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The limiting molar partial enthalpies of mixing of iron, cobalt, nickel, palladium and platinum in liquid gallium and indium
Journal of
ALLOYS
ANDCONPOUND5 ELSEVIER
Journal of Alloys and Compounds 220 (1995) 189-192
The limiting molar partial enthalpies of mixing of iron, cobalt, nickel, palladium and platinum in liquid gallium and indium P. Anres a R. H a d d a d a D. E1 Allam a M. Gaune-Escard a j.p. Bros a E. Hayer a Universitd de Provence, IUSTI-CNRS UA 1168, Avenue Escadrille Normandie-Niemen, 13397 Marseille Cddex 20, France b University of I/~enna, Institute of Inorganic Chemistry, Wahringerstrasse 42, 1090 Vienna, Austria
Abstract Gallium and indium have been used as solvents for the determination of the molar partial enthalpy of mixing Amah~,(TM, Ga or In) (denoting liquid transition metal (TM) in infinite liquid gallium or indium) of the pure liquid transition metals Fe, Co, Ni, Pd and Pt by direct reaction calorimetry between 1000 K and 1500 K with the exception of Amixh°(Fe, In) (because of the shape of its equilibrium phase diagram). All the limiting enthalpies listed below refer to the liquid state. With pure gallium as solvent, they correspond to the reaction TM(liq)-nGa(liq)
, TM1Gan(liq)
at the experimental temperature Te, with n >> 1. (i) A,,i,h~, in gallium is found for Fe, Co, Ni, Pd and Pt to be - 2 , -44, -82, -144 and -155 kJ mol-1. (ii) Am~xh° in indium is found for Co, Ni, Pd and Pt to be +28, -25, -127 and -114 kJ mo1-1. In both solvents, these limiting enthalpies vary with a similar trend. This observation makes it possible to predict the limiting molar partial enthalpy ~m~xh°(Fe, In) of mixing of iron in indium as +70 kJ mo1-1. The results have been compared with the data proposed by Miedema and co-workers. Keywords: Thermodynamics; Enthalpy of formation; High temperature calorimetry; Liquid alloys
1. Introduction
Information on the thermodynamic properties of binary alloys of group VIIIA transition metal (TM) (columns 8, 9 and 10 of the table of elements) with A1 or Ga or In binary alloys is very scarce. Only the phase diagrams, the crystallographic parameters of the intermediate compounds and a few experimental data (activities and enthalpies of formation) obtained from the solid state, are available. However, for the past few years, much information has been accumulated by our group on the thermodynamics of liquid binary alloys formed with Fe, Co, Ni, Pd or Pt and a group IIIB polyvalent element (aluminium, gallium and indium column 13) [1-5]. From a theoretical viewpoint, the determination of the excess properties of formation of the liquid phase provides information giving a better knowledge of the nature of the chemical bond in these metallic liquid binary alloys [6].
0925-8388/95/$09.50 © 1995 Elsevier Science S.A. All rights reserved SSDI 0925 -8388(94)06019-3
Experimental thermodynamic data obtained by high temperature solution calorimetry, using two metallic solvents (gallium and indium) with very similar chemical properties are presented below.
2. Experimental details 2.1. T h e c a l o r i m e t e r
All calorimetric measurements were performed with a very high temperature automated calorimeter (working temperature range, 1200 K-1700 K) described elsewhere; experimental details and precautions taken have also been published [7,8]. The calorimeter has been equipped with an automatic charger unit allowing 30 successive additions of samples (metals or alumina) to obtain enthalpy data on a wide molar fraction range. The main modification is the use of a long gas-tight alumina crucible (470 mm height and 12 mm external
P. Anres et al. / Journal of ,4lloys and Compounds 220 (1995) 189-192
190
diameter), the lower part of which fits snugly into the crown of thermocouples. The long tube extending up to the cold region of the calorimeter furnace prevents any contact of metal vapours with the thermocouples. Inside the alumina crucible a thin-walled boron nitride crucible is located in which the alloying process takes place. Before starting a series of measurements, the small crucible was charged with about 0.2-2 g gallium or indium (the larger mass of solvent allows the determination of the limiting molar partial enthalpy of mixing).
