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ts1201f07 - EMSE 201 Introduction to Ma teria ls Science...

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EMSE 201 — Introduction to Materials Science & Engineering 26 September 2007 Department of Materials Science and Engineering 1 of 6 Case Western Reserve University Solution: Test #1 — 75 minutes; 150 points; 6 questions; 6 pages; 15% 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) Gallium nitride, GaN, has the hexagonal ZnS structure. Solid solutions between GaN and other semiconducting compounds are used to make blue light-emitting diodes. a) (10 points) Briefly state the rules for solid solution formation, as applied to compounds. ( 2 pts ) The two compounds must have the same crystal structure. ( 2 pts ) The electropositive elements must have similar EN to each other (within 0.6, preferably within 0.4); likewise for the electronegative elements. ( 2 pts ) The radii of the electropositive elements must differ from each other by <15%; likewise for the electronegative elements. ( 2 pts ) The electropositive elements must have at least one valence state in common; likewise for the electronegative elements. If all ( 1 pt ) the rules are met, complete ( 1 pt ) solid solution is expected. The terms “cations” and “anions” are acceptable for “electropositive elements” and “electronegative elements,” respectively. 2 pts were deducted if the rules were not expressed in terms of compounds. b) (10 points) Would you expect any of the following compounds — InN, GaAs, or ZnO — to form a complete solid solution with GaN? Justify your answers using the data below. compound: GaN GaAs InN ZnO structure: hexagonal ZnS cubic ZnS hexagonal ZnS hexagonal ZnS element: Ga N As In Zn O atomic radius, nm: 0.122 0.070 0.121 0.163 0.134 0.066 electronegativity: 1.81 3.04 2.18 1.78 1.65 3.44 valences: +3 ±3,+5,+4,+2 ±3, +5 +3 +2 –2 ( 3 pts ): InN does not satisfy the radius rule ( r In is 34% larger than r Ga ), barely satisfies the electronegativity rule ( EN In EN Ga = 0.41), and satisfies the structure and valence rules. ( 3 pts ): GaAs satisfies neither the structure rule, the electronegativity rule ( EN N EN As = 0.86), nor the radius rule ( r As is 73% larger than r N ), but satisfies the valence rule. ( 3 pts ): ZnO does not satisfy the valence rule for either the electropositive or the electronegative elements, but satisfies the radius rule ( r Zn is 10% larger than r Ga , and r O is 5.7% smaller than r N ), the structure rule, and the electronegativity rules ( EN Ga EN Zn = 0.16, and EN O EN N = 0.40). ( 1 pt ): None of these compounds is expected to form a complete solid solution with GaN. In practice, GaN-InN solid solutions, (Ga 1– x In x )N are fabricated and widely used in LEDs.
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EMSE 201 — Introduction to Materials Science & Engineering 27 September 2007 Department of Materials Science and Engineering 2 of 6 Case Western Reserve University It was not necessary to evaluate all four rules for all three compounds. If you correctly
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