EMS172-2009-Homework3_Solutions

EMS172-2009-Homework3_Solutions - UNIVERSITY OF CALIFORNIA,...

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EMS 172 Profs. Y. Takamura and A. Moulé, 2009 UNIVERSITY OF CALIFORNIA, DAVIS Department of Chemical Engineering and Materials Science EMS 172: Electronic, Magnetic, and Optical Properties of Materials Homework 3 - Solutions Due Date: Tuesday, Oct. 20 th , 2009, in-class Note: You must show all the steps you used to obtain your answer in order to receive full credit. 1. Conductivity of Metals and Their Alloys [15 pts] The experimental data for pure Cu and a Cu-Ni alloy is shown in the figure below. This system forms a solid solution across the composition range shown. (a) Using the data presented in the graph, determine the linear temperature coefficient of resistivity for pure Cu. () [] 1 2 1 2 1 T T + = α ρ Hummel Eqn. 7.27 [1 pt for eqn] The value for α depends on the value taken for ρ 1 , however, here is not a well defined value used. Some conventions use the value at T 1 = 273K, where ρ 1 = 16 n m. Taking T 2 = 100K, ρ 2 = 4 n m, then () [] () 1 1 2 1 2 00433 . 0 273 100 1 16 4 1 = = Ω Ω = K K K m n m n T T Alternatively, using T 1 = 100K, T 2 = 300K, ρ 1 = 4 n m, and ρ 2 = 18 n m [2 pts for values, does not have to be same values] and rearranging the equation above, we get: () 1 0175 . 0 100 300 1 4 18 = = Ω Ω K K K m n m n [1 pt for trying, 1 pt for value] (b) What is the linear temperature coefficient of resistivity for Cu alloyed with 3.32%? Repeating the same calculation as above with T 1 = 273K, where ρ 1 = 56 n m, T 2 = 100K, ρ 2 = 42 n m, α = 0.00145 K -1 . [2 pts] It should be noted, however, that for small alloying concentrations, the slope should remain unchanged from the case in (a) for the pure metal. (c) Briefly explain the trends in the data a. the deformed samples have higher resistivity than the annealed sample
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EMS 172 Profs. Y. Takamura and A. Moulé, 2009 b. the Cu-Ni alloys have higher resistivity than pure Cu. a. The defects in the deformed sample serve as scattering sites for the electrons causing the resistivity
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EMS172-2009-Homework3_Solutions - UNIVERSITY OF CALIFORNIA,...

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