2.2. Materials A small gas flow of high purity argon (from Air Liquid Co.) was maintained in the experimental crucible and in the furnace during experiments. At the end of each experiment, the calorimeter was calibrated by means of five or six additions of a-alumina [9], correlating the measure of the thermoelectric signal vs. time curve and the corresponding enthalpies. High purity metals (99.999 wt.% TM) were employed. Generally these metals were rinsed with high purity acetone, dried and cut into small pieces. The purity of gallium and indium is 99.99 wt.% and 99.999 wt.% respectively. The gallium, melted under a dilute solution of hydrochloric acid (5%) in warm water, divided into small droplets, rinsed with cold distilled water after solidification, and then dried, was used without any purification step.
the molar fraction on the Ga- (or In-) rich side of systems. Moreover, this discrepancy leads to an uncertainty of about 0.5% in the enthalpies. Several factors influence the final accuracy: experimental temperature, chemical properties of pure metals (oxidability, vapour tension .... ), shape of the binary phase diagram ..... In this study, it is the nature of the binary system which is the main factor: if the phase diagram of the investigated binary alloy exhibits a liquid miscibility gap (as for example the Co-In system) the experimental time to reach complete equilibrium is long, and heat of mixing is weakly endothermic. In this case enthalpies of mixing were measured with an uncertainty of about +8%. On the contrary, when the phase diagram shows a large single liquid phase (as for example the Ga-Pd system) the equilibrium is quickly reached: in this case the enthalpy of mixing, strongly exothermic, was obtained at +5%.
3. Results
The enthalpy of formation of each binary system was measured in large temperature and molar fraction ranges; these experimental conditions are given in the following together with the corresponding literature references: Pt-Ga system: 1169< T (K) < 1461 and 0
2.3. Accuracy
Pd-In system: 1425< T (K) < 1679 and 0
Ni-Ga: 1304< T (K) < 1616 and 0
Table 1 E x p e r i m e n t a l a n d p r e d i c t e d [14] v a l u e s (in kilojoules per m o l e of T M ) of the l i m i t i n g partial m o l a r e n t h a l p i e s of liquid Fe, Co, Ni, P d a n d Pt in liquid g a l l i u m or i n d i u m as a s o l v e n t Solvent
Fe
Co
Ni
Pd
Pt
Ga (experimental)
- 2 - 5 4 [15] - 8
-44 - 6 6 [16] - 39
-82
- 144
- 155
-53
- 163
- 148
+ 28
-25 - 3 7 [18] - 3 3 [14] +5
-
- 114 - 1 2 9 [18] - 1 2 8 [19] -77
Ga (calculated) In ( e x p e r i m e n t a l )
+ 1.6 [17] In ( c a l c u l a t e d )
+63
+ 22
127 128 [18] 133 [19] 111
O u r d a t a listed in this t a b l e have b e e n d e t e r m i n e d by d i r e c t c a l o r i m e t r y b e t w e e n 1300 K a n d 1700 K. T h e v a l u e p r o p o s e d for Am~xh&(Fe, In) for liquid F e in infinite liquid In has b e e n o b t a i n e d by e x t r a p o l a t i o n . T h e previously p u b l i s h e d d a t a [15-19] are also indicated.
P. Anres et al. / Journal of Alloys and Compounds 220 (1995) 189-192
Using the heat capacities and the enthalpies of fusion of the transition elements published by Barin and Knacke [12] and Hultgren et al. [13] and assuming a constant Cp value for the liquid and the supercooled liquid slates the experimental results have been referred to the liquid state. From these measurements the main thermodynamic features may be deduced. (i) Taking into account the experimental uncertainty and the temperature range investigated, the enthalpy of formation of the TM + Ga and TM + In liquid systems may be considered as not temperature dependent (except for the I n + N i system), (ii) These melts exhibit strong departure from thermodynamic ideality: their enthalpies of formation are strongly negative for the (Ni or Pd or Pt) + (Ga or In) system and positive for the Fe- and Co-based alloys. The molar partial enthalpies of mixing of the group VIIIA transition metals in gallium and indium correspond to the reaction TM(liq) +nGa(liq)
191
-110
o E.
