Coherent Potential Method Research Articles

Role of electronic structure in the formation of the properties and characteristics of interatomic interaction in alloys of iron with chromium and vanadium

In this work, the electronic structure and the magnetic state of Fe-Cr, Fe-V, and Fe-Cr-V alloys are investigated by the method of coherent potential in the approximation of Hartree-Fock. The effective fields on the nuclei of Fe of the ternary alloys are calculated using the results that have been obtained. The effective fields on Fe nuclei in Fe-Cr-V alloys have been experimentally measured. Comparison with the experimental results shows that the electronic and magnetic states of both the binary and ternary alloys are reasonably described by the coherent potential method. Analysis of the available results allows one to explain the differences existing in the phase diagrams of binary alloys as well as to reach conclusions about the shape of the equilibrium phase diagram of the ternary alloy.

Coherent potential method for a Heisenberg ferromagnet with nonmagnetic impurities

Coherent potential method for a Heisenberg ferromagnet with nonmagnetic impurities

Calculation of the scanning tunneling microscope image in the case of Cu(100)

The Tersoff and Hamann approach has been used in order to find the scanning tunneling microscope image in the case of the Cu(100) surface. In the derivation of the local density of states the generalized coherent potential method has been applied.

Some results from the radiative wave equation for a slab of random, densely-distributed scatterers

Using the ladder-approximated Bethe-Salpeter equation, the radiative wave equation for a slab of random, densely-distributed small spherical scatterers is constructed. The quasicrystalline approximation with coherent potential method is used for calculation of the effective propagation constant. The coherence of random scatterers is taken into account. The first and second-order bistatic scattering and transmission coefficients through the slab are obtained by iteration. Constructive interferences due to the boundaries are computed. The radiative wave equation for thermal emission from this slab is solved by a discrete ordinate method. Comparison with the independent scattering assumption in the conventional radiative transfer equation is discussed.

Cluster generalisation of the KKR coherent potential methods for random metallic alloys

A generalisation of the single-site KKR-CPA to include effects of clustering is presented here. The formalism combines the usual KKR ideas with the augmented space formalism introduced by the author.

Generalized coherent-potential method for disordered systems. II. Numerical results.

An elaboration and numerical study is presented for a coherent-potential-alloy (CPA) theory which gives the next step beyond the single-site CPA by including nearest-neighbor correlations. The theory includes all aspects of disorder including short-range order. Although the theory does not strictly have the Herglotz property, it gives physically reasonable results. Numerical results are presented for the electron density of states of binary alloys which show the effects of diagonal and off-diagonal disorder, nearest-neighbor correlations, shielding of the potential, and short-range order. Short-range order is shown to have the largest effect on the shape of the density of states.

Polarons by the coherent potential method

La methode du potentiel coherent dans la formulation du locateur est reformulee pour le calcul de la fonction de Green du polaron du reseau du a l'interaction locale d'un electron (exciton) avec des phonons de largeur de bande nulle. Le resultat est une bonne interpolation entre les limites resolubles. Consequences pour le spectre d'absorption des excitons dans les cristaux moleculaires

Coherent Potential Approximation of Short‐Range Order in Cluster Models of Alloys

AbstractIn cluster approximation of coherent potential method the density of electron states of transitional element alloys with short‐range order is obtained. On the base of these calculations the configurational part of the total energy is determined and the equilibrium value calculated of the short‐range order parameter on the first co‐ordination sphere. The obtained parameter of orderliness in most of the considered systems agrees by sign with the experimental data and qualitatively they depend on the concentration on the right way.

Multiple scattering of electromagnetic waves by random distributions of discrete scatterers with coherent potential and quantum mechanical formalism

An experimental observed fact in scattering of electromagnetic waves by dense distribution of discrete scatterers is that the assumption of independent scattering leads to overestimation of scattering effects. To account for this phenomenon in the present paper, the method of coherent potential is applied to the study of multiple scattering of electromagnetic waves by random distribution of discrete scatterers. Comparisons are made with results obtained by using the effective field approximation and the quasicrystalline approximation. Numerical results of the effective dielectric constant and the scattering attenuation rates, as a function of the fractional volume occupied by the scatterers, are illustrated using parameters frequently encountered in the microwave remote sensing of snow and soil moisture. It is shown that the coherent potential method as applied to quasicrystalline approximation is superior to the other approximations in accounting for the overestimation factor.

