Effect of small additions of silver on the eutectic temperature in the lead-tin system
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I.
INTRODUCTION
THE addition of a third component to binary alloy solders is of importance both in terms of modifying the flow properties and solidification temperature to suit fabrication processing, and of controlling and improving the mechanical properties to prevent their degradation with time. A typical example of such a system is the addition of a few percent silver to the lead-tin binary eutectic] a ternary solder commonly used for making printed circuit connections. There is only limited information on this particular system and for many other lead-tin based ternary systems now in common use. It will be shown here, however, that reasonable estimates can be calculated for the change in the eutectic temperature of a binary system with small additions of a third component. Recent work by Esdaile, Ng, and Siviourz on the correlation of the thermodynamic properties and phase diagram of the lead-tin system provides an excellent basis for the calculation of the effect of small additions of a third component on the eutectic temperature of this system. This study considers the influence of silver on the depression of the eutectic temperature using the analytic approach described by Lupis.3' 4 II.
NOMENCLATURE
The subscripts 1, 2, and 3 refer to tin, lead, and silver, respectively, while S and L refer to the solid and liquid states. Values of free energy (G) and latent heat of fusion (Li) are in J/mole; heat capacities (Ct,) have units of J/mole-deg. In the following equations, X is the atomic fraction, T is temperature in ~ y is the activity coefficient, y~ is the activity coefficient in the infinitely dilute solution, and t~ is the stability function. The parameters Cs, C, D, and w~ which appear in Sections III and IV have been defined by Esdaile, Ng, and Siviour; 2"6 C~ and C have units of J/mole. III.
Pb-Sn SYSTEM PARAMETERS
The eutectic temperature and composition used in this analysis are those of Esdaile et al., 2 namely Te = 456.363 K and X~b = 0.2586, while the other eutectic compositions of X~b = 0.7095 (Pb-rich solvus boundary A) and X~b = 0.0145 (Sn-rich solvus boundary B) were obtained from the Metals Handbook. 5 S. K. TARBY and M. R. NOTIS are Professors of Materials Science and Engineering, Lehigh University, Bethlehem. PA 18015. Manuscript submitted April 8, 1986. METALLURGICALTRANSACTIONSB
A. Maximum Depression Possible The lowering of the eutectic temperature of a given binary system 1-2 by any ternary addition cannot exceed a certain limit. Lupis4 has shown this limit, El2, to be: dT) El2
~3
-1 E, hm =
dXL/L+IS
?,
E e dXL/L+2S Xll//~2
7f (x2~ - x ~ ) " ( x A - x 2~) (x~ - x ~ )
[1]
where the designations L / L + 1S and L/L = 2S represent the liquidus curves toward the tin-rich and lead-rich sides of the phase diagram, respectively. Further, ]dX~'L+lS/dT dX~/L+2S/dTI can be determined from an extrapolation of the liquidus lines dT degrees below the eutectic temperature, and ~0L can be evaluated from thermodynamic data of the liquid phase. From the careful work of Esdaile et al., 2 val
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