A Cell Cluster Theory for the Mean Square Atomic Displacement in an Anharmonic Crystal

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Abstract
The cell cluster method is applied to the calculation of the mean square atomic displacement in an anharmonic crystal, in the high temperature or classical limit. The result is expressed in terms of a series of multidimensional integrals in real space. The lowest order and first correction terms, involving three and six dimensional integrals respectively, are evaluated to high numerical accuracy for a model including Mie–Lennard–Jones interactions between nearest neighbor atoms. The results are in fairly good agreement with experimental data for krypton.

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