141A_PS1_sp07 - c a ratio is that of the ideal value(25 3(a...

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PHYSICS 141A S. G. LOUIE SPRING 2007 Problem Set #1 Due: Friday, 01/26/07 Reading: Chapters 1 and 2 of Kittel’s book, Introduction to Solid State Physics (25) 1. Consider the two-dimensional crystal shown in the figure below. The red and black dots represent two kinds of atoms with nearest neighbor distance a . Determine: a) a set of lattice points b) a choice of primitive translation vectors c) the Wigner-Seitz cell and its area d) the basis of atoms associated with a primitive unit cell. (25) 2. a) Problem 3, Chapter 1 of ISSP. b) Sodium transforms from bcc to hcp at about 23K (the “martensitic” transformation). Assuming that the density remains fixed through this transition, find the lattice constant a of the hexagonal phase, given that a = 4.23 Å in the cubic phase and that the
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Unformatted text preview: c a ratio is that of the ideal value. (25) 3. (a) NaCl has a density of 2.167 g/cm 3 . What is the distance between adjacent atoms? (b) Given the distance in a), calculate the energy due to the gravitational attraction between two neighboring atoms. If these two atoms have a typical magnetic moment of that of a free electron, calculate the energy due to the magnetic dipole attraction. Lastly, compare these energies with that from the Coulomb attraction of two oppositely charged ions. (25) 4 (a) Show that the volumes of the primitive cell for sc, bcc, and fcc lattices are a 3 , 1 2 a 3 , 1 4 a 3 , respectively, where a is the length of the edge of the conventional unit cell. (b) What are the corresponding Brillouin zone volumes for the above three lattices?...
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