Cellular approximation of the method of the model electron density functional. Alloys of alkali metals

The expression obtained in Part 1 of this work for the total energy of a disordered binary substitution alloy is employed to calculate the thermodynamic characteristics of alloys of the systems Na-Rb, Na-Cs, Li-Na, Li-K, k-Rb, Rb-Cs, K-Cs, Na-K. A model expression, whose parameters are calculated starting from the equilibrium characteristics of the metals studied, is employed to describe the energy of interaction of ions with conduction electrons. In order to calculate the properties of alloys no additional parameters are introduced into the theory, but rather the values of the parameters of the pure components are employed.Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 5, pp. 77–83, May, 1991.     

Multiparticle interatiomic interaction potentials for alloys using the model electron density functional method

A method for calculating multiparticle interatomic interaction potentials for binary alloys within the framework of a model electron density functional is presented. An expression for the total ground state energy of metals and alloys is obtained. It is shown that in simplicity of the computational scheme and speed of computation, this approach does not yield to the method of inserted atoms, but has a more rigorous physical basis in comparison with the latter.Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 4, pp. 90–99, April, 1996.     

Ground state of alloys by the method of the electron density functional

An expression for the total energy of an alloy with an arbitrary degree of long-range order is written within the framework of the method of the electron-density functional. A method is proposed for calculation of the Coulomb, kinetic, and exchange-correlation energies. The ground state of the alloys Na-Li and Rb-K is investigated.Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 11, pp. 35–41, November, 1978.     

Calculation of the formation energy of alloys using the method of the model functional of electron density

Calculation of the formation and ordering energies of the alloys Fe-V and V-Ti has been performed on the basis of the method of the electron-density functional. It is shown that alloys of the system V-Ti should be dissolvable, whereas in the system Fe-V the most favorable state is an ordered alloy state with CsCl structure. Estimates of dissolving and ordering temperatures are performed.Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 1, pp. 32–35, January, 1982.     

Thermodynamic properties of noble-metal alloys using the cell approximation in the method of a model electron-density functional

The thermodynamic properties of the main ordered and disordered phases of copper, silver, and gold alloys are investigated theoretically using the cell approximation in the method of a model electron-density functional. Theoretical and experimental data for the energy of alloy formation, equilibrium volume, omnidirectional compression modulus, and order—disorder transition temperature are in satisfactory agreement.Institute of Strength Physics and Materials Science, Siberian Branch, Russian Academy of Sciences. Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 12, pp. 30–36, December, 1993.     

Local approximation of the correlation energy functional in the density matrix functional theory

A local approximation formula of the correlation energy functional E(c) in terms of the first-order reduced density matrix (1-RDM) is presented. With the contracted Schr?dinger equation the principal dependence of E(c) on the natural occupation numbers n(i) is identified. Using the effective mass theory, E(c) is expressed as a functional of the local density and the local variable, J = SUM (i)[square root of (n(i)(1-n(i))] /phi(i)/(2), where phi(i) are the natural spin orbitals. This local approximation satisfies the homogeneous coordinate scaling relation, gives the exact result for a one-electron system, and is almost free from the exchange energy error. It reproduced about 90% of the correlation energies of atoms and molecules.     

A time dependent density functional method for the interaction site model

A new method is developed to study nonlinear dynamics of molecular liquids. It is a time dependent density functional method for the interaction site model. The nonlinear Langevin theory provides the formulation of the method. An approximation is introduced to calculate the reversible term.     

Calculation of the nonlinear susceptibilities of interacting homogeneous electron gas by the density functional method

The density functional method is used for the calculation of nonlinear susceptibilities of an interacting electron gas. It is shown that this approach leads to the expression for nonlinear susceptibilities which satisfy exactly the strict sum rules derived previously. By using the local densities approximation we obtain the expression for the exchange-correlation contribution in the first non-linear susceptibility of interacting electron gas. It is shown that such a contribution may have a noticeable effect on the binding energy and phonon spectrum of polivalent simple metals.     

Local density functional approximation applied to Compton profiles

We have applied a self-consistent psuedopotential approach in the density functional approximation to study the dependence of the Compton profile of silicon on the choice of the exchange correlation potential. We find that the Compton profile depends strongly on the value of the exchange-correlation potential.Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 1, pp. 76–79, January, 1996.     

