EMS162-2010-Homework2_Solutions

EMS162-2010-Homework2_Solutions - UNIVERSITY OF CALIFORNIA,...

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EMS 162, page 1/4 Prof. Y. Takamura, 2010 UNIVERSITY OF CALIFORNIA, DAVIS Department of Chemical Engineering and Materials Science EMS 162: Structure and Characterization of Engineering Materials Homework 2 - Solutions Due Date: Tuesday, Jan. 20 th , 2010, in class Note: You must show all the steps you used to obtain your answer in order to receive full credit. 1. Tetragonal Crystal System [22 pts] (a) What are the defining conditions for the 3D tetragonal crystal system in terms of a b, c and α , β , γ ? (b) What are the possible Bravais lattices for the tetragonal crystal system? (c) Show using diagrams how the other special positions are composed of other simpler unit cells with a smaller volume. (d) What are the lattice parameters of the new lattice in terms of the original lattice parameters. (e) For each case below, draw the following planes on a tetragonal unit cell. In each case, show the cell axes and use separate drawings as necessary for clarity. (i) Draw the {100} family of planes. Which specific planes are part of the {100} family of planes? (ii) Draw the {110} family of planes. Which specific planes are part of the {110} family of planes? Solution: (a) The defining conditions for the 3D tetragonal crystal system are a=b c, [1pt] α = β = γ =90°. [1pt] (b) The possible Bravais lattices are simple and body centered. [2pts] (c) The based centered and face centered retragonal unit cells can be drawn as smaller tetragonal unit cells.

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EMS162-2010-Homework2_Solutions - UNIVERSITY OF CALIFORNIA,...

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