Vibrational entropies of defects in solids

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Abstract
We present a new method for calculating the perturbed phonon spectrum of defect crystals and show how this can be used to obtain entropies. The method considers a periodic structure in which a cluster of ions around the defect, placed in their relaxed positions, is embedded in a non-primitive unit cell. The normal modes of this structure may be used to calculate local modes and, since a reasonable representation of k space may be obtained by projection, considering only the Γ point of this cell, we may readily obtain values for the partition function and hence for thermodynamic quantities.