+ All Categories
Home > Documents > Summary of the proceedings of the thirteenth calphad meeting

Summary of the proceedings of the thirteenth calphad meeting

Date post: 02-Jan-2017
Category:
Upload: dangduong
View: 215 times
Download: 0 times
Share this document with a friend
30
CALPHAD Vo1.8, No.3, pp. 191-220, 1984 Printed in the USA. 0364-5916/84 $3.00 + .OO (cl 1984 Pergamon Press Ltd. SUMMARY OF THE PROCEEDINGS OF THE THIRTEENTH CALPHAD MEETING lo-14 May 1984, Villard de Lans Grenoble, France Organized by: I. Ansara, C. Bernard and M. Allibert Laboratoire de Thermodynamique et Physico-Chemie Metallurgiques ENSEEG, Domaine Universitaire St. Martin d'Heres, France Sponsored by: Centre National de la Recherche Scientifique Centre Inter-Universitaire de Calcul de Grenoble European Research Office, U.S. Army G3S-Info 10 Institut de Recherche de la Siderurgie Francaise Lafarge Coppee Pechiney Societe Nationale d'Etude et de Construction de Moteurs d'Aviation Ugicarb-Morgon Calphad, Inc. Rapporteur: L. Kaufman ManLabs, Inc. Cambridge, Massachusetts, USA 1. Introduction The thirteenth CALPHAD meeting, organized by members of LTPCM/ENSEEG, Domain Universitaire, France was held at the beautiful resort of Villard de Lans 30 km from Grenoble during IO-14 May 1984. It was attended by 101 researchers from thirteen countries. While it is expected that many of the papers presented will appear as future articles in the CALPHAD journal, the following summary is provided to permit a timely interchange of information between interested parties. 191
Transcript
Page 1: Summary of the proceedings of the thirteenth calphad meeting

CALPHAD Vo1.8, No.3, pp. 191-220, 1984 Printed in the USA.

0364-5916/84 $3.00 + .OO (cl 1984 Pergamon Press Ltd.

SUMMARY OF THE PROCEEDINGS OF THE THIRTEENTH

CALPHAD MEETING

lo-14 May 1984, Villard de Lans

Grenoble, France

Organized by: I. Ansara, C. Bernard and M. Allibert

Laboratoire de Thermodynamique

et Physico-Chemie Metallurgiques

ENSEEG, Domaine Universitaire

St. Martin d'Heres, France

Sponsored by: Centre National de la Recherche Scientifique

Centre Inter-Universitaire de Calcul de Grenoble

European Research Office, U.S. Army

G3S-Info 10

Institut de Recherche de la Siderurgie Francaise

Lafarge Coppee

Pechiney

Societe Nationale d'Etude et de Construction

de Moteurs d'Aviation

Ugicarb-Morgon

Calphad, Inc.

Rapporteur: L. Kaufman

ManLabs, Inc.

Cambridge, Massachusetts, USA

1. Introduction

The thirteenth CALPHAD meeting, organized by members of

LTPCM/ENSEEG, Domain Universitaire, France was held at the beautiful resort of

Villard de Lans 30 km from Grenoble during IO-14 May 1984. It was attended by

101 researchers from thirteen countries. While it is expected that many of

the papers presented will appear as future articles in the CALPHAD journal,

the following summary is provided to permit a timely interchange of

information between interested parties.

191

Page 2: Summary of the proceedings of the thirteenth calphad meeting

192 L. KAUFMAN

2. Summary of Papers

A.K. Niessen and A.R. Miedema recalled that existing experimental

information on the enthalpy of formation of alloys in binary systems based on

SC, Ti, V, Cr, Mn and Fe (l-3) can be reproduced within the experimental --

uncertainties by means of the semi-empirical model developed by Miedema and

coworkers (Q) and presented a comparison between prediction and experiment for

the binary alloys based on Co and Ni (2). Since the binary alloys of all 3d

metals are now covered it can be concluded that the calculated values agree

quite satisfactorily with the available experimental data for binary systems

of a 3d metal with a transition metal, except where Ni is the minority partner

in alloys with the more electropositive metals like Y, La and Ti. Here the

model tends to overestimate the enthalpy effects. In the binary systems where

a 3d metal is alloyed with a non-transition metal systematic differences are

present between predicted and experimental enthalpy values. An analysis of

these differences leads to a different interpretation of the hybridization

term (the R-term) for alloys of transition and non-transition metals.

H. Ruppersberq discussed the methods by which chemical short-range

order (CSRO) can be deduced from diffraction data (6,7). Information about --

the chemical short-range order (CSRO) which may be deduced from diffraction

data was discussed. For crystalline disordered substitutional alloys the

diffraction pattern consists of Bragg peaks characterising the topological

long-range order, of the thermodiffuse scattering due to the vibration of the

atoms and of the Laue diffuse scattering (LDS) related to disorder.

Modulations in the LDS, from which the short-range order parameterti may be

calculated, indicate that the atoms are not distributed at random. Preferred

heterocoordination of nearest neighbours yields a negative value of the

corresponding o( 1 and the alloys were said to have "short-range order". At

lower temperature general formation of a superlattice generalloy occurs and

the LDS transforms into superlattice peaks. A positive &I is related to

preferred selfcoordination ("cluster formation") indicating a tendency for

phase separation. Nowadays any deviation ofti from zero is called

"short-range order" which sometimes creates confusion. For substitutional

liquid alloys the situation is quite similar. However, deviations in the

distribution of the different atomic species from randomness are now called

chemical short-range order, to distinguish them from the topological

short-range order (TSRO) of the non-crystalline material. In the few cases

which have been studied so far no drastic variation of the CSRO has been

observed on melting a substitutional disordered alloy.

H. Brodowsky and J. Maaz reported on the activity coefficients of In

measured between BOO and 1050 K in Au-In alloys below 14 at% In by means of

the EMF method with Zr02 as the electrolyte. Partial molar excess Gibbs

Page 3: Summary of the proceedings of the thirteenth calphad meeting

PROCEEDINGS OF THE THIRTEENTH CALPHAD MEETING 193

energies of In between -50 and -57 kJ/mol were obtained at 900 K, displaying a

shallow minimum near 3 at% In. These values are appreciably lower than the

three data points of about -40 kJ/mol reported by C.R. Alcock et al. (8). The

heats of mixing calculated from the temperature coefficients are in excellent

agreement with calorimetric data of Kleppa (2). Extensive DTA and X-ray work

on these alloys lead to some modifications of the lattice constants, of the

liquidus and solidus lines, and, in particular, of the position of the ordered

phase Au71n. The results were interpreted in terms of a model involving

elastic lattice distortion and Fermi energy rise. The minimum near 3 at% In.

which is quite typical for Au-, Ag- or Cu- based alloys, is attributed to a

charge screeening effect.

M. Hoch used the complex model developed by Hoch and Arpshofen to

describe the thermodynamic behaviour of the liquid iron-carbon and

iron-silicon systems, the standard states being the pure liquids. In the

first approximation ,AG’” =AH, = n(x-x")awhere n is the size of the complex,

(number of atoms),9 is the interaction parameter, and x is the atom fraction

of the component with the lower binding capacity. The data used were taken

from the compilation of Hultgen, and the phase diagrams from Hansen. In both

systems, x is the atom fraction of Fe, and n=3. The data used in the Fe-C

system were KG~~c,~G~~F~, at 1873 K, the eutectic composition at 1426 K, and

the carbon liquidus from 1426 K to 3010K.

+ (0.9617 + 0.28)x10W3T in kK.

In this systemRIR =-(3.081 + 0.42)

For the Fe-Si system,aexSi, andAHm at 1873

K were used, and from the phase diagram five points: Fe in equilibrium with

liquid, three points: FeSi(s) in equilibrium with liquid, and Si(s) in

equilibrium with liquid. The average value ofa/, was found to equal to -2.98

+ 0.79 kK. -

Th. Hehenkamp reported that after development of several techniques

designed particularly to measure thermodynamic activities in dilute and very.

dilute alloys as Knudsen-effusion evaluated by electronprobe or

quasi-isopiestic measurements (10) a comparison with recent data becomes - possible, which have been obtained by EMF-techniques (11,12) and diffusion

experiments for alloys of copper and silver with antimony and arsenic. It was

be shown that it is necessary to take even very small contribution of Sb3

besides SbI, Sb2 and Sb4 into account. Otherwise a 30% deviation of the value

of the chemical excess potential at infinite dilution results, whereas the

curvature of this potential as function of composition will not be changed

significantly. For Ag-Sb-alloys four different techniques give strikingly

identical results after making these corrections (13) properly. -

Th. Hehenkamp, R. Kossak and Th. Muschik showed that solid-liquid

equilibrium reported in the literature (14,16) for the Cu-Sb system is

incorrect (17). - An even larger error up to 200°C has been observed in Cu-In

alloys for the solidus line. Two experimental techniques have been used for

these investigations, differential calorimetry and microprobe measurements on

Page 4: Summary of the proceedings of the thirteenth calphad meeting

194 L. KAUFMAN

samples quenched rapidly from a two-phase solid-liquid field. Both

measurements give the solidus in very good agreement, where the deviations

from published results are the most severe. In particular, the curvature in

Cu-In now behaves in. a normal way and is concave instead of convex as

published (14,15).

S.C. Jha and K.P. Gupta studied ordering near FeNi by means of

electrical resistivity, DTA and electron diffraction to define SRO. There has

been considerable difference of opinion regarding the order of reaction, the

critical temperature and mechanism of the ordering reaction (18,22). The --

ordering mechanism is expected to depend on the state of the alloy above the

critical temperature. Very little structural and property change information,

however, is available above the critical temperature of the FeNi alloy. The

present results suggest homogeneous SRO at T> 534'C and nucleation of ordered

domains at 514'C <T<534'C possibly giving rise to a microdomain SRO state.

A.F. Guillermet, P. Gustafson and J.O. Andersson presented a recent

assessment of the thermochemical properties of iron, chromium, molybdenum,

tungsten and carbon. The new results were employed to calculate several

binary systems based on these elements.

