Diffusion and coupled fluxes in concentrated alloys under irradiation: a self-consistent mean-field approach

When an alloy is irradiated, atomic transport can occur through the two types of defects which are created: vacancies and interstitials. Recent developments of the self-consistent mean field (SCMF) kinetic theory could treat within the same formalism diffusion due to vacancies and interstitials in a multi-component alloy. It starts from a microscopic model of the atomic transport via vacancies and interstitials and yields the fluxes with a complete Onsager matrix of the phenomenological coefficients. The jump frequencies depend on the local environment through a ‘broken bond model’ such that the large range of frequencies involved in concentrated alloys is produced by a small number of thermodynamic and kinetic parameters. Kinetic correlations are accounted for through a set of time-dependent effective interactions within a non-equilibrium distribution function of the system. The different approximations of the SCMF theory recover most of the previous diffusion models. Recent improvements of the theory were to extend the multi-frequency approach usually restricted to dilute alloys to diffusion in concentrated alloys with jump frequencies depending on local concentrations and to generalize the formalism first developed for the vacancy diffusion mechanism to the more complex diffusion mechanism of the interstitial in the dumbbell configuration. To cite this article: M. Nastar, C. R. Physique 9 (2008).     

A self-consistent mean field calculation of the phenomenological coefficients in a multicomponent alloy with high jump frequency ratios

We present an improvement of the self-consistent mean field (SCMF) approximation of the L _ij which extends its applications to alloys presenting high jump frequency ratios. The theory uses a vacancy–atom exchange model which depends on temperature and local composition through thermodynamic and kinetic parameters. Kinetic correlations due to the vacancy mechanism are represented by a time-dependent effective Hamiltonian. In the case of high jump frequency ratios it is shown that long return paths of the vacancy need to be considered, which is shown to be equivalent to introducing many-body long-range effective interactions. We compare this theory to existing formalisms and Monte Carlo simulations for systems both without and with atomic interactions.     

Phenomenological coefficients in a dilute BCC alloy for the dumbbell mechanism

The self-consistent mean field (SCMF) method is applied to calculate the transport coefficients in a dilute BCC alloy with the dumbbell diffusion mechanism. The first degree of approximation (first shell) of the SCMF formalism coincides with the formerly derived pair association method, and the second degree of approximation (second shell) leads to a more accurate analytical formulation. The SCMF results are compared with other formalisms as well as existing and new Monte Carlo simulations, including the solute–dumbbell binding energy. This theory shows a good balance between accuracy and complexity in the investigated systems, and a simple criterion is proposed for the preferential use of the first and second shell approximations.     

Theory of the spontaneous polarization of the adsorbed monolayer of polar molecules. The collective variables method

The theory of the spontaneous polarization of the adsorbed monolayer of polar molecules is developed using the collective variables method. The total potential of the system is represented as the sum of the one-body and two-body interaction potentials. The one-body potential depends on the orientation of the molecular dipoles in the external electric field and on the interactions between the molecules and the substrate. The two-body potential consists of the sum of intermolecular potentials which can be separated into the short-range part describing the orientation-independent interaction at distances, and the long-range part dependent on both the coordinates and the orientations of the interacting species. The variation of the configurational Helmholtz free energy of the system related to the long-range orientational interactions is shown to consist of three terms describing different modes of interactions of density fluctuations: (a) neglect of particle's density fluctuation or self-consistent mean field approximation (SCMF), (b) harmonic oscillations of the particle's density-the random phases approximation (RPA), and (c) various unharmonic interactions of the fluctuation waves. In the SCMF approximation using the assumption of the multiplicative separation of the high-order distribution function the singlet distribution function is calculated and the polarization vector of the adsorbed monolayer is determined. The corrections to the singlet distribution function arising from the terms (b) and (c) of the free energy are calculated. It is shown that the spontaneous polarization of the adsorbed monolayer of polar molecules may be regarded as the first-order phase transition.     

Statistical calculations of tracer and intrinsic diffusion coefficients in concentrated alloys and estimates of microscopic parameters of diffusion from experimental data

The earlier-developed statistical theory of diffusion in concentrated alloys based on the master equation approach is generalized to treat tracer diffusion in binary alloys. The theory developed is used to describe concentration dependencies of both tracer and intrinsic diffusion coefficients and to estimate microscopic parameters of diffusion in alloys CuNi, CuZn and AgCd for which necessary experimental data are available. We show that all main features of strong and peculiar concentration dependencies of diffusion coefficients observed in these alloys are naturally explained by the theory. Signs and scales of interatomic interactions important for diffusion in these alloys are found to strongly depend on the ratio of atomic sizes of alloy components, and types of these dependencies agree with simple physical considerations. We also discuss physical reasons for sharp concentration dependencies of diffusion coefficients characteristic of real alloys.     

