Calculation of enhancement factors for solute diffusion in the fcc dilute random alloy

In this paper, we address the enhancement of solute diffusion by solute addition. We focus on the little studied kinetic effect leading to solute enhancement arising from the kinetics of the encounter of a solute atom with a vacancy in the presence of other solute atoms. The study complements an earlier study by two of the present authors of the enhancement of the solvent diffusivity. In the present paper, the fcc random alloy model is employed at the dilute limit. We employ Monte Carlo techniques to calculate the solute diffusion enhancement factors B ₁ and B ₂. Solute correlation factors, upon which the enhancement factors rely in this model, are calculated to a very high precision using long runs and averaging over a very large number of atoms. There is fair agreement with the kinetic treatments of Manning and of Holdsworth and Elliott, and excellent agreement with the self-consistent theory of Moleko et al.     

Monte Carlo Simulation of Hard Hyperspheres in Six,Seven and Eight Dimensions for Low to Moderate Densities

The pair correlation function of hard hyperspheres in six, seven and eight dimensions is obtained from Monte Carlo simulations. The value of the pair correlation function at contact is compared with the results from molecular dynamics calculations and a variety of theoretical approaches. Remarkably good agreement is found with the simple, closed-form equations of Y. Song, E. A. Mason and R. M. Stratt, J. Phys. Chem., 93:6916–6919 (1989). The Monte Carlo results for the equation of state are compared with the theoretical expressions of M. Baus and J. L. Colot, Phys. Rev. A, 36:3912 (1987), M. Luban and J. P. J. Michels, Phys. Rev A, 41:6796 (1990), and high order virial expansions. In addition, in seven dimensions, comparisons are made with the exact PY solution provided by M. Robles, M. L. de Haro and A. Santos, J. Chem. Phys., 120:9113 (2004). Very good agreement was observed between theory and computer simulation in all dimensions.     

Properties of the finite-mass helium ground state

ABSTRACT

We describe a simple method of incorporating the finite mass of the nucleus directly into atomic variational Monte Carlo calculations. To test this algorithm we computed the energy and 20 other properties of ⁴He. We then compared these values with those obtained from our earlier infinite nuclear mass algorithm. All of our expectation values are in excellent agreement with previous results on this system.     

Description of the migration of a cation vacancy in mixed alkali-halide crystals having a common cation

For mixed alkali-halide crystals having a common cation (of the type KCl + KBr), a new equation is proposed for calculating the hopping diffusion coefficient of a cation vacancy. It is based on the concepts of probability theory and gives good agreement with numerical calculations by the Monte Carlo method. Fiz. Tverd. Tela (St. Petersburg) 41, 431–432 (March 1999)     

Calculating the low temperature vapour line by Monte Carlo

A combination of canonical and grand-canonical ensemble Monte Carlo calculations, together with the virial expansion, have been used to calculate the thermodynamic properties of the liquid/vapour co-existence curve of the (6 : 12) Lennard-Jones fluid for reduced temperatures, [Ttilde] ? 1·1. The results for the liquid density and energy and the latent heat of vaporization are believed to be precise, with the exception of the point at [Ttilde]=1·1 which may lie outside the range of the function fitting the liquid phase Monte Carlo data. The liquid density and the saturated vapour pressure are in very good agreement with the results of perturbation theory. The latent heat of vaporization does not agree well with the experimental data for argon though the fit to liquid density and internal energy is good.     

Comparison of Monte Carlo simulations and macroscopic theories of diffusion in systems with non-ideal sources and sinks for vacancies

A new concept of generation and annihilation of vacancies at non-ideal dense sources and sinks for vacancies is incorporated into the standard Monte Carlo model for vacancy-mediated diffusion. This model enables to treat the vacancy wind as well as the deformation of the specimen and the shift of the Kirkendall plane. The Monte Carlo model is used for testing the recent macroscopic theories of diffusion by Darken [Trans. Am. Inst. Min. Eng. 175 184 (1948)], Manning [Phys. Rev. B 4 1111 (1971)] and Moleko et al. [Phil. Mag. A 59 141 (1989)]. The agreement with the self-consistent Moleko et al. theory is excellent. On the other hand, the agreement with the classical Darken theory frequently used in the open literature for the explanation of the Kirkendall effect is rather poor.     

