Enthalpies of Formation of Liquid and Solid (Gallium + Palladium) Alloys

DRISS EL ALLAM, MARCELLE GAUNE-ESCARD, JEAN-PIERRE BROS, and ERHARD HAYER

The enthalpies of formation of liquid (Ga + P d ) alloys were determined by direct reaction calorimetry in the temperature range 1322 < T / K < 1761 and the molar fraction range 0 < xpd < 0.87. The enthalpies are very negative with a minimum Ami• = - 7 0 . 4 -+ 3.0 kJ mol- at xpd = 0.6, independent of the temperature. Limiting partial molar enthalpies of palladium and gallium were calculated as Ahm (Ga liquid in *cliquid P d ) = - 2 6 5 +- 10 kJ mo1-1 and Ahm (Pd liquid in ~liquid Ga) = - 1 4 4 + 5 kJ mol 1. The integral molar enthalpy is given by AmixH m = x(1 - x) ( - 143 .73 - 232.47x + 985.77x 2 - 4457.8x 3 + 6161.1x 4 + 2577.4x5), where x = xpd. Moreover, values for the enthalpies of formation and fusion of PdGa, PdzGa, and the solid solution (with xpd = 0.8571) have been proposed. These results have been dis- cussed taking into account the equilibrium phase diagram.

I. INTRODUCTION

T H E R E is not much information available on the palladium-gallium system. The phase diagram of Elliott, Ixl redrawn by Massalski, 121 is shown in Figure 1. The crys- tallographic parameters and the stability range of the five compounds PdGas, Pd3GaT, PdGa, PdsGa3, and PdzGa are well known: I1,31 PdGa5 (body-centered tetragonal), Pd3Ga7 (cubic, Ir3Sn7 type), and PdsGa3 (orthorhombic, Ge3Rh5 type) melt peritectically at 473, 733, and 1278 K, respectively. GaPd (cubic, FeSi type) melts at 1318 K, and PdzGa (orthorhombic, Co2Si type) melts congruently at 1538 K. A high-temperature phase, Pdo.55Gao.45 (W type), existing above 1200 K has been confirmed by Khalaff and Schubert.J4] The existence of another high-temperature phase, Pd0.szsGa0.475, has been claimed. I31 All compounds show a very small homoge- neity range except PdzGa at high temperatures. The Pd3Ga phase reported by Elliott t~J according to Schubert et al.,t31 was reinvestigated by Khalaff and Schubert, I41 and alternatively, the formation of three phases, Pd7Ga3, PdsGa2, and Pdl3Gas, has been reported. The limits of the Pd-rich terminal phase are not yet known.

Pratt et al. I51 and Vogelbein et al. I61 measured enthal- pies of formation of PdGa and of Pdo.ssGa012 and Pdo.vsGa0.25, respectively. No free energy measurements were apparently performed on this system. Since no en- thalpy data of the liquid alloy phase were measured, the present investigation was undertaken.

This research is part of a systematic study of the thermodynamic properties of liquid binary alloys with A1, Ga, and In. I7,81

DRISS EL ALLAM, formerly Ph.D. student, Universit6 de Provence, MARCELLE GAUNE-ESCARD, Director of Research, and JEAN- PIERRE BROS, Professor, Universit6 de Provence, are with SETT-UA 1168, Centre de Sainte Jrrrme, Av. Escadrille Normandie-Niemen, 13397 Marseille Cedex 13, France. ERHARD HAYER, Assistant Professor, University of Vienna, is with the Institute of Inorganic Chemistry, Wahringerstr. 42, 1090 Vienna, Austria.

Manuscript submitted January 21, 1991.

II. EXPERIMENTAL PROCEDURE

High-purity metals (99.999 wt pct Pd plate from ALFA-Ventron, Karlsruhe, Federal Republic of Germany, and 99.99 wt pct Ga rods from Koch and Light Ltd., London) were employed in this study. The palladium was rinsed with acetone pa dried, and cut into small pieces. The gallium was melted under a dilute solution of hy- drochloric acid (5 pct) in warm water, divided into small droplets, and dried after rinsing with cold distilled water.

