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J. S. Faulkner - One of the best experts on this subject based on the ideXlab platform.

  • Electronic structure calculations on alloys using the polymorphous Coherent-Potential Approximation
    Physical Review B, 2004
    Co-Authors: S Pella, J. S. Faulkner, G. Malcolm Stocks, Balazs Ujfalussy
    Abstract:

    We present self-consistent calculations of the electronic density of states of disordered copper-palladium and silver-palladium alloys using the polymorphous Coherent-Potential Approximation and the Korringa-Kohn-Rostoker Coherent-Potential Approximation. We find that the agreement between the theoretical partial density of states of palladium $d$ bands in copper-rich copper-palladium alloys and experiment is significantly improved when the polymorphous Coherent-Potential Approximation is used. The densities of states of silver-palladium alloys calculated with the two versions of the Coherent-Potential Approximation are identical and agree with experiment. This indicates that the improved treatment of Coulomb effects in the polymorphous Coherent-Potential Approximation is necessary only for alloys such as copper palladium that have considerable charge transfer.

  • The mathematics of the polymorphous Coherent Potential Approximation
    Journal of Physics: Condensed Matter, 2001
    Co-Authors: J. S. Faulkner, Balazs Ujfalussy, Nassrin Y. Moghadam, G. M. Stocks, Yang Wang
    Abstract:

    The original Coherent Potential Approximation (CPA) used for calculating the electronic states in substitutional solid-solution alloys contains the implicit assumption that the alloy is isomorphous. That is, all of the atoms of a given chemical type are assumed to be identical. The extension of the CPA philosophy to treat an alloy model in which all of the atoms are allowed to have distinct charges and Potentials is called the polymorphous CPA (PCPA). This extension requires some interesting changes in the mathematical formalism that is used to develop the CPA equations. Aspects of the mathematical formalism of the PCPA will be discussed. In particular, the ergodic theorem from measure theory will be invoked to justify the new equations for the average Green's function.

  • Ergodicity in the polymorphous Coherent-Potential Approximation
    Physical Review B, 2001
    Co-Authors: J. S. Faulkner
    Abstract:

    The mathematical theory of ergodicity is used to clarify the derivation of the polymorphous Coherent Potential Approximation presented in a recent publication.

  • Calculating properties with the polymorphous Coherent-Potential Approximation
    Physical Review B, 2000
    Co-Authors: Balazs Ujfalussy, J. S. Faulkner, Nassrin Y. Moghadam, G. M. Stocks, Yang Wang
    Abstract:

    The formulas for calculating properties of an alloy such as the density of states, the charge density, and the Bloch spectral density function are derived from multiple-scattering theory for the polymorphous Coherent-Potential Approximation (PCPA). The chemical shifts obtained for three alloy systems using the PCPA, the Korringa-Kohn-Rostoker CPA, and the locally self-consistent multiple-scattering method are compared with experiment. A significant improvement in the treatment of Coulomb effects is achieved using the PCPA with only a little more computational effort than for the older isomorphous CPA's. (c) 2000 The American Physical Society.

  • Tests of the Polymorphous Coherent Potential Approximation
    Properties of Complex Inorganic Solids 2, 2000
    Co-Authors: J. S. Faulkner, Balazs Ujfalussy, Nassrin Y. Moghadam, G. M. Stocks, Yang Wang
    Abstract:

    The Coherent Potential Approximation (CPA) is a powerful mathematical technique for approximating the electronic structure of substitutional solid solution alloys. Most applications of the CPA to date have assumed an isomorphous model of the alloy in which all of the A atoms are assumed to be the same, as are all of the B atoms. The derivation of self-consistent Potentials for the alloys within the framework of the CPA and the isomorphous model leads inevitably to the conclusion that the Madelung Potential at each site must be zero. The approximate theory resulting from this derivation is called the KKR-CPA. The polymorphous CPA (PCPA) makes use of supercells that contain many atoms, and the Madelung Potentials at all of the sites are calculated exactly. PCPA calculations produce a polymorphous alloy model in which every atom in the supercell is different. Tests will be shown that demonstrate the advantages of the PCPA over the KKR-CPA in explaining experiments that depend critically on the charge transfer in an alloy.

D A Rowlands - One of the best experts on this subject based on the ideXlab platform.

