Damping of lattice vibrations in solids.

The damping of lattice vibrations in solid compounds is treated using kinetic theory analogous to damping in gases. It is based on the collision frequency of atoms, taking into consideration the atomic coordination due to the crystalline structure, the cross section of collision, the radius ratio of the component atoms (atomic size factor), as well as an anharmonic factor which is an expression for the anharmonicity of lattice vibrations. A semiempirical formulation is derived without need for constants fitted to experimental data. This formulation of damping is shown valid for more than eighty solids, mostly binary compounds, also some ternary compounds and elements. They may have either ionic or covalent or metallic binding. They cover ten different structures and valencies from one through four. In addition, a close relationship is shown between damping and thermal expansion as a function of temperatures. Based on this relationship, the temperature dependence is empirically expressed by an exponential function of the coefficient of thermal expansion. This function agrees with the variation of ir energy absorption vs temperatures. The complete damping formulation is shown valid for the entire temperature range of solids, from absolute zero to the melting point, for a variety of solids for which all pertinent data were on hand.