The effects of vacancies on the thermodynamic properties of harmonic crystals: cell cluster method

Abstract

The effects on the thermodynamic properties of harmonic, monatomic crystals with first-neighbor interactions due to the presence of vacancy defects are studied. A general derivation of the cell-cluster theory for harmonic systems is given. This theory is then used to calculate the zero point energy of pure crystals. The changes in the high-temperature Helmholtz free energy, zero point energy and constant volume heat capacity due to the presence of a vacancy defect were also calculated. Finally, the effect on the high-temperature Helmholtz free energy due to the presence of two interacting vacancy defects in the crystal was evaluated. Numerical results were obtained for both a face-centered cubic crystal and a two dimensional triangular lattice.