  • Dynamical nonlocal Coherent-Potential Approximation for itinerant electron magnetism
    Journal of physics. Condensed matter : an Institute of Physics journal, 2014
    Co-Authors: D A Rowlands, Yu-zhong Zhang
    Abstract:

    A dynamical generalisation of the nonlocal Coherent-Potential Approximation is derived based upon the functional integral approach to the interacting electron problem. The free energy is proven to be variational with respect to the self-energy provided a self-consistency condition on a cluster of sites is satisfied. In the present work, calculations are performed within the static Approximation and the effect of the nonlocal physics on the formation of the local moment state in a simple model is investigated. The results reveal the importance of the dynamical correlations.

  • Reformulation of the nonlocal Coherent-Potential Approximation as a unique reciprocal-space theory of disorder
    Physical Review B, 2008
    Co-Authors: D A Rowlands, Xiaoguang Zhang, Antonios Gonis
    Abstract:

    The nonlocal Coherent-Potential Approximation (NLCPA) has recently been introduced for describing short-range correlations in disordered systems, for example short-range ordering e ects in alloys. As a generalisation of the widely-used Coherent-Potential Approximation (CPA), the NLCPA determines an e ective medium via the self-consistent embedding of a cluster with periodic Bornvon Karman boundary conditions imposed. Whilst this approach has the advantageous property of preserving the single-site translational invariance of the underlying lattice, it has recently been shown to yield spurious and non-unique results below some critical cluster size. In this paper we reformulate the NLCPA as a unique and systematic theory and show that the previous formalism is a specific limiting case of the new formulation. We explicitly demonstrate the theory for a one-dimensional tight-binding model in order to compare with exact numerical results.

  • Relativistic formulation of the Korringa-Kohn-Rostoker nonlocal Coherent-Potential Approximation
    New Journal of Physics, 2007
    Co-Authors: Diemo Ködderitzsch, D A Rowlands, Hubert Ebert, Arthur Ernst
    Abstract:

    The recently introduced Korringa–Kohn–Rostoker nonlocal Coherent-Potential Approximation (KKR-NLCPA) provides a sound basis for systematically including important environmental effects within an ab initio description of disordered systems. Here we propose a fully relativistic formulation of the KKR-NLCPA which is designed for the treatment of magnetically-ordered alloys. Crucial to its implementation is a reformulation of the basic algorithm and a symmetrization of the fundamental coarse-graining procedure, which we describe in detail. As a first application of the approach we study the electronic and magnetic properties of the ferromagnetic FePt system.

  • Investigation of the nonlocal Coherent-Potential Approximation
    Journal of Physics: Condensed Matter, 2006
    Co-Authors: D A Rowlands
    Abstract:

    Recently the nonlocal Coherent-Potential Approximation (NLCPA) has been introduced by Jarrell and Krishnamurthy for describing the electronic structure of substitutionally disordered systems. The NLCPA provides systematic corrections to the widely used Coherent-Potential Approximation (CPA) whilst preserving the full symmetry of the underlying lattice. Here an analytical and systematic numerical study of the NLCPA is presented for a one-dimensional tight-binding model Hamiltonian, and comparisons with the embedded cluster method (ECM) and molecular Coherent Potential Approximation (MCPA) are made.

  • korringa kohn rostoker nonlocal Coherent Potential Approximation
    Physical Review B, 2003
    Co-Authors: D A Rowlands, J B Staunton, B L Gyorffy
    Abstract:

    We introduce the Korringa-Kohn-Rostocker nonlocal Coherent-Potential Approximation (KKR-NLCPA) for describing the electronic structure of disordered systems. The KKR-NLCPA systematically provides a hierarchy of improvements upon the widely used KKR-CPA approach and includes nonlocal correlations in the disorder configurations by means of a self-consistently embedded cluster. The KKR-NLCPA method satisfies all of the requirements for a successful cluster generalization of the KKR-CPA; it remains fully causal, becomes exact in the limit of large cluster sizes, reduces to the KKR-CPA for a single-site cluster, is straightforward to implement numerically, and enables the effects of short-range order upon the electronic structure to be investigated. In particular, it is suitable for combination with electronic density-functional theory to give an ab initio description of disordered systems. Future applications to charge correlation and lattice displacement effects in alloys, and spin fluctuations in magnets amongst others, are very promising. We illustrate the method by application to a simple one-dimensional model.

