Angular structure of radiation scattered by monolayer of polydisperse droplets of nematic liquid crystal

We considered light scattering by a polydisperse ensemble of droplets of a nematic liquid crystal. To model light scattering by a monolayer of polymer-dispersed spherical droplets of a nematic liquid crystal with cylindrical symmetry of its internal structure, we proposed a semianalytical modeling method. The method is based on interference approximation of the theory of multiple wave scattering, anomalous diffraction approximation, and effective-medium approximation. The method takes into account cooperative optical effects in concentrated, partially ordered layers and can be used to analyze the small-angle structure of the intensity of scattered radiation in relation to the concentration, size, polydispersity of liquid crystal droplets, orientation of their optical axes, and refractive indices of the liquid crystal and polymer. The obtained relations can be applied to solving direct and inverse problems of light scattering in composite liquid crystal materials using data of polarization measurements. We present graphical results of solving the direct problem for components of the polarization vector of scattered wave. These results illustrate the formation of an angular structure for monolayers with a high concentration of polydisperse droplets of the liquid crystal in the range of small scattering angles (0 < θ _s ≤ 8°).     

Mean spherical approximation for a model liquid metal potential

The solution of the Ornstein-Zernike equation for a direct correlation function c(x) with damped oscillations and a hard core condition imposed upon the total correlation function h(x) has been proposed by Cummings as a means of treating a simple model potential for liquid metals in the mean spherical approximation [1]. Here some numerical results are given for this model and their significance is discussed. The solution of the Ornstein-Zernike equation is also extended; the hard core condition is generalized to a soft core condition, and Yukawa terms are added to the oscillatory c(x). Ways in which these extensions can be incorporated into more accurate liquid metal models, as well as into more accurate approximations for these models, are discussed. Finally, it is shown that our solution of the Ornstein-Zernike equation, after a change in the core condition, yields the structure of a spin glass model considered by Høye and Stell in the MSA-like approximation they propose [22].     

A density functional study of plutonyl trifluoroacetone complexes in the gas phase and in solution

The results of a density functional study on a plutonyl compound with two trifluoroacetone ligands are presented. Several conformations of the complex have been examined, namely the structure in which the two ligands are in a cis conformation one with respect to the other, in a trans conformation one with respect to the other, and the structure in which the two ligands lie on the same plane. The calculations have been carried out at the local density approximation level of theory. The relative energies of the conformers have been determined and their geometries have been optimized in the gas phase and in an organic solution. The liquid-state environmental effects are included via a simple cavity model and by using the self-consistent reaction field method. This study shows that the trends in stability of the different conformers in the gas and liquid phases are similar and that the most stable conformer has a cis structure.     

Mean spherical model-structure of liquid argon

A new formulation forS(k), the structure factor, has been obtained, treating the square-well potential as a perturbation on the hard-core in the mean spherical model approximation. The potential parameters have been varied not only to get a satisfactory peak height at the fitted temperature but also over a wide range of temperatures and densities. The agreement between the computed and experimental structure factor values shows that the representation of the attractive tail by a square-well potential yields a satisfactory method in understanding the structure of liquid argon.     

Leptodermous expansion of nuclear ground state energies and the anomaly in the nuclear curvature energy

The leptodermous expansion of the total ground state energy of a nucleus into volume, surface, curvature and gauss curvature contributions has been studied starting from a semi-classical energy density formalism of extended Thomas Fermi type. A numerical procedure was used to obtain the surface energy and curvature energy contributions from surface moments of energy density profilesH(r) for a sequence of nuclei withN=Z and neglecting the coulomb interaction for the three Skyrme forces. A transition to the liquid drop model type expansion in increasing powers ofA ^−1/3 is then made, taking into account the dependence of the central density and the surface structure on the mass of the nucleus. It is found that there is no inconsistency between the curvature contribution to the total energy in the leptodermous expansion and theA ^−1/3 term contribution in the liquid drop model expansion. It has been shown that the earlier apparent anomaly between the above two methods arises due to the use of semi-infinite approximation and the mass dependence of the central density and the surface structure of finite nuclei.     

Structure of some liquid transition metals using integral equation theory

We present the results of calculations of the structure factorS(q) of some liquid 3d transition metals using the self consistent hybridized mean spherical approximation (HMSA) integral equation. The local pseudopotential used is composed of the empty core model and a part that takes care of s-d mixing through an inverse scattering approach to model the interionic pair potential. The results presented are in very good agreement with experiment for most of the systems investigated near freezing, as well as for the noble metals Cu, Ag and Au, thus, confirming the reliability of the pseudopotential in the present integral equation scheme.     

