Lihl et al [7] have reported the viscosity measurements for pure Mg shown in Figure 5, withif = 1.25mPas.

Temperature (0C)

Figure 5 Viscosity of liquid magnesium as a function of temperature [7].


Keene [8] reviewed the measurements of surface tension reported for pure Mg andrecommended the following relation (shown in Figure 6).

Y(HiNm'1) = 577 - 0.26 (T - 650 0C) (4)

Vis

cosi

ty,

TI (

mP

as)

The

rmal

Con

duct

ivity

, A,

(Wm

"1 K

'1)

Temperature (0C)

Figure 6 Surface tension of pure Mg as a function of temperature.

7 Emissivity

Shiraishi [9] reported values of Sx at 0.65 |tim at 25 0C of 0.74 but with Sx decreasing rapidlywith decreasing wavelength. Touloukian [5] also reported a hemispherical total emissivityvalue of 0.12 for a polished surface at temperatures between 70 and 200 0C.

References


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

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

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

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

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

7. Lihl, P; Nachigall, E and Schwaiger, A: Z Metallk 59 (1968) 213.

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


Sur

face

Ten

sion

, y

(mN

m"1)

Table 1

Recommended values for thermophysical properties of pure Mg

T0C25100200300400500600650a

650a

7008009001000

PTkgm'3

1740172817131697168116661650164215901577155115251499

Jg1 k-11.0251.061.111.161.191.241.301.321.321.321.321.321.32

(H1-H25)

Jg1

O7818730041854066773310811213134514771609

106aHi2S-1

8784807674716867373943.54852

XWm'1 K0

15615415215014814614514579828996103

T!mPas

1.251.120.910.80-

YmNm'1

577564538512486

s(a)

0.65 jam

0.590.590.590.59

a = melting point

Mg-Ag-Ce (QE22)


Ag2.5

Ce2.5

Mg94.4

Zn0.1

Zr0.5

2 Transitions

T501 = 550 0C THq = 640°C

3 Density

P25 = 1820kgm'3 [I]: METALS model estimates p25 - 1820 kgm'3 [2]a = 26.7 x 10'6 K'1 [1] a = 29.8 x 10'6 K'1 [2]

The values estimated for the solid are in good agreement with reported values [I]. In theabsence of measured values for the liquid alloy METALS model estimates have been adoptedand are given in Table 1 and Figure 1.

ps (kg.m~3) ~ 1820 - 0.146 (T-25°C) (1)

pc (kg.m"3) - 1667-0.26 (T-640 0C) (2)

Temperature (0C)

Figure 1 Density of Mg-Ag-Ce alloy (QE22) as a function of temperature. (UseEqun 6.1 to calculate properties in the 'mushy' region.)

Den

sity

, P

(K

g m

"3)


Richardson et al [3] measured Cp and (H1-H25) using DPSC, the results are given in Figures 2and 3, respectively. No measurements were obtained above 430 0C, because of the excessivevapour pressure of Mg. The alloy showed a small peak at ca 280 0C in the rerun samplewhich was absent in the as-received state. The values estimated by METALS model [2] werein excellent agreement with the measured values and consequently have been used fortemperatures above 400 0C and for the value of AH618.

The following values were obtained:

Cp25 = 0.97 Wm-1K'1: Estimated [2] Cp25 = 0.98 JKV [2]AH*18 - 342 Jg1 [2]: Cp(O = 1.33 JKV [2]

Temperature (0C)

Figure 2 Heat capacity of Mg-Ag-Ce alloy as a function of temperature; o, ,measured DPSC [3], - - -, A5 estimated by METALS model [2]. (Use Equn 6.1to calculate properties in the 'mushy' region.)

Temperature (0C)

Figure 3 Enthalpy of Mg-Ag-Ce alloy as a function of temperature; O, measured values[3], (Use Equn 6.1 to calculate properties in the 'mushy' region.)

Ent

halp

y, H

7-H

25 (

Jg'1)

Hea

t C

apac

ity,

Cp

(J g

'1 K

'1)


A value of A, = 113 Wm'1 K'1 for the alloy at 25 0C has been reported [I]. Szelakowski [7]measured the thermal diffusivity using the laser pulse method, the results are given inFigure 4. There seems to be some displacement in the temperature scale on the basis of thefusion range for these measurements; the values given in Table 1 relate to an adjustedtemperature scale. Thermal conductivity values given in Table 1 and Figure 5 werecalculated from the values given for thermal diffusivity, density and Cp. Values reported forthe liquid phase [4] seem to be in reasonable agreement with estimates based on (k™ /A,™)for pure Mg which indicate a value of about 60 Wm-1K"1.

Temperature (0C)

Figure 4 Thermal diffusivity of Mg-Ag-Ce alloy as a function of temperature. (Notethe temperature scale has been adjusted). (Use Equn 6.1 to calculate propertiesin the 'mushy' region.)

Figure 5 Thermal conductivity of Mg-Ag-Ce alloy as a function of temperature (usingdata given in Table 1). (Use Equn 6.1 to calculate properties in the 'mushy'region.)

Temperature (0C)

The

rmal

Conduct

ivity

^

(Wm

"1 K

1)

RT

herm

al D

iffus

ivity

, 1O

a

(mV

)

6 Viscosity

The viscosity values given in Table 1 were estimated by comparison with values for pure Mg.

References

L Elektron Database version 2.1. The comprehensive guide to lightweight magnesiumalloys, Magnesium Elektron and Engineering Information Company (1994).

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

3. Richardson, M J; Hayes, D; Day, A P; Mills, K C. Final report on differentialscanning calorimetry (DSC: Final Report MTS programme on processability:Thermophysical property data for commercial alloys measured in PMP 1, 2 and 3(1/4/93-31/3/96)) National Physical Laboratory (1996).

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

Table 1

Recommended thermophysical properties for Mg-Ag-Ce alloy (QE22)

Temp(0C)25100200300400500

550(c)

640(c)

640700800

Densitykgm"3

1820180917951780176517511744

[1730](a)

[1667](a)

[1650](a)

[1623](a)

Cp(Jg1K-1)

0.971.001.041.071.11

[1.18](a)

[1.20](a)

[1.24](a)

[1.33](a)

[1.33](a)

[1.33](a)

(Hx-H25)(Jg1)

O74176281390

[504](a)

[564](a)

[671]w

[1013](a)

[1093](a)

[1226](a)

A,(Wm-1K'1)

109(d)

U9(Ci)

129(d)

137(d)

134(d)

128(d)

(d)

66(d)

66<d)

75(d)

106aHi2S-1

606468706561

303035

T|(mPas)

[1.5](b)

[1.4](b)

[1.15](b)

[ ](a) = estimated by METALS model

[ ] = estimated valuefc)v } = melting range

= temperature scale adjusted values

Date: March 1999

Mg-Ce-Zn (EZ33)


Ce3.0

Mg94.1

Zn2.0

Zr0.6

2 Transitions

T501-545 0C: Tliq = 640°C

3 Density

P25 = 1800 kgm'3 [I]; Estimated (METALS) p25 - 1816 kgm'3 [2]of = 26.8 x IQ-6 K'1 [I]; Estimated (METALS) a = 29.8 x 10'6 K"1

Since METALS model provided values for the solid in good agreement with measuredvalues, estimated values for the liquid can be used with confidence, these are given inFigure 1 and Table 1.

p(l) = 1663 kg m'3 a = 166XlQ-6K'1

ps (kg.m~3) = 1800 - 0.143 (T-25°C) (1)

p, (kg.nT3) = 1663 - 0.27 (T - 640 0C) (2)

Temperature (0C)

Figure 1 Density of Mg-Ce-Zn alloy (EZ33) as a function of temperature. (UseEqun 6.1 to calculate properties in the 'mushy' region.)

Den

sity

, P

(K

g m

'3)


The heat capacity and enthalpy were measured by Richardson et al [3] using DPSC and areshown in Figures 2 and 3, respectively, and Table 1. The samples after cooling from 430 0Cexhibited a small peak at ca 230 0C which was absent in the as-received material. The valuesestimated by METALS model [2] were found to be within 1% of the measured values. NoCp or enthalpy values could be obtained above 430 0C because of vaporisation of the Mg.Consequently, values given in Table 1 and Figures 2 and 3 were calculated with METALSmodel.

Cp25 = 0.98 JKV: Cp(I) = 1.336 JKVAH*8 = 343 Jg1

Temperature (0C)

Figure 2 Heat capacity as a function of temperature for Mg-Ce-Zn alloy (EZ33); ,o? experimental values; A, estimated values. (Use Equn6.1 to calculateproperties in the 'mushy' region.)

Temperature (0C)

Figure 3 Enthalpy of Mg-Ce-Zn alloy (EZ33) as a function of temperature. (UseEqun 6.1 to calculate properties in the 'mushy' region.)

Ent

halp

y, H

7-H

25 (

Jg'1)

Hea

t Cap

acity

, C

p (J

g"1 K

'1)


A thermal conductivity value, X25 = 100 Wm-1K"1 has been reported for EZ33 [I].

Szelagowski [4] measured the thermal diffusivity values shown in Figure 4 using the laserflash method. Thermal conductivity values given in Figure 5 were calculated using thevalues of a, p and Cp given in Table 1. Values for the liquid were also estimated byassuming (X8A^) was identical to that of pure Mg. It can be seen that the calculated values (ca85 Wm-1K"1) were in good agreement with the measured values.

Temperature (0C)

Figure 4 Thermal diffusivity (a) of Mg-Ce-Zn alloy (EZ33) as a function oftemperature. (Use Equn 6.1 to calculate properties in the 'mushy' region.)

Temperature (0C)

Figure 5 Thermal conductivity (X) as a function of temperature, —, experimental [4];X5 estimated by (XS/X^). (Use Equn 6.1 to calculate properties in the 'mushy5

region.)

The

rmal

Con

duct

ivity

, A,

(Wm

-1K

'1)

The

rmal

diff

usiv

ity,

106a

(mV

)

6 Viscosity

The viscosity values given in Table 1 were estimated by comparing this with valuesrecommended for magnesium.

References

1. Elektron Database version 2.1. The comprehensive guide to lightweight magnesiumalloys produced by Magnesium Electron and Engineering Information Company(1994).

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

3. Richardson, M J; Hayes, D; Day, A P; Mills, K C. NPL Report "MTS Programme onProcessability." Thermophysical property data for commercial alloys 4/93 to 3/96.


Table 1

Recommended thermophysical properties for Mg-Ce-Zn alloy (EZ33)

Temp(0C)25100200300400500545(c)

640(c)

640700800

Densitykgm-3

18001789177517601746173217251711166316471620

Cp(Jg1K-1)0.981.0251.081.111.145[1.19](a)

[1.21](a)

[1.25][1.336](a)

[1.336](a)

[1.336f>

(H1-H25)(Jg-1)O75179288400517571688103111111241

X(Wm-1K'1)

131142147151154156

919089

106amY1

0.7150.740.750.7550.7450.745

0.410.410.41

*1(mPas)

[1.5]w

[1.4](b)

[1.15](b)

[ ](a) = estimated with METALS model (c) = fusion range

[ ] - estimated value

Date: March 1999

NiPure Nickel


mp = 1455 0C [1] Curie Temperature = 302 0C [1]


P25 (solid) = 8900 kg m'3 [2]; a = 17.3 x 10'6 K'1 [2]

The density-temperature relationship is given in Figure 1 and Table 1.

Temperature (0C)

Figure 1 Density of pure nickel as a function of temperature.

