Evaluation of isomorphous models of alloys

Faulkner, John; Moghadam, Nassrin Y.; Wang, Yang; Stocks, G. M.

doi:10.1103/physrevb.57.7653

Cited by 17 publications

(18 citation statements)

References 41 publications

(24 reference statements)

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“…84 As one can see from Fig. 5, the separation between the Cu and Zn d bands is of the order of the bandwidth and this is a case where a comparison between the CPA and the ''exact'' re- sults for the simple analytical models shows large discrepancies.…”

Section: A Density Of States For a Completely Random Alloymentioning

confidence: 96%

Applicability of the coherent-potential approximation in the theory of random alloys

Abrikosov

Johansson

1998

Phys. Rev. B

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The applicability of the coherent-potential approximation ͑CPA͒ for the description of electronic properties of completely random alloys is investigated. This is done by calculating the density of states and the total energy for different systems and by comparing the results with those obtained for large supercells consisting of up to 320 atoms in the framework of the order-N locally self-consistent Green's function method. Thereby it is found that in the framework of the CPA one obtains a reliable description of the electronic structure of random alloys. The total energy of a completely disordered alloy can also be reliably estimated provided an appropriate account is given for the electrostatic contribution to the one-electron potential and energy. Therefore, we conclude that the CPA can be safely applied to study the influence of disorder on various properties of metallic alloys for which the muffin-tin or atomic sphere approximation is sufficient and the chemical contribution to the total energy dominates. ͓S0163-1829͑98͒03122-1͔

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Section: A Density Of States For a Completely Random Alloymentioning

confidence: 96%

Applicability of the coherent-potential approximation in the theory of random alloys

Abrikosov

Johansson

1998

Phys. Rev. B

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“…This failure has stimulated many authors that envisaged CPA generalizations aimed to include the effects of different chemical environments. [42][43][44][45][46] In this paper, we define a class of approximations for DFT-based electronic theories in which most of the above CPA generalizations can be included. We shall refer to the approximations belonging to such a class as GCPA.…”

Section: A Generalized Coherent-potential Approximations For the Scamentioning

confidence: 99%

Coarse-grained density functional theories for metallic alloys: Generalized coherent-potential approximations and charge-excess functional theory

et al. 2008

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The class of the generalized coherent-potential approximations ͑GCPAs͒ to the density functional theory ͑DFT͒ is introduced within the multiple scattering theory formalism with the aim of dealing with ordered or disordered metallic alloys. All GCPA theories are based on a common ansatz for the kinetic part of the Hohenberg-Kohn functional and each theory of the class is specified by an external model concerning the potential reconstruction. Most existing DFT implementations of CPA-based theories belong to the GCPA class. The analysis of the formal properties of the density functional defined by GCPA theories shows that it consists of marginally coupled local contributions. Furthermore, it is shown that the GCPA functional does not depend on the details of the charge density and that it can be exactly rewritten as a function of the appropriate charge multipole moments to be associated with each lattice site. A general procedure based on the integration of the qV laws is described that allows for the explicit construction of the same function. The coarse-grained nature of the GCPA density functional implies a great deal of computational advantages and is connected with the O͑N͒ scalability of GCPA algorithms. Moreover, it is shown that a convenient truncated series expansion of the GCPA functional leads to the charge-excess functional ͑CEF͒ theory ͓E. Bruno et al., Phys. Rev. Lett. 91, 166401 ͑2003͔͒, which here is offered in a generalized version that includes multipolar interactions. CEF and the GCPA numerical results are compared with status of art linearized augmented plane wave ͑LAPW͒ fullpotential density functional calculations for 62 bcc-and fcc-based ordered CuZn alloys, in all the range of concentrations. Two facts clearly emerge from these extensive tests. In the first place, the discrepancies between GCPA and CEF results are always within the numerical accuracy of the calculations, both for the site charges and the total energies. In the second place, the GCPA ͑or the CEF͒ is able to very carefully reproduce the LAPW site charges and a good agreement is obtained also about the total energies.

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“…In the LSGF approach all the atoms in the supercell are different due to their different local environment while in the usual SS-DFT-CPA approach one deals only with average quantities, i.e., in terminology of the Ref. [35], the LSGF supercell approach is equivalent to the polymorphous model of the alloy while the effective-medium approach is equivalent to the isomorphous model. However, it is obvious, that this can be done on average.…”

Section: Net Charge and Madelung Potential In Metallic Alloysmentioning

confidence: 99%

“…Based on the fact, that a single impurity in a metallic host is a particular case of a dilute random alloy, one would expect, and the results for a single Cu impurity in Pt presented in the previous section unambiguously indicate this, that the screening effects in the two cases are similar. It is therefore surprising that Faulkner et al [35] and Ujfalussy et al [22] claim that the screening in a random alloy is qualitatively different from that found in a single impurity system. In fact, these authors found extremely long-range correlations between the Madelung potential at some particular site and the net charges at the other sites.…”

Section: Screening Charge In Metallic Alloysmentioning

confidence: 99%

Screened Coulomb interactions in metallic alloys. I. Universal screening in the atomic-sphere approximation

2002

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We have used the locally self-consistent Green's function (LSGF) method in supercell calculations to establish the distribution of the net charges assigned to the atomic spheres of the alloy components in metallic alloys with different compositions and degrees of order. This allows us to determine the Madelung potential energy of a random alloy in the single-site mean field approximation which makes the conventional single-site density-functionaltheory coherent potential approximation (SS-DFT-CPA) method practically identical to the supercell LSGF method with a single-site local interaction zone that yields an exact solution of the DFT problem. We demonstrate that the basic mechanism which governs the charge distribution is the screening of the net charges of the alloy components that makes the direct Coulomb interactions short-ranged. In the atomic sphere approximation, this screening appears to be almost independent of the alloy composition, lattice spacing, and crystal structure. A formalism which allows a consistent treatment of the screened Coulomb interactions within the single-site mean-filed approximation is outlined. We also derive the contribution of the screened Coulomb interactions to the S (2) formalism and the generalized perturbation method.

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Evaluation of isomorphous models of alloys

Cited by 17 publications

References 41 publications

Applicability of the coherent-potential approximation in the theory of random alloys

Applicability of the coherent-potential approximation in the theory of random alloys

Coarse-grained density functional theories for metallic alloys: Generalized coherent-potential approximations and charge-excess functional theory

Screened Coulomb interactions in metallic alloys. I. Universal screening in the atomic-sphere approximation

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