-115
E ~.
-12o
P o
.¢
-125 0
0,004
0,005
0,012
Xpt
Fig. 2. The Pt + In liquid system: partial molar enthalpies of liquid Pt (in kilojoules per mole of Pt) measured at 1169 K (Q) and 1173
(o).
K
100
I
I
/'~
inGa I
0 in In
~ TMlGan(liq)
with n :>>1. Performing consecutive additions of the TM, the reaction was given by TM(liq) + TM~Ga~(liq) -
""
m
> TM~+aGa~(liq)
The corresponding limiting enthalpies have been extrapolal:ed to xTM = 0, xTM being the molar fraction of TM, from the graph of the partial molar enthalpies by takir~g the experimental enthalpies at the mean molar fractiorL
\
!
o E
0
\
A \
\A I-\
E
0
e-
XTM, i = (XTM, i 4- 1 " ~ X T M , i ) / 2
where J: is the number of the addition. Moreover, special experimental runs have also been performed on the Ga- and In-rich side, on very short molar fraction ranges (0
.x -100
E
-200
I Fe Atomic
-150
I Co
I Ni number
Fig. 3. Trends of the variation in Ami~h°(TM, Ga or In) for liquid TM in infinite liquid gallium or indium vs. the position of the transition metal in group VIIIA: ~, extrapolated value of Amixh~(Fe, In).
o
E. -155
-160 0,004
Xpt
0,008
Fig. 1. The Pt + G a liquid system: partial molar enthalpies of liquid Pt (in kilojoules per mole of Pt) measured at 1169 K.
those predicted by Miedema and co-workers [14]. Experimental data given in the literature are also given in Table 1 to allow a comparison: the limiting molar partial enthalpies of nickel, palladium and platinum in liquid indium obtained by Predel and co-workers [19] and Colinet et al. [18] are in good agreement with our
192
P. Anres et al. / Journal of Alloys and Compounds 220 (1995) 189-192
results. On the other hand, other experimental data already published [15-17] show large discrepancies with our results. Fig. 3 shows the trend of variation in Amixh°(TM liq.) with respect to the position of the transition metal in the periodic table. With liquid gallium or liquid indium as a solvent the trends are similar. Thus the limiting molar partial enthalpy of liquid iron in liquid indium may be predicted as about + 7 0 kJ mol-1. This value can be compared with that proposed by Miedema and co-workers: +63 kJ mo1-1.
4. Conclusion The calorimetric determinations of Am~h~(TM, Ga or In) for a TM liquid in infinite liquid gallium or indium of the following pure liquid transition metals (TM = Fe, Co, Ni, Pd and Pt) point to the following. (i) The enthalpy of mixing is not dependent on temperature, except for the In + Ni system. (ii) A high negative value of Amixh°(TM) when TM is Ni, Pd and Pt corresponds to a transfer of electrons from the sp metal to the transition metal. (iii) A similar trend is found for the variation in Amixh°(TM) vs. the position of the transition metal in group VIIIA for Ga and In as a solvent. This observation makes it possible to predict the limiting molar partial enthalpy Amixh°(Fe, In) of mixing of iron in indium as + 70 kJ mol- 1 (iv) W h e n Pd a n d Pt a r e dissolved in gallium a n d indium, a quite correct agreement is found between predicted values of Amixh°(W!VI) proposed by Miedema and co-workers [14] and our experimental results.
