Method Of Concentration Waves Research Articles

Concentration wave method for description of all possible energy states of A2BC ordered alloy

The procedure for describing all possible energy states of an alloy based on the concentration wave method proposed by Khachaturian is employed to describe all possible energy states of ordered A 2 BC alloy based on N-dimensional lattice. Within the framework of this method, a complete enumeration of the structures obtained by the superposition of N plane concentration waves with all possible wave vectors is carried out, provided that the given stoichiometry is preserved. For each such superposition, the order parameters on the first I coordination spheres are calculated, thereby determining the point in the I-dimensional order parameter space corresponding to the given structure. For the case of I = 2 it is shown that a complete enumeration of all structures generated by one plane concentration wave fills a non-convex figure in the space of two order parameters.

Kinetic pathways of ordering and phase separation using classical solid state models within the steepest-entropy-ascent quantum thermodynamic framework

The kinetics of ordering and concurrent ordering and phase separation are analyzed with an equation of motion initially developed to account for dissipative processes in quantum systems. A reduced-order energy eigenstructure, or pseudo-eigenstructure, is constructed from a static concentration wave method to describe the configuration-dependent energy in a binary alloy. This pseudo-eigenstructure is used in conjunction with an equation of motion that follows steepest entropy ascent to calculate the kinetic path that leads to ordering and phase separation in a series of hypothetical alloys. By adjusting the thermodynamic solution parameters, it is demonstrated that the model can predict: (a) the stable equilibrium state, (b) the unique thermodynamic path and kinetics of continuous or discontinuous ordering, and (c) the kinetics of concurrent processes involving simultaneous ordering and phase separation.

Possible energy states of stoichiometric AB alloys based on fcc, bcc, and sc lattices

A simple computer algorithm is proposed to describe all possible energy states of stoichiometric alloys; its application is illustrated with AB alloys having fcc, bcc, and sc lattices. This algorithm is based on the concentration-wave method, which uses the rigid-sphere approximation and takes into account pair atomic interactions in the first few coordination spheres.

Thermodynamics of f.c.c.-Ni–Fe Alloys in a Static Applied Magnetic Field

Within the scope of the self-consistent field and mean (‘‘molecular’’) self-consistent field approximations, applying the static concentration wave method, the thermodynamics of f.c.c.-Ni–Fe alloys undergoing the static applied magnetic field effects is studied in detail. Under such conditions, the analytical corrections to expressions for the configuration-dependent part of free energy of macroscopically ferromagneticL12-Ni3Fe-type orL10-NiFe-type ordering phases are taken into account. The obtained results for thermodynamically equilibrium states are compared with the refined phase diagram for f.c.c.-Ni–Fe alloys calculated recently without taking into account the applied magnetic field effects. Considering the specific character of microscopic structure of the magnetic and atomic orders in f.c.c.-Ni–Fe alloys, the changes of shape (and in arrangement) of order-disorder phase-transformation curves (Kurnakov points) are thoroughly analysed. A special attention is addressed to the investigation of the concentration, temperature, and magnetic-field induction-dependent atomic and magnetic long-range order parameters, especially, near their critical points. As revealed unambiguously, influence of a static applied magnetic field promotes the elevation of Kurnakov points for all the atomically ordering phases that is in an overall agreement with reliable experimental data. On the base of revealed phenomenon, the magneto external field analog-to-digital converter of the monochromatic radiations (X-rays or thermal neutrons) is hypothesized as a claim.

Phase stability and ordering in diluted magnetic III–V semiconductors

We study the energetics of diluted ferromagnetic III–V semiconductors on an ab initio level using the tight-binding linear muffin-tin orbital–coherent potential approximation method and treating magnetic disorder within the disordered local moment model. Based on calculated total energies, we examine the stability of these alloys with respect to segregation and estimate formation energies of antisite defects and substitutional and interstitial Mn atoms. By using the generalized perturbation method, we calculate the parameters of an effective alloy Ising Hamiltonian including long-range Coulomb interactions. We investigate possible types of ordering, that is correlations of spatial positions of defects using the linearized concentration wave method and Warren–Cowley short-range-order parameters. The theory is illustrated for a GaAs alloy system.

Superordering of nonstoichiometric solid solutions. A basic B2 superstructure

A modified version of the statistical concentration wave method is used to predict ordered phases of nonstoichiometric composition with a basic B2 superstructure. An exhaustive list of predicted ordered phases is given, with their number being much larger than that obtained within the framework of the traditional statistical concentration wave method.