Diffusion kinetics of isolated and paired species: a Monte Carlo study

In this paper, we address a four-frequency diffusion model that allows diffusion of paired and unpaired atoms (or small molecular species) in an otherwise empty lattice. The model is useful for describing tracer and collective diffusion of interstitials in dilute interstitial solid solutions and of adsorbed species on surfaces. Diffusion kinetics of this model have been treated analytically by McKee, Le Claire and Okamura and Allnatt. We use Monte Carlo computer simulation to calculate, for the first time, the correlation factors and the linear solute diffusion enhancement factor. Absolute values of the tracer correlation factors and the linear enhancement factors are in excellent agreement with the results of the theory of Okamura and Allnatt, but only in semi-quantitative agreement with results of the other theory. A general argument is also presented to show that the chemical diffusion coefficient does not exhibit correlation effects. This is verified by computer simulation.     

The Limiting Kinetic Equation of the Consistent Boltzmann Algorithm for Dense Gases

This paper establishes a theoretical foundation for the Consistent Boltzmann Algorithm (CBA) by deriving the limiting kinetic equation. The formulation is similar to the proof by one of the authors that the Boltzmann equation is the limiting kinetic equation for Direct Simulation Monte Carlo [W. Wagner, J. Statist. Phys. 66:1011 (1992)]. For a simplified model distilled from CBA, the limiting equation is solved numerically, and very good agreement with the predictions of the theory is found.     

Equilibrium charge distribution on annealed polyelectrolytes

Monte Carlo simulations are used to study the non-uniform equilibrium charge distribution along a single annealed polyelectrolyte chain under θ solvent conditions and with added salt. Within a range of the order of the Debye length charge accumulates at chain ends while a slight charge depletion appears in the central part of the chain. The simulation results are compared with theoretical predictions recently given by Castelnovo et al. In the parameter range where the theory can be applied we find almost perfect quantitative agreement. Received 7 March 2002 and Received in final form 28 May 2002     

Theoretical study of keto–enol tautomerism by quantum mechanical calculations (the QM/MC/FEP method)

In this study, the tautomeric equilibrium between the keto and enol forms has been studied for five typical ketones and aldehydes: i‐butanal, acetaldehyde, acetone, acetylacetone, and dimedone. The level of theory used in the gas‐phase calculation was Becke, three‐parameter, Lee–Yang–Parr/6‐311G(d,p)//Becke, three‐parameter, Lee–Yang–Parr/6‐31G(d). The free energies of solvation were included in the calculation by using the free‐energy perturbation method based on Monte Carlo simulation, that is, the quantum mechanical/Monte Carlo/free‐energy perturbation method. Three different models, incorporating no‐water, one‐water, and two‐waters, were adopted. The results showed that in the gas phase the addition of water molecules to the reaction mechanism caused the activation barriers (ΔG^?_gas) to decrease by half relative to the water‐free mechanism, but there was no effect on the relative difference in free energy, ΔG_gas. The solvation effects (ΔG_sol), based on quantum mechanical/Monte Carlo/free‐energy perturbation calculations, were added to those of the gas‐phase results of the one‐water and two‐waters models. The two‐waters model produced values that were very consistent with the experimental data for all of the tautomers. The differences in the relative Gibbs free energy (ΔG_rxn) were less than 1.0 kcal mol^–1. In summary, the inclusion of solvent molecules in gas‐phase calculations plays a very important role in producing results consistent with experimental data. Copyright © 2012 John Wiley & Sons, Ltd.     

Estimate of the gluon condensate from Monte Carlo calculations

Using existing Monte Carlo data we estimate the value of the gluon condensate φ = 0|(β(g)/g)F_μν²|0. Given the limitations of the method and the available data we find reasonable agreement in both sign and magnitude with the value needed in QCD sum rule calculations.     

Ionization of sodium by the impact of alpha particle

A one channel distorted wave approximation has been used to calculate the ionization cross section for the 3s electron of Na atom by alpha particle impact. For a consistency check we have also run the standard CDW-EIS code of McSherry et al. [Comput. Phys. Commun. 155, 144 (2003)] and found reasonable agreement in the high energy region among the present results, the CDW-EIS results and the classical trajectory Monte Carlo (CTMC) calculations. It is also found that the present results tend to agree qualitatively with the low energy measurement of Knoop et al. [J. Phys. B 38, 1987 (2005)] at as low as 10 keV amu^-1, although the present theoretical approach is expected to be suitable in the high energy area. This qualitative agreement in the low energy region is attributed to the partially correlated ground state wave function used in the present calculation.     

