CALPHAD Vol. 16, No. 2, pp. 111119. 1992 Printed in the USA.
THERMODYNAMIC
Y.
0x45916/92 $5.00 + .oo (c) 1992 Pefgamon Press Ltd.
EVALUATION
FEUTELAIS,
Laboratoire
G.
OF THE SYSTEM BISMUTHANTIMONY
and J.
MORGANT
R.
DIDRY
de Chimie MinOrale II, 5 rue J.B. ClCment 92296 ChltenayMalabry Cedex France J. SCHNITTER’
Universitit
ABSTRACT:
Osnabriick, Anorganische Barbarastr. 7 4500 Osnabriick Germany
Chemie
Thermodynamic data for the binary system bismuthantimony taken from literature have been evaluated critically with respect to consistency. A coefEcient set describing the thermodynamic properties of the binary mixtures is prcscnted. Two enthalpy and one entropy coefficient are sufficient to describe the liquid phase, while an excess C, term h,as to be added for the solid solution.
Introduction In order to study the system bismuthantimonytellurium it is necessary to establish consistency between the thermodynamic properties and the phase diagram for the bounding binary systems. A recent work has been devoted to the thermodynamic assessment of the antimony tellurium system (89Gho]. In the present study we analyse the bismuth antimony system whose phase diagram, according to the compilation of HANSEN and ANDERKO[58Han ] , sh ows a continuous solid solution. While the liquidus curves given by different authors are in good agreement the solidus line seems to be not well defined. The enthalpy of mixing presented by several authors shows a slightly positive deviation from ideality which does not agree with the values derived from partial Gibbs energy measurements. Using a set of computer programs [77Luk] a thermodynamic evaluation of the system has been done.
Literature
Data
Base
Phase Diagram Data. In an early study of the system BiSb by GAUTIER [96Gau] the liquidus curve obtained by solidification experiments exhibits a single arc involving the presence of a continuous solid solution. By means of hardness experiments ZAPOZIINIKOV [OSZap] Ia t er confirmed the existence of solid solutions up to 30% Bi. Using thermal analysis on cooling, H~~TTNERand TAMMANN [05Hut], obtained a liquidus with a kink in the region of Xs, = 0.63. As the melting point of pure bismuth was found to be more than two degrees lower ‘)
Present
address:Technische
tlochschule
Darmstadt,
Physikalische
Received on 24 October 1991
111
Chemie
I, Petersenstr.
20, D6100
Darmstadt
112
Y. FEUTEWS
et al.
than the currently accepted value from NBS [81BAP], we can suppose the existence of some contamination problems. By examining cooling curves COOK [22&o] obtained the same smooth liquidus curve as in [96Gau]. Both these studies [OSHut, 22&o] show a solidus with a large horizontal part. This phenomenon, generally obtained when studying solid solutions by cooling, is due to the fact that the equilibrium state has not been reached because of hindered diffusion in the solid state. Therefore we only used the liquidus data from [22&o]. CHARPY[97Chaj and PARRAVANOand VIVIANI [lOPar] confirm the existence of a continuous solid solution by microscopic and hardness studies. Xray investigations on annealed samples [32Bow, 34Ehr] showed that the change of the unit cell edge with composition is almost linear. A structural study [53Zap] confirms this assumption. Later, by measuring the temperature dependence of the electrical resistivity, OTANI [250ta] obtained a liquidus in good agreement with those found previously, but the time of annealing reported does not seem to be long enough to completely overcome diffusion problems in the solid state. For that reason the solidus data were not used in the evaluation. MASINGet al. [49Mas] obtained some solidus points from resistivity measurements on annealed samples (between 3 and 100 days of annealing). Using a high frequency method on nonannealed alloys, WEBER and CRUSE [59Web] found a flat solidus. We only kept the liquidus data.
Based on data obtained by thermal analysis on heating of samples of different annealing times PELZEL [59Pel], CAMPBELL and WINKLER [63Cam] and YIM and DISMUKES [67Yim, 74Dis] described the solidus as a single arc. The latter authors also reported data obtained by wet chemical determination of the distribution coefficient k. They checked the homogeneity of the alloys by xray fluorescence, density and lattice parameter measurements, and emission and mass spectrographic analyses. On homogeneous alloys obtained by diffusionless crystallization VIGDOROVICH et al. [73Vig] determined liquidus and solidus in the bismuth rich side. An attempt to determine the solidus by microhardness measurements has been done by GLAZOV [61Glal, 6lCla2], but later he concluded [62Cla] that precise solidus data could not be obtained by this technique. More recently, PETROV and GLAZOV (85Petj reported data on the dependence of cooling rate on the solidus obtained by means of a hypercooling method. They showed that this technique is equivalent to annealing a very long time.
