THEORY OF LATTICE SPECIFIC HEAT OF AN ISOTOPICALLY DISORDERED ANHARMONIC CRYSTAL

Expressions are obtained for the phonon density of states (DOS), lattice energy and lattice heat capacity (LHC) of an isotopically disordered anharmonic crystal. The cubic and quartic anharmonicities are taken into account besides both the force constant changes and mass difference caused by the substitutional impurities. The method of double time thermal Green's Function (GF) is used in the development. It is shown that in the low concentration limit the LHC depends on mass and force constant changes, cubic and quartic anharmonicities and impurity-anharmonicity interactions. At low temperatures the largest contribution is found due to the defects. It is observed that the non-diagonal terms contribute significantly in the lattice energy of isotopically disordered crystal.