In Introduction to Solid State Physics (Kittel), it assumed the force constant between plane $s$ and $s+p$ $C_p=A\frac{\sin pk_0a}{pa}$ in metals to represent a Kohn anomaly. It says such a form is expected in metals. But I have no idea why. Thinking of typical potential energy-distance curve with one inflection point, shouldn't $C_p$ has only one node? Why only metals have such shape of $C_p$ and thus Kohn anomaly?

I guess there are much complex quantum mechanical principles underlying the Kohn anomaly. Is it possible to explain the reason of that $C_p$ shape and Kohn anomaly in the classical manner?


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