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Thermodynamic properties of solid InSn alloys
J~u~~~ of the Less-Common
THERMODYNAMIC
Metals,
141 (1988)
11
11 - 27
PROPERTIES OF SOLID In-Sn ALLOYS
0. CAKIR and 0. ALPAUT department
of C~ern~s~~, ~a~ette~e
(Received March 27,1987;
~l~~~ersit~, Ankara (Turkey}
in revised form September 23, 1987)
The thermodynamic properties of solid In-Sn between 75 and 120 “C over the entire concentration of cells of the form -
In(pure
solid)/InCl,(formamide)/In,Snl
_ Jsolid
alloys are studied range. The e.m.f.
alloy)
-I-
is measured as a function of alloy composition and temperature. The activities ai,j (i = In, j = Sri), the activity coefficients x,j, the partial molar Gibbs free energies AGi,j as well as the partial enthalpies hEl,,j of the components in the alloys are determined for various alloy concentrations, Also, the integral properties (i.e. AG and AH) are calculated. In connection with a survey of the concentration dependenees of all these properties, the locations of the phase boundaries in the solid state are discussed.
1. Introduction
The thermodynamic properties of liquid In-Sn alloys [l - lo] and also the pertinent phase diagram [5, 10 - 141 have recently been subjected to extensive studies. However, this is not true for the thermodynamics of the solid alloys in this system. The only work worth mentioning is the calculation of the enthalpy of mixing of solid In--&r alloys which has been carried out by Alpaut and Heumann [ 151 studying the differential thermal analysis curves of In-Sn alloys. Because a proper electrolyte has not been available, the e.m.f. method has not yet been applied to the solid alloys of this system. In this study a solution of InCls in formamide (CH,NO) is used as the electrolyte for the galvanic cells at any concentration. Formamide is unusual as its dielectric constant (110) is signific~tly larger than that of water. Nevertheless, it has a convenient liquid range (2.5 - 193 “C) and a low vapour pressure at room temperature. Electrical conductance measurements of InCl, in formamide solution show that InCls dissolves in formamide ionically. The cell established thus works reversibly [ 161. 0022-5088/88/$3.50
@ Elsevier Sequoia/Printed
in The Netherlands
12
2. Experimental details A potentiometric measuring system operating at minimum current was arranged to measure the e.m.f. of the galvanic cell -
In( pure solid)/InCl,( formamide)/In, Sn 1_ x
+
at various temperatures and alloy compositions. 2.1. Elec &odes 27 alloy electrodes were prepared by melting the proper amounts of indium (purity, 99.9995%; supplied by the PREUSSAG Company) and of tin (from BDH) together in a porcelain crucible under a purified argon atmosphere. The liquid alloys were cast into a stainless steel mould which has the following dimensions: top diameter, 1.0 cm; bottom diameter, 0.5 cm; length, 6.0 cm. The bars are used as solid electrodes. Pure indium and tin electrodes were prepared in the same way. The alloys were annealed under an argon atmosphere for 90 days at 10 “C below their corresponding solidus points. This process is required for the homogenization of the alloys and for the elimination of internal strains. 2.2. Electrolyte The electrolyte containing pure InCls was prepared by dissolving the salt in fractionally distilled and carefully purified formamide (99.5% from BDH) under an argon atmosphere. The anhydrous indium trichloride was synthesized by the chlorination of pure metallic indium in a stream of carefully dried and purified Cl* gas in a thoroughly dried quartz apparatus. 2.3. Cell The cell used is shown schematically in Fig. 1. The cell is placed in a stainless steel block set in a vertical furnace and closed with a Teflon cover. Three alloys and two pure indium electrodes are placed, at the same time, in this cell and the e.m.f.s between the In-In and indium-alloy electrodes are measured in the same run. A small flow of purified and dried argon was passed through the cell. 2.4. Temperature regulator A proportional temperature controller was used to control and regulate the temperature with a precision of +O.l “C!. A Leads-Northrup type 7554K4 potentiometer and an appropriate galvanometer were used. 2.5. E.m. f. measurements After the cell was set up, the temperature was regulated to 70 “C. Two pure indium and three alloy electrodes were inserted tightly into the cell through the holes of the Teflon cover. They were isolated with Teflon gaskets. After inserting the electrodes, one has to wait for 1 h before starting the measurements so that equilibrium conditions can be established at the
13
12
11
10
1, thermometer; 2, electrode connections; 3, Teflon Fig. 1. E.m.f. cell construction: 5, stainless steel block; 6, electrode; 7, brex cuvette; 8, electrolyte; cover; 4, furnace; 9, control probe cavity; 10, probe; 11, connection to proportional temperature controller; 12, electrode-potentiometer connections and argon gas inlet.
electrodes and within the electrolyte at the given temperature. Each run comprised at least three complete heating and cooling cycles in the temperature interval between 75 and 125 “C with small temperature steps between the measurements. The e.m.f. of the cell was reasonably stable to the order of +O.Ol mV. In-In e.m.f.s were controlled continuously in order to perceive any mechanical or other disturbances. During the measurements, the cell was under an argon atmosphere. Each measurement was been carried out from the upper potential to the lower and vice versa in order to enable continuous control of the reversibility. In order to measure the thermoelectrical potentials without an electrolyte at the same temperatures, the electrodes were connected to each other at the bottom while they were inside the cell. The resulting potentials were very small and within the limits of experimental reproducibility. The reproducibility of the measurements has a precision of +O.l mV. After the runs, apart from slight etching marks on the electrodes, there was no significant attack and there was no detectable change in their surface compositions. 3. Experimental
results
The resulting e.m.f. values are plotted U.S.temperature in Fig. 2 for various alloy compositions. In almost all cases good linearity is observed,
14 1 F: (rnV) 25.0
24.0
23.0
22.0
21.0
Xl.0
19.0
? 7.0
6.0
5.0
4.D
3.0
2.0
1.0
0.0
1 *
75
85
95
105 Temperature
Fig. 2. E.m.f. us. temperature are indicated at Table I).
115
125
("C)
plots for the In-Sn solid alloys (compositions
of the alloys
so that linear regression analysis has been applied. The results, i.e. the ensuing parameters, intercept a and slope b of the straight lines, together with their standard margins of confidence, are reported in Table 1. E.m.f.temperature data are not reproducible and could not be fitted to a straight line for tin-rich alloys (alloys 14 and 22 - 27).
15 TABLE
1
The coefficients of the E = a + bT temperature data for each alloy
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27
0.040 0.050 0.060 0.100 0.115 0.133 0.170 0.220 0.277 0.390 0.440 0.500 0.660 0.720a 0.750 0.770 0.792 0.810 0.820 0.830 0.860 0.894a 0.920a 0.9408 0.948a 0.96Qa 0.9808
aE.m.f.-temperature for these alloys.
equation
derived
0.12 0.10 0.39 1.19 0.67 0.67 0.99 1.25 1.45 3.54 1.00 0.52 0.88 -
f + * f f + 5 * + * + + *
0.09 0.04 0.13 0.15 0.20 0.11 0.21 0.24 0.12 0.14 0.08 0.17 0.18
0.0087 0.0102 0.0123 0.0108 0.0121 0.0131 0.0116 0.0206 0.0227 0.0255 0.0477 0.0624 0.0542 -
+_0.0008 + 0.0004 + 0.0012 rt 0.0015 + 0.0032 f 0.0011 + 0.0022 i 0.0024 f 0.0012 f. 0.0014 + 0.0042 f 0.0017 It: 0.0019
21 21 22 13 27 27 27 25 30 27 26 37 35 -
12.82 13.86 15.14 15.58 15.74 15.82 16.22 -
f. + + + 4 f f
0.31 0.29 0.57 0.38 0.42 0.39 0.22
0.0930 0.0855 0.0763 0.0735 0.0730 0.0730 0.0720 -
f f i f * f f
31 28 23 19 16 22 20 -
-
data are not reproducible
from
and could
the
0.0030 0.0028 0.0056 0.0039 0.0041 0.0040 0.0022
analysis
not be fitted
of
e.m.f.
