Vibrational density of states in the disordered solid using classical density functional model

Abstract

Abstract The inhomogeneous density n ( x ) of an amorphous solid is expressed as a sum of Gaussian profiles. Average width of these profiles represents a characteristic length l signifying the degree of mass localization in the system. We demonstrate that as l spreads beyond a critical value l 0 , the corresponding vibrational density of states g ( ω ) deviates from the Debye form g D ( ω ) . We estimate the g ( ω ) assuming a single peak form similar to the boson peak. For a hard core system of diameter σ we obtain l 0 ≈ 0.2 σ . At an optimum l = l h the boson peak height h B of g ( ω ) reaches a maximum.