Abstract
Localized states occur in a solid when the translational invariance is lost. The most obvious case of interrupting the translational symmetry is the surface of the crystal lattice. Another case is the presence of a foreign atom in the lattice. In both cases, the force constants of the surface atoms or the foreign atom differ from that in the uniform bulk volume of the lattice and the atoms concerned have vibrations out of the perfect crystal. These vibrations are called “localized modes.”
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Balkanski, M. (1986). Dynamics of Localized Phonon Modes. In: Butcher, P.N., March, N.H., Tosi, M.P. (eds) Crystalline Semiconducting Materials and Devices. Physics of Solids and Liquids. Springer, Boston, MA. https://doi.org/10.1007/978-1-4757-9900-2_5
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