(Solved): Consider the hypothetical eutectic phase diagram for metals A and B, which is similar to that for t ...

Consider the hypothetical eutectic phase diagram for metals A and B, which is similar to that for the lead-tin system, (shown in the figure below.) Assume that (1) \( \alpha \) and \( \beta \) phases exist at the \( A \) and \( B \) extremities of the phase diagram, respectively; (2) the eutectic composition is 36 wt\% A-64wt\% B; and (3) the composition of the \( \alpha \) phase at the eutectic temperature is 88 wt\% A-12 wt\% B. Determine the composition of an alloy that will yield primary \( \beta \) and total \( \beta \) mass fractions of \( 0.360 \) and \( 0.780 \), respectively.