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

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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 \( \% \mathrm{~A}-64 \) wt \( \mathrm{B} \); and (3) the composition of the \( \alpha \) phase at the eutectic temperature is 88 wt \( \% \mathrm{~A}-12 \) wt \( \% \). Determine the composition of an alloy that will yield primary \( \beta \) and total \( \beta \) mass fractions of \( 0.365 \) and \( 0.773 \), respectively. wt \( \% \)