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

•The vibrational modes in solid are described in a continuum model with inhomogeneous density function.•Boson peak in the density of states g(ω)g(ω) is linked to the mass localization of the order-parameter.•g(ω)g(ω) starts changing from the Debye form with mass localization spreading beyond a value l0l0.•For a hard sphere system of diameter σ   we find that l0≈0.2σl0≈0.2σ.

The inhomogeneous density n(x)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 l0l0, the corresponding vibrational density of states g(ω)g(ω) deviates from the Debye form gD(ω)gD(ω). We estimate the g(ω)g(ω) assuming a single peak form similar to the boson peak. For a hard core system of diameter σ   we obtain l0≈0.2σl0≈0.2σ. At an optimum l=lhl=lh the boson peak height hBhB of g(ω)g(ω) reaches a maximum.