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HW _1 Solutions

# HW _1 Solutions - 25 wt tin 75 wt lead at 170 C ANS a α...

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CE 3020 Construction Materials HOMEWORK Question 1 In hard sphere model for FCC structure, illustrated below, the atoms touch one another across a face-diagonal length which measures 4 R , where R is atomic radius. If the cube edge length is a , calculate the FCC unit cell volume, V c , in terms of R . ANS. V c = a 3 To get a in terms of R, use Pythagorean theorem for right triangles, using the diagonal on the face of the cube as the hypotenuse: a 2 +a 2 = (4R) 2 a = 2R 2 then, V c = 16R 3 2 Question 2 Consider the lead-tin phase diagram below. (The material may be familiar to those of you who have ever soldered electronic equipment.) For each of the four points described, determine (a) which phases are present at the point (b) the composition of each phase, (c) the proportion of each phase, and (d) sketch the microstructure ( See Diagram for Sketches) . The four points are: 1. 25 wt % tin +75 wt% lead at 170 C 2. 75 wt% tin + 25 wt% lead at 170 C 3. 5 wt% tin + 95 wt% lead at 170 C 4. 50 wt% tin + 50 wt% lead at 200C

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Unformatted text preview: 25 wt % tin +75 wt% lead at 170 C ANS. a) α and β , both of which are solid solutions of lead and tin b) α is composed of 17% Sn and 83% Pb (from tie line); β is composed of 98% Sn and 2% Pb c) using the lever rule, % β = (25-17)/(98-17) x 100 = 10% % α = (98-25)/(98-17) x 100 = 90% 75 wt% tin + 25 wt% lead at 170 C ANS. a) α and β , both of which are solid solutions of lead and tin b) α is composed of 17% Sn and 83% Pb (from tie line); β is composed of 98% Sn and 2% Pb c) using the lever rule, % β = (75-17)/(98-17) x 100 = 72% % α = (98-75)/(98-17) x 100 = 28% 5 wt% tin + 95 wt% lead at 170 C a) α, a solid solution of lead and tin b) is composed of 5% Sn and 95% c) 100% α 50 wt% tin + 50 wt% lead at 200C a) α and liquid, L b) α is composed of 19% Sn and 81% Pb (from tie line); L is composed of 58% Sn and 42% Pb c) using the lever rule, % L = (50-19)/(58-19) x 100 = 80% % α = (58-50)/(58-19) x 100 = 20%...
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HW _1 Solutions - 25 wt tin 75 wt lead at 170 C ANS a α...

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