Equation of state of hollandite type-structure

Abstract

The room-temperature compression of BaFeMn₇O₁₆hollandite has been determined to 519 kbar with X-Ray methods. With a 1-bar molar volume of V₀=339±2 cm³/mol and a Birch-Murnaghan equation of state, we obtain for the bulk modulus K'₀=2304±150 kbar and for the pressure derivative K'₀=1.73±0.45.If these moduli are typical of a hollandite structure, then the high-pressure density of the Ca_0.5Mg_0.5Al₂Si₂O₈pseudo-hollandite could be similar to those of silicates with a perovskite structure.     

Kinetics of heavy fermions

A transport equation is derived for the distribution function of heavy fermions in electric and magnetic fields that allows for potential and spin-spin interactions between the heavy fermions. The spectrum of the spin waves in the paramagnetic heavy-fermion state is calculated. Finally, processes associated with pair collisions of heavy fermions and the scattering of such fermions by charged impurities are studied. Zh. éksp. Teor. Fiz. 113, 1778–1786 (May 1998)     

Calculating the thermodynamic parameters of dense gases and weakly ionized plasmas including three-body interactions

A model is developed for the equation of state of dense gases and nonideal plasmas in the approximation of three-body interactions. The reduced third virial coefficient is calculated for a number of spherically symmetric pairwise additive interaction potentials of neutral and charged particles. Its temperature dependence is constructed for various potentials. The density and composition of plasmas in a number of pure substances are calculated numerically. Zh. Tekh. Fiz. 68, 130–132 (July 1998)     

Ab initio study of lattice dynamics and thermal equation of state of Ni

Lattice dynamics and thermal equation of state of fcc nickel have been studied in the framework of density functional perturbation theory. The influence of the GGA+U on the structure is considered. The calculated phonon dispersion curve accords excellently with the experimental data. Within the quasi-harmonic approximation, the thermal equation of state, thermal expansion coefficient, thermal pressure, bulk moduli and Debye temperature are well reproduced. The thermal properties confirm the available experimental data and are extended to a wider pressure and temperature range.     

Equation of state and elastic properties of lithium: Isotope effects

The equations of state and elastic properties of the lithium isotopes Li⁶ and Li⁷ at high pressures are investigated at a temperature of 76 K by a pulsed ultrasonic method. Proofs of the existence of appreciable quantum contributions to the pressure and elastic moduli of lithium are given. Pis’ma Zh. éksp. Teor. Fiz. 69, No. 1, 36–40 (10 January 1999)     

Hydrostatic pressure derivatives of the single crystal elastic moduli of Gd,Dy and Er

The hydrostatic pressure derivatives of the single crystal elastic moduli of Gd, Dy and Er have been measured at 298°K, to pressures near 5 Kbar. The very small pressure derivatives of the adiabatic bulk moduli indicate that a small ion core model should be appropriate for interpreting the data. The long-range electrostatic contributions to the shear moduli have a dominant influence on the pressure derivatives of the shear moduli of Er, whereas the Gd and Dy data evidently reflect band structure contributions. The values of the longitudinal stiffnesses correspond remarkably well with the Bohm-Staver model for velocity of waves in an ion plasma dispersed in a sea of electrons, where the ionic interaction is perely Coulombic. This model is extended to provide an interpretation of the volume derivatives of the longitudinal moduli in terms of the volume derivative of the density of electron states at the Fermi energy.The Grüneisen parameters calculated from averages of the acoustic model gammas are in relatively poor agreement with those determined from thermal expansion data. An explanation based on the changes in c/a ratio with volume change is tested quantitatively and found to be reasonably successful. The values of dK_T/dP, where K_T is the isothermal bulk modulus, are applied to the Murnaghan equation of state and give excelent agreement with Bridgman's direct compression data for Dy and Er to 40 Kbar. For Gd, Bridgman's data indicate either that (dK_T/dP)_p=0 should be considerably larger than deduced from the adiabatic dK_s/dP measurements or that a phase change occurs near 20 Kbar. The occurrence of a phase change in Er at ～90 Kbar is definitely indicated when comparing the Murnaghan equation with X-ray diffraction data.     

Lattice dynamics of crystalline In4Se3

Calculations of the phonon spectrum of crystalline In₄Se₃ in a model of central-pair interactions with neglect of the long-range forces are presented. The model developed contains five unknown parameters, which are determined from experimental values of the elastic moduli without consideration of the internal displacement of the sublattices. The phonon spectrum obtained contains a large number of low-frequency modes, which deform the acoustic branches. Some common features are discovered in the dispersion curves of the electron and phonon spectra. Fiz. Tverd. Tela (St. Petersburg) 40, 2103–2108 (November 1998)     

Spectral Analysis for Systems of Atoms and Molecules Coupled to the Quantized Radiation Field

