A contribution to the study of cluster interactions in binary alloys

An exact analytical expression for cluster interactions of a total band energy expansion is constructed. Previously introduced approximations are discussed and improvement upon them suggested.     

Interfacial contribution to cluster free energy

The Monte Carlo technique of “overlapping distributions” is used for computing directly the free energy difference F_{N + 1} ?F_N between two clusters containing respectively N + 1 and N solute atoms, in the square and the simple cubic Ising model with nearest neighbour interactions. High accuracy results are obtained within reasonable computer times. The capillarity approximation gives a good fit to the data, provided the following is taken into account: (i) the specific bulk and surface energies are given their macroscopic equilibrium values; (ii) a curvature correction to the surface specific energy has to be introduced: it is positive for two dimensions and negative for three dimensions; (iii) a size independent term is to be added in three dimensions; it may be viewed as a corner contribution; (iv) the coefficient of the logarithmic term is given its more recent value. When introduced in the master equation which describes the kinetics of the cluster population, within the simplifying assumptions of the classical nucleation theory, good agreement is found, for the shapes of the cluster size distributions, with the numerical experiments on the kinetic Ising model in two dimensions. However, the time scales of both computations do not match linearly. Possible reasons for this discrepancy are discussed.     

Simulation of the decomposition of binary alloys on the basis of the free energy density functional method

Physics of the Solid State - The simulation of the decomposition of a three-dimensional fragment of a solid solution satisfying the regular solution approximation has been carried out based on the...     

Proof of the existence of the cluster free energy

LetZ _p be the partition function over internal configurational degrees of freedom of ap-particle cluster. The existence of the limit, asp, of (p)^–1 logZ _p is demonstrated for the square, triangle, hexagon, simple cubic, face-centered cubic, and body-centered cubic lattice gas models, and for continuous space models with potentials satisfying stability and tempering conditions. Pairwise, finite-range bonding is assumed throughout.Supported in part by the Robert A. Welch Foundation.     

Surface concentration profile and surface energy in binary alloys

An improved formulation for the orientation-dependence of multi-layer surface segregation is developed in terms of bond enthalpy and strain energy minimization. Inclusion of this result in the Gibbs adsorption isotherm yields the surface energy. Sample calculations of the surface energy isotherm for solid AuCu and liquid CuNi alloys are in good agreement with published experimental data. The conditions for the existence of an extremum in the surface energy isotherm, originally derived by Defay et al. from a monolayer model, are re-examined on the basis of a multi-layer model. Their results are found applicable to this more general situation in the absence of strain energy. An orientation-dependence of the extremum surface energy, but not of the composition at which the extremum surface energy occurs, is demonstrated.     

Relative grain boundary free energy and surface free energy of some metals and alloys

By the method of thermal etching measurements were carried out of the ratio of grain boundary free energy _GB to the surface free energy _s in silver, copper, nickel, gamma-iron and cobalt of 99·999 pct. purity each, three copper-aluminium alloys and eight nickel-cobalt alloys, the total concentration of impurities in each alloy not exceeding 0·01 pct, as a function of the temperature and sometimes of the annealing medium.     

Correlation correction to the free energy for the ising model of a binary alloy

We consider correlation corrections to the free energy of the Ising model of a binary solid solution. The correlation free energy is represented in the form of a high-temperature series, in which only the leading terms in the parameter 1/z are retained, where z is the number of lattice sites inside the effective interaction sphere of the interatomic potential. In some cases the series can be assumed and an explicit formula can be obtained for the correlation corrections. As one of the consequences of our results, we obtain a correction to the mean field theory expression for the order-disorder transition point.Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 3, pp. 86–91, March, 1987.     

Final state core level binding energy shifts in binary alloys

The final state or relaxation contribution to core level binding energy shift is calculated for some noble metal/transition metal alloy systems, using the pseudopotential linear response method developed previously for pure metals. The core hole perturbation is described by an ab-initio pseudopotential. A basic parameter of the method is the homogeneous electron gas density for which, in the present case, a mean value between those corresponding to each pure metal is adopted. The final state contribution is generally found to be important and sometimes dominant. From the experimental core level shifts and the calculated final state shifts, some considerations about initial state contribution are given.     

