Abstract
A theoretical study using the analytic approach of the coherent-potential approximation (CPA) and numerical solutions has been made of vectoral vibrational excitations in a simple disordered system, namely a fcc lattice with force-constant disorder. A “phase diagram” (disorder versus freauency) for the vibrational excitations in this system has been determined. It is found that the boson peak for this system is generically related to the lowest-freauency van Hove singularity and arises from disorder-induced level-repelling and hybridization effects. For most degrees of disorder, the boson peak in this system occurs at the same freauency as the low-frequency Ioffe-Regel crossover between weak and strong scattering of vibrations. The trajectory of the mobility edge for spatial localization of vector vibrations in this model has been established by a multifractal and CPA analysis. Only states at the high-frequency edge of the acoustic band are localized.