hmwk4q1 - | s (0) | 2 of a crystal atom about its...

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Problem set for chapter 4, Due Mon. Feb. 12 Useful references for this problem set include: Callaway, chapter 1. 1. Argon is a Van der Waals FCC crystal, for which the pair potential is of the Lennard-Jones type: V ( r ) = 4 ² σ r · 12 - σ r · 6 , where ² = 1 . 05 × 10 - 2 eV and σ = 3 . 4 ˚ A . Neglecting all be nearest-neighbor forces, calculate the dispersion ω ( k ) for the longitudinal phonons in the (1,0,0) direction. 2. Read about the theory of elasticity in Ashcroft and Mermin. Then, consider a crystal of Ag, and look up its atomic mass and elastic constants. Obtain an expression, in terms of the lattice frequency spectrum, for the mean-squared excursion
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Unformatted text preview: | s (0) | 2 of a crystal atom about its equilibrium position. Look up the atomic mass, elastic constants, and melting temperature T M of Ag, and estimate | s (0) | 2 at T = 0 and T = T M . 3. Calculate the dispersion of a simple linear chain of atoms each of mass M , bound together with springs of spring constant f . Now, reconsider the example of a diatomic linear chain discussed in Ibach and Luth Sec. 4.3. Show that when M = m for the latter example, the two results are consistent ( hint remember that when M = m that the principle translation distance halves). 1...
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This note was uploaded on 01/10/2012 for the course PHYSICS 707 taught by Professor Electrodynamics during the Fall '11 term at LSU.

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