Density values for the liquid have been reviewed by Iida and Guthrie [3] (p = 7900 - 1.19 (T-1455 0C) kg m'3) and Watanabe et al [4] (7910 - 1.27 (T-1455 0C) kg m'3). More recentlySharan et al [22] reported a value of p = 7680 kg m"3 at 1550 0C and Nasch and Steinemann[5] reported (7810 - 0.076 (T-1455 0C) kg m"3) from y-ray attenuation measurements with acalculated maximum uncertainty of ± 0.75%. They point out that their measurements pertainto constant volume whereas the others refer to constant mass. The following relation hasbeen adopted:

ps (kg.nT3) - 8900 - 0.463 (T-25°C) (1)

p^ (kg.nT3) = 7850-1.20 (T-1455°C) (2)

There is a 4.7% decrease in density at the melting point on the basis of the data given inFigure 1 and Table 1.

Den

sity

, P

(K

g m

"3)


Heat capacity and enthalpies are plotted as functions of temperature in Figures 2 and 3respectively and are also given in Table 1. There is an increase in Cp due to the Curietemperature (302 0C) followed by a sharp decrease associated with X-type transformations.

Dinsdale [1] reported the following values for the melting of Ni at 1455 0C in

CP25 = 0.426 J K'1 g'1 : AH*18 = 298 Jg1 : Cp (f) = 0.734 J K'1 g 1

Temperature (0C)

Figure 2 Heat capacity of pure Ni as a function of temperature [I].

Temperature (0C)

Figure 3 Enthalpy (Hx-H25) of pure Ni as a function of temperature [I].

Ent

halp

y, H

T-H

25 (

Jg

1)

Hea

t C

apac

ity,

Cp

(Jg

'1 K

'1)


Touloukian et al [6] reviewed the reported thermal conductivity data, most of the results fellwithin a scatterband of 5%. Zinovyev [7] and Monaghan [8] have reported thermaldiffusivity values for Ni. It can be seen (Figure 4) that there is reasonable agreement betweenthe two studies for temperatures below 1000 0C but for T > 1000 0C the thermal diffusivitiesreported by Monaghan increase steadily whereas those due to Zinovyev remain reasonablyconstant. Thermal conductivity values reported by Touloukian [6] are compared in Figure 5with the values calculated from thermal diffusivity data [7,8]. It can be seen that at hightemperatures the values recommended by Touloukian agree with the values given byMonaghan. Electrical resistivity data have been reported by several investigators, valuescalculated for A£ using the WFL rule yielded the following values (Wm'1 K'1) 65 [9] 73 [10]

68 [11] 76 [12] and 80 [13]. Equivalent values for ̂ were 50 [9,10] 49 [11] 56 [12] 53 [13].Thus the calculated values of A,, for the liquid are significantly lower than the measured value

X = 69 Wm"1 K"1 and some of the calculated values for A,s fit better with the values reported byZinovyev et al. The values obtained by the laser flash method [8] have been adopted since ithas proved a more reliable technique and these are given in Table 1.

Temperature (0C)

Figure 4 Thermal diffusivity of pure Ni as function of temperature, o,recommended values, A, Monaghan [8], •••, D, Zinovyev et al [7].

The

rmal

Diff

usiv

ity,

lfia

(mV

)

Figure 5 Thermal conductivity of Ni as a function of temperature; D, Touloukian et al[6]; values derived from thermal diffusivity measurements; O, Zinovyev etal [7]; A9 Monaghan [8]; ©, *, values calculated from WFL Rule for solid andliquid, respectively.

5 Viscosity (TJ)

Iida and Shiraishi [14] have reviewed the viscosity measurements for pure Ni reported byseveral investigators (Figure 6). Recently, Andon and Day [15] measured the viscosity ofpure Ni using oscillation viscometry. These values were slightly lower than other reportedvalues including the recent measurements reported by Sato and Yamamura [21] but arepreferred, the recommended equation being

2029loglo TI (mPas) - -0.5038 +-p (3)

where T is in K.

Temperature (0C)

Ther

mal

Con

duct

ivity

^

(Wm

-1KT

1)

Temperature (0C)

Figure 6 Viscosity of liquid Ni as a function of temperature as reported by differentinvestigators; recommended values, , [15]; •••, limits of values reportedby Iida and Shiraishi [14]; x, Sato [21].


Keene [16] reviewed the published measurements for the surface tension of pure Ni andrecommended the following relation:

Y(InNm'1) = 1796 - 0.35 (T-1455 0C) (4)

More recent measurements carried out in four different laboratories [17] resulted in arecommended relation in good agreement with Keene's equation.

Y(InNm'1) - 1781 - 0.285 (T-1455 0C) (5)

This latter equation is recommended.

Temperature (0C)

Figure 7 Recommended surface tension of pure Ni as a function of temperature, [17],, o; Keene [16], —.

Sur

face

Ten

sion

, Y

(m

N m

"1)

Vis

cosi

ty,

TI (m

Pa

s)

The surface tension of nickel will be dependent upon the concentration of oxygen and othersurface active elements. The effect of Oxygen on yNi can be clearly seen in Figure 8 [18].

Oxygen Content (at%)

Figure 8 Surface tension of Ni as a function of oxygen content at 1600 0C [15].

7 Emissivity (s)

Shiraishi [19] cites the following values for Sx at 0.65 |uim:at 1000 0C: polished surface: Sx = 0.34; oxidised surface Sx = 0.84;

120O0C s, = 0.33; Sx = 0.82.

Kashnitz et al [20] report values for Sx at 0.85 (j,m of Sx = 0.35 and 0.32 for the liquid phase at1450 and 1700 0C respectively.

Shiraishi [16] also cites the following values for the total normal emissivity, S1^5

for a polished surface:

T0C(S11,): 500(0.10): 700(0.13): 1000(0.17); 1200(0.19);

and for an oxidised surface:

T0C(S^): 500(0.53) 700(0.65).

References

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

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

Sur

face

Ten

sion

, Y

(m

N m

"1)

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

4. Watanabe, W; Ogino, K and Tsu, Y: Handbook of Physico Chemical Properties atHigh Temperatures published ISIJ, Tokyo edited Y Kawai and Y Shiraishi, SpecialIssue No 41, Chapter 1.

5. Nasch, P M and Steinemann, S G: Phys. Chem. Liquids 29 (1995) 43/58.

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

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

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

9. Regeli, cited in reference 3, p 233.

10. Ono, Y; Yagi, T: Trans. ISIJ, 12 (1972) 314.

11. Kita, Y; Oguchi, S and Morita, Z: Tetsu-to Hagane 654 (1978) 711.

12. Pottlacher, G; Jager, H; Neger, T: High-Temp - High Pressures, 19 (1989) 19.

13. Guntherodt, H J; Hauserm E; Kunzi, H U; Mueller, R: Phys. Lett. A, 54 (1975) 291.

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

15. Andon, R J L; Chapman, L; Day, A P and Mills, K C: Viscosities of liquid metals andcommercial alloys. NPL Report CMMT(A) 167.

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

17. Brooks, R F; Mills, K C; Egry, I; Grant, D; Seetharaman, S; Vinet, B: NPL ReportCMMT(D)136, Sept (1998).

18. Ogino, K and Taimatsu, H: J. Jap. Inst. Metals 43 (1979) 871.

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

20. Kashnitz, E; Pottlacher, G; Jager, H: Intl. J. Thermophys. 13 (1992) 699.

21. Sato, Y; Yamamura, T: private communication, Tohoku Univ., Sendai, Japan,Aug (1999).

22. Sharan, A; Nagasaka, T and Cramb, A W: Met. Trans. B, 25B (1994) 939.

Table 1

Recommended values for thermophysical properties of pure Ni

T0C

25100200300302"400500600700800900100011001200130014001455(c)

1455(c)

15001600

PTkgm'3

89008865881987738772872686808634858885428495844984028356831082648238785077967676

Jg1 k-10.4260.4800.5470.7000.7040.5360.5350.5400.5570.5740.5900.6050.6110.6170.6170.6170.6170.7340.7340.734

(H1-H25)Jg1

O3485147149195249302357414472532593654716778812110911421215

10" aHi2S-1

23.720.515.8--12.813.414.014.114.514.51515.515.916.316.717121212

XWm'1 K-'90877664

606265677172.776.779.58283.58586.5696969

*1mPas

4.74.43.8

YmNm"1

178117681740

F (a)8X

0.340.335

0.330.320.320.38

W polished surface Curie temperature melting point

Ni - CMSX-4

1 Chemical composition (wt %)

Typical chemical composition for CMSX-4.

Al

5.6

C

0.006

Co

10

Cr

6.5

Fe

0.15

Mo

0.6

Ni

60.5

Re

3.0

Si

0.04

Ta

6.5

Ti

1.0

W

6.4

2 Transitions

Values of Tsol = 1322 0C and Tliq = 1380 0C have been quoted for the homogenised alloy.Transitions were observed (see Figure 2) in DSC experiments to occur around 650-700 0C andthere was a gradual increase in Cp above 1000 0C resulting in a peak around 1200 0C; this isprobably associated with the y -> y' transformation but could also contain some eutecticmelting. Melting occurred between 1320 and 1385 0C, a value of Tliq = 1380 0C has beenadopted.

3 Density (p) thermal expansion coefficient ( a)

P25 = 8700 kg m"3 pestimated = 8820 kg in3

ps (kg.m~3) = 8700 - 0.458 (T-25 0C) (1)

pc (kg.m"3) - 7754-0.9 (T-13800C) (2)

Linear thermal expansion coefficient (25-1000 0C) a = 18.8 x 10"6 K"1; estimated a =15XlO-6K'1 .

The density results (given in Figure 1 and Table 1) were derived using the measured density andthe estimated expansion coefficient. The density value of 8820 kg m'3 was estimated byapplying the Al correction to METALS model. Values for the liquid were estimated by alsoapplying the Al correction to the METALS model value and correcting for the small differencebetween the estimated and measured values of p25.

Temperature (0C)

Figure 1 Density of nickel-alloy CMSX-4 as a function of temperature. (Use Equn 6.1 tocalculate properties in the 'mushy' region.)


The Cp-T and (HT-H25)-T relations, given in Figures 2(a,b) and 3, respectively, and in Table 1,were derived from DSC measurements [I]. Estimated values are also given in these figures, itcan be seen that the deviation of the estimated from measured values is much larger than usuallyobserved and may be associated with using W in the calculations as a substitute for Re, forwhich we have no data. It should be noted that the Cp values for the transition ranges areapparent Cp values and estimated values should be used for these temperature ranges.

CP25 3 = 0.397 JK'1 g1 [1] Estimated (Metals) Cp - 0.42 J K'1 g l .

Values of AH*3"5 and AH^8 were derived assuming (i) that the enhanced Cp values culminatingin the 120O0C peak (Figure 2a) was related purely with a solid/solid transformation and (ii)using the estimated Cp values as a baseline.

AH1™8= 115 Jg1

Den

sity

, P

(K

g m

"3)

Temperature (0C)

(b)

Figure 2 Heat capacity as a function of temperature showing (a) apparent Cp ( , x) inthe transition regions (b) recommended values ( , o); A, estimated values.

This is a high value for a solid/solid transition and thus may indicate the inclusion of somepremelting. The value of AH^15 = 240 ±10 Jg"1 was derived from integrating under the fusionpeak and from the enthalpy-temperature plots.

The estimated value of AHftls of 276 Jg"1 is higher than the measured AHftls which may be relatedto the fact that the enhanced Cp values around 1200 0C result, or partially result, from a smallamount of eutectic melting.

