Frequency spectra of disordered metals: especially liquid Rb

The phonon frequency spectrum g(ω) of a crystal, such as body centred cubic (bcc) Rb, is known to be characterized by the Van Hove singularities at ω?≠?0. However, for a liquid metal like Rb, g(ω) has a single, hydrodynamic-like singularity, namely a cusp ∝ ω ^(1/2), at ω?=?0. Here, we note first that computer simulation on liquid Rb near freezing has revealed a rather well-defined Debye frequency ω_D. Therefore, we propose here a zeroth-order model g ₀ (ω ) of g(ω) for Rb, which combines the Debye model with the ‘hydrodynamic’ ω ^(1/2) cusp. The corresponding velocity autocorrelation function 〈 v (t)·v (0)〉 has correctly a long-time tail ∝ t ^-(3/2). The terms from g ₀ (ω ) involving ω_D are then damped by weak exponential factors exp (-α _i t), and the resulting first-order approximation, g ₁ (ω ) say, to the frequency spectrum is found to have features in common with the molecular dynamics (MD) simulation form. Thus ω_D is fixed, as well as transport coefficients for the known thermodynamic state. The article concludes with a more qualitative discussion on supercooled liquids, and on metallic glasses such as Fe, for which MD simulations exist.