Binary Substitutional Alloys Research Articles

Density of states and asphericity of electron distribution in ferromagnetic Co-Ni alloys

The coherent potential approximation has been extended in order to treat the case of multiple bands in ferromagnetic substitutional binary alloys. The concentration dependence of total magnetic moments and their aspherical contribution, e g and t 2 g , were derived and compared with experimental data in Co-Ni f.c.c. alloys.

Bethe—Peierls Approximation in the Electronic Theory of Disordered Materials

The effect of local environment on the total and partial densities of states of a disordered substitutional binary alloy is calculated within a Bethe---Peierls-type approximation. Compared to a molecular-field approximation, this method yields more precise results on the shape and structure of the alloy density of states.

Strong Correlations in Disordered Systems

The effects of strong correlations in a substitutional binary alloy ${A}_{x}{B}_{1\ensuremath{-}x}$ having a single nondegenerate tight-binding band are examined by use of the coherent-potential approximation and the alloy analogy of Hubbard to treat the effects of disorder and Coulomb interactions, respectively. It is shown that there are no ferromagnetic instabilities in the $B$ band for any band structure, carrier number and the concentration of $B$ atoms, if the potential at $A$ atomic sites are assumed to be positive infinite. This assumption causes the $A$ sites to be inaccessible to electrons. Moreover, the spin susceptibility is found to remain finite even if the density of states is vanishing at the Fermi energy in the limit of the half-filled $B$ band.

Many-Site Interactions and Correlations in Disordered Binary Alloys

An approximate method for obtaining the pair and higher-order correlation functions specifying the site-occupancy correlations in disordered substitutional binary alloys of arbitrary composition is described. The method is easily generalized from the usual pairwise interaction model to alloys with multi-site interactions. The value of $\frac{1}{z}$, where $z$ is the number of sites interacting with a given site, is used as a parameter of smallness to obtain a set of quasilinear equations which may be solved numerically for the correlation functions. The long range of the interatomic interactions found in many alloys would make $\frac{1}{z}$ seem a good expansion parameter. The validity of the solution is discussed. We use the method in a numerical analysis to investigate the effect of three-site interactions in a disordered face-centered-cubic binary alloy with a nearest-neighbor pair interaction and a nearest-neighbor-triangle triplet interaction. A simple analytic solution for a corresponding idealized meanfield situation is also carried out. An enlightening result is that the mean-field solution and the more realistic computer solution have similar general features. We also compare our solution with others for a choice of parameters in which comparison is possible.

Plastic flow in binary substitutional alloys of BCC iron-effects of wire drawing and alloy content on work hardening and ductility

The strength of cold-drawn, titanium-gettered iron wires can be substantially increased by substitutional solutes. For the elements studied, strengthening is progressively less in the order Si, Pt, Mn, Ni, Cr, and Co. The strengthening effect of the solute increases with strain, but at a greatly diminishing rate for true strains greater than unity. Six at. pct Si reduces the strain necessary to achieve a tensile strength of 200,000 psi (1380 MN/m2) from 7.3 for iron to 3.7. This effect of alloying on strain hardening appears to be related to the strength of the annealed alloy rather than to the specific alloying element used to achieve that strength. Also, the reduction-of-area ductility of the drawn wires is more closely related to the tensile strength of the wire than to its alloy content or degree of cold work. A fibrous cellular substructure is formed in all the alloys, but the formation of these cells is displaced to higher strains, the greater the strengthening effect of the solute. The transition from homogeneously distributed, tangled dislocations to a cellular substructure has no effect on the rate of strain hardening of the alloy-alloying can be used effectively as a substitute for cold work without adversely affecting the resistance of the alloy to ductile failure.