N. Saunders and A.P. Miodownik recalled the difficulty in applying

sub-regular models to calculation of the Cu-fn system (23). Moreover the -

conventional methods of modelling ordering do not lend themselves easily to

intermetallic electron compounds such as the gamma phase. The ordering

formalism eventually adopted to cover these systems does however yield the

same free energy values for the A2/B2 change in the copper-zinc system as

previously calculated by Inden using the polynomial version of the BUG

formalism (24). - An interesting feature of the calculated versions of both

systems is that when the phase is characterised to correctly reproduce the

well known regions of that phase, it also reappears at higher concentrations

in regions which topologically are almost identical to the areas designated

the phase in the Cu-Zn system and the phase in the Cy-Al system. Both these

phases have never been accurately determined crystallographically but are

generally accepted to be defect variants of either a simple BCC lattice (Q)

or analogous to the phase (which itself is also derived from units with the

BCC arrangement). The thermodynamic properties of the hexagonal phases have

been made consistent with the known stacking fault energies of copper rich

alloys (25). - It is hoped that in the next stage of the calculations it will

be possible to incorporate some of the features of the martensitic

transformations in these alloys (26). -

L. Kaufman and L. Tanner reported that a data base covering the

transition metals has been developed which permits coupling of thermochemical

and phase diagram data and can readily be employed to compute ternary and

higher order systems. Previous papers in this series of CALPHAD publications

Page 5: Summary of the proceedings of the thirteenth calphad meeting

PROCEEDINGS OF THE THIRTEENTH CALPHAD MEETING 195

have illustrated development of the hase through utilization of experimental

phase diagram and thermochemical data. The present work examines the phase

diagrams and thermochemical properties of the iron-berylli urn,

cobalt-beryllium, nickel-beryllium and copper-beryllium systems in order to

evaluate the characteristic of the A2/B2 (bcc/CsCl) ordering reactions and

their dependence on composition. This paper appeared in CALPHAD 2 121 (1984).

J. Mikler, A. Janitsch and K.L. Komarek discussed the temperature

dependence of thermodynamic properties of liquid alloys which until recently

have been assumed to be independent of temperature. A comprehensive survey of

heat capacities of liquid alloys has shown that for about 80 binary systems

some information about the temperature dependence can be found in the

literature (27). -

In a previous publication on thermodynamic properties of liquid

gold-indium alloys (28) a noticeable temperature dependence of the enthalpy of -

mixing was observed. Therefore, similar to an investigation of gold-tin

alloys (29) the heat capacities of gold-indium melts were carefully measured -

by differential scanning calorimetry. Eight different compositions between 30

and 80 at% In plus pure indium were studied between the liquidus temperature

and 920 K. The heat capacities at all compositions decrease with increasing

temperature, at most compositions with a decreasing slope. The data for pure

indium are in good agreement with the results of Gronvold obtained by

adiabatic calorimetry (30). The relative heat capacity isotherms, referred to -

liquid indium and liquid supercooled gold show over the entire composition

range a positive deviation from the Neumann-Kopp rule, one distinct maximum at

55 at% In, another at high gold concentrations (<30 at% In), and in between a

minimum at 45 at% In.

J.K" -1

At 800 K the maximum value of Cp at 55 at% In is 6.1

.mol . All extreme values decrease with increasing temperature. The

positive deviations from additivity at the same temperature are larger for

gold-indium alloys than for the gold-tin system. A tentative explanation of

the behaviour of these melts in terms of their structure was given.

R. Krachler, H. Ipser and K.L. Komarek presented studies of the

manganese vapor pressure over Pd-Mn alloys determined between 48 and 58 at% Mn

and between 1125 and 1350 K with an especially adapted isopiestic method. The

partial molar properties of manganese at 1273 K were derived from these data.

A statistical model for BP-phases assuming a substitutional defect mechanism

(31,32) was applied. The agreement of the theoretical equation with the

experimental activities is excellent. The disorder parameter which

corresponds to the atomic fraction of Mn-atoms situated on Pd-lattice sites at

stoichiometry was found to be 1.7 x 10 -4

. due to the limited concentration

range on the palladium-rich side accessible with the experimental method the

evaluation of the second nearest neighbor parameter r\ proved to be

questionable (n is the ratio of the first and second nearest neighbor

interchange energies VAB = HAB- (HAA + HBB). Under these circumstances a

Page 6: Summary of the proceedings of the thirteenth calphad meeting

196 L. KAUFWAN

value_ of r\ = 0 was assumed.

A. Watson, F.H. Hayes and T.G. Chart measured the enthalpy of mixing

of nfckel-vanadium alloys.

Due to its deleterious effect on mechanical properties, the

formation and stdbf lity of sigma phase continues to be of considerable

interest in connection with nfckel -based superalloys. Thus there is a need to

develop reliable methods for calculating the conditions under which sigma

phase can form fn multicomponent dllOyS. In thfs regard the Nf-V alloy system

is of partfcular interest since it is the only known binary nickel alloy

system to exhibit a stable sigma phase. The enthalpies of mixing of Ml-V

alloys in the solid state across the entire composition range were measured

using the High Temperature Setardm Calorimeter. The calorimetric technfque

employed has been tested by measurements of the enthalpies of mixing of solid

Hi-Cr alloys which have been measured by previous workers using other

technfques. Experimental results for both systems were presented. The

measured enthdlpies of mixing for Ni-V alloys, together with previous

thermodynamic date, lattice stabfllty data and phase boundary data have been

optlmised using the Lukas programs to produce a self-consfstent set of data

for all of the phases in the Nf-V system.

S. Hassom, H. Gaune-Escard and J.P. Bras reported on a thermodynamic

investigation of the ternary systems Ag-Au-K (with X = Si. Ge, Sn). For the

Ag-Au-Ge system, the llquldus of the equl1lbrium phase diagram was determined

by dffferrntfal thermal analysis over the whole concentration range.

Measurements by fsoperibollc calorimetry at 1375 K yielded the

enthalpy-of-mixing function. For the Ag-Au-Si system, the enthdlpfes of

nixing were measured at 1423.K. A partial explordtlon of the equilibrfum

phase diagram was performed. For the Ag-Au-S1 system, calorimetric,

potentfometrlc and differential thermal analysis experiments yielded a

complete set of thermodynamic data. These experimental data were used to

calculate the other thermodynamic functions of mixing.

C. Girard, J.P. Bros, J. Agren and L. Kaufman discussed development

of a data base covering binary and ternary systems of metals covering a wide

variety of metallic systems. In the present case analytic descriptions of the

Aluminum-Bismuth and Bismuth-Gallium systems were developed and combined with

a previous descrfption of the Alumfnum-Gallium system to describe the

Alumfnum-Bismuth-Gallium system by means of the Wuggianu Equation. Ternary

isothermal Sectfons were computed in this system and then compared with

experimental measurements of the calorimetric properties and phase equilibria

In thfs system. The agreement was very good.

L. Kaufman reviewed recent findings on the lattice stability of pure

metals, thermochemical data for Ti-Cu alloys, phase diagram data for the

Hf-Be, Ni-no-Al, Y-Ni-Cr. Ni-Ti-Fe, W-Cr-Co, Co-Ho-Cr, Cr-W-Nb, Tf-Al-Nb and

Tl-AI-Y systems as compared with predictions made on the basis of the CALPHAO

Page 7: Summary of the proceedings of the thirteenth calphad meeting

PROCEEDINGS OF THE THIRTEENTH CALPHAD MEETING 197

method. Very good agreement was observed between recent results and earlier

predictions.

J.P. Hajra, M. Venkatraman, S. Ranganathan and M. Mohan Rao

discussed thermodynamic properties and phase equilibria in Co-Ni-Mn alloys.

Thermodynamic properties were measured in the temperature range of 1000-1100 K

using a solid state electrnchemical cell involving CaF2 as electrolyte. The

cell arrangement is designated as Pt, Mn MnF2/CaF2/Co-Ni-Mn MnF2, Pt.

Partial Gibbs free energy values of Mn in the alloys were derived

from the emf data obtained. The activities show negative deviations from

ideality. The ternary activity values of Mn were presented as isoactivity

curves connecting those of the corresponding binary values. Although the

Co-Ni alloys behave almost ideally, the observed deviations in the ternary

alloys are consistent with fairly high interactions which exist between

elements of Co-Mn and those of Ni-Mn binaries. Isothermal sections were

proposed in conformity with those of the constituent binary systems. Various

isothermal Gibbs free energy functions proposed for ternary systems were

reviewed. The equations have been shown to be useful in interpreting the

present data and those found in the literature.

R. Uhrenius and K. Forsen investigated the Co-W-Ti-C system

experimentally by carburizing the equilibrating binary Co-Ti, Co-W and ternary

Co-W-Ti alloys at 1100°C. Quenched specimens were analyzed by using electron

microprobe, X-ray techniques and chemical analysis. The results indicate the

presence of a new hexagonal (Ti,W) C-carbide after prolonged heat-treatment at

lloo"c. An analysis of the lower binary and ternary systems was made by using

a thermodynamic model to facilitate the description of the quaternary system.

Equilibria concerning the cobalt-rich part of the system and involving the

carbides WC, (Ti,W)C(hex), (Ti,W)C(cub), (Co,W)12C, (Co,W)CC and graphite were

evaluated and as one result an isothermal section of the Co-Ti-C system was

calculated. The description of the quaternary system was done by presenting a

number of sections at constant carbon activities through the phase diagram at

11oo”c.

V. Kattner, H.L. Lukas and E. Th. Henig calculated the Sn-Pb-Te

system on the basis of the edge binaries. The Sn-Pb system is a simple

eutectic system with limited solubilities in the two solid phases, (Sn) and

(Pb). The coefficients used were evaluated by T.L. Ngai and Y.A. Chang (33). - The Sn-Te and Pb-Te systems were optimized using a thermodynamic optimization

least squares method (34). - The analytical description of the liquid of both

systems considers the formation of an associate of the stoichiometry SnTe and

PbTe, respectively. Since the intermetallic phases SnTe and PbTe reveal small

ranges of homogeniety, they were described by the triple defect structure of

the Wagner-Schottky model (antistructure atoms on the Te-sublattice and

vacancies on the Sn-Pb-sublattice, respectively). The natural way to

extrapolate the associate model description from n-component systems to the

Page 8: Summary of the proceedings of the thirteenth calphad meeting

L. KAUFMAN

(n+l)-component system should be the application of the generalized Muggianu

or Kohler formulas to the species instead of the Components. Therefore the

liquid of the Sn-Pb-Te system is described by 5 species, Sn, Pb, Te, SnTe, and

PbTe, and the polynomial terms used in the binary Systems. The (Sn,Pb)Te

phase is described with 2 sublattices. One sublattice contains the species

Sn, Pb, and vacancies, the other one contains the species Te, Sn-, and

Pb-antistructure atoms. Using the program PMLFKT (35) the ternary system as -

well as the heat of mixing of the liquid was calculated without additional

ternary terms.

H.L. Lukas, E. Th. Henig and U. Kattner discussed the least squares

method for optimizing multicomponent systems based on the Algorith of Gauss.

The latter is equivilent to the Newton-Raphson Method with the additional

simplification, that the "equations of error" are replaced by their

Taylor-expansions with respect to the adjustable coefficients cut after the

linear terms. If the equations of error are linear in the coefficients, the

Guass method has always one and only one Solution and this solution must be

aminimum of the sum of squares of errors. If not all the equations of error

are linear in the coefficients there may possibly exist other extrema (minima

or maxima) of the sum of squares of errors. Which of them is found depends on

the starting values of the coefficients. Therefore starting the calculation

using only the values with linear equations of error may facilitate the

calculation. In multicomponent systems measured phase diagram values are

described by a set of several concentration coordinates. By the equation of

error the error must be defined as one single value. This definition should

be an analytical function without singularity in the vicinity of error = 0.

