Junzo Chihara

Structure factor and electronic structure of compressed liquid rubidium

We have applied the quantal hypernetted-chain equations in combination with the Rosenfeld bridge functional to calculate the atomic and the electronic structure of compressed liquid rubidium under high pressure ~0.2, 2.5, 3.9, and 6.1 GPa!; the calculated structure factors are in reasonable agreement with experimental results measured by Tsuji et al. along the melting curve as a whole. It is found that the effective ion-ion interaction is practically unchanged with respect to the potential at room pressure under these high pressures. All structure factors calculated for this pressure-variation coincide almost into a single curve if wave numbers are scaled in units of the Wigner-Seitz radius a although no corresponding scaling feature is observed in the effective ion-ion interaction. This scaling property of the structure factors signifies that the compression in liquid rubidium is uniform with increasing pressure; in absolute Q values this means that the first peak position (Q1) of the structure factor increases proportionally to V 21/3 ~V being the specific volume per ion! ,a s was experimentally observed by Tsuji et al. Obviously, this scaling property comes from a specific feature characteristic for effective ion-ion potentials of alkali liquids. We have examined and confirmed this feature for the case of a liquid-lithium potential: starting from the liquid-lithium potential at room pressure we can easily find two sets of densities and temperatures for which the structure factors become practically identical, when scaling Q in units of a. @S0163-1829~98!00533-5#

Nucleus-electron model for states changing from a liquid metal to a plasma and the Saha equation

We extend the quantal hypernetted-chain (QHNC) method, which has been proved to yield accurate results for liquid metals, to treat a partially ionized plasma. In a plasma, the electrons change from a quantum to a classical fluid gradually with increasing temperature; the QHNC method applied to the electron gas is in fact able to provide the electron-electron correlation at an arbitrary temperature. As an illustrating example of this approach, we investigate how liquid rubidium becomes a plasma by increasing the temperature from 0 to 30 eV at a fixed normal ion density 1.03x10(22)/cm(3). The electron-ion radial distribution function (RDF) in liquid Rb has distinct inner-core and outer-core parts. Even at a temperature of 1 eV, this clear distinction remains as a characteristic of a liquid metal. At a temperature of 3 eV, this distinction disappears, and rubidium becomes a plasma with the ionization 1.21. The temperature variations of bound levels in each ion and the average ionization are calculated in Rb plasmas at the same time. Using the density-functional theory, we also derive the Saha equation applicable even to a high-density plasma at low temperatures. The QHNC method provides a procedure to solve this Saha equation with ease by using a recursive formula; the charge population of differently ionized species are obtained in Rb plasmas at several temperatures. In this way, it is shown that, with the atomic number as the only input, the QHNC method produces the average ionization, the electron-ion and ion-ion RDFs, and the charge population that are consistent with the atomic structure of each ion for a partially ionized plasma.

Thermodynamics in Density-Functional Theory and Force Theorems

The density-functional (DF) theory provides a simple method for calculating the properties of an interacting system under an external potential by associating it with a corresponding non-interacting system. Here, we find some relations in this non-interacting system that enable us to set up the thermodynamic relations for a neutral electron-nucleus mixture in terms of quantities of the non-interacting system and the exchange-correlation effect. In this way, Andersens force theorems are clearly described and easily proved in conjunction with other types of force theorems, Janaks theorem extended to a finite-temperature system, pressure formulas, and some thermodynamic relations. For this purpose, thermodynamics in the DF theory is presented in a systematic and explicit way.

Effective Interatomic Interactions in Liquid Metals

Abstract Some liquid metals can be regarded as a binary mixture of ions and electrons interacting via binary interparticle interactions with each other. It is shown exactly on the basis of the density-functional method that a liquid metal can be taken as a quasi one-component system only via a pairwise interatomic interaction (without a many-body force) to obtain the radial distribution function, provided that a liquid metal can be thought of as an ion-electron mixture with binary interactions.

Electron and Nuclear Pressures in Electron-Nucleus Mixtures

It is shown for an electron-nucleus mixture that the electron and nuclear pressures are defined clearly and simply by the virial theorem; the total pressure of this system is a sum of these two pressures. The electron pressure is different from the conventional electron pressure being expressed as the sum of two times of kinetic energy and the potential energy in that the nuclear virial term is subtracted; this fact is exemplified by several kinds of definitions for the electron pressure enumerated in this work. The conventional definition of the electron pressure in terms of the nuclear virial term is shown inappropriate. Similar remarks are made about the definition of the stress tensor in this mixture. It is also demonstrated that both of the electron and nuclear pressures become zero at the same time for a metal in the vacuum, in contrast to the conventional viewpoint that the zero pressure is realized by a result of the cancellation between the electron and nuclear pressures, each of which is not zero. On the basis of these facts, a simple equation of states for liquid metals is derived, and examined numerically for liquid alkaline metals by use of the quantum hypernetted chain equation and the Ashcroft model potential.

