Distribution of atoms in a ternary alloy with a free surface in the self-consistent field approximation

Analytical form for the functions describing atomic distribution of the components in the subsurface layer of a ternary alloy has been found in a closed form in the self-consistent field approximation, without taking correlation into account. The functions obtained allow one to construct concentration profiles of the components near the surface, to calculate the component surface concentration, and to investigate the dependence of the composition on the surface of the alloy crystal on temperature, and surface relaxation of coordination numbers and energies of the nearest neighbor interatomic interaction in an alloy. An analysis of the character of temperature dependencies of the composition on the surface has been performed for various alloys.Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 8, pp. 47–52, August, 1982.     

Nuclear level densities in self-consistent field approximation

The effect of two-body nature of the nuclear shell model potential on the recent numerical calculations of the nucleai level density has been examined. For the two most widely used single particle energy level schemes based on harmonic oscillator and Woods-Saxon potential, this effect is shown to significantly modify the excitation energy dependence of the level densisties.     

Quasiharmonic approximation for a crystal in the self-consistent field method

An equation of state is derived for fcc crystals on the basis of earlier studies, and the stability of the crystalline phase and polymorphic transitions are discussed.Translated from lzvestiya Vysshikh Uchebnykh Zavedenii Fizika, Vol.12, No. 1, pp. 18–23, January, 1969.     

Ordering of substitutional ternary alloys with an fcc lattice

The possible types of ordering diagrams of ternary substutional alloys with an fcc lattice are analyzed, taking account of interactions in two coordination spheres.Ural Polytechnic Institute. Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 12, pp. 38–41, December, 1992.     

Model boson fluid with disorder in the self-consistent field approximation

We study the ground-state properties of a model neutral boson fluid in the presence of disorder effects. The effective interaction between the bosons is obtained through the self-consistent field method which renormalizes the bare interaction consisting of a hard-core repulsive potential with an attractive tail at zero temperature. We introduce disorder effects within a number-conserving approximation by modifying the density–density response function. Our results for the static structure factor and the collective mode dispersion reflect the effect of disorder in qualitative agreement with other calculational approaches.     

Ising model of a dilute ferromagnet in the self-consistent field approximation

The method of averaging over the exchange interaction fields has been considered as applied to clusters of one and two magnetic atoms in the Ising model of a dilute ferromagnet, and a variant of fixed-scale group renormalization on the basis of this method has been constructed. It has been shown that the approximation obtained makes it possible to distinguish models with the site and bond dilutions.     

A special class of states in the self-consistent mean field approximation

In the self-consistent mean field approximation, two-level atoms penetrating an interacting medium have a special class of dressed states which, when probed with an optical field, exhibit a decreasing coupling strength to the optical field for increasing field intensities. The position of the resonance is fixed in frequency space for these states, but the linewidth varies with the intensity of the optical field.     

Ordering processes and activation energy in Ni3Fe-based ternary alloys

The measurement of electrical resistance () has been used, to study the kinetics of isothermal ordering in the range 200 °–545 ° C in Ni₃(FeMn) alloy quenched from 970 ° C, and the kinetics of ordering at 390 ° C in the alloy quenched from various temperatures in the 600 °–800 ° C range. The sections method and the gradient of the (t) curves were used to find the activation energy for migration and vacancy formation in this alloy on the assumption that the excess vacancies frozen in the alloy by quenching at temperatures above T_c are responsible for ordering. The activation energies for vacancy formation and migration were respectively U₀ = 33 ± 3 kilocal/mole and U_m = 39 ± 4 kilocal/mole, which in total give the activation energy for diffusion Q = 72 ± 7 kilocal/mole in the alloy studied; this approximates to the activation energy for diffusion in pure nickel.     

Ordering in alloys

Abstract

The continuous ordering process can be viewed as a development and a gradual amplification of concentration modulations with wave lengths of the order of a few lattice spacings. How the development of different concentration modulaltions leads to different superlattice structures in cubic systems is explained with the help of some illustrative examples. The importance of concentration modulations with special point wave vectors in the stability of the various coherent superlattice structures is discussed. Experimental evidences for such continuous ordering is cited from recent results on ordering in Ni-Mo alloys.

The evolution of ordering in some systems can also be viewed as progressively tiling the disordered lattice by superlattice tiles. When more than one type of coherent superlattice tiles compete, juxtaposition of different types of tiles can occur during the course of ordering. The transitional states between the short range and the long range ordered Ni-Mo alloys indeed exhibit such structures where different types of superlattice tiles decorate the fcc lattice. The role of special point concentration waves in the development of such structures will be discussed in relation to the secondary ordering processes involving two perpendicular ?1 ½ 0? waves and a combination of an ?1 ½ 0? and an appropriate ?100? wave.     

Ordering of body-centered cubic ternary alloys with three types of site. I

The ordering theory of A-B-D alloys with body-centered cubic (bcc) lattices and three types of site is examined by the Gorskii-Bragg-Williams approximation. It is shown that under certain conditions there can be two critical temperatures (T₀) for the order-disorder phase transition. The case of alloys with a quasi-binary BA-BD section is examined in detail.     

