The lattice dynamics (phonons) of bicrystals with stable grain-boundary structures are computed and the results of these calculations are linked with continuum elasticity solutions of interface waves. Through comparisons of the lattice-dynamics calculations for ideal crystals with those for the corresponding bicrystals, the low-frequency acoustic branches of the dispersion curves associated with the interface vibrations are identified. These vibrational modes, in the limit of long wave length and low frequency, are the ones for which we seek to establish connections with continuum solutions for localized interface waves that decay exponentially with distance from the interface. We find that the perfect-bonding assumption over-restricts the nature of these latter waves, that is, these solutions do not reproduce the atomistic results for continuum-like waves. The reason lies in the fact that these localized waves are significantly influenced by the local properties of the interfacial region associated with its distinct structure.

Phonon spectra of bicrystals with relaxed grain-boundary structure display a variety of localized modes including long-wavelength acoustic modes. Continuum solutions for localized waves that incorporate atomiclevel elastic properties of the interface via discontinuity relations agree well with the latter modes. In contrast, classical solutions that depend only on bulk elastic properties do not. This demonstrates that the distinct atomic structure of the interface is a controlling factor, and it is shown how local, atomic-level properties can be incorporated into continuum analyses of interfacial phenomena. Phonon spectra of bicrystals with relaxed grain-boundary structure display a variety of localized modes including long-wavelength acoustic modes. Continuum solutions for localized waves that incorporate atomiclevel elastic properties of the interface via discontinuity relations agree well with the latter modes. In contrast, classical solutions that depend only on bulk elastic properties do not. This demonstrates that the distinct atomic structure of the interface is a controlling factor, and it is shown how local, atomic-level properties can be incorporated into continuum analyses of interfacial phenomena.

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