842
0. J. KLEPPA
Vol. 60
A CALORIMETRIC INVESTIGATION OF SOME BINARY AND TERNARY LIQUID ALLOYS RICH IN TIN BY 0. J. KLEPPA Institute f o r the Study of Metals, University of Chicago, Chicago, Illinois Received August 1 1 , 1066
Some new measurements are reported on the heat of solution of indium, antimony, copper and gold in liquid tin. The results are compared with heat data obtained in earlier calorimetric and equilibrium studies. The enthalpy change associated with the formation of the ternary alloys Sn-A-B from the binaries Sn-A (A = Cu, Ag, Au) and Sn-B (B = Cd, In, Sb) was studied by quasi-binary mixing experiments in the tin-rich range. The results are expressed in terms of an interaction parameter characteristic of each quasi-binary system. I n all cases studied this parameter was algebraically larger than a corresponding parameter for the pure binary.
Introduction The introduction of tin solution calorimetry for determination of the heats of formation of solid alloys represents an important development in the field of alloy therm0chemistry.l This method shows promise of providing far more accurate data on the heats of formation of solid alloys than has been possible by earlier work in this field. Using this technique the author has initiated a study of the thermochemistry of the alloys of group 1B metals (Cu, Ag, Au; below designated by the letter A) with other group B metals. It is first planned to explore a series of binary alloys where one of the components is changed in a systematic sequence (ie., Cd, In, Sn, Sb; below designated by B). In this work use is made of a new high-temperature reaction calorimeter developed by the author.2 In tin solution calorimetry, as in all non-differential solution calorimetry, the desired heat of formation of the solid alloy is obtained as a difference between two independently observed quantities. One of these is the heat of solution of the alloy in liquid tin to form a ternary liquid alloy. The other is the heat of formation of the same ternary alloy from the pure elements. A logical first step in the study of these ternary liquid alloys is the exploration of the tin-rich range of the binary systems which are of interest. Previously the author has reported the necessary data for such systems as Sn-Ag3 and S I I - C ~ . ~I n the present communication some new results will be presented on the liquid alloys in the systems Sn-Cu, Sn-Au, Sn-In and Sn-Sb. The reported work was generally carried out a t 450°, although some measurements on tin-gold were also performed a t 350, 270 and 242". If the ternary alloy which is formed when the alloy AB is dissolved in tin contains only very small concentrations of the two solutes, it may be permissible to neglect the interaction between A and B. In this case we may calculate the heat of formation of the ternary alloy Sn-A-B from data relating only to the two binaries Sn-A and Sn-B. However, in the calorimeter used by the author it is convenient to work with solute concentrations falling in the range 2 4 atomic per cent. Under these conditions the interaction between the solutes (1) L. B. Ticknor and M. B. Bever, J . Metals, 4, 941 (1952). 12) 0. J. Klepprt, THISJOURNAL, 69, 175 (1955). (3) 0. J. Kleppa, Acta Met., 8 , 255 (1955). (4) 0. J. Kleppa, THISJOURNAL,59, 354 (1955).
cannot be neglected entirely, although it usually will represent only a very small percentage of the total heat of formation. To correct for this interaction a simple formula containing a single interaction parameter for each system was adopted. A series of quasi-binary mixing experiments were performed in order to determine the magnitude of these parameters. Experimental General.-The binary solution and mixing experiments reported in the present work did not involve any modification of the previously reported experimental procedures, and readers are referred to earlier paper^^-^ for experimental details. The metals used were generally stock metals of 99.9+% purity. Prior to their use in calorimetric experiments all metals (with the exception of gold) were remelted in graphite crucibles and cast into1/Zf' rods. Suitable samples were then cut or machined from the rods. The gold, which was of 99.98% purity, was purchased from Goldsmith Bros. in the form of 2 mm. wire, and was used in this form. I n the quasi-binary mixing experiments one of the binary alloys was always prepared from weighed amounts of the pure components in the crucible of the calorimeter. The other binary alloy containing the same mole fraction of tin was melted down in an evacuated 12 mm. i.d. Pyrex ampoule, and cast into the desired hollow cylindrical shape in one end of this ampoule. After quenching in an air jet, the ampoule was broken and the I/4" graphite core drilled out. In this manner it was ensured that the two binary alloys maintained their original composition. Alternative Calibration of Calorimeter.-Numerically the heats of solution of gold in tin given below are 7-8 per cent. lower than those reported in other recent calorimetric investigations. It was considered desirable therefore to check the adopted electrical calibration by a "drop method." The comparison was carried out as follows. The charging and stirring device2 which normally connects the center of the calorimeter with the outside of the furnace insulation was replaced by a Pyrex tube of 8 mm. i.d. and about 60 cm. long. Through this tube sections of pure copper and tungsten rod of about l/4" diameter were dropped from room temperature into the calorimeter. In these experiments the calorimeter temperature was 242 f 0.4' as measured by a chromel-alumel thermocouple calibrated (before and after the run) a t the melting point of tin (231.9'). Prior to each drop experiment the temperature of the rod section was determined to 0.1'. The heat capacities of copper and tungsten were taken from compilations published by Kelley . 6 Before or after the drop calibration a conventional electrical calibration was carried out, and the two results were compared. It was found that the drop method consistently gave about 3% higher calibrations than the electrical method. There was no significant difference between the results obtained with copper and tungsten rods. Previously the maximum systematic error in the electrical calibration used throughout the present series of calorimetric studies was estimated to be 0.2 to 0.3%.a I n the light of more recent experience it appears that this estimate may have been too optimistic, and that a figure closer to 1% is more likely. The most probable source of error is that a (5) K. K. Kelley, U. 9. Bureau of Mines Bull., 476 (1949).
