Paper

MMB 312 – Test #1_Solution

Date: September 20, 2011 Marks: 50

Question 1

One kilogram of alloy of 70 wt% Pb – 30 wt% Sn is slowly cooled from 300oC See Figure 3 below for the Pb – Sn system. Calculate

a) What phases form when the alloy is cooled to 250 oC? [2] b) Determine the weight percent of the phases that form at 250oC. [3] c) The weight percent of the eutectic structure and proeutectic alpha just below the eutectic temperature (183oC) and the weight in kilograms of these phases. [5] d) The weight in kilograms of alpha, (α), and beta, (β), formed by the eutectic reaction. [5] e) Show schematically in a clearly labeled diagram the microstructure that forms just below the eutectic temperature ((183oC). [5]

Solution:

a) What phases form when the alloy is cooled to 250 oC?
Phases are L (liquid) & ( (solid).

b) Determine the weight percent of the phases that form at 250oC.
Phases are ( & L & their compositions are ~ 12 wt.% Sn & 30 wt.% Sn, respectively.

Wt% L = (30-12)/(40-12)100 = 64 %

Wt% α = (30-12)/(40-12)100 = 36 %

c) The weight percent of the eutectic structure and proeutectic alpha just below the eutectic temperature (183oC) and the weight in kilograms of these phases.

Wt% pro-eutectic alpha, α = (61.9 - 30)/(61.9 – 18.3)100 = 74.7%

Wt% eutectic structure = (30 - 18.3)/(61.9 – 18.3)100 = 25.3%

Weight in kilograms of these phases: pro-eutectic alpha is 0.747 kg, and eutectic structure is 0.253 kg.

d) The weight in kilograms of alpha, (α), and beta, (β), formed by the eutectic reaction. Wt% of total α (proeutectic α + eutectic α) = (97.8-30)/(97.8-18.3) = 0.8528 mass fraction of eutectic ( = mass fraction of total ( - mass fraction of pro-eutectic ( = 0.8527 –