References [1] D. El Allam, Th~se de l'Universit~ de Provence, Marseille, 1989. [2] R. Haddad, Thdse de l'Universit~ de Provence, Marseille, 1993. [3] D. El Allam, M. Gaune-Escard, J.P. Bros and E. Hayer, Metall. Trans. B, 23 (1992) 39. [4] D. El Allam, M. Gauue-Escard, J.P. Bros and E. Hayer, submitted to Metall. Trans. B. [5] R. Haddad, M. Gaune-Escard and J.P. Bros, The Fe-Ga system: enthalpy of formation, TMS Meet., San Francisco, CA, 1994. [6] E. Hayer and J.P. Bros: The Fermi energy and the enthalpy of mixing, Thermodynamics of Alloys, Genova, April 25-28, 1994. [7] G. Hatem, P. Gaune, J.P. Bros, F. Gehringer and E. Hayer, Rev. Sci. Instrum., 52 (1981) 585. [8] E. Hayer, F. Gehringer, M. Gaune-Escard and J.P. Bros, Joum. Calorim~trie Anal Therm., 18 (1987) 317. [9] NIST: National Institute of Standards and Technology, US Department of Commerce, Washington, DC, 1989. [10] P. Anres, M. Gaune-Escard and J.P. Bros, Thermodynamics of the P t + G a liquid system, to be published. [11] P. Anres, M. Gaune-Escard, J.P. Bros and E. Hayer, Enthalpies of formation of liquid (indium+ platinum) alloys, submitted to J. Alloys Comp. [12] I. Barin and O. Knacke, Thermochemical Properties oflnorganic Substances, Springer, Berlin, 1973. [13] R. Huttgren, P.D. Desai, D.T. Hawkins, M. Gleiser, K.K. Kelley and D.D. Wagman, Selected Values of the Thermodynamic Properties of the Elements, ASM, Metals Park, OH, 1973. 114] F.R. de Boer, R. Boom, W.C.M. Mattens, A.R. Miedema and A.K. Niessen, Cohesion in Metals, North-Holland, Amsterdam, 1989. [15] B. Predet and W. Vogelbein, Thermochim. Acta, 13 (1975) 133. [16] E.Th. Henig, H.L. Lukas and G. Petzov, Z. Metallkd., 73 (1982) 87. [17] S.P. Yatsenko and E.N. Dieva, Russ. J. Phys. Chem., 47 (1973) 1658. [18] C. Colinet, A. Bessoud and A. Pasturel, Z. Metallkd., 77 (1986) 798. [19] W. Vogelbein, M. Ellner and B. Predel, Thermochim. Acta, 44 (1981) 141. W. Vogelbein, Thesis, University of Stuttgart, 1976.
ALLOYS
ANDCONPOUND5 ELSEVIER
Journal of Alloys and Compounds 220 (1995) 189-192
The limiting molar partial enthalpies of mixing of iron, cobalt, nickel, palladium and platinum in liquid gallium and indium P. Anres a R. H a d d a d a D. E1 Allam a M. Gaune-Escard a j.p. Bros a E. Hayer a Universitd de Provence, IUSTI-CNRS UA 1168, Avenue Escadrille Normandie-Niemen, 13397 Marseille Cddex 20, France b University of I/~enna, Institute of Inorganic Chemistry, Wahringerstrasse 42, 1090 Vienna, Austria
Abstract Gallium and indium have been used as solvents for the determination of the molar partial enthalpy of mixing Amah~,(TM, Ga or In) (denoting liquid transition metal (TM) in infinite liquid gallium or indium) of the pure liquid transition metals Fe, Co, Ni, Pd and Pt by direct reaction calorimetry between 1000 K and 1500 K with the exception of Amixh°(Fe, In) (because of the shape of its equilibrium phase diagram). All the limiting enthalpies listed below refer to the liquid state. With pure gallium as solvent, they correspond to the reaction TM(liq)-nGa(liq)
, TM1Gan(liq)
at the experimental temperature Te, with n >> 1. (i) A,,i,h~, in gallium is found for Fe, Co, Ni, Pd and Pt to be - 2 , -44, -82, -144 and -155 kJ mol-1. (ii) Am~xh° in indium is found for Co, Ni, Pd and Pt to be +28, -25, -127 and -114 kJ mo1-1. In both solvents, these limiting enthalpies vary with a similar trend. This observation makes it possible to predict the limiting molar partial enthalpy ~m~xh°(Fe, In) of mixing of iron in indium as +70 kJ mo1-1. The results have been compared with the data proposed by Miedema and co-workers. Keywords: Thermodynamics; Enthalpy of formation; High temperature calorimetry; Liquid alloys
1. Introduction
Information on the thermodynamic properties of binary alloys of group VIIIA transition metal (TM) (columns 8, 9 and 10 of the table of elements) with A1 or Ga or In binary alloys is very scarce. Only the phase diagrams, the crystallographic parameters of the intermediate compounds and a few experimental data (activities and enthalpies of formation) obtained from the solid state, are available. However, for the past few years, much information has been accumulated by our group on the thermodynamics of liquid binary alloys formed with Fe, Co, Ni, Pd or Pt and a group IIIB polyvalent element (aluminium, gallium and indium column 13) [1-5]. From a theoretical viewpoint, the determination of the excess properties of formation of the liquid phase provides information giving a better knowledge of the nature of the chemical bond in these metallic liquid binary alloys [6].
