Three-dimensional Lattice Gas Model Research Articles

Inhibition effect of low-temperature pre-irradiation of helium ions on the growth of helium bubble in stainless steel：a Monte Carlo simulation

Zhang Chong-Hong group has found that pre-irradiation of helium ions at low temperature with very low dose could effectively suppress helium bubble growth in materials. This experimental result lacks theoretical explanation. In this paper, we use Monte Carlo simulation to study the effects of different temperature modes on helium bubbles based on a three-dimensional lattice gas model under continued particle injection, and find that the phenomenon that pre-irradiation of helium atoms at low temperature can suppress the helium bubble growth occurs in simulation results as it does in the experiments. The reason is that small helium bubbles with high number density are produced by pre-irradiation at low temperature, and the high number density of bubbles controls the increase of sizes of helium bubbles.

Study on early stage of phase-separation process with low volume ratio using lattice gas model in three dimensions

The phase separation process in a three-dimensional lattice gas model with a low volume ratio c=0.01 was studied. Using Monte Carlo simulation, the evolution behaviors of sc, fcc, bcc lattices, and 5 relative temperatures T/Tc=0.450.85 were simulated. It was found that the structure factor functions did not satisfy the scaling relationship, and the growth index was 1/6, less than the value of Lifshitz-Slyozov theory.

An energy landscape model for glass-forming liquids in three dimensions

We present a three-dimensional lattice-gas model with trivial thermodynamics, but non-trivial dynamics. The model is characterized by each particle having its own random energy landscape. The equilibrium dynamics of the model were investigated by continuous time Monte Carlo simulations at two different densities at several temperatures. At high densities and low temperatures the model captures the important characteristics of viscous liquid dynamics. We thus observe non-exponential relaxation in the self part of the density auto-correlation function, and fragility plots of the self-diffusion constant and relaxation times show non-Arrhenius behavior.

Decoupling-coupling of rotations as a mechanism of glass transition

We introduce a three-dimensional lattice gas model to study the glass transition. In this model the interactions come from the excluded volume and particles have five arms with an asymmetrical shape, which results in geometric frustration that inhibits full packing. Each particle has two degrees of freedom, the position and the orientation of the particle. We find a second order phase transition at a density $\rho\approx 0.305$ , this transition decouples the orientation of the particles which can rotate without interaction in this degree of freedom until $\rho = 0.5$ is reached. Both the inverse diffusivity and the relaxation time follow a power law behavior for densities $\rho\le 0.5$ . The crystallization at $\rho = 0.5$ is avoided because frustration lets to the system to reach higher densities, then the divergencies are overcome. For $\rho > 0.5 $ the orientations of the particles are coupled and the dynamics is governed by both degrees of freedom.

Three-dimensional hydrodynamic lattice-gas simulations of ternary amphiphilic fluids under shear flow

We describe the implementation of shear flow in a three-dimensional lattice-gas model for amphiphilic fluids. We investigate the effect of shear on the morphology of the bicontinuous ternary microemulsion phase, and in particular its effect on the formation and stability of a lamellar phase. Metastable lamellar phases were observed for both 32(3) and 64(3) systems subjected to shear, and the stability of preformed lamellar phases under shear flow established for both 64(3) and 128(3) systems. The effect of micellization on interfacial behaviour in these phases is discussed in the context of the linear non-equilibrium thermodynamic theory of rate processes and nonlinear Becker-Döring aggregation theory.

Cosegregation-Induced Formation of Two-Dimensional Surface Compounds on Multicomponent Alloy Surfaces

