State dependent particle dynamics in liquid alkali metals

Abstract

This paper gives a survey of the particle dynamics in the liquid alkali metals observed with inelastic x-ray and neutron scattering experiments. Liquid rubidium and sodium are chosen as model fluids to represent the behaviour of this group of fluids. In the dense metallic monatomic melt the microscopic dynamics is characterized by collective excitations similar to those in the corresponding solids. The collective particle behaviour is appropriately described using a memory function formalism with two relaxation channels for the density correlation. A similar behaviour is found for the single particle motion where again two relaxation mechanisms are needed to accurately reproduce the experimental findings. Special emphasis is given to the density dependence of the particle dynamics. An interesting issue in liquid metals is the metal to non-metal transition, which is observed if the fluid is sufficiently expanded with increasing temperature and pressure. This causes distinct variations in the interparticle interactions, which feed back onto the motional behaviour. The associated variations in structure and dynamics are reflected in the shape of the scattering laws. The experimentally observed features are discussed and compared with simple models and with the results from computer simulations.

Multiple time scales in the microscopic dynamics of simple and complex liquids as studied by radiation scattering

“…Equation (2) yields the mode-coupling contribution to the Laplace trans-form of the memory-function associated with the normalized particle velocity autocorrelation function v(t) · v(0) / v 2 at zero frequency. It yields a value of 11.2 ps −1 which comes to be about twice the value reported for molten Na at an equivalent temperature [14].…”

“…The value for the diffusion coefficient comes significantly short of the macroscopic value of 0.327 meVÅ 2 . Such retardation of diffusive processes at microscopic scales is usually attributed to a strong coupling with longitudinal collective modes [13,14]. Put into different words, under the present conditions mass diffusion only takes place after a relatively large lapse of time where liquid cages become incapable of maintaining collective oscillatory motions.…”

“…The picture that emerges from these theoretical approaches portrays motions within the kinetic regime, that is, for time-length scales comparable with inter-particle separations and microscopic times mediated by collective modes. For temperatures close to melting, coupling of particle diffusion to a longitudinal mode results in a retardation of diffusive motions if compared to the hydrodynamic prescription [14]. In contrast, diffusive dynamics at higher temperatures is thought to couple to transverse modes.…”

“…In contrast, the S s (Q, ω) spectra comprising the single-particle dynamics is known to follow, within the hydrodynamic realm, an exponential relaxation process, as dictated by Fick's Law with a decay constant given in terms of the self-diffusion coefficient D s which in frequency space translates into a lorentzian line shape of width D s Q 2 and peak height proportional to 1/D s Q 2 . Beyond the hydrodynamic limit, usually located at momentum transfers of the order of 10 −2Å−1 , the behavior of S s (Q, ω) is now understood quantitatively [13,14], mostly as a consequence of developments of kinetic theories of the mode-coupling family. These have provided us with predictive capabilities of accounting for the shape and characteristic parameters (i.e.…”

“…These ideas can be put into numbers by first evaluating the diffusion coefficient for a hard-sphere fluid D E within the Enskog prescription in terms of the temperature, particle mass and packing fraction as [14],M…”