0925-8388/95/$09.50 © 1995 Elsevier Science S.A. All rights reserved SSDI 0925 -8388(94)06019-3
Experimental thermodynamic data obtained by high temperature solution calorimetry, using two metallic solvents (gallium and indium) with very similar chemical properties are presented below.
2. Experimental details 2.1. T h e c a l o r i m e t e r
All calorimetric measurements were performed with a very high temperature automated calorimeter (working temperature range, 1200 K-1700 K) described elsewhere; experimental details and precautions taken have also been published [7,8]. The calorimeter has been equipped with an automatic charger unit allowing 30 successive additions of samples (metals or alumina) to obtain enthalpy data on a wide molar fraction range. The main modification is the use of a long gas-tight alumina crucible (470 mm height and 12 mm external
P. Anres et al. / Journal of ,4lloys and Compounds 220 (1995) 189-192
190
diameter), the lower part of which fits snugly into the crown of thermocouples. The long tube extending up to the cold region of the calorimeter furnace prevents any contact of metal vapours with the thermocouples. Inside the alumina crucible a thin-walled boron nitride crucible is located in which the alloying process takes place. Before starting a series of measurements, the small crucible was charged with about 0.2-2 g gallium or indium (the larger mass of solvent allows the determination of the limiting molar partial enthalpy of mixing).
2.2. Materials A small gas flow of high purity argon (from Air Liquid Co.) was maintained in the experimental crucible and in the furnace during experiments. At the end of each experiment, the calorimeter was calibrated by means of five or six additions of a-alumina [9], correlating the measure of the thermoelectric signal vs. time curve and the corresponding enthalpies. High purity metals (99.999 wt.% TM) were employed. Generally these metals were rinsed with high purity acetone, dried and cut into small pieces. The purity of gallium and indium is 99.99 wt.% and 99.999 wt.% respectively. The gallium, melted under a dilute solution of hydrochloric acid (5%) in warm water, divided into small droplets, rinsed with cold distilled water after solidification, and then dried, was used without any purification step.
the molar fraction on the Ga- (or In-) rich side of systems. Moreover, this discrepancy leads to an uncertainty of about 0.5% in the enthalpies. Several factors influence the final accuracy: experimental temperature, chemical properties of pure metals (oxidability, vapour tension .... ), shape of the binary phase diagram ..... In this study, it is the nature of the binary system which is the main factor: if the phase diagram of the investigated binary alloy exhibits a liquid miscibility gap (as for example the Co-In system) the experimental time to reach complete equilibrium is long, and heat of mixing is weakly endothermic. In this case enthalpies of mixing were measured with an uncertainty of about +8%. On the contrary, when the phase diagram shows a large single liquid phase (as for example the Ga-Pd system) the equilibrium is quickly reached: in this case the enthalpy of mixing, strongly exothermic, was obtained at +5%.