On the low temperature anomalies in the properties of the electrochemical interface. A non-local free-energy density functional approach

The restricted primitive model has proved to be a useful system to describe the behaviour of electrical double layers. In this model, ions are represented by charged hard spheres of equal diameter and the solvent is represented by a uniform dielectric constant. Classical Gouy-Chapman's theory, and its modification by Stern, always predicts a monotonically decreasing capacitance for this system when the fluid's temperature is increased. Similar results are given by the mean spherical approximation. These predictions are in qualitative agreement with experiment for dissolved electrolytes, but disagree with molten salt experiments where capacitance increases with temperature. Additionally, recent Monte Carlo (MC) simulations for this model show that at very low temperatures, the capacitance of the interface, near its point of zero charge, increases with increasing temperature for both diluted and highly concentrated salts. In this work we apply a particular model of a non-local free-energy density functional theory to study the capacitance of the electrical interface. In our calculations we considered symmetrical 1:1 systems for both diluted electrolytes and highly concentrated salts at very low electrode surface charge. Density functional theory agrees very well with MC results for capacitance at high temperature, but fails to predict a positive slope for this property at low temperatures. Comparison of theoretical density profiles with MC results allows the exploration of possible causes of failure.     

Reflection approach for the analytical description of light ion implantation into bilayer structures

Abstract

One of the main problems while developing analytical multilayer models for ion implantation is how to make them ‘physical'. Satisfactory agreement between results obtained with existing multilayer models and the Monte Carlo prediction cannot always be expected, since mostly none of the important physical effects is accounted for. Extensive Monte Carlo study has been performed in order to extract some guiding principles for the construction of a more physically based multilayer model. Ion reflection accross the interfaces has a very strong impact on the final shape of a multilayer profile. First attempts to include this phenomenon in a multilayer model have been made. In this paper, a simple approach for light ion reflection at an interface is presented and the incorporation into a multilayer model is discussed.     

The symmetric heavy-light ansatz

The symmetric heavy-light ansatz is a method for finding the ground state of any dilute unpolarized system of attractive two-component fermions. Operationally it can be viewed as a generalization of the Kohn-Sham equations in density functional theory applied to N -body density correlations. While the original Hamiltonian has an exact Z₂ symmetry, the heavy-light ansatz breaks this symmetry by skewing the mass ratio of the two components. In the limit where one component is infinitely heavy, the many-body problem can be solved in terms of single-particle orbitals. The original Z₂ symmetry is recovered by enforcing Z₂ symmetry as a constraint on N -body density correlations for the two components. For the 1D, 2D, and 3D attractive Hubbard models the method is in very good agreement with exact Lanczos calculations for few-body systems at arbitrary coupling. For the 3D attractive Hubbard model there is very good agreement with lattice Monte Carlo results for many-body systems in the limit of infinite scattering length.     

A three-component model on the structure of colloidal solution with size-asymmetric electrolytes

ABSTRACT

A three-component model on the structure of colloidal solution with size asymmetric electrolytes is attempted here using density functional theory and Monte Carlo simulation. The solvent is represented as an individual component along with that as a dielectric continuum. The theory uses a weighted density approximation for the hard-sphere contribution to the free energy, whereas the ionic contribution is evaluated through a perturbation expansion around the bulk density. The theory is found to reproduce the simulation data quite well for a wide range of parametric conditions. The present study reflects the importance of the presence of the solvent in determining the structural behaviour of spherical double layers.     

Effects of thickness on the spin susceptibility of the two dimensional electron gas

Using available quantum Monte Carlo predictions for a strictly 2D electron gas, we estimate the spin susceptibility of electrons in actual devices taking into account the effect of the finite transverse thickness and finding very good agreement with experiments. A weak disorder, as found in very clean devices and/or at densities not too low, just brings about a minor enhancement of the susceptibility.     

Computer simulation of solute-enhanced diffusion kinetics in dilute fcc alloys

This paper describes a Monte Carlo study of the linear enhancement factor for the solvent tracer diffusivity in dilute fcc alloys. The model used is the well-known five-frequency model with isolated solute atoms. It is shown that the analytical treatments by Howard and Manning and by Ishioka and Koiwa have major shortcomings in their handling of correlation effects for certain combinations of the atom-vacancy exchange frequencies. Many of the values of the exchange frequency ratios that have been determined from experiment by way of these treatments are probably in some error.