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Ashcroft, N. W.

Publications and source records attributed to Ashcroft, N. W..

At least 37 records · Page 2
All sourcesNASA NTRSDOE OSTI
NASA NTRS1980

Simulation studies of a model of high-density metallic hydrogen

Upper bounds for the ground-state energies of liquid and solid phases of metallic hydrogen and metallic deuterium have been calculated with variational methods and Monte Carlo techniques. At four densities (0.8, 1.2, 1.36, and 1.488) crystalline phases are clearly preferred in the sense that the energy difference, when compared to the liquid, is in excess of the errors inherent in the numerical procedures. At a fifth density (1.6), the energy differences between solid and liquid phases are smaller than these errors.

Mon, K. K.↗
NASA NTRS1979

Mean-spherical model for soft potentials - The hard core revealed as a perturbation

The mean-spherical approximation for fluids is extended to treat the case of dense systems interacting via soft potentials. The extension takes the form of a generalized statement concerning the behavior of the direct-correlation function c(r) and the radial-distribution function g(r). From a detailed analysis that views the hard-core portion of a potential as a perturbation on the whole, a specific model is proposed which possesses analytic solutions for both Coulomb and Yukawa potentials, in addition to certain other remarkable properties. A variational principle for the model leads to a relatively simple method for obtaining numerical solutions.

Rosenfeld, Y.↗
NASA NTRS1979

A new theory of simple classical fluids

The paper presents a unified structural and thermodynamic theory of simple classical fluids in which the interactions between the particles can be represented by spherically symmetric pairwise potentials. Both the excess entropy and the gross features of the radial distribution function are determined mainly by excluded volume effects, which are in turn governed by a hard-core property intrinsic to any pair potential. The potential beyond this effective hard core is considered relatively weak and can be treated as a perturbation. It is also considered essential to sum all subclasses of diagrams to infinite order. The basic form of a diagrammatic scheme which allows both summation and the determination of the structure and excess entropy is presented, and a statement of universality is derived. The statement has been confirmed within the accuracy of present-day computer simulations, and a possible procedure for calculating both the structure and thermodynamics of every physically conceivable pair potential is presented.

Rosenfeld, Y.↗
NASA NTRS1978

Astrophysical materials science: Theory

Research papers of the discoveries and work carried out over the past six or so years are presented. Hydrogen and helium constitute by far the most abundant of the elements and it is no accident that the research has focussed heavily on these elements in their condensed forms, both as pure substances and in mixtures. The research has combined the fundamental with the pragmatic.

Ashcroft, N. W.↗
NASA NTRS1978

On the ground state of metallic hydrogen

A proposed liquid ground state of metallic hydrogen at zero temperature is explored and a variational upper bound to the ground state energy is calculated. The possibility that the metallic hydrogen is a liquid around the metastable point (rs = 1.64) cannot be ruled out. This conclusion crucially hinges on the contribution to the energy arising from the third order in the electron-proton interaction which is shown here to be more significant in the liquid phase than in crystals.

Chakravarty, S.↗
NASA NTRS1978

A mean spherical model for soft potentials: The hard core revealed as a perturbation

The mean spherical approximation for fluids is extended to treat the case of dense systems interacting via soft-potentials. The extension takes the form of a generalized statement concerning the behavior of the direct correlation function c(r) and radial distribution g(r). From a detailed analysis that views the hard core portion of a potential as a perturbation on the whole, a specific model is proposed which possesses analytic solutions for both Coulomb and Yukawa potentials, in addition to certain other remarkable properties. A variational principle for the model leads to a relatively simple method for obtaining numerical solutions.

Rosenfeld, Y.↗
NASA NTRS1977

Thermodynamics of Thomas-Fermi screened Coulomb systems

We obtain in closed analytic form, estimates for the thermodynamic properties of classical fluids with pair potentials of Yukawa type, with special reference to dense fully ionized plasmas with Thomas-Fermi or Debye-Hueckel screening. We further generalize the hard-sphere perturbative approach used for similarly screened two-component mixtures, and demonstrate phase separation in this simple model of a liquid mixture of metallic helium and hydrogen.

Firey, B.↗
NASA NTRS1977

Self-consistent structure of metallic hydrogen

A calculation is presented of the total energy of metallic hydrogen for a family of face-centered tetragonal lattices carried out within the self-consistent phonon approximation. The energy of proton motion is large and proper inclusion of proton dynamics alters the structural dependence of the total energy, causing isotropic lattices to become favored. For the dynamic lattice the structural dependence of terms of third and higher order in the electron-proton interaction is greatly reduced from static lattice equivalents.

Straus, D. M.↗
NASA NTRS1977

Phase separation of metallic hydrogen-helium alloys

Calculations are presented for the thermodynamic functions and phase-separation boundaries of solid metallic hydrogen-helium alloys at temperatures between zero and 19,000 K and at pressures between 15 and 90 Mbar. Expressions for the band-structure energy of a randomly disordered alloy (including third order in the electron-ion interaction) are derived and evaluated. Short- and long-range orders are included by the quasi-chemical method, and lattice dynamics in the virtual-crystal harmonic approximation. It is concluded that at temperatures below 4000 K, there is essentially complete phase separation of hydrogen-helium alloys and that a miscibility gap remains at the highest temperatures and pressures considered. The relevance of these results to models of the deep interior of Jupiter is briefly discussed.

