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Prob.set.1 - Physics 361 P1.1 Decorated cubic lattices...

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Physics 361 Problem set 1 due in class October 7, 2009 P1.1. Decorated cubic lattices ( cf. A&M p. 92) Find a Bravais lattice and (if needed) a basis for each of these arrangements of points: a) Base-centered cubic, that is, a simple cubic lattice with additional points in the centers of the horizonal faces of the cubic cell. b) Side-centered cubic, that is, simple cubic with additional points in the centers of the vertical faces. c) Edge-centered, with points added at the center of each edge joining nearest neighbors. P1.2. skipping alternate lattice points ( cf. A&M prob 2, page 80) Investigate the lattices formed by all points with Cartesian co-ordinates ( n 1 , n 2 , n 3 ) such that a) only even n i are allowed? b) only odd n i are allowed? c) The sum of the n i is required to be even? d) The sum is required to be odd? Each of these is a simple Bravais lattice discussed in the chapter. Identify the lattice type and state a primitive basis set for each.
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