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Showing papers on "Coherent potential approximation published in 1976"


Journal ArticleDOI
TL;DR: In this paper, a generalized perturbation method for disordered alloys is proposed, where the unperturbed state is taken to be the completely disordered state treated in the coherent potential approximation, and explicit formulae are given for the variations of the electronic energy and of the densities of states induced by partial long and short-range orders.
Abstract: Ordering effects in disordered alloys are studied by means of a generalized perturbation method. The unperturbed state is taken to be the completely disordered state treated in the coherent potential approximation. Explicit formulae are given for the variations of the electronic energy and of the densities of states induced by partial long- and short-range orders. The validity of the perturbation expansion is discussed in relation to the possible existence of a small parameter and the results are compared with those provided by the usual phenomenological models involving pair interactions.

290 citations



Journal ArticleDOI
Takeo Jo1
TL;DR: In this paper, the Hartree-Fock calculation combined with the coherent potential approximation is shown to give two magnetic states for Mn and Fe atoms in Ni-Mn and Ni-Fe alloys, respectively.
Abstract: The electronic structures of ferromagnetic Ni-Mn and Ni-Fe alloys are investigated theoretically. The Hartree-Fock calculation combined with the coherent potential approximation is shown to give two magnetic states for Mn and Fe atoms in Ni-Mn and Ni-Fe alloys, respectively. By introducing the ternary alloy picture in which Mn(Fe) atoms having antiparallel moments to the bulk magnetization are distinguished from Mn(Fe) atoms having parallel moments for a given Ni-Mn(Ni-Fe) alloy, the possibility of the coexistence of the two magnetic states is shown by an energy consideration. On the basis of the results obtained by this calculation, various magnetic properties are discussed.

76 citations


Journal ArticleDOI
TL;DR: In this paper, the role of charge transfer in the order-disorder transition of CsCl type structure transitional alloys such as VMn, TiFe and ScCo is investigated.
Abstract: Intra- and inter-atomic Coulomb interactions have been accounted for in the band theory of the order-disorder transition in binary alloys. The variation of the energy levels of the two kinds of atoms on the two sublattices is determined self-consistently using an extension of the coherent potential approximation (CPA). As an application, the authors investigate the role of the charge transfer in the order-disorder transition of CsCl type structure transitional alloys such as VMn, TiFe and ScCo.

36 citations


Journal ArticleDOI
TL;DR: In this paper, the coherent potential approximation (CPA) and the random phase approximation (RPA) were extended to the case of NiFe alloys and it was shown that D is very sensitive to the assumed exchange splitting in pure nickel and that within the RPA reasonable agreement with experiment is obtained only by assuming an unusually large value for this parameter.
Abstract: Previous numerical calculations for a model of nickel alloys, employing the coherent potential approximation (CPA) and the random phase approximation (RPA), are extended to iron alloys. It is shown that often the effective scattering potentials are sufficiently weak for a rigid band calculation of the spin wave stiffness constant D to be a good guide to the more elaborate CPA calculations. The case of NiFe alloys is re-examined in the light of a recent calculation by Riedinger and Nauciel-Bloch (ibid., vol.5, p.732 (1975)). It is shown that D is very sensitive to the assumed exchange splitting in pure nickel and that within the RPA reasonable agreement with experiment is obtained only by assuming an unusually large value for this parameter.

26 citations


Journal ArticleDOI
TL;DR: In this article, an effective medium theory is presented for the substitutionally disordered transverse Ising model above its transition, where the equations of motion for the relevant Green functions are decoupled in RPA.
Abstract: An effective-medium theory is presented for the substitutionally disordered transverse Ising model above its transition. The equations of motion for the relevant Green functions are decoupled in RPA. The disorder then occurs through a local parameter and can be treated in the spirit of the single-site coherent potential approximation. Fully self-consistent results are computed at the transition for the transition temperature, densities of states and spectral function. Simple features of the results can be understood using a generalized virtual-crystal approximation which accounts for damping due to disorder. Extensions of the theory to include intrinsic damping, more than one spin per unit cell and coupling to phonons are discussed.

