Permanent Movement in the Crystal Lattice
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The quantized energy of the vibrations of the atoms in the crystal lattice contributes to the specific heat and the thermal conductivity. As noted first by Albert Einstein, the energy spectrum of the phonons is given by Planck’s radiation law, resulting in a distinct deviation from the classic law of Dulong and Petit. Subsequently, the Einstein model, based on a single phonon frequency, was extended by Peter Debye by including the complete phonon spectrum.