Balazs Ujfalussy - One of the best experts on this subject based on the ideXlab platform.

  • Electronic structure calculations on alloys using the polymorphous Coherent-Potential Approximation
    Physical Review B, 2004
    Co-Authors: S Pella, J. S. Faulkner, G. Malcolm Stocks, Balazs Ujfalussy
    Abstract:

    We present self-consistent calculations of the electronic density of states of disordered copper-palladium and silver-palladium alloys using the polymorphous Coherent-Potential Approximation and the Korringa-Kohn-Rostoker Coherent-Potential Approximation. We find that the agreement between the theoretical partial density of states of palladium $d$ bands in copper-rich copper-palladium alloys and experiment is significantly improved when the polymorphous Coherent-Potential Approximation is used. The densities of states of silver-palladium alloys calculated with the two versions of the Coherent-Potential Approximation are identical and agree with experiment. This indicates that the improved treatment of Coulomb effects in the polymorphous Coherent-Potential Approximation is necessary only for alloys such as copper palladium that have considerable charge transfer.

  • The mathematics of the polymorphous Coherent Potential Approximation
    Journal of Physics: Condensed Matter, 2001
    Co-Authors: J. S. Faulkner, Balazs Ujfalussy, Nassrin Y. Moghadam, G. M. Stocks, Yang Wang
    Abstract:

    The original Coherent Potential Approximation (CPA) used for calculating the electronic states in substitutional solid-solution alloys contains the implicit assumption that the alloy is isomorphous. That is, all of the atoms of a given chemical type are assumed to be identical. The extension of the CPA philosophy to treat an alloy model in which all of the atoms are allowed to have distinct charges and Potentials is called the polymorphous CPA (PCPA). This extension requires some interesting changes in the mathematical formalism that is used to develop the CPA equations. Aspects of the mathematical formalism of the PCPA will be discussed. In particular, the ergodic theorem from measure theory will be invoked to justify the new equations for the average Green's function.

  • Calculating properties with the polymorphous Coherent-Potential Approximation
    Physical Review B, 2000
    Co-Authors: Balazs Ujfalussy, J. S. Faulkner, Nassrin Y. Moghadam, G. M. Stocks, Yang Wang
    Abstract:

    The formulas for calculating properties of an alloy such as the density of states, the charge density, and the Bloch spectral density function are derived from multiple-scattering theory for the polymorphous Coherent-Potential Approximation (PCPA). The chemical shifts obtained for three alloy systems using the PCPA, the Korringa-Kohn-Rostoker CPA, and the locally self-consistent multiple-scattering method are compared with experiment. A significant improvement in the treatment of Coulomb effects is achieved using the PCPA with only a little more computational effort than for the older isomorphous CPA's. (c) 2000 The American Physical Society.

  • Tests of the Polymorphous Coherent Potential Approximation
    Properties of Complex Inorganic Solids 2, 2000
    Co-Authors: J. S. Faulkner, Balazs Ujfalussy, Nassrin Y. Moghadam, G. M. Stocks, Yang Wang
    Abstract:

    The Coherent Potential Approximation (CPA) is a powerful mathematical technique for approximating the electronic structure of substitutional solid solution alloys. Most applications of the CPA to date have assumed an isomorphous model of the alloy in which all of the A atoms are assumed to be the same, as are all of the B atoms. The derivation of self-consistent Potentials for the alloys within the framework of the CPA and the isomorphous model leads inevitably to the conclusion that the Madelung Potential at each site must be zero. The approximate theory resulting from this derivation is called the KKR-CPA. The polymorphous CPA (PCPA) makes use of supercells that contain many atoms, and the Madelung Potentials at all of the sites are calculated exactly. PCPA calculations produce a polymorphous alloy model in which every atom in the supercell is different. Tests will be shown that demonstrate the advantages of the PCPA over the KKR-CPA in explaining experiments that depend critically on the charge transfer in an alloy.

Yang Wang - One of the best experts on this subject based on the ideXlab platform.