Calculation of the thermodynamic properties of noble-metal alloys in the model electron-density functional method

The thermodynamic properties of the stable and metastable phases of theCu−Au, Ag−Au, andCu−Ag systems have been calculated in the representation of the many-body interatomic interaction potential within the framework of the model electron-density functional method. The calculated values of the thermodynamic properties are in good agreement with experimental data and help explain the laws of alloy formation in the given systems. Factors that affect the magnitude of the tetragonal distortion of theL1 ₀ structure of equiatomic alloys have been investigated. The possibility of a transition by the Bayne scheme from theL1 ₀ structure toB2 for alloyCuAu upon application of an external uniaxial [001] stress is discussed. Institute of Strength Physics and Materials Science, Siberian Division of the Russian Academy of Sciences. Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 5, p. 9–19, May, 1997.     

Simulation of the decomposition of binary alloys on the basis of the free energy density functional method

Physics of the Solid State - The simulation of the decomposition of a three-dimensional fragment of a solid solution satisfying the regular solution approximation has been carried out based on the...     

Calculation of the mixing energy of alloys by the method of a model electron-density functional. Ni-Al system

Using a model electron-density functional the authors proposed earlier, calculations are performed for the ground state of alloys of the system Ni-Al to obtain characteristics such as mixing and ordering energies, equilibrium volumes per atom, and equilibrium charge transfers. The calculated results agree well with experimental data and make it possible to explain laws governing the formation of alloys of this system.Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 12, pp. 36–41, December, 1986.We thank E. G. Maksimov for his useful discussion of the results of our study and several valuable observations that were contributed.     

Density functional approximation for van der Waals fluids： based on hard sphere density functional approximation

A universal theoretical approach is proposed which enables all hard sphere density functional approximations (DFAs) applicable to van der Waals fluids. The resultant DFA obtained by combining the universal theoretical approach with any hard sphere DFAs only needs as input a second-order direct correlation function (DCF) of a coexistence bulk fluid, and is applicable in both supercritical and subcritical temperature regions. The associated effective hard sphere density can be specified by a hard wall sum rule. It is indicated that the value of the effective hard sphere density so determined can be universal, i.e. can be applied to any external potentials different from the single hard wall. As an illustrating example, the universal theoretical approach is combined with a hard sphere bridge DFA to predict the density profile of a hard core attractive Yukawa model fluid influenced by diverse external fields; agreement between the present formalism's predictions and the corresponding simulation data is good or at least comparable to several previous DFT approaches. The primary advantage of the present theoretical approach combined with other hard sphere DFAs is discussed.     

Nonlocal density functional theory of solids: Applications of the weighted density approximation to silicon

Using the density functional formalism together with the weighted density approximation (WDA), we have carried out selfconsistent bandstructure studies of bulk Si in order to identify the influences of different WDA potentials and different pair correlation functions on the electronic spectrum. Improvements of band energies due to consideration of nonlocalities in exchange and correlation energy depend very sensitively on the particular correlation function used. For the prototype semiconductor Si, only one of the six WDA versions tested seems useful.     

Calculation of the thermodynamic properties of the phases and analysis of their stability for the Ni-Al system in the model functional electron density method

We have calculated the thermodynamic properties of the ground state of the ordered and disordered phases in the Ni-Al system and a number of complex structures with noncubic symmetry within the framework of the model electron density functional method and the assumed calculation scheme for the multiparticle interatomic interaction potentials. The calculations which were done agree well with experimental data and allow one to explain the rules for alloy formation in this system.Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 4, pp. 100–110, April, 1996.     

Determination of the electron density at the Cu nucleus in Cu-Au alloys

The half-life of⁶⁴Cu in Cu–Au solid solutions has been measured as a function of the Cu concentration. Relative changes of electron densities (0)/(0) at the Cu nucleus are deduced. The observed nonlinear concentration dependence of (0)/(0) is discussed in terms of volume and charge transfer effects.     

Electron density and electron redistribution in alloys—II: Electron density in alloys and intermetallic phases

Electron density for alloys which have close-packed metallic structures is calculated by assigning valence electrons to octahedral and tetrahedral interstices, a method which has been previously used for elemental metals. Some localization of electron density is proposed for β -phases when there is considerable difference in ion core sizes. This method of characterizing electron density in alloys can be used to derive structures with the amount of electron transfer if an assumption is made for the volume fraction occupied by each component of the alloy. In general, the electronic structure of intermetallic phases appears to be dominated by the correspondence of a definite number of valence electrons with the number of interstices in the metallic structure (the Hume-Rothery $\text{e}\text{a}$ ratios). The model used can also accommodate electron distributions which include both ionic and covalent components of electron density. This is the case for Laves phases and the metallic A-15 compounds. There is a preponderance of intermetallic phases where one component is a d-shell metal. Evidence is presented that in several such alloys there is a change in d-shell configuration of the elemental metal which serves to minimize size differences of the ion cores of the alloy.