Direct experimental determination of the crossover frequency between phonon and fracton regimes and its scaling behavior in superionic silver borate glasses

Abstract

We determined the crossover frequency ${\mathrm{\ensuremath{\omega}}}_{\mathrm{co}}$ between phonon and fracton regimes from the study of the low-frequency inelastic light scattering in superionic borate glasses of the type (AgI${)}_{\mathit{x}}$(${\mathrm{Ag}}_{2}$O\ensuremath{\cdot}${\mathrm{B}}_{2}$${\mathrm{O}}_{3}$${)}_{1\mathrm{\ensuremath{-}}\mathit{x}}$. The scaling of ${\mathrm{\ensuremath{\omega}}}_{\mathrm{co}}$ with the fractal characteristic length was studied by variation of the AgI concentration x. We thus obtained the diffusion coefficient scaling exponent theta and the spectral dimensionality d\ifmmode \tilde{}\else \~{}\fi{} which characterizes energy diffusion on a fractal.