*
very small fraction (< 0.5%) of the electrical current, which is measured outside the furnace system, may actually bypass the calibrating heater. If this is really the case, the electrical calibrations would tend to be high. A realistic evaluation of the error involved in the drop calibrations is difficult, particularly because of the unknown amount of heat picked up by the sample during the drop. A very conservative estimate indicates that the uncertainty from this and other sources should be of the order of 1 % and may very well be larger. Heat transferred to the sample during the fall would tend to make the calibrations high. I n conclusion it may be stated that a t least a significant part of the 3% difference between the two methods of calibration may be accounted for by the assumed experimental uncertainties. It is believed that the electrical method is more reliable than the drop method.
I
Total
ZIn
g. atoms
0.0570 ,0731 .1178 .2269 ,3388
1.8345 1.3537 0,9234 ,4555 ,2928
I
0.0 I
I
:I--::
0.7 I
I
0.6 I
I
]
450'
Sn-In,
-1
.
Ai+, joule/g. atom
-
32.4 41.6 61.6 -115 - 154 -22
Tin-Antimony.-The results of 13 experiments, in which solid antimony was dissolved in liquid tin, are listed in Table 11, and are plotted in Fig. 1. The following linear relation is found between A H M . / Z S b and 2 s b
+ 1.02S2Sb kj./g. atom
AHM = 15.392~1,
0.9 I
$? 1
TABLE I MIXINQ FOR INDIUM-TIN ALLOYSAT 450 '
Composition
-XSn*
Sn 1.0
Experiments on Binary Alloys. Comparison with Earlier Data Tin-Indium.-The results for- this system are listed in Table I and are plotted, together with those for the other systems studied, in Fig. 1. The values of A H M / X 1 n are found to vary linearly with respect to XI^, according to the relation AHM = -59521. 4- 4 0 9 ~ ~j./g. 1 . atom (1) MOLARHEATSOF
84 3
BINARY AND TERNARY LIQUID ALLOYSRICHIN TIN
,July, 195G
I
0
Fig. 1.-Heat
I
0.I
I
I
0.2 Xsolute-
I
I 0.3
I
I
0.4
of solution of indium, antimony, copper and gold in tin.
