Frequency spectra of disordered metals: especially liquid Rb

The phonon frequency spectrum g(omega) of a crystal, such as body centred cubic (bee) Rb, is known to be characterized by the Van Hove singularities at omega not equal 0. However, for a liquid metal like Rb, g(w) has a single, hydrodynamic-like singularity, namely it cusp proportional to omega((1/2)), at omega = 0. Here, we note first that computer simulation on liquid Rb near freezing has revealed a rather well-defined Debye frequency omega(D). Therefore, we propose here it zeroth-order model g(0)(omega) of g(omega) for Rb, which combines the Debye model with the 'hydrodynamic' omega((1/2)) cusp. The corresponding velocity autocorrelation function (v(t) . v(0)) has correctly a long-time tail proportional to t(-(3/2)). The terms from g(0)(omega) involving omega(D) are then damped by weak exponential factors exp(-alpha(i)t), and the resulting first-order approximation, g(t)(omega) say, to the frequency spectrum is found to have features in common with the molecular dynamics (MD) simulation form. Thus omega(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.