202
T. YOKOKAWA, X.DOI.%XU KICHIZOS I R A 4
Vol. 65
THERMODYSAPIIIIC STUDIES ON LIQUID TERYARY ZINC SOLUTIOKS1 BY TOSHIO YOKOKAWA, AKIRADOI AND KICHIZOXIWS Department of Chemistry, Faculty of Science, Hokkaido Cniversity, Sapporo, J a p a n Recczvcd B p i d 9. 1960
Vapor pressure of zinc has been measured as to three ternary metallic solutions: tin-zinc-bismuth, indium-zinc-bismuth and tin-zinc-indium in the range 0 to 0.3 in zinc mole fraction a t the neighborhood of 625'K. by Knudsen's effusion method. The results show that the excess partial molar free energv of mixing of zinc in the indium-zinc-bismnth system gives a maximum, when plotted against concentration of bismuth, mole fraction of zinc being kept constant a t 0.1. This fact is concordant nith the calculation, which is based upon the assumption of a simple pair bond model. In the other two systems the above comparison is not successful. I t has been suggested that this mav be attributed to the influence of the third component on pair interaction.
Recently much effort has been made toward the theoretical interpretation of electro-magnetic and thermodynamic properties of metallic solutions. Thermodynamic properties have been established for a wide variety of binary solutions. On the other hand, only a fern studies have been cariied out on ternary systems except multi-component systems in high dilution. It would be interesting to find any new character in ternary systems beyond what is expected from three separate binary systems. In the case of multi-valent B-metals in the periodic table, the comparison of a ternary system with a binary one is especially interesting because in these metals the electronic state and accordingly ionic radius show complex behavior 011 alloying. Thus in the present work the vapor pressure of zinc in ternary liquid solutions of SnZii-Bi, In-Zn-Bi and Sii-Zn-In was measured by means of Knudsen's effusion method. The results are discussed in comparison with those found in binary solutions. Experimental Knudsen's effusion method was employed. Euperimental apparatus and procedure have been described in the previous paper.* A Pyrex crucible, on the lid of which an orifice is groiind, is hung by platinum wire from a thermobalance. Effusion velocity is determined by current change of a linear differential transformer, the central core of which is.attached to the beam of the balance through platinum wire. The effective area of the orifice is determined by combining the effusion velocity of solid pure zinc and its vapor pressure, the latter having been established by Barrow, et ~ 1 . ~ The applicability of this method to zinc liquid alloys has been tested in the system.2 Vaporization velocity is great enough compared with effusion loss in spite of disturbance of oxide film and diffusion of zinc through bulk phase t o surface is grtJat enough to keep the surface concentration constant. Purities of metals used are 99.9% (zinc), chemical pure (tin), 99.9cl, (bismuth), and 99.999% (indium). hlloys were prepared in the follonTing way: pure metals of desired composition were sealed in small Pyrex tubes under vacuum and kept a t about 450" for about ten hours, then quenched. For the case of ternary alloys, a binary alloy nithout zinc n a s made a t first and then zinc was added. For the sources of error of determining vapor pressures by the present method, there should be taken into consideration temperature, sensitivity of the thermobalance, the rate of current change in the linear differential transformer, and the orificrl area. Then the fractional average deviation of (1) (a) Presented at the 44th annual meeting of the J a p a n Institute of Metals in Tokyo, April, 1959: (b) this paper is a part of the thesis presented hy T. Yokokaiva to Hokkaido University in partial fulfillment of the requirements for a D.Se. degree. (2) K. Ni>!-a. T. Yokokawa and H. Wada, J . Chem. Sac. J a p a n 33, 1345 il9RO). (3) R . F, Barrow, c f a l . , Trans. FarndaU SOC.,51, 1354 (1955).
vapor pressure amounts to 3.247,. activity is estimated to be 47,.
