Localized vibrations in crystal associated with straight screw dislocation

An equation is obtained which describes the vibrations of a crystal containing a straight screw dislocation. It is shown that, irrespective of the conditions in the dislocation core, this equation may have solutions in the form of the modified Bessel function with an imaginary index. These solutions describe bands of localized vibrations. The dispersion laws for these bands are found for simple cubic, face centered cubic, and body centered cubic lattices.

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