Modification of Lattice Vibrations by an Imperfection

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Abstract
The optical absorption or emission by an electron localized at a point imperfection in a crystal is broadened by lattice vibrations. In a fundamental discussion the normal modes of vibration of the whole crystal must be considered. The effect of a mode depends on the displacements it produces in ions near the imperfection. The presence of the imperfection will modify the modes, and, in particular, change the displacements of ions near the imperfection even when the modes do not become localized at the imperfection. In the case of the F center the temperature dependence of the breadth of the F band suggests that this effect must enhance the broadening produced by low‐frequency modes (which will certainly not be localized). That this is to be expected from the dynamical theory of normal modes will be shown by discussing: (1) the vibrations of a one‐dimensional chain of particles with two adjacent weakened links, (2) the spherical vibrations of an elastic continuum with a spherical cavity, (3) the vibrations with cubic symmetry round the F center in NaCl if only the first eleven shells of ions round the center are allowed to vibrate. Results obtained with this last model will be compared with experimental results for the breadth of the F band in NaCl as a function of temperature.

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