Infrared Lattice Absorption in Ionic and Homopolar Crystals

Abstract

The evidence, from the photoelastic properties of alkali halides and MgO, and from the deviations from the Cauchy relation among the elastic constants in these crystals, for the existence of an appreciable deformation of the charge distribution about the atoms during lattice vibration, is discussed. The deformation of the charge distribution is suggested as a possible alternative explanation to that of anharmonic forces for the auxiliary bands in the infrared absorption and reflection spectra of the alkali halides and MgO. It is suggested, on the other hand, that the infrared absorption spectra of pure homopolar crystals, such as diamond, silicon, and germanium in which a linear moment is absent, must involve the deformation of the charge distribution during vibration, since anharmonic forces alone cannot account for any infrared absorption in the absence of a linear moment.The deformation of the charge distribution in a crystal during vibration is shown to lead to a second order electric moment (quadratic in the displacements) as well as to a modification of the first order moment. A qualitative understanding of the contribution of the second order moment to infrared absorption is obtained with the help of a one-dimensional calculation.An analysis is made of the infrared absorption in diamond, silicon, and germanium. Part of the absorption is judged to be intrinsic and to be reasonably explained by a second order electric moment arising from charge deformation. The remainder seems to vary with the specimen and is explained as an impurity-induced first order moment. The second order electric moment can also be used to explain the side bands in the absorption and reflection spectra of the alkali halides. However, it fails to explain the observed broadening of the main absorption line, indicating that anharmonic forces are probably the principal mechanism in the latter phenomenon.