(2)
late a value of -6.15 kj. If we adopt 19.8 kj. for the heat of fusion of antimony,8 these earlier invesMOLARHEATS OF FORMATION OF LIQUID ANTIMONY-TIN tigations yield 10 and 13.65 kj ., respectively, ALLOYS FROM SOLIDANTIMONY A N D LIQUIDTIN AT 450' for the limiting heat of solution of solid antimony AHM, AHM Comjoule/ ComJoule/ in liquid tin. This should be compared with our position Total g. position Total g. 15.39 kj. Similarly, Frantik and Mcvalue of XSb g. atoms atom XSb g. atoms atom Donald give the values -4.2 cal. (18 joule) and 0.00882 1.6647 133.8 0.05344 0.6856 830 - 12.0 cal. (50 jou1e)jor the relative partial molal .01706 0.9109 266 ,07574 .4228 1199 heat content of tin ( L s n ) a t ZSn = 0.9 and 0.8. In ,01736 .8637 267 ,08455 .3806 1320 this concentration range we caiculate the same ,01953 .8357 307 .1362 .2504 2093 quantity from the expression L s n = - 1 . 0 2 x 2 s b ,02755 .8673 420 .1485 ,4589 2331 kj.4 For the mentioned compositions we get - 10 ,02852 .8700 434 ,2492 .2881 3864 and -41 joule, respectively. The agreement with ,04080 .8560 619 the work of Frantik and McDonald must be considThe mean deviation of the observed values of ered as satisfactory. AHM/xsbfrom this equation is 0.20 kj. Tin-Copper.-The results for this system are It is possible to compare these results with heat given in Table I11 and plotted (AH'/xcu uersus data obtained calorimetrically a t 800" by Kawa- zcU) in Fig. 1 along with the data for the other kamP and indirectly from e.m.f. cell work a t 632" systems. by Frantik and McDonald.' The data reported by The following linear relation is found between Kawakami indicate that the limiting partial molal AHM/xcuand xcU heat content of liquid antimony in liquid tin AHM = 1 1 . 6 8 ~ 0-~ 13.66 z2cUkj./g. atom (3) ( h b ) should be of the order of -10 kj./g. atom. The mean deviation of experimental values of AHMI Frantik and McDonald, on the other hand, calcuzcUfrom this equation is 0.10 kj . TABLEI1
+
,
+
+
(6) M. Kawakami, Sci. Rep. TBhoIcuInp. Univ. ( I ) ,19, 521 (1930). (7) R. 0. Frantik and H. J. McDonald, Trans. Electrochem. Xoc.,
88, 243 (1945).
(8)0. Kubaschewski and E. L1. Evans, "Metallurgical Thermochemistry," Butterworth-Springer, London, 1951.
0. J. KLEPPA
844
Vol. 60
TABLE I11 TABLEIV MOLAR HEATB OF FORMATION OF LIQUID GOLD-TINALLOYS MOLARHEATS OF FORMATION OF LIQUIDCOPPER-TIN FROM SOLIDGOLDAND LIQUID TIN ALLOYSFROM SOLIDCOPPERAND LIQUIDTIN AT 450" AHM.
Composition zcu
g. atoms
Total
.de) g. atom
0.03855 .04100 ,04448 ,04461 ,04813
0.8527 .9132 .8954 ,8438 .8311
429 454 480 498 538
AHM.
Composition zcu
0.06871 .Of3051 .09745 .1560 ,1646
Com-
Total
position ZA u
g. atoms
joule) g. atom
0.6473 .8787 .4190 .3694 .2555
734 854 1028 1495 1535
0.00923 ,00994 .01083 .01582 .01641 .03213 .06685 .1346 .2373 .3084
Total
g. atoms
450" 1 .3673 1.4636 0.8615 .8300 .go19 .4472 ,2323 ,1745 .1979 .07689 (b) 350" 0.8385 .8426 .5461 .3047 .1604 .09196 .07093 .07945 (c) 270" 0.8266 .8394 (d) 242' 0.8866 ,8454 .8784 ,8581 .8519 .8212 ,8709
-A H M ,
joule/g. atom
(a)
180 196 212 311 327 62 1 1272 2505 4222 5279
The present results may be compared with data obtained in earlier calorimetric work. Ticknor and Bever' measured the limiting heat of solution of copper in tin a t 300°, and report a value of 10.75 kj., with an estimated uncertainty of about 600 joule. This compares with our value 11.68 kj. a t 450". It is estimated that the uncertainty in our figure 0.00933 195 should be of the order of 2%. .01116 235 KawakamP and later Korberg measured the heat .01798 372 of mixing in liquid copper-tin alloys a t 1200 and a t .03632 759 1150°, respectively. From their data we derive .07606 1594 the values -8 and *O kj. for the relative partial .1529 3104 m-olal heat contents of liquid copper in liquid tin .2067 4180 .2339 4705 (Leu). If we assume, for simplicity, that the heat of fusion of copper8 is independent of temperature between the melting point (1083") and 450") we 0.01142 253.5 find from the present work that the corresponding .01196 269 value a t 450" is about - 1kj. It will be noted from Fig. 1 that the slope of the curve for the tin-copper system is very nearly the 0.00932 215 .00944 216.4 same as for the previously studied system tin-sil.01124 259 ~ e r .The ~ negative slope, which corresponds to a ,01133 262 negative curvature of the heat of formation in the dilute range, is expected for solutes of lower valence .01203 276.6 ,01212 282 than the solvent, according to theoretical considera.01251 892.6 tions of Friedel.lo These theoretical aspects will be discussed further in the succeeding paper." Tin-Gold.