Measurements at 1322 < T / K < 1760 were per- formed using a very high temperature (THT) calorimeter of the Eyraud-Petit type described elsewhere. E9"l~ It was equipped with an automated thermostated sample charger, t1~ The calorimeter cell employed was an alu- mina tube closed at the lower end, with about 0.012-m external diameter and 0.47-m height. At the closed end, it was shaped to fit the thermopile dimension. The al- loying process was performed in a thin-walled graphite crucible of about 0.050-m height and 0.0065-m inside diameter. The crucible fits tightly in the alumina tube. Before starting a series of measurements, the crucible was charged with about 0.2 to 0.5 g Ga and put into the long alumina tube. The alumina tube extending to the cold region of the calorimeter furnace prevented any contact of the metal vapors with the thermocouples. High- purity argon was passed over a Cu-based catalyst held at 420 K and over a titanium sponge heated to 1120 K before entering the calorimeter compartment. A small flow of argon was maintained while measurements were performed by a series of direct additions of Pd to the liquid bath formed by Ga and the alloy. The calorimeter was calibrated either from the first additions of the pure element or from supplementary additions of c~-alumina (NISTII,I).

Enthalpy contents of the added material were taken for palladium from Barin and Knacke 1121 assuming a con- stant Cp for the liquid and the supercooled liquid phase. Some other published enthalpy contents for palladium exist. However, Cp data and enthapy contents of Pd given by Hultgren et al. 1~31 are not consistent. Treverton and Margrave I141 measured the heat contents of solid Pd at

METALLURGICAL TRANSACTIONS B VOLUME 23B, FEBRUARY 1992--39

0

L

B

Weight P e r e e n L

o to ao 3o 4o ~o 6o 1600 +~ . . . . . . ~- , - - - + . . . . , ' +~ . . . . . : . . . . . . . .

?+

+l

4 1 4 0 0 ~

L

I000-~

t 8 0 0 -~

4

goo -1

P a l l a d i u m 70 80 90 I00

j+ s sS

s SS s S ~ L

I:~85~

I | I I

s J s J

j J S J

J J 7

s S I

/

/ I

4 (ed)

\

I I i

200-I / ~ GaLled -

0 ~r . . . . . . . . . . . . . j t . . . . . . . . o i'o 2'o Ga

Fig. l - - P h a s e d i a g r a m o f the G a - P d sys t em, pl

30 40 S0

A t o m i c P e r c e n t

0-I

sb r'o So g'o ~oo

Palladium Pd

the melting point and of liquid Pd at temperatures above. Their results indicate an enthalpy of fusion of Pd lower by 0.8 kJ mol -~ than Barin and Knacke's value. Taking into account that the experimental temperatures in the present work were below the range of Treverton's mea- surements tt4j and since the difference to Barin and Knacke I121 is not significant, those data were not applied. Enthalpy contents for gallium were taken from Gluschko et al . E~51 and for the a-alumina from NIST. I~q

Two series of measurements were started with empty crucibles, dropping at first some solid palladium bits fol- lowed by small pieces of solid gallium. The correspond- ing integral enthalpies of formation of solid Pd are - 17.00 and - 17.64 kJ mol ~ calculated at 1400 K and 1761 K, respectively, from the difference between the enthalpy contents of solid Pd and supercooled Pd taken as the ref- erence state. Accordingly, the data were marked with a dagger in Table I. However, only a few concentrations could be measured at the Pd side. Measurements at 1761 K starting from pure Pd had to be recalculated for the higher Ga concentrations due to the loss of some Ga during the drops. In Table I, recalculated values are marked by a double dagger. Nevertheless, partial en- thalpies connected with these data were not affected by the recalculation. For all other series investigated, the difference between the mass of the alloy at the end of the experiment and the sum of the metals put into the calorimeter cell was less than 1 mg. That discrepancy corresponding to about 0.1 pct of the mass of the sample

caused uncertainties of about (a) 0.2 pct in the molar fraction and (b) 0.1 pct in the integral enthalpies.