Perturbation theory for non-axial molecular fluids

The thermodynamic perturbation theory in which all angle-dependent interactions are considered as a perturbation of the central potential is applied to study the equilibrium properties of a fluid composed of non-axial molecules. The influence of a large number of anisotropic pair and three-body non-additive interactions have been taken into account. Using the same set of force parameters the calculation is made for gaseous pressure second and third virial coefficients and liquid phase thermodynamic properties (Helmholtz free-energy, configurational energy, pressure and entropy). It is shown that the non-axial approximation is an improvement over the axial one. Excellent agreement between theory and experiment is obtained for ethylene.     

Statistical theory of diffusion in concentrated bcc and fcc alloys and concentration dependencies of diffusion coefficients in bcc alloys FeCu,FeMn, FeNi,and FeCr

The statistical theory of diffusion in concentrated bcc and fcc alloys with arbitrary pairwise interatomic interactions based on the master equation approach is developed. Vacancy–atom correlations are described using both the second-shell-jump and the nearest-neighbor-jump approximations which are shown to be usually sufficiently accurate. General expressions for Onsager coefficients in terms of microscopic interatomic interactions and some statistical averages are given. Both the analytical kinetic mean-field and the Monte Carlo methods for finding these averages are described. The theory developed is used to describe sharp concentration dependencies of diffusion coefficients in several iron-based alloy systems. For the bcc alloys FeCu, FeMn, and FeNi, we predict the notable increase of the iron self-diffusion coefficient with solute concentration c, up to several times, even though values of c possible for these alloys do not exceed some percent. For the bcc alloys FeCr at high temperatures T ? 1400 K, we show that the very strong and peculiar concentration dependencies of both tracer and chemical diffusion coefficients observed in these alloys can be naturally explained by the theory, without invoking exotic models discussed earlier.     

Semiclassical description of isoscalar giant multipole resonances

The scaling approximation in a semiclassical theory of nuclear collective motions based on the Vlasov equation is applied to the study of isoscalar giant resonances. Analytic forms are obtained for the frequencies of any multipolarity, expressed just in terms of local density distributions, using realistic nuclear effective forces. The importance of non local interactions and diffuse surfaces is clearly shown. The limits of the scaling picture in describing high multipolarity resonances are finally discussed.     

Modeling of Multiple Scattering from an Ensemble of Spheres in a Laser Beam

This paper details the results of upgrading an effective numerical technique (derived for multiple-scattering simulations in photon correlation/cross-correlation with a plane-wave light source) for the modeling of multiple scattering in a laser beam. The off-axis shape coefficients of an arbitrary beam are computed starting from the set of known beam-shape coefficients for an on-axis location by using the addition theorem for the spherical vector wavefunctions of the first kind. The discussed technique is verified by comparison with a localized approximation for a focused Gaussian beam and with Barton's spheres-arbitrary beam interaction theory. An additional advantage of the proposed technique (self-testing of the computation accuracy by comparison of the off-axis beam-shape coefficients evaluated from two different on-axis origins) is demonstrated.     

Dynamical properties of strongly interacting Brownian particles : II. Self-diffusion

The self-diffusion process of Brownian particles is theoretically investigated for concentrated systems in the presence of strong potential interactions between particles. Starting from an N-particle diffusion equation, a formalism is developed to calculate the self-diffusion coefficient and the velocity autocorrelation function on the basis of the superposition approximation for the three-particle distribution function of non-equilibrium states. Explicit calculations are carried out for model systems of hard spheres with a screened Coulomb potential. Calculated time-dependent self-diffusion coefficients are compared with available data of the Brownian dynamics. Without introducing any phenomenological or adjustable parameters, quantitative agreement is achieved.     

Approximate study of the free vibrations of a cantilever anisotropic plate carrying a concentrated mass

This study is concerned with the vibration analysis of a cantilevered rectangular anisotropic plate when a concentrated mass is rigidly attached to its center point. Based on the classical theory of anisotropic plates, the Ritz method is employed to perform the analysis. The deflection of the plate is approximated by a set of beam functions in each principal coordinate direction. The influence of the mass magnitude on the natural frequencies and modal shapes of vibration is studied for a boron-epoxy plate and also in the case of a generic anisotropic material. The classical Ritz method with beam functions as the spatial approximation proved to be a suitable procedure to solve a problem of this analytical complexity.     

Luttinger liquid with one impurity: Equivalent field theory and duality

We derive by functional integral method one-dimensional theory equivalent to Luttinger liquid with one impurity. It is shown that the single quantity has to be calculated for the formulation the effective field theory is the electron density jump at the impurity. We show that duality which relates models with electron-electron attraction and repulsion, and simultaneous exchange of transition and reflection coefficients, is an exact property of the theory.     