Effect of the degree of ordering of structural vacancies on the fine structure of the valence-band top in cubic boron nitride

The electronic energy structure of the defect system of c-BN_x with ZnS-type structure is calculated in the multiple-scattering theory by the local coherent potential method. The cluster version of the MT approximation is used to calculate the crystal potential. The effect of the relaxation of the crystal lattice on the electronic structure of nonstoichiometric boron nitride c-BN_0.75 is studied and a comparison is made with the electronic energy structure of c-BN in the same approximation. Fiz. Tverd. Tela (St. Petersburg) 39, 1064–1065 (June 1997)     

Influence of interatomic repulsion on the structure of liquids at melting

Radial distribution functions and liquid structure factors for fluids of particles interacting through 1/rⁿ repulsive potentials are computed ‘exactly’ and systematically compared at crystallization for several values of n ranging between the two extremes of hard spheres (n = ∞) and Coulomb forces (n = 1). Striking similarities are pointed out in the large r behaviour (beyond the first peak) of the various radial distribution functions, and in the small k behaviour (including the first peak) of the various structure factors. Some information about the steepness of the repulsive potential in liquid rare gases and in liquid alkalis is gained from a comparison of the damping of successive peaks of the structure factors with experimental data.     

The absorption and magnetic circular dichroism of spectra of Cs2NaPrCl6

The room temperature absorption and magnetic circular dichroism spectra and the absorption spectrum at liquid helium (liquid He) temperature have been measured for Cs₂NaPrCl₆. At room temperature the crystal is cubic and the Pr³⁺ sites have O _h symmetry. All terms above 15 000 cm^-1, except ¹S₀, have been assigned and a previous assignment in PrCl₆ ^3- has been shown to be incorrect. The transition at 20 631 cm^-1 is assigned to ³H₄(A _1g ) →³P₁(T _1g ), in contradiction to previous assignments of Pr³⁺ spectra in other systems. A rich vibrational structure was observed in every transition. Vibrations have been assigned using the site group approximation and there is substantial agreement with the vibrational assignments in Cs₂NaEuCl₆. A crystal phase transition takes place between room temperature and liquid nitrogen temperature and the O _h forbidden transitions, A _1g →E_g and T _2g , are observed. At lower temperatures many additional lines are observed but it is unclear presently whether they are due to lower symmetry or a breakdown of the site group approximation.     

The earthquakes network: the role of cell size

It is demonstrated by molecular dynamics simulations that liquids interacting via the Buckingham potential are strongly correlating, i.e., have regions of their phase diagram where constant-volume equilibrium fluctuations in the virial and potential energy are strongly correlated. A binary Buckingham liquid is cooled to a viscous phase and shown to have isomorphs, which are curves in the phase diagram along which structure and dynamics in appropriate units are invariant to a good approximation. To test this, the radial distribution function, and both the incoherent and coherent intermediate scattering function are calculated. The results are shown to reflect a hidden scale invariance; despite its exponential repulsion the Buckingham potential is well approximated by an inverse power-law plus a linear term in the region of the first peak of the radial distribution function. As a consequence the dynamics of the viscous Buckingham liquid is mimicked by a corresponding model with purely repulsive inverse-power-law interactions. The results presented here closely resemble earlier results for Lennard-Jones type liquids, demonstrating that the existence of strong correlations and isomorphs does not depend critically on the mathematical form of the repulsion being an inverse power law.     

Quantum spin liquid on 2D rectangular frustrated AF lattice

The state of a 2D rectangular spin lattice with first, second and third nearest-neighbour anisotropic antiferromagnetic interactions is investigated. In a special line of parameter space, it is proved that the quantum spin liquid is the exact eigenstate of the system. For general parameter values, Green's function method with cut-off approximation is used to determine the phase diagram at zero temperature, and it is found that the quantum spin liquid appears on a rectangular lattice when the third nearest-neighbour interaction in the direction with shorter lattice spacing is introduced. The relations to the possibility of mixture of the spin liquid and the Fermi liquid in high-T _c superconductors are discussed.     

Anisotropy in the compton profile of copper

Directional Compton profiles of high statistical accuracy are measured by means of a 412 keV gamma-ray Compton spectrometer. The experimental anisotropies are in very satisfactory agreement with earlier measurements and there is good qualitative agreement between the experimental data and a recent band structure calculation. Quantitatively, however, the experimental anisotropy is significantly smaller than predicted by theory.A simple model calculation based on the Seitz approximation, in which higher order Fermi surface volumes all of spherical shape are taken into account in obtaining the momentum density, demonstrates that the major contribution to the Compton profile anisotropy in copper is due to the hybridization which has mixedd-electrons and nearly-free electrons in the top band. Any fine structure in the theoretical anisotropy due to the detailed shape of the Fermi surface cannot be resolved in the present experiment.The potential of analysing the electronic structure of transition metals in terms ofB(r), the Fourier transform of the momentum density, is discussed in detail. The major contribution to the anisotropy arises from localised peaks inB(r) centered on the sites of the translational lattice. Within the Seitz approximation it could be shown that these secondary maxima are caused by the presence of localisedd-electrons in the highest partly occupied band. In conclusion we anticipate that a proper treatment of electron correlation would produce a marked quantitative improvement in the agreement between the present experimental data and the Compton profiles obtained from current band structure calculations.     