22 citations


Journal ArticleDOI
TL;DR: In this paper, the density of states and local densities of states for ferromagnetic Ni-Cu alloys are calculated in the coherent potential approximation in the Hubbard model and the Hartree-Fock approximation is used.
Abstract: The density of states and local density of states for ferromagnetic Ni-Cu alloys are calculated in the coherent potential approximation. The Hubbard model is assumed and the Hartree-Fock approximation is used. The calculated densities of states for alloys are found to be strongly smoothened out by a rather large potential difference between Ni and Cu atoms. From the calculated results of the density of states, bulk and local magnetic moments and low temperature specific heat coefficient γ are calculated. Moreover, the high-field spin susceptibility at 0 K is calculated. These results are compared with the experimental ones and a qualitative agreement is obtained.

20 citations


Journal ArticleDOI
TL;DR: In this article, a theory of dynamical electron-electron correlation in a random A x B 1−x alloy is developed as an extension to the Kanamori model: two electrons in a narrow band, interacting via randomly varying contact pair interaction are considered.

17 citations


Journal ArticleDOI
TL;DR: In this paper, a system of rare-earth atoms with mixed valency is viewed as an alloy A1-nBn, where n denotes the probability of finding the rare earth atom in the state with valence three and (1 − n) is the probability that the rareearth atom is located at the other end of the spectrum.
Abstract: A system of rare-earth atoms with mixed valency is viewed as an alloy A1-nBn, where n denotes the probability of finding the rare-earth atom in the state with valence three and (1-n) is the probability of finding the rare-earth atom in the state with valence two. The coherent potential approximation (CPA) used in alloy theory is then applied to determine the d and f electron configuration in such systems. Thus, the various properties of systems with mixed valency can be determined. The theory also includes local environment effects. An explanation is offered for various properties observed for rare-earth compounds.

16 citations


Journal ArticleDOI
TL;DR: In this article, the averaged Green's function for an electron in non-simple liquid metals and alloys is evaluated in the tight-binding approximation (LCAO) when the effect of non-orthogonality and previously neglected diagonal terms are taken into account.
Abstract: The averaged Green's function for an electron in non-simple liquid metals and alloys is evaluated in the tight-binding approximation (LCAO) when the effect of non-orthogonality and previously neglected diagonal terms are taken into account. The actual formalism is given on the basis of self-consistent single-site approximations (SSSA)-particularly of the coherent potential approximation (CPA) for liquid metals and of the Ishida-Yonezawa theory. The averaged Green's function is well known to be related to one-electron properties such as the density of states and, within SSSA assumptions, even to the electric conductivity, the Hall coefficient, etc. Calculated densities of states with and without non-orthogonal terms are given for comparison and discussion.

15 citations


Journal ArticleDOI
TL;DR: In this paper, the Ioffe-Regel criterion for localisation is examined, and the coherent potential approximation is used to estimate the deviation of the density of states from a linear dependence on energy.
Abstract: The problem of an electron moving in a random potential in four dimensions is examined. It is argued that the apparent simplicity of the white-noise potential is due to an improper limiting process. It is demonstrated that localised states occur when finite ranged potential fluctuations are considered, and that they do not disappear as the range of the fluctuations gets shorter. The Ioffe-Regel criterion for localisation is examined, and the coherent potential approximation is used to estimate the deviation of the density of states from a linear dependence on energy.

Journal ArticleDOI
TL;DR: In this paper, the first nearest-neighbour exchange interaction was taken into account to calculate the electronic density of states in both the ferromagnetic and the paramagnetic phases of nickel-copper alloys.
Abstract: The coherent-potential approximation (CPA) has been employed to calculate the electronic density of states in both the ferromagnetic and the paramagnetic phases of nickel-copper alloys. The calculation takes into account in an approximate way the first nearest-neighbour exchange interaction, which is important in these alloys, the copper being nonmagnetic. The general satisfactory agreement with the available experimental data supports CPA as a good approach to the alloy problem.