and
to a straight line
The e.m.f. values with their standard deviations pertinent to the calculated straight lines are the basis for the computation of the partial molar Gibbs free energy of solution of the indium component in the alloys, by means of the usual relationship: A&, = --nEF where E is the e.m.f., AE,, (cal mol-‘) the partial molar Gibbs free energy of indium in the solution, n the valency of the transferred ions and F the Faraday constant (8’ = 96 487 C mol-I). Using the further relationship A&, = RT In aIn
16 TABLE2 Partial molarquantities of In-Snalloys at100 "C(indiumcomponent) Phase
0.960 0.950 0.940 0.900
0) (InI (InI
0.885 0.867 0.830 0.780 0.723 0.610a 0.560 0.500 0.340 0.250 0.230 0.208 0.190 0.180 0.170 0.140 0.106a 0.060a 0.052a
(InI + P
f P+r pp:; Y Y Y Y Y Y Y
Yin
0.912f 0.002 0.900f0.002 0.860+ 0.002 0.809+ 0.003 0.839f 0.004 0.831f 0.002 0.818f 0.003 0.734f 0.003 0.707* 0.002 0.566f 0.002 0.584f 0.003 0.532+ 0.002 0.556f 0.002 0.127+ 0.001 0.124+ 0.001 0.120+ 0.002 0.118+ 0.001 0.116+ 0.001 0.116+ 0.001 0.110+ 0.001 0.008f 0.001 0.010+ 0.001
0.950f 0.002 0.947+ 0.002 0.915+ 0.002 0.899+ 0.003 0.948f 0.005 0.958f 0.002 0.985f 0.004 0.941+ 0.004 0.978+ 0.003 0.928f 0.003 1.043t 0.005 1.064+ 0.004 1.635f 0.006 0.508f 0.004 0.539f 0.004 0.577+ 0.005 0.621f 0.005 0.644+ 0.006 0.682f 0.006 0.786f 0.007 0.130* 0.011 0.199f 0.018
-A&
AGIn=
(calmol-')
(caImol-')
68fl 78+1 112fl 156k2 13Ok3 137 +1 148 f2 228+2 257+ 2 421f2 399+4 468f2 435+2 1531f3 1550f3 1575+6 1586f5 1594 f5 1596f5 1634f5 3600f70 3400f70
-38f2 -33f2 -66+2 -79+3 -4Of4 -32+2 -11+3 -45+3 -16+3 -55*3 31+4 46+3 364+3 -502f6 -458f6 -407 f6 -353f6 -326+7 -284+7 -179f7 -1510f61 -1200 +64
I%) f:In(aIloy)(,). aPhaseboundaries. the indium activities a,, of the alloys have been obtained at a fixed temperature. From the activities and compositions, using the 71n = aI&rn relationship, the activity coefficients yin of indium in the alloys have been calculated by applying the relationship AC InxS = RT In yI,,
@a)
the excess partial molar Gibbs free energy AaInxS has been calculated: A&=
= AC,,, - AC,;’
Pb)
where AcInid is the partial molar Gibbs free energy of indium in an ideal solution. The corresponding partial molar quantities for the second component of the alloys may be satisfactorily determined by graphical integration of the Duhem-Margules relationship in the form *sn = xsn ln Yin ln xn (4) In YSn = ( 1 _ XIn)2 XInXSn - x_fSn = 1 (1 - XIn)2 d%n
17 TABLE3 Partial molar quantities of In-Snalloys at 100°C (tin component)
XSn 0.040 0.050 0.060 0.100 0.115 0.133 0.170 0.220 0.277 0.390a 0.440 0.500 0.660 0.750 0.770 0.792 0.810 0.820 0.830 0.860 0.894a 0.940a 0.948a
Phase
(In) + P
; P
“,+s P=r Y Y Y Y Y Y Y
asn
0.038f 0.003 0.051+ 0.003 0.070f 0.004 0.172+ 0.006 0.124f 0.005 0.132f 0.005 0.143-+0.005 0.222+ 0.007 0.255+ 0,006 0.392f 0.007 0.377f0.007 0.418f 0.007 0.409+ 0.007 0.760+ 0.004 0.765+ 0.004 0.770+ 0.004 0.772+ 0,004 0.775f 0.004 0.775f 0,004 0.780f 0.004 0.943+ 0.013 0.954+ 0.013
YSn
0.941f 0.080 1.022f 0.058 1.167f 0.065 1.719+ 0.060 1.080* 0.040 0.994+ 0.040 0.844f 0.040 1.011+ 0.030 0.922+ 0.020 1.006f 0.015 0.857f 0.015 0.837+ 0.015 0.620f 0.015 1.014f 0.005 0.993f 0.005 0.972f 0.005 0.953k 0.005 0.946f 0.005 0.934+ 0.005 0.907+ 0.005 1.003+ 0.010 1.007f 0.010
-A&,
AEsnXS
(Calmol-')
(calmol-')
2430f50 2205f45 1970+40 1305f27 155oi31 1500+30 1440 + 29 1115 zt24 1010 zt21 693 f14 723+15 645+13 663 f13 203 f4 199+4 194+4 192f4 189f4 189f4 184 k4 44 f10 35 f10
-45 16 114 402 57 -4 -126 8 -60 5 -114 -132 -354 +lO -5 -21 -36 -41 -50 -72 2.2 5.1
Sn(,)+ W~loy)(,). aPhaseboundaries.
The activities Ui,j, the activity coefficients yij, the partial Gibbs free energies ACi, j of solution as well as the excess partial Gibbs free energy ACi+jxs (i, j = In, Sn) determined in this way are given in Tables 2 (indium) and 3 (tin). The activities and the partial Gibbs free energies of the components as functions of the composition are plotted in Figs. 3 and 4. 3.2. Entropy of formation The partial entropies As,,, of formation are given by the expression, A&, = nF(dE/dT),
of indium
at any temperature (5)
The dE/dT values are the slopes of the best straight lines through the experimental points (b values in Table 1). These values increase with increasing mole fraction of the tin component. The increasing scatter of the points at high temperatures stems from the increase in the standard deviations of the entropy values. The partial molar entropies of formation are reported in Tables 4 and 5 and these are plotted in Fig. 5.
18
aa a0 In
02
0.4 46 --An--c
0.6
1.0 Sn
0.0
0.2
0.4
In
0.6
0.8
1.0
sn
----XSll-
Fig. 3. Relative activity curves of indium and tin in their binary systems at 100 “C. usn is calculated from the GibbeDuhem equation. Fig. 4. Partial Gibbs free energies of solid In-Sn alloys at 100 “C. TABLE 4 Partial molar enthalpy, (indium component)
entropy
and excess entropy
of In-&
XIIB
Phase
0.960 0.950 0.940 0.900 0.886 0.867 0.830 0.780 0.723 0.610a 0.560 0.500 0.340 0.250 0.230 0.208 0.190 0.180 0.170 0.140
fW
wn
a.n
155 f 23 186 k 13 205 * 31 122 f 39 182 f 35 201 f 31 151+ 38 302 f 65 327 f 32 238 f 39 830 f 112 1143 + 47 963 + 51 875 + 85 658 f 74 395 + 151 3llk 106 290 * 109 278 + 109 246 f 72
0.60 0.71 0.85 0.75 0.84 0.90 0.80 1.42 1.57 1.77 3.30 4.32 3.75 6.45 5.92 5.28 5.09 5.05 5.03 5.01
(caI mol-i)
(In) (In) (In) + P ; P $1; + Y Y Y’ Y Y Y Y
In(s) * In(alloy)(,.. aPhase boundary.
