Volume effects in the theory of equilibrium and quasiequilibrium states of multicomponent solid solutions

A phenomenological theory of equilibrium and quasiequilibrium states of multicomponent solid solutions is constructed taking account of volume effects. Quasiequilibrium states are characterized by the fact that only some of the conditions for thermal dynamic equilibrium of the system are satisfied. The short-range parts of the interatomic interactions are taken into account by introducing the proper volumes of the atoms based on a generalized lattice model. The long-range parts of the potentials are taken into account in the effective-field approximation. The equations for the quasiequilibrium components in the solutions are introduced taking account of the nonuniformity in the distributions of the less mobile nonequilibrium components. The conditions for spinodal decomposition of a solid solution with an arbitrary number of components in the equilibrium and quasiequilibrium cases are obtained. An equation for equilibrium spinodal decomposition of a three-component microheterogeneous solid solution is found. Fiz. Tverd. Tela (St. Petersburg) 41, 1609–1613 (September 1999)     

Quasiequilibrium states of solid solutions

A phenomenological theory of quasiequilibrium states of solid solutions with at least three components is constructed under the assumption that the atomic mobilities of the components differ in order of magnitude. The short-range parts of the interatomic interactions are taken into account by introducing atomic self-volumes. The long-range parts of the potentials are taken into account in the effective-field approximation. The equations for the quasiequilibrium components in the solutions are derived neglecting the mobility of the least mobile component. It is shown that, for a nonuniform distribution of this component, the nonequilibrium critical temperature ceases being unique within the sample and acquires a local character. In consequence, opposing processes occur in the system in the temperature interval between T _c ^min and T _c ^max — homogenization in some sections and formation of interphase boundaries in others. Fiz. Tverd. Tela (St. Petersburg) 41, 60–63 (January 1999)     

A general Mobius inversion transform formula for hcp lattices and its application

In this paper,we present a general Mobius inversion transform formula for hcp lattices.This formula can be applied to hcp lattices with a non-ideal c/a value and to obtain the pair potential between atoms in these lattices from the cohesive energy.Also,the three-body interaction among atoms in the lattices can be taken into account in the method.This method gives a useful means to obtain interatomic interactions in the interatomic force model.The method has been applied to zinc,and the pair potential obtained is used to calculate the phonon dispersion relations for some high-symmetry directions.It is found that,by properly considering a three-body interaction,one can acquire satisfactory results.     

Elastic moduli of solid helium at megabar pressures

Abstract

Elastic moduli and equation of state of highly compressed solid He are calculated up to the pressure 1.5 Mbar. While calculating the energy of the crystal, pair interatomic interactions and three-body interactions are taken into account. Three-body contribution is significant to a great extent both for the equation ofstate and for the elastic moduli and makes considerable softening of the equation of state. On the other hand, vibrational characteristics, such as the sound velocity and the Debye temperature, do not strongly depend on the inclusion of non-additive interactions.     

On the balance laws of extended thermodynamics (ET) for non-ideal gases

The conservation laws of mass and momentum and the equations of balance of momentum flux and energy flux as well as the higher order balance laws are derived by means of the modified Klimontovich kinetic equation for non-ideal gases. The effect of the body forces and inertial forces during the persistence of a collision is taken into account in order to have the balance laws valid for general frames of reference. The sequence of macroscopic quantities appearing in the balance equations is decomposed into convective and non-convective parts and this decomposition is explained on the basis of statistical mechanics. A problem of symmetry or non-symmetry of tensors associated with the presence of interactions between microscopic particles is discussed from a molecular point of view. Explicit expressions for the energy density, the pressure, the pressure tensor, the heat flux and the other expressions characteristic for ET are given in terms of microscopic variables.     

Calculation of Vacancy Induced Properties in FCC Metals Using an Alternative Lattice Dynamical Model

Combining the conventional Kanzaki's lattice statics method with an alternative lattice dynamical model called decoupling transformation, a new approach is proposed to calculate the vacancy induced properties in FCC metals. This approach has the advantage over the traditional least-square fit approach in the way that all the model parameters are linearly independent and so it can avoid the problem of non-uniqueness in dynamical model parameters when interactions with more distant atoms are taken into account by fitting to the experimental phonon frequencies only. Numerical results on the lattice dynamical properties such as phonon dispersion curves and interatomic interaction force constants and the vacancy induced properties such as the atomic displacements, lattice relaxation energy, divacancy interaction energy and relaxation volume are obtained specifically for two similar FCC metals, to wit, Cu and Ni and are compared with previous calculations. It is concluded that the interatomic interactions up to the fourth nearest neighbours are already good enough for describing both the lattice vibrational and vacancy induced properties for both metals.     

