Showing papers on "Coherent potential approximation published in 1970"

Paramagnetic Ni Cu Alloys: Electronic Density of States in the Coherent-Potential Approximation

Abstract: The coherent-potential approximation (CPA) is extended to study general band shapes and systems having orbital degeneracy. This permits its application to realistic systems, in particular the $\mathrm{Ni}\mathrm{Cu}$ alloys. The effects of alloying on a highly asymmetric model density of states characteristic of some of the features of the density of states in fcc transition metals are considered in detail. A model Hamiltonian for paramagnetic $\mathrm{Ni}\mathrm{Cu}$ is constructed using a basis of orthogonalized plane waves and tight-binding $d$ functions. Orbital degeneracy and hybridization are treated as in paramagnetic Ni. Effects of alloying are assumed to be restricted to the diagonal elemensts of the $d\ensuremath{-}d$ block. The model is applicable to the Ni-rich alloys, as is the approximation used to obtain simple solutions of the full CPA equations. The results are consistent with recent photoemission data on $\mathrm{Ni}\mathrm{Cu}$, and with the "minimum polarity" hypothesis used by Lang and Ehrenreich. They are incompatible with the rigid-band model because the scattering potential of the random alloy is strong compared to the peak widths. Rather than a rigid shift of the density of states, the calculated concentration dependence shows that the main peaks remain stationary while changing magnitude and shape. Decomposition of the total density of states into Ni and Cu contributions confirms that, for the expected position of the Fermi level, the $d$ holes are located primarily on Ni sites.

Application of the Coherent Potential Approximation to a System of Muffin-Tin Potentials

Abstract: The coherent potential approximation for the electronic density of states in a disordered substitutional alloy is applied in detail to a system of muffin-tin potentials. All expressions are formulated in terms of the phase shifts of the individual atomic scatterers. A simple example, illustrating a tight-binding system in which the pure constituents have different bandwidths, is discussed.

Electronic Transport in Alloys: Coherent-Potential Approximation

Abstract: The coherent-potential approximation, which has been successfully used to describe the electronic structure of a nondilute binary alloy ${A}_{x}{B}_{1\ensuremath{-}x}$, is reformulated in a diagrammatic way suitable for the calculation of more complicated transport coefficients. This approach is applied to the calculation of three elementary transport coefficients: the conductivity $\ensuremath{\sigma}$, the thermoelectric power $Q$, and the low-field Hall coefficient ${R}_{H}$. The appropriate response functions are evaluated for a simple cubic tight-binding model. The rigid-band limit is considered in detail, with emphasis on the role of critical points. As the random alloy potential increases, deviations from rigid-band behavior --- for example, Nordheim's rule --- become more pronounced for unexpectedly small scattering strengths. However, the usual relations among the transport coefficients, e.g., Mott's equation between $Q$ and $\ensuremath{\sigma}$, are maintained. The conductivity is no longer symmetrical with respect to electron and hole concentrations. Furthermore, the change in sign of $Q$ and ${R}_{H}$ may not occur when the band is half-full. Therefore, the identification of the carrier sign becomes ambiguous. For the model treated, numerical calculations are quite tractable. Examples are given which illustrate the behavior for a wide range of alloy parameters.

Band Structure of SiGe: Coherent-Potential Approximation

Abstract: The band structure of SiGe has been calculated using the coherent-potential approximation in conjunction with a realistic but local pseudopotential model. The effects of alloy disorder manifest themselves in complex band energies, each with an imaginary part inversely proportional to the electron lifetime. Spectral functions and the alloy denisty of states are also computed. The damping proves to be small, though it is not always given accurately by low-order-perturbation theory about the virtual crystal. Moreover, within the present local pseudopotential approximation, it affects only $s$ electrons capable of penetrating the ionic cores, since outside the core region the alloy pseudopotential is like that of either limiting pure crystal. The effect of the damping on experimental quantities such as the optical absorption and electrical resistivity is very small.

Electronic structure of disordered alloys: Optical and photoemission measurements on Ag-Au and Cu-Au alloys

Abstract: Optical and photoemission measurements on Ag-Au and Cu-Au alloys over the whole composition range are reported. It is found that for these alloys, which represent the situation in many binary alloy systems, neither the commonly used virtual crystal model (and thus not that of the rigid band), nor the independent band model describes the observed results. Calculations in the recently developed coherent potential approximation however reproduce the main features of the observed density of states for the alloys.

Optical Constants of Disordered Binary Alloys: Intraband Transitions in the Coherent-Potential Approximation

Abstract: The optical constants of disordered binary alloys ${A}_{x}{B}_{1\ensuremath{-}x}$ have been computed in the coherent-potential approximation for all frequencies, all $x$, and all reasonable scattering strengths, using a simple one-band model. Our results are compared with the classical Drude formula, and deviations are found stemming from critical points and the effects of alloying. In addition, the high-frequency behavior is shown to be dependent on the concentration $x$ and scattering strength in the alloy.

Indirect exchange in alloys of general composition

Abstract: A discussion is given of the Rudermann-Kittel interaction in binary alloys for a wide range of compositions. The authors extend earlier work (1969) in which was discussed the effect of spin-independent scattering of electrons on the indirect exchange. The coherent potential approximation is used as it is ideally suited to the Green function formalism of the earlier work. The important new feature appearing is an exponentially decaying factor that will cause a more rapid falloff in the range of the interactions than the normally assumed R-3 form.

Hall Effect and Or hi tal Magnetism of Binary Alloys

Abstract: The Hall conductivity and the orbital magnetic susceptibility in a weak magnetic field are calculated for binary alloys within the framework of coherent potential approximation. The model is the one of tight-binding limit with two kinds of atoms distributed at random over lattice sites. The atomic levels are assumed to be non-degenerate and the transfer energy is taken to be independent of the kind of atoms. The results show two characteristic features coexisting, one inherent to propagating Bloch electrons and the other to localized atomic electrons, depending on the composition and the difference of atomic energy.