-Pure gold was dissolved in liquid data on the limiting heat of solution of gold in tin tin in 10 experiments a t 450", in 8 experiments are plotted against temperature. It will be noted that the difference between the a t 350°, in 2 experiments a t 270°, and in 7 experiments a t 242'. The results are recorded in Table results of the present work and those of the other IV, and the data for 350 and 450" are plotted, calorimetric investigations is of the order of 7-80/,. along with the data for the other systems, in Fig. This is considerably more than the uncertainty indicated by the reported experimental precisions, 1. The following linear relations were derived for and suggests some systematic error, either in the present work or in the earlier work or in both. The the dependence of AH'/x~, on X A a~t 450 and 350" other investigators both calibrate their calorimeters -150': AHM = - 1 9 . 7 3 ~ ~ + . 8 . 3 9 9 kj./g. ~ ~ atom (4a) by dropping small pieces of tungsten wire into their tin baths. Therefore a series of similar cali350": AHM = - 2 0 . 9 8 ~ ~ + " 3 . 7 0 kj./g. ~ ~ ~atom ~ (4b) brations were carried out in the author's apparatus. At both temperatures the mean deviation of the results are compared with those obtained by experimental values of A H ' / x ~ , , from these equa- The the electrical method under "Experimental" above. tions was 0.10 kj. A t 270" the mean value of AHM/ We recall that the drop method consistently X A , was -22.35 f 0.15, a t 242" - 23.08 0.09 gavehere about 3y0 higher values than the electrical kj. These results may be compared with calori- method. Thus even if the drop calibrations were metric measurements carried out by Ticknor and as correct, the agreement with the other Bever a t 240 and 300°,by HultgrenI2 and co-workers accepted calorimetric studies on gold-tin is not entirely satisa t 243O, and also with heat data for 600" derived indirectly from e.m.f. cell measurements and factory. relatively strong dependence on temperature previously reported by the author.la This com- of The the heat of solution of gold in tin is a very interparison is presented in Fig. 2, where all available esting phenomenon, which appears to have no (9) F. Karber, Stahl und Eiaen, 66, 1401 (1936). clear-cut parallel in the case of solutions of copper (10) J. Friedel, Advances in Phvs., 3, 446 (1954). and silver in tin. It should be stressed that the (11) 0. J. Kleppa. THISJOURNAL, 60, 846 (1956). change of the limiting heat of solution with tem-. (12) R. Hultgren. private communiaation. perature represents a change in the strength of the (13) 0. J. Kleppa, J . Am. Chsm. Soc., 78, 3346 (1950).
*
c
BINARY AND TERNARY LIQUIDALLOYS RICHIN TIN
July, 1956
845
chemical bond proper, and is not due to a change in the short range order in the solution. An increased short range order is, on the other hand, T TICKNOR B. BEVER, CALORIMETRY probably associated with the reduction of the I HULTGREN et 0 1 , CAL.Iprelim.) “curvature” of the heat of formation (ie., the slope PRESENT WORK, GAL. of AHM/x~,vs. X A ~ as ) we go from 450 to 350”. In & -22 this temperature range the slope is reduced by a factor of two, but remains positive. Thus the system does not obey Friedel’s rule.lOsll However, it is worth noting that the curvature is very small when the strong interaction is taken into account. Finally it may be pointed out that the increase I -18 Iin AHMwith temperature must be associated with a similar increase in the entropy of formation. We - 17 X -I may here have a t least a partial explanation of the large excess entropy of mixing found in liquid gold200 300 400 500 600 700 tin alloys a t 600°.1sIt should be mentioned, howTemperature, “C. ever, that the gold-tin system in this respect is dif- Fig. 2.-The temperature dependence of the limiting heat of ferent from certain other liquid alloy systems (e.g., solution of gold in tin. tin-zinc and tin-cadmium) where both the heat and the excess entropy of mixing are reduced as the determined with precision in the apparatus. Therefore it was necessary to carry out the quasi-binary temperature is i n ~ r e a s e d . ~ experiments in mixtures with total solute concenQuasi-binary Mixing Experiments trations of the order of 10 to 20 atomic per cent. General.