Generalized Perturbation Method Research Articles

Effective cluster interactions at alloy surfaces and charge self-consistency: Surface segregation in Ni-10 at. % Al and Cu-Ni.

First-principles results are presented for the effective cluster interactions at the surface of a random Ni\char21{}10 at. % Al alloy. The derivation is based on an extension of the generalized perturbation method to semi-infinite inhomogeneous binary alloys, using a layer version of the Korringa-Kohn-Rostocker multiple-scattering approach in conjunction with the single-site coherent potential approximation to compute the self-consistent electronic structure of the system. When applied to the bulk, the method yields effective pair interactions that have the full point-group symmetry of the lattice to a very high level of numerical accuracy, despite the fact that intra- and interlayer couplings (scattering-path operators) are treated differently, and which are in perfect agreement with those of a recent three-dimensional treatment. Besides the pair terms, a selected class of triplet and quadruplet interactions are calculated, as well as the point interactions induced by the presence of the surface. The value of the latter in the first lattice plane is strongly exaggerated in our approach, leading to a complete segregation of the minority species to the surface. Using a value corresponding to the difference in the surface energies of the pure components for this term leads to the observed Al concentration of \ensuremath{\approxeq}25% at the surface. Possible reasons for the shortcomings of the theory are analyzed, and test calculations for the well studied Cu-Ni system show that the free energy of the semi-infinite alloy cannot be approximated by the sum over the single-particle band energies, once charge self-consistency is enforced at the surface.

First-principles study of stability and local order in bcc-based Fe-Cr and Fe-V alloys.

A parameter-free approach is applied to the study of the electronic structure properties and the local chemical order in Fe-Cr and Fe-V alloys. The method is based on a multiple-scattering description of the electronic-structure properties of the random alloys. Configurational order is treated within the generalized perturbation method, and temperature effects are examined with standard statistical methods, namely, the cluster-variation method and Monte Carlo simulations. In reasonable agreement with experiments, FeV exhibits a tendency toward order with a B2 superstructure in contrast to FeCr which shows an overall tendency toward phase separation around equiatomic composition. A more detailed study is performed for Fe-Cr alloys as a function of temperature and concentration, in the light of recent diffuse-scattering experiments. Finally, some conclusions are drawn regarding the structural transformation which occurs in both alloys from the bcc solid solution to a complex Frank-Kasper phase upon cooling.

Magnetism-induced ordering in two and three dimensions.

A first-principles theory of alloy ordering in two and three dimensions in the presence of ferromagnetism is described. Using the generalized perturbation method, the order-disorder transition from the bcc ${\mathrm{Fe}}_{50}$${\mathrm{Co}}_{50}$ random alloy into the ordered CsCl-structure FeCo alloy and its ordering temperature are found to agree reasonably well with available experimental data. A similar ordering tendency for the formation of the ordered c(2\ifmmode\times\else\texttimes\fi{}2) phase of the ${\mathrm{Fe}}_{50}$${\mathrm{Co}}_{50}$ surface alloy on fcc Cu(001) is investigated.

Superfluid density in inhomogeneous 4He with applications to thin films.

A general perturbative method for finding the zero-temperature superfluid density ${\mathrm{\ensuremath{\rho}}}_{\mathit{s}}$ in $^{4}\mathrm{He}$ in the presence of weak inhomogeneous external potentials is developed. The lack of translational invariance reduces ${\mathrm{\ensuremath{\rho}}}_{\mathit{s}}$ below the average mass density \ensuremath{\rho}\ifmmode\bar\else\textasciimacron\fi{}, leading to an inert, or normal, part, even at temperature T=0. A variational formula for 1-${\mathrm{\ensuremath{\rho}}}_{\mathit{s}}$/\ensuremath{\rho}\ifmmode\bar\else\textasciimacron\fi{} is given in terms of the density response function for uniform $^{4}\mathrm{He}$. Approximations lead to a result in terms of the uniform fluid structure factor and the single-atom effective mass. Explicit numerical predictions are given for thin $^{4}\mathrm{He}$ films adsorbed on ${\mathrm{H}}_{2}$ and other substrates.