(cal mol-’
K-* 1
f 0.06 f 0.03 f 0.08 f 0.10 ?r 0.22 f 0.08 zk0.15 + 0.17 f 0.08 + 0.10 + 0.29 kO.12 ?I 0.13 f 0.22 + 0.19 + 0.39 + 0.27 f 0.28 f 0.28 + 0.18
alloys at 75 - 125 “C
ASn.,=s (cal mol-’
K-’ 1
0.52 f 0.06 0.61 f 0.03 0.73 + 0.03 0.54 f 0.10 0.60 + 0.22 0.62 k 0.08 0.43 + 0.15 0.93 k 0.17 1.06 + 0.08 0.79 * 0.10 2.15 + 0.29 2.94 f 0.12 1.61 + 0.13 3.70 + 0.22 3.00 * 0.19 2.16 f 0.39 1.79 + 0.27 1.64 f 0.28 1.51+ 0.28 1.10 5 0.18
19 TABLE 5 Partial molar enthalpy, entropy and excess entropy of In-Sn alloys at 75 - 125 “C (tin component)
-&I
Phase
0.040 0.050 0.060 0.100 0.115 0.133 0.170 0.220 0.277 0.390a 0.440 0.500 0.660 0.750 0.770 0.792 0.810 0.820 0.830 0.860
(InI (In) (In) (In) + P (In) + P
A%ll
(Cal mol-‘)
i
2271+ 335 1530 f 107 1346 k 203 1890 f 388 1353 f 332 1196 f 184 1461 f 361 846 + 182 766 f 74 800 + 131 10 f 2 -317 f 13 -243 f 13 -199 k 19 -129 ?r 15 -57 * 22 -32 + 11 -28 k 10 -26 f 10 -19+6
Ass,
(caI mol-’
Ai&=
K-.’ )
12.6 f 0.9 10.0 f 0.3 8.9 + 0.6 8.4 f 1.6 7.7 + 1.7 7.2 f 0.5 7.8 * 1.5 5.2 5 0.5 4.8 10.2 4.0 f 0.4 1.96 + 0.03 0.88 f 0.05 1.12 f 0.05 0.01 + 0.06 0.19 + 0.04 0.37 + 0.06 0.43 * 0.04 0.43 + 0.03 0.44 * 0.03 0.44 + 0.02
(caf moi-’
K-l)
6.2 +_0.9 4.0 f 0.3 3.3 + 0.6 3.8 + 1.6 3.4 f 1.7 3.2 k 0.5 4.3 + 1.5 2.2 i 0.5 1.8 5 0.2 2.1 i 0.4 0.33 * 0.03 0.58 f 0.05 0.29 f 0.05 -0.56 + 0.06 -0.33 5 0.04 -0.09 + 0.06 0.01 + 0.04 0.04 f 0.03 0.07 f 0.03 0.14 + 0.02
SW * W~lw)(,).
*Phase boundary.
3.3. Heats of forenoon Partial heats A!.&, of solution of indium may be obtained from the above partial properties by applyyingthe Gibbs-Helmholtz relationship A&
= AC,,, + T A&
(6)
The accuracy of heats determined in this way is very strongly dependent on the precision with which the temperature coefficient of the cells can be established. The results for A&, at 100 “C show considerable scatter; the values indicated positive integral heats of fo~ation, e.g. about 1140 cal mol-’ at the equiatomic composition. Partial heats of solution m, of the tin component are calculated from the MI, values by graphical integration of the Gibbs-Duhem relationship in the form
(7) The values obtained are valid for temperature intervals ranging from 75 to 125 “C. On the basis of these values and the partial Gibbs- free energies
In
Sn
pxSn-
Fig. 5. Partial entropies of formation of solid In-Sn alloys (7.5 - 125 “C).
A&, of formation, the partial entropies A&, of formation of the solution of the tin component can be computed by using the relationship A$& = ms, - A&,,/T. The thermodynamic quantities calculated thus are given in Tables 4 and 5. The partial excess entropy values A&,.,= are calculated from the relationship ASi,j= = ASi,j -R
In xi,j
(i, j = In, Sn)
for both components and given in the said tables. The dependences partial quantities on the composition are plotted in Fig. 6.
(6) of these
3.4. Integral quantities The integral Gibbs free energies AG, the enthalpies AH and the entropies AS of formation of these alloys are given by the following relationships: AG = xrn Ai?,, + xs,, AGsn AH = xin A&,
+ xsn A&
AS = x1, ASI, + xs,, A&
(9) (16) (11)
21
0
0.0
0.2
J”
0.4
~XSni
0.6
0.8
1 .o
sn
Fig. 6. Partial heats of solution of solid In-Sn alloys (75 - 125 “C).
The standard reference states throughout are the pure solid components. In Table 6, AH and AS values are given for temperature intervals ranging from 75 to 125 “C; AG values are given for 100 “C.
4. Discussion Thermodynamic investigation of alloys by the e.m.f. method is based on the linearity of the e.m.f.-temperature curves within the given temperature interval under consideration. If dE/aT = constant, then aG/aT= nF(aE/aT) = AS = constant. Therefore AH has to be constant in this temperature range. From this point of view (C, - Cpo)rn= 0 and (C, - Cpo)sn= 0 in the range of experimental errors. Indeed, it seems to be true that in the system investigated within the chosen temperature interval linearity is obeyed within the 95% standard probability range, so that our evaluation procedure, the values of the thermodynamic quantities resulting from it and the conclusions on the basis of these values seem to be entirely justified. It ought to be mentioned here that a considerable error source in the application of the e.m.f. method may lie in the occurrence of the so-called displacement reaction. In our case, this reaction can be described as
(InI (InI
Phase
1.08f 0.10 1.17f 0.04 1.33+ 0.11 1.51f 0.25 1.67k 0.40 1.74f 0.14 1.98+ 0.40 2.26+ 0.24 2.45+ 0.11 2.63+ 0.22 2.71+ 0.18 2.60+ 0.08 1.96+ 0.08 1.62+ 0.10 1.50f 0.07 1.38+ 0.13 1.23+ 0.08 1.27f 0.07 1.22f 0.07 1.08+ 0.04 -
240+35 254+18 273+41 294+75 317 *,70 333+51 374f93 422+91 449f44 457+75 47lf64 413+30 167226 70*35 52f28 37k48 33529 30+28 26f26 18 +15 -
163k 2 184+2 224+2 271k3 293+4 308k2 367+3 423+3 466+44 527+-5 542+2 557+4 56524 535+44 51Ok4 481+4 428?r4 442+4 42854 387rf:4 257+10 209klO
aPhaseboundary.
- 125 ‘C)
(calmol-lK-l)
u(75
(calmol-')
(calmol-')
“C)
mc 15 - 125
--AC+ 100 w
(1 -x)In(,)+ xSn(,)* Inl_,Sn, tsj,
0.040 0.050 0.060 0.100 0.115 0.133 0.170 0.220 0.277 0.390a 0.440 0.500 0.660 0.750 0.770 0.792 0.810 0.820 0.830 0.860 0.894s 0.940a 0.948a
XSn
Integral propertiesof In-Snalloysat75 - 125°C
TA3LE6
oc)xs
38+2 37+2 5522 3124 29+4 28 f 3 3022 33 +4 28 +4 32+6 33+4 43 +4 11055 11824 10924 10154 96 lt4 92+4 90 f4 8723 88 +10 57 f10
(calmol-*)
--aG(loo 475
- 12sac)xs
0.74+ 0.10 0.77f 0.04 0.88+ 0.11 0.85+ 0.25 0.91f 0.40 0.97* 0.14 1.08f 0.40 1.20+ 0.24 1.25+ 0.11 1.30+ 0.22 1.34f 0.18 1.20+ 0.08 0.68f 0.08 0.50f 0.10 0.40f 0.07 0.35f 0.13 0.26+ 0.08 0.34f 0.07 0.31i 0.07 0.27f 0.04 -
(calmol-'K-l)
23
3Sn + 21n3+ e
3Sn2+ + 21n
Such reactions affect the cell potential by producing a mixed potential. The change of the Gibbs free energy which is due to this reaction can be quantitatively estimated; it is of positive sign and in most of the cases regarded here of negligible amount. Only in tin-rich alloys does it become noticeable. The following discussion of the results obtained will have two parts: (1) the phase diagram and (2) the thermodynamic quantities proper. 4.1. Phase diagram As Fig. 2 shows, the e.m.f. values of the cell increased with increasing tin mole fraction of the alloys. The behaviour of the e.m.f. us. temperature lines, the activity isotherms and the e.m.f. values indicated that the phase boundaries of the In-Sn phase diagram agree with previous values given by Heumann and Alpaut [ 51. The alloy having the composition xsn = 0.720 yields different e.m.f. values during cooling and heating. Therefore the reproducibility was very poor. The reason for this may be the phase transformation from the /3 + y field to the y phase region. Heumann and Alpaut said that this boundary lies in the xSn = 0.750 - 0.770 range for the 75 125 “C temperature interval [5] (Fig. 7). In the present investigation this boundary has been found to be located at the xsn = 0.720 composition, thus being in a vertical position. The alloys which have compositions xSn = 0.770, xsn = 0.792, xsn = 0.810, xSn = 0.820 and xSn = 0.860 belong to a
0
10
20
30
40
50
60
I" Atom
%
Sn
10
80
90
100 S"
Fig. ‘7. The phase diagram of In-Sn [ 51, showing the compositions and temperature intervals for the alloys studied. The y phase boundary obtained from our experimental results (x) departs from tbe phase boundary of Heumann and Alpaut.
