Test 1 Solution

# Test 1 Solution - EMSE 201 Introduction to Materials...

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EMSE 201 — Introduction to Materials Science & Engineering 22 September 2010 Name: S O L U T I O N Department of Materials Science and Engineering 1 of 6 Case Western Reserve University Test #1 — 75 minutes; 100 points; 5 questions; 6 pages; 10% of course grade Partial credit will be given for correct set-ups and reasoning. Give units on numerical answers where appropriate and use the correct number of significant figures. Please write all answers on these pages; use the backs if needed. Boltzmann’s constant, k B = 1.381 × 10 -23 J K -1 = 8.620 × 10 -5 eV K -1 Avogadro’s number, N A = 6.023 × 10 23 mol -1 gas constant, R : 8.314 J mol -1 K -1 1) The unit cell of crystalline polyethylene, (C 2 H 4 ) n , has the following lattice parameters: a = 0.494 nm b = 0.741 nm c = 0.255 nm α = β = γ = 90° a) (1 point) To what crystal system does this structure belong? orthorhombic b) (5 points) Each unit cell of crystalline polyethylene contains two –C 2 H 4 – repeat units. Compute the density of totally crystalline polyethylene. The atomic masses of carbon and hydrogen are 12.01 and 1.008 g mol –1 , respectively. density = (mass of atoms per cell)/(volume per cell) ρ = n 2 AW C + 4 AW H ( ) N A V cell ( 2 pts ) V cell = a × b × c ( 1 pt ) = 2 2 × 12.01 + 4 × 1.008 ( ) g/mol [ ] × 10 21 nm 3 / cm 3 6.023 × 1023 mol -1 ( ) 0.494 × 0.741 × 0.255 ( ) nm 3 = 0.998 g/cm 3 ( 1 pt set-up, 1 pt answer + units) c) (5 points) Compute the atomic packing factor of crystalline polyethylene. Use values for the atomic radius of carbon of 0.077 nm and for hydrogen of 0.033 nm. Compare your result to the typical atomic packing factors of the inorganic crystalline structures described in this course. APF = (volume of atoms in cell)/(volume of cell) ( 1 pt ) cell = × × ( 1 pt ) APF = 4 3 π × 2 2 r C 3 + 4 r H 3 ( ) abc = 4 3 × 2 2 0.077 ( ) 3 + 4 0.033 ( ) 3 ( ) nm 3 0.494 × 0.741 × 0.255 ( ) nm 3 = 9.5% ( 2 pts set-up, 1 pt answer + units) continued on next page

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EMSE 201 — Introduction to Materials Science & Engineering 22 September 2010 Department of Materials Science and Engineering 2 of 6 Case Western Reserve University 1) d) (5 points) The diffusion of inert gas molecules (e.g. helium or argon) through polymers occurs via a mechanism similar to interstitial diffusion. Which material would have higher diffusion coefficients for inert gases: totally crystalline polyethylene, or solid polyethylene that is 50% crystalline and 50% non-crystalline? Justify your answer. (Hint: consider the glass transition phenomenon, and the differences between glasses and crystalline solids.) The 50% crystalline polyethylene will have higher diffusion coefficients for inert gases ( 1 pt ). The glassy form of a substance is less dense than the crystalline form ( 1 pt ), i.e. it has a higher volume per unit mass. Therefore totally crystalline polyethylene will have lower volume (
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Test 1 Solution - EMSE 201 Introduction to Materials...

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