L.
1736
w. DILLER,R. L. ORR A N D RALPHHULTGREN
Acknowledgment.-The authors wish to thank Professor E. L. King for helpful discussions concerning this work. This work was supported in
Vol. 64
part by the Research Committee of the Graduate School from funds supplied by the Wisconsin Alumni Research Foundation.
THERMODYNAMICS OF THE LEAD-ANTIMOXY SYSTEM' BY LINDAWARNERDILLER,RAYMOND L. ORRAND RALPHHULTGREN Department of Mineral Technolopg, University of California, Berkeley, California Received M o y $1, 1960
Heats of formation of solid a-phase Pb-Sb alloys have been measured by solution calorimetry. These data have been combined with previously known data in the liquid state and the phase diagram to complete the thermodynam.i!iq description of the a-phase. The thermodynamic data for both solid and liquid alloys and the phase dlagram have been critically evaluated and discussed, and selected thermodynamic properties have been tabulated. An attempt is made to interpret the unusually large positive values found for the excess partial molar entropy of Sb in the a phase.
Introduction Although a considerable number of thermodynamic measurements have been made on liquid Pb-Sb alloys, there exist none a t all on the alloys in the solid state. Thermodynamic properties of the I'b-rich solid phase are calculable from the phase diagram and the liquid data, but entropies of formation so derived seem imdausiblv high (e.g., AS;;; = 10.8 e.u. a t ZSb '= O.O& a i d 525OK.). _-_ I n o&er to establish better the thermodynamic properties of the solid phases, it was decided to measure directly heats of formation within the Pb-rich (a) solid solution. These data, together with a critical analysis of the liquid data and the phase diagram, are presented in this paper. Experimental Materials.-Antimony in the form of rods was obtained from Johnson-Matthey and Go., Ltd., Toronto, Canada, who stated it to be 99.9+% pure. Lead rods specified to be 99.998% pure were obtained from the American Smelting and Refining Co. Preparation of Alloys.-Four 10-g. ingots, containing 2.00, 3.00,4.00 and 5.00 at. .% Sb, all in thea-solid solution range, were prepared by melting together at 500" the weighed components in evacuated, sealed Vycor tubes. The tubes were shaken briskly for five minutes while in the furnace, then quenched rapidly in ice-water to minimize segregation. Weight losses on fusion were less than 0.03%; the weighed compositions of the alloys were therefore taken to be correct. The ingots were cold worked, resealed in evacuated Pyrex tubes, and homogenized for seven weeks a t 252", the eutectic temperature. They were again quenched in ice-water and stored in a refrigerator until used. Filings taken from both ends of each ingot mere strain annealed at 250" and quenched in ice-water. The sharp X-ray diffraction lines obtained from the filings indicated the alloys to be homogeneous. Measured lattice constants were in excellent agreement with the measurements of Tyzack and Raynor,* while disagreeing with the older measurements of Ageev and K r ~ t o v . ~ Apparatus and Methods.-Heats of solution in liquid P b of pure Sb and the alloys were measured using the ralorimetric apparatus and methods described previously.4 Samples were dropped from an initial temperature, Ti, near 52OCK., into the lead-bath at temperature Tt, near
-
( I f Based on a thesis by Linda Warner submitted in partial satis-
faction of the requirements for the degree of Master of Science in Engineering Science to the University of California, 1959. This work was supported in part by grants from the Office of Ordnance Research, U. S. Army, and the U. S. Atomic Energy Commission. (2) C . Tyaack and G. V. Raynor. Acta Cryst., 7, 505 (1954). (3) N. V. Ageev and I. V. Krotov, J . Inst. Metals, 69, 301 (1936). (4) R . L. Orr, A, Goldberg and R . Hultgren, Reu. Sci. Instr., 28, 767 (1957).
677°K. The heat capacity of the calorimeter was determined by dropping specimens of pure Pb from room temperature, using the heat content values of Kelley.6 From these data heats of formation a t temperature Ti were calculated in the usual way.' During the runs the concentra tion of Sb in the liquid Pb-bath never exceeded 0.4 at. 3. Within this dilute range the heat of solution of Sb was mdependent of Sb concentration within the experimental uncertainty.
Results The experimental results are given in Table I. The heats of formation have been referred to a common temperature, 525" K. , assuming Kopp's law of additivity of heat capacities in correcting the results for the small deviations of Ti from that temperature. The heats of formation (Fig. 1) appear to be best represented by the straight line, AH = 6300xsb, with an average deviation of 14 cal./g.-atom. The relative partial molar heat .b = contents thus obtained are M P b = 0 and A& 6300 cal./g.-atom. TABLE I EXPERIMENTAL RESULTS AHtam.,
Sample comp., at. % Sb
100.00
2.00
3.00 4.00 5.00
OK.