24
separate homogeneous region in which the e.m.f. values are increasing with temperature. From this region to pure tin (3csn= 1.00) the boundaries found are the same as those of Heumann and Alpaut. 4.2. Thermodynamic quantities The partial Gibbs free energies of solution which are calculated for the e.m.f. values give precise results, but the results of the entropy and enthalpy calculations are increasingly affected by errors. These errors ought to be discussed in detail. The plots of the activities us. composition are shown in Fig. 3 for a temperature of 100 “C. The activities are constant in the @+ 7 heterogeneous phase region and also in the narrow In (= a) + p region. Therefore the partial molar Gibbs free energies of the components must also be constant in the same regions. The integral Gibbs free energies of solution thus exhibit linear courses within the heterogeneous composition ranges (Fig. 8), as common tangents to the more curved parts pertinent to the adjacent homogeneous phase ranges, so that the actual points along the curve are always representing the minimum possible values of AG.
0.0
0.2
04 -
0.6
08
1.0
a-
Fig. 8. Integral entropies (75 - 125 “C), enthalpies (75 - 125 “C) and Gibbs free energies (100 “C) for the formation of In-Sn solid alloys: @, this study; l, from Alpaut and Heumann [ 15 ] ; AHmL, from Bros and Laffitte [ 11.
25
In order to calculate the entropies, the slopes of the e.m.f.-temperature lines have to be known with high precision. Caution should be taken in considering the temperature coefficient of A&, measured in a two-phase region lest the composition of the phase change with temperature. In a homogeneous phase for a constant indium composition xln, the partial entropy change A$, is given by A&, = -(a
(12)
A8,,/aT),
while in a heterogeneous d AG,,/dT
mixture
= (a A&/aT),
there is
+ (a A&/ax),
d,/dT
If the last term of eqn. (13) can be ignored, than the equation d A&]dT
= -A&,
(13) becomes (14)
Therefore there are some additional errors in heterogeneous regions. The integral enthalpies are calculated from the integral entropies and the integral Gibbs free energies. Therefore the errors of these properties accumulate to yield the errors of the enthalpy results. Therefore, it is better to determine the enthalpy of solution directly by other methods, such as calorimetrically. The calculated integral enthalpies of formation of solid In-Sn alloys are depicted in Fig, 8. The integral enthalpies have positive values with a maximum to 471 + 64 cal mol- 1 in the heterogeneous region. Alpaut and Heumann [ 151 have given the only data as yet, with a maximum value of 500 cal mol-’ (Fig. 8). These results agree with each other within the it has not been range of experimental errors. At the xsn = 0.860 composition possible to obtain a satisfacto~ result so that the second maximum Alpaut and Heumann have given could not be affirmed. The enthalpies of mixing for liquid In-Sn alloys which have been reported by Bros and Laffitte [l] are also shown in Fig. 8. The integral mixing enthalpies of solid alloys are, in general, additively composed of three major terms, which are regarded as being independent of each other, namely A&s
= bH,s
+ A&s
+ A&s
(15)
where AlY,’ 1s . due to bonding changes on alloy formation, disregarding structural and atomic radii differences, which are taken into account by the other two terms. AHBs depends on the chemical character of the constituents, Le. on their relative positions in the periodic table of the elements. This term predominates in intermetallic phases. A.&’ stems from the strain due to atomic radii differences and thus is always positive. Its importance, obviously, increases with increasing atomic size difference of the alloying partners. It may be mentioned that this term is also effective in the liquid state. As the single bond covalent
26
radii of indium and tin are 1.44 a and 1.40 A respectively, in the system regarded here CLHn’ IS * negligible in the solid as well as in the liquid state. Finally, AJ!lr’ results from the transformation enthalpy which has to be expended in order to transform either component from its stable structure at the temperature in question into the stable structure of the alloy. This term is equal to zero on the formation of most liquid alloys. Thus, for liquid In-& alloys A&L = AHaL. At the same time LWBS = MnL. This assumption is particularly true when the components have similar chemical properties as a result of their similar electronic structures. Indium is in the neighborhood of tin in the periodic table. On the basis of the above assumptions Al&s = A.&n + AHns + AZ&s
(16)
can be written. According to Bros and Laffitte [l] as well as Gauley et al. [ 4], AHmL has a maximum value of about 50 cal mol-’ and AHi,’ has to be small according to the above discussion. Then it can be said that 90% of Mm’ results from the ARrs term. This is obviously due to the tr~sition from the thermodynamically stable tetragonal white tin to the f.c.c, structure in the alloy. This transformation term thus causes the enhanced value of the formation enthalpy of the solid In-Sn alloys. The positive enthalpy in the solid alloys causes narrowing of the phase regions of the homogeneous solid solutions with decreasing temperature. The fl phase region shrinks more than the other phases when the temperature is lowered. The extrapolation of the equilibrium curves in this region shows that the decomposition of this phase ought to take place at a temperature of about -70 “C. Enthalpy as well as entropies show similar changes in a binary system but the Gibbs free energy is little affected by these changes. Positive enthalpy is usually connected with positive entropy. This is also valid in the In-Sn alloy system. Kubaschewski has shown that, if A&, is positive, the excess entropy As”” in a binary system also has to be positive and, according to the AC”” = M - T ASXs relationship, negative AG values and positive M values imply that ASXs has to be positive: this obviously is also valid in the region in which maxima or minima occur. ASxs has indeed a maximum value of +2.0 cal KM1 mol-’ in this system (Fig. 9). In strictly regular solutions A,!? has to be zero. Usually one can say that this condition is fulfilled if ASxs lies within the range 0.0 - 0.2 cal K-’ mol-‘. Thus it can be stated that the system under consideration is not a strictly regular solution but is rather close to such a system in its thermodyn~ic behaviour, especially in the j3 and y homogeneous phases owing to the small values of ASxS in these regions, The dependences of ASxs as well as of AGXS on the concentration are given in Fig. 9. These results are in an accordance with the results of calculations by Alpaut and Heumann for the concentration range xs, = 0 - 0.40 within a margin, for ASxs, of +0.5 cal K-’ mol-‘.
27
-160 t
0.0
0.2
0.6
0.4
-x
sn
0.8
1.0
-
Fig. 9. Integral excess Gibbs free energy (100 “C) and excess entropy (75 - 125 “C) of formation curves of solid In-Sn alloys.
Acknowledgment This study is a part of a Ph.D. Thesis submitted Hacettepe, Department of Chemistry.
to the University
of
References 1 J. P. Bros and M. Laffitte, J. Chem. Thermodyn., 2 (1970) 151. 2 J. B. Cohen, B. W. Howlett and M. B. Bever, Trans. Metall. Sot. AZME, 261 (1961) 683. 3 0. Nittono and Y. Koyama, Chem. A&t., 96 (1981) 33654f. 4 R. I. Gauley, E. A. Lynton and B. Serin, Phys. Rev., 126 (1962) 43. 5 T. Heumann and 0. AIpaut, J. Less-Common Met., 6 (1964) 108. 6 0. J. Kleppa, J. Phys. Chem., 60 (1956) 842. 7 R. L. Orr, Trans. Metall. Sot. AZME, 236 (1966) 1445. 8 R. L. Orr and R. Hultgren, J. Phys. Chem., 65 (1961) 378. 9 J. Terpiiowski and E. M. Prezezdziecka, Arch. H&n., 5 (1960) 281. 10 F. E. Wittig and P. Scheidt, 2. Phys. Chem., 28 (1961) 120. 11 S. F. Bortram, W. G. Moffatt and B. W. Roberts, J. Less-Common Met., 62 (1978) 9. 12 Z. Wojtaszek and H. Kuzyk, Zesz. Nauk, Uniw. Jagiellon. Pr. Chem., 21 (1976) 27. 13 Z. Wojtaszek and H. Kuzyk, Zesz. Nauk. Uniw. Jagiellon. Pr. Chem., 19 (1974) 281. 14 B. Predel and F. Gerdes, J. Less-Common Met., 45 (1976) 23. 15 0. Alpaut and T. Heumann, Acta Met&., I3 (1965) 543. 16 0. Cakir, Ph.D. Thesis, Hacettepe University, 1983, p. 123.
