homework 1

homework 1 - Physics 518 Problem Set #1 Due Wednesday...

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Physics 518 Problem Set #1 Due Wednesday 1/27/10 1. What is the Bravais lattice formed by all points with Cartesian coordinates ( n 1 ,n 2 ,n 3 ) if (a) The n i are all even integers? (b) The n i are either all even or all odd? (c) The sum of the n i is even? 2. If atoms in a crystal are considered as hard spheres which are touching each other use elementary geometry to show that (a) The b.c.c. lattice has packing fraction 0.68. (b) The f.c.c lattice has packing fraction 0.74. (c) The h.c.p. lattice has a ratio c/a = 1 . 633. 3. For the cubic lattice of side a show that the separation between the lattice planes indexed by ( hkl ) is d hkl = a/ h 2 + k 2 + l 2 . What is d hkl in an orthorhombic lattice? 4. The primitive translation vectors of the hexagonal lattice may be taken as a 1 = a ( 3 / 2 , 1 / 2 , 0); a 2 = a ( - 3 / 2 , 1 / 2 , 0); a 3 = (0 , 0 ,c ). (a) What is the volume of the primitive cell? (b)
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homework 1 - Physics 518 Problem Set #1 Due Wednesday...

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