Showing papers on "Thomas–Fermi model published in 2015"

Two-temperature equation of state for aluminum and gold with electrons excited by an ultrashort laser pulse

Abstract: A short laser pulse converts metal into a two-temperature state with the electron temperature higher than the ion temperature. To describe the electron contributions to the total internal energy and pressure arising as a result of electron heating, we develop the new analytic approximation formulae for two-temperature thermodynamics of metal. Those approximations are based on quantum calculations performed with density functional theory (DFT) packages. DFT calculations provide the internal energies and pressures for densities of the order of solid-state density and for electron temperatures up to 55 kK. The new analytic approximations give a better accuracy in hydrodynamic simulation of laser–matter interaction and should be used instead of the less accurate expressions based on the Fermi model of ideal electron gas, which is widely used for two-temperature states of metal.

Minimization of energy per particle among Bravais lattices in R^2 : Lennard-Jones and Thomas-Fermi cases

Abstract: We prove in this paper that the minimizer of Lennard–Jones energy per particle among Bravais lattices is a triangular lattice, i.e. composed of equilateral triangles, in ℝ2 for large density of points, while it is false for sufficiently small density. We show some characterization results for the global minimizer of this energy and finally we also prove that the minimizer of the Thomas–Fermi energy per particle in ℝ2 among Bravais lattices with fixed density is triangular.

Wide-range equation of state for gas and liquid plasma

Abstract: A fundamentally new correction to the interaction of charged particles in plasma is proposed and substantiated. The substitution of this correction into the generalized Saha equation makes it possible to extrapolate these equations to zero temperature. This yields physically reasonable values of the ionization rate and thermodynamic functions and can significantly extend the applicability range of the Saha model to extremely high densities and moderate temperatures, i.e., the liquid plasma state. In passing, deficiencies are corrected inherent in the classical Debye model and the inadequacy of the model of simple harmonic oscillators is demonstrated. Liquid plasma is more accurately described by the Thomas–Fermi model with quantum and exchange corrections. An ultrafast algorithm has been developed for the solution of equations of this model. The calculations based on this model are joined with the calculations by the generalized Saha model by means of a special interpolation yielding a single wide-range equation of state for gas and liquid plasma. This equation of state is used to calculate shock adiabats with allowance for radiation contribution. The role of shell effects has been analyzed.

Cooking strongly coupled plasmas

Abstract: We present the orbital-free method for dense plasmas which allows for efficient variable ionisation molecular dynamics. This approach is a literal application of density functional theory where the use of orbitals is bypassed by a semi-classical estimation of the electron kinetic energy through the Thomas–Fermi theory. Thanks to a coherent definition of ionisation, we evidence a particular regime in which the static structure no longer depends on the temperature: the Γ-plateau. With the help of the well-known Thomas–Fermi scaling laws, we derive the conditions required to obtain a plasma at a given value of the coupling parameter and deduce useful fits. Static and dynamical properties are predicted as well as a a simple equation of state valid on the Γ-plateau. We show that the one component plasma model can be helpful to describe the correlations in real systems.

Correction to kinetic energy density functional using exactly solvable model

Abstract: Herein we present an accurate correction to the Thomas–Fermi (TF) approximation for the non-interacting kinetic energy. The correction is derived from an entirely solvable model and not through the application of the truncated gradient expansion. The used approach exploits the comparable nature of the difference between the TF approximation and the non-interacting kinetic energy and its analogue within a model of non-interacting electrons that resembles the actually studied problem. For the atom, the used model is a system of N non-interacting electrons moving independently in the Coulomb field of the nuclear charge. It is shown numerically that this correction enhances the accuracy of the TF approximation for atoms by an order of magnitude.

On dissociation in weakly doped ice

Abstract: Currently, there is some ambiguity in the problem of decay of a single donor into charged fragments. Thus, in the well-known Ostwald approximation used for semiconductors (ice being one of them) the donor dissociation degree of tends to its maximum value (i.e., unity) as the doping impurity concentration approaches zero. At the same time, the statistical theory of atom reveals within the Thomas–Fermi (or Debye–Huckel) approximation the existence of a thermodynamically equilibrium state of a single multi-electron atom (donor) where charged nucleus keeps the number of counterions just necessary for its neutralization. These scenarios do not show the atom dissociation at all. Discussed in the present paper is the alternative between the full dissociation of a single donor (i.e., dissociation degree equals unity) in a semiconducting media (ice, water, semiconductor) and zero dissociation degree.