X-ray studies on Debye characteristic temperatures of disordered binary substitutional alloys

An expression has been derived for the Debye characteristic temperatures of disordered binary substitutional alloys in terms of the Debye characteristic temperatures of the component metals, concentration of the solute atom and an unknown parameter which can be found from the Debye characteristic temperature of the alloy at any particular concentration. Debye temperatures of polycrystalline specimens of copper, nickel and copper-nickel (20, 30, 40, 50, 60, 80 and 90% nickel by weight) alloys have been determined by X-ray diffraction methods. Intensities of different reflexions have been measured with the help of a highly accurate counter-diffractometer technique and corrected for temperature diffuse scattering, diffuse scattering due to random distribution of guest atoms in host sites and difference in sizes of different atoms (in case of alloys only) and incorrect background. Debye temperatures have been plotted against concentration and the variation has been compared with theoretical predictions. Experimental results are found to agree satisfactorily with the predictions obtained during the present investigations.

Single-site approximations in the electronic theory of liquid metals

The electronic structure of liquid metals is described by a multiple scattering formalism. Alternate methods based on a single site description of the liquid are developed and compared. The first method, the quasicrystalline approximation of Lax, is used to interpret and extend the work of Ziman and Anderson and McMillan. The second method, discussed here for the first time, extends the coherent potential theory of binary substitutional alloys to the liquid problem. Formally, this method is based on the introduction of a local self-energy operator associated with each site, and the subsequent self-consistent decoupling of the multiple scattering hierarchy. The lowest-order effects of one and two atom clusters are then discussed in connection with the expansion of the total scattering operator. It is shown that in the liquid, as in the alloy, these effects are treated more accurately by the self-consistent methods than by their non-self-consistent counterparts, the quasicrystalline and average t matrix approximations. It is in fact possible to establish a parallel between the self-consistent and coherent potential approximations on the one hand and the quasicrystalline and average t matrix approximations on the other. In the evaluation of second-order corrections to the work of Anderson and McMillan, unitarity requirements suggest an expansion in terms of the reaction matrix rather than the scattering matrix. This procedure treats the damping of electrons more carefully, eliminating spurious contributions. These formal considerations are illustrated by a calculation of the complex band structure and density of states for liquid Cu.

Theory of the zener relaxation strength. I

A fenomenological theory of the Zener relaxation strength is given, based on the Bethe-Peierls-Guggenheim approximation to the Ising model of a binary substitutional alloy. It is thought to be free of some of the weaknesses of former theories. This does not dissolve the serious discrepancies that exist between theory and experiment with regard to temperature and orientation dependence. There is shown to exist also an appreciable quantitative discrepancy. An extension of the theory is proposed.

Fine Structure of Electronic Spectra of Binary Substitutional Alloys in a Single‐Band Model

AbstractThe fine structure of the electronic density of states due to clusters of impurity atoms in disordered binary alloys is studied for a single‐band model with a short‐range random scattering potential. The sum of the n‐centre contributions to the total T‐matrix is obtained for n = 1, 2, 3. The T‐matrix describes the scattering corrections to an optimum one‐centre approximation which is determined self‐consistently in each case. For n = 1, the method is identical with the coherent potential approximation (CPA). Comparison of the results for n = 1 and n = 2 gives a criterion for validity of the CPA. A simple one‐dimensional model is studied numerically in the two‐centre approximation and the results are compared with the CPA and the direct solution for a finite chain.

Discussion of “plastic flow in binary substitutional alloys of bcc iron —effects of strain rate, temperature, and alloy content”

Discussion of “plastic flow in binary substitutional alloys of bcc iron —effects of strain rate, temperature, and alloy content”

The use of quantum green functions for the calculation of the frequency spectrum of the lattice vibrations of isotopic binary substitutional alloys. I

The paper derives a new method for the calculation of the frequency spectrum of isotopic binary substitutional alloys. The distribution of the admixture in the alloys is described by means of an operator field. Thus an equation for the quantum Green function in the form of functional derivatives can be formulated. In a purely analytical way two methods of successive approximations for the solution of this equation and the expansion in the form of a series in powers of the mass defect are deduced. In the second part of the paper an expansion of the solution in the form of a series of concentrations of the admixture is deduced and a more detailed discussion of the character of the frequency spectrum is performed.