Ab Initio Molecular Dynamics for Simple Liquid Metals Based on the Hypernetted-Chain Approximation

Abstract We present an ab initio molecular dynamics (MD) method for simple liquid metals based on the quantal hypernetted-chain (QHNC) theory derived from exact expressions for radial distribution functions (RDFs) of the electron-ion model for liquid metals. In our method based on the QHNC equations, the classical MD is performed repeatedly to determine a self-consistent effective interionic potential, which depends on the ion-ion RDF of the system. This resultant effective ionic potential is obtained to be consistent with the density distribution of a pseudoatom and the electron-ion RDF, as well as the ion-ion RDF and the ion-ion bridge function, which are determined exactly as a result of the repeated MD simulation. We have applied this QHNC-MD method for Li, Na, K, Rb, and Cs near the melting temperature using upto 16,000 particles for the MD simulation. It is found that the convergence of the effective interionic potential is fast enough for practical applications; typically two MD runs are enough fo...

RUBIDIUM FROM A LIQUID METAL TO A PLASMA

Usually, a liquid metal is treated as a one-component liquid where the particles interact via a binary effective potential, which is determined within the pseudopotential formalism. However, this quite successful method for a liquid metal cannot be extended to calculate the structure of a plasma, since for such a system this kind of pseudopotential cannot be set up. In previous contributions, we have proposed a method which allows the calculation of the radial distribution functions (RDF’s) in an electron–ion mixture on the basis of the density functional (DF) theory; it is called the quantal hypernetted (QHNC) approximation: the QHNC equations are derived from exact expressions for the electron–ion and ion–ion RDF’s in an electron–ion mixture. Up to now, we have applied this approach to liquid metallic hydrogen, lithium, sodium, potassium and aluminum, obtaining ion–ion structure factors in excellent agreement with experiments. Recently, we have extended the formalism and have performed a first-principles molecular dynamics simulation based on the QHNC theory for alkali metals near the triple point: in this study those small deviations which were still observed between experimental results and QHNC data for the structure factor disappeared completely. In the present study we first show that the QHNC method can provide an accurate description of liquid metals in a wide range of densities and temperatures: we calculate the structure factors of compressed liquid rubidium, which have been studied experimentally at high pressures from 0.2 to 6.1 GPa by Tsuji; furthermore we calculate the structure factors of expanded rubidium states which have been studied by Franz et al. Secondly, we show that the QHNC method can be extended to treat a plasma: in such a system, both the ionic valency and the electron–ion interaction may vary over a wide range as temperature and density are changed. Our method is in particular suited to treat a plasma, since it is able to calculate these quantities in a self-consistent manner using the atomic number of the system as the only input data. In order to treat plasmas, the electron–electron correlation must be determined for arbitrary temperatures. In this work, we show that the QHNC method applied to the electron gas is in fact able to provide the electron correlation at arbitrary temperature. Using then this electron–electron correlation, we study how a liquid metal becomes a plasma for the case of rubidium by increasing the temperature at a fixed density. We can consider a liquid metal or a plasma as a mixture of electrons and ions interacting

Pressure-Variation of Structure Factor of Liquid Rb

We have calculated the atomic and the electronic structures of compressed liquid rubidium under high pressures up to 6 GPa on the basis of the quantal hypernetted chain equations in combination with the Rosenfeld bridge functional. The calculated structure factors are in reasonable agreement with the experimental results by Tsuji et al. under these high pressures using synchrotron radiation. All structure factors calculated for this pressure-variation coincide almost into a single curve if wavenumbers are scaled in units of the Wigner-Seitz radius; the compression in liquid rubidium is uniform with increasing pressures. The effective ion-ion interactions remains almost unchanged under this pressure-variation. Results of calculation on liquid lithium confirm that effective ion-ion potentials for alkali metals have the specific feature of scaling property in common. Furthermore, it is shown that the uniform compression of liquid Rb can be explained simply by the effective ion-ion interaction based on the Aschcroft pseudopotenital at the room pressure with use of the scaling property.

Comment on "Strong-coupling theory of hydrogen plasmas"

The integral equations applied to a hydrogen plasma by Yan, Tsai, and Ichimaru (Phys. Rev. A 43, 3057 (1991)) are shown to become inappropriate when the plasma begins to have a bound state which brings about a low degree of ionization: the bound-state contribution to forming an ion should be taken in the form needed to induce changes in the bare ion-ion and electron-ion interactions. Moreover, their definition of a degree of ionization shows an abrupt change when a bound state disappears, and this discontinuity is associated with a phase transition. However, this discontinuity in the ionization may not be a real one, since it is possible to define a degree of ionization, which remains continuous in the change from a bound to a continuum state.

Atomic Structure of an Impurity Neon in Liquid Metallic Hydrogen

The determination of the electronic structure of isolated atoms and molecules is easily performed within the framework of the density functional formalism. On the other hand, it is a difficult problem to calculate the electronic structure of an atom immersed in a liquid metal or a high-density plasma, since this contains two problems: combination of the liquid- and the atomic-structure. The “external problem” is to determine electron- and ion-density distributions around the impurity in the whole space, while the other “internal problem” is to calculate the atomic structure under this circumstance. There have been a number of studies on this problem in relevance to the inertial confinement fusion and the study of stellar interiors (for example, Skupsky 1980, Davis and Blaha 1982, Perrot and Dharma-wardana 1985, Fujima et al. 1985). A similar problem occurs in treating core-level shifts and Auger relaxation energies of an impurity in a solid metal (Williams and Lang 1978, Lang and Williams 1979). These calculations have shown that the excitation energies can be successfully obtained from the total energy difference between the initial and final states in the density-functional theory. Thus, we can expect that the electronic structure of an atom in a plasma may be calculated within the framework of the density-functional theory.