Consider a hypothetical eutectic phase diagram for metals A and B that is similar to that...

Consider a hypothetical eutectic phase diagram for metals A and B that is similar to that for the lead–tin system (Figure 9.8). Assume that: (l) α and β phases exist at the A and B extremes of the phase diagram, respectively; (2) the eutectic composition is 36 wt% A–64 wt% B; and (3) the composition of the α phase at the eutectic temperature is 88 wt% A–12 wt% B. Determine the composition of an alloy that will yield primary b and total b mass fractions of 0.367 and 0.768, respectively.

Figure 9.8 The lead–tin phase diagram.

[Adapted from Binary Alloy Phase Diagrams, 2nd edition, Vol. 3, T. B. Massalski (Editor-in-Chief), 1990. Reprinted by permission of ASM International, Materials Park, OH.]