Coherent potential method in the theory of disordered alloys

Coherent potential method in the theory of disordered alloys

On self-consistent approximations for random anharmonic systems

A model with random 1-, 2-, and 3-point potentials is used to study the elementary excitations in substitutionally disordered crystals. The equations of motion for the 1- and 2-point Green's functionsG(1),G(12) are derived and averaged over the ensemble of random configurations. An extension of the coherent potential method is proposed, which leads to a self-consistent set of equations for the averaged 1- and 2-point Green's functions, including corresponding conditional averages. The theory takes into account that randomness effects the anharmonic interactions both via the explicit configuration dependence of the cubic vertices and via the implicit dependence through the Green's functions. The final equations take a similar form as in the usual CPA if the harmonic potential of the pure system and the harmonic single-site impurity potential are replaced by corresponding functionals of averaged and conditionally averaged 1- and 2-point functions, and the definition of the single-site mass-operator is appropriately generalized.

Investigation of valence band structures in Cu-Pd alloys

With the use of a HP 5950 A spectrometer X-ray photoelectron spectra (XPS) of valence band were obtained for Cu-Pd alloys and the density of electron states was calculated by the coherent potential method. It is found that d-resonance states of Pd are present in the alloys containing a high percentage of copper but there are no apparant d-resonance states of Cu in the alloys containing a high percentage of palladium.

Generalized coherent-potential method for disordered systems

A tractable way to generalize the coherent-potential method beyond the coherent-potential approximation (CPA) is presented. Explicit expressions are derived for a single-band tight-binding-approximation model including the correlations between first nearest neighbors. The potential change when one atom type is replaced by another at a given site is assumed to extend beyond that site so as to satisfy perfect shielding and include hopping-term variations. By considering the restrictions imposed by perfect shielding throughout the whole concentration range, two more conditions on the potential are found in addition to that corresponding to the Friedel sum rule. It is shown how to modify the CPA so as to satisfy perfect shielding. The main effect of this modification is to rigidly shift the CPA density-of-states curve so as to maintain the Fermi energy fixed for all concentrations. The modified CPA is limited in the possible number of physical alloys that it can hope to accurately describe. When the hopping perturbation is large, correlations between first neighbors are important and the CPA is not adequate.

Contribution to the Many Site Theory of the Disordered System

The extension of the single site CPA to the many site approximation is investigated in the cellular disordered crystal. The crystal is divided into cells and considered as if it were a `molecular crystal' composed of the cells. The single site CPA is applied to this `mixed molecular crystal.' The three types of the coherent potentials; A) the cell diagonal, B) the k -dependent, C) the site diagonal coherent potential are proposed and their properties are discussed. The approximation by the cell diagonal coherent potential is shown to be equivalent to the cell method reported previously by the author. The method of the site diagonal coherent potential is very simple and convenient for the numerical calculation. The phonon spectrum of the isotopically disordered chain is calculated by this method and compared with the result by NFC.

Cluster Expansion Method for the Density of Excited Electronic States of Substitutionally Disordered Crystals

In this paper we introduce a cluster expansion method which is suitable for numerical calculations of the density of electronically excited states of substitutionally disordered molecular crystals. This method is based on an expansion of the density of states of the guest subband in terms of the localized densities corresponding to various clusters and is valid for a large scattering potential and for concentrations of guest molecules below the percolation concentration. The general features of the cluster expansion method are illustrated by calculations for a simple one-dimensional molecular crystal. These numerical calculations for the one-dimensional model are compared with the results obtained by the coherent potential approximation. The role of the localized states, which are not accounted for by the coherent potential method can be elucidated.

Electronic States of a Liquid Metal from the Coherent-Potential Approximation

A treatment of the electronic states in a liquid metal based on the coherent-potential method is given. The equations for the coherent potential and the average Green's function obtained from the requirement that the average $T$ matrix is zero are shown to have as solutions certain expressions that were previously derived by Klauder from a different point of view. Connections with other work are mentioned.