The microstructure of a lead-tin alloy at 180\(^{\circ}\)C consists of primary \(\beta\) and eutectic structures. If the mass fractions of these two microconstituents are 0.57 and 0.43, respectively, determine the composition of the alloy.
T = 180\(^{\circ}\)C
\( W_{{\beta}^\prime} \) = 0.57
\( W_{eutectic} \) = 0.43
\(C_0\)
\( W_{{\beta}^\prime}\) = \( {C_0 - C_{L} } \over {C_{\beta} - C_{L} } \)
\( C_{L} \) = 61.9 wt% Sn-38.1 wt% Pb
\(C_{\beta}\) = 97.8 wt% Sn-2.1 wt% Pb
Solve for \(C_{0}\):
\(C_{0}\) = \(W_{{\beta}^\prime} (C_{\beta} - C_L) + C_L \) = 0.57 (97.8 - 61.9 ) + 61.9
\(C_0\) = 82.4 wt% Sn-17.6 wt% Pb