Enthalpy Data. The first investigation of the enthalpy of mixing of the melt, done by direct calorimetric measurements, shows a positive deviation from ideality whose maximum is about 1250 J mol’ [30Kaw]. WITTIC and GEHRINC [59Wit] and YAZAWAet al. [SSYaz] h ave reported a slightly positive deviation at 973 K and 945 K, respectively, with a maximum at about 550 J mol’ [59Wit] and 650 J molr [SSYaz]. Both groups fitted the data to a subregular polynomial expansion. Since the data reported by KAWAKAMI(tOKaw] exhibit some scatter and deviate significantly from those found by the other authors they were not used in the calculation. KUBASCHEWSKIand SEITH [38Kub] measured the enthalpy of mixing of solid solutions at room temperature. They concluded that the solid phase does not exhibit a heat of mixing high enough to obtain experimental values outside the range of error (= f850 J). After annealing 1000 h at temperatures 3040 degrees below the solidus temperature VECHER et al. (83Vec] measured C, values on two single phase alloys by using an adiabatic calorimeter. More recently, BADAWI [87Bad] carried out calorimetric measurements in both the liquid and solid state by measuring the enthalpy differences between two temperatures in the range 323923 K.
By using a molten salt galvanic cell LOMOV and KRESTOVNIKOV (64Lom] measured Gibbs Energy Data. e. m. f. values in the temperature range 11151215 K. The partial Gibbs free energy of bismuth versus concentration curve shows a sharp break between Xs, = 0.2977 and Xs, = 0.4982; the high temperature range of these measurements suggests some evaporation problems in this study. The enthalpy of mixing derived shows both positive and negative deviation from ideality which is in significant disagreement with the calorimetric investigations. Therefore these data were discarded.
113
THERMOOYNAMlC EVALUATION OF THE SYS?EM Bi~~~nMONY
TABLE
1
Data sources used during final optimization liquidus
Reference
OTANI
[25Ota]
WEBER and CRUSE
solidus
H( 2’)  H( ‘I’,,)
Ati,H
ebX
X X
GAUTIER
:~~~“I
X
PELZEL
[59Peq;l
X
COOK
P2C4
X
BADAWI CAMPBELL and WINKLER VECHER et al. VICDOROVICH et al. YIM and DISMUKES WITTIG and GEHRING PETROV and GLAZOV MASING et al. HINO and AZAGAME
[B?Bad] [63Cam] ;!;:I ]67Yim, 74Dis]
p;;1 [49&s]
X
X X X
X
X
X
x
x
X
X X X
[77Hin]
X
An e. m. f. study involving solid oxide galvanic cells has been carried out by SATOSMI and TAKESHI [BSSat] in the temperature range 9731273 K. The activities of the elements show only slight deviation from ideality. The enthalpy of mixing derived from those data is negative in the whole range of concentration which is in Nevertheless, these values were included disagreement with the results of direct calorimetric investigations. initially. By measuring the partial vapour pressure of antimony by the Knudsen effusion method KAZALAEVA et al. [7OKaz] obtained activities of the components between 693 and 873 K. As the activity curves reported do not exhibit the typical behaviour for the twophase region we only kept the values obtained for the liquid phase during initial calculations. Two other vapour pressure studies by HINOand AZACAMI[77Bin] and SUNADA and AZAGAMI [79&n] have been carried out at 1273 K and 910 K, respectively. In ]77Hin] the vapour was ~sumed to consist of five different species; this evaluation resulted in a smaller deviation from ideal behaviour of the liquid phase than that found in [79Sun]. Since experimental data were not given in the latter study those results were discarded. Table 1 gives an overview on all the data sources used in the final data set.
Previous
system
Calculations.
bismuthantimony.
HISKES and TILLER were the first to perform thermodynamic calculations on the They used only the data given in [61Clal] and [67Kub] (taken from [59Wit]).
Later AJERSCH and ANSARA[74Aje] described the liquid phase as a subregular solution and the solid phase ss a regular one. They concluded that the experimentally determined phase diagram was best reproduced by assuming that for both phases the excess entropy is virtually zero. By applying the conformal solution theory BHATEAand MARCH(76Bha] obtained a phase diagram that closely resembles the one given in [58Hanf. Small d eviations were observed only on the bismuth rich side.
PELTONand BALE [86Pel] calculated the solidus from liquidus and liquid phase data assuming an excess entropy of zero for both phases. Calculations were done for both an ideal and a regular liquid solution using the data of [SOKaw]. Heats of mixing with a maximum shifted towards the Sbrich side were found for the solid phase. BALAKRISHNA and MALLIK [85Bal] compared the results of applying several solution models by using data from [59Wit, 61Glal] and concluded that both phases show a positive deviation from RAOULT’S law.
