A study was made of vibrational excitations in an array of dislocations which comprised the interfacial misfit structure of a small-angle grain boundary. Coupled oscillations of dislocation lines in the strain field of the interface were analyzed by taking account of the Peierls energy and line tension forces. The effective force constants of harmonic springs, which established correlations between vibrating dislocations, we calculated within the framework of isotropic elasticity theory. It was shown that these long-range force constants reorganized the spectrum of individual dislocation lines and created a band of collective vibrations. It was found that, in the dynamics of arrayed dislocations, a key role was played by non-Debye effects that were associated with a distinct frequency scale that was related to the grain misorientation angle and to the Debye frequency.

L.B.Hovakimian, S.Tanaka: Physical Review B, 1996, 54[21], 15125-35