The relative error of
Experimental Results liquid metals or alloys, to which zinc was added, were prepared from tin and bismuth, the atomic ratio being 0, 0.33, 0.5, 0.66 and Concentration of zinc ranged 0.05 to 0.2. Xt each concentration vapor pressures of zinc mere measured ten times over the temperature range of about SOo in two or three runs. Experimental results are summarized in Table I in the form of temperature equations, though the temperature coefficients are not as reliable as the absolute values on account of the rather narrow temperature range. Activity of zinc a t 625°K. is shown as a fuiiction of concentration in Fig. 1. Activity in tin-zinc alloy has been measured already by Taylor? by e.m.f. method. Present data are slightly lower than the value extrapolated from Taylor's data. As for the bismuthzinc binary system, the activity value of the present measurement agrees well with the previous data5. -4ctivity of zinc monotonously increases as tin is replaced by bismuth.
Sn-Zn-Bi System.-Mother 03.
TABLE I VAPORPRESSURE OF ZIKC IN TIX-ZINC-BISMUTHSYSTEM^ logP = - A/T B
+
SRi/SSn
0
S Zn
A
0.027 .lo4 .150 .252 ,304 ,050 ,149 ,294 ,066 ,102 ,201 .284 ,050
B
5206 5.546 5432 6.286 ,5976 7.312 5822 i ,349 5769 7.273 0.499 4225 4.051 5246 6.161 6966 $1,197 0.998 4508 4.776 4957 5.666 5249 6.286 5630 7.079 2.00 5395 6.041 ,100 4957 5.652 7.299 ,151 5867 .199 5666 7.095 m ,056 4195 4.355 .loo 5986 7.467 ,149 5206 6.290 The effective areas of orifices: 0.5795, 0.2433, 0.3579 and 0.2765 mm.2. (I
(4) N. F. Taylor, J . A m . Chem. Soc., 45, 2805 (1923). (5) 0. J. Kleppa, J . A m . Chem. SOC.,74, 0082 (1952).
THERMODYNAMIC STUDIESO N LIQCIDTERNARY ZINC SOLL-TIOSS
Feb., 1961
203
0.6
0.5
0.4 6
s" 0.3
0.2
0.1
0.1 Fig. 2-Activity
I
0.1 Fig. 1.-Activity
0.2
xz,.
0.3
0.4
of zinc in Sn-Zn-Bi a t 625'K.
In-Zn-Bi System.-3leasurements have been made in the sa,me way as for Sn-Zn-Bi. Vapor pressure and activity at 625°K. are shown in Table I1 and Fig. 2, respectively. Activity of zinc in JnZn has been measured by Svirbely and Selk6 The present data agree with theirs within the range of experimental error. As is seen in Fig. 2, activity of zinc increases with bismuth content and has a maximum on the bismuth-rich side of the equiatomic point with respect to indium and bismuth.
0.2 0 .8 xzn. of zinc in In-Zn-Bi at 625'K.
Sn-Zn-In System.-Master alloys of tin and indium with atomic ratios of 0.33, 1 and 3 were prepared to which zinc was added to the concentration of 0.05 and 0.1 mole fraction. T'apor pressure equations and the activity at 625°K. are shown in Table 111 and Fig. 3. The activity of zinc at its definite content increases with addition of indium. TABLE I11 ZINC I N TIX-ZINC-INDIUM SYSTEM' logP -A/T B
VAPOR PRESSURE O F
XI"/XS"
xzn
+
B
A
Table I 0.049 3557 3.003 TABLE I1 099 4693 6,009 VAPOR PRESSURE: OF ZINC IX INDIU.\.~-ZINC-BIS~~UTH ,153 6172 7.684 SYSTEM^ 0.920 ,049 4789 4.950 XHi/Xl" XZ" A B ,100 5747 6.847 0 0.052 4894 5.354 ,151 6367 7.973 ,085 5874 7.117 3.00 ,045 5426 6.155 ,151 6394 8.153 ,100 5228 5.997 0.501 ,040 6521 8.070 .149 4999 5.828 ,109 4989 5.906 a The effective area of the orifice: 0.2765 mm.2. 0,999 ,049 4319 4.711 ,101 4924 5.875 TABLE IV 2.01 ,033 6909 8.805 ,087 5523 6.755 P A R A M E T E R S O F SUB-REGULAR S O L C T I O N S ( E Q U A T I O N 7) m Table I AizO Asan An0 AIS' A2s' Aa' 1060 3100 -275 -430 1280 -125 (a) Sn(l)-Zn(2)-Bi(3) a The effective area of the orifice: 0.2765 mm.2.
