Vibrational properties of a bicrystal interface: Different-interface phonons and the low-temperature specific heat

The vibrational properties of a coherent interface between two different crystals are studied in this paper on an atomic model. In the long-wavelength approximation, we recover the well-known Stoneley waves of elasticity theory and their existence conditions. We establish also that when these localized Stoneley waves do not exist, one has nevertheless at least one semilocalized acoustic mode (localized in one of the crystals and resonant in the other one). We also report for the first time on a few other interface modes: localized in interface gaps appearing for some values of the propagation vector $k_{\parallel }$ parallel to the interface; localized, semilocalized, and resonant modes, some of them being in the optically active region. The relations between these different interface modes are discussed. We also derive in this paper for the first time an atomic model's variation in the low-temperature specific heat due to a bicrystal interface and to a planar bulk defect.