Question: Kohn anomaly we suppose that the inter planar force constant C between planes sands + p is of the form Cp = A sin pk

Kohn anomaly we suppose that the inter planar force constant C between planes sands + p is of the form Cp = A sin pk₀a/pa, where A and k( are constants and p runs over all integers. Such a form is expected in metals. Use this and Eq. (16a) to find an expression for w² and also for ∂w²/∂K. Prove that ∂w²/∂K is infinite when K = k₀. Thus a plot of w² versus K or of w versus K has a vertical tangent at k₀: there is a kink at k₀ in the phonon dispersion relation w(K

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