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
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
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
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
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
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
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
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
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
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
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
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
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
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
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
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
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
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
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
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.
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
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
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,
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
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
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.
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
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.
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