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This work is a continuation and application to two- and three-dimensional crystals of the methods of reference 1) for the evaluation of the changes in thermodynamic properties of a lattice due to the presence of defects of various kinds. In particular we consider the effects of an isotope defect and a pair of isotope defects on the zero point energy and free energy of two- and three-dimensional cubic lattices. In addition we evaluate the free energy and self entropy of a vacancy in a three-dimensional cubic lattice.
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Mahanty et al. (1960) studied this question.
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