3. Results
The enthalpy of formation of each binary system was measured in large temperature and molar fraction ranges; these experimental conditions are given in the following together with the corresponding literature references: Pt-Ga system: 1169< T (K) < 1461 and 0
2.3. Accuracy
Pd-In system: 1425< T (K) < 1679 and 0
Ni-Ga: 1304< T (K) < 1616 and 0
Table 1 E x p e r i m e n t a l a n d p r e d i c t e d [14] v a l u e s (in kilojoules per m o l e of T M ) of the l i m i t i n g partial m o l a r e n t h a l p i e s of liquid Fe, Co, Ni, P d a n d Pt in liquid g a l l i u m or i n d i u m as a s o l v e n t Solvent
Fe
Co
Ni
Pd
Pt
Ga (experimental)
- 2 - 5 4 [15] - 8
-44 - 6 6 [16] - 39
-82
- 144
- 155
-53
- 163
- 148
+ 28
-25 - 3 7 [18] - 3 3 [14] +5
-
- 114 - 1 2 9 [18] - 1 2 8 [19] -77
Ga (calculated) In ( e x p e r i m e n t a l )
+ 1.6 [17] In ( c a l c u l a t e d )
+63
+ 22
127 128 [18] 133 [19] 111
O u r d a t a listed in this t a b l e have b e e n d e t e r m i n e d by d i r e c t c a l o r i m e t r y b e t w e e n 1300 K a n d 1700 K. T h e v a l u e p r o p o s e d for Am~xh&(Fe, In) for liquid F e in infinite liquid In has b e e n o b t a i n e d by e x t r a p o l a t i o n . T h e previously p u b l i s h e d d a t a [15-19] are also indicated.
P. Anres et al. / Journal of Alloys and Compounds 220 (1995) 189-192
Using the heat capacities and the enthalpies of fusion of the transition elements published by Barin and Knacke [12] and Hultgren et al. [13] and assuming a constant Cp value for the liquid and the supercooled liquid slates the experimental results have been referred to the liquid state. From these measurements the main thermodynamic features may be deduced. (i) Taking into account the experimental uncertainty and the temperature range investigated, the enthalpy of formation of the TM + Ga and TM + In liquid systems may be considered as not temperature dependent (except for the I n + N i system), (ii) These melts exhibit strong departure from thermodynamic ideality: their enthalpies of formation are strongly negative for the (Ni or Pd or Pt) + (Ga or In) system and positive for the Fe- and Co-based alloys. The molar partial enthalpies of mixing of the group VIIIA transition metals in gallium and indium correspond to the reaction TM(liq) +nGa(liq)
191
-110
o E.
-115
E ~.
-12o
P o
.¢
-125 0
0,004
0,005
0,012
Xpt
Fig. 2. The Pt + In liquid system: partial molar enthalpies of liquid Pt (in kilojoules per mole of Pt) measured at 1169 K (Q) and 1173
(o).
K
100
I
I
/'~
inGa I
0 in In
~ TMlGan(liq)
with n :>>1. Performing consecutive additions of the TM, the reaction was given by TM(liq) + TM~Ga~(liq) -
""
m
> TM~+aGa~(liq)
The corresponding limiting enthalpies have been extrapolal:ed to xTM = 0, xTM being the molar fraction of TM, from the graph of the partial molar enthalpies by takir~g the experimental enthalpies at the mean molar fractiorL
\
!
o E
0
\
A \
\A I-\
E
0
e-
XTM, i = (XTM, i 4- 1 " ~ X T M , i ) / 2
where J: is the number of the addition. Moreover, special experimental runs have also been performed on the Ga- and In-rich side, on very short molar fraction ranges (0
.x -100
E
-200
I Fe Atomic
-150
I Co
I Ni number
Fig. 3. Trends of the variation in Ami~h°(TM, Ga or In) for liquid TM in infinite liquid gallium or indium vs. the position of the transition metal in group VIIIA: ~, extrapolated value of Amixh~(Fe, In).
o
E. -155
-160 0,004
Xpt
0,008
Fig. 1. The Pt + G a liquid system: partial molar enthalpies of liquid Pt (in kilojoules per mole of Pt) measured at 1169 K.
those predicted by Miedema and co-workers [14]. Experimental data given in the literature are also given in Table 1 to allow a comparison: the limiting molar partial enthalpies of nickel, palladium and platinum in liquid indium obtained by Predel and co-workers [19] and Colinet et al. [18] are in good agreement with our
192
P. Anres et al. / Journal of Alloys and Compounds 220 (1995) 189-192
results. On the other hand, other experimental data already published [15-17] show large discrepancies with our results. Fig. 3 shows the trend of variation in Amixh°(TM liq.) with respect to the position of the transition metal in the periodic table. With liquid gallium or liquid indium as a solvent the trends are similar. Thus the limiting molar partial enthalpy of liquid iron in liquid indium may be predicted as about + 7 0 kJ mol-1. This value can be compared with that proposed by Miedema and co-workers: +63 kJ mo1-1.