Therefore the length of the vector measured concentration-calculated

concentration given by a square root is not a useful function because it is

singular at zero. In a least squares programs for ternary and quaternary

systems we define the error by amounts of phases in the calculated equilibria,

taking the measured point as overall composition. The programing of different

types of measurable quanitities of ternary and quaternary systems were

described.

A.F. Guillermet and L. Ostland measured phase equilibria in the

Fe-Ni-W system by means of diffusion couples and microprobe analysis at 12OOOC

and 1300°C. The results were compared with available experimental data.

S. Laha, P.M. Ursekar, S. Pandian, K.P. Gupta, A.K. Mazumdar, T.A.

Padmavati Sankar, U. Ramakrishna, E.C. Subbarao and E.M.T. Velu presented

measurements of phase equilibria in the six component quasi ternary system

RE-Co-Fe. In this notation RE is a mischmetal with 45.2% W/O Ce, 21.6% w/o

La, 21.0% w/o Nd, 6.3% w/o Pr and 6.3% w/o Fe (36). - X-ray and thermomagnetic

analysis have been employed to study the region between 11.7 and 28.5 atomic

Percent RE in the quasi ternary between 700°C and 10oo"c. In this region

compound phase corresponding to RE2(Fe,Co)7, RE5(Fe,Co)19, RE(Fe,Co)5 and

Page 9: Summary of the proceedings of the thirteenth calphad meeting

PROCEEDINGS OF THE THIRTEENTH CALPHAD MEETING 199

RE2(Fe,Col17 were observed.

N. Saunders and A.P. Miodownik reported that the thermodynamic

approach to glass forming previously applied to selected binary alloys (37) -

has been extended to include kinetic factors. A systematic study of the six

glass forming systems, Au-Si, Pd-Si, Ti-Be, Zr-Be, Hf-Be and Ni-Ti, now yields

limits of glass forming ability related to predicted critical cooling rates

(Rc). By the use of a tangential construction, the molar heat of solution and

driving force can be calculated for potential precipitates of any COIIIpOSitiOn

from a chosen liquid. These quantities can then be combined with values of

the viscosity to obtain energies of nucleation (G*) and corresponding TTT

curves. The viscosity of the liquid has been approximated using hole

formation energies (EH) for the liquid, calculated from Tg (39) where: - -1

EH=57.86 Tg-5858 Jmol . Relative free volumes (f,) can then be estimated

(39) and substituted into a Doolittle expression (40) to yield viscosities. - -

The calculation of Rc below the To of a disordered solution phase is treated

in a fashion similar to that for massive transformation, such that the

kinetics of the liquid crystalline transformation (when the crystalline phase

is molecularly simple and no composition differences are involved) are only

limited by diffusion within the liquid-nucleus interface and not by the bulk

liquid diffusivity. This treatment shows that critical cooling rates below To

increase very rapidly, so confirming the importance of the To concept applied

in (37). - Critical cooling rates at compound compositions have been calculated

by the conventional treatment (38) on the assumption that bulk diffusion in -

the liquid is essential in such cases. The treatment successfully predicts

the suppression of the compound NiTi found experimentally. By using these

assumptions the Glass Forming Range (GFR) expected from liquid quenching can

be readily calculated, and excellent comparison with the reported GFR is

obtained. This technique can be readily extended to multi-component systems

if adequate characterisation of the binaries is available.

C. Bergman, I. Avromov, C.Y. Zahra and J.C. Mathieu conducted a

calorimetric investigation of structural relaxation and crystallization of

amorphous Ge16Te84 alloys. Oue to their interesting electronic and

Opto-electronic properties, glassy chalcogenides have been extensively sutdied

(41). However, - since glassy materials are not in equilibrium, their

properties strongly depend on the thermal history of the samples. In the

glass transition region, the properties are dependent on time because, in this

region, the experimental time scale becomes comparable to the time scale for

structural rearrangements; the material will relax towards equilibrium, this

phenomenon being called structural relaxation. In this study, both

differential scanning calorimetry and classica drop calorimetry have been used

to investigate either as-quenched or annealed samples in order to point out

the kinetic (non equilibrium) part from the whole experimental effect. These

Page 10: Summary of the proceedings of the thirteenth calphad meeting

L. KAUFMAN

measurements have been performed on Ge16Teg4 alloys which belong to the

chalcogenide class of glasses; concerning the relaxation times, this class can

be considered as intermediate between amorphous metals and oxide glasses. In

fact, these glassy alloys are not as thermally stable as oxide glasses since

Tg lies around 400 K; however according to the value of the crystallization

temperature (Tc=500 K), a rather large temperature range can be investigated.

Differential scanning calorimetric studies have already been performed on

these glassy alloys in order to measure glass transition temperature (43) and

heat capacities (42,44). A recent work (45) reports on measurements of the -- -

enthalpy relaxation of PdAuSi glassy alloys as well as CuZr and GeTe systems;

as far as is known, the published values concern only the PdAuSi alloys. Two

kinds of phenomena have been analyzed: First, the influence of kinetic

parameters (heating and cooling rate) at the vitreous transition by

differential scanning calorimetry. Then the activation energy is deduced and

compared to that obtained by shear viscosity measurements. Second, the

relaxation towards equilibrium when different thermal treatments combined with

those obtained by DSC experiments at higher temperatures yield the enthalpy

curve from 390 to 510 K, corresponding to the properties of the metastable

phase.

N. Clavaguera, M.T. Clavaguera-Mora and J. Onrubia noted that an

important part of the applied research effort on semiconductor glasses has

been directed towards ternary or quaternary chalcogenide alloy glasses.

Nevertheless, direct observation of chemical short range order by diffraction

methods in these materials is hindered by the high degree of compositional

ability and thermal stability are rather poorly understood. From the

thermodynamic point of view, the crystallization of a liquid at a temperature

T is driven by the affinity, which measures the Gibbs free-energy difference

between the liquid and the crystalline phases at that temperature. At the

eutectic temperature the minimum of the affinity occurs at the eutectic

composition. This is the basic thermodynamic arguement backing the

experimental observation that eutectic compositions are in general good

glass-formers. However, it is also a general fact that the best glass-forming

compositions are slightly shifted from the eutectic in many systems. To give

some insight on these experimental results we derive simplified expressions

for the thermodynamic quantities of the following systems: As2S3-S; Sb2Se3-Se;

GeSe2-Se and GeSeZ-Sb2Se3. All of them have in common a strong tendency for

chemical ordering both in the amorphous and in the liquid state. By treating

the liquid alloy as a strongly associated regular solution and neglecting

miscibility in the solid the affinity values calculated from the model and its

variations with both temperature and composition can be related to the

experimental critical cooling rate needed to avoid crystallization. Taking an

ideal glass transition temperature T, as that for which the entropy of the

supercooled liquid equals that of the crystalline phases, the composition

Page 11: Summary of the proceedings of the thirteenth calphad meeting

PROCEEDINGS OF THE THIRTEENTH CALPHAD MEETING 201

dependence of Ts can be calculated and compared with the experimental glass

transition temperature values.

Q. Zhiyu, M. Wenging, W. Shimin and Z. Yuankai reported that the

previously calculated NaCl-CaC12-SrC12 phase diagram was used as a guide for

measuring the diagram by high sensitivity MDTA. This system is a simple

eutectic system with a eutectic point at 41.9% NaCl, 40.0% CaC12, 18.1% SrC12,

471°C. In the liquidus surface for saturation with the CaC12-SrC12 solid

solution a univariant line starts from 24.8% NaCl, 50.1% CaC12, 25.1% SrC12,

and 550°C. The uncertainties in the liquidus temperatures are estimated to be

less than + 5 K, - since the errors due to supercooling and change of sample

compositions were reduced by out experimental method. Accurate measurement of

the NaCl-CaC12-SrC12 phase diagram serves as a criterion of judging the

reliability and adaptability of thermodynamic models which are used for

calculating phase diagram. It also offers significant information for better

understanding the effect upon the stability of calculated phase diagram. The

accuracy of the calculated phase diagram estimated on the basis of comparison

with'measured one is relatively sensitive to self-consistency between

thermodynamic properties and phase diagrams of binary systems. Because the

optimization of the thermodynamic properties and phase diagrams of binary

systems. Because the optimization of the thermodynamic properties and phase

diagrams of binary systems was performed, the agreement between our measured

and calculated phase diagram of NaCl-CaC12-SrC12 obtained via new asymmetric

method is within + 2.5 mol%.

G. Hatem, Y. Fouque, J.P. Bros and M. Gaune-Escard reported on a

thermodynamic properties data complilation for molten salt systems being

conducted in order to obtain thermodynamically consistent information. The

following procedure has been adopted including: collection of references,

gathering and critical evaluation of experimental excess functions and phase

diagrams, calculation of unknown excess functions, and generation of a

consistent set of thermodynamic functions and a phase diagram. A compilation

of binary mixtures of alkali nitrates was presented as an example.

B. Sundman, M. Hillert, B. Jansson and J. Agren presented a new

model for ionic liquids (46). - It is based on the suggestion made by Temkin

(47) that anions and cations mix separately. - The whole range from weak

ionisation to very strong can be described by the new model. Within these

limits it can be shown that the model is mathematically similar to the

substitutional model and the so called associated model (48) respectively. -

The model can be used to describe a liquid metal-salt system for all

compositions including the purely metallic liquid. Some model calculations

were also presented.

L. Kaufman and D. Birnie noted that discovery of glasses based on of

ZrF4 or HfF4 with other metallic fluorides by M. Poulain and co-workers offers

Page 12: Summary of the proceedings of the thirteenth calphad meeting

202 L. KAUFMAN

great potential in optical fiber, windows and source/detector application.

Due to limited phase diagram data for fluoride systems most of the progress in

identifying new compositions has proceeded empirically. To remedy this

situation, the CALPHAD method (49-51) has been applied to permit computation --

of multicomponent phase diagrams to identify the composition range where the

liquid is most stable, indicating opportunities for glass formation as

demonstrated by predictions of new metallic glasses. Currently the data base

covers combinations of 0.2 ZrF4 (ZF), 0.25 LaF3 (LF), 0.333 BaF2 (BF), 0.333

PbF2 (PF), 0.5 NaF (NF), 0.5 RbF (RF), 0.5 CsF (CF) and 0.5 KF (KF) derived

along the lines described for III-IV, II-VI and SIALON systems (50,51).