Determination of the mass spectrum of the bound state in the framework of the relativistic hamiltonian approach

We propose one a variant of calculation of the energy spectrum of bound state systems with relativistic corrections. In the framework of quantum field theory, an expression that takes into account relativistic corrections to the mass of the bound state with a known nonrelativistic pair interaction potential is proposed on the basis of calculating the asymptotic behavior of correlation functions of the corresponding field currents with the necessary quantum numbers. Excluding the time variables allows one to determine nonperturbative corrections to the interaction potential. The following results have been obtained in the framework of this approach. The nonperturbative corrections arising due to the relativistic nature of a system to the interaction Hamiltonian are determined. The dependence of the constituent mass of bound-state forming particles on the free state mass and on the orbital and radial quantum numbers is analytically derived. The energy level shift of muonic hydrogen taking into account relativistic corrections is calculated. The energy spectrum of a wide class of potentials that describe the Coulomb bound state is analytically derived with relativistic corrections. The mass spectrum of the glueballs and the constituent masses of the gluons are analytically calculated taking into account spin-orbit, spin—spin, and tensor interactions. Our numerical results have shown very good agreement with the lattice data. Taking into account nonperturbative and nonlocality characters of interactions, the mass spectrum of the mesons consisting of light-light and light-heavy quarks with orbital and radial excitations is determined. Our results show that good agreement with the experimental data for the slope and the intercept of the Regge trajectory can be obtained only taking into account the nonperturbative and the nonlocal characters of interactions. The dependences of the constituent masses of constituent particles on the masses of a free state are certain. When quarks are light, then the difference between current and valent masses of quarks is greater than valent masses of quarks, and when quarks are heavy, then the difference between these masses is insignificant. One of the alternative variants of taking nonlocality into account has been suggested for the definition of properties of hadrons at large distances. The dependence of the constituent masses of constituent particles on the radius of confinement is determined.     

Interface free energy and critical line for the ising model with nearest and next-nearest-neighbor interactions

A method due to Müller-Hartmann and Zittartz is used to calculate the free energy of a diagonal interface in an Ising model on a square lattice with interactions between nearest and next-nearest neighbors. Instead of solving the full bulk problem, one only takes into account a simple subset of interface configurations. The subset, which is somewhat different from that considered by Müller-Hartmann and Zittartz, is chosen in such a way that exact results for the interface free energy are reproduced if the system has only nearest or only next-nearest-neighbor interactions. When the critical line of ferromagnetic transitions is obtained by demanding that the interface free energy as a function of both couplings vanish, a surprisingly accurate approximation is obtained.     

Crystal-glass transition in ion-bombarded alloys

Summary A model for glass formation and crystal structure retainment in binary alloys undergoing irradiation by energetic ion beams is presented. The major physical features provided by experimental conditions, namely spike formation and evolution of bombardment-induced surface compositional variations, are taken into account. At spike-lattice interface interatomic interactions with charge transfer occur, which induce formation of amorphization, or crystallization nuclei. Qualitative differences are found between glass forming and crystalline systems. To speed up publication, the author of this paper has agreed to not receive the proofs for correction.     

四体相互作用对固氦压缩特性的贡献

运用从头计算自洽场方法和原子团簇理论计算了高压下固氦原子间的四体势分量.计算结果表明四体分量对结合能的贡献为正；随着压缩度增大四体势的贡献比例变大.采用两体、三体、四体势和Aziz吸引势计算固氦零温状态方程并与实验测量相比较，结果表明两体势对固氦的压缩性贡献了过多的正效应，加入三体分量的修正，仅在低于10GPa时理论值与实验值相符很好，但考虑了四体势修正后能将理论值与实验值符合程度提高到 27GPa. 关键词： 状态方程 固氦 四体势 从头计算     

Exact thermodynamics of the Hubbard chain: free energy and correlation lengths

We study the one-dimensional Hubbard model at finite temperatures in the quantum transfer matrix approach. The eigenvalue equations of this matrix are obtained by a nested Bethe ansatz. The largest and next-largest eigenvalues yield the free energy as well as the correlation lengths of the system. An equivalent set of four integral equations is derived from the Bethe ansatz equations. The limit of Trotter-Suzuki number N → ∞ is taken analytically. For half-filling the final equations are studied in the low-temperature limit yielding analytic expressions for the free energy and spin-spin correlation length. Numerical results are presented for intermediate temperatures.     

