Ts1201f08 - EMSE 201 Introduction to Materials Science Engineering 24 September 2008 Solution to Test#1 75 minutes 100 points 4 questions 4 pages

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EMSE 201 — Introduction to Materials Science & Engineering 24 September 2008 Department of Materials Science and Engineering 1 of 4 Case Western Reserve University Solution to Test #1 — 75 minutes; 100 points; 4 questions; 4 pages; 10% of course grade Partial credit will be given for correct set-ups and reasoning. Give units on numerical answers where appropriate. 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) A compound of copper and oxygen has the following lattice parameters and atom positions in the unit cell: a = b = c = 0.42696 nm α = β = γ = 90° Cu + : 1 4 1 4 1 4 ,, 3 4 3 4 1 4 3 4 1 4 3 4 1 4 3 4 3 4 O 2– : 0,0,0 1 2 1 2 1 2 a) (1 point) How many copper ions are there per unit cell? 4 (1 point) How many oxygen ions are there per unit cell? 2 b) (5 points) Based on your answers for part a), compute the density of this compound. The atomic weights of Cu and O are 63.55 and 16.00 g mol –1 , respectively. ! = + = + n A n A NV Cu cell Cu O cell O A cell ( )( . ) ( 4 63 55 2 16 00 6 023 10 0 42696 23 1 )( . ) / .. " # $ % × () & g mol mol × = & 10 6 105 7 3 3 cm g cm ./ 1 pt formula, 2.5 pts set-up, 1 pt answer, 0.5 pt units c) (3 points) Given that the ionic radius r O 2 ! of oxygen is 0.140 nm and that rr a O Cu 2 3 4 ! + += in this structure, compute the ionic radius of copper, r Cu + . r a r nm nm nm Cu O + ! = ! = ! = 3 4 3 0 42696 4 0 140 0 045 2 . 1.5 pts set-up, 1 pt answer, 0.5 pt units d) (4 points) Using your answer from part c), and considering radius ratios, what coordination number CN Cu + would be predicted for the copper ion in this structure? The critical radius ratio for CN = 8 is 3 – 1; for CN = 6 is 2 – 1; for CN = 4 is 3/2 – 1; and for CN = 3 is 4/3 – 1. r r nm nm Cu O + ! == 2 0 045 0 140 0 320 . . . This is in the range for CN=4 (i.e., between 0.225 and 0.414). 1 pt formula, 1 pt set-up, 2 pts reasoning and answer.
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Ts1201f08 - EMSE 201 Introduction to Materials Science Engineering 24 September 2008 Solution to Test#1 75 minutes 100 points 4 questions 4 pages

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