Density functional versus spin-density functional and the choice of correlated subspace in multi-variable effective action theories of electronic structure

Abstract: Modern extensions of density functional theory such as the density functional theory plus U and the density functional theory plus dynamical mean-field theory require choices, including selection of variable (charge vs spin density) for the density functional and specification of the correlated subspace. This paper examines these issues in the context of the "plus U" extensions of density functional theory, in which additional correlations on specified correlated orbitals are treated using a Hartree-Fock approximation. Differences between using charge-only or spin-density-dependent exchange-correlation functionals and between Wannier and projector-based definitions of the correlated orbitals are considered on the formal level and in the context of the structural energetics of the rare earth nickelates. It is demonstrated that theories based on spin-dependent exchange-correlation functionals can lead to large and in some cases unphysical effective on-site exchange couplings. Wannier and projector-based definitions of the correlated orbitals lead to similar behavior near ambient pressure, but substantial differences are observed at large pressures. Implications for other beyond density functional methods such as the combination of density functional and dynamical mean field theory are discussed.

A model for temperature dependent resistivity of metallic superlattices

Abstract: The temperature dependent resistivity of metallic superlattices, to first order approximation, is assumed to have same form as bulk metal, ρ(T) = ρo + aT, which permits describing these structures as linear atomic chain. The assumption is, substantiated with the derivation of the above expression from the standard magnetoresistance equation, in which the second term, a Bragg scattering factor, is a correction to the usual model involving magnon and phonon scatterings. Fitting the model to Fe/Cr data from literature shows that Bragg scattering is dominant at T < 50 K and magnon and phonon coefficients are independent of experiment conditions, with typical values of 4.7 × 10−4 μΩcmK−2 and −8 ± 0.7 × 10−7μΩcmK−3. From the linear atomic chain model, the dielectric constant eq,ω=8.33×10−2 at Debye frequency for all materials and acoustic speed and Thomas – Fermi screening length are pressure dependent with typical values of 1.53 × 104 m/s and 1.80 × 109 m at 0.5 GPa pressure for an Fe/Cr structure.

Theoretical investigation on structural and electronic properties of PdO2

Abstract: Theoretical studies on rutile type Palladium Dioxide were carried out with the aim of analyzing structural and electronic properties at ambient condition using the first principle calculation based on density functional theory. Within the framework of density functional theory, we used full potential linearized augmented plane wave method(FP-LAPW) in Wien 2k code. The exchange and correlation effect is treated with generalized gradient approximation (GGA) using the Perdew, Burke and Eruzeroff form. The charge density plots, density of states and band structure are plotted and discussed.

Sub-saturation matter in compact stars: Nuclear modelling in the framework of the extended Thomas-Fermi theory

Abstract: A recently introduced analytical model for the nuclear density profile [1] is implemented in the Extended Thomas-Fermi (ETF) energy density functional. This allows to (i) shed a new light on the issue of the sign of surface symmetry energy in nuclear mass formulas, as well as to (ii) show the importance of the in-medium corrections to the nuclear cluster energies in thermodynamic conditions relevant for the description of core-collapse supernovae and (proto)-neutron star crust.

Poisson-Fermi Model of Single Ion Activities

Abstract: A Poisson-Fermi model is proposed for calculating activity coefficients of single ions in strong electrolyte solutions based on the experimental Born radii and hydration shells of ions in aqueous solutions. The steric effect of water molecules and interstitial voids in the first and second hydration shells play an important role in our model. The screening and polarization effects of water are also included in the model that can thus describe spatial variations of dielectric permittivity, water density, void volume, and ionic concentration. The activity coefficients obtained by the Poisson-Fermi model with only one adjustable parameter are shown to agree with experimental data, which vary nonmonotonically with salt concentrations.

Self-consistent total-energy approximation for electron gas systems

Abstract: Employing a local formula of Parr [J. Chem. Phys. 93, 3060 (1988)] for the electron–electron interaction energy, we derive a self-consistent approximation for the total energy of a general N-electron system. Our scheme works as a local variant of the Thomas–Fermi approximation and yields the total energy and density as a function of the external potential, the number of electrons, and the chemical potential determined upon normalization. Our tests for Hooke's atoms, jellium, and model atoms up to 1500 electrons show that reasonable total energies can be obtained with almost negligible computational cost. Our approximation may serve as a useful tool to provide initial results for more advanced approaches that also include binding.