0 0.334
( b ) In(l)-Zn(2)-Bi(3> (6)
W.,J. Srirbely ?nd S. hI. Selis. zbid., 76, 1532 (1'353).
Sn(l)-Zn(2)-In(3)
2320 3100 2320 1000
-700 0
-420 -430
1280 420
0 0
204
AND
I
1
i I
Vol. 65
of zinc of 0.1 in the three solutions, respectively. The value of lrzne changes almost linearly in SnZn-Bi and Sn-Zn-In systems, while it shows a maximum in the In-Zn-Bi system. The meaning of these behaviors is to be examined on the basis of the facts known about binary solutions. -issuming that pze in a ternary solution is a function of second order of the mole fraction of the third component, pze is expressed in general as
I
i
KICHIZO NIWA
II
0.7
0.6
pze
=
A
+ BX3 + CXj2
(1)
where A , B and C are constants independent of concentration. Differentiating equation 1 with respect to Xd,there is obtained
0.5
Then dj.~*~/dX3 = B when X3 is taken as zero, and dpze/dXa = B 1.8B when X3 is taken as 0.9. That is to say, B and B 1.8C give the slopes of pze at X3 = 0 and XI = 0, respectively. Therefore, the p2e-curvebecomes linear, concave or convex to abscissa, according as C = 0, C < 0 or C > 0, respectively. The physical significances of B and C are not known as simple functions of mole fraction of each component. But one can approximately derive explicit formulas of B and C, provided that these solutions obey the pair-bond model as in the case of non-metallic solutions and further are regarded as regular solutions. I n that case the excess molar free energy of solution is given by
+
z1 ; 0.4
0.3
0.2
0.1
F"
= X1X?A1?
+
+ X2X3A23 f XlXlA3l
(3)
where Aij is a constant determined for the i-j pair and independent of the third component. Equation 3 yields an expression for pze 0.1
Fig. 3.-Activity 2000
I
I
I
0.2 0.3 XZ,. of zinc in Sn-Zn-In a t 625°K. I
I
I
I
I
I
p2e
= (Xi2
+ XlX3)AlZ + (X3? + X I X ~ ) A-Z ~
X3XlA31 (4)
I
Putting Xz = 0.1 and differentiating equation 4 with respect to X3 d&e
dXa
=
O.g(AZ3 -
A12
- -421)f
2dY3A31
(5)
By comparing equation 2 with 5 one obtains B = 0.9(AZ3- A,? -
A31)j
and C = A31
The above calculation shows that curvature of pze in a 1-2-3 ternary system is determined by AS1 or the interaction of the 1-3 binary system. If, here, the following notations are employed to represent the orders of the components of the three systems, 3-1 pairs are Bi-Sn, Bi-In and In-Sn. 1000
I
I
0
0.2
0.4
x, = xsi.
0.6
I
I
0.8
(a) Sn(l)-Zn(2)-Bi(3) (b) I n (1)-Zn(2)-Bi(3) (c) Sn(l)-Zn(2)-In(3)
Bi-Sn and In-Sn systems behave almost as ideal solutions, while the Bi-In system shows a negative deviation from ideality. Then, thisl analysis predicts that the pze-X3 curve is linear in (a) and (c) soluDiscussion tions and concave to the abscissa in the (b) solution. Thermodynamic properties of alloys can be This prediction may be qualitatively concordant appropriately given in terms of excess functions. with experimental results graphed in Figs. 4, 5 In Figs. 4, 5 and 6 are shown the trends of excess and 6. A more quantitative treatment is tried under the chemical potential of zinc, pzne, defined as the difference of the partial molar free energy of solution assumption of the "sub-regular" character for of zinc from that of ideal solution, at mole fraction each binary system, since most metals behave as
Fig. I.--Excess partial molar free energy of mixing of zinc in Sn-Zn-E:i a t Xzn = 0.1 a t 625"I
