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What does the phonon dispersion, that is, the vibrational frequency as a function of wave vector...

What does the phonon dispersion, that is, the vibrational frequency as a function of wave vector ω(k), look like for an infinite chain of atoms with two atoms per unit cell? Why does one speak of optical and acoustic branches?

What predictions does the so-called Dulong-Petit law make about the heat capacity of a solid and its temperature dependence (and why)? How does it compare to the experiment

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