The coherent potential approximation is applied to a study of the DC electrical conductivity of substitutionally disordered off-diagonal binary and ternary alloys in the presence of phonons. The effect of strain on the temperature variation of the conductivity is also investigated. Superposition of thermal and off-diagonal disorder produces some effects not observed in the previous one-band theories.

http://iopscience.iop.org/0022-3719/11/2/014/pdf/0022-3719_11_2_014.pdf

Electronic transport in disordered alloys: effect of thermal and off-diagonal disorder

The coherent potential approximation is applied to a study of the DC electrical conductivity at zero temperature of disordered ternary alloys. In the model a semielliptical density of states is used for numerical purposes. The comparison between the conductivities of binary alloys and the corresponding, in some sense, ternary alloy is given as well as the discussion of the influence of the parameters describing ternary alloys on the DC electrical conductivity.

http://iopscience.iop.org/article/10.1088/0022-3719/9/23/011/pdf

Calculation of the DC electrical conductivity of the disordered ternary alloys

Spin‐disorder resistivity of ternary alloys in the CPA weak scattering limit

Within the framework of the coherent potential approximation the de electrical resistivity is calculted for random ternary substitutional magnetic alloys with partial atomic long-range order. The special case of nonmagnetic alloys with potential scattering only is included. The case of a two sublattice system with two long-range order parameters is studied. The spin-disorder contribution to the resistivity is treated using the s–d exchange model. The calculations are done for a single-band tight-binding model with diagonal disorder, three kinds of localized spins, arbitrary concentrations, and arbitrary order parameters. A general closed resistivity formula in terms of alloy, spin, and order parameters is given in second order of the scattering potential and is discussed for a number of special cases including antiferromagnetic ordering.



Im Rahmen der Naherung des koharenten Potentials wird der elektrische Gleichstromwiderstand fur ungeordnete ternare substitutionelle magnetische Legierungen mit partieller atomarer Fernordnung berechnet. Der Spezialfall nichtmagnetischer Legierungen mit alleiniger Potentialstreuung ist mit eingeschlossen. Es wird der Fall eines systems mit zwei Untergittern und zwei Fernordnungsparametern untersucht. Der Spin-Unordnungs-Anteil zum Widerstand wird mit dem s-d-Austausch-Modell behandelt. Die Rechnungen werden durchgefuhrt fur ein Einbandmodell mit starker Bindung, mit diagonaler Unordnung. drei Arten von lokalisierten Spins, beliebigen Konzentrationen und beliebigen Ordnungsparametern. Eine allgemeine geschlossene Formel fur den Widerstand als Funktion der legierungs-, Spin- und Ordnungsparameter wird in zweiter ordnungs in Streupotential hergeleitet und fur eine Anzahl von spezialfallen einschlieslich dem der antiferromagnetischen Ordnung diskutiert.

Statistical Theory of Electrical Resistivity of Magnetic Ternary Alloys with Partial Long-Range Order

A version of the coherent potential approximation is applied to study the density of states and the conductivity of binary and/or ternary alloys. A tight-binding one-band Hamiltonian including diagonal thermal and diagonal and off-diagonal substitutional disorders is used. The superposition of thermal and off-diagonal disorders produces some effects not observed in the previous one-band theories. The concentration dependence of the AuxAg1−x alloys density of states is calculated.



[Russian Text Ignored].

Effect of temperature on the off-diagonal alloy properties

The single-band model Hamiltonian used by Velick\'y, Kirkpatrick, and Ehrenreich (VKE) in their classic paper on the electronic theory of nondilute binary alloys is extended to the ternary-alloy case, and a number of results are derived. It is shown by direct calculation that the coherent-potential approximation (CPA) preserves the first seven moments of the density of states and the spectral density. Diagrammatic considerations put the highest moments at eight and seven, respectively. Exact information concerning the effective Hamiltonian leads via the Kramers-Kronig dispersion relation to a series of sum rules involving the self-energy. The localization theorem predicts the existence of two or three well-separated subbands for which the self-energy may have a pole between adjacent subbands. These singularities are also found in the CPA. Within the appropriate limits, all calculated quantities and various limiting behaviors (virtual crystal, dilute alloy, and the atomic limit), reduce to the binary-alloy results of VKE. A semielliptic reference density of states is used for a numerical presentation of the CPA description of the model ternary alloy. New numerical examples of the $\stackrel{\ensuremath{\rightarrow}}{\mathrm{k}}$-independent properties of the CPA are exhibited for the self-energy, the total density of states, and the partial densities of states, over a wide range of concentrations and scattering-potential strengths. Results are also displayed for the Bloch-wave spectral density. This $\stackrel{\ensuremath{\rightarrow}}{\mathrm{k}}$-dependent quantity provides information concerning the validity of describing the states of the disordered alloy in terms of quasiparticles with wave vector $\stackrel{\ensuremath{\rightarrow}}{\mathrm{k}}$.

James D. Chlipala

Papers

Single-band model of substitutional disordered ternary alloys in the coherent-potential approximation