Thermodynamics of the nickel-titanium system: A tight-binding-bond approach

Tight-binding electronic band structure calculations are combined with a free-energy expression from the cluster variation method to study phase equilibria in the Ni-Ti system. The effective pair interactions used in the cluster variation calculations are evaluated by means of the generalized perturbation method. The configurational entropy for disordered solutions and for ordered compounds are obtained using the tetrahedron approximation of the cluster variation method. A phase diagram is calculated and is found to be in good agreement with the experimental one.

First-principles study of surface segregation in Cu-Ni alloys.

A method coupling electronic structure calculations with Monte Carlo simulations has been developed to determine surface compositions in Cu-Ni alloys. The calculations are based on an effective Ising model with parameters as defined within the framework of the generalized perturbation method and as calculated by means of the tight-binding version of the linear-muffin-tin-orbital method. Properties of Cu-Ni bulk alloys are discussed in terms of bulk effective interatomic interactions. The composition profiles are obtained for the fcc (001) surface for three bulk compositions, namely, ${\mathrm{Cu}}_{75}$${\mathrm{Ni}}_{25}$, ${\mathrm{Cu}}_{50}$${\mathrm{Ni}}_{50}$, and ${\mathrm{Cu}}_{25}$${\mathrm{Ni}}_{75}$. The major role played by the layer-dependent site-diagonal terms in the Ising model is emphasized. Our results are found to be in agreement with available experimental data.

Effective cluster interactions using the generalized perturbation method in the atomic-sphere approximation.

We describe the generalized perturbation method in the atomic-sphere approximation (ASA) for calculating the effective cluster interactions. Based on our development of Korringa-Kohn-Rostoker coherent-potential approximation in the ASA [Singh et al., Phys. Rev. B 44, 8578 (1991)], the present approach is the next step towards developing a first-principles method that can be easily applied to describe substitutionally disordered alloys based on simple lattice structures as well as complex lattice structures with low symmetry. To test the accuracy of the ASA results, we have calculated the effective pair interactions (EPI) up to fourth-nearest neighbors for the substitutionally disordered ${\mathrm{Pd}}_{0.5}$${\mathrm{V}}_{0.5}$ and ${\mathrm{Pd}}_{0.75}$${\mathrm{Rh}}_{0.25}$ alloys. Our calculated EPI's are in good agreement with the respective muffin-tin results.

Origins of surface alloy formation: Cu(001)c(2 x 2)-Pd as a case study.

We present a rigorous theoretical treatment which, in agreement with recent experiments, supports the formation of the ordered c(2x2) phase of the CuPd surface alloy on the Cu(001) substrate, and does not support the formation of an ordered overlayer of only Pd atoms on such a substrate. Based on ab initio electronic structure of random CuPd and Pd-vacancy overlayers, we study their stability against ordering using the generalized perturbation method adapted to strongly inhomogeneous systems. The approach, the first of its kind, is general and can be applied to other metal-on-metal overlayers

Effective interatomic interactions in inhomogeneous semi-infinite systems.

The parameters entering the effective Ising model of disordered alloys with nonuniform composition at the sample surface are derived within the framework of the generalized perturbation method. The tight-binding version of the linear-muffin-tin-orbital method and its generalization to inhomogeneous alloys is used to describe the electronic structure in the local-density approximation, while the semi-infinite nature of the problem is included via the surface Green's-function approach. The method is applied to evaluate the site-diagonal terms of the Ising model as well as the effective interatomic interactions between sites within

Monte Carlo Simulations of Surface Segregation in Cu Ni Alloys

ABSTRACTA new method coupling electronic structure calculations with Monte Carlo simulations has been developed to determine surface compositions in Cu-Ni alloys. The calculations are based on an effective Ising model with parameters as defined within the framework of the Generalized Perturbation Method (GPM) and as calculated by means of the tight-binding version of the linear muffin-tin orbital method. The composition profiles are obtained for the fcc(OOl) surface for three bulk compositions, namely Cu75Ni25, Cu50Ni50, and Cu25Ni75 and compared with available experimental data.

