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Structure.questions_X_answer

Structure.questions_X_answer - 1 eV = 0.160 x 10-18 J n/N =...

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MTLE-2100 Structure of Engineering Materials, Questions X-Answers 1. Explain the number of the distinguishable arrangement for the following structure is given by 15!/(2!13!) There are 13 white balls and 2 black balls to be placed on 15 spots. First as- sume that all 15 balls are distinguishable. There are 15 ways to place the first ball, 14 ways to place the second ball, etc. The total number of ways =15!. In reality, 13 white balls are indistinguishable and two black balls are indistinguishable. In other words, when two black balls are switched, the arrangement looks identical. There are 2! ways to switch among black balls and 13! ways to switch white balls. The number of distinguishable ways is given, therefore, 15!/2!13! 2. Calculate the fractional vacancy concentration of Al at just below its melting temperature, 660 ° C, using n/N = exp (- Q/kT) k = 86.1x10 -6 eV/K = 13.8x10 -24 J/K Q = Enthalpy of a vacancy formation for Al = 0.68 eV

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Unformatted text preview: 1 eV = 0.160 x 10-18 J n/N = exp (- 0.68x0.160x10-18 /13.8x10-24 x 933) = 2.1x10-4 . 1. A crystal has an enthalpy of formation for vacancies of 1.5 eV, establishing a cer-tain equilibrium concentration of vacancies at the temperature 1200 K. By how much does the temperature have to be raised to increase the vacancy concentra-tion by a factor of 10? n/N = exp (-1.5 x0.160x10-18 /13.8x10-24 x1200) = exp(-14.49) = 5.094x10-7 10n/N = 5.094x10-6 = exp [-1.5 x0.160x10-18 /13.8x10-24 x (1200+t)] = exp [- 17391/(1200+t)]-12.187 = - 17391/(1200+t); 1200+t = 1427 t = 227 ° C 2. The figure on the next page represents a (100) section through the structure of CaO, which has the NaCl (rock salt) structure type. Five defects are shown in the structure. Write the defect symbols using the common convention, e.g. V Na ’ V O .. A B ’. V ca ”, V O .. , F O . , Fe Ca . , Li Ca ’...
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Structure.questions_X_answer - 1 eV = 0.160 x 10-18 J n/N =...

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