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) a and ß phases exist at the A and B extremities of the phase diagram, respectively; (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 ß and total ß mass fractions of 0.357 and 0.764, respectively.

A 50 wt% Pb-50 wt% Mg alloy is slowly cooled from 700 °C (1290 °F) to 400 °C (750 °F). (a) At what temperature does the first solid phase form? (b) What is the composition of this solid phase? (c) At what temperature does the liquid solidify? (d) What is the composition of this last remaining liquid phase? Temperature (°C) 700 600 500 400 300 200 100 2 0 0 (Mg) 560°C First solid (21 wt% Pb) α 20 465°C 5 a + L Composition (at% Pb) 40 10 L a + Mg₂Pb 20 60 Composition (wt% Pb) Last liquid (67 wt% Pb) 30 Mg₂Pb 40 T T L + Mg₂Pb M 18 80 L + Mg₂Pb 70 100 B B+ Mg₂Pb T B + L D T 1200 1000 800 600 400 200 100 (Pb) Temperature (°F)

Referring to Figure 1, please answer the following [NOTE: SHOW YOUR WORK on Figure 1]:a. provide the specific name for the phase boundary lines denoted by A and B. b. identify the phases present at equilibrium in the phase fields denoted by C, D, and E. c. identify the specific name for the point denoted by F. d. What is the maximum solid solubility of Mg in Al? At what temperature does it occur? e. An Al-Mg alloy (10 wt% Mg, 90 wt% Al) is heated slowly (to insure equilibrium) from a temperature of 200 C:    i. At what temperature does the first liquid phase form?    ii. What is the composition of the liquid phase at the temperature in part i.?  iii. At what temperature does complete melting (no solid phase remaining) occur?  iv. What is the composition of the last solid remaining prior to complete melting? f. Using the equilibrium phase diagram of Figure 1, identify the phases present, their compositions, and their relative mass fractions at equilibrium for a 70 wt% Mg – 30 wt% Al…

Given the equilibrium phase diagram (a) below, briefly describe the mechanisms of precipitation hardening/strengthening of an aluminium alloy making reference to the transitions shown in (b) below to X, X to A, X to D, A to B and A to C. а +0 D B Time (a) (b) - anedua Temperature