The chemical composition of multicomponent alloy surfaces may exhibit significant deviations from the bulk composition due to thermally activated segregation and cosegregation processes. In many systems cosegregation phenomena result in the formation of two-dimensional surface compounds such as CrN on Fe-15% Cr-N(100), VC on Fe-3% V-C(100) and on Fe-3% Si-0.04% V-C(100), and TiC on Fe-6% Al-0.5% Ti-C(100). These surface compounds are epitaxially stabilized on the bcc(100) alloy surfaces, their thicknesses are about one or two atomic layers. In the present work we report results of a Monte Carlo study on the cosegregation-induced formation of surface compounds on bcc(100) surfaces. The simulations are performed utilizing a three-dimensional lattice gas model with two free (100) surfaces and periodic boundary conditions in x and y directions. It is assumed that the lattice consists of two types of lattice sites M and X. The metal sites M form a body-centered cubic (bcc) lattice, whose quasi-octahedral interstices constitute the nonmetal sublattice. The M sites are accessible to either M A or M B atoms, while the nonmetal sites either are occupied by X atoms or remain empty. Pairwise repulsive nearest and attractive next nearest neighbor interactions between M A -X and M B -X atoms are considered as well as up to fourth nearest neighbor X-X repulsions. The simulations indicate that cosegregation-induced formation of the surface compound M B X is basically due to preferential next nearest M B -X neighbor attractions. With an increase of the strength of the preferential next nearest M B -X attractions, surface compound formation is accompanied by a first-order phase transition. Depending on the relative magnitude of the nearest neighbor M-X repulsions, we observe a strong M B subsurface enrichment, which has been verified by XPD for the CrN surface compound on Fe -15% Cr-N(100). For repulsive fourth nearest X-X neighbor interactions, our lattice gas model shows c(2x2) ordering of the X atoms on the bcc(100) surface.

Existence of enantiomeric phase separation in a three-dimensional lattice gas model

A three-dimensional lattice gas model for enantiomeric phase separation is introduced. The enantiomeric molecules (d andl) are the two nonsuperimposable mirror images having the molecular structure C(AB)2, where C is a tetrahedrally bonded carbon atom with one bond to each end of two AB groups. The lattice gas model consists of a body-centered cubic lattice, each site of which can be either vacant or occupied by a molecule oriented so that the A and B groups point toward neighboring lattice sites. Pairs of molecules interact with short-range, orientationally-dependent interactions. For a domain of interaction parameters, the Pirogov-Sinai extension of the Peierls argument is used to prove thatd-rich andl-rich phases exist in the model at sufficiently low temperature. For another domain of interaction parameters, at sufficiently high chemical potential there is an infinite number of ground states, each containing a racemic mixture ofd andl molecules.

Collective diffusion of lattice gases in disordered lattices in the absence of a single-particle diffusion coefficient

Collective diffusion of particles is studied in a three-dimensional lattice-gas model with site-energy disorder. The distribution of the site energies is exponential, and the diffusion coefficient of independent particles may vanish. It is demonstrated by numerical simulations that a coefficient of collective diffusion exists. An estimate of the diffusion coefficient for smaller particle concentrations suggests a power-law dependence on concentration, consistent with the simulations. An effective-medium calculation of the coefficient of collective diffusion gives good agreement with the data at smaller particle concentrations and rough agreement at larger concentrations.

On the ordering of interstitials in BCC metals and BCT martensites: A lattice gas approach

In the present work the authors focus on body-centered cubic (bcc) metals such as [alpha]-Fe, [beta]-Ti and [beta]-Zr with interstitially dissolved nonmetals like carbon, nitrogen and oxygen. The solubilities of these elements in [alpha]-Fe is generally relatively small, while the solubilities in the high temperature modifications [beta]-Ti and [beta]-Zr are about 5--10 atom percent. On the other hand, the solubilities of interstitial in face-centered cubic (fcc) [gamma]-Fe or hexagonal closed packed (hcp) [alpha]-Ti and [alpha]-Zr are significantly larger. Upon quenching, homogeneous austenitic solutions of [alpha]-Fe with high carbon or nitrogen contents displacive phase transformations to nitrogen and carbon martensites with body-centered tetragonal (bct) structures are observed. Despite the fact that these martensites are thermodynamically instable with respect to the formation of [alpha]-Fe and carbides or nitrides, martensitic phase transformations play an important role in industrial processes such as steel hardening. Upon aging, ordering of the interstitial is observed in some martensites, e.g. in Fe-N martensites leading to Fe[sub 16]N[sub 2]. In the present work a three-dimensional lattice gas model for the description of bcc and bct gas-metal solutions is introduced. Pairwise interactions between adjacent interstitial are considered. Characteristic properties of such lattice gas models are calculated utilizing the Monte Carlomore » method. It will be demonstrated below that ordering of the interstitial is the rule rather than the exception, at least at low temperatures. The ordered lattice gas phases observed are identified and will be discussed in detail.« less