-The molar heat of formation of a Even so the observed heat effectswere quite small, ternary tin alloy may be expressed in the following and the values of CABmay very well beinerror by as much as 10%. This will be obvious from an exway amination of Table V where all the results obtained AH%-A-B = XA/(XA XB) AH‘sn-~ XB/(XA XB) in quasi-binary mixing experiments are recorded. AH%-B L ~ H ~ ( z A , z (5) B) Here X A and XB are the mole fractions of A and B in TABLEV the ternary alloy, while A H M s n - A and A H M S n - B are MIXING AT 450’ ACCORDING TO FORMAL the molar heats of formation of the two binary al- QUASI-BINARY CHEMICAL EQUATION loys which have mole fractions of tin ZSn = l Y Sn,A1-,(1) (1 - y)SnZB1-4l) = Sn2,,Ad3,B(1) ZA - XB. The term hH‘(xg, Q) represents the AHM AHM/ molar change in enthalpy associated with the quasi- Systeiii Final composition Total j./g.’ ZAAEB, .4-B zsn AEA ZB g. atoms atom kj. binary mixing process, L e . , when the ternary is + 8.6 formed from the two binaries while xsn is kept con- Cu-Cd 0.8424 0.1026 0,0550 0.371 f 48 ,0607 ,8281 0.351 .1112 4- 63 + 9.r stant. This last term may conveniently be ex,0914 Ag-Cd .8950 1.078 ,0136 - 9.1 - 7.4 pressed by means of a single interaction parameter, ,1110 0.393 ,8330 .0560 46 - 7.4 CAB(Z), thus .8330 ,0953 I382 .0717 - 47 - 6.e
c
+
+
+
1
+
+
A H M ( z a ,X B )
CAB(X)ZAZB
(6)
It is well known that for higher concentrations of A and B this interaction parameter will depend both on the total concentration of A and B and on the relative amounts of A and B in the mixture. However, in moderately dilute solutions, ie., when X A XB 5 0.2, this dependence is expected to be fairly weak. In this range we may to a good first approximation consider CABas independent of concentration. l 4 This essentially implies the assumption of nearest neighbor interaction between A, B and Sn. Other things being unchanged the number of nearest neighbor contacts or “bonds” in a random mixture is of course proportional to the product of the mole fractions of the two considered species. For ternary solutioiis resulting from typical calorimetric solution experiments in the author’s apparatus the product ZAXB usually falls in the range 10-3 With values of CABof the order of 10 kj., to the total molar heat effect of quasi-binary mixing experiments in this concentration range will be 1to 10 joules. These heat effects are too small t o be
+
(14) The independence of CAB on composition was not checked in detail. However, for the Byatem silvercadmium an increase of Z A ~ Zcd from about 0.10 to about 0.34 was found t o hare only a inoderate effect on the value of CAB(see Table V).
+
Au-Cd Cu-In Ag-In Au-ln Cu-Sb
Ag-Sb Au-Sb
.6588 ,8785 ,8962 ,8354 ,8466 .8330 ,7638 ,8800 .8971 .a300 .8400 ,8250 .7515 .8516 .8978 ,8501
,2104 ,0637 ,0543 ,1123 .0962 ,0964 ,0794 .OB13 .0522 ,1032 .IO12 ,1073 .1656
.O92G
,0512 ,0613
,1308 ,0578 ,0495 .0523 ,0572 ,0706 ,1568 .0587 .0507 .0668 .0588 .0677 ,0829 ,0558 ,0510 ,0886
.422
,230 ,244 ,375 ,315 ,362 ,381 .247 .254 ,338 .360 .NO
.374 .370 .249 ,229
-282 -109 73
-10.2 -29.8 -27.2
C 73
f14.1 +13.a 4.8
-
+ 83
+ 33 + 65
+ +
86 55 $100 91 4-126 +305 f115 4- 25 48
-23.0 -20.8 4-14.6 +15.8 +17.a 4-22.2 +22.n 9.0
-
+
+
5.2
+ + 8.8
Discussion.-It is of considerable interest to compare the quasi-binary interaction parameter CAB)^^^ with the corresponding parameter for simple binary interaction. The latter will in general be some function of composition, and we shall presently focus our attention on its value in pure liquid B, ( C A B ) ~ B 1. We note that this is in fact our old acquaintance, the relative partial molal heat content of liquid A in pure liquid B . The author recently has measured the heat of solution a t 450’ of copper, silver and gold in liquid cadmium
0. J. KLEPPA
846
and i n d i ~ m . ~From ~ ~ ’ ~these results the desired interaction parameters may be obtained by adopting reasonable values for the heats of fusion of copper, silver and gold. I n Table VI these parameters are given along with average values of CAB)^^^ tl 1 obtained from the experimental data recorded in Table V.