4. Conclusion The calorimetric determinations of Am~h~(TM, Ga or In) for a TM liquid in infinite liquid gallium or indium of the following pure liquid transition metals (TM = Fe, Co, Ni, Pd and Pt) point to the following. (i) The enthalpy of mixing is not dependent on temperature, except for the In + Ni system. (ii) A high negative value of Amixh°(TM) when TM is Ni, Pd and Pt corresponds to a transfer of electrons from the sp metal to the transition metal. (iii) A similar trend is found for the variation in Amixh°(TM) vs. the position of the transition metal in group VIIIA for Ga and In as a solvent. This observation makes it possible to predict the limiting molar partial enthalpy Amixh°(Fe, In) of mixing of iron in indium as + 70 kJ mol- 1 (iv) W h e n Pd a n d Pt a r e dissolved in gallium a n d indium, a quite correct agreement is found between predicted values of Amixh°(W!VI) proposed by Miedema and co-workers [14] and our experimental results.
References [1] D. El Allam, Th~se de l'Universit~ de Provence, Marseille, 1989. [2] R. Haddad, Thdse de l'Universit~ de Provence, Marseille, 1993. [3] D. El Allam, M. Gaune-Escard, J.P. Bros and E. Hayer, Metall. Trans. B, 23 (1992) 39. [4] D. El Allam, M. Gauue-Escard, J.P. Bros and E. Hayer, submitted to Metall. Trans. B. [5] R. Haddad, M. Gaune-Escard and J.P. Bros, The Fe-Ga system: enthalpy of formation, TMS Meet., San Francisco, CA, 1994. [6] E. Hayer and J.P. Bros: The Fermi energy and the enthalpy of mixing, Thermodynamics of Alloys, Genova, April 25-28, 1994. [7] G. Hatem, P. Gaune, J.P. Bros, F. Gehringer and E. Hayer, Rev. Sci. Instrum., 52 (1981) 585. [8] E. Hayer, F. Gehringer, M. Gaune-Escard and J.P. Bros, Joum. Calorim~trie Anal Therm., 18 (1987) 317. [9] NIST: National Institute of Standards and Technology, US Department of Commerce, Washington, DC, 1989. [10] P. Anres, M. Gaune-Escard and J.P. Bros, Thermodynamics of the P t + G a liquid system, to be published. [11] P. Anres, M. Gaune-Escard, J.P. Bros and E. Hayer, Enthalpies of formation of liquid (indium+ platinum) alloys, submitted to J. Alloys Comp. [12] I. Barin and O. Knacke, Thermochemical Properties oflnorganic Substances, Springer, Berlin, 1973. [13] R. Huttgren, P.D. Desai, D.T. Hawkins, M. Gleiser, K.K. Kelley and D.D. Wagman, Selected Values of the Thermodynamic Properties of the Elements, ASM, Metals Park, OH, 1973. 114] F.R. de Boer, R. Boom, W.C.M. Mattens, A.R. Miedema and A.K. Niessen, Cohesion in Metals, North-Holland, Amsterdam, 1989. [15] B. Predet and W. Vogelbein, Thermochim. Acta, 13 (1975) 133. [16] E.Th. Henig, H.L. Lukas and G. Petzov, Z. Metallkd., 73 (1982) 87. [17] S.P. Yatsenko and E.N. Dieva, Russ. J. Phys. Chem., 47 (1973) 1658. [18] C. Colinet, A. Bessoud and A. Pasturel, Z. Metallkd., 77 (1986) 798. [19] W. Vogelbein, M. Ellner and B. Predel, Thermochim. Acta, 44 (1981) 141. W. Vogelbein, Thesis, University of Stuttgart, 1976.