THERMODYNAMIC
Metals,
141 (1988)
11
11 - 27
PROPERTIES OF SOLID In-Sn ALLOYS
0. CAKIR and 0. ALPAUT department
of C~ern~s~~, ~a~ette~e
(Received March 27,1987;
~l~~~ersit~, Ankara (Turkey}
in revised form September 23, 1987)
The thermodynamic properties of solid In-Sn between 75 and 120 “C over the entire concentration of cells of the form -
In(pure
solid)/InCl,(formamide)/In,Snl
_ Jsolid
alloys are studied range. The e.m.f.
alloy)
-I-
is measured as a function of alloy composition and temperature. The activities ai,j (i = In, j = Sri), the activity coefficients x,j, the partial molar Gibbs free energies AGi,j as well as the partial enthalpies hEl,,j of the components in the alloys are determined for various alloy concentrations, Also, the integral properties (i.e. AG and AH) are calculated. In connection with a survey of the concentration dependenees of all these properties, the locations of the phase boundaries in the solid state are discussed.
1. Introduction
The thermodynamic properties of liquid In-Sn alloys [l - lo] and also the pertinent phase diagram [5, 10 - 141 have recently been subjected to extensive studies. However, this is not true for the thermodynamics of the solid alloys in this system. The only work worth mentioning is the calculation of the enthalpy of mixing of solid In--&r alloys which has been carried out by Alpaut and Heumann [ 151 studying the differential thermal analysis curves of In-Sn alloys. Because a proper electrolyte has not been available, the e.m.f. method has not yet been applied to the solid alloys of this system. In this study a solution of InCls in formamide (CH,NO) is used as the electrolyte for the galvanic cells at any concentration. Formamide is unusual as its dielectric constant (110) is signific~tly larger than that of water. Nevertheless, it has a convenient liquid range (2.5 - 193 “C) and a low vapour pressure at room temperature. Electrical conductance measurements of InCl, in formamide solution show that InCls dissolves in formamide ionically. The cell established thus works reversibly [ 161. 0022-5088/88/$3.50
@ Elsevier Sequoia/Printed
in The Netherlands
12
2. Experimental details A potentiometric measuring system operating at minimum current was arranged to measure the e.m.f. of the galvanic cell -
In( pure solid)/InCl,( formamide)/In, Sn 1_ x
+
at various temperatures and alloy compositions. 2.1. Elec &odes 27 alloy electrodes were prepared by melting the proper amounts of indium (purity, 99.9995%; supplied by the PREUSSAG Company) and of tin (from BDH) together in a porcelain crucible under a purified argon atmosphere. The liquid alloys were cast into a stainless steel mould which has the following dimensions: top diameter, 1.0 cm; bottom diameter, 0.5 cm; length, 6.0 cm. The bars are used as solid electrodes. Pure indium and tin electrodes were prepared in the same way. The alloys were annealed under an argon atmosphere for 90 days at 10 “C below their corresponding solidus points. This process is required for the homogenization of the alloys and for the elimination of internal strains. 2.2. Electrolyte The electrolyte containing pure InCls was prepared by dissolving the salt in fractionally distilled and carefully purified formamide (99.5% from BDH) under an argon atmosphere. The anhydrous indium trichloride was synthesized by the chlorination of pure metallic indium in a stream of carefully dried and purified Cl* gas in a thoroughly dried quartz apparatus. 2.3. Cell The cell used is shown schematically in Fig. 1. The cell is placed in a stainless steel block set in a vertical furnace and closed with a Teflon cover. Three alloys and two pure indium electrodes are placed, at the same time, in this cell and the e.m.f.s between the In-In and indium-alloy electrodes are measured in the same run. A small flow of purified and dried argon was passed through the cell. 2.4. Temperature regulator A proportional temperature controller was used to control and regulate the temperature with a precision of +O.l “C!. A Leads-Northrup type 7554K4 potentiometer and an appropriate galvanometer were used. 2.5. E.m. f. measurements After the cell was set up, the temperature was regulated to 70 “C. Two pure indium and three alloy electrodes were inserted tightly into the cell through the holes of the Teflon cover. They were isolated with Teflon gaskets. After inserting the electrodes, one has to wait for 1 h before starting the measurements so that equilibrium conditions can be established at the
13
12
11
10
1, thermometer; 2, electrode connections; 3, Teflon Fig. 1. E.m.f. cell construction: 5, stainless steel block; 6, electrode; 7, brex cuvette; 8, electrolyte; cover; 4, furnace; 9, control probe cavity; 10, probe; 11, connection to proportional temperature controller; 12, electrode-potentiometer connections and argon gas inlet.
electrodes and within the electrolyte at the given temperature. Each run comprised at least three complete heating and cooling cycles in the temperature interval between 75 and 125 “C with small temperature steps between the measurements. The e.m.f. of the cell was reasonably stable to the order of +O.Ol mV. In-In e.m.f.s were controlled continuously in order to perceive any mechanical or other disturbances. During the measurements, the cell was under an argon atmosphere. Each measurement was been carried out from the upper potential to the lower and vice versa in order to enable continuous control of the reversibility. In order to measure the thermoelectrical potentials without an electrolyte at the same temperatures, the electrodes were connected to each other at the bottom while they were inside the cell. The resulting potentials were very small and within the limits of experimental reproducibility. The reproducibility of the measurements has a precision of +O.l mV. After the runs, apart from slight etching marks on the electrodes, there was no significant attack and there was no detectable change in their surface compositions. 3. Experimental
results
The resulting e.m.f. values are plotted U.S.temperature in Fig. 2 for various alloy compositions. In almost all cases good linearity is observed,
14 1 F: (rnV) 25.0
24.0
23.0
22.0
21.0
Xl.0
19.0
? 7.0
6.0
5.0
4.D
3.0
2.0
1.0
0.0
1 *
75
85
95
105 Temperature
Fig. 2. E.m.f. us. temperature are indicated at Table I).
115
125
("C)
plots for the In-Sn solid alloys (compositions
of the alloys
so that linear regression analysis has been applied. The results, i.e. the ensuing parameters, intercept a and slope b of the straight lines, together with their standard margins of confidence, are reported in Table 1. E.m.f.temperature data are not reproducible and could not be fitted to a straight line for tin-rich alloys (alloys 14 and 22 - 27).
15 TABLE
1
The coefficients of the E = a + bT temperature data for each alloy
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27
0.040 0.050 0.060 0.100 0.115 0.133 0.170 0.220 0.277 0.390 0.440 0.500 0.660 0.720a 0.750 0.770 0.792 0.810 0.820 0.830 0.860 0.894a 0.920a 0.9408 0.948a 0.96Qa 0.9808
aE.m.f.-temperature for these alloys.
equation
derived
0.12 0.10 0.39 1.19 0.67 0.67 0.99 1.25 1.45 3.54 1.00 0.52 0.88 -
f + * f f + 5 * + * + + *
0.09 0.04 0.13 0.15 0.20 0.11 0.21 0.24 0.12 0.14 0.08 0.17 0.18
0.0087 0.0102 0.0123 0.0108 0.0121 0.0131 0.0116 0.0206 0.0227 0.0255 0.0477 0.0624 0.0542 -
+_0.0008 + 0.0004 + 0.0012 rt 0.0015 + 0.0032 f 0.0011 + 0.0022 i 0.0024 f 0.0012 f. 0.0014 + 0.0042 f 0.0017 It: 0.0019
21 21 22 13 27 27 27 25 30 27 26 37 35 -
12.82 13.86 15.14 15.58 15.74 15.82 16.22 -
f. + + + 4 f f
0.31 0.29 0.57 0.38 0.42 0.39 0.22
0.0930 0.0855 0.0763 0.0735 0.0730 0.0730 0.0720 -
f f i f * f f
31 28 23 19 16 22 20 -
-
data are not reproducible
from
and could
the
0.0030 0.0028 0.0056 0.0039 0.0041 0.0040 0.0022
analysis
not be fitted
of
e.m.f.