Cp(Hq) = 0.685 Jg1 K"1 Estimated (Metals) Cp(liq) = 0.636 Jg"1 K"1

Temperature (0C)

DPSCHTDSCEstimated

Hea

t C

apac

ity,

Cp

(J g

"1 K"1)

Temperature (0C)

FigureS Enthalpy (H1-H25) of Ni-alloy CMSX-4 as a function of temperature;recommended values, , o; estimated (Metals model), x. (Use Equn 6.1 tocalculate properties in the 'mushy' region.)


Thermal diffusivity (a) values have been measured for the temperature range 25-160O0C bySzelagowski [2] using the laser pulse method (Figure 4). A peak in the measurements at ca.1300 0C was observed which corresponds with Tsol.

Thermal conductivity measurements were derived from the thermal diffusivity results(A, = a Cpp) using the density a, and Cp results given in Figures 1 and 2 and Table 1. However,because of the doubt over the origin of the enhanced Cp values in the 800-1200 0C range, twosets of thermal conductivities have been calculated for this range (i) based on the recordedvalues and (ii) based on estimated Cp values which assumes that the enhancement in Cp iscaused by enthalpy associated with a solid/solid transition or fusion. Estimated thermalconductivity values for the solid [3] lie between the sets of values but are closer to those basedon the estimated Cp values. These latter values are preferred.

Ent

halp

y, H

T-H

25 (

Jg'1)

Temperature (0C)

Figure 4 Thermal diffusivity of CMSX-4 as a function of temperature [2]. (Use Equn 6.1to calculate properties in the 'mushy' region.)

Temperature (0C)

Figure 5 Thermal conductivity of CMSX-4 as a function of temperature; , — O9

values based on the recorded Cp values which may contain enthalpycontributions; x, values based on estimated Cp values; A values estimated byMills et al [3]. (Use Equn 6.1 to calculate properties in the 'mushy' region.)

Ther

mal

Con

duct

ivity

^,

(Wm

"1 KT1)

The

rmal

Diff

usiv

ity,

106a

(mV

)

6 Viscosity (r|)

Viscosity values for CMSX4 were estimated by assuming that they would be similar to thoserecorded for IN 718.

7 Surface tension

The surface tension values have been reported, the values given in Table 1 were estimated by acomparison with the values reported for IN 718. It should be noted that the surface tension ofthese alloys are very sensitive to the concentrations of soluble oxygen and sulphur in the alloy.


The fraction solid was determined from DSC experiments, the results are shown in Figure 6 andTable 2. The big difference in the temperature separating the two curves may be due to using alarge specimen mass, in this specific case.

Temperature (0C)

Figure 6 Fraction solid as a function of temperature for Ni alloy CMSX-4 obtained forheating (- -, O) and cooling ( , o) rates of 10 K min"1. (Note temperaturescale may be in error, see Section 5.5).

References

1. Richardson, M J; Hayes, D; Day, A P and Mills, K C: Unpublished heat capacity andenthalpy data, National Physical Laboratory, (1997).

2. Szelagowski, H: PhD Thesis, Materials Science and Metallurgy Department, UMIST,(1999).

3. Mills, K C; Day, A P and Quested, P N: Proc. of Osaka Univ.-Nottingham UniversityJoint Symp. held Nottingham, Sept (1995).

Fra

ctio

n S

olid

, f s

Table 1

Recommended thermophysical properties for alloy CMSX-4

TemperatureOC

25

100

200

300

400

500

600

700

800

900

1000

1100

1200

1300

1320°

1380C

1400

1500

1600

Density (p)kgm'3

8700

8665

8618

8572

8525

8479

8433

8387

8342

8296

8251

8206

8161

8116

8107

7754

7736

7646

7756

JK-^g-1

0.397

0.415

0.431

0.445

0.456

0.466

0.488

0.532

0.57a

(0.53)b

0.63a

(0.54)b

0.71a

(0.55)b

0.85a

(0.56)b

1.15a

(0.57)b

1.0a

(0.58)b

1.0a

(0.58)b

0.675

0.675

0.675

[0.675]

(HT-H25)Jg-1

O

31

73

117

162

208

256

308

363

423

490

568

668

783

803

1080

1093

1161

1228

106a

m2s-l

2.4

2.7

3.0

3.4

3.7

4.0

4.25

4.5

4.7

4.75

5.0

5.3

5.5

4.9

4.9

4.9

[4.9]

XWm-1 K-I

8.65

10.1

11.6

13.4

14.9

16.8

19.4

21.4a

(20.6)b

24.6a

(21.8)b

27.8a

(22.3)b

34.9a

(23.9)b

49.7a

(25.8)b

44.6a

(27.2)b

25.6

25.6

25.3

25.0

T]

mPas

[6.7]

[6.5]

[5.3]

[4.1]

ymNm-l

[1850]

[1850]

[1850]

[1850]

assuming solid/solid transition and enhanced Cp values are genuine and not a manifestation of AHtrans.

value calculated assuming (i) estimated Cp values and (ii) that enhanced Cp values represent a AHtrans

contribution.Q

[ ] estimated value. fusion range

Table 2

Fraction solid as a function of temperature for heatingand cooling rates of 10 K min"1 (see Section 5.5)

Fraction solid, fs0CHeatingCooling

O13851362.5

0.113821361

0.21379.51359.5

0.31377.31358

0.41374.61355.7

0.513721352.3

0.61368.81348

0.713651341.5

0.81360.31334.4

0.91352.51324

0.9513461315

1.013201296


Ni - Hastelloy-X


The alloy has a nominal composition of (mass %).

C0.1

Co1.5

Cr22

Fe18.5

Mn0.5

Mo9

Ni47

Si0.5

W0.6

2 Melting range, transitions

A transition at ca 700 0C was reported by Maglic et al [1]

T501 = 1260 0C [2] Tliq = 1355 0C [2]

3 Density (p), thermal expansion coefficient (a)

P25 = 8240 kgm'3 [I]; p25 - 8171, 8242 kgm'3 [2]

Touloukian [4] reported data which yielded a (T-25 0C) = (10 + 5 x 10'3 T 0C) x 10'6 K'1.

Estimated (Metals model) p25 - [82 40] kgm'3; a (1000-25) = [15.9JxIO-6K-1.

The density data given in Figure 1 and Table are based on the values p = 8240 kgm"3 and themeasured a . No density data have been reported for the liquid. Metals model gave valuesof pT = [7558] kgmf3. A value of pTu = [7420] kgm"3 was obtained by assuming a 4%

decrease in density at the liquidus temperature, the latter value has been adopted.

ps (kg.m~3 ) - 8240 - 0.381 (T-25°C) (1)

p^ (kg.m~3) = 7420-0.83 (T-1355°C) (2)

Temperature (0C)

Figure 1 Density of Ni alloy Hastelloy X as a function of temperature.


Maglic et al [1] (using rapid pulse calorimetry) and Taylor [3] (using DSC and multi-propertydeterminations) reported the values shown in Figure 2 which can be seen to be in goodagreement. Metals model estimates are in good agreement up to 600 0C where a sharpincrease in Cp shows that a transition occurs in the alloy (seen also in electrical resistivity andthermal diffusivity measurements). No values have been reported for the liquid so theestimated values have been adopted. Enthalpy (H7-H25) values are given in Figure 3 and werederived from the recommended Cp values Cp(Hq) = [0.677] JK^g'1, AHfus - [276] Jg"1.

Temperature (0C)

Figure 2 Heat capacity of Ni-alloy Hastelloy X as a function of A, O, Taylor [3]; —,Maglic [I]; X, estimated values (Metals model).

Hea

t ca

pac

ity,

Cp (J

g1K

1)

Densi

ty,

p (

Kg

m~3)

Temperature (0C)

Figure 3 Enthalpy (H1-H25) of Ni-alloy Hastelloy X as a function of temperature; -O,recommended values; X5 estimated (Metals model).

5 Thermal diffusivity (a) thermal conductivity

Hust et al [5] measured the thermal conductivity at room temperature, X = 10 Wm-1K"1.Thermal diffusivity values for the solid have been determined by Maglic et al [1] and byTaylor [3] and Neumann [6] all using the laser pulse method. The results are in goodagreement as can be seen from Figure 4. Thermal conductivity values were calculated fromthe thermal diffusivity values using the Cp and density values given in Table 1 and arepresented in Figure 5. A value of X - 28 WnT1K'1 was calculated for the solid at 1200 0Cusing the electrical resistivity value reported by Maglic [I].

Temperature (0C)

Figure 4 Thermal diffusivity of Ni-alloy Hastelloy X as a function of temperature; •,Maglic [I]; Taylor [3], Neumann [6].

Th

erm

al d

iffu

sivi

ty,

106a

(mV

)

En

thal

py,

HT

- H

25

(Jg

1)

Temperature (0C)

Figure 5 Thermal conductivity of Ni-alloy, Hastelloy X as a function of temperature;-O, Maglic [1] and Taylor [3]; 4, Hust [5]; A9 Neumann [6], ®, calculated byWFL Rule; — estimated values [7].

No values have been reported for the liquid phase. A value of A, = [29] Wm-1K"1 wasestimated by comparison with the measurements reported for IN718.

6 Viscosity (r|)

A value of TI = [7.5] mPas at the liquidus temperature and other values shown in Table 1 wereestimated by comparison with measured values for alloy IN718.


A value of y = [1880] mNm"1 at the liquidus temperature and values for other temperaturesshown in Table 1 were estimated for an alloy with low sulphur and oxygen contents.

8 Emissivity (s)

Touloukian [8] has collated emissivity data for the solid alloy, these are presented in Figure 6.

Therm

al

conduct

ivity

, K

(W

rrr

1 K

"1)

Wavelength, X (nm)

Figure 6 Spectral emissivity Sx as a function of wavelength; , 250 0C; - -, 500 0C;••••,750 0C [8].

References

1. Maglic, K D; Perovic, N L and Stanimirovic, A M: High Temp - High Pressure 25(1993)429/434.

2. Inco Technical Data.

3. Taylor, R E9 TPRC, Purdue University, private communication cited in reference 1.

4. Touloukian, Y S; Thermophysical properties of matter, volume 12, Thermalexpansion, publ. 429/434. IFI Plenum, New York (1970) volume 12 p!216.

5. Hust, J G; Wetzel, D H and Powell, R L: J. NaL Bur. Stand. A75 (1979) 269/277.

6. Neumann, W; Internal Report, Austrian Research Centre, Siebersdorf, Austria, ReportOEFZ AO-557 (1984) cited in reference 1.