114
Y. FEUTEWS et al.
Analytical
Description of the Phase Stabilities
In the case of a binary phase consisting of the pure components A and B the dependence Gibbs energy C, on composition and temperature is given by the general formula C,(Xn,
T) = X,C,,(T)
+ XnC,.n(T)
+ RT(X,
In X, + Xn In XB) + C,‘(XB, 0
of the molar
(1)
dependent molar Gibbs energies of the respective pure components where G,,,* and G,,,, are the temperature and Cz = Hg  T.52 is the molar excess Gibbs energy which depends on composition Xn and temperature T. For the description of the temperature dependence of the Gibbs energy of the pure elements we chose the series representation according to SCTE:
C,,(T)
= Ai + BiT t CiT In T t C DijTj.
(2)
A database [89D in ] is available from SCTE which contains the coefficients Ai, B,, C, and Dij of this series for the pure elements i in various structures. The coefficients for bismuth and antimony respectively were taken from that source. The molar excess Gibbs energy of both the liquid and the solid phase is described in terms of the respective Q function ctG
=
c/X,(
For the a function
~c(XevT) =
I  X,).
(3)
a series representation
c dW,(l
based on Legendre
polynomials
[74Bal, 75Bal, 8GPelj was chosen:
 2x13).
I
The gi are temperature dependent coefficients and the f,(z) arc the Lcgcndrc polynomials of ith degree with dependcncc of the coefiicicnts gi is described in the respect to the argument z = 1  2X,. The tcmpcrature same way as for the pure elements, i. e. g,(T) = ai t biT f c,T In T t c
dilT’.
These coefficients were fitted to the experimental by LUKAS et al. [77Luk].
(5)
data by a least squares technique
described
and programmed
Results and Discussion Isomorphous systems often can be considered as ideal or nearly ideal systems. Lack of data for the solid phase in the system BiSb has led us to start the optimization by adjusting the parameters of the liquid state. Since the only enthalpy of mixing data to be considered for the liquid phase were the calorimetric values from [59Wit] and [SSYaz] it was necessary to choose among the following three possibilities: (a) a subregular description with an excess C, term to describe of mixing using both these data sets;
the temperature
dependence
(b) a subregular
model using only the data given by YAZAWA et al. [68Yaz];
(c) a subregular
model using only the data given by WIT’HG and GEMRING [59Wit].
of the enthalpy
THERMODYNAMIC EVALUATION OF THE SYSTEM BISMUTKANTIMONY
For each of these possibilities a significantly lower mean square error was observed when removing the partial Gibbs energy values of [‘IOKaz], [79Sun], and [84Sat]. No matter whether these data were taken into account or disregarded, calculating with an excess C, term always resulted in a higher error than the solutions (b) and (c) which led to very similar mean square errors. In order to choose between (b) and (c) several optimization runs with different sets of additional data were performed to check each set of enthalpy values ([59Wit] and [SSYaz]) for consistency with the solid state and phase diagram data. From both these sets the two subregular coefficients were calculated and kept fixed in all further calculations. Since the data from [59Wit] always gave lower error values than those from [68Yaz] we chose (c) as the final description of the enthalpy of mixing of the liquid phase. The next step was to derive a description of the solid phase from the liquid phase description, the phase diagram data, and the H(T)  H(T,,) data available for the solid phase. An intermediate set of enthalpy coefficients for the solid phase was obtained by fitting these coefficients to the available data. As shown by KUBASCHEWSKI et al. [67Kub], th e re g u Iar solution model does not well describe the deviations from ideality for metallic solutions. In the case of semimetallic systems, the deviation from regularity can be substantial, and CHART [73Cha] g ave a relationship between enthalpy and excess entropy of formation for a large number of alloys. This relationship has been used here to obtain starting values for excess entropy coefficients of both the liquid and the solid phase. The extensive set of enthalpy data given in (87Badj (343 out of a total of 601 data points) turned out to be problematic because the mean square error was mostly determined by the huge number of particular deviations calculated for those data. In order to avoid that the resultant coeffnzients were dominated by data from a single source we introduced those values with only 10 % of th e normal weight into the programs. During the final optimization runs the set of data listed in table I has been used. The coefficients obtained referring to SI units are given in table 2 for both phases.
