fs201f10(1) - EMSE 201 Introduction to Materials Science &...

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EMSE 201 — Introduction to Materials Science & Engineering 14 December 2010 Department of Materials Science and Engineering 1 of 10 Case Western Reserve University Name: S O L U T I O N Final Exam — 180 minutes; 200 points; 8 questions; 10 pages; 20% of course grade You may use a calculator, pencils or pens, eraser, and a straight edge. Handwritten notes on both sides of a single 8.5 ″× 11 sheet of paper are permitted. Please turn in your note page with your test. No other form of stored information is permitted. Write all answers on these pages; use the back if needed. Partial credit will be given for correct set-ups and reasoning. On numerical answers use the correct number of significant figures and give appropriate units. Constants : Avogadro’s number, N A = 6.023 × 10 23 mol –1 Boltzmann’s constant, k B = 1.381 × 10 –23 J K –1 = 8.620 × 10 –5 eV K -1 gas constant, R : 8.314 J mol -1 K –1 Charge on an electron, | q e | = 1.602 × 10 -19 C Faraday’s constant, F = 96,500 C mol –1 1) The unit cell of a compound of molybdenum (Mo) and silicon (Si) has the following characteristics: f201s04 Mo: 0, 0, 0 1 2 , 1 2 , 1 2 Si: 0, 0, 1 3 0, 0, 2 3 1 2 , 1 2 , 1 6 1 2 , 1 2 , 5 6 a = b = 0.3202 nm c = 0.7851 nm α = β = γ = 90° a) (6 points) In the space at right, sketch the unit cell. Clearly identify the atoms. b) (4 points) How many atoms of each type are in the unit cell? ( 2 pts each) Mo: 2 Si: 4 c) (4 points) What is the Bravais lattice of this structure? ( 2 pts + 2 pts ) body-centered tetragonal d) (2 points) How many nearest-neighbor Si atoms does each Mo atom have? 10 (Hint: the Si atoms at 0, 0, 1 3 and 1 2 , 1 2 , 1 6 are almost exactly equidistant from the Mo atom at 1 2 , 1 2 , 1 2 .) e) (2 points) How many nearest-neighbor Mo atoms does each Si atom have? 5 Sketch the arrangement of atoms on the specified planes in this structure. Label the atoms in your sketches. f) (5 points) (100) g) (7 points) (110) continued on next page Si Mo Si Mo Si Mo
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EMSE 201 — Introduction to Materials Science & Engineering 14 December 2010 Department of Materials Science and Engineering 2 of 10 Case Western Reserve University 1) h) (10 points) A compound of tungsten (W) and silicon forms with the same stoichiometry and struc- ture as the compound discussed above. Would you expect these two compounds to form a continu- ous solid solution with each other? Evaluate each of the Hume-Rothery rules to justify your an- swer. atomic ra- dius, nm electronegativity allowed valences Mo 0.136 2.16 6, 5, 4, 3, 2 W 0.137 2.36 6, 5, 4, 3, 2 Same structure (given): ( 1+1 pts ) r/r < 15%: ( 1+1 pts ) EN < 0.4: ( 1+1 pts ) similar valences: ( 1+1 pts ) Yes, we expect MoSi 2 and WSi 2 to form a continuous solid solution ( 2 pts ). (They do.) Various properties of the Mo-Si compound are listed at right. i)
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fs201f10(1) - EMSE 201 Introduction to Materials Science &...

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