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In the empty lattice approximation, we define: h^2k^2. Now we'd... | Filo
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Zero point lattice displacement and strain. (a) In the Debye approximation, show that the mean square displacement of an atom at absolute zero is (R^2⟩= 3 ħωD^2 / 8 π^2 p v^3, where v is the velocity of sound. S tart from the result (4,29) summed over the independent lattice modes: ⟨R^2⟩=⟨h̅ / 2 ρV) Σω^-1. We have included a factor of (1)/(2) to go from mean square amplitude to mean square displacement. (b) Show that Σω^-1 and ⟨R^2⟩divenge for a one-dimensional lattice, but that the nean square
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