Proceedings ArticleDOI
01 Jan 1976
TL;DR: The split-band model was used in this paper to explain the spin-down bands of f.c.c alloys and explain many of their properties, such as the anomalous Hall coefficient and magnetic resistivity.
Abstract: In concentrated alloys where the nuclear charges or exchange fields of the components differ sufficiently, the coherent potential approximation predicts that each alloy component has its own 3d band, having minimal overlap with the 3d bands of other components. As we pointed out earlier, this “split‐band model” applies well to the spin‐down bands of f.c.c. Ni‐Fe, Ni‐Fe‐Cu, etc., and explains many of their properties. For example, several physical quantities exhibit anomalies when the Fermi level eF crosses the boundary T between nickel and iron bands. A systematic search for b.c.c. iron‐base alloy series where the spin‐up band might be split, and where eF might cross a boundary T between bands, yields Fe‐V. As expected, the electronic specific heat coefficient γ of Fe‐V has a minimum when eF is at T, around 15 at % V. The electrical resistivity ρ, the slope ρ−1 dρ/dH, and the anomalous Hall coefficient Rs have sharp anomalies close by. The magnetoresistance Δρ/ρo is unusually large in Fe‐V. A scattering r...

Journal ArticleDOI
TL;DR: In this paper, the coherent potential approximation is applied to a study of the DC electrical conductivity at zero temperature of disordered ternary alloys, where a semielliptical density of states is used for numerical purposes.
Abstract: The coherent potential approximation is applied to a study of the DC electrical conductivity at zero temperature of disordered ternary alloys. In the model a semielliptical density of states is used for numerical purposes. The comparison between the conductivities of binary alloys and the corresponding, in some sense, ternary alloy is given as well as the discussion of the influence of the parameters describing ternary alloys on the DC electrical conductivity.

Journal ArticleDOI
TL;DR: In this paper, a coherent potential approximation of the electronic densities of states for V-Cr, Nb-Mo and Ta-W alloys is calculated in order to estimate the temperature dependences of the electrical resistivity R and the paramagnetic spin susceptibility χ.
Abstract: Electronic densities of states for V–Cr, Nb–Mo and Ta–W alloys are calculated in the coherent potential approximation. From these calculated results, temperature dependences of the electrical resistivity R and the paramagnetic spin susceptibility χ at high temperature are estimated. The calculated results are compared with experiments and a qualitative agreement is obtained. It is shown that the concentration variations of the temperature dependences in R / T and χ are strongly dependent on the shape of the density of states near the Fermi level.

Journal ArticleDOI
TL;DR: In this article, a model binary alloy AxB1-x which exhibits long-range order was considered, and the electronic transport was treated in the coherent potential approximation (CPA).
Abstract: A model binary alloy AxB1-x which exhibits long-range order is considered. The electronic transport is treated in the coherent potential approximation (CPA). The tensor of the electrical conductivity calculated from the Kubo-Greenwood formula depends on a long-range order parameter. The strongest dependence takes place for x=0.5. Also the numerical results indicate the possibility that the conductivity may increase or decrease with temperature according to alloy composition.

Journal ArticleDOI
TL;DR: In this paper, the excitations of the diluted anisotropic Heisenberg antiferromagnet are studied using the coherent potential approximation by extending previous work for the isotropic case.
Abstract: The excitations of the diluted anisotropic Heisenberg antiferromagnet are studied using the coherent potential approximation by extending previous work for the isotropic case. The excitations of the system are described in terms of an effective medium, which is self-consistently determined using the CPA condition to treat the scattering of a vacancy and its shell of neighbours coherently. The results of calculations for the density of states and for the spectral weight function are presented using values of the parameters appropriate to the system (Co1-xZnx)F2. Preliminary comparison with neutron scattering data is made and a brief discussion is given of analytical difficulties in this and other similar approximation schemes.

Journal ArticleDOI
TL;DR: The density matrix of an Ising model with quenched random interactions is written in terms of a translationally invariant effective Hamiltonian, Heff, with a random perturbation as mentioned in this paper.
Abstract: The density matrix of an Ising model with quenched random interactions is written in terms of a translationally invariant effective Hamiltonian, Heff, with a random perturbation Heff is determined by requiring, as in the coherent potential approximation, that repeated scatterings from a single site do not affect the partition function It is shown that Heff describes an annealed random system