Multi-photon cooperative radiation from two-level atoms in self-consistent field approximation (SCFA)

We give analytical solutions for k-photon cooperative radiation from two-level atoms for arbitrary k.     

Novel self-consistent mean field approximation and its application in strong interaction phase transitions

We propose a novel self-consistent mean field approximation method by means of a Fierz transformation,taking the Nambu-Jona-Lasinio model as an example.This new self-consistent mean field approximation introduces a new free parameter a to be determined experimentally.When a assumes the value of 0.5,the approximation reduces to the mean field calculation commonly used in the past.Subsequently,we study the influence of the undetermined parameter a on the phase diagram of the two-flavor strong interaction matter.The value of a plays a crucial role in the strong interaction phase diagram,as it not only changes the position of the phase transition point of strong interaction matter,but also affects the order of the phase transition.For example,when a is greater than the critical valueαc = 0.71,then the strong interaction matter phase diagram no longer has a critical end point.In addition,in the case of zero temperature and finite density,we found that when a1.044,the pseudo-critical chemical potential corresponds to ～4-5 times the saturation density of the nuclear matter,which agrees with the expected results from the picture of the hadrons degree of freedom.The resulting equations of state of strong interaction matter at low temperatures and high densities will have an important impact on studies concerning the mass radius relationship of neutron stars and the merging process of binary neutron stars.     

The possibility of describing a two-particle quantum system and interparticle correlations in the self-consistent field approximation

The possibility of determining the energy spectrum and the wave function structure of the stationary states of a model two-particle system is examined in the self-consistent field approximation. The results of exact calculations are compared with the data obtained in the self-consistent field approximation with the use of orthogonal and nonorthogonal orbitals. The possibility of using these approximations for describing the interparticle quantum correlations is discussed.     

Renormalization of relativistic self-consistent Hartree-Fock approximation

The renormalization of the relativistic self-consistent Hartree-Fock approximation is restudied. It is shown that the renormalization procedure suggested by Bielajew and Serot can be greatly simplified and the renormalization achieved in a way no more complicated than that of the relativistic self-consistent Fock approximation, if the parameters in the counterterms are allowed to be density-dependent and the renormalization of the tadpole self-energy is treated appropriately. A transformation relation between the four- and three-dimensional representation of the baryon self-energy is presented and a self-consistent Hartree-Fock scheme different from that considered by Bielajew and Serot studied. The renormalized integral equations for the baryon self-energy which includes effects from the Dirac sea are reformulated in a three-dimensional form. Explicit expressions are derived. Received: 29 August 1997 / Revised version: 30 April 1998     

Ordering in binary FCC alloys

A new method of approximation for studying the order-disorder transition in binary alloys is presented. The formulation is in terms of face-centered cubic alloys, although the method can also be applied to other structures. The technique is essentially a generalization of the constant-coupling approximation. We have applied the principles of that method to derive the free energy of the alloy using a tetrahedral cluster of nearest neighbouring sites as the basic unit of the calculation. We only consider the case of nearest neighbour pair interactions, but show how the method can be generalized to include many body and second neighbour interactions. Numerical results are presented and comparison of these results is made with results of cluster variation calculations on the same system and with experimental results on the copper-gold alloy system.     

Weak self-consistent approximation scheme in many-body systems

In this paper we show a possibility of restricting the usual self-consistency conditions in approximations to many-body systems. Instead of requiring thermodynamic consistency for even non-physical one-particle quantities, we impose it for the physically relevant quantities only. As a consequence of this less severe requirement, one does not lose any physically relevant information, but one can construct new types of approximations. As an example a parametric approximation scheme is given.     

QCD phase diagram at finite isospin and baryon chemical potentials with the self-consistent mean field approximation

The self-consistent mean field approximation of the two-flavor NJL model,with a free parameter a to reflect the competition between the "direct" channel and the "exchange" channel,is employed to study the QCD phase structure at finite iso spin chemical potential μ_I,finite bary on chemical potential μ_B and finite temperature T,and especially to study the location of the QCD critical point.Our results show that in order to match the corresponding lattice results of iso spin density and energy density,the contributions of the "exchange" channel need to be considered in the framework of the NJL model,and a weighting factor α=0.5 should be taken.It is also found that for fixed isospin chemical potentials,the lower temperature of the phase transition is obtained with increasing a in the T-μ_I plane,and the largest difference of the phase transition temperature with different a's appears at μ_I~1.5 mπ.At μ_I=0 the temperature of the QCD critical end point(CEP) decreases with increasing a,while the critical baryon chemical potential increases.At high isospin chemical potential(μ_I=500 MeV),the temperature of the QCD tricritical point(TCP) increases with increasing a,and in the low temperature regions the system will transition from the pion superfluidity phase to the normal phase as μ_B increases.At low density,the critical temperature of the QCD phase transition with different a's rapidly increases with μ_I at the beginning,and then increases smoothly around μ_I 300 MeV.In the high baryon density region,the increase of the iso spin chemical potential will raise the critical baryon chemical potential of the phase transition.