Mössbauer Fractions and Specific Heats of Diatomic Lattices

A simplified analysis using one-parameter models (like the Debye model for monatomic lattices) without details of the normal-mode spectrum (acoustic, optic) is proposed and applied to the alkali iodides. The theoretical basis is the insensitivity of 〈x²〉 and 〈p²〉 of a given lattice atom to changes in masses of other lattice atoms. The calculations utilize simple relations between the M\"ossbauer fraction and the specific heat of an alkali iodide crystal and the corresponding properties of a fictitious monatomic iodine crystal where all the atoms have the iodine mass but the forces between atoms are those of the alkali iodide crystal. A Debye model for the fictitious crystal is used to fit experimental data. A good fit is obtained with one parameter, the Debye temperature of the fictitious crystal.