Errors in the results were estimated to be of the same order of magnitude as the scatter determined by calibra- tion drorps of a measurement series, which varied be- tween 1.5 and 3 pct. The main sources of error were heat-transfer processes during the drop. From calibration measurements with pure gold, an absolute temperature uncertainty of about -+2 K was determined. In that way, a negligible error of about -+0.1 kJ mol 1 was generated in the experimental enthalpies.

Enthalpies of the formation of solid alloys were de- termined by direct reaction calorimetry analogous to the measurements on liquid alloys but with the exception that solid alloys were formed on the addition of one of the constituents. In a series of measurements, the precipi- tation of solid alloys is indicated by a break in the en- thalpy vs concentration curves. In Table I, those alloy data with solid phases present were marked by a double asterisk. However, some enthapies taken at 1322 K could not be unequivocally assigned to liquid or solid alloy formation. In these cases, the data have been marked with an asterisk.

I I I . RESULTS AND DISCUSSION

The experimental integral molar enthalpies of forma- tion (AmixHm) of liquid and solid alloys are given in Table I. Some enthalpies of the liquid phase referred to

4 0 - - V O L U M E 23B, FEBRUARY 1992 METALLURGICAL TRANSACTIONS B

Table I. Molar Integral Enthalpies of Formation of (Pd + Ga) Alloys Referred to Liquid Ga and Supercooled Liquid Pd (A~ixHm in kJ m o l - b

T/K = 1322 T/K = 1397 T/K = 1410

x(Pd) 0.0000 0.0484 0.0940 0.1368 0.1776 0,2157 0.2505 0.2840 0.3153 0.3451 0.3736 0.4013 0.4275 0.4526 0.4771 0.5001 0.5221 0.5425 0.5619 0.5810 0.5987

AH 0.00

- 6.96 -13 .52 -19.81 -25 .76 -25.46* -30.70* -35.73* -35.00* -34.33* -49.63 -53 .64 -61 .02 -64 .13 -66 .90 -86.07** -78.13"* -72 .91" -73.74* -74 .19" -71 .26"

x(Pd) zMt/ 0.0000 0.00 0.0540 - 7.59 0.1026 -13 .94 0.1472 -20 .83 0.1880 -26 .26 0.2275 -31.61 0.2642 -36 .59 0.2977 -41.07 0.3285 -45.01 0.3607 -49 .16 0.3912 -52 .72 0.4202 -56.71 0.4468 -59 .14 0.4732 -61 .23 0.4974 -62.88 0.5209 -64 .09 0.5433 -64 .53 0.5637 -65 .72 0.5837 -66 .14 0.6031 -66.18 0.6225 -65.35

T/K = 1410 T/K = 1461

x(Pd) AH 1.0000 -17 .00 ' 0.8571 -44.92** 0.7431 -60.88** 0.6554 -88.91"* 0.5852 -75.51"* 0.5253 -70 .2 0.4740 -64 .5 0.4308 -58.93 0.3947 -54.23 0.3642 -50.18 0.3378 -46 .68

x(pd) AH 0.0000 0.00 0.4888 -66 .30 0.5860 -71 .79 0.6468 -70.48 0.6912 -67 .14"* 0.7227 -57.85** 0.7473 -53.73** 0.7669 -49.91 0.7832 -46 .92 0.7964 -44 .26 0.8079 -41 .97"*

0.3142 -43 .42 0.292 -40 .22 0.272 -37 .52 0.2544 -35 .10 0.2383 -32.81 0.2232 -30 .80 0.2661 -35 .74 0.2546 -34 .24 0.2440 -32.73

T/K = 1517

x(Pd) ,M-/ 0.0000 0.00 0.1223 -16 .92 0.2314 -33 .64 0.3323 -47 .39 0.4135 -58 .70 0.4774 -65.93 0.5312 -70 .77 0.5895 -73 .14

x(Pd) AH 0.0000 0.00 0.032l - 4.63 0.0627 - 9.04 0.0921 -13 .06 0.1216 -17 .30 0.1509 -21 .39 0.1808 -25 .63 0.2091 -29.65 0.2367 -33 .46 0.2637 -37 .14 0.2889 -40 .57 0.3155 -44 .16 0.3413 -47 .5? 0,3661 -50.97 0.3895 -53.97 0.4121 -56 .70