Calculation of isothermal sections in LF-ZF-BF illustrates the range of

composition in which the liquid has the greatest stability (52) and agrees -

well with discovery of glass formation (53,54). The data base has been

extended to cover A1F3(AF=0.25A?F3) by employing experimental data provided by

Thoma (55) to evaluate AFAFLT=13389-8.368T J/g.at and LAFZF=25104 -

J/g.at=LZFAF, LAFBF=4184 J/g.at=LBFAF and LAFLF=20920 J/g.at=LLFAF. These

parameters along with those found previously permit calculation of the range

of maximum stability of the liquid phase for ternary LF-ZF-BF glasses with

additions of 4, 9 and 15 atom percent of AF in agreement with the experimental

findings of Lecoq and Poulain (56). -

B. de Cremoux noted that compounds formed from elements in columns

III and V of the Mendeleieff table - for instance Gallium Arsenide, GaAs -

form a class of semiconducting materials which are now extensively used in the

manufacture of electronic and opto electronic devices. Their interest is in

great part due to their ability to form solid solutions such as GaI_xAlxAs or

GaxInI_xAsyPI_y. the properties of which vary continuously with the

composition parameters x and y. The active part of nearly all devices

comprises several thin expitaxial layers with different compositions, their

total thickness is a few micrometers. To get high performance and reliability

devices these layers have to be nearly lattice matched to substrates on which

they are grown. Several techniques are currently used to grow such

semiconducting layers. Attention was focused on liquid phase epitaxy (LPE),

in which the solid solution is grown from a liquid solution in one of the

elements III (Ga or In), because it is quite near equilibrium and gives

therefore insight in the thermodynamic properties. Several results however,

are relevant of the other epitaxial techniques as well. One major problem of

Lo5 engineers is to choose a liquid solution suitable to grow a given solid

solution, thus they need precise phase diagrams models. The relevant liquid

solutions are most often dilute and satisfactorily represented by the regular

or simple models (57). - The ternary solid solutions are in fact pseudo-binary

soluti OnS which al SO can be represented by the regular solution mode (58). - For the quaternary solid solutions, the situation depends on their type.

Solutions with mixing on one sublattice (e.g. InGaAlAs) are pseudo-ternary

Page 13: Summary of the proceedings of the thirteenth calphad meeting

PROCEEDINGS OF THE THIRTEENTH CALPHAD MEETING

solid solutions and can also be represented by the regular solution model. In

solutions with mixing on both sublattices (e.g. GaInAsP), an excess free

energy of mixing cannot be defined. Stringfellow (59) successfully proposed -

to relate the free energy directly to the composition through a semi-empirical

formula. When the epitaxial layers are slightly mismatched with their

substrate, they are strained and thus an elastic energy is stored in the solid

solution. This energy can be calculated from the known elastic constants of

the materials and has to be added to the free energy in order to give a

correct description of the equilibrium properties (60). - Two phenomena are

directly related to this effect.

1) Lattice pulling (61-63). -- It has been observed that the composition

variations of the solid solution epitaxial layers when the liquid solution

composition is varied are much less that they should be if the solution was

free: the composition seems pulled-back toward the value giving exact

lattice-matching to be substrate.

2) Stabilization in a miscibility gap (60). - The growth of homogeneous

epitaxial solid solutions has been achieved in composition regions where the

thermodynamic models without strain predicts their immiscibility, while other

experiments with free solid solutions show indeed a phase separation (64). -

N. Saunders and A.P. Miodownik suggested that the use of thin films

in the field of Equilibrium Phase Diagram (EPD) studies holds great

promise, in that it is possible to produce alloy films by simultaneous vapour

deposition which exhibit composition gradients that contain the relevant

phases of binary or ternary alloys at a preselected temperature. Depending on

the substrate temperature, either equilibrium or metastable phases are

produced. It has been shown that the formation of multiphase structures in

films produced this way appears to be controlled by diffusional breakdown of

the initially homogeneous depositing atoms, so that three kinetics regions are

observed as the substrate temperature is varied.

(1) At low T/Tm the surface mobility is insufficient for the

decomposition of the initially homogeneous depositing atoms, and the films are --

single phase.

(2) With increasing substrate temperature decomposition to

metastable two phase structures is observed, often characterised by

supersaturation of the phases that are present.

(3) Finally with increasing temperature the atomic mobility is

sufficient to allow the full atomic rearrangement necessary for equilibrium

Phase formation.

There is a straightforward connection between regime (3) and

thermodynamic equilibrium calculations but of equal interest is Convincing

evidence that the metastable single phase products of regime (I) can alSO be

predicted from Free Energy vs. Composition curves. It seems that since atoms

depositing from the vapour lose their kinetic energy within a few atomic

Page 14: Summary of the proceedings of the thirteenth calphad meeting

L. KAUFMAN

vibrations, the possibility of a transformation involving an intermediate high

temperature phase is unlikely. Nucleation and subsequent growth processes are

governed by the temperature of the substrate and it is postulated that the

phase which is found in regime (1) is the energetically most stable single

phase at the temperature of the substrate. The extent of such single phase

regions should be given by the intersection of the relevant free energy

curves. Very good correlation is shown in the systems Cu-Fe, Fe-C, Fe-Ni,

Cu-Sn and Fe-Ni-Cr, using current thermodynamic characterisation parameters.

The occurrence of the sigma phase in vapour deposited Ni-Cr alloys (where this

phase is metastable) indicates that the gradient vapour deposition technique

may also be an important input to the problem of characterising of metastable

counterphases where the necessary thermodynamic data is currently not

available. This follows from the possibility for experimentally determining

the composition limits of a metastable single phase, and combining this

information with known free energy curves of the neighbouring stable phases.

B. Sundman, M. Hillert, J. Agren, B. Jansson, J.O. Andersson, A.F.

Guillermet, P. Gustafson and A. Lindquist described a new data bank with

software called Thermo-talc which is now available on the X.25 network

(Euronet). A number of examples illustrating its application to alloys were

presented.

H. Gaye described the main attempts for classifying the

thermodynamic properties of metallurgical slags as falling into three

categories; first, fitting of slag-metal equilibria data on the basis of

simple molecular or ionic solution models. Among those, most noteworthy are

applications of FLOOD-GRJOTHEIM's model and various adaptations, the use of

which, however, is strictly restricted to the domain of highly basic

multicomponent slags; second, polymerisation models (MASSON) using the concept

of a different behavior of free, singly or doubly bonded oxygen ions

(TOOP-SAMIS). These models do stick very closely to the structure of binary

silicates and cover a much wider range of basicities; however, no major

breakthrough for the representation of complex systems has yet evolved; third,

statistical thermodynamics models, assuming overlapping sub-lattices of oxygen

anions and metals cations (YOKOKAWA-NIWA, KAPOOR-FROHBERG . ..). The model

developed at IRSID belongs to the thrid group. Its aim is, taking into

account information on both phase diagrams and activities data, to provide

reliable estimates of complex steelmaking slags properties, especially in

domains where direct experimental data is lacking and difficult to obtain.

The model is based on the description of the liquid in terms of cells composed

of an oxygen anion surrounded by two cations, and makes use of only binary

parameters (2 to 3 parameters per binary system, representing the energy of

formation and interaction of the cells). The calculation provides: 1.) the

thermodynamic activities of all oxide components (and related enthalpy and

entropy integral and partial function); 2.) the phase diagram (liquid

Page 15: Summary of the proceedings of the thirteenth calphad meeting

PR~EEDINGS OF THE THIRTEENTH CALPH~ MEETING 205

miscibility gaps, equilibria with stoichiometric compounds or solid solutions

of two compounds).

Extensive tests have been made for systems containing up to six

components chosen among SiO2 -A1203-Fe203-CaO-FeO-MgO-MnO. Agreement with

experimental data (activities and phase diagrams) was found very satisfactory

over wide ranges of composition (from basic slags to silica saturation) and

temperature (e.g. miscibility gap close up). This, combined with efficiency

of calculation (a fraction of a second CPU for a composition in a six

component system) makes this model suitable for routine estimations in complex

steelmaking slags.

M. Tetenbaum and C.E. Johnson reported that the temperature

dependence of partial pressure of H20(g) above the Li20(s)-LiOH(s,l) system

has been measured between 513 and 890 K by means of a flowing gas technique

combined with continuous monitoring of the concentration of water vapor in a

helium carrier gas. Below the melting point of LiOH (723 K), the minimum

water vapor pressure required to form a two phase system is given by: log p

(H20,g,Pa) = -6718/T + 11.46. Above the melting point of LiOH, the critical

water vapor pressure is given by log p (H20,g,Pa) = -4406/T + 8.28. For the

reaction values ofAH' = 128.4 + 2.5 kJ mol-’ andAS’ = 123.4 + 4.2 J mol-*

K-1 were obtained. Above the melting point of LiOH,dH' = 83.52 2.5 J mol"

and A So = 61.9 f 3.3 J mol -1

K-l. _ The heat of melting of LiOH is estimated

to be 22.6 + 1.7 J mol". The results of these measurements can be used to

partially describe the behavior of a Li20 solid breeding blanket in

anticipated fusion reactor environments.

M. Blander and A.D. Pelton discussed semi-empirical equations which

inherently take into account the types of concentration and temperature

dependence expected of the thermodynamic properties of ordered quaternary

systems. These equations, were used to analyze the thermodynamic properties

of ternary silicates in which the only acid component is silica. For a

particular asymmetric representation of the energy parameters in the

equations, it was found that data for ternary systems are will represented

with only data on the subsidiary binary systems as input. If generally true,

this result suggests that reasonable predictions could be made of the

properties of such ternary and higher order silicate systems based solely on

the properties of the binary subsystems. A theoretical justification for this

result was discussed. The CaO-FeO-Si02 system was used to illustrate why this

method appears to be more successful for a prior predictions than the more

common methods in which the excess functions are interpolated.

J.N. Pratt reviewed atomic ordering effects in the liquid phases of

the Mn-Cu, Mn-Ni, Mn-Si, Mn-Au and Mn-Sn systems. The varied deviations from

ideal behavior exhibited by these systems was examined by using the known

composition dependence of the Gibbs energy to define Darken's excess stability

function and to display the composition dependence of this function. The

Page 16: Summary of the proceedings of the thirteenth calphad meeting

206 L. KAUFMAN

behavior was examined in terms of established statistical and associated

stable models. Concentration flucterations indicated by the analysis were

discussed in relation to the possible alloying factors responsible.

J. Hafner noted that it was now well established that the structure

of the elements in the liquid state follow characteristic trends reminiscent

of the trends among the crystal structures of the elements. The crystal

structures have been discussed very recently by Hafner and Heine in terms of

the systematic variations of the effective interatomic potentials with

electron density and pseudopotential. The first part of this lecture

presented an analysis of the liquid structures based on the same set of

interatomic potentials and on the mean sperical approximation for the

calculation of the liquid structure. It was shown that the structural trends

in the liquid and in the crystalline states have the same physical origin.