  • Applications of Coherent Potential Approximation to HEAs
    High-Entropy Alloys, 2016
    Co-Authors: Fuyang Tian, Yang Wang, Douglas L. Irving, Levente Vitos
    Abstract:

    This chapter details the Coherent Potential Approximation (CPA) to describe the chemically and magnetically disordered phases for systems of arbitrary number of components. Two widely used CPA implementations, namely, the exact muffin-tin orbitals (EMTO) and the Korringa–Kohn–Rostoker (KKR) methods, are briefly reviewed. Applications to predict lattice stability, electronic and magnetic structure, elasticity properties, and stacking fault energies of single-phase HEAs are presented.

  • The mathematics of the polymorphous Coherent Potential Approximation
    Journal of Physics: Condensed Matter, 2001
    Co-Authors: J. S. Faulkner, Balazs Ujfalussy, Nassrin Y. Moghadam, G. M. Stocks, Yang Wang
    Abstract:

    The original Coherent Potential Approximation (CPA) used for calculating the electronic states in substitutional solid-solution alloys contains the implicit assumption that the alloy is isomorphous. That is, all of the atoms of a given chemical type are assumed to be identical. The extension of the CPA philosophy to treat an alloy model in which all of the atoms are allowed to have distinct charges and Potentials is called the polymorphous CPA (PCPA). This extension requires some interesting changes in the mathematical formalism that is used to develop the CPA equations. Aspects of the mathematical formalism of the PCPA will be discussed. In particular, the ergodic theorem from measure theory will be invoked to justify the new equations for the average Green's function.

  • Calculating properties with the polymorphous Coherent-Potential Approximation
    Physical Review B, 2000
    Co-Authors: Balazs Ujfalussy, J. S. Faulkner, Nassrin Y. Moghadam, G. M. Stocks, Yang Wang
    Abstract:

    The formulas for calculating properties of an alloy such as the density of states, the charge density, and the Bloch spectral density function are derived from multiple-scattering theory for the polymorphous Coherent-Potential Approximation (PCPA). The chemical shifts obtained for three alloy systems using the PCPA, the Korringa-Kohn-Rostoker CPA, and the locally self-consistent multiple-scattering method are compared with experiment. A significant improvement in the treatment of Coulomb effects is achieved using the PCPA with only a little more computational effort than for the older isomorphous CPA's. (c) 2000 The American Physical Society.

  • Tests of the Polymorphous Coherent Potential Approximation
    Properties of Complex Inorganic Solids 2, 2000
    Co-Authors: J. S. Faulkner, Balazs Ujfalussy, Nassrin Y. Moghadam, G. M. Stocks, Yang Wang
    Abstract:

    The Coherent Potential Approximation (CPA) is a powerful mathematical technique for approximating the electronic structure of substitutional solid solution alloys. Most applications of the CPA to date have assumed an isomorphous model of the alloy in which all of the A atoms are assumed to be the same, as are all of the B atoms. The derivation of self-consistent Potentials for the alloys within the framework of the CPA and the isomorphous model leads inevitably to the conclusion that the Madelung Potential at each site must be zero. The approximate theory resulting from this derivation is called the KKR-CPA. The polymorphous CPA (PCPA) makes use of supercells that contain many atoms, and the Madelung Potentials at all of the sites are calculated exactly. PCPA calculations produce a polymorphous alloy model in which every atom in the supercell is different. Tests will be shown that demonstrate the advantages of the PCPA over the KKR-CPA in explaining experiments that depend critically on the charge transfer in an alloy.

Karol I. Wysokiński - One of the best experts on this subject based on the ideXlab platform.

  • Coherent Potential Approximation for 'd - wave' Superconductivity in Disordered Systems.
    Physical Review B, 1999
    Co-Authors: Andrew M. Martin, Grzegorz Litak, Balazs L. Gyorffy, James F. Annett, Karol I. Wysokiński
    Abstract:

    A Coherent Potential Approximation is developed for s–wave and d–wave superconductivity in disordered systems. We show that the CPA formalism reproduces the standard pair-breaking formula, the self-consistent Born Approximation and the self-consistent T-matrix Approximation in the appropriate limits. We implement the theory and compute Tc for s–wave and d–wave pairing using an attractive nearest neighbor Hubbard model featuring both binary alloy disorder and a uniform distribution of scattering site Potentials. We determine the density of states and examine its consequences for low temperature heat capacity. We find that our results are in qualitative agreement