Electron-ion and ion-ion potentials for modeling warm-dense-matter: applications to laser-heated or shock-compressed Al and Si

The pair-interactions U_{ij}(r) determine the thermodynamics and linear transport properties of matter via the pair-distribution functions (PDFs), i.e., g_{ij}(r). Great simplicity is achieved if U_{ij}(r) could be directly used to predict material properties via classical simulations, avoiding many-body wavefunctions. Warm dense matter (WDM) is encountered in quasi-equilibria where the electron temperature $T_e$ differs from the ion temperature T_i, as in laser-heated or in shock-compressed matter. The electron PDFs g_{ee}(r) as perturbed by the ions are used to evaluate fully non-local exchange-correlation corrections to the free energy, using Hydrogen as an example. Electron-ion potentials for ions with a bound core are discussed with Al and Si as examples, for WDM with T_e \ne T_i, and valid for times shorter than the electron-ion relaxation time. In some cases the potentials develop attractive regions, and then become repulsive and `Yukawa-like' for higher $T_e$. These results clarify the origin of initial phonon-hardening and rapid release. Pair-potentials for shock-heated WDM show that phonon hardening would not occur in most such systems. Defining meaningful quasi-equilibrium static transport coefficients consistent with the dynamic values is addressed. There seems to be no meaningful `static conductivity' obtainable by extrapolating experimental or theoretical \sigma(\omega, T_i, T_e) to \omega \to 0, unless T_i \to T_e as well. Illustrative calculations of quasi-static resistivities R(T_i,T_e) of laser-heated as well as shock-heated Aluminum and Silicon are presented using our pseudopotentials, pair-potentials and classical integral equations. The quasi-static resistivities display clear differences in their temperature evolutions, but are not the strict \omega \to 0 limits of the dynamic values.Comment: 12 pages, 6 figues, Latex file

Directional Soliton and Breather Beams

Solitons and breathers are nonlinear modes that exist in a wide range of physical systems. They are fundamental solutions of a number of nonlinear wave evolution equations, including the uni-directional nonlinear Schr\"odinger equation (NLSE). We report the observation of slanted solitons and breathers propagating at an angle with respect to the direction of propagation of the wave field. As the coherence is diagonal, the scale in the crest direction becomes finite, consequently, a beam dynamics forms. Spatio-temporal measurements of the water surface elevation are obtained by stereo-reconstructing the positions of the floating markers placed on a regular lattice and recorded with two synchronized high-speed cameras. Experimental results, based on the predictions obtained from the (2D+1) hyperbolic NLSE equation, are in excellent agreement with the theory. Our study proves the existence of such unique and coherent wave packets and has serious implications for practical applications in optical sciences and physical oceanography. Moreover, unstable wave fields in this geometry may explain the formation of directional large amplitude rogue waves with a finite crest length within a wide range of nonlinear dispersive media, such as Bose-Einstein condensates, plasma, hydrodynamics and optics

Liquid-liquid phase transition in Stillinger-Weber silicon

It was recently demonstrated that the Stillinger-Weber silicon undergoes a liquid-liquid first-order phase transition deep into the supercooled region (Sastry and Angell, Nature Materials 2, 739 (2003)). Here we study the effects of perturbations on this phase transition. We show that the order of the liquid-liquid transition changes with negative pressure. We also find that the liquid-liquid transition disappears when the three-body term of the potential is strengthened by as little as 5 %. This implies that the details of the potential could affect strongly the nature and even the existence of the liquid-liquid phase.Comment: 13 page

Structural and dynamical properties of liquid Si. An orbital-free molecular dynamics study

Several static and dynamic properties of liquid silicon near melting have been determined from an orbital free {\em ab-initio} molecular dynamics simulation. The calculated static structure is in good agreement with the available X-ray and neutron diffraction data. The dynamical structure shows collective density excitations with an associated dispersion relation which closely follows recent experimental data. It is found that liquid silicon can not sustain the propagation of shear waves which can be related to the power spectrum of the velocity autocorrelation function. Accurate estimates have also been obtained for several transport coefficients. The overall picture is that the dynamic properties have many characteristics of the simple liquid metals although some conspicuous differences have been found.Comment: 12 pages, 11 figure