The complex structures of the light polvalent metals (Ga, Si, Ge) (65) were -

shown to arise from the interplay of two characteristic distances: the

effective diameter of the hard core expressing the geometrical requirements of

sphere packing, and the Friedel wavelength of the oscillatory part of the

potential characterizing the electronic effects in the metallic bonding. The

return to hard-sphere-like structures for the heavy elements stems from the

disappearence of the leading term of the Friedel oscillations as the core

radius R, approaches a value for which 2kFRc = /2 (i.e. the pseudopotential

form factor vanishes for q=2kF). The second part of this lecture was devoted

to the problem of chemical ordering in liquid alloys (66). - In a large number

of liquid alloys, the short-range chemical order has a dominating influence

upon the physical and chemical properties of the alloy: the thermodynamic

properties, the static structure factors, the electronic transport properties

and the magnetic properties all show anomalies at the same characteristic

compositions. Here again the variation of the interatomic potentials can

serve as a guideline: in a series of alloys such as Li-Na, Li-Mg, Li-Al,

Li-Pb, Li-Bi the ordering potential: at mean nearest neighbour distance

increases with the difference in valence, electron density and

electronegbtivity of the constituents. These changes were shown to be

associated with a redistribution of the conduction electron charges. The

influence of this ordering potential upon the thermodynamic and structural

properties can be modelled with reference to a system of hard spheres carrying

yukawa potentials. In spite of its extreme simplicity, this model yields

realistic results for a wide range of liquid alloys with a strong chemical

interaction among the constituents.

A. Pasturel, C. Colinet and P. Hitter observed that the binary

transition metal-p metal and transition metal-transition metal alloys display

remarkable physical properties based on important electronic rearrangement,

Simple models using a tight-binding description of d electrons and a free

Page 17: Summary of the proceedings of the thirteenth calphad meeting

PROCEEDINGS OF THE THIRTEENTH CALPHAD MEETING 207

electron model for valence electrons of p metal permit calculation the

thermocyanmic data of these alloys. In the case of d metal-p metal alloys the

highly negative values of the thermodynamic properties of mixing have been

explained by the filling of the d band of the transition metal by the sp

electrons of the p metal. The enthalpies of formation of (Fe, Co, Ni)-(Si,

Al) compounds are calculated with a good accuracy. For the liquid (Fe, Co,

Ni)-(Si, Al) alloys the estimate of the enthalpy and entropy of mixing in

function of composition has been made from the evolution of the density of d

states with the composition of the p metal. For these alloys in their solid

state a similar treatment can be applied by adding a positive energy

contribution due to the delocalization of covalent electrons to free

electrons. The enthalpies of formation of disordered transition

metal-transition metal alloys are related to moments of the density of states

within an analytical tight-binding model for the d band. We show that the

values of the difference in energy levels and of the bandwidths are two

dominant effects on alloying. The d charge transfer is evaluated in a

self-consistent way from the knowledge of the partial densities of states.

First this approach was applied to the determination of the

enthalpies of formation of binary alloys in function of composition. The

input parameters of the model, i.e. bandwidths and atomic energy levels, are

allowed to vary within certain constraints. A comparison between experimental

and calculated values of the heats of formation permited determination of an

electronegativity scale and a bandwidths set. These parameters were used to

calculate the partial enthalpies. Finally the model was extended to

multicomponent alloys. The calculated values of the enthalpies of formation

of some ternary alloys were compared with the experimental data as well as

with calculated values using empirical formulations or statistical models with

good results.

J.F. Smith compared the measured enthalpies of formation of Y-Fe,

Y-Ni, and Y-Co compounds with values predicted by Miedema's theory (67) and -

the Bennett-Watson theory (68). Solid electrolyte electromotive force cells -

have been used to determine the Gibbs energies as well as the enthalpies and

entropies of formation of compound phases in the above noted systems between

900 and 1300K. The enthalpies of formation were compared with the theoretical

values in order to assess the current usefulness of the theoretical

predictions and help to develope improved theoretical models. These results

will appear in CALPHAD 5 295 (1984).

C. Bergman and R. Castanet conducted a calorimetric study of

hypoeutectic and hypereutectic GeTe alloys in order to test the sensitivity of

heat capacities to modifications in the structure (69). As the heat -

capacities are very sensitive to structural modifications as pointed out

recently (69), a calorimetric study of eutectic GeTe alloys was undertaken on

both sides of the melting point. The temperature dependence of the enthalpy

Page 18: Summary of the proceedings of the thirteenth calphad meeting

208 L. KAUFMAN

of the GeO 15Te0 85 alloy was measured by drop calorimetry from 600 to IlOOK . .

and the heat capacities were deduced by derivation. The observed heat content

results show an important variation from the eutectic temperature (64810 UP to

780K. Then from this temperature, the heat capacity remains constant at 36 J

mol -1

K-1 up to 1100K. This value is in agreement with that calculated

assuming the additivity of the corresponding values of the pure COmPOnentS

(Kopp-Newmann rule), 36.2 J mol-' K-l. On the other hand, calorimetric

measurements were performed on glassy Gee 16Te0 84 alloys by drop calorimetry . .

and differential scanning calorimetry. The crossing of the vitreous

transition permits the attainment of supercooled liquids in a temperature

range well below the eutectic temperature. In that temperature range, the

experiments yield a Cp value of 35 J mol -1 K-1

, very similar to the previous

one. Between these two regions (low and high temperature ones) where the heat

capactiy is constant and equal to the same value, there is a transition which

occurs in the vicinity of the eutectic temperature, which can be interpreted

as resulting from the destruction of short range order in the liquid. This

behaviour is completely different from that observed in the case of Gee 5Te0 5 . . alloys for which similar study in crystalline and liquid state doesn't

indicate the important variation observed on the Cp value in eutectic alloys.

C. Colinet, A. Pasture1 and P. Hitter calculated the heats of

formation (AH) in disordered alloys involving transition metals from the Ti

through Ni columns in the periodic table by using a tight-binding scheme for

the d band (70). - Neglecting the contribution toAH arising from changes in

magnetic interactions, the heat of formation can be written in the

Hartree-Fock approximation (71) in terms of the change in the one-electron -

band energy and double counting energy respectively on going from the pure

metals A and B to the alloy A l_xBx by using an effective intra-atomic Coulomb

integral (72) which is assumed to be identical for the two metals. - In order

to calculate the d band contribution, they used the techniques of moments and

continued fraction (73,74) and considered the continued fraction developed to --

the first step. The charge transfer was calculated in a self-consistent way

for the equiatomic composition. The value of the charge transfer for other

compositions is given by linear interpolation (75). The determination of the - heats of formation requires the knowledge of the number of d electrons in the

Pure metals (taken from standard band calculation), the electron-electron

intraatomic interaction U, its value is chosen to be equal to 6 eV, the

relative position of the atomic energy levels, ET and the bandwidth of the

pure metals, Wi. These two last parameters are allowed to vary within certain

constraints and they are chosen to approximate the known values of H. For

this Purpose they presented a collection of experimental enthalpy data on

binary transition alloys. The database has been established using several

compilations (76-82) and the more recent experimental results. The values for

Page 19: Summary of the proceedings of the thirteenth calphad meeting

PROCEEDINGS OF THE THIRTEENTH CALPHAD MEETING 209

the heat of formation of disordered alloys of five differnet compositions as

well as the limiting partial heats of solution were predicted. Calculated

values were compared with experimental data as well as with predicted values

from several workers (79-86). -- Although the model as it stands does not deal

with the structural effects, its success rests in its ability to provideAH

values for any composition in binary transition alloys.

M. Tmar, A. Pasture1 and C. Chatillon reported that estimation of

the thermodynamic properties of the III-V compounds has been performed in two

ways: the estimate of the enthalpy of formation of binary III-V compounds and

the estimate of the enthalpy of mixing of pseudo-binaries (ternary liquids and

solids). the enthalpy of formation of binary III-V compounds has been firstly

estimated through thermodynamic cycles in which an electronic model based on

the delocalisation of electrons (87) and an estimate of the enthalpy of mixing -

for liquids from the electronic gas theory (88) is used. - The resulting

enthalpies were compared with experimental determinations and selected values

from an optimisation approach (89) (CALPHAD XI). The electronic model has -

been extended.to the liquid pseudo-binary systems of III-V compounds. The

resulting enthalpies of mixing were compared to published models (90,91). The

thermodynamic properties of mixing for the solid mixtures of the III-V

compounds were estimated through a statistical model where the interaction

energies have been estimated with the MIEDEMA procedure. The results were

compared with the delta lattice parameter estimation used by STRINGFELLOW

(92). Calorimetric and Mass - The theoretical estimates are very different.

spectrametric studies were proposed for further progress in determining the

thermochemical properties of III-V compounds.

J. Buth and G. Inden calculated phase equilibria in Co-Cr alloys

taking the magnetic ordering effect into account. Due to the strong variation

of the Curie temperature with the Cr-content the calculations predict

immiscibility regions close to the Curie temperature as already discussed by

Nishizawa (93). - In order to verify these predictions a series of alloys with

'Cr =.05, .08, .lO, .15, .20, .30, .40 were heat treated at various

temperatures for 14 days and subsequently analysed by X-ray diffraction in a

high resolution Guinier camera. The determination of the phases present and

the evaluation of the lattice parameters confirm partly the calculated

equilibria. The remaining differences can be attributed to elastic effects

which may prevent the alloy from reaching the equilibrium state.

K.T. Jacob, J.P. Hajra and M. Iwase reported that activities of Mn

in solid and liquid Fe-Mn alloys have been measured using solid State galvanic

cells with Y203-Th02 electrolytes. The oxygen potentials of Fe-Mn/Mn between

1050-1174K and Fe-Mn/MnA12+2x04+3x + A1203 three phase electrode at 1823K

were measured as a function of Mn concentration using novel cell designs. The

use of three phase equilibria minimises the effect of dissolved oxygen on

Page 20: Summary of the proceedings of the thirteenth calphad meeting

210 L. KAUFMAN

activity of Mn in the liquid alloys. Analysis of partial electronic

conductivity of Y203 -Th02 electrolyte suggests that the measured activities at

1823K can be derived from Nernst law without significant error. The measured

activities show negative deviation from Raoult's law. The data, which can be

represented by the sub-regular solution model, is consistent with phase

diagram for the Fe-Mn system. The results of the study indicate that

evaluations of Hultgren et al and Sigworth and Elliot, which show positive

deviation from ideality, may need revision.