Tt,
no.
OK.
A Hao~n. cal./g.atom
64-3 64-15 65-3 65-15 64-5 65-13 647 65-11 6411 65-7 64-13 65-5
523.7 519.1 523.5 514.9 523.6 515.6 526.5 519.7 522.3 526.0 522.5 522.4
676.6 677.3 676.5 677.2 677.5 677.5 677.6 677.3 677.8 677.3 677.8 677.3
5652 5713 5729 5692 2190 2264 2130 2203 2195 2151 2130 2117
I
Run
Ti,
525'K.. cal./g.atom
138 124 220 188 211 234 310 321
Selecting from published data the value (HWK 1000 cal./g.-atom for Sb, the relative partial molar heat of solution of Sb(,, at infinite dilution in Pba, at 677°K. may also be evaluated from the data yielding
- H 6 r 6 0 ~=)
ARSb. 677OK. m b - 1 = 4670 Cd./g.-atOm (5) K. K. Kelley, U. S. Bur. Mines Bull. 584, 1960.
THERMODYNAMICS OF THE LEAD-ANTIMONY SYSTEM
Nov., 1960
Evaluation of Thermodynamic Data Phase Diagram.-The selected diagram of Hansen6 is shown in Fig. 2. The liquidus is estimated to be accurate to f 2 ' from 0 to 25 at. % Sb, and there is good agreement in published n-ensurements of the liquidus from 87 to 100 at. % Sb. However, in the intermediate ranges there is wide dix-ergence in reported liquidus temperatures, due, probably, to strong tendencies to supercooling. The Pb-rich solidus and solvus seem to be reasonably well established. For the Sb-rich solidus and solvus no accurate data exist. Hansen concludes that the solubility of P b in Sb a t the eutectic temperature lies between 1.5 and 2.7 at. %. The eutectic temperature seexns to have been well established a t 251.5 f 0.5'. Liquid Alloys.-The e.m.f. measurements of Seltz and DeWitt' and Elliott and Chipman* are in excellent agreement, not only in free energies derived from them, but also iii ent,ropies calculated from their temperature coefficients. These data have been used in evaluating the thermodynamic properties of liquid alloys given in Table IT. Later e.m.f. measurements of Eremenko and Eremenko,S while showing more scatter, check well .i\-ith the free energies of the former investigators. Their entropies agree well a t high Sb content,s (m, = 0.7 - 1.0) but diverge to values lower by as much as 0.15 e.u. a t lower Sb contents. Fig. 1.-Integral
heats of formation of a-phase leadantimony alloys at 525'K.
TABLE TI LIQUIDALLOYSAT 900°K. (1 - z)Pbn) rSbw = [Ph~-~Sn,lo)
+
xsb
0.1 .2 .3 .4 .5 .6 .7 .8 .O
AF,
AH,
cal./g.atom
cal./g.atom
-
625 - 970 -1195 -1325 -1365 (130) -1325 -1200 - 975 - 625
I
I
AS. e.u.
0.70 10 0 1.08 -20 1.31 1.43 -40 1.45 -GO (5100) (3xO.11) 1.39 -70 -80 1.24 1.00 -70 -50 0.64
UPb
0.899 .794 .685 .575 ,466
(iO.008) .361 ,261 .187 .079
1737
QSb
600
( 8 ) M. Hansen and X. Anderko, "Constitution of Binary Alloys," 2nd Edition, McGraw-Hill Book Co., Inc., New York, N. Y., 1958. (7) H. Seltz and B. J. D e w i t t . J . Am. Chem. Sac., 61,2594 (1939). (8) J. F. Elliott and J. Chipman. ibid... '78.. 2682 (1951). . . (9) V. N. Eremenko and 0. M.Eremenko, Ukrain. Khim. Zhur., 18, 232 (1952). (10) M. Kawakami, Sei. Repta.. Tohoku I m p . Uniu., 19, 521 (1930). (11) W. Oelsen, F. Johannsen and A. Podgornik. Z . Errbergbau Melallhzcttenw., 9,459 (1956). (12) E'. Wiist and R. Durrer, Forsch. Gebiete Ingenieurn., 341, 3 (1921).
t I
LIQUID
0.080 .166 .259 .360 .465 (zk.008) .573 .682 ,791 .897
Calorimetric determinations by Kawakami'o of heats of formation by direct reaction agree in general with the selected values with a maximum deviation of - 70 cal./g.-atom. Oelsen, Johannsen and Podgornikl' calculated integral heats of formation from measurements of heat contents of solid and liquid alloys, obtaining results as much as 125 cal./g.-atom more exothermic. Wiist and DurrerI2 by a similar method checked the selected values better but with wider scatter. I n this case it was felt that the values obtained from the
I
1
0 0
Fig. 2.-Phase
20
40 ATOMIC
80
60
PERCENT
I00
Sb,
diagram of the lead-antimony system.
