Consider the hypothetical eutectic phase diagram for metals A and B, which is si
ID: 1071937 • Letter: C
Question
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, respective; (2) the eutectic composition is 36 wt % A-64 wt% B; and (3) the composition of the a 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 0.363 and 0.762, respectively.Explanation / Answer
We are given a hypothetical eutectic phase diagram for which Ceutectic = 36 wt% A, C = 88 wt% A at the eutectic temperature, and also that W' = 0.363 and W = 0.762; from this we are asked to determine the composition of the alloy. Let us write lever rule expressions for W' and W
W = (C C0) / (C C) = (88 - C0) / (88 - C) = 0.762 ..............i
W' = (Ceutectic C0) / (Ceutectic C) = (36 - C0) / (36 - C) = 0.363 ................ii
Thus, we have two simultaneous equations with C0 and C as unknowns.
Solving them for C0 gives C0 = 24.74 wt%