Vibrations of excited molecules at combination and difference frequencies

In the context of the theory of molecular vibrations, by applying the direct product operation of matrices, an equation for the vibrations of vibrationally excited molecules at combination and difference frequencies is obtained. From the solution of this equation, elements of vibration patterns and expressions that can be used for the study of changes in the molecular structural parameters and the coefficients of kinematic interactions are determined. The formulas obtained are applied to the calculation of the anharmonic electro-optical parameters of the molecules of water H₂O and its two isotopes H₂ ¹⁷O and H₂ ¹⁸O. These calculations are performed in terms of the semiempirical quantum-chemical CNDO/2 method and by numerical differentiation of dipole moment functions by employing a cubic spline approximation.     

Radiative quenching and excitation of metastable states upon differential scattering of atoms: I. Uniform quasi-classical theory

A theory of radiative-collisional transitions between the ground and metastable ¹S states of a colliding atom is proposed. The theory uses the uniform quasi-classical approximation generalized to the case of spherically asymmetric interactions. The theory takes into account the angular momentum of an emitted (absorbed) photon and allows one to calculate the total and differential scattering cross sections in a wide range of radiation frequencies including both wings and the center of the line of a forbidden atomic transition. The range of admissible collision energies and intensities of an external radiation field is restricted by the use of the adiabatic approximation, as well as the approximation of a weak coupling between the ground and excited states of a quasi-molecule, the potentials of which are assumed to be monotonically repulsive.     

Application of a method of linear scaling of frequencies in calculations of the normal vibrations of polyatomic molecules

The frequencies of the harmonic vibrations of 88 compounds consisting of atoms of the first period are calculated in the approximation of the hybrid density functional B3LYP with the 6-31G* basis set. Using 1189 frequencies from experimental IR and Raman spectra of these compounds in the gas phase and the corresponding theoretical frequencies, the coefficients of the function of linear scaling are found by the least squares method. The method of linear scaling of frequencies is applied to the prediction of the 108 vibrational frequencies of a porphin molecule. A conclusion is made that this method is promising for the interpretation of vibrational spectra of complex molecules and, in combination with the Pulay method of scaling of a quantum-mechanical field, for the determination of harmonic force constants.     

Natural sloshing frequencies and modes in a rectangular tank with a slat-type screen

Being installed in tanks, screens play the role of slosh-suppressing devices which may strongly change resonant sloshing frequencies and yield an extra nonlinear damping due to cross-flow resulting in either flow separation or jet flow. Employing the linear sloshing theory and domain decomposition method, we construct an accurate analytical approximation of the natural sloshing modes in a rectangular tank with a slat-type screen at the tank middle. Two-dimensional irrotational flow of an ideal incompressible liquid is assumed. Because the considered flow model does not account for flow separation and jet flow at the screen, the velocity field is locally singular at the sharp edges. The constructed solution captures this singularity. Analyzing this solution establishes a complex dependence of the natural sloshing frequencies on the solidity ratio, the number of submerged screen gaps, the liquid depth, and the position of perforated openings relative to the mean free surface. Results are compared with experimental data. Natural surface wave profiles are discussed in the context of a jump of the velocity potential at the screen and the local inflow component to the screen.     

北极典型冰下声信道建模及特性

将Burke-Twersky (BT)散射模型与射线理论相结合研究北极典型冰下的水声信道特性。BT模型将极地冰水界面的冰脊视为随机分布在自由表面的半椭圆柱。首先根据BT模型分别对高频和低频情况下的冰面反射系数取近似,计算不同频率的冰面反射系数。然后结合射线理论计算冰下声场并分析冰下信道特性,并与相同条件下绝对软界面的水声信道进行对比研究。结果显示,由于冰界面的存在,冰水界面与绝对软界面相比,冰面反射系数较小,使得部分声线不会传播很远,且随频率的增加衰减越发严重,因此不利于声信号远距离传播;此外在信道结构上,由于冰层反射系数较小,冰下信道多径相较于无冰的水-空气界面其多途现象不明显。研究结果对认知极地冰下水声信道特性以及开展极地水声系统性能预报具有一定意义。      

Vibrational coordinates in the electron jump model

The role of quantization of vibrational coordinates in the electron jump model of alkali atom, dimer plus halogen molecule collisions is examined. Despite the bound states of the molecule ions involved, a classical approximation may offer good approximation over a wide collision energy range for the energy distributions of the ions in a single electron jump. Some results are calculated for K + Br₂ and K₂ + Br₂. The theory assumes that the electron jump probability is governed by the electronic matrix element H₁₂ alone. Elementary arguments are offered to suggest that this may be a reasonable approximation.