Journal ArticleDOI
TL;DR: In this article, it is shown how the coherent potential approximation (CPA) can be extended to describe the properties of paramagnetic alloys, and the results presented here differ from those of the single impurity approximation.
Abstract: It is shown how the coherent potential approximation (CPA) can be extended to describe the properties of paramagnetic alloys. The properties of conduction electrons are discussed. Even at very low concentrations of magnetic impurities, results presented here differ from those of the single impurity approximation. As an example the temperature dependence of the resistivity of alloys in the s–d exchange model is analysed. For T much lower than the Kondo temperature, T2 behaviour of the resistivity is derived, which then goes through a more or less pronounced linear region to logarithmic dependence for temperatures higher than TK. Es wird die Koharent-Potential-Approximation erweitert, um die Eigenschaften paramagnetischer Legierungen beschreiben zu konnen, und es werden die Eigenschaften der Leitungselektronen diskutiert. Sogar bei sehr kleinen Konzentrationen magnetischer Verunreinigungen weichen die erhaltenen Ergebnisse von denen in der Approximation einfacher Storstellen ab. Als Beispiel wird im s–d-Austauschmodell die Temperaturabhangigkeit des spezifischen Widerstandes der Legierungen behandelt. Fur Temperaturen T viel kleiner als die Kondo-Temperatur TK wird ein T2-Verhalten des spezifischen Widerstandes erhalten. Bei hoheren Temperaturen schliest sich ein mehr oder weniger ausgedehnter linearer Bereich an, und dieser mundet fur T > TK: in eine logarithmische Abhangigkeit ein.

Journal ArticleDOI
TL;DR: In this article, an extension of the CPA technique is presented to account for the long-range order of atoms and/or antiferromagnetic solutions for simple cubic or body centred cubic crystallographic structures.
Abstract: An extension of the CPA technique is presented to account for the long-range order of atoms and/or antiferromagnetic solutions for simple cubic or body centred cubic crystallographic structures. Numerical calculations indicate that the influence of the ordering of atoms on the density of states is small for Fe1-xNix alloys. The electronic energy shows that the non-ordered state is favourable. For Cr in antiferromagnetic state is obtained with energy close to the energy of the paramagnetic state. For Cr0.5Fe0.5 alloy the minimum of the free energy corresponds to the fully ordered state, which is a non-magnetic one.

Journal ArticleDOI
TL;DR: In this article, an extended coherent potential approximation is applied to electron-phonon interaction in disordered binary alloys, and numerical calculations are performed for a stochastic tight-binding model including off-diagonal randomness in the additive limit.
Abstract: An extended coherent potential approximation is applied to electron-phonon interaction in disordered binary alloys. Numerical calculations are performed for a stochastic tight-binding model including off-diagonal randomness in the additive limit and results for the temperature dependence of the electronic self-energy and density of states are presented. The density of states can display in the minority band fine structure caused by combined impurity and electron-phonon scattering. The role of the phonon-modulated hopping integrals is discussed.

Journal ArticleDOI
TL;DR: The averaget-matrix approximation has been used to describe librons in mixtures of ortho-and para-hydrogen at T = 0 and low p-H2 concentrations.
Abstract: The averaget-matrix approximation (ATA) has been used to describe librons in mixtures of ortho- and para-hydrogen atT=0 and low p-H2 concentrations. The librons are treated within a harmonic approximation with coupling parameters fitted to the anharmonick=0 frequencies of Coll and Harris. It is shown that the spurious librational degrees of freedom at the p-H2 sites can be completely removed with the help of a hard core pseudopotential similar to that of Elliott and Pepper. The density of states and the density of states of thek=0 lines are calculated as a function of the p-H2 concentrationc p-H 2 forc p-H 2<0.20. The averagek=0 libron frequencies are compared with the experimental data of Hardy, Silvera and McTague. Finally, first numerical results for the density of states atc p-H 2=0.20 in the coherent potential approximation and the ATA which uses the virtual crystal approximation as a reference system are reported.

Book ChapterDOI
01 Jan 1976
TL;DR: Some basic terms used in catalytic literature will be defined and some examples of the experimental techniques (conventional and modern) will be presented in this article, where the authors also present an introductory lecture.
Abstract: In this introductory lecture some basic terms used in catalytic literature will be defined and some examples of the experimental techniques (conventional and modern) will be presented.