We consider systems of static nuclei and electrons – atoms and molecules – coupled to the quantized radiation field. The interactions between electrons and the soft modes of the quantized electromagnetic field are described by minimal coupling, p→p−e A (x), where A(x) is the electromagnetic vector potential with an ultraviolet cutoff. If the interactions between the electrons and the quantized radiation field are turned off, the atom or molecule is assumed to have at least one bound state. We prove that, for sufficiently small values of the fine structure constant α, the interacting system has a ground state corresponding to the bottom of its energy spectrum. For an atom, we prove that its excited states above the ground state turn into metastable states whose life-times we estimate. Furthermore the energy spectrum is absolutely continuous, except, perhaps, in a small interval above the ground state energy and around the threshold energies of the atom or molecule. Received: 3 September 1998 / Accepted: 17 March 1999     

Open-Closed Moduli Spaces and Related Algebraic Structures

We set up a Batalin–Vilkovisky Quantum Master Equation (QME) for open-closed string theory and show that the corresponding moduli spaces give rise to a solution, a generating function for their fundamental chains. The equation encodes the topological structure of the compactification of the moduli space of bordered Riemann surfaces. The moduli spaces of bordered J-holomorphic curves are expected to satisfy the same equation, and from this viewpoint, our paper treats the case of the target space equal to a point. We also introduce the notion of a symmetric Open-Closed Topological Conformal Field Theory (OC TCFT) and study the L _∞ and A _∞ algebraic structures associated to it.     

Quaternionic monopoles

We present the simplest non-abelian version of Seiberg-Witten theory: Quaternionic monopoles. These monopoles are associated withSpin ^h (4)-structures on 4-manifolds and form finite-dimensional moduli spaces. On a Kähler surface the quaternionic monopole equations decouple and lead to the projective vortex equation for holomorphic pairs. This vortex equation comes from a moment map and gives rise to a new complex-geometric stability concept. The moduli spaces of quaternionic monopoles on Kähler surfaces have two closed subspaces, both naturally isomorphic with moduli spaces of canonically stable holomorphic pairs. These components intersect along a Donaldson instanton space and can be compactified with Seiberg-Witten moduli spaces. This should provide a link between the two corresponding theories.Partially supported by: AGE-Algebraic Geometry in Europe, contract No ERBCHRXCT940557 (BBW 93.0187), and by SNF, nr. 21-36111.92     

Stability of two-dimensional,controlled, Bose-Einstein coherent states

Two-dimensional stability of a controlled Bose-Einstein condensation state, in the form of a nonlinear Schr?dinger soliton [JETP Lett. 80 535 (2004)], is studied for the condensations with both repulsive and attractive inter-atom interactions. The Gross-Pitaevski equation is solved numerically, taking initialy a controlled soliton whose “effective mass” is several times bigger than the critical value for a weak collapse in the absence of a potential well, and allowing for reasonably large errors in the experimental realization of the trapping potential required by the theory. For repulsive and sufficiently weak attractive interactions, the controlled state is shown to remain stable inside a breathing potential well, for a time that is an order of magnitude longer than the characteristic periods of the forced and eigenoscillations of the soliton. The collapse is observed only for attractive interactions, when the nonlinear attraction exceeded the appropriate threshold. Electronic supplementary material  Supplementary Online Material     

Elastic properties of metastable crystalline and amorphous gasb-ge semiconductors synthesized under high pressure

We present the systematic study of the elastic shear G and bulk B moduli in amorphous and crystalline metastable ternary solid solutions (GaSb)_1?x Ge_2x . It is found that the moduli of crystalline phases initially decrease with Ge concentration, falling down to minimum values at 20-30% Ge. The minimal values of elastic moduli for amorphous samples are observed at 50-60% Ge. Elastic softness of crystalline solid solutions is assumed to be related to the increase of chemical disorder and, consequently, of static (non-thermal) geometrical disorder in positions of atoms. An additional topological disorder in amorphous solid solutions leads to additional elastic softening.     

Application of B-splines finite basis sets to relativistic two-photon decay rates of level in hydrogenic ions

A theoretical study of the one- and two-photon spontaneous emission rates from the 2 s1/2 state of one-electron ions is presented. High-precision values of the relativistic emission rates for ions with nuclear charge Z up to 100 are obtained through the use of finite basis sets for the Dirac equation constructed from B-splines. Furthermore, we analyze the influence of the inclusion of quantum electrodynamics corrections in the initial and final state energies. Received: 6 January 1998 / Accepted: 31 March 1998     

Vector Bundle Moduli

We give the general presciption for calculating the number of moduli of irreducible, stable U(n) holomorphic vector bundles with positive spectral covers over elliptically fibered Calabi–Yau threefolds. Explicit results are presented for Hirzebruch base surfaces B = F _r. Vector bundle moduli appear as gauge singlet scalar fields in the effective low-energy actions of heterotic superstrings and heterotic M-theory.     

Perturbation theory by flow equations: dimerized and frustrated S = 1/2 chain

The flow equation method (Wegner, 1994) is used as continuous unitary transformation to construct perturbatively effective Hamiltonians. The method is illustrated in detail for dimerized and frustrated antiferromagnetic S =1/2 chains. The effective Hamiltonians conserve the number of elementary excitations which are S =1 magnons for the dimerized chains. The sectors of different number of excitations are clearly separated. Easy-to-use results for the gap, the dispersion and the ground state energies of the chains are provided.     

