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# hmwk5q1 - speciFc heat at 100K? c. Is the Debye-Waller...

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Problem set 5, Due March 1 This problem deals with the vibrations of the two-dimensional gas-atom surface. A monolayer of gas atoms is deposited on an atomically perfect surface. Consider Frst a model in which the e±ect of the surface is simply to constrain the atoms to move in the z = 0 plane. The atoms form a square lattice (with a = 3 ˚ A ), and for small k = ( k x , k y ), the equations of motion give - 2 e i ( k ) = - A ( k 2 x + k 2 y ) e i ( k ) i = x, y where M = 6 . 7 × 10 - 23 gm, and A = 6 . 7 × 10 - 12 gmcm 2 / sec 2 a. ²ind the normalized density of states (frequencies) per unit frequency near ω = 0. b. Give an expression for the low temperature speciFc heat as a function of temperature. What is the
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Unformatted text preview: speciFc heat at 100K? c. Is the Debye-Waller factor Fnite or zero and why? Now account for the potential of the surface, ie. allow for the corrugation of the surface by adding a potential energy φ = K 2 X n,i s 2 ni where s is, as usual, the displacement from equilibrium, and K = 6 . 7 × 10 4 gm / sec 2 . The wave solutions are of the form s ni = e ni e ( i k · r n-ωt ) d. What are the new frequencies for k = 0? e. What is the form of the temperature dependence of the speciFc heat neat T = 0? f. Is the Debye-Waller factor Fnite or zero and why? 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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