Quantum Theory of the Equilibrium Order Parameters for Disordered Solid Solutions

Equations for the equilibrium order parameters of substitutional binary alloys are derived from both a classical (bond energy) and a quantum approach. The classical case is presented so as to exhibit that Cowley's equilibrium equations are not valid, principally as a consequence of an incorrect calculation of the internal energy. The work of Flinn is utilized to show that the equilibrium equations have the same form in the classical and the quantum cases. Moreover, the quantum approach is made practical by a simplification of certain integrals which Flinn was unable to evaluate. In both cases, a transition temperature for each atomic distance is found. With these developments, it is now possible to predict order parameters quantum mechanically and to test the predictions directly by x-ray measurements or indirectly by resistivity measurements via Asch and Hall's theory of residual resistivity. Numerical calculations required to compare experiment and theory have not been completed, but a presentation of the theory alone seems justified in view of the appearance of theses and papers based on Cowley's incorrect equations.

On the influence of volume effects on order-disorder transitions

Synopsis An attempt is made to study in a simplified model of a binary substitutional alloy the influence of the differences in atomic radii of the constituent atoms and in the potential energies of the various possible pairs of atoms. The theory is developed for linear, simple cubic, and body centred cubic lattices, and it is found that the order-disorder transition in the three-dimensional lattices can be either first or second order depending on the differences between the various potential energies. The results are applied to the case of -brass. The agreement of theory with experiment is as good as can be expected from a theory involving necessarily a large number of simplifying assumptions. The effect of lattice vibrations on our results is considered briefly.

Extreme frequencies of lattice vibrations for disordered binary alloys

The extreme frequencies of various branches of the spectrum for a binary substitutional alloy can be estimated by using a variational procedure. In particular, the maximum frequency of the optical modes can be determined approximately as a function of the various force constants and the composition.

A GENERAL THERMODYNAMICAL THEORY OF INTERNAL FRICTION (II) INTERNAL FRICTION IN ORDERED ANO DISORDERED STATES

The purpose of the present article is to calculate the internal friction of binary substitution-al alloys in different states of order by the application of the general thermodynamical theory of internal friction of linear type. To begin with, free energies are deduced for specimens under the action of a uniform stress, which, so far as the degree of order is concerned, is not in equilibrium. In this paper two mechanisms, the preferential distribution of atom-pairs and the change of degrees of short range order that give rise to the internal friction are suggested. In either case the internal friction is found to be proportional to the first and second power of (1-S), where is the degree of long range order. Thus, in the state of complete order, the internal friction would vanish, whereas it would be a maximum in the state of complete disorder. Theoretical results are in perfect accord with Nowick's data for the complete order in the Ag-Zn alloys and with the work of the Artman for the ordered states of β-brass. However, according to the theory, these experimental findings seem to indicate that it is the ordering pairs rather than the change of short range order that appear to be the cause of these two internal friction peaks.

Statistical Mechanics of Nearest Neighbor Systems

In many solids the intermolecular forces are sufficiently short ranged so that practically the entire potential energy of the system results from interactions between nearest neighbors. The thermodynamic properties of a solid with respect to a given coordinate, α, (for example, in a ferromagnetic system α might represent the excess unpaired electron spin at a given lattice point; or in a substitutional binary alloy α might denote which of the two possible kinds of atoms are at a given lattice point) can be found from the factor of the partition function which averages over all possible configurations of α at all lattice points. Here the evaluation of such a factor of the partition function is reduced to the calculation of the largest characteristic value of a linear homogeneous operator equation involving the potential energy between two adjacent layers of lattice points in the solid. By assuming that all possible configurations of a layer are equally probable, a lower bound for the partition function for a simple cubic lattice is found in terms of the partition function of a cube of eight molecules. The operator equation for a real crystal becomes quite complex, but in some problems it is possible to obtain characteristic vectors and characteristic values (and thus the partition function) at high and low temperatures. For intermediate temperatures a theory of resonance between the low temperature ``almost ordered'' characteristic vectors and the high temperature ``almost disordered'' characteristic vectors is developed. In cases where the operator equation can be solved for microcrystals a few layers thick, a perturbation method is discussed in which interactions between the individual microcrystals are treated as perturbations. Some remarks are made concerning phase transitions and finally the general theory is applied to a superficial treatment of two-dimensional ferromagnetic plates.