Journal ArticleDOI
TL;DR: A new CPA theory for spin waves in the diluted ferromagnet gave excellent results for the simple cubic nearest-neighbour case as mentioned in this paper, where the spin wave was generated by a spin wave generator.
Abstract: A new CPA theory for spin waves in the diluted ferromagnet gives excellent results for the simple cubic nearest-neighbour case.

Journal ArticleDOI
TL;DR: In this paper, a hierarchy of equations for conditionally averaged Green functions is derived for an isotopically disordered one-dimensional model of a mixed crystal and a definite single-site approximation leads to the random element isodisplacement model (REI-model).
Abstract: For an isotopically disordered one-dimensional model of a mixed crystal a hierarchy of equations for conditionally averaged Green functions is derived. A definite single-site approximation leads to the random element isodisplacement model (REI-model). This approximation is shown to be equivalent to a somewhat modified average t-matrix approximation (ATA) and, for a self-consistent formulation, to a somewhat modified coherent potential approximation (CPA). Fur ein isotopisch ungeordnetes Modell eines Mischkristalls wird eine Hierarchie von Gleichungen fur bedingt gemittelte Greensche Funktionen abgeleitet. Eine bestimmte Einzentrennahernng liefert das sogenannte REI-Modell. Es wird gezeigt, das diese Naherung einer etwas modifizierten t-Matrix-Naherung (ATA) bzw., fur eine selbstkonsistente Formulierung, einer etwas modifizierten NLherung des kohirenten Potentials (CPA) entspricht.

Journal ArticleDOI
TL;DR: In this paper, the coherent potential approximation has been generalized to incorporate the effects of the local environment in the energy spectrum of disordered alloys described by the simple tight-binding approximation, and the density of states has been calculated for a binary alloy AxB1-x having diamond lattice structure.
Abstract: The coherent potential approximation has been generalized to incorporate the effects of the local environment in the energy spectrum of disordered alloys described by the simple tight-binding approximation. The effective medium has been characterized by an effective local potential Sigma 1 and an effective hopping integral Sigma 2 between the nearest neighbours though the off-diagonal elements of the alloy Hamiltonian are not assumed to be disordered in the present calculation. The density of states has been calculated for a binary alloy AxB1-x having diamond lattice structure.

Journal ArticleDOI
TL;DR: In this paper, a new method based on the single-site coherent potential approximation (CPA) has been applied to a quantitative calculation of the low temperature Raman spectra of isotopically disordered KDP crystals.
Abstract: Recent experimental1 and theoretical2 work on mixed K(H1-x Dx)2 PO4 systems has offered new support for the coupled proton (deuteron) tunnelling-lattice polar optic mode model of KH2PO4 (KDP)-type ferroelectric.3 In a related theoretical study4, a new method based on the single-site coherent potential approximation (CPA) has been applied to a quantitative calculation of the low temperature Raman spectra of isotopically disordered KDP crystals. Although the formalism developed there is quite general, only the dynamics of the collective modes near q = 0, relevant to the Raman scattering has been explicitly investigated so far. The purpose of the present study is to extend these results to all wave vectors in the Brillouin zone in order to further test the consistency of the model and to estimate the effects of the shape of the proton-proton and proton-lattice couplings on the spectra of the collective modes. Furthermore, we hope that the results at q # 0 will stimulate the need for neutron scattering experi...

Journal ArticleDOI
TL;DR: In this article, a band theory of order-disorder transition in an AB alloy is studied using the locator formalism in the coherent potential approximation. And the influence of the difference in the band widths of A and B metals on the transition temperature is discussed.

Journal ArticleDOI
TL;DR: The generalized cluster expansion of the coherent potential approximation as applied to the case of a disordered binary alloy is discussed and extended to include the random off-diagonal elements of the Hamiltonian.

Journal ArticleDOI
TL;DR: In this article, a reinterpretation of nuclear relaxation data on a dilute ferromagnetic Ni0.98Pd0.02 alloy is made in the light of multiple scattering theory and the coherent potential approximation.
Abstract: A reinterpretation of nuclear relaxation data on a dilute ferromagnetic Ni0.98Pd0.02 alloy is made in the light of multiple scattering theory and the coherent potential approximation. The resultant value of the magnetic moment on the Pd site is higher than previous estimates using rigid band theory.