Density functional theory for disordered alloys with short-range order: Systematic inclusion of charge-correlation effects

Abstract

For many years, density-functional-based calculations for the total energies of substitutionally disordered alloys have been based upon the Korringa-Kohn-Rostoker coherent-potential approximation ͑KKR-CPA͒. However, as a result of the single-site nature of the KKR-CPA, such calculations do not take into account important local environmental effects such as charge correlations ͑the Madelung energy͒ and chemical shortrange order ͑SRO͒. Here the above approach is generalized by combining the recently developed Korringa-Kohn-Rostoker nonlocal coherent-potential approximation with density functional theory, showing how these effects may be systematically taken into account. As a first application of the theory, total energy calculations for the bcc Cu 50 Zn 50 solid solution are presented, showing how the total energy varies as a function of SRO. The fcc Cu 60 Pd 40 and Cu 77 Ni 23 systems are also investigated.

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

“…In this paper, we have described a way to make quantitative calculations of the resistivity of disordered systems which possess short-range order or clustering. The ab initio theory starts from the density functional theory for these systems recently devised by Rowlands et al 38 using the SCF-KKR-NLCPA electronic structure method. Our first calculations for Cu c Zn 1−c and Ag c Pd 1−c show the expected decrease of resistivity when short-range order is imposed, whereas short-ranged clustering produces an increase.…”

“…37 and 38 In Ref. 38, in a generalization of the work of Johnson et al, 4,5 it is described how to specify a configurationally averaged electronic Grand potential ⍀ in terms of KKR-NLCPA quantities and charge densities ␥ C ͑r I ͒ and one-electron potentials v ␥ C ͑r I ͒ different for each cluster configuration. The functional minimization of ⍀ with respect to the charge densities, ␥ C ͑r I ͒'s, determines the total energy of the system and requires ␥ C ͑r I ͒'s and v ␥ C ͑r I ͒'s to be found self-consistently.…”

“…The functional minimization of ⍀ with respect to the charge densities, ␥ C ͑r I ͒'s, determines the total energy of the system and requires ␥ C ͑r I ͒'s and v ␥ C ͑r I ͒'s to be found self-consistently. Rowlands et al 38 applied this DFT to investigate how the total energy, charge densities, and densities of states are affected by SRO. Tulip et al 47 showed how further information can be found about the effects of SRO on the electronic structure by formulating and calculating the Bloch spectral function at the cluster momenta and averaged over tiles, while Batt and Rowlands 48 explained how the spectral function at any point in the Brillouin zone can be found.…”

“…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.…”

“…48 Given its ability to successfully address such issues and its proven incorporation into an electronic DFT 38 for disordered systems with SRO, it makes sense then to extend it to the calculation of transport properties. To this end, by invoking time dependent DFT 49 within the adiabatic approximation, in this paper, we present a formalism for the determination of the residual resistivity in the KKR-NLCPA and explicitly demonstrate the efficacy of the method through application to several realistic alloy systems.…”