Path Integral Formalism for Line Broadening in Plasmas: Lyman‐α case

Using the path integral formalism, the fine structure and dynamics effects are taken into account for the study of the spectral line broadening in plasmas. A compact expression of the dipolar autocorrelation function (DAF) for an emitter in the plasma is derived for Lyman alpha lines with fine structure. The expression of the DAF takes into account the dynamics effects, which are represented by the time autocorrelation function of the electric microfield. The spectral line for the Lyman‐alpha case has been obtained in a compact form and plotted in the quasi‐static approximation and compared to a line obtained by a simulation. (© 2014 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)     

Nonlinear resonances in the near-field interaction between atoms

It has been shown that nonlinear near-field optical resonances occur in diatomic nanostructures consisting of identical or different two-level atoms in the presence of a radiation field when the dipole-dipole interaction is taken into account. The frequencies of these resonances depend strongly on the intensity of the external optical radiation, on the initial conditions, on the polarization of the external field with respect to the axis of the nanostructure, and on the interatomic distance. The interatomic interaction is taken into account beyond perturbation theory. For this reason, the effective polarizabilities of the atoms of the nanostructure are expressed in terms of the polynomials of both the interatomic distance and the electric field strength of the external optical wave. A “falling tower” effect that is caused by the nonlinear behavior of the local dipole moments of atoms in the nanostructure is predicted.     

Lattice dynamics of molecular solids by a phenomenological model

A quasiharmonic central-force rigid-atom model has been used to study the dispersion of phonon waves in molecular (rare-gas) solids. The model derives the interatomic forces by Buckingham-Corner potential and takes account of all neighbor interactions. Zero-point anharmonic effects have been taken into account through the potential parameters by a method of iteration. It is found that out of all the conventional power and exponential potentials the Buckingham-Corner potential function is best suited to this class of molecular solids. Further, the possibilities of the improvement of the present model have been discussed.     

Nonlinear size-dependent longitudinal vibration of carbon nanotubes embedded in an elastic medium

In this paper, we study the longitudinal linear and nonlinear free vibration response of a single walled carbon nanotube (CNT) embedded in an elastic medium subjected to different boundary conditions. This formulation is based on a large deformation analysis in which the linear and nonlinear von Kármán strains and their gradient are included in the expression of the strain energy and the velocity and its gradient are taken into account in the expression of the kinetic energy. Therefore, static and kinetic length scales associated with both energies are introduced to model size effects. The governing motion equation along with the boundary conditions are derived using Hamilton's principle. Closed-form solutions for the linear free vibration problem of the embedded CNT rod are first obtained. Then, the nonlinear free vibration response is investigated for various values of length scales using the method of multiple scales.     

Collision operator for relativistic electrons in a cold gas of atomic particles

The collision operator of relativistic electrons with a cold gas of atomic particles is derived consistently taking into account elastic interactions, excitation of electron shells, and ionization. The creation of secondary electrons is described accurately. In the range of energies exceeding the binding energy of atomic electrons, the operator implicates only the angular scattering by nuclei and the ionization integral that automatically allows for scattering by atomic electrons. The collision operator used earlier for studying the kinetics of avalanches of relativistic runaway electrons is analyzed. A more exact operator derived in the present study is simpler in form and saves time in computer calculations.     

Derivation of classical Markovian kinetic equations via generating functional technique

An exact Markovian kinetic equation for a classical system of particles interacting via pair forces is derived by means of Bogoljubov's Generating Functional method. A nondiverging collision integral is obtained for Coulomb plasmas, which takes into account the screening effects and the energy and momentum transfer between two colliding particles and their surroundings.     

Physical optics theory for the scattering of waves by an impedance strip

The physical optics integral of the scattered waves by an impedance strip is derived by using the modified theory of physical optics. The surface currents of the physical optics integral, which was introduced for the scattered waves by an impedance half-plane, are taken into account. The uniform diffracted fields of the impedance strip are evaluated asymptotically. The second order diffraction terms are also obtained. The total scattered field and its subcomponents are plotted and the effect of the second order diffraction and strip width to the scattering is investigated numerically.     

Ionic effects on overstretching transition of B-DNA

A three-dimensional model is proposed herein to study the ionic effects of a NaCl solution on the overstretching transition of long B-DNA molecules. In this model, the bending deformations of DNA backbones, cooperativity of base-stacking interactions, electrostatic interactions, and spatial effects of the DNA double-helix structure are taken into account. The energy of electrostatic interactions is given as a function of the ionic strength and of the folding angle based on the Poisson-Boltzmann equation. An expression is derived, which shows that the overstretching force is linear with the natural logarithm of the ionic strength. The analytical results of this model are in good agreement with recently reported experimental results.