Lattice heat capacity and thermal vibrations of rare-gas crystals

The lattice heat capacity Cν the mean-square displacement ⟨u2⟩, and the Lindemann parameter are calculated for Ne, Ar, Kr, and Xe by using the lattice dynamics model of rare-gas crystals1 in the harmonic approximation. A fairly good description of Cν of the Debye temperature, and of the zero-point energy indicates a high accuracy of reproducing theoretically the elastic constants and phonon frequencies in the entire Brillouin zone. The insignificant excess (∼ 3%) of the calculated Cν(T) over the experimental value and the smallness of the Lindemann parameter imply a small role of anharmonicities at high temperatures. The Lindemann parameter is 0.106±0.002 for Ar, Kr, and Xe, and is somewhat higher for Ne. The role of zero-point oscillations in the thermodynamics of these crystals is analyzed, particularly concerning the Lindemann melting criterion.

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