and
to a straight line
The e.m.f. values with their standard deviations pertinent to the calculated straight lines are the basis for the computation of the partial molar Gibbs free energy of solution of the indium component in the alloys, by means of the usual relationship: A&, = --nEF where E is the e.m.f., AE,, (cal mol-‘) the partial molar Gibbs free energy of indium in the solution, n the valency of the transferred ions and F the Faraday constant (8’ = 96 487 C mol-I). Using the further relationship A&, = RT In aIn
16 TABLE2 Partial molarquantities of In-Snalloys at100 "C(indiumcomponent) Phase
0.960 0.950 0.940 0.900
0) (InI (InI
0.885 0.867 0.830 0.780 0.723 0.610a 0.560 0.500 0.340 0.250 0.230 0.208 0.190 0.180 0.170 0.140 0.106a 0.060a 0.052a
(InI + P
f P+r pp:; Y Y Y Y Y Y Y
Yin
0.912f 0.002 0.900f0.002 0.860+ 0.002 0.809+ 0.003 0.839f 0.004 0.831f 0.002 0.818f 0.003 0.734f 0.003 0.707* 0.002 0.566f 0.002 0.584f 0.003 0.532+ 0.002 0.556f 0.002 0.127+ 0.001 0.124+ 0.001 0.120+ 0.002 0.118+ 0.001 0.116+ 0.001 0.116+ 0.001 0.110+ 0.001 0.008f 0.001 0.010+ 0.001
0.950f 0.002 0.947+ 0.002 0.915+ 0.002 0.899+ 0.003 0.948f 0.005 0.958f 0.002 0.985f 0.004 0.941+ 0.004 0.978+ 0.003 0.928f 0.003 1.043t 0.005 1.064+ 0.004 1.635f 0.006 0.508f 0.004 0.539f 0.004 0.577+ 0.005 0.621f 0.005 0.644+ 0.006 0.682f 0.006 0.786f 0.007 0.130* 0.011 0.199f 0.018
-A&
AGIn=
(calmol-')
(caImol-')
68fl 78+1 112fl 156k2 13Ok3 137 +1 148 f2 228+2 257+ 2 421f2 399+4 468f2 435+2 1531f3 1550f3 1575+6 1586f5 1594 f5 1596f5 1634f5 3600f70 3400f70
-38f2 -33f2 -66+2 -79+3 -4Of4 -32+2 -11+3 -45+3 -16+3 -55*3 31+4 46+3 364+3 -502f6 -458f6 -407 f6 -353f6 -326+7 -284+7 -179f7 -1510f61 -1200 +64
I%) f:In(aIloy)(,). aPhaseboundaries. the indium activities a,, of the alloys have been obtained at a fixed temperature. From the activities and compositions, using the 71n = aI&rn relationship, the activity coefficients yin of indium in the alloys have been calculated by applying the relationship AC InxS = RT In yI,,
@a)
the excess partial molar Gibbs free energy AaInxS has been calculated: A&=
= AC,,, - AC,;’
Pb)
where AcInid is the partial molar Gibbs free energy of indium in an ideal solution. The corresponding partial molar quantities for the second component of the alloys may be satisfactorily determined by graphical integration of the Duhem-Margules relationship in the form *sn = xsn ln Yin ln xn (4) In YSn = ( 1 _ XIn)2 XInXSn - x_fSn = 1 (1 - XIn)2 d%n
17 TABLE3 Partial molar quantities of In-Snalloys at 100°C (tin component)
XSn 0.040 0.050 0.060 0.100 0.115 0.133 0.170 0.220 0.277 0.390a 0.440 0.500 0.660 0.750 0.770 0.792 0.810 0.820 0.830 0.860 0.894a 0.940a 0.948a
Phase
(In) + P
; P
“,+s P=r Y Y Y Y Y Y Y
asn
0.038f 0.003 0.051+ 0.003 0.070f 0.004 0.172+ 0.006 0.124f 0.005 0.132f 0.005 0.143-+0.005 0.222+ 0.007 0.255+ 0,006 0.392f 0.007 0.377f0.007 0.418f 0.007 0.409+ 0.007 0.760+ 0.004 0.765+ 0.004 0.770+ 0.004 0.772+ 0,004 0.775f 0.004 0.775f 0,004 0.780f 0.004 0.943+ 0.013 0.954+ 0.013
YSn
0.941f 0.080 1.022f 0.058 1.167f 0.065 1.719+ 0.060 1.080* 0.040 0.994+ 0.040 0.844f 0.040 1.011+ 0.030 0.922+ 0.020 1.006f 0.015 0.857f 0.015 0.837+ 0.015 0.620f 0.015 1.014f 0.005 0.993f 0.005 0.972f 0.005 0.953k 0.005 0.946f 0.005 0.934+ 0.005 0.907+ 0.005 1.003+ 0.010 1.007f 0.010
-A&,
AEsnXS
(Calmol-')
(calmol-')
2430f50 2205f45 1970+40 1305f27 155oi31 1500+30 1440 + 29 1115 zt24 1010 zt21 693 f14 723+15 645+13 663 f13 203 f4 199+4 194+4 192f4 189f4 189f4 184 k4 44 f10 35 f10
-45 16 114 402 57 -4 -126 8 -60 5 -114 -132 -354 +lO -5 -21 -36 -41 -50 -72 2.2 5.1
Sn(,)+ W~loy)(,). aPhaseboundaries.
The activities Ui,j, the activity coefficients yij, the partial Gibbs free energies ACi, j of solution as well as the excess partial Gibbs free energy ACi+jxs (i, j = In, Sn) determined in this way are given in Tables 2 (indium) and 3 (tin). The activities and the partial Gibbs free energies of the components as functions of the composition are plotted in Figs. 3 and 4. 3.2. Entropy of formation The partial entropies As,,, of formation are given by the expression, A&, = nF(dE/dT),
of indium
at any temperature (5)
The dE/dT values are the slopes of the best straight lines through the experimental points (b values in Table 1). These values increase with increasing mole fraction of the tin component. The increasing scatter of the points at high temperatures stems from the increase in the standard deviations of the entropy values. The partial molar entropies of formation are reported in Tables 4 and 5 and these are plotted in Fig. 5.
18
aa a0 In
02
0.4 46 --An--c
0.6
1.0 Sn
0.0
0.2
0.4
In
0.6
0.8
1.0
sn
----XSll-
Fig. 3. Relative activity curves of indium and tin in their binary systems at 100 “C. usn is calculated from the GibbeDuhem equation. Fig. 4. Partial Gibbs free energies of solid In-Sn alloys at 100 “C. TABLE 4 Partial molar enthalpy, (indium component)
entropy
and excess entropy
of In-&
XIIB
Phase
0.960 0.950 0.940 0.900 0.886 0.867 0.830 0.780 0.723 0.610a 0.560 0.500 0.340 0.250 0.230 0.208 0.190 0.180 0.170 0.140
fW
wn
a.n
155 f 23 186 k 13 205 * 31 122 f 39 182 f 35 201 f 31 151+ 38 302 f 65 327 f 32 238 f 39 830 f 112 1143 + 47 963 + 51 875 + 85 658 f 74 395 + 151 3llk 106 290 * 109 278 + 109 246 f 72
0.60 0.71 0.85 0.75 0.84 0.90 0.80 1.42 1.57 1.77 3.30 4.32 3.75 6.45 5.92 5.28 5.09 5.05 5.03 5.01
(caI mol-i)
(In) (In) (In) + P ; P $1; + Y Y Y’ Y Y Y Y
In(s) * In(alloy)(,.. aPhase boundary.