7. Mills, K C; Day, P N and Quested P N: Proc. Joint Symp. Osaka Univ - NottinghamUniv, held Nottingham, Sept (1995).

8. Touloukian, Y S: Thermophysical properties of matter, volume 7, RadiativeProperties, p 1364.

Sp

ectr

al e

mis

sivi

ty, B

Table 1

Recommended values for the thermophysical propertiesofHastelloyX

T I p I Cp I H1-H25 I Wa I X I TJ I j0C kgm'3 JK- 'g 1 J g 1 m2s-' Wm''K'1 mPas mNm'1

25 8240 0.439 33.4 2.85 10.3100 8221 0.454 79.7 3.09 11.5200 8193 0.473 128 3.41 13.2300 8162 0.493 178 3.73 15.0400 8130 0.512 230 4.06 16.9500 8095 0.532 284 4.38 18.8600 8058 0.551 341 4.70 20.9700 8019 0.582 400 4.90 22.8800 7978 0.604 461 4.96 23.8900 7934 0.626 525 5.22 25.91000 7889 0.648 591 5.49 28.01100 7841 0.670 659 5.75 30.21200 7792 0.692 730 6.02 32.41260a 7761 0.710 772 6.18 33.7

1355a [7420]b [0.677]b [1112]b [29]b [7.5]b [1880]b

1400 [7363]" [0.677]b [1146]b [29]b [6.8]b [1875]b

1500 I [7280]b I [0.677]b | [1214]b | | [29]b | [5.5]b | [1865]b

a = melting range

= estimated value

Ni - IN 718


Al

0.5

C

0.08

Co

1

Cr

19

Cu

0.3

Fe

16.7

Mn

0.35

Mo

3.1

Nb

5.2

Ni

52.5

Si

0.35

Ti

0.9

2 Transitions

Tsol = 1260 0C : T,iq = 1336 0C [1]

High temperature DSC measurements [2] revealed endothermic transitions on heating withpeaks at 700, 830 and 1170 0C (see Figure 2a). The latter endotherm could be due to either asolid-solid transition (y -» y') or to eutectic melting. MTDATA calculations indicated that itwas probably caused by eutectic melting, so a Tsol of 1170 0C has been tentatively adopted.

3 Density (p), thermal expansion coefficient

p = 8190kgm"3:a(21-93°C) = 13 XiQ-6K'1 (1)

Solid: Estimated p = 8104 kg m'3: Estimated a (25 -1000° C) = 16.3 x 1Q"6 K"1 (2)

The values of p(T) given in Table 2 and Figure 1 for the solid phase were calculated using theexperimental density and the estimated thermal expansion coefficient. Values for the solidrecently reported by Overfelt and Taylor [3] and by Henderson [5] are in excellent agreement(Figure 1). The density values for the liquid phase determined with the levitated drop technique[4] are given in Equation 4 and are 4% lower than values obtained with the piston methodreported by Henderson [5] and estimated values [6] (Equation 5). The recommendedtemperature dependence for the liquid is given by Equation (5).

ps (kg.m~3) = 8190 - 0.392 (T-25 0C) (3)

Liquid: p ,(kg.nT3) = 7033-0.745 (T-1336 0C) (4)

p, (kg.m'3) = 7400-0.88 (T-13360C) (5)

Temperature (0C)

Figure 1 Density of nickel alloys, IN 718, as a function of temperature measured values;, o recommended values; A; Overfelt [3], • Henderson [5], McCormick

and Brooks [4] •••; estimated values [5], x.

4 Heat capacity, (Cp), enthalpy

The Cp-T relation given in Figures 2(a) and (b) and Table 2 was derived from DSC [2] and hightemperature DSC [2,7] results, the two studies being in good agreement. Cp values reported forlower temperatures by Brooks [8] and Sweet [9] are slightly lower than those shown inFigure 2. Enthalpy values are given in Figure 3. Recently, Pottlacher [10] has reported (Hx-H25)values using the explosive wire technique, the value of AHftls = 220 Jg"1 was obtained and it canbe seen that (H1-H25) values are in excellent agreement with the DSC results [2]. Estimated Cp

and (Hx-H25) values are in good agreement (< ± 3%) except in the transition ranges. It should benoted that the estimated values should be used for Cp in the fusion range (1170-1336 0C) andprobably for the transition responsible for the peak at 830 0C.

Cp25 = 0.435 J K-1 g"1 [2]

AHi^o8 = 2 to 3 Jg-1 [2]

A H*8 = 210 J g ~l [2] Estimated A H*8 = 270 J g"1

The discrepancy between experimental and estimated AHftls values is due to the disorderingoccurring in the solid/solid transitions (note (Hx-H25) for the liquid alloy is in good agreement).

Densi

ty,

p (

Kg rrr

3}

(b) Temperature (0C)

Figure 2 Heat capacity of nickel alloy, IN 718, as a function of temperature (a) showingapparent Cp in transition range ( , Cpapp), (b) Cp on a more sensitive scale;measured values; —o— Richardson [2]; x, Henderson [7] O, Brooks [8]; A9

Sweet [9] and estimated values [5]. Estimated values should be used intransition ranges. (Use Equn 6.1 to calculate properties in the 'mushy' region.)

Temperature (0C)

Specific heat capacity1241b, 10°C/min, IN7240b, 10°C/min, IN718EMT EMT

Hea

t ca

pac

ity,

Cp (

J g~

1 K~1)

Temperature (0C)

Figure3 Enthalpy (H1-H25) of nickel alloy, IN 718, as a function of temperature;recommended values [2], —o—; Pottlacher [10] •; estimated values, X. (UseEqun 6.1 to calculate properties in the 'mushy' region.)

5 Thermal conductivity (X) thermal diffusivity (a)

Thermal diffusivity values have been measured from temperatures between 200 and 1400 0C bySzelagowski [11], Henderson [7] and by Monaghan [12] using the laser flash method. It can beseen from Figure 4 and Table 2 that there is good agreement in the results for the solid alloy butthere is a 20-30% difference for the liquid phase results. One possible reason for this differencemay be a higher convectional contributions to the thermal diffusivities reported by Henderson[7] and by Monaghan [12]; lower values are usually preferred for the measurements for theliquid phase. However, thermal conductivity values calculated from electrical resistivity values[10] using the Wiedemann-Franz-Lorenz (WFL) relation were found to be in good agreementwith the higher values reported by Henderson. Thus, these data are preferred. The experimentalvalues obtained for the mushy phase are spurious since heat from the energy pulse is partiallyconverted into enthalpy of fusion, the values for this range should be derived from the relation

(fs af + f t a f ) where m denotes the melting point (Tliq) value.

Enth

alp

y, H

1-H

25(J

g-1

)

Temperature (0C)

Figure 4 Thermal diffusivity of nickel alloy, IN 718, as a function of temperature,measured values —o— recommended values; • Henderson [7]; —,Szelagowski [U]; A, Monaghan [12]. (Use Equn 6.1 to calculate properties inthe 'mushy' region.)

Thermal conductivity (A,) values, shown in Figure 5, were calculated from thermal diffusivityvalues using the measured values of Cp and p. These values are in good agreement with valuesreported by Filoni [13], McElroy [14], Sweet et al [9]. The discrepancies (± 5-10%) lie withinthe combined uncertainty of the methods and probably reflect differences in (i) thermal andmechanical treatment of the specimens and (ii) chemical composition and impurity levels.

Thermal conductivity values for the liquid derived from thermal diffusivity values reported byHenderson [7] and Monaghan [12] yield values of around 28.3 Wm"1 K"1 for temperaturesbetween 1350 and 1550 0C. These are preferred to values of around 23 Wm"1 K"1 obtained bySzelagowski [11] since the values of 29.0 Wm"1 K"1 and 33.9 Wm"1 K"1, respectively, wereobtained for 1350 and 1550 0C using the electrical resistivity data [10] and the WFL rule.

Estimated values [5] for the solid alloy are in excellent agreement with measured values. Forthe liquid alloy, estimated values based on electrical conductivity predictions give high values

but the values based on using (A,™ / X^) for the parent metal (Ni) are in excellent agreement.

Th

erm

al diffu

siv

ity,

106a

(IT

i2S"1)

Temperature (0C)

Figure 5 Thermal conductivity of nickel alloy, IN 718, as a function of temperature; thisstudy derived from measurements of thermal diffusivity, Cp and density;experimental values; +, Filoni [12], D, McElroy [13], —, Sweet [9]; •,Henderson [7], +, Szelagowski [U]; A, Monaghan [12]; estimated values [6]; ̂* based on WFL rule. (Use Equn 6.1 to calculate properties in the 'mushy'region.)

6 Viscosity

Viscosity values have been reported by Overfelt and co-workers [3,15] and Andon andDay [16]. The results are in good agreement. The results due Andon and Day [16] have beenadopted since they were subject to much less variability. The following equations arerecommended:

f5848^T| (mPas) = 0.196 exp-—

^ T J (6)

(2539\or log]0Ti (mPas) = -0.708 + -=~

V T J (7)

where T is in K in both equations.

Therm

al

conductivity,

K (

W m

~1 K

r1)

Temperature (0C)

Figure 6 Viscosity as a function of temperature for the nickel alloy, IN 718,recommended values; , o; [16], Overfelt [3,15], A.


Surface tension values have been measured by the oscillating drop method by Brooks et al [17].The alloy formed an oxide film which prevented oscillations below the melting point of theoxide (ca 1720 0C). In some cases the normal 5 peak spectra were obtained and in others acomplex 7 or 9 peak spectra were obtained. An analysis of these 7 and 9 peak spectra indicatedthat it was necessary to utilise all the recorded frequencies (and not just the 5 most prominentfrequencies) to obtain surface tension values which were consistent with those obtained from 5-peak spectra (Figure 7). The surface tension-temperature relation will be dependent upon thesoluble O and S contents; the values reported in Figure 7, Table 2 and Equation 8 are for analloy containing 10 ppm S (total).

y^Nm"1)- 1842-0.11(T-1725 0C) (8)

Temperature (0C)Figure 7 Surface tension of IN 718 as a function of temperature.

Su

rfac

e te

nsi

on

,y (

mN

m'1)

Vis

cosi

ty,

T^ (m

Pa

s)


The fraction solid has been determined in high temperature DSC experiments [2,7] and inquantitative directional solidification experiments. The results given in Figure 8 indicate that:

(i) Overfelt [3] pointed out that fs values obtained with DSC are appreciably lower thanthose recorded using cooling curves; the DSC results recorded by Richardson [2] liebetween the two sets of results reported by Overfelt [3].

(ii) the values obtained by Richardson [2] for the cooling cycle are similar to those for theheating cycle but are displaced to lower temperatures and are at much highertemperatures than those reported in the DSC studies reported by Overfelt [3].

(iii) the supercooling increases with increasing cooling rate and possibly sample weight usedin DSC experiments (sample used by Henderson [7] was considerably larger than that in[2].

Temperature (0C)

Figure 8 Fraction solid of nickel alloy, IN 718, as a function of temperature; Richardsonet al [2], heating rate of+10 K min"1; Richardson et al [2], — cooling rate-10 K min1; Overfelt [3], -5 K min1, A; -20 K mitf1, X; Jardy [18], -10 K min1,adjusted to Tliq in [2], •••; D, cooling curves, Overfelt [3]. (Note temperaturescale may be in error, see Section 5.5).

Frac

tion

solid

, fs

References

1. Inco Alloys Intl: Product Handbook, Publ. No. IAL-38 (1988).

2. Richardson, M J, Hayes, D, Day, A P and Mills, K C: NPL Report on DSC MTSProgramme on Processability: Thermophysical property data for commercial alloysmeasured in PMPl, 2 and 3, NPL, (1996).

3. Overfelt, RA and Taylor R E: Thermal Conductivity 23, edited K E Wilkes,R B Dinwiddie and R S Graves (Technomic, Basle, 1996) pp 538-549.

4. McCormick, A J and Brooks, R F: Report Measuring Density using the levitated dropmethod as in reference 2.

5. Henderson, J B and Strobel, A: Thermal conductivity 23 edited K E Wilkes,R B Dunwiddie and R S Graves (Technomic, Basle, 1996) pp 530-537.

6. Mills, K C, Day, A P and Quested, P N: Proc. Nottingham Univ. - Osaka Univ. JointSymp. held Nottingham, Sept 1995.

7. Henderson, J B and Strobel, A: Thermal Conductivity 23 edited by K E Wilkes,R B Dinwiddie and R S Graves (Technomic, Basle, 1996), pp 530-537.

