Question

Question 1: (16 points: 4 pts each) A 45 wt% Pb - 55 wt% Mg alloy is slowly cooled from 700°C to 400 °C. (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? Composition (at% Pb) 10 20 30 40 70 100 700 L 600 L + MezPo M 500 400 Temperature (°C) + M&P 300 200 M82Pb 100 MgPb Mg, PD 20 80 100 40 60 Composition (wt% Pb) (Mg) (Pb)

Answer 1

Composition (at% Pb) 10 20 30 40 70 100 700 L 600 P L + MRPDM 500 Q 400 Temperature (°C) L + L Mg, PD 300 200 Mg2Pb 100 Mg Pb Mg, PD A B D 20 40 50 80 100 (Mg) Composition (wt% Pb) (Pb)

For our reference to the given conditions in the questions:

The red line in the diagram above shows the process of cooling 45wt% Pb from 700C to 400C.

a) The solid phase is the $\alpha$ phase which forms when the first trace of $\alpha +L$ phase is found, which is when the temperature is at point P which is around 575 Celcius.

b) For calculating the composition at this point we use the level rule for the point, which is between points A and B

The $\alpha$ phase is given by  $\chi_{\alpha} = \frac{\bar{XB}}{\bar{XB}+\bar{AX}}$ where XB = 50-45=5 and AX = 45-16.5 = 28.5. So,

$\chi_{\alpha} = \frac{5}{5+28.5}\approx 15\%$ and also

XL = 1- Xa 85%

Here $\alpha$ is the solid phase which has a composition of 15%

c) The liquid solidifies when the L phase diminishes and the $\alpha$ , $Mg_{2}Pb$ phase are there. This is denoted by the point Q, which is around 465 Celcius.

d) For calculating the composition at this point we use the level rule for the point, which is between point C and B.

The phase is given by  $\chi_{L} = \frac{\bar{CX}}{\bar{CX}+\bar{XB}}$ where XB = 50-45=5 and CX = 45-41.5 = 3.5. So,

$\chi_{L} = \frac{3.5}{3.5+5}\approx 41.2\%$ and also $\chi_{\alpha} = 1- \chi_{L} = 58.8\%$

Here is the solid phase which has a composition of 41.2%

Note: If they would have asked for the solid composition $\alpha+Mg_{2}Pb$ we would have used the points C and D.