First-Principles Calculation of the Residual Electrical Resistivity of Random Alloys

Abstract

Results of numerical calculations of the electrical resistivity of the following primary solidsolution alloys are presented: Cu(Zn), Cu(Ga), Cu(Ge), Ag(Pd), and Ni(Mo). Our theoretical model is one reported earlier by Butler and uses a charge-self-consistent Korringa-Kohn-Rostoker coherent-potential approximation. The calculations are valid for strong as well as weak scattering, and for the first time, vertex corrections are included. Excellent agreement is obtained with experiment for the resistivity. PACS numbers: 72.10.Fk, 71.15.JfWe report here rigorous and realistic ab initio calcurequire the existence of well-defined quasiparticles. lations of the dc residual resistivity of random substi-We believe that the model is valid in the regime where tutional alloys. The calculations do not use adjustable the Boltzmann equation breaks down because energy parameters and they start with only the atomic bands are not defined. The model includes vertex numbers, the alloy concentrations, and the lattice corrections, and it properly treats the momentum maparameters as input. 1 The model is based on the trix elements. In this paper we discuss our results for Korringa-Kohn-Rostoker coherent-potential approxicopper-rich alloys of zinc, gallium, and germanium, mation (KKR-CPA) 2 and the one-electron Kubo forfor silver alloys containing palladium, and for nickel mula. 3 It goes beyond any previous model for deteralloyed with molybdenum. mination of transport properties of random alloys inThe dc electrical conductivity tensor in the onethat it is not limited to weak scattering and does not electron approximation can be written in the Kubo for-' malism as 1where the current operators are * e 9 • * e 9 ei\ * m 9r M m 8r v For a spherical nonoverlapping muffin-tin potential, the imaginary part of the Green's function can be expressed as 4 ImG(r,r',€ + ir\) G{t,x\z)~^XT™Xz)Z?{t mt z)Zl,(x' n ,z)for the complex energy z The point r is in unit cell m while the point r' is in cell n with r = R m + r m , where R m is the vector to the center of cell m (We consider, for simplicity only, one atom per unit cell) Zp(r m ,z) is the wave function of angular momentum L (= /,/x) centered on cell m which is regular at the origin and which satisfies the one-electron Schrodinger equation with the spherical muffin-tin potential and complex energy z The T^ is the scattering-path operator which propagates the electron from site m to site n taking into account scatterings at all possible sites.For a binary alloy of atoms A and 5, the potential site n depends on whether it is occupied by an A or B atom. To represent a real random system, we take a configurational average considering all possible arrangements of the two species on the fixed lattice and for the given concentration. We assume that the arrangements are completely random with no shortrange chemical order. We then carry out the configurational average within the CPA. The scattering-path operator r^ for a given configuration is replaced by T cnm (jfaQ scattering-path operator for the CPA ef...

Theory of electronic transport in random alloys with short-range order: Korringa-Kohn-Rostoker nonlocal coherent potential approximation

“…Below c = 0.3, the effect is negligible, whereas for larger concentrations, short-range order depresses the resistivity a little show- ing how the current is enhanced on a site when surrounded by unlike neighbors. Experimental measurements on Ag c Pd 1−c alloys find that annealing has a smaller effect 22,58 than in Cu c Zn 1−c in line with our calculations. It is also found that cold work causes little change to the resistivity suggesting that additional defects such as dislocations may already be present affecting the measurements.…”

“…Omission of the effect of the latter can lead to an underestimate of the conductivity. 21,22 Although in principle the recently developed SCF-KKR-NLCPA method 38 can provide the appropriate self-consistent one-electron charge densities and potentials, ␥ C ͑r I ͒'s and v ␥ C ͑r I ͒, for our transport calculations, in these first applications, we use those generated by the faster, simpler SCF-KKR-CPA method 4,5 in order to explore the new aspects of our theory.…”

“…Owing to the deviation of its resistivity from the common Nordheim ͓ ϳ c͑1−c͔͒ behavior 54 and to earlier extensive studies made of it, 16,22,55 the AgPd series of solid solutions provides the ideal initial test bed for our new method. We implement the formalism with NLCPA clusters containing four sites ͑N C =4͒ for this fcc based system.…”

“…Although the formal developments of this work followed Velický's quite closely, the use of a realistic single-electron muffin-tin Hamiltonian allowed connection with first-principles methods to be made. The method has been applied with success to a range of alloy systems 22,23 and it has also been successfully extended to the relativistic regime. 24 Of course, all of these calculations suffer from the main drawback of the CPA; namely, that as a single-site meanfield theory, it is incapable of incorporating the effects of local-environment fluctuations in the alloy crystal potential.…”

Non-collinear magnetoelectronics

“…To study transport, however, a configuration-averaged product of Green's functions hGG * i is required, a more formidable undertaking. Worked out by Butler [183] and applied to binary alloys in a single site approximation, the multiple-scattering theory implementation [184] of transport theory in the CPA gave results in very good agreement with experiment and later on with supercell calculations [185]. The application to more complex systems, however, appeared daunting.…”