T/K = 1457

x(Pd) A/-/ 0.0000 0.00 0.1221 -16 .72 0.2364 -32 .54 0.3285 -44.93 0.4061 -54 .72 0.4741 -62 .14 0.5331 -66.65 0.5827 -68 .70 0.6244 -68 .94 0.6586 -67 .00 0.6873 -65.26** 0.7116 -61.74"* 0.7339 -54.98** 0.7542 -52 .02 0.7717 -49 .30 0.7878 -46 .29 0.8036 -43.34** 0.8179 -41 .06"* 0.8310 -39.41"* 0.8436 -37.79** 0.8548 -36.39**

T/K = 1519

x(Pd) AH 0.0000 O. 00 0.0587 - 8.51 0.1124 -16.35 0.1624 -23 .77 0.2077 -30 .14 0.2594 -37 .84 0.3050 -44 .20

T/K = 1516 T/K = 1761

x(Pd) M-/ 0.0000 0.00 0.0581 - 8.45 0.1102 -16 .22 0.1617 -23.68 0.2082 -30.08 0.2538 -37 .62 0.3012 -44 .03

T/K = 1516

x(Pd) Nat/ 0.000 0.00 0.1684 -24.13 0.2916 - 4 t . 9 1 0.3972 -56.51 0.4831 -66 .22 0.5486 -71.55 0.5997 -72 .62

T/K = 1517

x(Pd) ~r / 0.0000 0.00 0.1682 -24.35 0.3060 -44 .42 0,4118 -58 .76 0.4951 -68 .10

T/K = 1520

x(Pd) ~ / 0.0000 0.00 0.0463 - 6.77 0.0941 -13.58 0.1416 -20 .34 0.1876 -26.93 0.2292 -32 .64 0.2669 -37 ,75 0.3057 -43.12 0.3411 -48.05 0.3771 -52 .94 0.4108 -57 .30 0,4718 -64,73 0.4986 -67.17 0.5235 -69 .32 0.5461 -70 .70 0.5683 -71 .52 0.5906 -72.07

x(Pd) 1.0000 -17 .49 t 0.8715 -33 .66 0.7699 -59.18 0.5539 -69 .01 ' 0.5765 -70.03* 0.6000 -70 .39 ~ 0.6238 -70 .24 ~ 0.6479 -69 .42 * 0.6704 -68 .20 * 0.6903 -66.64* 0.7085 -64 .92;

T/K = 1761

x(Pd) 0.0000 0.00 0.0353 - 5.31 0.0697 -10 .27 0.1042 -15 .19 0,1373 -19,78 0,1684 -24 .26 0.1979 -28 .57 0.2269 -32 .62 0.2554 -36 .64 0,2820 -40.17 0.3070 -43 .44 0.3318 -46 .72 0.3560 -50.48 0.3785 -53.25 0.4003 -56 .00 0.4208 -58.23 0.4404 -60 .42 0.4587 -62 .74 0.4762 -64.33 0.4930 -65 .66 0.5109 -67.28

*Presence of nonequilibrium solid phase(s) is not ascertained but possible. **Solid phase(s) present.

tSolid Pd referred to supercooled liquid Pd. *Values were recalculated due to the loss of some Ga.

l iquid Ga and supercooled liquid Pd are shown in Figure 2. The exper imental data presented in Figure 2 indicate a very strong interaction in the l iquid (Ga + Pd) alloys by the v-shaped enthalpy vs concentrat ion curve, with a min imum o f A m i x H m = - 7 0 . 3 -+ 3.0 kJ tool -1 at xpd = 0.59. Up to xpa = 0.40, the enthalpies are located at one curve, independent of the temperature of the mea-

surements. With the exception of the 1397 K series, which shows a min imum AmixHm = - 6 6 . 2 kJ tool 1, all other min imums in the enthalpies are found between - 6 8 . 1 and - 7 3 . 1 kJ tool l, not correlated with temperature. Given the large temperature range scanned (about 450 K) and the very high temperature o f the measure- ments, the scatter is very low. Thus, one can conclude