Straus, D. M.↗
NASA NTRS1976

Phase separation of metallic hydrogen-helium alloys

Calculations are presented for the thermodynamic functions and phase separation boundaries of solid metallic hydrogen helium alloys at temperatures between 0 K and 19,000 K and at pressures between 15 and 90 megabars. Expressions for the band structure energy of a randomly disordered alloy (including third order in the electron ion interaction) are derived and evaluated. Short and long range order are included by the quasi-chemical method, and lattice dynamics in the virtual crystal harmonic approximation. We conclude that at temperatures below 4,000 K there is complete phase separation of hydrogen helium alloys, and that a miscibility gap remains at the highest temperatures and pressures considered. The relevance of these results to models of the deep interior of Jupiter is briefly discussed.

Straus, D. M.↗
NASA NTRS1975

Aluminum under high pressure. I - Equation of state

A curve of applied pressure versus lattice constant is calculated for single-crystal aluminum. It results from an application of the method of structural expansions for deriving the energies of simple metals, a method known to give reasonable results for the elastic constants even at second order in the effective electron-ion interaction. The latter is taken from Fermi-surface analysis, and it is verified that the extant face-centered cubic structure remains the preferred crystalline phase up to the highest pressures considered. Arguments are given to suggest that the curve should have reasonable a priori accuracy and can admit possible improvement if experimental data in the intermediate-pressure region can be provided to refine the (in principle) energy-dependent pseudopotential. At three megabars, the lattice constant is reduced by only 22 per cent; the ion cores at this pressure are still very well separated.

Friedli, C.↗
NASA NTRS1975

Thermal diffuse X-ray scattering in simple metals

Calculations are reported for the ionic structure factor and X-ray scattering cross section of sodium (at T=0 K and 90 K) and lithium (both isotopes at T=0 K) within the harmonic approximation. An evaluation of the appropriate displacement- displacement correlation function by the special point method circumvents the need for a multiphonon expansion. In the case of sodium, the structure in the one-phonon scattering was straightforwardly accounted for, and an approximate expansion was obtained for all multiphonon scattering. By treating core and conduction electrons on an equal footing, it is shown that information on the conduction electron system is present in the forward scattering component. In lithium the one-phonon cross section at small angles aids in the determination of the effective electron-ion interaction.

Straus, D. M.↗
NASA NTRS1975

Aluminum under high pressure: 1 equation of state

A curve of applied pressure P versus lattice constant a is calculated for single crystal aluminum. It results from an application of the method of structural expansions for deriving the energies of simple metals, a method known to give reasonable results for the elastic constants even at second order in the effective electron-ion interaction. The method is taken from Fermi surface analysis . This essentially experimental information is used to verify that the extant face-centered cubic structure remains the preferred crystalline phase up to the highest pressures considered. Arguments are given to suggest that the P versus a curve should have reasonable a priori accuracy, which may be improved if experimental data in the intermediate pressure region can be provided to refine the energy dependent pseudo-potential. At 3 megabars the lattice constant is reduced by only 22%; the ion cores at this pressure are still very well separated.

Friedli, C.↗
NASA NTRS1975

A combined representation method for use in band structure calculations. 1: Method

A representation was described whose basis levels combine the important physical aspects of a finite set of plane waves with those of a set of Bloch tight-binding levels. The chosen combination has a particularly simple dependence on the wave vector within the Brillouin Zone, and its use in reducing the standard one-electron band structure problem to the usual secular equation has the advantage that the lattice sums involved in the calculation of the matrix elements are actually independent of the wave vector. For systems with complicated crystal structures, for which the Korringa-Kohn-Rostoker (KKR), Augmented-Plane Wave (APW) and Orthogonalized-Plane Wave (OPW) methods are difficult to apply, the present method leads to results with satisfactory accuracy and convergence.

Friedli, C.↗
NASA NTRS1974

Conduction in fully ionized liquid metals

Electron transport is considered in high-density fully ionized liquid metals. Ionic structure is described in terms of hard-sphere-correlation functions and the scattering is determined from self-consistently screened point ions. Applications to the physical properties of the deep interior of Jupiter are briefly considered.

Stevenson, D. J.↗
NASA NTRS1974

Ground-state energies of simple metals

A structural expansion for the static ground-state energy of a simple metal is derived. Two methods are presented, one an approach based on single-particle band structure which treats the electron gas as a nonlinear dielectric, the other a more general many-particle analysis using finite-temperature perturbation theory. The two methods are compared, and it is shown in detail how band-structure effects, Fermi-surface distortions, and chemical-potential shifts affect the total energy. These are of special interest in corrections to the total energy beyond third order in the electron-ion interaction and hence to systems where differences in energies for various crystal structures are exceptionally small. Preliminary calculations using these methods for the zero-temperature thermodynamic functions of atomic hydrogen are reported.

Hammerberg, J.↗
NASA NTRS1973

Conduction in fully ionized liquid metals

Electron transport is considered in high density fully ionized liquid metals. Ionic structure is described in terms of hard-sphere correlation functions and the scattering is determined from self-consistently screened point ions. Applications to the physical properties of the deep interior of Jupiter are briefly considered.

Stevenson, D. J.↗