8. Brooks, R B, Cash, A, Garcia, A: J. Nuclear Mater. 78 (1996) 593.

9. Sweet, J N, Roth, E P, Moss, M: Intl. J. Thermophys. 8, 593 (1987).

10. Pottacher, G and Seifter, A: private communications, Inst. f. Experimentalphysik, Univ.Graz, Austria, (1998).


12. Monaghan, BJ and Waters, MJD: Laser flash liquid metal thermal diffusivitymeasurements, WPZ Report CMMT(D)196, (1999).

13. Filoni, L and Rocchini, G: High-Temp - High Pressures, 19, pp 381-387 (1987).

14. McElroy, DL et al: Thermal Conductivity 15 edited by V V Mirkovich (Plenum,New York 1978) pp 149-161.

15. Overfelt, RA and Banerjee, P: Proc. 13th Symp. Thermophysical Properties heldBoulder, CO, USA, June 1997. (See also Overfelt et al, Met. Trans, 27B (1996).

16. Andon, RJL, Chapman, L, Day, L P, Mills, K C. NPL Report CMMT(A) 167(1999).

17. Brooks, R F et al: Intl J. Thermophys. 171151 (1996).

18. Jardy, A, Ablitzar D and Wadier J: Europ. Mater. Res. Soc. (1986), 285/294.

Table 1

Recommended values for thermophysical properties in EV 718

Solid

Liquid

TemperatureOC

25

100

200

300

400

500

600

700

800

900

1000

1100

1170(b)

1336"

1400

1500

1600

Densitykgm-3

8190

8160

8118

8079

8040

8001

7962

7925

7884

7845

7806

7767

7727

7400

7340

7250

7160

JK-lV1

0.435

0.455

0.479

0.497

0.515

0.527

0.558

0.568

0.680

0.640

0.62

0.640

0.650

0.720

0.720

0.720

0.720

(H1-H25)Jg-1

O

33

80

129

180

232

285

343

405

473

536

600

645

975

1012

1084

1156

A.Wm- IK-I

8.9

10.8

12.9

15.2

17.4

18.7

20.8

21.9

26.9

25.8

26.7

28.3

29.3

29.6

29.6

29.6

(29.6)

106a

m^s'l

2.5

2.9

3.3

3.75

4.15

4.4

4.6

4.75

4.9

5

5.35

5.5

5.6

5.6

5.6

5.6

(5.6)

io^nPa.s

7.20

6.46

5.31

SurfaceTensionymNnrl

1882a

1877a

1866a

1855a

results extrapolated from 1725 °C for sample containing 10 ppm S. melting range

Table 2

Fraction solid as a function of temperature from DSC results reported byRichardson et al [2] for heating and cooling rates of 10 K min~l (see Section 5.5)

f,HeatingCooling

O13461335

0.113411332

0.213361328

0.313311324.5

0.413261320

0.513191315

0.613111310

0.713021300

0.812901291

0.912791277

0.9512661263

1.01250

-

The difference in Tf values shown in Tables 1 and 2 is associated with the fact that TIiq is usuallytaken as the peak temperature whereas the temperature where the endotherm on heating returns to thebaseline is used when calculating fs. Supercooling results in a decrease in Tf for the cooling cycle.

SiPure Silicon


Melting point, mp = 1414 0C [I].


P25 (solid) = 2330 kgm'3 [2] a - 3.8 x 10'6 K'1 [2]

Ohsaka et al [3] have reported a value of p™ =2311 kgm"3 for the solid near the meltingpoint, 1% higher than the recommended values (Table 3).

There have been several determinations of the density of liquid silicon. Details of the investigationsare given in Table 1 and the results are plotted in Figure 1. Rhim et al [3,12,13] have reported threeslightly different values for the density at the melting point; it has been assumed that the most recentvalue, pm = 2580 kgm"3 is the definitive value from their measurements.

A mean value of pm = 2560 kgm"3 has been adopted since the experimental uncertaintiesassociated with individual methods are probably +30 kgm"3 (>1%) [15].

Recommended values for the liquid:

pe = 2560 - 0.30 (T-Tm) kgm"3 (1)

Temperature (0C)


Figure 1 Density of a) Solid [15] and b) Liquid silicon as a function of temperature(a)—, Rhim [3,12,13] Recommended; (b) [4,5], — Recommended.

Den

sity

(kg

/m3)

Den

sity

(k

g/m

3)


The heat capacity (Cp) and enthalpy values reported by Dinsdale [1] have been adopted andare given in Figures 2(a) and (b) respectively.

Cp25(s) = 0.712 JKVCp(*) = 0.968 JKVAH615 - 1787Jg-1: ASft's = 1.06 JKV

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 therecommended value).

Temperature (0C)

Temperature (0C)(b)

Figure 2 (a) Heat capacity and (b) enthalpy (H1-H25) as functions of temperature forsilicon.

Enth

alp

y (

HT

-H25)

J g

~1

10

3 H

eat

Capacity (

JK~

1 g

~1)

4 Thermal diffusivity (a) conductivity (A,)

Touloukian [2] reported values for the thermal conductivity of solid silicon and values havebeen derived by Yamasue et al [16], Glassbrenner et al [17] and Fulkerson et al [18]. Theresults 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]; O9 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 thevalues 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)

Th

erm

al

Co

nd

ucti

vit

y (

Wrr

r1 K

~1}

Temperature (0C)

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


Figure 4 (a) Thermal conductivity and (b) thermal diffusivity; liquid silicon as afunction of temperature.

Therm

al

Diff

usi

vity

(x1

04 m

2/s)

Therm

al

Conduct

ivity

(W

rrr1

K~1)

5 Electrical conductivity (a)

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 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)

6 Viscosity (r|)

Viscosities have been reported for liquid silicon by several investigators [5,25,26,27]. Theresults, shown in Figure 6, show an appreciable amount of scatter. This can be attributed totwo factors [28];

(1) the type of analysis used to obtain the viscosity from the damping data recorded withthe oscillating viscometer; the modified Roscoe equation has been reported [28] to besuperior to the Shvidovski and Knappwost equations;

(2) if the crucible is non-wetting to the liquid metal there will be slip at the crucible wallwhich 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 thanthose recorded with a 'non-wetting BN crucible. Kimura, Sasaki and Tereshima [8,26] havereported that changing from the Shvidovski approach to the Roscoe equation resulted in anincrease in viscosity of 0.2 mPas or 35%. The crucible used by Kimura et al [8,26] had arelatively small (height/radius) ratio and it was not stated whether these workers appliedcorrections for end effects.

Sato et al [27] carried out viscosity measurements using crucibles fabricated from a variety ofmaterials. Their results (i) showed some variation and (ii) were lower than those reported byother workers. The average of these values has been tentatively adopted.

Resis

tivity

(p,

ohm

cm

)

100OT (0C)

Figure 6 The viscosity (on a logarithmic scale) as a function of the reciprocaltemperature (0C"1); •, average viscosity Sato [27]; D, Glazov [5]; • • • • • • •Kakimoto [25]; O9 Sasaki, Kimura [8,26] with SiC crucible; A, with PBNcrucible.


The surface tension (y) and its temperature dependence (dy/dT) have been measured by alarge number of workers [29-38]. Keene [38] noted that the values tended to fall into twobands and he suggested that (i) high values of y and (dy/dT) pertained to the pure elementwith a low p02 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 tooxygen-saturated silicon.

Average viscosity (mPas) Sato

Glazov

Kakimoto

Sasaki SiC

Sasaki PBN

Linear (average viscosity (mPas))

Vis

cosity

(m

Pas)

Temperature (0C)

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

The effect of p02 on y and (dy/dT) was investigated by Niu et al [43,44] the results are shownin Figure 8a and 8b, respectively.

The recommended values are

pure Si: ym = 825 mNm'1

oxygen-saturated Si: yT = 730 - 0.104 (T-1414 0C) mNm'1 (4)

Figure 8 (a) Surface tension y and (b) (dy/dT) as functions of partial pressure of oxygen[44,45].

log P02 (MPa)log P02 (MPa)

calculatedcalculated

Tem

pera

ture

coe

ffici

ent o

fSu

rfac

e Te

nsio

n (m

N/m

K)

Surf

ace

Tens

ion

(mN

/K)

Su

rf ac

e T

ensi

on

(m

N/m

)

9 Emissivity (s)

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

Wavelength (nm)

(b) Wavelength (nm)

Figure 9 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]; OAoyama [54].

Norm

al

Spectr

al E

mis

siv

ity

Norm

al

Spectr

al

Em

issiv

ity

References

1. Dinsdale, A T. CALPHAD 15 (1991) 317.

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

3. 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.

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

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

7. 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. Proc. 4th Asian Conf.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.

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

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

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

17. Glassbrenner, G A; Slack, G A. Phys. Rev. 134-140 (1964) 1058.

18. Fulkerson, W; Moore, J E; Williams, R K; Graves, R S; McElroy, D L. Phys. Rev.167(1968)765.

19. Beers, D S; Cody, G D; Abeles, B. Proc. Intl. Conf. Semiconduct. Inst. Phys. Soc.London(1962)41.

20. Yamamoto, K; Abeand, T; Takasu, S. Jpn. J. Appl. Phys. 30 (1991) 2423.

21. Takasuka, E; Tokizaki, E; Terashima, K; Kimura, S. Proc. 4tn Asian Conf.Thermophys. Prop. Tokyo, Sept 1995 paper Bl d3.

22. Glazov, V M; Koltsov, V B; Kurbatos, V A. Sov. Phys. Semicond. 20 (1986) 1351.

23. Sasaki, H; Ikari, A; Terashima, K; Kimura, S. Jpn. J. Appl. Phys. 34 (1995) 3426.

24. Schnyders, H S; van Zytveldt, J B. J. Phys. Cond. Matt. 8 (1996) (50) 10875.

25. Kakimoto, K; Eguchi, M; Watanabe, H; Hibiya, T. J. Cryst. Growth 94 (1989) 412.

26. Sasaki, H; Tokizaki, E; Terashima, K; Kimura, S. Jpn. J. Appl. Phys. 34 (1995) 3432.

27. Sato, Y; Yamamura, T. Private Communication, Tohoku University, Sendai,(Nov 1999).

28. Iida, T; Guthrie, R I L. The Physical Properties of Liquid Metals, Oxford Sci. Pub.Oxford, UK, 1987.

29. Keck, V H; van Horn, W. Phys. Rev. 91 (1953) 512.

30. Dzhemilev, N K; Popel, S I; Tsarevskii, B V. Phys. Met. Metallog. (USSR) 18 (1964)(1)77.

31. Levin, JES; Geld, P V; Baum, B A. Russ. J. Phys. Chem. 42 (1968) (11) 1455.

32. Kingery, W D; Humenik, M. J. Phys. Chem. 57 (1953) 359.

33. Tavadze, F N e / al. Surface Phenomenon of Melts, ed V.M. Eremenko, Nauk, Kiev,USSR (1968) 159.

34. Elyutin, V P; Kostikov, V I; Levin, V Y. Izv. VUZ: Tsvet. Met. (1970) (1) 53.

35. Naidich, V I; Perevertailo, V M; Obushchak: Sov. Powder Metall. Met. Ceram. 14(1975) (5) 403.

36. Lukin, S V; Zhukov, V I; Vatolin, N A; Koslov, Y S. J. Less-Common Met. 67(1979)407.

37. Hardy, S C. J. Cryst. Growth 69 (1984) 456.

38. Keene, B J. Surf. Interface Anal. 10 (1987) 367.

39. Przyborowski, M; Hibiya, T; Eguchi, M; Egry, I. J. Cryst. Growth 151 (1995) 60.

40. Sasaki, H; Anzi, Y; Huang, X; Terashima, K; Kimura S. Jpn. J. Appl. Phys. 34(1995)415.

41. Huang, X et al; J. Cryst. Growth 156 (1995) 52.

42. Chung, S. Izunome, K; Yokotani, A; Kimura, S. Jpn. J. Appl. Phys. 34 (1998) L631.

43. Kawasaki, N; Watanabe, K; Nagasaka, Y. High Temp. High Press. 30 (1998) 91.

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

45. Hibiya, T; Mukai, K et al. Proc. Royal Soc. (London), (1998) Ser. A, A356 899.

46. Nogi, K. Technology for Production of High Quality Crystal, No Nedo (1998).

47. Watanabe, H; Susa, M; Fukuyama, H; Nagata, K. High Temp. High Press. In press.

48. Shvarev, K M; Baum, B A; Geld, P V. Fiz. Tverda. TeIa. 16 (1974) 3246.

49. Li, K D; Fauchet, P M. Solid State Commun. 61 (1987) 207.

50. Lampert, M P; Koebel, J M; Siffert, P. J. Appl. Phys. 52 (1981) 4975.

51. Jellison, G E Jnr; Lowndes, D H. Appl. Phys. Lett. 51 (1987) 352.

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 determinationsof molten silicon

