An expression for the elements of the dielectric susceptibility tensor for an ionic crystal has been derived in a manner analogous to that employed by Kubo in his treatment of magnetic susceptibility. In the high-temperature (classical) limit, this expression reduces to the Laplace transform of the autocorrelation function of the single normal coordinate which interacts directly with the external radiation field. We have applied this formalism to the calculation of the high-temperature linear optical absorption coefficient of an anharmonic ionic crystal for which we have retained only cubic anharmonic terms in the lattice Hamiltonian. We have solved directly for the Laplace transform of the autocorrelation function to lowest order in the anharmonic coupling constant by solving the equations of motion for the normal coordinates after they have been linearized. The linear absorption coefficient obtained from the susceptibility tensor is of Lorentzian form with a frequency-dependent damping constant which varies linearly with temperature. The absorption coefficient for a diatomic linear chain with nearest neighbor interactions has been evaluated.

• Received 24 March 1961

DOI:https://doi.org/10.1103/PhysRev.123.777