Theory of Impurity-Induced Infrared Absorption in Alkali Halide Crystals
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A study is made of the impurity-induced infrared absorption of alkali halide crystals containing alkali or halide ions as substitutional impurities. Specific but exactly soluble crystal and impurity models are used to take into account the change in force constants as well as the change in mass accompanying the introduction of the impurities. The absorption coefficient of the crystal is calculated within the framework of the harmonic approximation using the method of double-time Green's functions. An expression for the total dipole moment of the crystal is reduced to a form which can be expressed entirely in terms of the displacements of the impurities. Particular attention is paid to one-impurity problem assuming the concentration of the impurities to be small. It is shown that all the quantities entering into the oneimpurity problem can be expressed entirely in terms of the diagonal part of phonon Green's functions for the pure crystal. A detailed discussion is given on the properties of infraredactive phonon impurity modes, such as localized modes or localized gap modes (modes appearing in the gap between optical and acoustical branches of phonons) or resonant modes. Some analytic properties of high-frequency localized modes and low-frequency resonant modes are obtained, and they do not seem to be sensitive to crystal and impurity models. Results for the eigenfrequencies of the localized modes, the gap modes, and the resonant modes and those for the residual width of the resonant modes are compared with a series of experimental data on the infrared lattice absorption of mixed alkali halide crystals which have been obtained by Schaefer and by Sievers. The importance of the effect of the change in force contants in studying the vibrational properties of mixed alkali halide crystals is elucidated.
- 理論物理学刊行会の論文
- 1967-11-25
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