Dielectric susceptibility and infrared absorption in an imperfect anharmonic crystal

Abstract

Using the technique of thermodynamic double-time Green's function and Kubo formalism an expression is obtained for the dielectric susceptibility of an imperfect anharmonic crystal taking into account the second-order terms in the dipole moment expansion and third- and fourth-order anharmonic terms in the crystal potential energy. The crystal contains randomly distributed substitutional impurities. Mass changes as well as force constants changes between the impurity atoms and host-lattice atoms are explicitly included. The polarization operators of the Green's functions are obtained in the lowest-order approximation using renormalized Hamiltonian. The results are used to obtain an expression for the frequency and temperature dependence of the infrared absorption coefficient. It is observed that in the temperature region above the Debye temperature, the width of the fundamental lattice absorption peak is proportional to the first and second powers of the absolute temperature which is in agreement with the experimental observations and the absorption at high frequencies is caused due to the fourth- and higher-order anharmonicity. It is also observed that at sufficiently high temperature, the damping constant associated with the fundamental lattice vibration absorption will vary as T 2 in agreement with experimental observations.