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 good agreement with experimental results measured by Tsuji et al. along the melting curve. We found that the Rb-pseudoatom remains under these high pressures almost unchanged with respect to the pseudoatom at room pressure; thus, the effective ion-ion interaction is practically the same for all pressure-values. We observe that 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 $a$ 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 ($Q_1$) of the structure factor increases proportionally to $V^{-1/3}$ ($V$ being the specific volume per ion), as was experimentally observed by Tsuji et al.Comment: 18 pages, 11 figure

Exact limiting relation between the structure factors in neutron and x-ray scattering

The ratio of the static matter structure factor measured in experiments on coherent X-ray scattering to the static structure factor measured in experiments on neutron scattering is considered. It is shown theoretically that this ratio in the long-wavelength limit is equal to the nucleus charge at arbitrary thermodynamic parameters of a pure substance (the system of nuclei and electrons, where interaction between particles is pure Coulomb) in a disordered equilibrium state. This result is the exact relation of the quantum statistical mechanics. The experimental verification of this relation can be done in the long wavelength X-ray and neutron experiments.Comment: 7 pages, no figure

An accurate determination of the Avogadro constant by counting the atoms in a 28Si crystal

The Avogadro constant links the atomic and the macroscopic properties of matter. Since the molar Planck constant is well known via the measurement of the Rydberg constant, it is also closely related to the Planck constant. In addition, its accurate determination is of paramount importance for a definition of the kilogram in terms of a fundamental constant. We describe a new approach for its determination by "counting" the atoms in 1 kg single-crystal spheres, which are highly enriched with the 28Si isotope. It enabled isotope dilution mass spectroscopy to determine the molar mass of the silicon crystal with unprecedented accuracy. The value obtained, 6.02214084(18) x 10^23 mol^-1, is the most accurate input datum for a new definition of the kilogram.Comment: 4 pages, 5 figures, 3 table

Analysis of Granular Packing Structure by Scattering of THz Radiation

Scattering methods are widespread used to characterize the structure and constituents of matter on small length scales. This motivates this introductory text on identifying prospective approaches to scattering-based methods for granular media. A survey to light scattering by particles and particle ensembles is given. It is elaborated why the established scattering methods using X-rays and visible light cannot in general be transferred to granular media. Spectroscopic measurements using Terahertz radiation are highlighted as they to probe the scattering properties of granular media, which are sensitive to the packing structure. Experimental details to optimize spectrometer for measurements on granular media are discussed. We perform transmission measurements on static and agitated granular media using Fourier-transform spectroscopy at the THz beamline of the BessyII storage ring. The measurements demonstrate the potential to evaluate degrees of order in the media and to track transient structural states in agitated bulk granular media.Comment: 12 Pages, 9 Figures, 56 Reference

Dynamical properties of Au from tight-binding molecular-dynamics simulations

We studied the dynamical properties of Au using our previously developed tight-binding method. Phonon-dispersion and density-of-states curves at T=0 K were determined by computing the dynamical-matrix using a supercell approach. In addition, we performed molecular-dynamics simulations at various temperatures to obtain the temperature dependence of the lattice constant and of the atomic mean-square-displacement, as well as the phonon density-of-states and phonon-dispersion curves at finite temperature. We further tested the transferability of the model to different atomic environments by simulating liquid gold. Whenever possible we compared these results to experimental values.Comment: 7 pages, 9 encapsulated Postscript figures, submitted to Physical Review

Microscopic Surface Structure of Liquid Alkali Metals

We report an x-ray scattering study of the microscopic structure of the surface of a liquid alkali metal. The bulk liquid structure factor of the eutectic K67Na33 alloy is characteristic of an ideal mixture, and so shares the properties of an elemental liquid alkali metal. Analysis of off-specular diffuse scattering and specular x-ray reflectivity shows that the surface roughness of the K-Na alloy follows simple capillary wave behavior with a surface structure factor indicative of surface induced layering. Comparison of thelow-angle tail of the K67Na33 surface structure factor with the one measured for liquid Ga and In previously suggests that layering is less pronounced in alkali metals. Controlled exposure of the liquid to H2 and O2 gas does not affect the surface structure, indicating that oxide and hydride are not stable at the liquid surface under these experimental conditions.Comment: 12 pages, 3 figures, published in Phys. Rev.