Concentration-wave analysis of atomic pair correlations disordered ternary alloys: Application to Cu 2NiZn

We outline the use of the method of concentration waves to analyze the atomic pair correlations in disordered ternary alloys. We present an analysis of the correlations in the disordered state of Cu 2NiZn calculated by first principles. The correlations in the disordered state are found to be a precursor to the partially-ordered state observed experimentally.

On the Problem of the Description of the Ordered Structures in Binary Solid Solutions with a Hexagonal Crystal Lattice

Within the framework of the static concentration-wave method, by means of the geometrically complete procedure, the list of all types of thermodynamically stable, with respect to macroscopic inhomogeneities (Lifshitz), ordered structures arising from the disordered state of binary substitutional solid solutions with a hexagonal crystal lattice is established, as is the list of corresponding isomorphic interstitial structures based on simple hexagonal and h.c.p. crystal lattices.

To the Problem of the Description of Ordered Structures in Binary Cubic Solid Solutions

AbstractWithin the framework of the static concentration wave method by means of the geometrically complete procedure a number of new types of ordered substitutional structures with the stoichiometric structural formulae AB, AB3, and A3B5, as well as of corresponding isomorphic interstitial structures, A2X, A4X, and A8X3 (A, B, and X are the types of atoms situated at sites and interstices, respectively) are established that complete the list of all thermodynamically stable with respect to the violations of macroscopic homogeneity (Lifshitz) ordered structures arising from the disordered state of f.c.c. and b.c.c. binary solid solutions.

Pseudotetragonal and orthorhombic ordered structures in substoichiometric YBa2Cu3O6+x oxides at x

The previous analysis [S. Semenovskaya and A.G. Khachaturyan, Phys. Rev. B 46, 6511 (1992); Physica D 66, 205 (1993)] of the structural transformations in nonstoichiometric YBa{sub 2}Cu{sub 3}O{sub 6+{ital x}} oxides is extended to a ``tetragonal`` stoichiometry region, {ital x}{lt}0.4. Available diffraction data [Th. Zeiske, D. Hohlwein, R. Sonntag, F. Kubanek, and G. Collin, Z. Phys. B 86, 11 (1992); Tan Kemin, Hu Meisheng, and W. Yening, J. Phys. Condens. Matter 1, 1049 (1989)] (on the {radical}2 {ital a}{sub 0}{times}2 {radical}2 {ital a}{sub 0} structures formed at small {ital x}{lt}0.4) are analyzed by the concentration-wave method and computer-simulation technique. It is found that at small {ital x}{lt}0.4, oxygen ordering results in a sequence of transformations different from those observed at {ital x}{gt}0.5. It produces the pseudotetragonal and orthorhombic ({l_brace}1/4 1) / 4 0{r_brace} phases formed by the (1/21/20) and ({l_brace}1/4 1) / 4 0{r_brace} concentration waves. These phases form a family of [110] oxygen-atom chain structures, which are different from the [010] Cu(1)-O chain structures formed at {ital x}{gt}0.5. These differences can be explained only if a significant change in oxygen-oxygen (O-O) potential near {ital x}{similar_to}0.4 (where the superconductivity disappears) is assumed. The O-O interaction potential at {ital x}{lt}0.4 wasmore » estimated and used to perform computer simulations of oxygen ordering kinetics at {ital x}=0.25.« less

Dynamic model of epitaxial growth in ternary III-V semiconductor alloys.

A concentration-wave method for several interpenetrating Bravais sublattices is presented by considering the intralayer and interlayer effective interactions and the difference between the surface layers and the deep layers of ternary III-V alloys. The most stable ordered structures of ternary III-V semiconductor alloys are deduced and a dynamic model for epitaxial growth is proposed. The present results are compared with the experimental observations, and the relations between interaction parameters are also given.

A Dynamic Model of III-V Ternary Semiconductor Alloys in the Epitaxial Growth

ABSTRACTA concentration wave method for several interpenetrating Bravais sublattices is presented by considering the intralayer and interlayer effective interactions and the difference between the surface layers and the deeper layers in III – V alloys. The ground state ordered structures of ternary III – V semiconductor alloys are deduced and a dynamic model is established.