Reference

Lucas 1 41Glazov [5]Kimura [6-

101Langen [11]

Rhim[3,12,13]

Niu [14]

Method

AM

AM

LD

LD

SD

Container/Probe

Al7O1

SiC

None(EML)

None (ESL)

BN

Temp range0C

1410-16501450-16401415-1650

1160-1500

300-1530

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

P-252625302570

2520

2580

253025602520

b0.3520.350.20

0.35

0.171

0.1680.169

C

0.161 x 10'J

0.174 x 10-j

0.175 x ID'3

*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

YamamotoF201

Kimura[7,8,21]

Yamasue[16]

Method

LP

LP

HW

Containermaterial

SiC

SiO2Quartz

Al2O3

(Pt coatedSiO7.)

Temp rangeOC

25-1456

1320-1500

1427-1351

Analysismethod

tO.5

(i) tQ.5 forradiation(ii) Curve

fittingAr,

^surface >

1 base

Results aj = am + b(Tm-T)m

105am

(m^s-1)2.28

2.38

Wn = 56.5Wm-I K-1

105b(m2s-l)

0.06 x 10-2

0.15 XlO'2

Methods: LP = laser pulse; HW = hot wire method

Table 3

Recommended values for thermophysical propertiesof silicon

Temperature0C25100200300400500600700800900100011001200130014001414141415001600

P (kgm"3)

2330232823252323232023172314231323092306230423022299229622942293256025342504

Cp (Jg-1K-)

0.7120.7700.8200.8600.8770.8970.9160.9320.9490.9640.9800.9951.0101.0241.0371.0400.9680.9680.968

H1-H25(Jg-1)O561362203063954855786727688659641064116512681283307031533251

Jl (Wm-1K-')

14110882665042383228242221201918

58.260.462.9

105a(m2s-')

8.56.04.33.32.452.021.81.481.281.080.970.910.860.810.76

2.332.462.60

TI (mPas)

0.580.520.51

TiPure Titanium


(cph) -» (bcc) - Ttr - 8820C [1]

mp = 16680C [1]


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 wereused 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)

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

Temperature (0C)

Figure 1 Density of pure Ti as a function of temperature.

Den

sity

, P

(K

g m

"3)


The heat capacity and enthalpy values are given in Figures 2 and 3 respectively, and inTable 1.

Dinsdale [1] reported the following values:

AH*2 = 87Jg-'

AHJT68 = 295Jg-1

CpCO = 0.965Jg1K-1

Temperature (0C)

Figure 2 Heat capacity of pure Ti as a function of temperature [I].

Temperature (0C)

Figure 3 Enthalpy of pure Ti as a function of temperature [I].

Ent

halp

y, H

7-H

25 (

Jg'1)

Hea

t Cap

acity

, C

p (J

g'1

KT1)


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. Valuescalculated from electrical resistivity data and the WFL Rule are slightly lower and showed asmall 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 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.

The

rmal

Diff

usiv

ity,

106a

(mV

)

The

rmal

Con

duct

ivity

, A

(Wm

-1K

'1)

5 Viscosity (TI)

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


Keene [12] collated the surface tension values for pure titanium and did not recommend avalue 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 residualpressure 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 andit is difficult to remove the oxygen from the metal. Consequently, it is difficult torecommend 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 ofoxygen solubility.

yc (mNm"1) = 1525 - 0.28 (T-1668° C) (3)

7 Emissivity

Shiraishi [15] reported the following values for the spectral emissivity, B^ at 0.65 |tim for asmooth 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 S1̂

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

and Touloukian cites for a polished surface

T 0C (STN): 1300 to 1500 0C (0.42).

References


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 hightemperatures, 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 heldSmolenice 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.


Table 1

Recommended thermophysical properties for pure Ti

T0C

25100200300400500600700800882b

882"90010001100120013001400150016001668C

1668°17001800

PTkgm'3

45404529451444994484446944544439442444124412440943944379436443494334431943044294414041334110

CPJg1 K-1

0.5220.5490.5800.6010.6220.6430.6610.6850.7030.7180.6120.6140.6260.6410.6620.6890.70807320.7600.7830.9650.9650.965

(H1-H25)Jg1

O4097156217280346413483540627638700763828895965103711121189148415151611

10" amV8.658.77.37.16.76.56.36.05.96.67.77.88.18.48.68.79.09.19.29.27.87.87.8

XWm'1 K-'20.52019.21918.818.818.418.218.420.820.82122.323.624.926.227.528.830.131313131

TlmPas

2.2

YmNm"1

152515161488

P (a)£x

0.500.500.490.490.490.480.470.460.460.460.45

polished surface and X = 0.65 |tim

phase transition - density change assumed to be zero

melting temperature

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


Al

5.5-6.7

Fe

0.03

Ti

90

V

3.5-4.5

H

0.0125

02+N2

0.25

Ref

[1]

2 Transitions

T (oc->p Transition) = 995 ± 15 0C Tliq = 1650 0C


P20 = 4420 kg m"3 [1] Estimated value p25 - 43 74kg m'3

Mean linear thermal expansion coefficient.

T0C

a.106

25-200

9

25-300

9.5

25-400

9.8

25-500

16

Estimated

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

The density values in Table 1 were derived from the measured p20 value and the estimatedvalues of a for the solid. McCormick and Brooks [2] measured density values for the liquidalloy over the temperature range (1600-1880 0C) using the levitated drop technique. The resultsshown in Figure 1 indicate that the density is very close to the values estimated using additivityrules (METALS model) and can be expressed by Equation (2).

ps (kg in3) = 4420 - 0.154 (T- 25 0C) (1)

p^ (kg m'3) = 3920 - 0.68 (T-1650 0C) (2)

Temperature (0C)

Figure 1 The density of TI/6A1/4V as a function of temperature; , o, recommendedvalues [2]; x, Metals model estimates.


Values for Cp and (H1-H25) have been measured by Bros [3] and Richardson [4] for temperaturesup to 600 0C; it can be seen from Figure 2 that estimated values are in excellent agreement withthe measured values. Heat capacity values were obtained to 1100 0C by Hayes [4] using a hightemperature 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 usinglevitated 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 agreementwith the value AHfos = 286 Jg"1 recorded by Cezairliyan and McClure [6] using the explodingwire technique Very recently, Brooks [11] has obtained drop calorimetry results for solid Ti-6A1-4V, as can be seen from Figure 3, these results are in excellent agreement with theextrapolated values, with the one exception of the (H1-H25) at 1650 0C. This could be due toeither partial melting of the sample or the electronic contribution to Cp of the solids. METALSmodel predicts a value of 306 Jg"1 and the (H1-H298) values estimated by METALS model arewithin 1% of the experimental values. The Cp obtained from the drop calorimetry [11] workyields Cp = 0.67 Jg-1K"1, significantly lower than the estimated value (Cp = 0.9 Jg-1K"1). Therecommended values are

AH9T = 48 ± 10 Jg1 , AHp6SO = 286 Jg1, Cp(liq) = 0.83 Jg1 K'1 [5]

Den

sity

, P

(K

g m

"3)

Figure 2 Heat capacity of T1/6A1/4V as a function of temperature; , o, recommendedvalues; A5 Bros [3]; •, Richardson [4].

Temperature (0C)

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

Temperature (0C)

Ent

halp

y, H

1-H

25 (

Jg

1)

Hea

t Cap

acity

, C

p (J

g"1 K

'1)

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 solidmetals which can be affected by thermal and mechanical history and any minor differences inimpurity levels and chemical composition.

Polev et al [10] used the plane temperature wave method to measure the thermal diffusivity of aTi/Al/1 V/2 Zr/1 Mo from (700-1700 0C).

The thermal diffusivity value calculated from the thermal conductivity results (Figure 4) arecompared with the thermal diffusivity data reported by Polev et al in Figure 5. In addition, thelatter 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 toconvectional contributions to the conductivity and diffusivity results. Estimated values, whichare usually high by ca 10%, were obtained:

X11650 = 30.6 Wm-1K'1 : X1

1800 = 32.5 Wm-1K"1

a!650 = 0.80 mV : a!800 = 0.866 mV

Thus a value at 1650 0C X1 = 27.5 Wm-1K'1 and a = 0.7 mV might be expected. Theexperimental 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].

The

rmal

Con

duct

ivity

, A.

(Wm

-1K

'1)

Temperature (0C)

Figure 5 Thermal diffusivity values for Ti-6Al-4V as a function of temperature; , o,recommended values based on results due to Polev [1O]; values calculated fromconductivity measurements due to Touloukian [9], ••••; and Filoni [7],. A; x,estimated values.

6 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: Thermophysicalproperty data for commercial alloys measured in PMPl9 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.

The

rmal

Diff

usiv

ity,

106a

<m

V)

9. Touloukian, Y S; Powell, R W; Ho, CY; Klemens, P G: Thermophysical Properties ofMatter, 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 1Recommended values for thermophysical properties of

90 Ti/6 A1/4V; estimated uncertainties are given at the foot of the table

Temperature0C

25

100

200

300

400

500

600

700

800

900

995

995

1100

1200

1300

1400

1500

1600

1650

1650"

1700

1800

1900

Uncertainty

Densitykgm"3

4420

4406

4395

4381

4366

4350

4336

4324

4309

4294

4282

4282

4267

4252

4240

4225

4205

4198

4189

3920

3886

3818

3750

±3%

JK-1V1

0.546

0.562

0.584

0.606

0.629

0.651

0.673

0.694

0.714

0.734

0.753

0.641

0.660

0.678

0.696

0.714

0.732

0.750

0.759

0.831

0.831

0.831

0.831

±3%

(H1-H25)Jg1

O

42

99

158

220

284

350

419

489

561

636

684

749

816

885

956

1028

1102

1184

1466

1508

1591

1674

±3%

1Wm-1K'1

7.0

7.45

8.75

10.15

11.35

12.6

14.2

15.5

17.8

20.2

22.7

19.3

21.0

22.9

23.7

24.6

25.8

27.0

28.4

33.4

34.6

-

-

± 10%

106amV

2.9

3.0

3.4

3.8

4.1

4.4

4.8

5.1

5.7

6.3

6.9

6.9

7.3

7.65

7.8

7.9

8.1

8.3

8.6

8.6

9.0

-

-

± 10%

*1Pa.s

[3.25]a

[3.03]a

[2.66]a

[2.36]a

± 30%n K

estimated value melting pointDate: May 1999

ZnPure Zinc


mp = 419.40C [1]


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-419 0C) (2)

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

Temperature (0C)

Figure 1 Density of pure Zn as a function of temperature.

