Question

11) (20 points) For alloys of two hypothetical metals A and B, there exist an a, A-rich, phase and a B, B-rich, phase. From the mass fractions of both phases for two different alloys provided in the table below, (which are at the same temperature), determine the composition of the phase boundary (or solubility limit) for both a and ß phases at this temperature. Alloy Composition Fraction a Phase Fractionſ 60 wt% A-40 wt% B 30 wt% A-70 wt% B 0 0 .57 .14 Phase 0.43 0.86

Answer 1

Given Alloy Composition Fraction a Phase Fraction Phase 60 wt% A - 40 wt% B 30 wt% A -70 w4% 0.57 0.14 0.43 Composition of phase boundary More ...(2) If Co= 48 wt% of B, We = 0.51 Amount of a Phase 0.57, 40-40 - CA-6 0.576,-0.57C2 =(3-40 Elt0:57) 6 -0.5747-40 -0.434 -0.576x =-40 0.43 68 +0.5764=40 ......(2) If Co=70 wt% of B, Wp = 0.14 Amount of a phase

0.14 50-70 0.14 CR-0.1440=60-70 (1 +0.14)62 -0.1467-70 -0.86CB-0.1467-76 0.86C870.1464 370 ...... Solve equation (2) and (3) Ca = 10 wt%B Substitute Carlo in equation () 0.86 CB toild ca 770 0.86 Cp 70.14 418 70 0.86 CP 70-14 Cp = 70 - 14 Cp = Ses CB = 79.8 wt% B Hence, « Phase boundoy composition, Ca =90 wt% A - 10 wt% B Hence, f Phase boundary composition, co - 2012 wt% A -79.8 wt%B