Singularity in density of states (a) From the dispersion relation derived for a monatomic linear lattice of
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Singularity in density of states
(a) From the dispersion relation derived for a monatomic linear lattice of N atoms with nearest-neighbor interactions, show the density of modes is D(w) = 2N/π 1 /(w2m – w2)1/2, where wm is the maximum frequency.
(b) Suppose that an optical phonon branch has the form w(K) = w0 – AK2, near K = 0 in three dimensions. Show that D(w) = (L/2π)3 (2π/A3/2) (w0 – w)1/2 for w < w0 and D(w) = 0 for w > w0. Here the density of modes is discontinuous.
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a The dispersion relation is sinKa We solve this for K to obtain ...View the full answer
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