Analysis of energy distributions for molecular and cluster secondary ions

Energy distributions of positive ion species sputtered from various target materials have been studied in terms of the exponent of N of E^?N in the high energy part. The N value of physically sputtered ion species had a linear relationship extending over a wide range of mass numbers for both homo- and hetero-nuclear molecules, while a trunk-branch relationship with the parent ion species was observed for chemically sputtered ion species. The same significant relationship was discovered for the rearranged experimental data obtained by others.     

Determinant formulas for matrix model free energy

The paper contains a new nonperturbative representation for the subleading contribution to the free energy of a multicut solution for a Hermitian matrix model. This representation is a generalization of the formula proposed by Klemm, Marino, and Theisen for a two-cut solution, which was obtained by comparing the cubic matrix model with the topological B-model on the local Calabi-Yau geometry \(\widehat{II}\) and was checked perturbatively. In this paper, I give a direct proof of their formula and generalize it to the general multicut solution.     

Vacancies in binary alloys: III. The energy of vacancy formation

A general expression for the energy of formation of a single vacancyE _F in substitutional binary alloys having two types of lattice sites is derived, which takes into account the interaction of neighbouring atoms. It is shown, that near the Curie temperature Θ the formation energy exhibits an anomaly.     

Orientation dependence of the solid/liquid interfacial free energy in binary systems

A first-order theory of compositional segregation at solid/liquid interfaces, based on a pair-bonded, lattice-liquid interfacial model, has been applied to predict the effect of segregation on the orientation dependence of the interfacial free energy in binary metallic systems. The results show that the sharpness of the cusps in the gamma plot is reduced due to preferential segregation at layer edges as compared to layer faces, and cusps may be eliminated under certain conditions. The reduction in cusp sharpness is the greatest when the composition difference of the solid and liquid phases is large and the solutions are appreciably non-ideal. The relative reduction of sharpness due to segregation is less pronounced for cusps which are sharper in the unsegregated condition, so segregation tends to smooth the form of the gamma plot. Graphical results are presented for calculation of segregational anisotropy effects in general systems.     

Vacancies in binary alloys

General expressions for the concentrations of divacancies and single vacancy-atom complexes in substitutional binary alloys is derived, using a model taking into account the interaction of neighbouring atoms as well as the interaction between vacancies and neighbouring atoms. The results of this paper are compared with those obtained with help of former theories, based on more restricted conditions.     

Free energy of quenched binary alloys and the time evolution of their structure function

An idea about the free energy of a binary alloy system under phase separation at low temperatures is discussed. Slow asymptotic decays in the structure functions for both a conserved and a non-conserved order parameter are studied.     

Local distribution approach to disordered binary alloys

We study the electronic structure of the binary alloy and (quantum) percolation model. Our study is based on a self-consistent scheme for the distribution of local Green functions. We obtain detailed results for the density of states, from which the phase diagram of the binary alloy model is constructed, and discuss the existence of a quantum percolation threshold.     

Electromigration in non-dilute binary alloys

This paper comments the recently published works on the electromigration in non-dilute binary alloys and gives a general analysis for calculating the effective valences $\text{Z}{}_{\mathrm{i}}{}^1$ of both components from experimental measurements. The proposed expressions for $\text{Z}{}_{\mathrm{i}}{}^1$ can be reduced to simple forms when Manning's expressions [5] for the phenomenological coefficients are used. These results allow us to calculate the effective valences of Silver and Gold in non-dilute Ag-Au alloys from Hofman and Guy's experimental data.     

Optical modes in binary alloys

The existence of a high-frequency, long-wavelength mode in a binary alloy is discussed on the basis of the fourth frequency moment of the correlation between concentration fluctuations.