METALLURGICAL TRANSACTIONS B VOLUME 23B, FEBRUARY 1992--41

O E

<3

o

-20

-40

-60

-80 0,0

I i I , I I I

u

/ /

/

1 i /

/

./

x/ x/ /

I I I I

0,2 0,4 0,6 0,8 1,0 Ga x(Pd) Pd

Fig. 2--AmixH m = f(Xpd ). Some selected curves of the molar enthalpy of mixing vs palladium molar fraction at 1397 K (�9 1457 K (• 1517 K (~), and 1761 K (O).

no temperature dependence o f the enthalpies within the limits of the exper imental errors (1.5 to 3 pet). This phe- nomenon is also revealed by the Xi function being more sensitive to any deviat ions (Figure 3). Starting from the Xi function, AmixH,, was calculated by a least-squares method, taking into account the l iquid alloy data:

Xi = A raixnm/x( l - - X)

= ( - 1 4 3 . 7 3 - 232.47x + 9 8 5 . 7 7 x 2 - 4457.8x 3 + 6161. lx 4 - 2577.4x s)

with x = xpa. Smoothed values of the Xi function, enthalpy, and

partial enthalpies are g iven in Table II. Partial enthalpies were der ived by numerical differentiat ion of the integral data. The computed values are found very close to the exper imental partial enthalpies (Figure 4). The l imiting partial enthalpies of Ga in pure l iquid Pd and of l iquid Pd in pure l iquid Ga were computed to Ahm (Ga liquid in o01iquid Pd) = - 2 6 5 --- 10 kJ tool -~ and Ahm (Pd liq- uid in ~ l iqu id Ga) = - 1 4 4 -+ 5 kJ mol -~, respect ively.

The partial enthalpies of Pd v s concentrat ion (Figure 4) show a very small l inear dependence on the concentrat ion in the atomic fraction range o f 0 < Xpd <

o E

x

" 1 0 0 , I , I , I , I ,

-200 " ~ ~ - -

-300 \~'~'~=~#.~.u... /o/ / / o

-4OO 0,0 Ga

I I I I

0,2 0,4 0,6 0,8 1 . 0 Pd

x(Pd) Fig. 3 - -Xi = f(xpa). Xi function vs palladium molar fraction at 1322 K (O), 1397 K ([]), 1410 K ([]), 1457 K (A), 1520 K (�9 and 1761 K (O,&).

0.4 fo l lowed by a transition interval between 0.4 < Xpd < 0.75, raising the partial enthalpy values of Pd close to zero. Converse ly , in the concentrat ion range 0 < Xed < 0.4, the partial enthalpies of Ga are almost con- stant, with values close to zero fo l lowed by a change to

Table II. Smoothed Values of the Xi Function, Molar Integral, and Partial Enthalpies of Liquid

(Pd + Ga) Alloys between 1322 and 1761 K*

P~Pd Amixn m A h m ( P d ) Ahm(Ga) Xi

0.00 0.00 -143.7 0.0 -143.7 0.05 - 7.29 -145 .9 0.0 -153 .4 0.10 -14 .49 -142 .2 - 0.3 -161 .0 0.15 -21.49 -139 .2 - 0.7 -168.5 0.20 -28 .39 -138.7 - 0.8 -177 .4 0.25 -35.31 -139 .8 - 0.5 -188.3 0.30 -42.31 -140 .4 - 0.3 -201.5 0.35 -49 .26 -138 .4 - 1.3 -216 .6 0.40 -55.91 -132.3 - 5.0 -233 .0 0.45 -61 .84 -121 .3 - 13.2 -249 .9 0.50 -66 .56 -105 .9 - 27.2 -266 .2 0.55 -69.55 - 87.3 - 47.9 -281 .0 0.60 -70 .36 - 67.2 - 75.2 -293 .2 0.65 -68.67 - 47.6 -107.8 -301.8 0.70 -64 .34 - 30.5 - 143.3 -306 .4 0.75 -57 .46 - 17.1 -178 .4 -306 .4 0.80 -48.35 - 8.1 -209 .4 -302 .2 0.85 -37.51 - 3.0 -233 .0 -294 .2 0.90 -25 .55 - 0.9 -247 .7 -283 .9 0.95 - 12.97 - 0.2 -255 .6 -273 .0 1.00 0.00 0.0 -264.5 -264.5