(cal mol-’
K-* 1
f 0.06 f 0.03 f 0.08 f 0.10 ?r 0.22 f 0.08 zk0.15 + 0.17 f 0.08 + 0.10 + 0.29 kO.12 ?I 0.13 f 0.22 + 0.19 + 0.39 + 0.27 f 0.28 f 0.28 + 0.18
alloys at 75 - 125 “C
ASn.,=s (cal mol-’
K-’ 1
0.52 f 0.06 0.61 f 0.03 0.73 + 0.03 0.54 f 0.10 0.60 + 0.22 0.62 k 0.08 0.43 + 0.15 0.93 k 0.17 1.06 + 0.08 0.79 * 0.10 2.15 + 0.29 2.94 f 0.12 1.61 + 0.13 3.70 + 0.22 3.00 * 0.19 2.16 f 0.39 1.79 + 0.27 1.64 f 0.28 1.51+ 0.28 1.10 5 0.18
19 TABLE 5 Partial molar enthalpy, entropy and excess entropy of In-Sn alloys at 75 - 125 “C (tin component)
-&I
Phase
0.040 0.050 0.060 0.100 0.115 0.133 0.170 0.220 0.277 0.390a 0.440 0.500 0.660 0.750 0.770 0.792 0.810 0.820 0.830 0.860
(InI (In) (In) (In) + P (In) + P
A%ll
(Cal mol-‘)
i
2271+ 335 1530 f 107 1346 k 203 1890 f 388 1353 f 332 1196 f 184 1461 f 361 846 + 182 766 f 74 800 + 131 10 f 2 -317 f 13 -243 f 13 -199 k 19 -129 ?r 15 -57 * 22 -32 + 11 -28 k 10 -26 f 10 -19+6
Ass,
(caI mol-’
Ai&=
K-.’ )
12.6 f 0.9 10.0 f 0.3 8.9 + 0.6 8.4 f 1.6 7.7 + 1.7 7.2 f 0.5 7.8 * 1.5 5.2 5 0.5 4.8 10.2 4.0 f 0.4 1.96 + 0.03 0.88 f 0.05 1.12 f 0.05 0.01 + 0.06 0.19 + 0.04 0.37 + 0.06 0.43 * 0.04 0.43 + 0.03 0.44 * 0.03 0.44 + 0.02
(caf moi-’
K-l)
6.2 +_0.9 4.0 f 0.3 3.3 + 0.6 3.8 + 1.6 3.4 f 1.7 3.2 k 0.5 4.3 + 1.5 2.2 i 0.5 1.8 5 0.2 2.1 i 0.4 0.33 * 0.03 0.58 f 0.05 0.29 f 0.05 -0.56 + 0.06 -0.33 5 0.04 -0.09 + 0.06 0.01 + 0.04 0.04 f 0.03 0.07 f 0.03 0.14 + 0.02
SW * W~lw)(,).
*Phase boundary.
3.3. Heats of forenoon Partial heats A!.&, of solution of indium may be obtained from the above partial properties by applyyingthe Gibbs-Helmholtz relationship A&
= AC,,, + T A&
(6)
The accuracy of heats determined in this way is very strongly dependent on the precision with which the temperature coefficient of the cells can be established. The results for A&, at 100 “C show considerable scatter; the values indicated positive integral heats of fo~ation, e.g. about 1140 cal mol-’ at the equiatomic composition. Partial heats of solution m, of the tin component are calculated from the MI, values by graphical integration of the Gibbs-Duhem relationship in the form
(7) The values obtained are valid for temperature intervals ranging from 75 to 125 “C. On the basis of these values and the partial Gibbs- free energies
In
Sn
pxSn-
Fig. 5. Partial entropies of formation of solid In-Sn alloys (7.5 - 125 “C).
A&, of formation, the partial entropies A&, of formation of the solution of the tin component can be computed by using the relationship A$& = ms, - A&,,/T. The thermodynamic quantities calculated thus are given in Tables 4 and 5. The partial excess entropy values A&,.,= are calculated from the relationship ASi,j= = ASi,j -R
In xi,j
(i, j = In, Sn)
for both components and given in the said tables. The dependences partial quantities on the composition are plotted in Fig. 6.
(6) of these
3.4. Integral quantities The integral Gibbs free energies AG, the enthalpies AH and the entropies AS of formation of these alloys are given by the following relationships: AG = xrn Ai?,, + xs,, AGsn AH = xin A&,
+ xsn A&
AS = x1, ASI, + xs,, A&
(9) (16) (11)
21
0
0.0
0.2
J”
0.4
~XSni
0.6
0.8
1 .o
sn
Fig. 6. Partial heats of solution of solid In-Sn alloys (75 - 125 “C).
The standard reference states throughout are the pure solid components. In Table 6, AH and AS values are given for temperature intervals ranging from 75 to 125 “C; AG values are given for 100 “C.
4. Discussion Thermodynamic investigation of alloys by the e.m.f. method is based on the linearity of the e.m.f.-temperature curves within the given temperature interval under consideration. If dE/aT = constant, then aG/aT= nF(aE/aT) = AS = constant. Therefore AH has to be constant in this temperature range. From this point of view (C, - Cpo)rn= 0 and (C, - Cpo)sn= 0 in the range of experimental errors. Indeed, it seems to be true that in the system investigated within the chosen temperature interval linearity is obeyed within the 95% standard probability range, so that our evaluation procedure, the values of the thermodynamic quantities resulting from it and the conclusions on the basis of these values seem to be entirely justified. It ought to be mentioned here that a considerable error source in the application of the e.m.f. method may lie in the occurrence of the so-called displacement reaction. In our case, this reaction can be described as
(InI (InI
Phase
1.08f 0.10 1.17f 0.04 1.33+ 0.11 1.51f 0.25 1.67k 0.40 1.74f 0.14 1.98+ 0.40 2.26+ 0.24 2.45+ 0.11 2.63+ 0.22 2.71+ 0.18 2.60+ 0.08 1.96+ 0.08 1.62+ 0.10 1.50f 0.07 1.38+ 0.13 1.23+ 0.08 1.27f 0.07 1.22f 0.07 1.08+ 0.04 -
240+35 254+18 273+41 294+75 317 *,70 333+51 374f93 422+91 449f44 457+75 47lf64 413+30 167226 70*35 52f28 37k48 33529 30+28 26f26 18 +15 -
163k 2 184+2 224+2 271k3 293+4 308k2 367+3 423+3 466+44 527+-5 542+2 557+4 56524 535+44 51Ok4 481+4 428?r4 442+4 42854 387rf:4 257+10 209klO
aPhaseboundary.
- 125 ‘C)
(calmol-lK-l)
u(75
(calmol-')
(calmol-')
“C)
mc 15 - 125
--AC+ 100 w
(1 -x)In(,)+ xSn(,)* Inl_,Sn, tsj,
0.040 0.050 0.060 0.100 0.115 0.133 0.170 0.220 0.277 0.390a 0.440 0.500 0.660 0.750 0.770 0.792 0.810 0.820 0.830 0.860 0.894s 0.940a 0.948a
XSn
Integral propertiesof In-Snalloysat75 - 125°C
TA3LE6
oc)xs
38+2 37+2 5522 3124 29+4 28 f 3 3022 33 +4 28 +4 32+6 33+4 43 +4 11055 11824 10924 10154 96 lt4 92+4 90 f4 8723 88 +10 57 f10
(calmol-*)
--aG(loo 475
- 12sac)xs
0.74+ 0.10 0.77f 0.04 0.88+ 0.11 0.85+ 0.25 0.91f 0.40 0.97* 0.14 1.08f 0.40 1.20+ 0.24 1.25+ 0.11 1.30+ 0.22 1.34f 0.18 1.20+ 0.08 0.68f 0.08 0.50f 0.10 0.40f 0.07 0.35f 0.13 0.26+ 0.08 0.34f 0.07 0.31i 0.07 0.27f 0.04 -
(calmol-'K-l)
23
3Sn + 21n3+ e
3Sn2+ + 21n
Such reactions affect the cell potential by producing a mixed potential. The change of the Gibbs free energy which is due to this reaction can be quantitatively estimated; it is of positive sign and in most of the cases regarded here of negligible amount. Only in tin-rich alloys does it become noticeable. The following discussion of the results obtained will have two parts: (1) the phase diagram and (2) the thermodynamic quantities proper. 4.1. Phase diagram As Fig. 2 shows, the e.m.f. values of the cell increased with increasing tin mole fraction of the alloys. The behaviour of the e.m.f. us. temperature lines, the activity isotherms and the e.m.f. values indicated that the phase boundaries of the In-Sn phase diagram agree with previous values given by Heumann and Alpaut [ 51. The alloy having the composition xsn = 0.720 yields different e.m.f. values during cooling and heating. Therefore the reproducibility was very poor. The reason for this may be the phase transformation from the /3 + y field to the y phase region. Heumann and Alpaut said that this boundary lies in the xSn = 0.750 - 0.770 range for the 75 125 “C temperature interval [5] (Fig. 7). In the present investigation this boundary has been found to be located at the xsn = 0.720 composition, thus being in a vertical position. The alloys which have compositions xSn = 0.770, xsn = 0.792, xsn = 0.810, xSn = 0.820 and xSn = 0.860 belong to a
0
10
20
30
40
50
60
I" Atom
%
Sn
10
80
90
100 S"
Fig. ‘7. The phase diagram of In-Sn [ 51, showing the compositions and temperature intervals for the alloys studied. The y phase boundary obtained from our experimental results (x) departs from tbe phase boundary of Heumann and Alpaut.