TABLE 2
Calculated
Phase liquid
solid
i 1 2 I 2
cocfficicnt ai
2 176.50 25.50 11837.48 I 764.27
set; cf. eqns. (4) and (5). bi
ci
0.659 72 1.80843
 1.696 387
Figure 1 shows the calculated phase diagram and the experimental data including those omitted from the final data set. Experimental data are in good agreement with the calculated curves. The main difference occurs between the solidus points obtained from nonannealed samples and the calculated solidus curve. The phase diagram exhibits a flat solidus which can be interpreted in terms of some tendency to demixtion in the solid state. By calculating the borders of the miscibility gap we obtained a critical point at T, = 498 K and X,, = 0.637. In figure 2 the enthalpy of mixing as a function of composition is presented. The enthalpy of mixing shows a slightly positive deviation from ideality in the whole concentration range. This result seems to be in agreement with the results of a neutron diffraction study of the BiSb system [76Kno]. In that work KNOLL showed that BiSb melts contain two different kinds of structure: l
a metallike
l
a mixture
one consisting
of randomly
distributed
atoms and
of Bi, and Sb, tetrahedra.
The concentrations of the Bi, and Sb, species in the melt are identical for Xs, c 0.40. The existence of repulsive forces between the Bi, and Sb, molecules can explain the positive values of the enthalpy of mixing.
115
116
Y. FEUTEWS et al.
On the other hand, the low concentration of the tetrahedron species (15%) at that composition may be an explication for the small magnitude of A,,,&,,. Figure 3 shows that the molar heat capacity C,,_ of the solid phase calculated at Xs, = 0.5 is in relatively good aggreement with the results of (83Vecj. The partial Gibbs energy of mixing calculated for three temperatures (873, 973, and 1273 K) is presented in figure 4 together with the data from [Morn, 77Hin, 70Kaz, 84Sat]. The data obtained by HINO [77Hin] at 1273 K are in good agreement with the calculated curve while the data taken from other sources deviate considerably. Comparison with experimental data shows that it is well justified to describe the melt by the quasisubregular approach while the solid phase needs an additional excess C,, term. Nevertheless it must be noted that the coefficients which extend the regular model are of small magnitude so that in a first approximation both phases can be considered as being regular.
650 600
. BI FIG. 1 0
V X 0 II
+
0.1
0.2
0.3
0.4
0.5
0.6
0.7
XSb
[96Gau] [OSHut] (22Cooj (250ta]
‘) Solidus data not used in the final optimization ‘) Liquidus and solidus data not used in the final optimization
0.9
Sb
Calculated phase diagram of the system bismuthantimony
GAUTIER MTTNER and TAMMANN~) COOK’) ~TANI~) MASINGet al. PELZEL
0.8
and experimental data
0 0 4 + A m
WEBERand CRUSE*) CAMPBELLand WINKLER YIM and DMNIKES VICDOROVICH et al. VECHER PETROVand GLAZOV
(59Webj [63Cam] [67Yim. 740;s) [73Vig]
117
THERMOOYNAMIC EVMUATlON OF THE SYSTEM BlSMUTKANTlhfONY
350
FIG. 2
FIG. 3
Calculated molar enthafpy of mixing of the
bismuth antimony
melt at 973K
(1073 K)
0 B
A
KAWAKAMI
[30Kaw]
(97310
WITTIG and GEHRING
]59Wit]
(945K)
YAZAWA
[68Yar]

‘;
550
so0
:;I
Calculated molar heat capacity C, of the solid
solution phase at Xs, = 0.5.
and experimental
values obtained at various temperatures. It
I
400
LECHER
[83Vec]
10
5 E 15
2420 .pJ 1: 25 .fi._ Em t 30
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.6
0.9
Xsb
FIG. 4 jt 0
Calculated chemical potentials of the components at 873 K (
(1215K) (873 K) ‘f Data
 .  .), 973 K (   ). and 1273 K ().
LOMOV and KRESTOVNIKOV’)
[64Lom]
V
(1273 K)
KAZHCAEVA et al. ‘)
[70Kaz]
A
(973K)
not usedin the final optimization
HINO and AZAGAMI
[77Hin]
SATOSHI and TAKESHI’)
f84Satj
Y. FEUTEWS et al.
118
Acknowledgements We would like to thank H. L. LURASand U. KATTNERfor supplying the programs used and additional help on how to use them, C. A. ~OUGHAN~WRfor her tho~ugh introduction into the program set and I. ANSARA for a Iong, helpful discussion. This study has been done as part of the PROCOPE program.
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IL
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119
THERMODYNAMIC EVALUATIONOF THE SYSTEM BISMUTHANTIMONY
[74Bai]
C. W. BALE
f?QDisf
J. P. DISMUKESand W. M. Y1r.t‘ J. Crysr. Growth 22 (19741, 287294.
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[75Bal]
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[?9Sun]
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[83Vec]
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[S4Sat]
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[SSBaI]
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(89&n]
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M&l/.
Trans.
Al7 A (19S6), 10571063.
NPL Report DMA (A) 195, September 1989.
Z. ~~cfa~~kde.80 (1989), 731736.