Effect of Pressure on Order and Stability in Alloys: The Case of Al-Ge

ABSTRACTA parameter-free approach to phase stability in substitutional alloys is applied to the influence of pressure on order-disorder phenomena in Al-Ge. The methodology is based upon an application of the Generalized Perturbation Method to the Korringa-Kohn-Rostoker scattering formulation of the Coherent Potential Approximation. For fcc-based Al-Ge alloys, it is shown that the tendency towards phase separation at normal pressure originates from a structural difference between the pure species. By applying pressure, the structural energy difference is reduced, and a significant increase in the tendency towards order, especially for Al-rich alloys, is theoretically observed, leading, as an example, to the possible observation of a DO22 ordered state around 25 at. pct. Ge. The electronic origin of the ordering tendencies induced by pressure is discussed and the theoretical predictions are related to experimental facts.

Electronic Structure and Phase Stability Properties in Ternary Substitutional Alloys

ABSTRACTElectronic structure and stability properties of ternary-metal alloys are examined using an extension of the Coherent Potential Approximation -Generalized Perturbation Method approach within the Tight-Binding description of the chemically random alloy. In particular, we report on calculations of density of states, mixing energies and effective cluster interactions which build up the ordering energy. The study focuses on the Ti-V-Fe system and its binary components.

First-principles study of phase stability in Cu-Zn substitutional alloys.

A parameter-free approach to phase stability in Cu-Zn substitutional alloys is shown to describe order-disorder phenomena and structural transformations with remarkable accuracy. The method is based on a multiple-scattering description of the electronic structure properties of the random alloy. Configurational order is treated within the generalized perturbation method and the concentration-functional theory. Thermodynamical properties of \ensuremath{\alpha} and \ensuremath{\beta} brasses are derived from the cluster variation method. This advanced scheme is of general validity and is expected to yield similarly accurate results for other Hume-Rothery alloys.

Phase stability and short range order in magnetic transition metal alloys: I. Electronic structure and interplay between chemical and magnetic cluster interactions

The role of the interplay between magnetism and chemical order on phase stability and chemical short range order, in transition metal alloys, has been investigated by means of the generalized pertubation method. This method, we introduced previously for non-magnetic systems, is now extended to take account of itinerant magnetism. The electronic energy of any alloy configuration, characterized by a given atomic distribution and a given distribution of magnetic moments, is then determined from a rapidly convergent cluster expansion. In a first step, it is shown that for ferromagnetic alloys magnetism induces, through a very simple mechanism, the stability of most of the atomically ordered structures observed in alloys with magnetic transition metals (Cr to Ni). In a second step, the structure of the cluster expansion for antiferromagnetic alloys in the ground state and more generally for magnetic alloys at finite temperatures is discussed in the framework of itinerant magnetism in the static approximation. In this first paper devoted to magnetism and order in transition metal alloys, we show that the generalized perturbation method enables to define chemical and magnetic pair and multiatom interactions from the electronic structure. As a result of the angular dependence of the transfer integrals it is shown that a simple extension of the theory for non-magnetic alloys allows to derive the most important chemical and magnetic interactions coming from “d” bands; as in non-magnetic systems, these interactions do not correspond to the most compact clusters (triangles, tetrahedron, …) but to straight self-retraced paths. The pair approximation and the relative importance of the multiatom chemical and magnetic interactions are discussed in view of the numerical results obtained in a simple tight binding scheme for “d” bands. For fcc and bcc lattices, the hierarchy of the cluster interactions allows to understand, at least qualitatively, the nature and the origin of the observed antiferromagnetic ordered structures and of the multiple spin density waves observed in some transition metal alloys.

Electronic structure, alloy phase stability and phase diagrams

We review the relevance of electronic structure calculations to the determination of alloy phase stability and alloy phase diagrams. The Connolly-Williams method, the generalized perturbation method, the embedded cluster method and the method of concentration waves are presented and their main features are discussed and compared. The results of calculations of effective cluster interactions in substitutionally disordered alloys and of phase diagrams for specific alloy systems, e.g. PdRh, PdV and AlLi, are shown and work currently in progress is briefly described.