*Values are in kJ mol ~. All data are referred to liquid gallium and supercooled liquid palladium.

42--VOLUME 23B, FEBRUARY 1992 METALLURGICAL TRANSACTIONS B

50

-50

-100

-150

-200

-250

-300 0,0 Ga

""" oq~ooo . ~ o - " ~ . * . ~'~

Ah(Ga) ~ o "\.\ /

. �9 \

\ Ah(Pd) \

\ \

k

0 , 2 0 , 4 0 , 6 0 , 8 1 ,0 x ( P d ) P d

Fig. 4 - - A h ~ ( G a ) = f(xpd) and Ah~(Pd) = f(xp~). Mola r part ial en- thalpies of mixing vs palladium molar fraction at 1410 K (~), 1457 K (O), 1520 K (IlL and 1761 K (~,[:]).

more negative data at higher Pd concentrations. In two- phase regions, partial enthalpies are constant. In the sys- tem investigated, the nearly constant partial enthalpies or the v-shaped enthalpy vs concentration curve could be taken as an indication of the formation of associates in the liquid phase. Similar effects have been found in other systems with strong interaction, e .g . , in the Au-A1 I71 and the Au-Ga tSj systems.

The strong interatomic attraction might be due to the d-electrons of Pd hybridizing with the s- and p-electrons of Ga. Colinet et al. t161 have applied hybridization model calculations to Pd-A1 and Pd-In liquid alloy systems, predicting that the energy of interaction is due to a hy- bridization of the atoms rather than to an interaction of ions in those alloys. Since there is no significant differ- ence between Pd-A1, Pd-Ga, and Pd-In systems, the hy- bridization model seems preferable.

In some measurement series, the formation of solid alloys was established. The enthalpies of formation of these solid alloys are given in Table III, comparing ex- perimental results with published data. Measurements at 1322 K indicate a crystallization of GaPd in the concen- tration range 0.48 < xed < 0.54. Although the thermo- couple error might be +2 K, the melting point reported by Elliott t~l seems to be too low. The molar enthalpy of fusion calculated by the difference in the enthalpies of formation of the liquid 1:1 alloy and solid GaPd, A~sHm(Pd0.50Gao.50) = 13.6 kJ mol - ' , relates to an en- tropy of fusion of about AfusSm(Pdo.50Gao 5o) = 9.4 J K ' mol - ' Pratt et al.ISl established the enthalpy of formation of GaPd to A//a~(PdosoGa0.50) = -72 .19 +- 0.26 kJ mol- ' referred to solid Pd and solid superheated Ga at 320 K. Referring to solid Pd and liquid Ga at 320 K, the en- thalpy is calculated to AiH,~(Pdo.50Gaos0) = - 7 5 . 0 + 1 kJ tool -1, showing good agreement with the high- temperature value of this work.

The enthalpy of formation of the compund PdzGa taken from the value measured at xvd = 0.6554 at 1410 K is calculated t o A /H~ : - 7 7 . 9 kJ mol 1 re- ferred to solid palladium and liquid gallium. An enthalpy of fusion AfusHm(Pdo.666Gao.334) = 20.6 kJ mol -l is computed from these data. With a differential scan- ning calorimetry apparatus, 12~ the enthalpy of fusion of a Pd2Ga sample was measured, retrieving Afusnm(Pd0.666Ga0.334) = 14.7 kJ tool ' from a melting interval 1553 < T / K < 1593, with a maximum at 1583 K. This value, however, is about the same order of magnitude, taking into account the extrapolation pro- cedure used to calculate the enthalpy of melting and the extension of the melting process by differential thermal analysis. Nevertheless, this value seems to be too small compared with the present work.

