Disorder classification of the vibrational spectra of modern glasses

Using the coherent-potential approximation in heterogeneous-elasticity theory with a log-normal distribution of elastic constants for the description of the Raman spectrum and the temperature dependence of the specific heat, we are able to reconstruct the vibrational density of states and characteristic descriptors of the elastic heterogeneity of a wide range of glassy materials. These descriptors are the nonaffine contribution to the shear modulus, the mean-square fluctuation of the local elasticity, and its correlation length. They enable a physical classification scheme for disorder in modern, industrially relevant glass materials. We apply our procedure to a broad range of real-world glass compositions, including metallic, oxide, chalcogenide, hybrid, and polymer glasses. Universal relationships between the descriptors on the one side, and the height and frequency position of the boson peak, the Poisson ratio and the liquid fragility index on the other side are established.