R. Luck and B. Predel observed that numerous binary metallic systems

in which a miscibility gap occurs in the liquid state, are composed of atoms

with large size differences. This has an important influence on the critical

temperature. Since the shape of the miscibility gaps may depend on the size

difference of the constituents, too, this question is the topic of this

investigation. Thermodynamic properties are influenced by the size

difference. In binary systems an asymmetry of the thermodynamic functions is

caused by this difference. The extremal value of these curves is shifted

towards higher atomic fractions of the component which has the smaller atomic

radius. To obtain a quantitative expression of the Gibbs free energy, it was

assumed, after Lacmann (93) that the mixing enthalpy depends on the respective - fractions of the atomic surfaces instead of the atomic fractions, in a Similar

way, the configurational entropy of mixing is represented in a manner

suggested by Flory (94) and generalized by Huggins (95). In this case the -

volume fractions, not the molar fractions are decisive. These two

replacements were carried out in the thermodynamic expressions according to

the regular solution model as well as to the quasichemical approximation. It

was found that these functions describe the asymmetry of experimental data of

binary systems quite well without appreciably chemical short range order, the

ratio of the atomic radii found, differ from data given in the literature by

about a few percent. The influence of the atomic size difference on the

miscibility gaps according to this model was extensively tested. The results

are as follows:

(i 1 The miscibility gaps are nearly symmetrical, whereas the thermodyanmic

functions are appreciably asymmetrical.

(ii) The critical temperature of 'the miscibility gaps increases with

increasing ratio of the atomic radii when the other parameters are kept

constant.

(iii) The miscibility gaps become narrower with increasing ratio of the

atomic radii when the critical temperature is kept constant.

These findings, especially the last one, are confirmed by the miscibility gaps

published in the literature. Quantitative agreement between predicted and

experimentally determined miscibility gaps is found, if the uncertainty of the

initial thermodynamic data is taken into account.

Page 21: Summary of the proceedings of the thirteenth calphad meeting

PROCEEDINGS OF THE THIRTEENTH CALPHAD MEETING 211

R. Castanet, Z. Moser, K. Kryman and S. Randzio pointed out that the

thermodynamic behaviour of Cd-Ga alloys exhibits Positive departure from

ideality. vet until now no measurements were performed to check whether or

not, enthalpy and entroping of mixing depends on the temperature. The

enthalpy of formation was thus measured by direct reaction calorimetry at 602,

657 and 969K. These measurements showed an increase ofhHf with respect to

temperature. The following values were deduced:

AH fmax = -2.38 J.mol-' at 602K

= -2.70 J.mol-' at 657K

= -2.80 J.mol-' at 696K

The value at 657K agrees with Hultgren et al's value at 700K.

A. Dhima and M. Allibert developed a model based on binary entities

called "neutral cells" aimed at taking into account short range order in

iono-covalent liquids by means of statistical thermodynamics. The model

describes a multicomponent mixture as the assembly of binary neutral cells

without interactions (ideal mixture of associated species). Such a simplistic

behavior is valid only for predicting multicomponent thermodynamics of mixing

using a few adjusted parameters. Applied to divalent metals silicates it

seems to be reliable and gives activities within a 30% relative error for

quaternary system, when compared with available experimental results. These

results were discussed specifically with respect to the absence of polymers

that it implies for divalent metal silicates, and more generally with respect

to its structural significance.

A. Pelton reviewed the thermodynamics of molten salt solutions.

Particular attention was given to models which permit the thermodynamic

properties to be represented, interpolated and extrapolated for purposes of

phase diagram calculations. Topics discussed included similarities and

differences between phase diagram calculations involving alloys and molten

salts, the Temkin sublattice model, applications of the Kohler and Toop

interpolation techniques in molten salts, the Conformal Ionic Solution Theory,

reciprocal ternary and quaternary salt solutions, ordering in molten salt and

oxide solutions, ionic association and "complex ions", polymerization in

silicate and other melts, general quasichemical equations for ordered

solutions, calculation of ternary silicate systems.

J.P. Poirier discussed the large variety of phase diagrams which are

used in earth sciences. Many of these diagrams are concerned with metastable

reactions in addition to the conventional equilibrium diagram covering a wide

range of temperature and pressure. It was shown how combination of the

measurements of the velocity of shear and compressive waves through the

interior of the earth can be employed to develope a description of the

density, temperature and pressure in the crust, upper mantle, lower mantle and

core of the earth. Specific examples of phase diagrams of particular interest

Page 22: Summary of the proceedings of the thirteenth calphad meeting

212 L. KAUFMAN

are those for iron and the olivine, pyroxene and spine1 transitions.

Scientific Group Thermodata Europe (SGTE) reported on the

development of a databank called IMPACT (Inorganic and Metallurgical Process

Analysis by Chemical Thermodynamics). IMPACT will combine a broad database

covering alloys, semiconductors, molten salts, slags, mattes, aqueous

solutions, individual substances and gases with powerful software for

calculation of multicomponent phase equilibria. Users will control the

databank through a friendly multilingual interface and will have access to a

wide range of thermodynamic models, user data facilities and graphics for

phase diagram presentation. Examples were given of the types of calculation

that will be possible, including phase equilibria in the Fe-W-C and

CaC12 -KCl-ZnC12 systems, solubility of gypsum in the Na2S04-NaCl-CaS04-H20

system and the input conditions for production of titanium carbo-nitride by

chemical vapour deposition. IMPACT is scheduled for on-line use from January

1986.

B. Cheynet and P.Y. Chevalier discussed THERMODATA an integrated

information system for providing help and advice concerning the physical

chemistry of metals and alloys the components of this service include

THERMODOC, a bibliographic data base containing 28,000 selected references

concerning thermodynamic properties, HYDROGEN INFORMATION, a bibliographic

data base with 10,000 references covering hydrogen in metals and hydrogen as

an energy carrier, NUMERICAL DATA, covering thermodynamic properties for more

than 3000 chemical elements, compounds or alloys with a computer library for

computation of complex equilibria and phase equilibria in multicomponent

systems. In addition THERMODATA has a research team available for responding

to specific questions.

A. Prince and D.S. Evans reported that the Au-Sb phase diagram has

been substantially redetermined by thermal analysis. Anomalous thermal

effects were observed at the liquid-liquid AuSb2 phase boundary which may be

associated with ordering in the liquid.

I. Ansrra and J.P. Nabot discussed the optimization of the Au-Pb,

Au-In and In-Pb systems by means of the Lukas program as a first step in

evaluation of the Au-In-Pb system.

K. Hack and P.J. Spencer described the THERDAS databank by

presenting examples of calculations in the Fe-MO-0 (Ar) system in which

several possible equilibria for the temperatures of 1173K and 1804K have been

calculated using thermodynamic data from the literature and the database

THERDAS. Various combinations of the oxide phases Fe0 and Mo02, the double

oxides Fe2Mo04, FeMo03 and Fe2M0308 and the metallic phases liquid Fe-MO,

sigma Fe-MO, bee Fe-MO and Fe3M02 have been considered in the presence of a

gas phase containing O2 and Ar. The results show that different equilibria

between the condensed phases are possible with almost identical 02_partial

Page 23: Summary of the proceedings of the thirteenth calphad meeting

PROCEEDINGS OF THE THIRTEENTH CALPHAD MEETING 213

pressures. Changes in the composition in the liquid phase of a nine component

nickel base superalloy during evaporation were also calculated for comparison

with similar changes during evaporation of a nickel-chromium alloys. The

influence of small changes in the Gibbs energies on the phase stability of

CaO-A1203-Si02 system was discussed in addition to illustration of a new

aqueous database. As an example of the latter, equilibria in the Cu-H20

system was considered at a given concentration of copper at varying potential

and pH values at 298K. Concentrations of the various aqueous species and the

pure solid phases present at equilibrium were displayed as a function of the

varied intensive quantities.

K.J. Bhansali, J. Sims and J. Murray discussed the NBS database

structure designed for on-line searching of binary phase diagram information.

Key components of the database include searching capabilities based on pure

metal properties, i.e. invariant reactions, crystal structure and homogeneity

ranges of the phases. The database is set up to search in inter and

intra-mode. In inter-mode, the database can be searched to provide a number

of binary systems having specific phase diagram features querried by the user.

In the intra-mode, the database will provide information on a specific system

of interest. Examples of inter searching based on crystal structure were

shown. The algorithms designed to assist in searching for invariant reactions

based on topographic features were explained. The entire database structure

was discussed.

I. Ansara and 8. Dutartre used a thermodynamic approach, to

establish the phase diagram of the gallium-aluminum-arsenic-germanium system

for liquid phase epitaxy applications. The calculated phase diagram was

compared with experimental information. It was found that at 1073K and at a

given aluminum concentration in the liquid phase, the solubility of arsenic

and the distribution coefficient of aluminum have a very low variation when

large amounts of germanium are added (up to xk, = 0.6).

P. Potter and P. Rogl reported on development of a self-consistent

set of thermochemical and phase diagram data for the Hf-B, Zr-B and V-B

systems using the Lukas program.

J. Agren discussed simple models for representing anomalous

thermodynamic behaviour. He noted that properties for pure substances and

solutions are usually represented by polynomials in temperature and

composition. In cases with a complicated temperature dependence, e.g. below

the Debye temperature or when there is a magnetic transition, different

polynomials in different temperature ranges are often applied. In solutions

there may be a more complicated behaviour than the regular or subregular one

due to ordering or formation of molecular species (associates). In such cases

many coefficients are needed in the Redlich-Kister polynomial and the

extension to higher order systems by means of the ordinary methods (Kohler,

Page 24: Summary of the proceedings of the thirteenth calphad meeting

214 L. KAUFMAN

Muggianu etc.) is somewhat arbitrary. It was demonstrated how simple physical

models can give some guidance in choosing the type of polynomials and the

coefficients. The Debye model can be introduced as a polynomial except at

very low temperatures. Inden's simplified treatment of magnetic ordering and

its application to solutions were reviewed. Some serious discrepancies

between theory and experiments were shown. Solutions exhibiting a long-range

chemical ordering are best treated by a sublattice-model. Short-range order

was discussed and it was argued that an associate or molecular model does not

have the right behaviour. Instead a quasichemical approach is recommended.

For cases where there is evidence for formation of molecules an associate

model is recommended, e.g. in gases or in aqueous solutions.

K. Spear reviewed a thermochemical/mass transport model for

describing the deposition behaviour of steady-state CVD processes. Although

quantitative predictions are still typically not possible because of the.,lack

of mechanistic information and basic data, the model always provides insights

into trends in deposition behaviour as a function of experimental variables.