Furthermore, Table III shows the good agreement be- tween our result and the value obtained by Vogelbein et al.,I61 using the dissolution calorimetric method, for the Pdo 88Ga0,2 alloy corresponding to a one-phase solid solution. Nevertheless, the value proposed by Predel for the Pdo.75Gao25 alloy seems too small; in this case, the discrepancy may be attributed to the diphasic state of that sample. TM

Experimental enthalpies of Pd-A1, I~618"211 Pd-Ga (this work), and Pd-In IIgl are compared in Table IV, with data given by the Miedema and Niessen model. I~7~ Although the agreement between experimental and calculated data of the limiting partial enthalpies of Pd is surprisingly good, the difference in the other limiting data and the mini- mums of the enthalpy is eye-catching in the Pd-Ga and

Table I l l . Molar Integral Enthalpies of Formation of Some Solid (Pd + Ga) Alloys ( A I H m in kJ tool-')

(Referred to supercooled liquid Pd + liquid Ga)

AH I AH/(liq) (Referred to solid (Referred to supercooled P d + liquid Ga) AHfu s liquid Pd + liquid Ga) T / K

Ga0.5oPdo.50 -80.2 -+ 5 -71.7 --+ 5 13.6 -66.56 1322 -75.0 • 1 [4] 310

Gao.3333Pdo.6667 -88.9 • 5 -77.9 • 5 20.6 -67.51 1410 Gao.25Pdo.75 -59.2 --- 1.3 TM -57.46 1000 Gao.143Pd0.857 -44.9 • 5 -30.3 • 5 9.0 -35.87 1410 Gao.~2Pdo.88 -27.1 • 1.4 TM 1000

METALLURGICAL TRANSACTIONS B VOLUME 23B, FEBRUARY 1992--43

T a b l e I V . C o m p a r i s o n o f E x p e r i m e n t a l D a t a a n d T h o s e D e r i v e d f r o m M i e d e m a ' s M o d e l ( A f H m i n k J m o l - ~ ) *

Pd-A1 Pd-Ga Pd-In

- 198.8 t l6l - - 145 (this work) - 1291'91 - 1 7 7 . 5 tlSl -197.012~1

- 1 8 7 - 1 6 3 - 1 1 1 - 2 0 6 tlSl - 2 6 2 (this work) - 2 5 0 [191 - 1 7 6 - 1 7 0 - 1 3 7 - 53.01~81 - 70.4 (this work) - 60.0 [17]

0.6 0.59 0.6 - 4 6 - 4 2 - 31

0.5 0.5 0.5 PdGa Pd2Ga PdsGa

- 71.7 - 77.9 - 30.3 - 7 9 - 6 6 - 34

Ahm(Pd in ~A1 /Ga / In ) exp.

Ah~(Pd) calc. 1171

Ahm(A1/Ga/In in ooPd) exp. Ah~(A1/Ga/In in ~Pd) calc. [171 m m i x n m (minimum) exp. at Xpd

AmixHm (minimum) calc. I171 at xpd

A/Hm exp. (this work) A/Hm calc. I~71

*Liquid data are referred to both liquid constituents; solid data are referred to liquid gallium and solid palladium.

Pd-In systems. Despite unlike limiting partial enthalpies, the Miedema model computes the minimum of the en- thalpies at 50 at. pct. Furthermore, it fails to correctly predict the limiting partial enthalpy of Ga. Using a sort of subregular solution model which can be represented by a nearly linear dependence of the Xi function on the concentration, this model is not able to predict a big neg- ative hump like that detected with the Xi functions of the Pd-Ga and Pd-In systems.

Comparing experimental enthalpies of formation of the solid alloys measured with Miedema's calculation for PdGa, Pd2Ga, and PdsGa, the agreement appears much better. The compound with the most negative enthalpy of formation, however, is calculated at Xpd = 0.50, con- trary to the experimental results. Nevertheless, the dif- ference between calculated and experimental errors with the three alloys measured is lower than + 15 pct.

