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Unformatted text preview: PHYSICS 880.06 (Fall 2004) Problem Set 3 Solution 3.1 A&M Chapter 4 Problem 1 (a) Base-centered cubic: is a Bravais lattice, with a set of three primitive vectors that can be chosen as a 1 = a 2 ( x- y ) , a 2 = a 2 ( x + y ) , a 3 = a z , where a is the length of the side of the cube. Other choices of the primitive vectors include, e.g., a 1 = a x , a 2 = a 2 ( x + y ) , a 3 = a z . (b) Side-centered cubic: is NOT a Bravais lattice, since it contains a 2 ( x + z ) and a 2 ( y + z ), but not the sum a 2 ( x + y +2 z ). One representation of this structure with the smallest basis is a simple cubic (Bravais) lattice of side a with a three-point basis , a 2 ( x + z ) , a 2 ( y + z ) . (c) Edge-centered cubic: is NOT a Bravais lattice, since it contains a 2 x and a 2 y , but not the sum a 2 ( x + y ). This structure can be described by a simple cubic lattice of side a with a four-point basis , a 2 x , a 2 y , a 2 z . A&M Chapter 4 Problem 3 See Fig. 4.18 in A&M for a picture of the diamond structure. Look at the triangle formed by the three points located at p 1 = , p 2 = a 4 ( x + y + z ), and p 3 = a 2 ( x + y ). The angle between the two vectors ( p 1- p 2 ) and ( p 3- p 2 ) is cos = ( p 1- p 2 ) ( p 3- p 2 ) | (...
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This note was uploaded on 06/07/2010 for the course MECH 1122 taught by Professor Dont during the Spring '10 term at A.T. Still University.
- Spring '10