Surface elasticity and Fréedericksz’ threshold in a nematic cell weakly anchored

Summary The presence in the distortion free energy of theK ₁₃-term, depending on the first derivatives of the walls’ tilt angles, leads to some paradoxes. ButK ₁₃ can be shown to vanish in the linear elastic theory. Instead, the saddle splayK ₂₄-term is independent of the first derivatives of the anchoring angles. This fact allows us to obtain Fréedericksz’ threshold as a function of the involved elastic constants and of the anchoring strengths in the frame of the standard continuum theory. Work presented at the First USSR-Italy Bilateral Meeting on Liquid Crystals held in Portonovo, Ancona (Italy), September 30–October 2, 1987.     

Temperature dependence of the uniaxial magnetic anisotropy of rhombohedral antiferromagnetic crystals with ions in the <Emphasis Type="Italic">S</Emphasis> state

The contributions of the anisotropic exchange to the firstand second-order uniaxial anisotropy constants have been calculated for hematite at T = 0 K and arbitrary temperatures. The results of the calculations and the most significant mechanisms are taken into account in interpreting the temperature dependence of the anisotropy in rhombohedral antiferromagnetic crystals. The first-order anisotropy constant for hematite is described by the dipole interaction, contributions of the “single-ion” nature, and relatively small contributions of the anisotropic exchange. The second-order constant for hematite includes the “single-ion” contribution and the contribution of the anisotropic exchange. For FeBO₃ and MnCO₃ crystals, the main contributions to the first-order anisotropy constant come from the dipole and single-ion mechanisms.     

Perturbative solution to order βɛ of the Percus-Yevick equation for triangular well potential forn=2

The radial distribution function for a fluid in which the molecules interactvia a triangular well potential is considered. Expanding the radial distribution function in pwoers of βɛ, where ɛ is the depth of the potential andβ=1/k _BT the first-order terms are calculated analytically using the Percus-Yevick theory in the Baxter’s formulation. The first-order terms in the direct correlation functionc(r) are also calculated. The first- and second-order terms in the free energy obtained from the energy equation of state are calculated and compared with other calculations. An erratum to this article is available at .     

Director dynamics near the nematic-smectic-A phase transition

The Landau-de Gennes model for the free energy of a nematic liquid crystal near the phase transition to the smectic A-phase is used to determine the frequency dependence of the fluctuation corrections to the Frank elastic constants. It is shown that the interaction of the fluctuations of the smectic order parameter and the director results in corrections to all the Frank elastic constants. In the low-frequency limit (ω→0), the corrections to the Frank elastic constants K ₂₂ and K ₃₃ are the largest, and decrease to zero in the infinite-frequency limit. The correction to K ₁₁ is negative, and vanishes in both limits. The absolute value of the correction to K ₁₁ is the largest at frequencies in the megahertz range. It is shown that in oriented nematics the interaction of the smectic fluctuations and the director limits deviations of the director from the direction of preferred orientation, as a result of which relaxation of both inhomogeneous and homogeneous distortions of the director field can be observed. It is also shown that this gives rise to a frequency interval in the megahertz range in which shear waves begin to propagate in the nematic. The propagation speed of these waves is roughly a hundred times smaller than that of sound and strongly depends on the direction of propagation. Zh. éksp. Teor. Fiz. 114, 2022–2033 (December 1998)     

Four constant potential function of amorphous selenium and evaluation of its thermodynamic and acoustic properties

Litov and Anderson after various considerations suggested a four constant potential function for a-Se as well as a-As₂S₃. Hence we also used a four constant potential function with the sole purpose of applying this potential function to obtain several acoustic, thermodynamic and other properties. We calculated several acoustic properties of a-Se like second order elastic constants (SOECs), their pressure derivatives, the longitudinal and transverse Grüneisen constant by two different methods, phonon frequencies, absorption band position through the use of Nath-Smith-Delaunay’s equation, and the thermodynamic properties like heat capacity, bulk modulus, thermal Grüneisen constant, the pressure derivative of the bulk modulus (dK _T/dP=C ₁), the pressure derivative ofC ₁ which is related to Anderson-Grüneisen parameter, pressure derivative of Grüneisen constant namelyγ′ _g which is related to second Grüneisen constant, characteristics of phonon frequencies, potential energy function through the use of fitted parameters and third order elastic constants. Finally we calculatedK _T at the reduced density ofρ/ρ ₀=1.1.K _T is obtained from the potential function with the fitted parameters. In all the above cases the calculated values are found to be in good agreement with experiment wherever available. In this connection it is important to point out that we eliminated ‘C’ a constant in the potential function using the equilibrium condition as was done by Litovet al in a-Se and Gerlichet al in the case of a-As₂S₃ as all amorphous substances are isotropic as mentioned by several authors. We contemplate to calculate several other properties for a-Se and a-As₂S₃ and present them at a later stage.     