Individual mechanistic steps inia CVD process were described with the aid of a

schematic physical model. The discussion illustrated the types of useful

information concerning a CVD process which can be obtained frotn,relatively

simple thermodynamic and mass transport calculations. The detailed modeling

of CVD processes is still beyond reach, but a simplified model can be

extremely valuable in producing "road maps" which indicate how changes in

experimental variables can affect the deposition behaviour of complex chemical

systems. It provides a logical, efficient approach to be followed in

developing an understanding of complex CVD processes. Also, the use of a

physical model as an aid in visualizing the mechanistic steps which occur in a

CVD process greatly helps in the design of critical experiments which will

further test and enhance the quantitative nature of the overall model. The

mathematical aspects of the model described were kept simple so that the

physical nature of the mechanistic steps, and the coupling of these steps

through elemental flux balances are more readily understood. If the physical

model is realistic, and if the linking of the mechanistic steps to describe

the completely coupled CVD process is logically sound, then the predictions

made with the use of this model should be as good as mathematical descriptions

of the individual steps, and knowledge of the properties of the system.

C. Bernard and P. Salles reported on a determination of the

thermochemistry and phase diagram of the Zr-C system based on Chemical Vapor

Deposition experiments. A Redlich-Kister model for the monocarbide and liquid

phase was employed to describe the system.

M.L. Saboungi, A. Rahman and M. Blander provided molecular dynemus

calculations for molten MX, AX3 and MAX4 for four different ionic radius

ratios. The aim was to emulate expected properties of binary mixtures of

complexing molten salts such as chloroaluminates and fluoroyttriates. The

Page 25: Summary of the proceedings of the thirteenth calphad meeting

PROCEEDINGS OF THE THIRTEENTH CALPHAO MEETING

radial distribution functions were analyzed along with the

the coordination numbers and of the angles of the A-A-A-A,

triplets; these calculations yield detailed information on

215

distributions of

A-X-A, and X-A-X

the nature and

extent of the species in solution. The influence of changes of cation/anion

radius ratios on the overall structure as well as on the formation and

stability of complexes has been examined. For the two extreme values of these

ratios, the nearest neighbor coordination number of A +3

ions changed from four

to about six. One of the most significant conclusions is that the structure

and ordering characteristic of complexing can extend beyond the local

configurations of nearest neighbors and involve more distant ions. In

addition, typical behaviour often ascribed in the literature to covalency is

detected in these simulated purely ionic melts.

3. Teaching of Phase Diagrams using the Thermodynamic Approach

F.H. Hayes was chairman of a round table discussion of the

teaching of phase diagrams and thermochemistry using computer methods: The

widespread availability of microcomputers and access to larger mainframes

and databases provides an exciting opportunity for new approaches in the

teaching of phase equilibria to metallurgists, materials scientists and

engineers. It is also important that young graduates are aware of the types

of calculations that can now be done with computers via the CALPHAD approach

for real engineering materials. Many CALPHAD members have already

incorporated this into their teaching of undergraduates. The discussion

provided an opportunity for the exchange of experiences that people have

gained in this area and how this relates to traditional approaches in

teaching. 0. Kubaschewski opened the discussion with an overview of the

history of data assessment and was followed by F.H. Hayes, T.A. Meyers,

K. Spear and J.N. Pratt who described the methods they currently use in

their courses at the undergraduate and the graduate level. L. Kaufman

reviewed the generation of lattice stability values and M. Hillert and

A. Pelton described mid career training courses. D.S. Evans and A. Prince

reviewed experimental phase diagram measurement methods and industrial

requirements for personel trained in this area. A.P. Miodownik illustrated

the use of non-equilibrium, metastable and martensitic transformation data

to equilibrium data.

4. List of Participants

A partial list of participants at the thirteenth CALPHAD is given

below.

J. Agren Sweden M. Ignat France

C. Allibert France G. Inden Sweden

M. Allibert France E. Jacobsson Sweden

J.-O. Andersson Sweden B. Jansson Sweden

Page 26: Summary of the proceedings of the thirteenth calphad meeting

216

I. Ansara

H. Baker

J. Bard

C. Bergman

C. Bernard

K. Bhansali

B. Bjorkman

M. Blander

J. Bouvaist

H. Brodowsky

J.P. Bros

C. Carter

R. Castanet

T.G. Chart

C. Chatillon

P.Y. Chevalier

B. Cheynet

N. Clavaguera

M.T. Clavaguera-Mora

C. Colinet

B. De Cremoux

S. Dermarkar

P. Desre

J.D. Dubois

J. Dubois

B. Dubost

F. Durand

D. Dutartre

6. Eriksson

D. Evans

A. Gabriel

B. Gather

H. Gaye

A.F. Guillermet

K.P. Gupta

P. Gustafson

K. Hack

J. Hafner

J.P. Hajra

F.H. Hayes

Th. Hehenkamp

E.T. Henig

L. KAUFMAN

France

U.S.A.

France

France

France

U.S.A.

Sweden

U.S.A.

France

W. Germany

France

U.S.A.

France

U.K.

France

France

France

Spain

Spain

France

France

France

France

France

France

France

France

France

Sweden

U.K.

France

W. Germany

France

Sweden

India

Sweden

W. Germany

Austria

India

U.K.

W. Germany

W. Germany

J.C. Joud

V. Kattner

L. Kaufman

K.L. Komarek

0. Kubaschewski

C. Laugee

B. Legendre

G. Lesoult

M. Liautaud

R. Luck

H.L. Lukas

J.C. Mathieu

G.P. Martins

M.A.J. Michels

A.P. Miodownik

A. Mikula

2. Moser

F.H. Myers

J.P. Nabot

A.K. Niessen

A. Pasture1

L. Pejryd

A. Pelton

A. Percheron

J.P. Poirier

P.E. Potter

J.N. Pratt

A. Prince

G. Purdy

8. Predel

2. Qiao

M.H. Rand

0. Relave

P. Rogl

H. Ruppersberg

P. Salles

N. Saunders

B. Schaub

M.C. Schouler

J.F. Smith

F. Sorrentino

K.E. Spear

France

W. Germany

U.S.A. Austria

W. Germany

France

France

France

France

W. Germany

W. Germany

France

U.S.A.

Netherlands

U.K.

Austria

Poland

U.K.

France

Netherlands

France

Sweden

Canada

France

France

U.K.

U.K.

U.K.

Canada

W. Germany

China

U.K.

France

Austria

France

France

U.K.

France

France

U.S.A.

France

U.S.A.

Page 27: Summary of the proceedings of the thirteenth calphad meeting

PROCEEDINGS OF THE THIRTEENTH CALPHAD MEETING 217

P. Hitter

M. Hoch

J.L. Holm

M. Hillert

France

U.S.A.

Norway

Sweden

B. Sundman

M. Tmar

B. Uhrenius

P. Willemin

Sweden

France

Sweden

France

5. Subjects and Sites for Future CALPHAD Meetings

The times, locations and organizers for future CALPHAD meetings

were selected and are listed below.

CALPHAD

XIV

xv XVI

XVII

XVIII

XIX

xx

Location Date Organizers

Cambridge, MA, U.S.A. lo-14 June 1985 L. Kaufman, W.S. Owen

London, England July 1986 A.P. Miodownik, T.G. Chart

Stuttgart, W. Germany May 1987 H.L. Lukas, G. Inden

Berkeley, California May 1988 L. Brewer, A. Searcy

Stockholm, Sweden May 1989 M. Hillert, B. Uhrenius

The Netherlands May 1990 H. Oonk, A.R. Miedema

Phoenix, Arizona May 1991 A. Navrotsky

At the conclusion of CALPHAD XII a number of topics were listed

for inclusion in future meetings (see CALPHAD volume 7 page 291 (1983)). A

number of these topics were considered at this meeting. In addition to the

forgoing topics the following subjects were recommended for future meetings

Physical Models, Software and Data Retrieval, Slags and Mattes, Phase

Equilibria at High Pressures, Assessment and Optimization of Data,

Application to Crystal Growth, Amorphous and Kinetic Problems.

6. An Overview of CALPHAD XIII

The thirteenth CALPHAD meeting was distinguished by a large number

of excellent poster presentations. The number of oral presentations was

reduced allowing for extented discussion. In addition a round table session

on teaching methods Hayes (page 215) was presented. Poirier (page 211)

provided an excellent review of current geological applications of phase

diagrams, renewing the CALPHAD group's interest in high pressure effects,

while de Cremoux's lecture on applications of phase diagram calculations in

the preparation of electro-optical devices (page 202) stimulated considerable

interest. A variety of databanks were described by Hatem (page 201), Sundman

(page 204), Hack, SGTE and Cheynet (page 212), and Bhansali (page 213).

Discussion of methods for predicting bonding energies and heats of mixing for

alloy and compound phases were presented by Niessen (page 192), Pasture1

Page 28: Summary of the proceedings of the thirteenth calphad meeting

218 L. KAUFMAN

(page 206), Colinet (page 208) and Tmar (page 209). Models for describing

ordered and associated phases, molten salts and slags were presented by

Rupersberg (page 192), Sundman (page 201), Blander (page 205), Hafner (page

2D6), Luck (page 210), Dhima and Pelton (page 211) and Agren (page 213).

Computational methods were discussed by Lukas (page 198). Papers emphasizing

experimental determination of phase equilibria, specific heats and enthalpy

of formation and mixing were presented by Brodowsky (page 192), Hehenkamp

(page 193), Jha (page 194), Mikler and Krachler (page 195), Bergman (page

199), Smith (page 207), Jacob (page 209), Castanet (page 211) and Prince

(page 212). Coupled thermochemical, physical property and phase diagram

analyses for pure metals and binary alloys were presented by Hoch (page 193),

Guillermet, Kaufman and Saunders (page 194), Watson (page 196), Inden (page

209), Ansara (page 212), Potter (page 213) and Bernard (page 214).

Calculation of phase equilibria in ternary and higher order systems was

performed by Hassom, Girard and Kaufman (page 196), Hajra, Uhrenius and

Kattner (page 197), Guillermet (page 198) and Zhiyu (page 201). Application

of the computational and experimental methods to practical problems in

multicomponent systems was discussed by Laha (page 198), Saunders (page 199),

Clavaguera (page 2DD), Saunders (page 2D3), Gaye (page 2D4), Tetenbaum (page

205)~ Kaufman (page ZOl), Ansara (page 213) and Spear (page 214).

The thirteenth CALPHAD was characterized by an expanding area of

application for computer based methods for dealing with a variety of

fundamental and practical problems in synthesizing and producing new

materials and improving their performance.

1. 2. 3.

4. 5.

6. 7.

8. 9. 10. 11. 12.

13. 14.