Symmetry of the mixing Hamiltonian in lattices with a basis

To determine substitutional and injection superstructures in alloys having a complex lattice with a basis by the method of concentration waves it is necessary to know the eigenvectors of the Fourier transform matrices Vpq(κ) of the mixing potential of a homogeneous solid solution. A technique has been developed, investigating the variations of the matrix elements Vpq(κ) for symmetry transformations of the spatial lattice group, to solve this problem. The symmetry elements belonging to the wave vector group determine the internal structure of the matrices Vpq(κ) for lattices with a basis. Symmetry elements not appearing in the wave vector group determine the relation between matrices belonging to different rays of the star wave vector. Restrictions on the matrix elements Vpq(κ), following from symmetry, are found for an h.c.p. lattice. The eigenvectors are calculated for the matrices Vpq(κ), whose vectors terminate in high-symmetry points, lines, and planes of the Brillouin zone. This made it possible to separate the problem of thermodynamic competition of intermediate phases in an alloy with a hexagonal lattice into symmetric and potential parts, similarly to the way this occurs in Bravais lattices.

The long-range-order structures of III-V semiconductor alloys

The concentration wave method is used to determine the ordered structures appearing in the epilayers of III-V semiconductor alloys. Based on a two-dimensional planar model, possible ordered structures of zinc-blende structure are deduced. Some experimental features are explained. Phase diagrams of interaction parameters are given.

Pseudopotential calculation of thermodynamic properties and glass transition temperatures of binary Ni-Al alloys

The pseudopotential method and thermodynamic perturbation theory are applied to investigate the thermodynamics of Ni-Al alloys. The Einstein model approximation in the solid phase and the Percus-Yevick hard-sphere approximation in the liquid phase are chosen as reference systems. In all the calculations the local Animalu pseudopotential and the non-local pseudopotential with resonant contribution in the case of a transition metal are used. The static concentration-wave method is applied to investigate the ordering process in the solid phase. Taking charge transfer into consideration within the framework of the non-local resonant potential model, the authors have described the features of the main excess mixing characteristics and the dynamic viscosity in the liquid system studied. It is shown that in Ni50Al50 alloy the Kauzmann reduced temperature is higher than in pure Ni but insufficient for ready glass formation.

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.

Phase Transition in Rb3H(SeO4)2‐Type Crystals. I. The Symmetry Analysis of Proton Ordering

AbstractProton ordering is analysed at the phase transition in superionic crystals of the type Rb3H(SeO4)2. The method of concentration waves is applied. The observed ordering of protons is described using basis functions of the irreducible representations of the groups of wave vectors at the L and Γ points of the Brillouin zone. Possible directions of the crystallographic axes of the low‐temperature phase are determined in the framework of the approach proposed. The jump of entropy is calculated. The results obtained are in good agreement with experiment.

Using the method of concentration waves for examining diffusion and capture of hydrogen in defective media

Using the method of concentration waves for examining diffusion and capture of hydrogen in defective media

Phase stability by the artificial concentration wave method

The effect of system fluctuations on the stability of alloy phases has been addressed by Khachaturyan.(1) A thermodynamic analysis of stability and transformations considers the dominance of either the thermal energy or interaction energy. At low temperatures, the interaction energy dominates. The phase state present may either be ordered, disordered, or some mixture of ordered and/or disordered. A redistribution of atoms over the crystal lattice sites accompanied by lattice rearrangements, further complicates the ordering or decomposition. The ordering and decomposition states may be interpreted by the loss of stability of a disordered solution with respect to static concentration waves (SCW). The loss of stability with respect to concentration waves characterized by asymptotically small wave vectors generates a, so called, spinodal miscibility. The loss of stability with respect to concentration waves characterized by finite wave vectors leads to the order-disorder transformation. The wave vector may be represented as 2π/λ, where λ represents the repeat period of the wave, i.e. the scale of heterogeneity.

Ordering and decomposition in the high-temperature superconducting compound YBa2Cu3Ox.

The method of concentration waves is applied to structural transformations in superconducting Y-Ba-Cu oxide. The method predicts an ordering reaction that results in a tetragonal-to-orthorhombic phase transformation, and also yields the correct structure of the Y${\mathrm{Ba}}_{2}$${\mathrm{Cu}}_{3}$${\mathrm{O}}_{7}$ orthorhombic ordered phase. The results suggest that at low temperature the off-stoichiometric orthorhombic phase is thermodynamically unstable with respect to secondary decomposition into a mixture of ordered orthorhombic and disordered tetragonal phases, whose microstructure can be anticipated.