Negative Poisson coefficient of fractal structures

On the basis of a fractal model the macroscopic elastic properties of an inhomogeneous medium with random structure have been determined. It is shown that if the ratio of the bulk moduli of the phases K ₂/K ₁→0, then the percolation threshold p _c the Poisson coefficient is equal to 0.2. A study of the behavior of a two-phase medium with negative Poisson coefficient is carried out. Fiz. Tverd. Tela (St. Petersburg) 41, 2147–2153 (December 1999)     

Isospin breaking in <Emphasis Type="BoldItalic">K</Emphasis><Subscript><Emphasis Type="BoldItalic">l4</Emphasis></Subscript> decays

Data on K _e4 decays allow one to extract experimental information on the elastic π π scattering amplitude near threshold, and to confront the outcome of the analysis with predictions made in the framework of QCD. These predictions concern an isospin symmetric world, while experiments are carried out in the real world, where isospin-breaking effects—generated by electromagnetic interactions and by the mass difference of the up and down quarks—are always present. We discuss the corrections required to account for these, so that a meaningful comparison with the predictions becomes possible. In particular, we note that there is a spectacular isospin-breaking effect in K _e4 decays. Once it is taken into account, the previous discrepancy between NA48/2 data on K _e4 decays and the prediction of π π scattering lengths disappears.     

Ab initio calculation of the electronic structure,Fermi surface,and elastic properties of the new 7.5-K superconductor Nb<Subscript>2</Subscript>InC

Ab initio calculations were performed to investigate electronic and elastic properties of the newly discovered 7.5 K superconductor: layered Nb₂InC. As a result, electronic bands, total and site-projected l—decomposed density of states at the Fermi level, shape of the Fermi surface for Nb₂InC were obtained for the first time. Besides, independent elastic constants, bulk modulus, compressibility, shear modulus, Young’s modulus, Poisson’s ratio together with the elastic anisotropy parameters and indicator of brittle/ductile behavior of Nb₂InC were evaluated and analyzed in comparison with the available data.     

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.     

Self-localized carrier states in disordered ferroelectrics

A theory of self-localized states of free carriers near polarization fluctuations (fluctuons) in disordered ferroelectrics is developed. Calculations are carried out for the model disordered ferroelectric K_{1− x} Li_xTaO₃ (x≪0.05). The basic characteristics of the fluctuon — the energy and radius of the fluctuon state — are calculated as functions of the impurity dipole concentration and temperature. The theory predicts the appearence of stable fluctuon states in both the mixed ferroelectric-dipole-glass phase (a dipole glass is the electric analog of a spin glass) and the dipole-glass state of disordered ferroelectrics. The possible role of fluctuons in kinetic phenomena such as conductivity in these substances is discussed. Pis’ma Zh. éksp. Teor. Fiz. 65, No. 5, 425–429 (10 March 1997) Published in English in the original Russian journal. Edited by Steve Torstveit.     

Thermoelastic properties of minerals at high temperature

The knowledge of elasticity of the minerals is useful for interpreting the structure and composition of the lower mantle and also in seismic studies. The purpose of the present study is to discuss a simple and straightforward method for evaluating thermoelastic properties of minerals at high temperatures. We have extended the Kumar’s formulation by taking into the account the concept of anharmonicity in minerals above the Debye temperature (θ _D). In our present study, we have investigated the thermophysical properties of two minerals (pyrope-rich garnet and MgAl₂O₄) under high temperatures and calculated the second-order elastic constant (C _ij ) and bulk modulus (K _T) of the above minerals, in two cases first by taking Anderson–Gruneisen parameter (δ _T) as temperature-independent and then by treating δ _T as temperature-dependent parameter. The results obtained when δ _T is temperature-dependent are in close agreement with experimental data.     