temperature coefficients of e.m.f. measurements were more reliable than the calorimetric. Solid Alloys.-The only thermodynamic measurements on solid alloys are the heats of formation reported in this paper. However, since the aphase liquidus and solidus are reasonably well established, free energies along the solidus can be calculated from the liquid data and the principle that partial molar free energies (or activities) of
1738
L. W. DILLER,R. L. ORR AND RALPHHULTGREK
each component are equal across the two-phase region when referred to the same standard state. The change in reference state requires an evaluation of the free energies of melting of the pure components at, the temperatures concerned. This may be done with fair certainty in the case of P b as its entropy of fusion (1.89 e.u.) is accurately known and the liquidus temperatures lie within 0 to 75” of its melting point. The change of reference state involves some problems in the case of Sb, however, as its entropy of fusion is not well established. However, the liquid alloy at the eutectic temperature and composition is in equilibrium with nearly pure Sb. Taking the concentration of Sb in the Sb-rich solid phase to be 98 at. % and assuming Raoult’s law, A&, = -22 cal./g.-atom in the (loexisling liquid phase referred to solid Sb. If the average entropy of fusion of Sb between 525°K. and the melting point, 903”K., is assumed to be 5.39 e.u., this value of A F S b at 525°K. will be in accord with the tabulated values of AFsb and for the liquid state. assuming A G s b = 0. Since this entropy of fusion is in reasonably good agreement with the scattered experimental values, it was adopted in referring liquid free energies to the solid components as standard states. Hence, partial molar free energies for P b and Sb in the a-phase can be calculated along the solidus. By assuming Kopp’s law of additivity of heat capacities, it is now possible to calculate the thermodynamic func>tions_for all temperatures and compositions. The AH values experimentally determined at 525°K. also apply at the solidus temperatures; hence values of AS al_ongthe solidus may be calculate4 from A F and AH for each component. These A S values are valid a t all temperatures. Slight adjustments are necessary to fulfill the Gibbs-lhhem conditions ; Raoult’s law applies to P b and Henry’s law to Sb well within experimental error. Results calculated for 525°K. are summarized in Table 111. Along the a-phase solvus line, where there is equilibrium with nearly pure Sb, A&, should lie between 0 and -22 cal./g.-atom. For the tabulated values and Hansen’s phase diagram, this is not quite the case. Agreement is obtained only if slightly larger solubilities of Sb in P b are assumed (the maximum increase being about 0.5
Vol. 64
TABLEI11 SOLID CY-PHASE ALLOYS AT 525OK. (1-r) ~ S b ( s= ) [Phl-z Sbzl (a)
+
Z S ~
0.01 .02 .03 .04
.05 .058
AF, oal./g.atom -30 -45 -50 (110) -60 -60 -60
AH,
cal./g.atom 65 125 190 (f20) 280 315 365
AS, e.u.
0.18 .32 .46 (zk .04) .59 .71 .81
aPb
0,990 ,980 ,970 (.t ,010) 960 ,950 .942
a8b
0.169 ,338 ,507 (+ ,024) ,676 ,845 ,980
at. % Sb a t 220’). The solvus curve given by Hansen6 is based solely on the solubility measurements of Obinata and Schmid13except a t the eutectic temperature where the value (5.8 at. % Sb) of Pellini and Rhines, l 4 derived from solidus measurements, is accepted. Since a straightforward extrapolation of Obinata and Schmid’s solubilities to the eutectic would lead to a smaller value (5.0 at. % Sb), it seems possible that all their solubilities may be low, in agreement with these calculations, due perhaps to precipitation in their quenched samples before X-raying.
Discussion The excess partial molar entropy found here for Sb in the a-phase, independent of composition, is A$: = 6.38 f 0.21 e.u. While this value is less than that obtained previously from the liquid data and phase diagram alone, it is still much larger than those usually encountered (0-1 e.u.) in similar eutectic systems. It seems likely that the large positive contribution to A%b is a t least partly due to an increase in the vibrationalentropy of Sb in the lattice of the Pb-rich solution over that in the pure metal. The “looser” nature of the Pb lattice is suggested by the high entropy of pure P b a t 525°K. which is about 4.8 e.u. higher than that of Sb a t the same temperature. That the vibrational entropy of pure solid Sb is abnormally low is iiidicated by its large entropy of fusion, 5.39 e.u., which is about 3 e.u. larger than for most other metals. The relatively high value of A H S b , 6300 cal./g.-atom, may also partly result from the absorption of increased vibrational energy. (13) I. Obinata and E. Schmid, Metallwirtschaft. la, 101 (1933). (14) W. S . Pellini and F. N Rhines, Trans. A I M & , 182, 65 (1943).
