Thermodynamic and electronic properties of a tight-binding lattice-gas model

Abstract

Thermodynamic and electronic properties are obtained for a lattice-gas model fluid with self-consistent, partial, occupation of its sites; the self consistency consists in obtaining ionic configurations from grand-canonical Monte Carlo simulations based on fits to the exact, electronic, tight-binding energies of isothermal ensembles of those same ionic configurations. The energy of an ion is found to be a concave-up function of its local coordination. Liquid-vapor coexistence densities and the electrical conductivity, which shows a metal-nonmetal transition, have been obtained. 1.IntroductionThe statistical mechanics of simple insulating liquids is a well developed subject, with different approaches being used to obtain the thermodynamics and the correlation structure, from the additive pairwise interaction potential between atoms or molecules [1]. A quantummechanical study of the atomic or molecular structures provides the interatomic potential, but, in all other aspects, the interaction is decoupled from the classical statistical-physics problem of obtaining the positions and correlations of the atoms. One of the more striking deviations from this simple liquid behavior is provided by liquid metals, in which the conduction electrons are fully delocalized and the system has to be treated as a mixture of ions ( with classical statistics) and electrons (with Fermi-Dirac statistics). The study of dense liquid metals, near the triple-point temperature, has been based on a double perturbative expansion [2] around a reference simple fluid for the ions, and around the jellium model for the conduction electrons. The vapor, at coexistence with the liquid metal, has a qualitatively different electronic structure, with the valence electrons localized in neutral atoms or clusters. At low temperature, the vapor has extremely low density and is almost trivial. In the neighborhood of the critical point, and of the metal-nonmetal transition region, the interrelation between electronic delocalization and ionic structure becomes crucial, and the approaches valid at low temperature fail qualitatively.Recent experimental data on the critical region of the alkali fluids [3] provide strong motivation for a more extensive theoretical study of these systems [4,5]. Our main objective here is to set a minimal model, including the main relevant features of the coupling between the electronic and the ionic structure, to analyze the statisticalphysics problem posed by these systems. We have reported [6] preliminary calculations using this approach. In our model, we forsake the 'state of the art' description of liquid metals in condensed matter physics, and our model neglects aspects of the problem which are certainly relevant for some properties of these systems. However, we show that many qualitative effects of the coupling between electronic and ionic structures are already present in a very simple model. This approach allows the study of the critical region through Monte Carlo simulation with system of large size, compared with ...

Hard-sphere fluid with tight-binding electronic interactions: A glue model treatment

“…The weak dependence of T c * on ␣*, for the TB-HS model, reflects the saturation of the electronic energy with increasing average number of neighbors which was already discussed in our previous lattice-gas model. 4 Further, the saturation of the electronic energy with the number of neighbors is also reflected in the value of the critical density, which in a mean-field pair-interaction model would depend only on the HS contribution. In the TB-HS model, the electronic free energy per ion has a large curvature at intermediate values of the density, associated with the saturation effect; these densities are about three times smaller for ␣*ϭ2.0 than for ␣*ϭ3.89.…”

“…We began with a oneelectron treatment. 4 Then, the effects of a Hubbard interaction among electrons was considered. 5 That work was recently reviewed.…”

Effects of electron correlation on thermodynamic properties of expanded alkali fluids

“…Among the approximations in this theory, the importance of improving the mean-field approximation for atomic arrangements has been pointed out by Reinald-Falagán et al [11,12]. They concluded that it is important to treat the local atomic configuration beyond the mean-field approximation self-consistently with the electronic energy to reproduce the asymmetric feature of the LV coexistence curve.…”

“…the curve describing the boundary of the coexisting liquid and vapour phases on the volume versus temperature plane, is strongly asymmetric and the law of the rectilinear diameter breaks down over a large temperature range for fluid alkalis such as Rb and Cs. Among recent theoretical research in relation to the above experimental results, the work most relevant to the present paper is that by Reinaldo-Falagán et al [11,12]. In the earlier paper [11], using a model which is the single-particle version of the latticegas Hubbard model presented above, and a self-consistent method for determining the ionic configurations and the electronic energies, they obtained results for the thermodynamic and electronic properties of expanded alkali fluids which agree qualitatively with the experimental results.…”

“…Among recent theoretical research in relation to the above experimental results, the work most relevant to the present paper is that by Reinaldo-Falagán et al [11,12]. In the earlier paper [11], using a model which is the single-particle version of the latticegas Hubbard model presented above, and a self-consistent method for determining the ionic configurations and the electronic energies, they obtained results for the thermodynamic and electronic properties of expanded alkali fluids which agree qualitatively with the experimental results. In particular, they concluded that the extreme asymmetry of the coexistence curves is reproduced by taking account self-consistently of the effect of the local coordination in determining the free energy per ion.…”