141A_PS4_sp07 - a mass M. This is a simple example of...

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PHYSICS 141A S. G. LOUIE SPRING 2007 Problem Set #4 Due: Friday, 02/16/07 Reading: Finish Chapter 5 of ISSP (25) 1. From Ibach and Luth: Calculate the eigenfrequency of a mass defect M " m in a linear chain at the position n = 0 by invoking the ansatz s n = s 0 e " k( # )|n| " i # t for the displacements. For which range of M do localized vibrations exist? [That is, consider an infinite monatomic chain consisting of particles of mass m connected to nearest neighbors with spring constant C, with the exception of one particle which has
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Unformatted text preview: a mass M. This is a simple example of defect induced localized states in a crystal.] (25) 2. ISSP, Ch. 5, Problem 1 (25) 3. ISSP, Ch. 5, Problem 2 (The bulk modulus B is defined by the relation U = B 2 , where U is the energy of a solid and " = # V $ V V = % V V is the dilation. See page 80 of ISSP.) Also, (c) Estimate the Debye-Waller factor for the first non-zero diffraction beam. (25) 4. ISSP, Ch. 5, Problem 3....
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