Analytic Equation of State of a Quasi One-Dimensional Model Lipid Monolayer

The equation of state of a quasi one-dimensional model lipid monolayer is obtained in analytic form. The method used is the Laplace transform approach leading to a homogeneous Fredholm integral equation. Two cases are studied. The first considers a purely short range repulsive potential, when we recover the results previously obtained by Gianotti et al. (J. Phys. A.: Math. Gen. 25:2889 (1992)). The second incorporates the long range attractive Kac potential, and the equation of state is calculated in the van der Waals limit. This extends the approach originally developed by Kac et al. (J. Math. Phys. 4:216 (1963)).     

Direct correlation functions and bridge functions in additive hard-sphere mixtures

A method to obtain (approximate) analytical expressions for the radial distribution functions in a multicomponent mixture of additive hard spheres that was recently introduced is used to obtain the direct correlation functions and bridge functions in these systems. This method, which yields results practically equivalent to the generalized mean spherical approximation and includes thermodynamic consistency, is an alternative to the usual integral equation approaches and requires as input only the contact values of the radial distribution functions and the isothermal compressibility. Calculations of the bridge functions for a binary mixture using the Boublik-Mansoori-Carnahan-Starling-Leland equation of state are compared to parallel results obtained from the solution of the Percus-Yevick equation. We find that the conjecture recently proposed by Guzman and del Rio (1998, 98, Molec. Phys., 95, 645), stating that the zeros of the bridge functions occur approximately at the same value of the shifted distance for all pairs of interactions, is at odds with our results. Moreover, in the case of disparate sizes, even the Percus-Yevick bridge functions do not have this property. It is also found that the bridge functions are not necessarily non-positive.     

A Riemann–Hilbert approach to Painlevé IV

The methods of [vdP-Sa, vdP1, vdP2] are applied to the fourth Painlevé equation. One obtains a Riemann–Hilbert correspondence between moduli spaces of rank two connections on ?¹ and moduli spaces for the monodromy data. The moduli spaces for these connections are identified with Okamoto–Painlevé varieties and the Painlevé property follows. For an explicit computation of the full group of Bäcklund transformations, rank three connections on ?¹ are introduced, inspired by the symmetric form for PIV, studied by M. Noumi and Y. Yamada.     

Equation of state of dense nuclear matter

An equation of state for cold nuclear matter for the region of densities ρ_nm−4ρ_nm, where ρ_nm is empirical nuclear-matter density, is constructed. We begin from the detailed calculation of Day and Wiringa for the two-body interactions; these give a saturation density of ∼2ρ_nm. This density is brought down to ρ_nm by the addition of relativistic corrections. Additional binding is obtained from three-body forces. A reasonable picture is obtained with the Day-Wiringa compression modulus for the two-body calculation, but the picture can be further improved by choosing this to be smaller.Our equation of state is similar to that of Friedman and Pandharipande in the region of nuclear matter denstiy ρ_nm, but, due to higher-order terms in the loop correction, is substantially softer at high density. Basically what happens is that the many-body effects saturate with increasing density, leaving only the two-body interactions.With this equation of state, prompt supernova explosions are very powerful when the compression modulus of neutron-rich matter (twice as many neutrons as protons) is ∼150 MeV, which corresponds to K_nm ∼ 190 MeV for symmetric nuclear matter.Analysis shows that hot nuclear matter formed in heavy ion collisions demands a very stiff equation of state. We understand this as arising from the strong velocity dependence in the real part of the optical model potential which follows chiefly from the Lorentz character of the interactions, the vector mean field growing with increasing density and the scalar one decreasing. This gives a substantial repulsive contribution to the energy per particle and produces a stiff effective equation of state for several hundred MeV heavy-ion collisions. With increasing degree of equilibration the magnitude of the repulsive energy decreases since equilibration decreases the effective momentum. Given the strong velocity dependence in the interaction, the hot equation of state can be reconciled with the cool one.     

A first-principles study on the structural and elastic properties and the equation of state of wurtzite-type cadmium selenide under pressure

A first-principles investigation on the crystal structural and elastic properties and the equation of state of wurtzite-type cadmium selenide (w-CdSe) has been conducted using the plane-wave pseudo-potential density functional theory and the quasi-harmonic Debye model. The elastic constants, the aggregate elastic moduli, the elastic anisotropy, and Poisson's ratio under pressure have been investigated. Our calculated equilibrium lattice constants, the elastic constants, and the aggregate elastic moduli at zero pressure are in good agreement with the experimental data and other theoretical results. The variations in the compressional and shear elastic wave velocities with pressure at zero temperature up to pressure 2.7 GPa have been studied; the computed Debye temperature at zero pressure and zero temperature is in reasonable agreement with the result of Bonello et al., In addition, the equation of state of w-CdSe in the pressure range of 0–2.7 GPa and up to a temperature of 900 K has also been obtained.