Electroresistance of some semiconductors in the phase transition region at high pressure

Abstract

In apparata of liquid type piston-cylinder up to 2GPa and toroid with solid anvil up to 25 GPa pressure (P) electrial resistance R(P) in sphere of phase transition (PT) CdSnAs₂,SnTeInP,GaAs is investigated, and GaP at T = 300K, and also R(T,P) VTSP YB₂Cu₃0_6+x in sphere of superconductive transition. In order to describe the substance behaviour in the vicinity of PT, that is, the region of gapped change of R the approximation geterophased structure is used - the effective environment (model GSEE) which checks different configuration of phases inserts and their dependence from P. In order to picture the solid substance behaviour in the vicinity of point PT at high pressure (HP) different methods are used [1–8].     

Evaluation of the SSC/LHNC,SSCF and PY approximations for short ranged,anisotropic potentials

Three approximations for the orientational correlation function of molecular fluids—the single super chain/linearized hypernetted chain (SSC/LHNC), single super chain f-expansion (SSCF) and Percus-Yevick (PY) approximation—are evaluated in the dense liquid state for a fluid inter-acting with short ranged anisotropic interactions. These interactions are prototypical of the forces that determine the non-spherical shape of symmetric linear molecules. We find that SSC/LHNC is very poor, failing to predict many of the structural features present in the Monte Carlo (MC) simulation results. The PY and SSCF approximations produce much better results; however, neither approximation is completely satisfactory.     

Towards efficient methods for the study of pattern formation in ferrofluid films

Hexagonal and labyrinthine patterns appear in thin ferrofluid films after application of a magnetic field perpendicular to the film. The pattern size and the stability of the hexagonal and labyrinthine structures can be predicted by free energy approaches. Several approximations are used in the literature to accelerate the calculation of the magnetic energy. They are usually based on the use of a uniform, average or constant magnetization. In the uniform approximation the magnetization at all points in the pattern is assumed to be equal to its value at the center of the stripes or cylinders in the labyrinthine or hexagonal patterns. Recent papers indicate that this approximation gives qualitatively wrong results. This is corroborated here by a comparison with accurate results. When a volume-averaged magnetization is used during the calculation of the demagnetization field, from which the magnetic energy is evaluated, the theoretical results are only slightly modified with respect to the accurate results. Thus, we can propose a new method which gives results in good agreement with the accurate values and accelerates the calculations by a factor of 1000. The influence of the approximations is explained by a study of the evolution of the demagnetization field in the patterns. This study indicates that the volume-averaged approximation might only be reliable for patterns with a homogeneously distributed magnetic fluid. Another approximation of a constant magnetization, which is widely used in the literature, assumes that the magnetization does not change during the pattern formation in contrast to the uniform and average approximations. A different way of computing the constant magnetization than that usually employed markedly improves the agreement with the accurate results. This is explained by the derivation of a direct relationship between the approximations of a constant and an average magnetization.Received: 28 October 2003, Published online: 2 March 2004PACS: 47.54. + r Pattern selection; pattern formation - 47.65. + a Magnetohydrodynamics and electrohydrodynamics - 77.84.Nh Liquids, emulsions, and suspensions; liquid crystals     

The zero-point energy in the molecular hydrogen crystal

We propose a modified Einstein approximation to describe zero-point energy vibrations in a quantum crystal. Our aim was to develop a computationally cheap tool suitable for lattice structure optimisation. As in the classical Einstein model the representative atom vibrates in an effective potential due to the surrounding atoms of the crystal; the atoms however are not strictly placed at the positions corresponding to the crystal potential energy minima but their positions are described by the quantum mechanical density distributions. The effective potential computed that way is suitable for the application in solid para-hydrogen in contrast to the normal (unmodified) Einstein approximation. We compute the cohesive energy of the para-hydrogen crystal and perform lattice structure optimisation. The hexagonal closed packed is more stable than the fcc closed packed lattice and the lattice constants obtained are in very good agreement with the experimental values.     

Low angle structure factor of liquid aluminium in the mean density approximation

The low angle structure factor of liquid Al is calculated in the mean density approximation. It agrees with the recently observed data of Waseda out to k≈0.4 Å^?1.     

Liquids in equilibrium: Beyond the hypernetted chain

Density functional techniques are used to derive a charging expression for the non-uniform density of a molecular liquid. In the atomic limit the equation reduces to an exact form due to Fixman. The theory is simplified greatly via a physical approximation that accounts for three-body correlations beyond those included in the hypernetted chain (HNC) closure of the Ornstein-Zernike (OZ) equation. The radial distribution function is obtained as a special case. The theory is tested by examining the phase behavior of two fundamental complex fluids: the homopolymer blend and diblock copolymer melts. For the former it is found, contrary to HNC theory and its molecular generalizations, that a critical temperature T_c is predicted from the structure route. This T_c scales linearly with degree of polymerization N in agreement with Flory theory. The simplest form of the theory can be considered as a way to incorporate attractive interactions within a formalism that is very similar to that of the OZ or reference interaction site model (RISM). The relevance of the theory to charged liquids is also discussed.