Computation of collective modes and acoustic investigations at different temperatures of vitrous silica

This paper is mainly concerned with elastic and acoustic properties of vitrous silica besides the computation of phonon frequencies. Thus the phonon frequencies of vitrous silica have been calculated assuming the electronic bulk modulus,K _e, as equal to zero. New equations have been derived to relate the pressure derivatives of second order elastic constants to the acoustic Gruneisen’s parameters using both Bhatia-Singh’s parameters and Schofield’s equations. The calculated longitudinal and transverse Gruneisen’s parameters and the predicted absorption band spectra from Nagendranath’s equation and Bhatia Singh’s parameters are in good agreement with experiment. The calculated mean acoustic mode Gruneisen’s parameter evaluated from the pressure derivative of Nagendranath’s equation is also in good agreement with experiment. An erratum to this article is available at .     

Statistical theory of the elastic constants of nematic liquid crystals

A statistical mechanical theory of the Frank elastic constants is formulated. The free energy functional is constructed for the deformed sample and the free energy density is defined for the case of small spatial gradients. The Frank constants are expressed in terms of the direct correlation function c(1, 2) and the orientational single particle distribution function. For the example of Onsager spherocylinders three constants K ₁, K ₂ and K ₃ are calculated. The results of these calculations are similar to those given by Priest and by Straley.     

A method for determination of higher-order magnetic anisotropy constants — Importance of the cubic K3 and K4 for certain energy levels models

A method for determination of magnetocrystalline anisotropy constants of arbitrary order is proposed. The method is based on a least squares fitting of a phenomenological anisotropy energy for a given symmetry truncated at an arbitrary order term to a theoretical anisotropy energy computed exactly for a given energy level model. Several applications of the method to cubic systems are considered. The study reveals that the widely used expressions in the literature for the cubic constants K₁ and K₂ in terms of free energy for the three symmetry direction are of rather limitedvalidity only. The higher-order cubic constants K₃, K₄ and K₅ are determined besides the usual K₁ and K₂ in temperature range 0 to 300 K. The importance of the higher- order terms with respect to the first term in the cubic anisotropy energy is discussed. The results show that the cubic constants K₃ and K₄ cannot be neglected for most of the energy level models studied at certain temperatures.     

Concentration dependences of the elastic constants of the two-dimensional graphene-silicene system

The concentration dependences of the elastic constants of the two-dimensional Si _x C_{1 − x} system have been investigated with the use of the Harrison bonding-orbital method and the Keating model. The central and non-central force constants and the Grüneisen parameter have been considered by means of the bonding-orbital method. All quantities under consideration have been shown to exhibit a nonlinear behavior during the transition from graphene to silicene. A nontrivial role of the short-range repulsion has been discussed. The second-order and third-order elastic constants, the pressure dependences of the second-order elastic constants, as well as the Poisson’s ratio and Young’s modulus have been investigated in the Keating model. It has been found that the elastic constants and Young’s modulus change almost linearly upon the transition from graphene to silicene, whereas the other quantities under consideration exhibit nonlinearity.     

Third-order elastic constants and pressure derivatives of the second-order elastic constants of β-tin

The second- and third-order elastic constants and pressure derivatives of second-order elastic constants of tetragonal β-tin have been obtained using the deformation theory. The strain energy density derived using the deformation theory is compared with the strain dependent lattice energy obtained from the elastic continuum model approximation to get the expressions for the second- and third-order elastic constants. Higher order elastic constants are a measure of the anharmonicity of a crystal lattice. The 12 non-vanishing third-order elastic constants and the six pressure derivatives of the second-order elastic constants in tetragonal β-tin are obtained in the present work and are compared with the available experimental values. The second-order elastic constant C₃₃ obtained in the present study is in reasonable agreement with the experimental values. The third-order elastic constants are generally one order of magnitude greater than the second-order elastic constants as expected of a crystalline solid. The third-order elastic constant C₃₃₃ is higher in magnitude than all other values. This shows a greater anharmonicity of β-tin along the c-axis direction of the crystal.     