Den

sity

, p

(Kg

m"3)


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

Dinsdale [1] also reported values of AHfos = 1 1 2 Jg'1 and for the liquid phase Cp(£) =0.480 Jg1.

Temperature (0C)

Figure 2 Heat capacity of pure Zn as a function of temperature.

Temperature (0C)

Figure 3 Enthalpy (HfH25) for pure Zn as a function of temperature [1]

Ent

halp

y, H

1-H

25 (

Jg'1)

Hea

t C

apac

ity,

Cp

(Jg

-1K

'1)


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

Xm(S) - 100 Wm*1 K-1 : A,™ = 50 Wm'1 K'1

(3)U= 50 + 6 x 10'2 (T-419 0C) WnT1 K'1

Temperature (0C)

Figure 4 Thermal conductivity (A,) as a function of temperature for pure Zn, , o,recommended values; - - Touloukian [5]; ••• Magmedov [7]; ̂ •#• calculatedfrom WFL Rule for solid and liquid respectively.

Figure 5 Thermal diffusivity derived from the recommended thermal conductivity (A,),Cp and p values (a = X/Cp. p) as a function of temperature.

Temperature (0C)

The

rmal

Diff

usiv

ity,

106a

(mV

)

The

rmal

Con

duct

ivity

, A,

(Wm

'1 K

'1)

5 Viscosity (r|)

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

1310In TI (mPas) - -0.614 + —- (4)

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

Temperature (0C)

Figure 6 Viscosity of pure Zn as a function of temperature [3].


Keene [9] reviewed surface tension data reported for pure Zn and recommended the followingequation:

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, S1̂ of 0.04 - 0.05 for a polished surfaceof zinc and S1̂ = 0.5 for an oxidised liquid surface at 1000 0C.

Vis

cosi

ty,

TI (

mP

as)

References


2. CRS Handbook of Chemistry and Physics, edited D R Lide, publ. CRC Press, 74thedition (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 hightemperatures, 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 hightemperatures, 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

T0C

25100200300400419.4419.45006007008009001000

PTkgm'3

7140709070286963689968866756667865806482638462866188

Jg1 k-10.3880.3980.4130.4310.4510.4540.4790.4790.4790.4790.4790.4790.479

(H1-H25)Jg1

O2970112156165277315363411459507555

106aHi2S-1

444139363332.015.417.219.321.523.826.228.2

XWm'1 K-1

12111711310710110050556167737985

nmPas

3.52.92.42.11.8--

YmNm"1

789111751730709

P (a)fcTN

0.0450.045

/a\v J polished surface

Zn-Al


Al Mg Zn

4.5 0.05 94.45

2 Transitions

The following transitions were observed in DPSC studies [I]:

solid state transition : 273 0Cfusion region : 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 goodagreement.

Density measurements for the liquid phase reported by Day et al [2], resulted in a value of6455 ± 100 kg m"3 for 545 0C using the hydrostatic probe method. This is 8% higher than thevalue estimated by METALS model [2] and would correspond to a very low density change onmelting. Consequently, METALS model density values have been adopted and are given inFigure 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)

Temperature (0C)

Figure 1 Density of Zn-Al alloy as a function of temperature. (Use Equn 6.1 to calculateproperties in the 'mushy' region.)


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

Temperature (0C)

Figure 2 Heat capacity as a function of temperature for Zn-Al alloy; —, o, experimentalvalues; x, estimated by METALS model. (Use Equn 6.1 to calculate propertiesin the 'mushy' region.)

Hea

t C

apac

ity,

Cp (

Jg-1

K'1

)D

ensi

ty,

P

(Kg

m'3)

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 tocalculate properties in the 'mushy' region.)

The following data were obtained [1]

Cp25 = 0.41 Jg-1 K-1: Estimated Cp25 = 0.411 Jg'1 K'1 [2]

AH^5C = 8 Jg'1 AH f u s - 114 Jg'1: Estimated A Hftls - 114 Jg~' [2]

Cp(liquid)-0.52-6xlO"5(T-387 0C) JKV1 !Estimated CpCO - 0.51 Jg-1KT1P] (3)


The thermal diffusivity has been measured by Szelagowski [4] and subsequently byMonaghan [5], both using the laser flash method. The results are shown in Figure 4. It can beseen that the values for the solid state are in good agreement but for the liquid there aredifferences of around 30%. Mean values have been adopted for the liquid phase and these areshown in Table 1.

Thermal conductivity values based on recommended values (Table 1) are given in Figure 5.

Temperature (0C)

Ent

halp

y, H

1-H

25 (

Jg'1)

Temperature (0C)

Figure 4 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 tocalculate properties in the 'mushy' region.)

Figure 5 Thermal conductivity (A,) of Zn-4% Al as a function of temperature (UseEqun 6.1 to calculate properties in the 'mushy' region.)

Temperature (0C)

The

rmal

Con

duct

ivity

, k

(Wm

-1K

'1)

The

rmal

Diff

usiv

ity,

106a

(mV

)

6 Viscosity

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

Temperature (0C)

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


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

8 Fraction solid

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

Temperature (0C)

Figure 7 Fraction solid (fs) of Zn-4%Al as a function of temperature in the fusion range.

Fra

ctio

n S

olid

, f s

Vis

cosi

ty,

TI (

mP

as)

References

1. Richardson, M J; Hayes, D; Day, A P; Mills, K C: Final Report MTS Programme onProcessability: 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 ofcommercial 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 diffusivitymeasurements. NPL Report CMMT(D) 196.

6. Andon, RJL; 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

T0C

25100200300357*387*387*400500600700800

Densitykgm'3

670066556595653465006482614261296026592758315738

Jg1 k-1

0.410.420.4750.500.50

L[0.51]a

0.5200.5180.5120.5060.500.494

(H1-H25)Jg1

O3176133161177291298349399449499

10" aHi2S-1

40

L_39

363230-12.5131620

XWm'1 K-'11010911310598-40414960

T!mPas

3.52.62.05

YmNm"1

[830]a

[827]a

[807]a

[787]a

g(a)

* melting range [ ]a = estimated value

Table 2

Fraction solid of Zn-4% Al as a function of temperature

Temperature 0CFraction solid, fs

387O

3850.08

3820.18

3770.46

3760.82

3750.96

3720.98

3621.0

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

Date: March 1999

APPENDIX

Details of METALS model to calculate thethermophysical properties of alloys

Paper presented at Joint Symposium Nottingham Univ.-Osaka Univ. held NottinghamSept (1995).

ESTIMATING THE THERMOPHYSICAL PROPERTIES OFCOMMERCIAL 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, viscositiesthermal and electrical conductivities of multi-component, commercial alloys in the solid andliquid states. The estimated values are compared with measured values for the properties ofvarious commercial alloys.

1 Introduction

Over the last two decades mathematical modelling has become an established tool forimproving both process control and product quality. These models have been applied to a widevariety of processes and industries such as the casting and foundry production, steelmaking,secondary refining of non-ferrous metals, welding, spray forming, dip coating, metallic powderand ribbon production. Model development has evolved to the point where one of the primerequirements at the present time is for accurate physical property data for the commercial alloysinvolved in these processes. Data are required for the factors affecting the fluid flow and heattransfer in the process viz density, viscosity, surface tension, enthalpy, heat capacity, thermalconductivity, thermal diffusivity. The absence of reliable data for commercial alloys reflects thedifficulties 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 andaluminium vary by ±50% and ±100% around the mean. Even greater uncertainties would beexpected with commercial alloys which are subject to segregation, and the presence of non-metallic inclusions, etc. The Department of Trade and Industry has recognised this need foraccurate thermophysical property data for commercial materials and has funded a researchprogramme to develop methods necessary to provide this information [2].

Industry frequently needs to react quickly to combat specific problems in process control orproduct quality. Even when experimental methods are available the production of accurate datais frequently time-consuming. Consequently, there is a need for the development ofmathematical 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 onreliable, traceable values for the material. Consequently we have always adopted a three-pronged 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 estimatevalues for the solid, liquid and 'mushy1 phases. It would also be advantageous if such a modelhad universal application ie it could be applied to a wide range of alloys spanning fromaluminium 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 beenincorporated 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 thethermophysical properties of alloys in the development of the model. Consequently, propertyvalues 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 developmentof models.

Table 1

Data sources used in model development

Property Pure elements Commercial alloys

Heat capacity, enthalpy [4] [5] [3]Density [6] [1] [3] [9]Viscosity [1] [7] [3]Thermal and electrical conductivity [1] [8] [10-17]

2.2 Models

Models based on partial molar quantities (denoted by a bar, egV for partial molar volume) havebeen widely used in this work ie Equn (1)

V = XiVi + X2V2 + X3V3

+ X4V4 + (1)

where x is the mole fraction and subscripts 1,2,3.... denote the various elements present in thealloy.

Both the temperature dependence of the properties and the other models used are describedbelow 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 satisfactorilyexpressed in the form shown in Equn 2, where a, b and c are constants, T is the thermodynamictemperature, K.

CP = a + bT + ̂ (2)

Values a, b and c for a multi-component alloy can be obtained from Equns 3-5

a = aixi + a2x2 + a3x3 (3)

b = bixi + b2x2 + b3x3 (4)

c = CiXi + C2X2 + C3X3 (5)

The enthalpy (Hx-H298) can be calculated using Equn 6

Hx-H 2 9 S= {CpdT = a(T-298) + ̂ (T2-2982)-c(^--M (6)298 v - i ^y*)

The enthalpy of fusion (AHftls) is calculated from the entropy of fusion (ASftls) as shown in Equns7 and 8 where Tliq is the liquidus temperature

ASfus = x,As?'s + x2As!r + X3As*'5 + ..- (7)

AHfils = TiiqAS*15 (8)

Values for the enthalpy of liquid alloys are calculated by Equn 9 where sol and 1 denote thesolid and liquid phases, respectively.

(Hr-H298) = CPly(Tliq-298) + TliqAS^y + CPllloy(T-T,iq) (9)

3.2 Validity of model

It has been found that the predicted values of Cp and (H7-H298) are typically within 2% ofmeasured values for a wide variety of alloys. However, the model predicts neither theoccurrence of phase transitions nor the enthalpies associated with these transitions. It can beseen 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 agreementwith measured values.

Temperature, K

Figure 1 Heat capacity of Al + si alloy as function of temperature; , measuredvalues, • estimated values.

4 Estimation of densities

4.1 Model

Molar volumes (V) and densities (p) for liquid and solid alloys can be derived usingEquns 10-13 where M is the molecular weight (= X1M1 + X2M2 + X3M3 +...) and p is the volumeexpansion coefficient (p = X1P1 + x2p2 + x3p3)

V = XiVi + X2V2 + X3V3 (10)

p = (MAV) (11)

solid: V = V298(I + P501 (T-298)) (12)

HqUIdIV = VTHqO + P1(T-T11,)) <13)

4.2 Validity of the model

The prediction of the model have been compared with experimental density data for the solidand liquid phases. The estimated densities for solid alloys always lay within 5% of themeasured values. Estimated density (p) values for nickel-based alloys at 298K tended to belower than measured values and this was attributed to the fact that Al took up interstitialpositions in the lattice. This view was corroborated by the fact that (pmeas-pcaic) was found toincrease with increasing Al content; using Equn 14 it should be possible to estimate densities ofsolid superalloys to ±1-2%.

