Question

Composition (at% Pb) 20 30 40 70 100 1200 a М MeәРЫ +L Temperature (°C) Temperature (°F) Mg2Pb a + Mg Pb B + Mg, Pb 200 Mg2Pb 40 60 100 (Mg) Composition (wt% Pb) (Pb) (10 minutes) Use the above Magnesium (Mg) - Lead (Pb) phase diagram. A 30%Pb - 70%Mg alloy is slowly cooled from 700°C to 300°C. Answer the following questions and don't forget the units. (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 completely solidify? (D) What is the composition of this last remaining liquid phase?

Answer 1

Solution:

A. To find the temperature at which solidification starts:

1.Firstly draw a vertical line from the X axis at which the weight percentage of Pb is 30%.

2.This vertical line will intersect the inclined line between $\alpha$ and $\alpha$ +L at A.

3.Now, draw the horizontal line parallel to X axis through this point.

4.This horizontal line will intersect the teperature axis (Y- axis), from where you can find temperature at which soidification starts.

5.This temperature is near about 5200C.

B. To find composition of this solid phase:

1.The horizontal line which you have drawn will intersect the temperature axis at B and the curve between $\alpha$ +L and L region at C.

2Now we use: Wt. % of solid phase = (concentration of Pb at C - concentration of Pb at A)$\div$(cocentration of Pb at C - concentration of Pb at B)

Wt.% of solid phase = (58 - 30)$\div$ (58-0) = 48.27%

C. 1.Similarly, to find the temperature at which liquid phase completely solidifies, we again draw a vertical line perpendicular to x axis from the point at which Pb concentration is 30%.

2.This vertical line will intersect the curve between $\alpha$ and $\alpha$ +Mg2Pb at point D.

3.Now we draw a horizontal line through this point which intersect the temperature axis at E. On extending this horizontal line towards right side, it will intersect the vertical line between ($\alpha$+Mg2Pb) and (L+Mg2Pb) at point F.

4.Point E will read temperature on temperature axis at which liquid solidifies.

5.It is near about 3800C.

D.1. To find the Wt.% of remaining liquid phase:

Wt.% of remaining liquid phase = (concentration of Pb at D - concentration of Pb at E)$\div$(cocentration of Pb at F - concentration of Pb at E)

  Wt.% of remaining liquid phase = (30 - 0)$\div$(80 - 0) =37.5%