REFERENCES

F.R. de Boer, R. Boom and A.R. Miedema, Physica 1OlB (1980) 294. F.R. de Boer, R. Boom and A.R. Miedema, Physica 1136 (1982) 18. R. Boom, F.R. de Boer, A.K. Niessen and A.R. Miedema, Physica 1158 (1983) 285. A.R. Miedema, P.F. de Chatel and F.R. de Boer, Physica 1ODB (1980) 1. A.K. Niessen, A.R. Miedema, F.R. de Boer and R. Boom, Physica B, to be published. P. Chieux and H. Ruppersberg, J. Physique Coll. 41 C8 145 (1980). H. Ruppersberg and W. Schirmacher, J. Phys, F. (%tal Phys.) (1984) inprint. C.B. Alcock, K.T. Jacob, and T. Palamutcu, Act. Met. 3, 1011 (1973). O.J. Kleppa, J. Phys. Chem. 60, 858 (1956). Th. Hehenkamp, Ber. Bunsenges. Phys. Chem. 87, 806 (1983). K.T. Jacob, Toronto, private communications. H. Brodowski, A. Fruma, H. Sagunski and H.J. Schaller, Z. Metallkde. 73, 354 (1982). r Kordis and K.A. Gingerich, J. Chem. Phys. 58, 5141 (1983). M. Hansen and K. Anderko, Book Co., New York (1958).

Constitution of Binary Alloys, McGraw-Hill

Page 29: Summary of the proceedings of the thirteenth calphad meeting

PROCEEDINGS OF THE THIRTEENTH CALPHAD MEETING 219

15.

16.

17. 18. 19. 20. 21.

22. 23. 24. 25. 26. 27. 28.

29. 30. 31.

32.

33. 34.

ii:

37.

38.

39.

40. 41.

42. 43. 44.

45.

46.

49. 50. 51. 52. 53. 54.

R.P. Elliott, Constitution of Binary Alloys, First Supplement, McGraw-Hill Book Co., New York (1965). F.A. Shunk, Constitution of Binary Alloy, Second Suppl., McGraw-Hill Book Co., New York (1969). Th. Hehenkamp and R. Kossak; Z. Metallkde. 74, 195 (1983). P. Leech and C. Sykes, Phil. Mag. 27, 742, v939). S. Iida, J. Phys. Sot. Japan, 2, 3n, (1954). R.J. Tarent and B. Ralph, Phys. Stat. Sol. (a) 2, 207, (1974). D.G. Morris, G.T. Brown, R.C. Pillar and R.E. Smallman, Acta Met. 24, 21, (1976). J.K. van Deen and F. van der Woude, Acta Met. 29, 1255, (1981). N. Saunders, Calphad XII Liege (1983). G. Inden, Calphad V, Dusseldorf (1976). K. Shubert and E. Wall, Z. Metallk. 40, 383 (1949). A.P. Miodownik, CALPHAD 1, (3), 207 -(T978). C. Bergman and K.L. Komarek, CALPHAO 8 283 (1984). R. Castanet, W. Ditz, K.L. Komarek, a;d E. Reiffenstein, Z. Metallkde. 72 176 (1981). A. Janitsch,K.L. Komarek and J. Mikler, Z. Metallkde. z 629 (1980). F. Gronvold, J. Thermal Analysis, 13 419 (1978). H. Ipser, J.P. Neumann and Y.A. ChGg, Monatsh. Chemie 107 1471 (1976). Y.A. Chang and J.P. Neumann, Progress in Solid State Chemistry W.L. Wore11 and G.R. Rosenblatt Eds. Pergamon Press, Oxford 14 221 (1982). T.L. Ngai and Y.A. Chang, CALPHAD 5, 267 (1981).

-

H.L. Lukas, E.-Th. Henig, and B. ZTmmermann, CALPHAD 1, 225 (1977). H.L. Lukas, J. Weiss, and E.-Th. Henig, CALPHAD 6, 229 (1982). R.C. Mittal, M.V. Satyanarayana, K.P. Gupta, H.O. Gupta, S.N. Kaul, A.K. Mazumdar, K. Shankara Prasad, T.A. Padmavati Sankar, E.C. Subbarao and E.M.T. Velu, J. Less. Common Metals, 78, 245, (1981). N. Saunders and A.P. Miodownik, Ber. Bunsenges. Phys. Chem. 31, 830 (1983). H.A. Davies, Phys. Chem. Glass 11, 159 (1976).

P. Ramachandrarao, B. Cantor and R. Cahn, J. Mat. SCi- 12, 2488 (1977). A. Doolittle, J. Appl. Phys. 22, I471 (1955). See for example: a) Proc. 4th Int. Conf. on amorphous and liquid semiconductors,

(1971) Ed. M.H. Cohen and G. Lucovsky, J. Non-Crystalline Solids, 8-10 l-1050 (1972).

b) "Amorphous semiconductors". Ed M.H. Brodsky, Springer-Verlag, (1979).

J .-P. deNeufville, J. Non-Crystalline Solids, 8-10 85 (1972). J. Schneider, These ingenieur, CNAM, Paris (19m P. Clechet, C. Martelet and Hguyen Dinh Cau, J. Thermal Anal., 16 59 (1979). R.O. Suzuki and P.H. Shingu, Proc. 5th Int. Conf. on Liquid and amorphous metals, Los Angeles, (1983); to be published in J. Non-Crystalline Solids. M. Hillert, B. Jansson, B. Sundman, J. Agren, Use of the Sublattice Concept in Modelling Molten Ionic Solutions, TRITA-MAC-218 (1983), Div. Phys. Metallurgy, KTH, 100 44 Stockholm. M. Temkin, Acta Phys, Chim. USSR 20 p 411 (1945). A.S. Jordan, in Calculation of Phase Diagrams and Thermochemistry of Allov Phases. Eds. Y.A. Chang and J.F. Smith, The Met. SOC. of AIME (1979) L. Kau L. Kau L. Kau L. Kau A. Let M. Pou

PP. loo- fman, CAL fman. F. fman; J. fman, J. oq and M. lain, M.

129. .PHAD 1 14 (1977). Hayes-and D. Birnie, CALPHAD f?. 163 (1981 Nell, K. Taylor and F. Hayes, CALPHAD 5 Agren, J. Nell and F. Hayes, CALPHAD 7, Poulain, J. Non-Crystalline Solids 38 1

Poulain and J. Lucas, Rev. de Chem. fine

1. 185 71 ( 01 ( ral

(1981). 1983). 1979). 16 267 -

(1979).

Page 30: Summary of the proceedings of the thirteenth calphad meeting

220 L. KAUFMAN

55.

56. 57. 58.

59. 60.

:::

63.

64.

65. 66.

67. 68. 69. 70.

R.E. Thoma, Advances in Molten Salt Chemistry, J. Braunstein, G. Manator and G.P. Smith Eds. Plenum Press, N.Y. (1975) page 302. A. Lecoq and M. Poulain, Verres Refract. 34 333 (1980). A.S. Jordan, J. Electra-them. SOC., 119, T23 (1972). M.B. Panish and M. Ilegems, Progressin Solid State Chemistry, vol 7, p 39, New York Pergamon (1972). G.8. Stringfellow, J. Cryst. Growth, 27, 21 (1974). B. de Cremoux, J. de Physique, 43 C5-m (1982). G.B. Stringfellow, J. Appl. Phyc, 43 3455 (1972). M.C. Joncour, J.L. Benchimol, J. Bu%ea and M. Quillec, J. de Physique, 43, C5-3 (1982). J. Ohta, M. Ishikawa, R. Ito and N. Ogazawara, Japanesse J. Appl. Phys., 22, L136 (1983). M. Quillec, C. Daguet, J.L. Renchimol and l-l. Launois, Appl. Phys. Lett., 40, 325 (1982). J. HafnG, Solid State Communications 49 1125 (1984). J. Hafner. A. Pasture1 and P. Hitter, % Phys. F. Met. Phys. 14 II37 (1984). - A.R. Miedema, J. Less Common Metals, 46 67 (1976). L.H. Bennett and R.E. Watson, CALPHADT 23, 40 (1981). C. Bergman and K.L. Komarek, CALPHAD i-283 (1984). A. Pasturel, P. Hitter and F. Cyrot-Lackmann, Solid State Commun. 2 561 (1983):

71. M.C. Desjonqueres and M. Lavagna, J. Phys. E, I733 (1979).

72.

73. 74. 75. 76.

77.

78. 79.

80.

81. 82.

83.

:::

86.

88::

ii: 91.

92. 93.

94.

9965: 97.

J. Friedel, the Physics of Metals (Edited by J.M. Ziman) chap. 8, Cambridge University Press, London (1969). F. Cyrot-Lackmann, J. de Physique, Suppl. C_l, 67 (1970). J.P. Gaspard and F. Cyrot-Lackmann, J. Phys. C6, 3077 (1973). A. Pasturel, C. Colinet, P. Hitter! Acta Met. (under press). R. Hultgren, P.D. Desai, D.T. Hawkins, M. Gleiser and K.K. Kelley, Selected values of the thermodynamic properties of binary alloys (New York; Am. Sot. Metals) (1973). 0. Kubaschewski and C.B. Alcock, Metallurgical Thermochemistry, Pergamon, New York (1979). L.H. Bennett and R.E. Watson, CALPHAD 5 19 (1981). F.R. de Boer, R. Boom and A.R. Miedema: Physica 113B 18 (1982).

Physica u (1980) 294 and

R. Boom, F.R. de Boer, A.K. Niessen and A.R. Miedema, Physica 1158 285 (1983). A.R. Miedema and A.K. Niessen, CALPHAD 7 27 (1983). A.K. Niessen and A.R. Miedema, Ber. Bunsenges. Phys. Chem. &7 717 (1983). J. van der Rest, F. Gautier and F. Brouers, J. Phys. F5, 2283 (1975). M. Cyrot and F. Cyrot-Lackmann, J. Phys. F6, 2257 (1976). D.G. Pettifor, Solid State Commun. 28 (1978) 621 and Phys. Rev. Letters 42 846 (1979). C.M. Varma, Solid State Commun. 31 295 (1979). B.K. Chakraverty, J. Phys. Chem. Solids, 30 454 (1968). D. Pines and Ph. Nozieres, (Benjamin, New York).

The Theory of Ouantum Liquids, (1966)

M. Tmar, C. Chatillon and I. Ansara, CALPHAD XI. G.B. Stringfellow, Mat. Res. Bull,q, 371-80 (1971). R. Boom, F.R. de Boer and A.R. Miedema, J. Less Common Met., s, 271-84 (1976). G.B. Stringfellow, J. Phys. Chem. Solids, 34 1749-1750 (1973). M. Hasebe, 577 (1982).

K. Oikawa and T. Nishizawa, J. Japan Inst. Metals Vol. 46,

R. Lacmann, Z. Phys. Chem. Neue Folge 35, 86 (1962). P.J. Flory, J. Chem. Phys. lo, 15 (194n. M.L. Huggins, Ann. N.Y. Acd. Sci., 44, 431 (1943). M.L. Saboungi, (1984).

A. Rahman and M. Blaii?ier, J. Chem. Phys. 80 2141 -


Recommended