Ground State Searches in Fcc Intermetallics

ABSTRACTA cluster expansion is used to predict the fcc groutnd states, i.e., the stable phases at zero Kelvin as a function of composition, for alloy systems. TFile internetallic structures are not assumed, but derived rigorously by minimizing the configurational energy subject to linear constraints. This ground state search includes pair and multiplet interactions which spatially extend to fourth nearest neighbor. A large number of these concentration-independent interactions are computed by the method of direct configurational averaging using a linearizedmuffin- tin orbital Hamiltonian cast into tight binding form (TB-LMTO). The interactions, derived without the use of any adjustable or experimentally obtained parameters, are compared to those calculated via the generalized perturbation method extention of the coherent potential approximation within the context of a KKR Hamiltonian (KKR-CPA-GPM). Agreement with the KKR-CPA-GPM results is quite excellent, as is the comparison of the ground state results with the fcc-based portions of the experimentally-determined phase diagrams under consideration.

Statics of Phase Transformation in Ni-Al, Ni-Ti And Cu-Zn: a First Principles Study

AbstractWe show that the interplay between electronic structure properties, crystalline effects and local chemical order is quite distinct for Ni-Al, Ni-Ti and Cu-Zn, although they all exhibit a first order displacive transformation upon cooling from a high temperature partially ordered B2 phase. For this purpose, electronic structure and phase stability properties of these three alloys are investigated with a first principles approach. The study is based upon the Generalized Perturbation Method applied to the Korringa-Kohn-Rostoker multiple scattering description of the Coherent Potential Approximation, and temperature effects are taken into account within a generalized mean field approach.

Real Space Multiple Scattering Description of Alloy Phase Stability

ABSTRACTWe present a brief overview of the advanced methodology which has been recently developed to study phase stability properties of substitutional alloys, including order-disorder phenomena and structural transformations. The approach is based on the real space version of the Generalized Perturbation Method, first introduced by Ducastelle and Gautier, within the Korringa-Kohn- Rostoker multiple scattering formulation of the Coherent Potential Approximation. Temperature effects are taken into account with a generalized meanfield approach, namely the Cluster Variation Method. The viability and the predictive power of such a scheme will be illustrated by a few examples, among them: (1) the ground state properties of alloys, in particular the ordering tendencies for a series of equiatomic bcc-based alloys, (2) the computation of alloy phase diagrams with the case of fcc and bcc-based Ni-Al alloys, (3) the calculation of antiphase boundary energies and interfacial energies, and (4) the stability of artificial ordered superlattices.

Electronic properties of binary alloys through direct configurational averaging: Comparison with conventional methods.

Effective cluster interactions (ECI's) are calculated from electronic tight-binding Hamiltonians of random binary systems by the recently developed method of direct configurational averaging (DCA). The key issue addressed presently is the correspondence that DCA has to the conventional approach of the coherent potential approximation--generalized perturbation method (CPA-GPM) and the recently introduced Connolly-Williams method (CWM). Calculations obtained by DCA of ECI's and energies of ordering and of the disordered state are compared with analogous results of the CPA-GPM and the CWM. Since the definition of the ECI's and the philosophy of approach differ among the three methods, correspondence of the DCA formalism with the other two is also discussed. Convergence of DCA-obtained quantities is examined and general behaviors arising from random averaging are assessed.

Electronic Structure and Phase Stability Properties of Ai-Li Alloys

AbstractRecently, the phase diagram of AI-Li alloys was calculated with the use of the Connolly-Williams method. In an effort to test the validity and to supplement the results of that study, equilibrium lattice constants and effective cluster interactions have been obtained using the generalized perturbation method within the first-principles multiple-scattering formalism of the Korringa-Kohn-Rostoker coherent-potential approximation. The implication of these effective interactions to the phase stability of these alloys is discussed.