A study of the electronic properties of liquid alkali metals: a self-consistent approach

Abstract

We study the electronic properties (density of states, conductivity and thermopower) of some nearly-freeelectron systems: the liquid alkali metals and two liquid alloys, Li-Na and Na-K. The study has been performed within the self-consistent second order Renormalized Propagator Perturbation Expansion (RPE) for the self-energy. The input ionic pseudopotentials and static correlation functions are derived from the neutral pseudoatom method and the modified hypernetted chain theory of liquids, respectively. Reasonable agreement with experiment is found for Na, K, Rb and Na-K, whereas for Li and Cs and Li-Na the agreement is less satisfactory. I IntroductionThe introduction of the diffraction model [1] together with the development of the pseudopotential concept, marked the beginning of extensive calculations of structural and electronic properties of liquid metals [2,3]. Based on this concept one can justify the use of simple second-order perturbation theory for weak scattering systems like the alkalis. The most used expression in this Nearly-Free Electron (NFE) model is the well-known Ziman formula for the resistivity. Two key ingredients appear in it, namely the static structure factor S(q) and the screened pseudopotential w(q). These two quantities are not independent, since the pseudopotential determines the forces between the ions, which ultimately determine the structure of the liquid. Therefore S(q) should be obtained from w(q) and the result used in the evaluation of the electronic properties, and from the new electronic density one should again derive a new pseudopotential. This is what we call a self-consistent calculation of the electronic properties of a liquid metal.Most of the calculations up to date are, with the exception of ab-initio Molecular Dynamics simulations, not self-consistent, i.e. for S(q) one takes either one from an analysis of the experimental structure factor data, or one obtained from a model for the interatomic interactions, like hard spheres, with parameters fitted to experimental data. This model is then used as input either in an approximate scheme to solve the Ornstein-Zernike equations like the Percus-Yevick or (Modified) HyperNetted Chain, or in a liquid structure computer simulation. Then a pseudopotential is chosen and the electronic properties, for example the electronic density of states (EDOS), are calculated. There have been some attempts to study the properties in a self-consistent way in a more restricted sense, that is, using the same pseudopotential for the structure factor, thermodynamic properties and conductivity. However up to the present day such a scheme has failed: it leads to disagreement with either the electronic properties, or with the atomic properties.There are at least two important exceptions in the previous works, which do make the calculations within the spirit of self-consistency. One is the work of Jank and Hafner [5], where molecular dynamics are performed with effective pair potentials derived from a given pseudopotential, and then some ionic con...

Unified study of electrical resistivity of simple and non-simple liquid metals

“…As they have fitted the potential parameter their results are very close to the experimental findings for simple metals while for Cu and Ag it deviates little. Very recently Geertsma et al [16] have calculated density of states, resistivity and thermopower of liquid alkali metals and two liquid alloys Li-Na and Na-K. they have used Linear Response Theory (LRT) to calculate the screened pseudopotential and the structure factor was obtained from the pair-potential using Modified Hyper Neted Chain (MHNC) theory of liquid. Their results of electrical resistivity for liquid alkali metals are very poor particularly for Li and Cs.…”

Electronic transport properties of liquid lanthanides

“…The experimental data on the structure factors obtained by neutron and X-ray diffraction methods are available only for some liquid lanthanides near their melting points [4]. The most popular method for studying the electronic transport properties of liquid metals is the electrical conduction theory developed by Ziman [5][6][7][8][9][10][11][12][13][14][15][16][17][18][19][20][21] using the concept of model pseudopotential. This concept has been extremely useful over the last few decades for simple liquid metals and liquid transition metals [5][6][7][8][9][10][11][12][13][14][15][16][17][18][19][20][21].…”

“…Ziman's theory is widely used to investigate the electrical resistivity [5][6][7][8][9][10][11][12][13][14][15][16][17][18][19][20][21]. Its starting point rest on first order time dependent perturbation theory [5].…”

“…It proves to be successful for liquid simple metals and their alloys [6,7]. Ziman's theory was further extended for noble and transition metals [8,9,[11][12][13][14][15][16][17][18][19][20][21]. The extended theory involves the t-matrix that depends on the relevant phase shift.…”

“…The phase shift is derived by solving the Schrödinger equation involving the muffin-tin potentials. Consequently, it is more computationally expensive than Ziman's original theory [5][6][7][8][9][10][11][12][13][14][15][16][17][18][19][20][21]. It is reported that when the t-matrix is expanded for multiple scattering the second and third terms increase the resistivity only by 7% and 1%, respectively [3].…”