Transport and vibrational lifetimes in amorphous structures

The lifetimes of high energy lattice vibrational states in amorphous or glassy materials are calculated on the basis of vibrational localization for energies omega > omega(c), where omega(c) signifies the mobility edge. Anharmonicity-induced localized vibrational slate hopping, with the emission of an extended vibrational state (a phonon), is found to be the dominant decay mechanism. Because of the contribution of the same vertex to thermal transport via localized vibrational state hopping, the vibrational lifetimes can be expressed in terms of this hopping contribution to the thermal conductivity, with only omega(c) as an undetermined variable. At low temperatures, the high energy vibrational lifetime is found to be proportional to the exponential of (omega/omega(c))(d phi/D) where d(phi) is the superlocalization exponent of the localized vibrational state, and D is the mass density scaling exponent (equal to the Euclidean dimension d for dense systems, and the fractal dimension for fractal systems). Excellent numerical agreement is found with the experiments of Scholten et al. which find a lifetime tau = 70 ns for the 480 cm(-1) TO vibration in a-Si:H.