STONELEY WAVES AND GRAIN-BOUNDARY PHONONS

The lattice dynamics (phonons) of bicrystals with stable grain-boundar y structures are computed and the results of these calculations are li nked with continuum elasticity solutions of interface waves. Through c omparisons of the lattice-dynamics calculations for ideal crystals wit h those for the corresponding bicrystals, the low-frequency acoustic b ranches of the dispersion curves associated with the interface vibrati ons 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 th at decay exponentially with distance from the interface. We find that the perfect-bonding assumption over-restricts the nature of these latt er waves, that is, these solutions do not reproduce the atomistic resu lts for continuum-like waves. The reason lies in the fact that these l ocalized waves are significantly influenced by the local properties of the interfacial region associated with its distinct structure.