Capillary condensation in the lattice gas model: A Monte Carlo study

A three-dimensional lattice gas model with nearest-neighbor attractive interaction confined to a slitlike adsorbing capillary of thickness D is studied by computer simulation, varying the chemical potential μ, temperature, T, as well as the strength of the short-range interaction between the walls of the capillary and the gas. We show that the chemical potential μc(D) at the condensation transition in the capillary is shifted relative to its bulk value μc(∞) according to the Kelvin equation, μc(D)−μc(∞)∝D−1, for large enough D. Deviations are found for small D, however (of the order of 10 lattice spacings), particularly under conditions where for μ=μc(∞) the surfaces of the capillary for D→∞ are wet. For D=16 lattice spacings we also locate a capillary condensation critical point, and study the distortion of the gas–fluid coexistence curve due to the attractive walls. Profiles of density and local energy across the capillary are studied, and data for the temperature dependence of the local density at the wall both in the gas and in the liquid phase are presented. It is shown that these quantities vary very smoothly near the wetting temperature TW of the bulk (D→∞) system.

Nature of the prewetting critical point.

In a Monte Carlo simulation of a three-dimensional lattice-gas model of the adsorption of a liquid film on a substrate, we have observed the thick-film--thin-film (prewetting) transition, located the prewetting critical point, and determined its nature via finite-size scaling. We find this critical point to be two-dimensional Ising type, confirming the conjecture that surface phase transitions out of bulk coexistence should belong to this universality class.

On exact bounds for the cluster free energy in the three-dimensional lattice-gas model

The exact bounds by Lebowitz and Penrose for the cluster distribution of the simple cubic lattice-gas model with attractive interactions lead here to exact upper and lower bounds for the limiting cluster free energy or free energy per particle of a cluster of macroscopic size and, consequently, for the renormalized fugacity relating cluster distribution and partition functions. We also give practical realizations of the bounds for the cluster distribution. Our upper and lower bound expressions are always close enough to each other for 4J/kBT>1.5. The nature of the bounds at higher temperatures is also analyzed.

Two-phase equilibria and nucleation barriers near a critical point

A liquid-gas system at temperatures below criticality and densities between the liquid and the gas density at the coexistence curve exhibits equilibrium between a spherical liquid domain and the surrounding gas. This two-phase state is studied for the three-dimensional lattice-gas model, with the use of Monte Carlo methods. In sampling the chemical potential of lattices which are finite but much larger than the correlation length for various densities, the radius $R$ of the liquid cluster is derived from the excess density without any ambiguities in the cluster definition. From the relation between cluster radius and excess chemical potential, information on the universal scaled interface free energy of clusters as a function of $\frac{R}{\ensuremath{\xi}}$ is obtained, in the range $3\ensuremath{\lesssim}\frac{R}{\ensuremath{\xi}}\ensuremath{\lesssim}10$, which is also the range of experimental interest. The resulting free-energy barriers against nucleation deviate distinctly from the capillarity approximation in most parts of this regime. At temperatures far below criticality, the present method is shown to agree with the standard approach where a cluster is defined in terms of the contour around occupied lattice sites. Finally, the consequences of our results for experiments and phenomenological droplet models are briefly discussed.

Monte Carlo calculation of the surface tension for two- and three-dimensional lattice-gas models

It is suggested that the interface free energy between bulk phases with a macroscopically flat interface can be estimated from the variation of certain probability distribution functions of finite blocks with block size. For a liquid-gas system the probability distribution of the density would have to be used. The method is particularly suitable for the critical region where other methods are hard to apply. As a test case, the two-dimensional lattice-gas model is treated and it is shown that already, from rather small blocks, one obtains results consistent with the exact solution of Onsager for the surface tension, by performing appropriate extrapolations. The surface tension of the three-dimensional lattice-gas model is also estimated and found to be reasonably consistent with the expected critical behavior. The universal amplitude of the surface tension of fluids near their critical point is estimated and shown to be in significantly better agreement with experimental data than the results of Fisk and Widom and the first-order $4\ensuremath{-}d$ renormalization-group expansion. Also the universal amplitude ratio used in nucleation theory near the critical point is estimated.

On the theory of critical point density fluctuations

The theories of critical point fluctuations due to Ornstein and Zernike and to M.S. Green are discussed with particular reference to the three-dimensional lattice gas model. By relating the pair correlation function G(⋎) = g (2)(⋎) − 1 to the ferromagnetic susceptibility of the Ising model it is concluded that G(⋎) ∼ 1 ⋎ 7 4 at the critical point. This is in disagreement with both theories but is closer to Green's result G(⋎) ∼ 1 ⋎ 2 .