24
separate homogeneous region in which the e.m.f. values are increasing with temperature. From this region to pure tin (3csn= 1.00) the boundaries found are the same as those of Heumann and Alpaut. 4.2. Thermodynamic quantities The partial Gibbs free energies of solution which are calculated for the e.m.f. values give precise results, but the results of the entropy and enthalpy calculations are increasingly affected by errors. These errors ought to be discussed in detail. The plots of the activities us. composition are shown in Fig. 3 for a temperature of 100 “C. The activities are constant in the @+ 7 heterogeneous phase region and also in the narrow In (= a) + p region. Therefore the partial molar Gibbs free energies of the components must also be constant in the same regions. The integral Gibbs free energies of solution thus exhibit linear courses within the heterogeneous composition ranges (Fig. 8), as common tangents to the more curved parts pertinent to the adjacent homogeneous phase ranges, so that the actual points along the curve are always representing the minimum possible values of AG.
0.0
0.2
04 -
0.6
08
1.0
a-
Fig. 8. Integral entropies (75 - 125 “C), enthalpies (75 - 125 “C) and Gibbs free energies (100 “C) for the formation of In-Sn solid alloys: @, this study; l, from Alpaut and Heumann [ 15 ] ; AHmL, from Bros and Laffitte [ 11.
25
In order to calculate the entropies, the slopes of the e.m.f.-temperature lines have to be known with high precision. Caution should be taken in considering the temperature coefficient of A&, measured in a two-phase region lest the composition of the phase change with temperature. In a homogeneous phase for a constant indium composition xln, the partial entropy change A$, is given by A&, = -(a
(12)
A8,,/aT),
while in a heterogeneous d AG,,/dT
mixture
= (a A&/aT),
there is
+ (a A&/ax),
d,/dT
If the last term of eqn. (13) can be ignored, than the equation d A&]dT
= -A&,
(13) becomes (14)
Therefore there are some additional errors in heterogeneous regions. The integral enthalpies are calculated from the integral entropies and the integral Gibbs free energies. Therefore the errors of these properties accumulate to yield the errors of the enthalpy results. Therefore, it is better to determine the enthalpy of solution directly by other methods, such as calorimetrically. The calculated integral enthalpies of formation of solid In-Sn alloys are depicted in Fig, 8. The integral enthalpies have positive values with a maximum to 471 + 64 cal mol- 1 in the heterogeneous region. Alpaut and Heumann [ 151 have given the only data as yet, with a maximum value of 500 cal mol-’ (Fig. 8). These results agree with each other within the it has not been range of experimental errors. At the xsn = 0.860 composition possible to obtain a satisfacto~ result so that the second maximum Alpaut and Heumann have given could not be affirmed. The enthalpies of mixing for liquid In-Sn alloys which have been reported by Bros and Laffitte [l] are also shown in Fig. 8. The integral mixing enthalpies of solid alloys are, in general, additively composed of three major terms, which are regarded as being independent of each other, namely A&s
= bH,s
+ A&s
+ A&s
(15)
where AlY,’ 1s . due to bonding changes on alloy formation, disregarding structural and atomic radii differences, which are taken into account by the other two terms. AHBs depends on the chemical character of the constituents, Le. on their relative positions in the periodic table of the elements. This term predominates in intermetallic phases. A.&’ stems from the strain due to atomic radii differences and thus is always positive. Its importance, obviously, increases with increasing atomic size difference of the alloying partners. It may be mentioned that this term is also effective in the liquid state. As the single bond covalent
26
radii of indium and tin are 1.44 a and 1.40 A respectively, in the system regarded here CLHn’ IS * negligible in the solid as well as in the liquid state. Finally, AJ!lr’ results from the transformation enthalpy which has to be expended in order to transform either component from its stable structure at the temperature in question into the stable structure of the alloy. This term is equal to zero on the formation of most liquid alloys. Thus, for liquid In-& alloys A&L = AHaL. At the same time LWBS = MnL. This assumption is particularly true when the components have similar chemical properties as a result of their similar electronic structures. Indium is in the neighborhood of tin in the periodic table. On the basis of the above assumptions Al&s = A.&n + AHns + AZ&s
(16)
can be written. According to Bros and Laffitte [l] as well as Gauley et al. [ 4], AHmL has a maximum value of about 50 cal mol-’ and AHi,’ has to be small according to the above discussion. Then it can be said that 90% of Mm’ results from the ARrs term. This is obviously due to the tr~sition from the thermodynamically stable tetragonal white tin to the f.c.c, structure in the alloy. This transformation term thus causes the enhanced value of the formation enthalpy of the solid In-Sn alloys. The positive enthalpy in the solid alloys causes narrowing of the phase regions of the homogeneous solid solutions with decreasing temperature. The fl phase region shrinks more than the other phases when the temperature is lowered. The extrapolation of the equilibrium curves in this region shows that the decomposition of this phase ought to take place at a temperature of about -70 “C. Enthalpy as well as entropies show similar changes in a binary system but the Gibbs free energy is little affected by these changes. Positive enthalpy is usually connected with positive entropy. This is also valid in the In-Sn alloy system. Kubaschewski has shown that, if A&, is positive, the excess entropy As”” in a binary system also has to be positive and, according to the AC”” = M - T ASXs relationship, negative AG values and positive M values imply that ASXs has to be positive: this obviously is also valid in the region in which maxima or minima occur. ASxs has indeed a maximum value of +2.0 cal KM1 mol-’ in this system (Fig. 9). In strictly regular solutions A,!? has to be zero. Usually one can say that this condition is fulfilled if ASxs lies within the range 0.0 - 0.2 cal K-’ mol-‘. Thus it can be stated that the system under consideration is not a strictly regular solution but is rather close to such a system in its thermodyn~ic behaviour, especially in the j3 and y homogeneous phases owing to the small values of ASxS in these regions, The dependences of ASxs as well as of AGXS on the concentration are given in Fig. 9. These results are in an accordance with the results of calculations by Alpaut and Heumann for the concentration range xs, = 0 - 0.40 within a margin, for ASxs, of +0.5 cal K-’ mol-‘.
27
-160 t
0.0
0.2
0.6
0.4
-x
sn
0.8
1.0
-
Fig. 9. Integral excess Gibbs free energy (100 “C) and excess entropy (75 - 125 “C) of formation curves of solid In-Sn alloys.
Acknowledgment This study is a part of a Ph.D. Thesis submitted Hacettepe, Department of Chemistry.
to the University
of
References 1 J. P. Bros and M. Laffitte, J. Chem. Thermodyn., 2 (1970) 151. 2 J. B. Cohen, B. W. Howlett and M. B. Bever, Trans. Metall. Sot. AZME, 261 (1961) 683. 3 0. Nittono and Y. Koyama, Chem. A&t., 96 (1981) 33654f. 4 R. I. Gauley, E. A. Lynton and B. Serin, Phys. Rev., 126 (1962) 43. 5 T. Heumann and 0. AIpaut, J. Less-Common Met., 6 (1964) 108. 6 0. J. Kleppa, J. Phys. Chem., 60 (1956) 842. 7 R. L. Orr, Trans. Metall. Sot. AZME, 236 (1966) 1445. 8 R. L. Orr and R. Hultgren, J. Phys. Chem., 65 (1961) 378. 9 J. Terpiiowski and E. M. Prezezdziecka, Arch. H&n., 5 (1960) 281. 10 F. E. Wittig and P. Scheidt, 2. Phys. Chem., 28 (1961) 120. 11 S. F. Bortram, W. G. Moffatt and B. W. Roberts, J. Less-Common Met., 62 (1978) 9. 12 Z. Wojtaszek and H. Kuzyk, Zesz. Nauk, Uniw. Jagiellon. Pr. Chem., 21 (1976) 27. 13 Z. Wojtaszek and H. Kuzyk, Zesz. Nauk. Uniw. Jagiellon. Pr. Chem., 19 (1974) 281. 14 B. Predel and F. Gerdes, J. Less-Common Met., 45 (1976) 23. 15 0. Alpaut and T. Heumann, Acta Met&., I3 (1965) 543. 16 0. Cakir, Ph.D. Thesis, Hacettepe University, 1983, p. 123.