Vol. 60
VI suggests that CAS^)^^^ probably in all cases If will be considerably larger than CAS^)^^ this is indeed the case, it is tempting to interpret the change in CABin terms of simple atomic size considerations. It may be postulated that for dilute solutions in any solvent metal there exists a tendency for the nearest neighbor “bonds” to assume the length characteristic of the nearest neighTABLE VI bor distance of that particular metal. On this INTERACTION PARAMETERS IN BINARY AND TERNARYmodel it may be argued that the bond lengths LIQUIDSYSTEMS AT 450” which eiist, e.g., in pure liquid B, will become comCzsn-1 pressed or extended (and the bond energies acSystem (CAB)+.- I (CAB~B-I CZB-I cordingly changed) when they are present in esA-B ki. kj. kJ * sentially pure liquid tin. We might expect the ef- 12 Cu-Cd 21 + 9 fect to depend in some manner on the difference in Cu-In 0 14 4-14 size between A, B and Sn, and to be particularly Cu-Sn - 1 - 1 .. large if the bonding A-B is strong (or “stiff”). Cu-Sb ? ? +16 There is a certain amount of semi-quantitative Ag-Cd -24 - 7 17 support for this simple picture in the data given in Ag-In -4 ..9 +5 Table VI. Ag-Sn +4 + 4 We recall first that the sequence Cd, In, Sn, Sb is ? Ag-Sb ? +22 one of increasing atomic size, as measured for ex-61 Au-Cd -28 33 ample by the atomic radii for coordination number Au-In -22 46 24 12. For any one of the reference metals, copper, Au-Sn -33 -33 .. silver and gold, we note that the parameter C A Cis~ ? Au-Sb ? f 9 increased more than CAI=in going to liquid tin. We It will be noted that it is a common feature of the further recall that among the metals copper, silver six systems for which full information is available and gold the two latter have very similar atomic that the binary interaction parameter, CAB,is in- radii, while copper is significantly smaller. If we creased (ie., interaction weakened) when we go first consider the alloys formed by silver and gold, from pure B to nearly pure tin. We also note that where the effect of size should be of the same order the increase in CABfor the cadmium systems is more of magnitude, we find that C A ~isBalways more inpronounced than the corresponding increase for the creased than C A ~ on B going from B to Sn. If we, indium systems. There is, however, no clear-cut on the other hand, look a t the alloys formed by copcorrelation between the increase in CAB and the per and silver, where the magnitude of the chemical magnitude of CABas we go from one binary system interaction is more nearly equal, while the size effect is different, we note that C C ~ is B somewhat to another. It is unfortunate that because of the high melting more increased than is C A ~ B . point of antimony there is as yet no reliabik informaAcknowledgments.-This work was supported tion on the heat of solution of copper, silver and in part by the Office of Naval Research through gold in liquid antimony. However, a systematic Contract No. N-6ori-02004 with the University survey of all interaction parameters listed in Table of Chicago. The indium metal used was a gift from the Anaconda Copper Company. (15) 0. J. Kleppa, THISJOURNAL,60, 858 (1956).
-
w
-’-
HEAT OF FORMATION OF SOLID AND LIQUID ALLOYS IN THE SYSTEMS SILVER-CADMIUM, SILVER-INDIUM AND SILVER-ANTIMONY AT 450’ BY 0. J. KLEPPA Institute f o r the Study of Metala, University of Chicago, Chicago 37, Illinois Received Auoust 11, 1066
The heats of formation of the liquid alloys of silver with cadmium and indium were determined calorimetrically a t 450” by dissolving silver in the low-melting liquid metals. The heats of formation of the solid alloys were obtained by the tin
solution technique. The new information is discussed along with data obtained earlier for the system silver-tin. The results are compared with recent theoretical calculations by Varley and by Friedel. Many of the results are in excellent agreement with theoretical predictions advanced by Friedel.
Introduction a recent communication the author has published new information on the integral heat of formation of the solid and liquid alloys of silver-tin as determined calorimetrically a t 450O.I I n the 111
(1) 0. J. Kleppa, Acta Met., 8, 255 (1955).
present paper equivalent data will be reported for the alloys of silver with cadmium, indium and antimony. A preliminary report on some of this work was given previously.2 For alloys which are liquid a t 450” the desired heat data were obtained di(2) 0. J. Kleppa. J . Am. Chem. Soc., 76, 6028 (1954).
0