Application of glancing‐emergent‐angle fluorescence for polarized XAFS studies of single crystals

X‐ray absorption fine‐structure (XAFS) data were obtained for the V K‐edge for a series of anisotropic single crystals of (Cr_xV_1–x)₂O₃. The data and the results were compared for the as‐prepared bulk single crystals (measured in fluorescence in two different orientations) and those ground to powder (measured in transmission). For the bulk single crystals, the glancing‐emergent‐angle (GEA) method was used to minimize fluorescence distortion. The reliability of the GEA technique was tested by comparing the polarization‐weighted single‐crystal XAFS data with the experimental powder data. These data were found to be in excellent agreement throughout the entire energy range. Thus, it was possible to reliably measure individual V–V contributions parallel and perpendicular to the c axis of the single crystals, i.e. those unavailable by powder data XAFS analysis. These experiments demonstrate that GEA is a premiere method for non‐destructive high‐photon‐count in situ studies of local structure in bulk single crystals.     

Two-Particle Lattice Green Functions on a Two-Dimensional Rectangular Lattice with Next-Nearest Neighbor Hopping

The paper shows a way to find two-particle lattice Green functions (LGF) on any site of a two-dimensional, rectangular lattice with hopping to nearest- and next-nearest neighbors. Exact, analytical formulas using elliptic integrals for the on-site—G _0,0, nearest neighbor—G _0,1 and G _1,0 and next-nearest neighbor—G _1,1 LGF’s are shown. Difference equation for general G _m,n is given together with five kind of recurrence relations among LGF’s and their derivatives. A way of assembling recurrence relations into closed sets of equations, enabling to find G _n,m on any lattice site (requiring the knowledge of five parameters) is described. The differences between one- and two-particle LGF’s are shown.     

The use of parallel and monochromatic beams for determining the composition of pseudobinary alloys by X-ray fluorescence

A simple X-ray fluorescence method using nearly parallel and monochromatic beams is analyzed and discussed in connection with the determination of the alloy fraction in pseudobinary A_1−x B _x C solid solutions. Applications to optoelectronic materials are considered. The reliability of the method has been analyzed and discussed for both bulk and thin film samples. Errors due to small angular divergence in the accepted beam are seen to be neglibile. Deviations from a symmetrical alignment of the sample can strongly influence the measured fluorescence intensity. The experimental analysis of this effect can be used for a perfect symmetrical orientation of thick samples. The measurement of the fluorescence intensity as a function of the glancing angle can give both thickness and composition in solid-solution thin-film samples. The contributions of the fluorescence radiation excited by the characteristic X-ray lines of atoms within the substrate is shown to be important in thin epitaxial layers. An approximate formula for calculating these contributions is given and discussed in the light of experimental results. Bulk crystals and thin-film samples, vapourphase grown Cd_1−x Zn _x S solid solutions, have been used for experiments in which the ZnK _α radiation excited by a MoK _α primary beam was measured.     

K<Superscript>+</Superscript> production in proton-nucleus reactions and the role of momentum-dependent potentials

The production of K⁺-mesons in proton-nucleus collisions from 1.0 to 2.5GeV is analyzed with respect to one-step nucleon-nucleon ( NN → NYK ⁺) and two-step Δ-nucleon ( ΔN → K ⁺ YN) or pion-nucleon ( πN → K ⁺ Y) production channels on the basis of a coupled-channel transport approach (CBUU) including the kaon final-state interactions. The influence of momentum-dependent potentials for the nucleon, hyperon and kaon in the final state are studied as well as the importance of K⁺ elastic rescattering in the target nucleus. The transport calculations are compared to the experimental K⁺ spectra taken at LBL Berkeley, SATURNE, CELSIUS, GSI and COSY-Jülich. It is found that the momentum-dependent baryon potentials affect the excitation function of the K⁺ cross-section; at low bombarding energies of ∼ 1.0GeV the attractive baryon potentials in the final state lead to a relative enhancement of the kaon yield, whereas the net repulsive potential at bombarding energies ∼ 2GeV causes a decrease of the K⁺ cross-section. Furthermore, it is pointed out that especially the K⁺ spectra at low momenta (or kinetic energy T _K) allow to determine the in-medium K⁺ potential almost model independently due to a relative shift of the K⁺ spectra in kinetic energy that arises from the acceleration of the kaons when propagating out of the nuclear medium to free space, i.e. converting the potential energy to the kinetic energy of the free kaon. Received: 28 January 2002 / Accepted: 3 June 2002 / Published online: 19 November 2002 RID="a" ID="a"e-mail: Wolfgang.Cassing@theo.physik.uni-giessen.de Communicated by P. Schuck