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

D. A. Rowlands, A. Ernst, B. L. Györffy, and J. B. Staunton

Phys. Rev. B 73, 165122 – Published 21 April 2006

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-CPA). 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 energy) and chemical short-range order (SRO). 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.

Received 11 November 2005

DOI:https://doi.org/10.1103/PhysRevB.73.165122

Authors & Affiliations

D. A. Rowlands¹, A. Ernst², B. L. Györffy¹, and J. B. Staunton³

¹H.H. Wills Physics Laboratory, University of Bristol, Bristol BS8 1TL, United Kingdom
²Max Planck Institut fr Mikrostrukturphysik, Weinberg 2, D-06120 Halle, Germany
³Department of Physics, University of Warwick, Coventry CV4 7AL, United Kingdom

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Vol. 73, Iss. 16 — 15 April 2006

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Images

Figure 1
(Color online) (a) Total average DOS for disordered bcc ${Cu}_{50} {Zn}_{50}$ using both the SCF-KKR-CPA and the KKR-NLCPA (non-SCF) with $N_{c} = 2$ . Also shown are the contributions from the four possible cluster configurations measured at the first site—i.e., Cu for $Cu – Cu$ , $Cu – Zn$ and Zn for $Zn – Cu$ , $Zn – Zn$ . (Owing to translational invariance, measurement at the second site would give the same results with a simple reversal of the labels.) (b) Same as above but using the new self-consistent-field (SCF)-KKR-NLCPA. (c) Plot of the difference between the total SCF-KKR-CPA and total SCF-KKR-NLCPA results.Reuse & Permissions
Figure 2
(Color online) (a)–(c) KKR-NLCPA (non-SCF) $N_{c} = 2$ DOS calculations for disordered bcc ${Cu}_{50} {Zn}_{50}$ with decreasing values of the SRO parameter $α$ , corresponding to short-range ordering. (d)–(f) Same as (a)–(c) but using the new SCF-KKR-NLCPA.Reuse & Permissions
Figure 3
(Color online) (a)–(c) Further KKR-NLCPA (non-SCF) $N_{c} = 2$ DOS calculations for disordered bcc ${Cu}_{50} {Zn}_{50}$ with decreasing values of the SRO parameter $α$ , corresponding to short-range ordering. (d)–(f) Same as (a)–(c) but using the new SCF-KKR-NLCPA.Reuse & Permissions
Figure 4
(Color online) (a) SCF-KKR-NLCPA calculation for bcc ${Cu}_{50} {Zn}_{50}$ with $N_{c} = 2$ showing the core $3 p$ levels for the $Cu - Cu$ and $Cu - Zn$ components, plotted as a function of SRO. The lower figure shows the variation in the difference between the $Cu - Cu$ and $Cu - Zn$ components as a function of SRO. (b) Same as (a) but for the $Zn - Cu$ and $Zn - Zn$ components. (c) Plot of the total energy as a function of SRO for bcc ${Cu}_{50} {Zn}_{50}$ using the SCF-KKR-NLCPA with $N_{c} = 2$ . The conventional SCF-KKR-CPA result is also shown.Reuse & Permissions
Figure 5
(Color online) (a) SCF-KKR-NLCPA total DOS calculation with $N_{c} = 4$ for fcc ${Cu}_{60} {Pd}_{40}$ . Also shown are the non-SCF KKR-NLCPA and conventional SCF-KKR-CPA results. (b) Plot of the difference between the total SCF-KKR-NLCPA and SCF-KKR-CPA results shown in (a). (c) SCF-KKR-NLCPA total DOS calculation with $N_{c} = 4$ for fcc ${Cu}_{77} {Ni}_{23}$ along with the component contributions from the $2^{4}$ cluster configurations measured on the first labeled site. (Owing to translational invariance, measurement at any other cluster site would give the same results with a simple permutation of the labels.) Here $A = Cu$ and $B = Ni$ and components that are equivalent due to symmetry have been added together. The total SCF-KKR-CPA result is also shown. (d) Same as (c) but with $α = + 1.0$ , corresponding to ideal short-range clustering.Reuse & Permissions

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