Pmeas = (l + 0.0116%Al)Pca|c (14)

It has proved difficult to check the validity of the model for the liquid phase densities due to thepaucity of experimental data for commercial alloys. Density values for various liquidcommercial alloys have been found to lie within 5% of the measured values.

5 Estimation of viscosities

5.1 Model

The viscosities are calculated by the Andrade relationship (Equn 15) using the calculated valuesof the molecular volume (Equn 13) and molecular weight (M) [I].

V = 1.8xlO-4^p^ mPs.s (15)vVT,iqJ

The temperature dependence is given by Equn 16 [1] where A and H are given by Equns 17 and18 respectively and R is the Gas Constant.

TI = Aexp(H/RT) (16)

H = 1.21T,42 (17)

A = 5.7xlQ-3(MT. iqr (18)

V-exp <L21 ̂( RT, iq J


It is difficult to check the validity of the predicted values since it is not known what are theexperimental uncertainties in the viscosity values for (i) the pure elements used in the modeltesting and (ii) the commercial alloys. (Note the experimental scatter bands around the meanfor Fe(liq) and Al(liq) are ± 50 and ± 100%, respectively.) Nevertheless, it can be seen fromFigure 2 that the estimated viscosities lie within 10% of the measured value for a molten Al + Sialloy [3].

Temperature, 0CFigure 2 Viscosities of Al + Si alloy as a function of temperature; , measured

values, • estimated value.

6 Thermal and electrical conductivities

Thermal conductivities of liquid metals are difficult to measure accurately since the measuredheat flux frequently contains contributions from convection and these difficulties becomeincreasingly important at the high temperatures. In recent years it has been shown that transienttechniques provide the most accurate values for liquid alloys since they minimise contributionsfrom convection.

6.1 Model for liquid alloys

At high temperatures the principal mechanism for thermal conduction in liquid metals is due tothe transport of electrons. Although phonon (or lattice) conduction can make a significantcontribution at lower temperatures, a recent review [8] concluded that electronic conduction isthe dominant mechanism for temperatures around the melting point. Consequently, theWiedemann-Franz-Lorenz (WFL) Rule relating thermal (X) and electrical (a) conductivities canbe used with confidence to predict thermal conductivities of molten alloys. The WFL relation isshown in Equn 19 where L0 is a constant with a theoretical value of 2.445 x 10~8 WQK"2 and T isthe thermodynamic temperature.

^ = L0 • T . a (19)

The electrical conductivities (unlike thermal conductivities) should not be affected byconvective flows in the molten metal pool. Consequently, it should be possible to calculatethermal conductivities for molten alloys from the electrical conductivity values. Iida andGuthrie [1] have reported electrical conductivity data for molten binary alloys and the valuesindicate that most alloys exhibit relatively small (< 10%) negative departures from linearity(Equn 20).

CJTl5q = (Ji Xl+ CT2 X2 + CT3 X3

+ (20)

The temperature dependence can be calculated using Equn (21).

ax = aTliq(l + [|p} alloy j (21)

Experimental

Estimate

Vis

cosi

ty,

mP

a.s

where (da/dT) = X1 (da/dT) + X2 (da2/dT) + X3 (da3/dT) + ....

The thermal conductivity for the liquid is calculated by inserting aT and the temperature, T intoEqun 19. However, it should be noted that this calculation will tend to produce a slightly highvalue for the thermal conductivity because the electrical conductivities were observed to exhibitnegative departures from linearity as represented by Equn 20.

An alternative method of calculating the thermal conductivity of the liquid alloy is to use [18]Equn (22) where K is a constant, m denotes the value at melting point and ASftls can becalculated from Equn 7.

In OS, / XS1) = K ASm (22)

Values of K have been derived from X and ASm values obtained for low melting, metallicelements; K had a mean value of 0.073 K mol J"1. The only disadvantage with this technique isthat it requires a knowledge of the thermal conductivity of the solid (X01) at the liquidustemperature.


Estimated thermal conductivity values (via Equn 22) are compared with experimental valuesobtained for the commercial Al + Si alloy in Figure 3 and it can be seen that they are slightlyhigher than the experimental values but the value derived from the entropy of fusion (Equn 22)is in good agreement with the experimental values.

Temperature, 0C

Figure 3 Thermal conductivity of Al + Si alloy as a function of temperature; , x,o, measured values; A, estimated by Equns 20,21, • estimated by Equn 22.

6.3 Model for solid alloys

When the model based on Equns 19 to 21 was applied to the calculation of thermalconductivities of solid alloys, the calculated values were found to be much larger than thoseobtained experimentally. This is due to the fact that both electronic and phonon (or lattice)conduction are important at lower temperatures. Furthermore, the ratio of electronic to latticeconduction differs appreciably from metal to metal; for instance electronic conduction is the

Lab ALab BEstimated

Trans. FusionTher

mal

con

duct

ivity

, W m

"1 K'1)

dominant mechanism for Al alloys (Xel » XIat) but Xel and Xlat are both important for steels andnickel-based superalloys. This means it is very difficult to develop a universal model and it isnecessary to develop methods for particular families of alloys such as steels, superalloys, Alalloys etc.

There is also the problem that the electrical and thermal conductivities are significantly reducedby the presence of dislocations and non-metallic inclusions and these are affected by both theheat treatment and mechanical treatment of the sample. Since aluminium alloys have highthermal conductivities the latter are particularly sensitive to their thermal and mechanicalhistories. The fully-annealed state has been used as the reference state and thus predicted valueswill tend to be higher than the values recorded for samples which have been subjected tomechanical working or heat treatments designed to precipitate second phases.

Aluminium alloys

Inspection of experimental thermal diffusivity (a) data for Al alloys indicated that thermaldiffusivity-temperature curves showed an increase of 5% between 298 and 573K and then adecrease of 10% between 573K and the solidus temperature. This behaviour is described byEquns 23 and 24.

[T 998^—— 2 x 10'2 (23)

(T -573^573K<T<Tso l:aT = 1-05Sa298 1- (^^^l4*^2 (24)

Thermal conductivities can be calculated using the following steps:

(i) calculate (J298 from chemical composition G298 = k(%l) + k2(%2) + k3(%3), where kvalues are constants derived by numerical analysis of electrical conductivity data foraluminium alloys

(ii) calculate X298 from G298 using Equn 19

(iii) calculate (X298 from X298 using the a = (X/Cp.p) estimated Cp (Equn 2) and density (Equns10,11) values and use Equns 23 and 24 to derive aT

(iv) calculate thermal conductivities X1 from aT using Equn 25.

XT = aT-CpTpT (25)

Steels, Ni-based superalloys, Ti-alloys

The resistance to electronic heat transfer is much higher in these alloys than in Al alloys,consequently, lattice conduction tends to be much more significant.

XT = X? + Jl? (26)

Steels

Inspection of thermal conductivities - (T) curves (Figure 4) for a variety of different steels,shows that:

(a) the thermal conductivities vary by almost an order of magnitude and

(b) the temperature coefficient (dA/dT) varies in sign according to the composition

(c) AT attains a reasonably constant value around 800 0C (1073 K) and then continues to risewith temperature.

Values of XT as a function of temperature are calculated using the following steps:

(i) Calculate G298 using the relation, G298 = (0XoI)Ic1 + (%2)k2 + (%3)k3, where k values werederived from numerical analyses of electrical conductivity data of annealed steels.

(ii) Calculate X29gifrom G298 using Equn 19.

(iii) Calculate X18̂ from the chemical composition (Xlat = Xmeas - Xel) and then numerical

analysis was used to determine the optimum values of c for X298 = (%l)ct + (%2)c2 +(%3)c3 + ...).

(iv) X298 for a steel of known composition can be derived from the compositionaldependencies of X6^8 and X1J98 and Equn 26.

(v) The X1 - temperature curve is then constructed using fixed values of X1- of 25 and31.5 Wm-1 K'1 at 800 0C (1073 K) and 1300 0C (1573 K), respectively (Equns 27,28).

298 < T < 1073 K : X1 = X298 + (25 - X298) x (T^8) (27)

1073<T<1573K : XT = 25 + 0.013(1-800) (28)

Nickel-based superalloys

The model used was identical to that used for steels except X1 at 1073 and 1573 K, respectively,were taken as 23 and 32 Wm"1 K"1, respectively and different compositional constants are used.

Ti-based alloys

A similar approach was also used for these alloys except a third range was introduced toaccount for the a -» p transformation which occurs between 700 (973K) and 1000 0C (1273K):

298<T<973K : XT = X298 + (23 - X298) ̂ "^ (29)675

973<T<1273K : XT = 15.2 + 0.0273(1-973) (30)

1273<T<1923K : XT = 23+ 0.0075 (T-1273 K) (31)

6.4 Validity of the models

The estimated thermal conductivities are compared with measured values for various steels andfor Ni based superalloys in Figures 4 and 5, respectively. It can be seen that the predictedthermal conductivities for solid alloys are in good agreement with the experimental values and ithas been found that values are usually within ± 10% of the experimental values.

This is particularly encouraging since experimental uncertainties associated with (a) the methodare usually cited as ± 5% and (b) the effects of thermal and mechanical treatments of thesamples are probably even larger. The principal disadvantage with the model lies in the factthat the calculated values for high temperatures do not differentiate between different alloycompositions.

Temperature, 0C

Figure 4 Thermal conductivities of various steels as a function of temperature, lines,measured values; symbols, estimated values.

Fixedpoint

Steels

Estimated SA182-F22

Estimated SA105-1

Electrolytic ironArmco iron

SA105-1

Austenitic stainlessThe

rmal

conduct

ivity

, (W

nrr1

K-1)

Estimated SA182-F11

Estimated austenitic stainless

Temperature, 0C

Figure5 Thermal conductivities of Ni-based superalloy IN718 as a function oftemperature measured value, • estimated values.

Conclusions

1) It is possible to estimate the physical properties of multicomponent alloys from aknowledge of the chemical composition and the melting range.

2) The uncertainties in the predicted values are approximately enthalpy, heat capacity (±2%) density (+ < 5%) viscosity (± 20%) thermal conductivity of liquids (< 25%) ofsolids (±10%).

Acknowledgements

This work was carried out as part of the Materials Measurement Programme of the Departmentof Trade and Industry. The valuable contributions of Dr Jack Counsell and Helen Quested aregratefully acknowledged.

References

1. Iida, T, Guthrie, R L: The Physical Properties of Liquid Metals (Clarendon, Oxford)1989.

2. Quested, P N, Mills, K C, Brooks, R F: Proc. Conf. Modelling of Casting, Welding andAdvanced Solidification Processes to be held in London, Sept 1995, pub. TMS.

3. Quested, P N: Unpublished physical property data, National Physical Laboratory,(1995).

4. Kubaschewski, O, Alcock, C B, Spencer, P J. Metallurgical Thermochemistry,Pergamon, London.

McElroy

Filoni

Sweet

Estimate

Experimental

R.E. Taylor

Th

erm

al c

on

du

ctiv

ity,

Wm

K"

5. Dinsdale, A T: CALPHAD, 15 (4) (1991), 317-425.

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Documents

K. C. Mills-Recommended Values of Thermophysical Properties for Selected Commercial Alloys (2002) (2)