IV. C O N C L U S I O N S

The calorimetric measurements of the enthalpy of for- mation of Pd-Ga alloy performed between 1322 and 1761 K have shown the following:

1. the asymmetry of the AmixH m = f(Xpd ) function; 2. the nondependence of A~xH,, on the temperature within

the limits of experimental errors; and 3. the high negative value of AmixHm.

For the alloys of Pd with A1, Ga, and In exhibiting strong interactions and asymmetrical enthalpy curves, the Miedema model provides a poor description of the en- ergetics of these systems.

R E F E R E N C E S

1. R.P. Elliott: Constitution of Binary Alloys, 1st suppl., McGraw-Hill Co., New York, NY, 1965.

2. T.B. Massalski: Binary Alloy Phase Diagrams, ASM, Metals Park, OH, 1986, vol. 2, p. 1153.

3. K. Schubert, H. Lukas, H.G. Messner, and S. Bhan: Z. Metallkd., 1959, vol. 50, pp. 534-42.

4. K. Khalaff and K. Schubert: J. Less-Common Met., 1974, vol. 37, pp. 129-40.

5. J.N. Pratt, A.W. Bryant, and D.T. Underhill: Final Technical Report, United States Army Research Contract DAJA 37-70-C-0632, Jan. 1971.

6. W. Vogelbein, M. Ellner, and B. Predel: Thermochim. Acta, 1981, vol. 44, pp. 141-49.

7. E. Hayer, F. Gehringer, K.L. Komarek, M. Gaune-Escard, and J.P. Bros: Z. Metallkd., 1989, vol. 80, pp. 186-91.

8. E. Hayer, K.L. Komarek, M. Gaune-Escard, and J.P. Bros: Z. Metallkd., 1990, vol. 81, pp. 233-38.

9. G. Harem, P. Gaune, J.P. Bros, F. Gehringer, and E. Hayer: Rev. Sci. lnstrum., 1981, vol. 52, pp. 585-89.

10. E. Hayer, F. Gehfinger, M. Gaune-Escard, and J.P. Bros: JCAT, 1987, vol. XVIII, pp. 317-21.

11. National Institute of Standards and Technology, U.S. Department of Commerce, Washington, D.C., 1989.

12. I. Barin and O. Knacke: Thermochemical Properties oflnorganic Substances, Springer, Berlin, 1973.

13. R. Hultgren, 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.

14. J.A. Treverton and J.L. Margrave: J. Phys. Chem., 1971, vol. 75, pp. 3737-40.

15. W.P. Gluschko, L.W. Gurwich, G.A. Bergman, I.W. Weitz, W.A. Medvedev, G.A. Chatzkurusov, and W.C. Youngman: Thermodynamic Properties of the Elements, Nauka, Moscow, 1981, vol. III/I.

16. C. Colinet, A. Bessoud, and A. Pasturel: Z. Metallk. 1986, vol. 77, pp. 798-804.

17. A.R. Miedema and A.K. Niessen: "Cohesion in Metals. Tran- sition Metal Alloys," Report, Philips Research Laboratories, Eindhoven, The Netherlands. F.R. de Boer, R. Boom, W.C.M. Mattens, A.R. Miedema, A.K. Niessen: Cohesion in Metals. Transition Metals Alloys, North-Holland Publishing Co., Amsterdam, 1989.

18. N.A. Vatolin, Yu. S. Kozlov, and Yu. O. Esin: lzv. Akad. Nauk SSSR Metall., 1974, vol. 3, pp. 107-10.

19. D. E1 Allam: Thesis, Universit6 de Provence, Marseille, France, 1989.

20. Cp of a PdzGa sample prepared by us was measured as a courtesy by Netzsch Geratebau GmbH, Selb, France, 1989.

21. J.J. Lee and F. Sommer: Z. Metallkd., 1985, vol. 76, pp. 750-54.

44--VOLUME 23B, FEBRUARY 1992 METALLURGICAL TRANSACTIONS B