A kinetic model for the premelting of a crystalline structure

An analytical kinetic approach to examine the premelting phenomenon is suggested by using a first passage time analysis. Premelting is considered to occur when the time of formation of a Frenkel type defect in the surface monolayer becomes sufficiently small. The mean time of defect formation on the surface lattice, i.e., the mean time necessary for a selected (surface-located) molecule to leave its lattice site and form a Frenkel defect, is calculated by using a first passage time analysis. The model is illustrated by numerical calculations for a crystalline structure composed of molecules interacting via the Lennard-Jones (LJ) potential. The lattice vectors in the plane parallel to the free surface of the crystal were assumed to be equal (to the lattice parameter) and the angle between them was varied. The model predictions of the Tammann temperature (of premelting) are very sensitive to the parameters of the LJ potential. In all the cases considered, the temperature dependence of the mean first passage time has two clearly distinct regimes: at low temperatures the dependence is sharp and at high temperatures it is weak.     

Reaction products and oxide thickness formed by Ti out-diffusion and oxidization in poly-Pt/Ti/SiO2/Si with oxide films deposited

In the paper, we present experimental results to enhance the understanding of Ti out-diffusion and oxidization in commercial poly-Pt/Ti/SiO₂/Si wafers with perovskite oxide films deposited when heat-treated in flowing oxygen ambient. It indicates that when heat-treated at 550 and 600 °C, PtTi₃+PtTi and PtTi are the reaction products from interfacial interaction, respectively; while heat-treated at 650 °C and above, the products become three layers of titanium oxides instead of the alloys. Confirmed to be rutile TiO₂, the first two layers spaced by 65 nm encapsulate the Pt surface by the first layer with 60 nm thick forming at its surface and by the next layer with 35 nm thick inserting its original layer. In addition, the next layer is formed as a barrier to block up continuous diffusion paths of Ti, and thus results in the last layer of TiO_2−x formed by the residual Ti oxidizing.     

Depinning transition of the quenched Mullins-Herring equation: A short-time dynamic method

The depinning phase transition of the Mullins-Herring equation with an external driving force and quenched random noise is studied in a short-time dynamic scaling scheme. Besides the critical driving force, all the critical exponents can be accessed, agreeing well with those in long-time steady-state simulations. The finite size effects on the critical exponents are also discussed. It is found that reasonable results can be achieved with a relatively small system, which highlights the advantage of the present approach.     

Molecular Dynamics Simulation of Thermal Conductivity in Si--Ge Nanocomposites

Thermal conductivity of nanocomposites is calculated by molecular dynamics （MD） simulation. The effect of size on thermal conductivity of nanowire composites and the temperature profiles are studied. The results indicate that the thermal conductivity of nanowire composites could be much lower than alloy value; the thermal conductivity is slightly dependent on temperature except at very low temperature.     

Two-dimensional chiral segregation of the bent hard needles model with Lennard-Jones sites

Assuming the aggregates of a single chiral component as a pure phase, chiral segregation can be considered as a coexistence of two phases, therefore the formalisms of phase transitions in Statistical Mechanics can be applied. That is, chiral segregation can be considered as phase equilibrium. The standard mechanism to understand phase equilibrium considers the complete van der Waals forces, including repulsions and attractions. However, during the last few years, a particular kind of fluid-fluid equilibrium, explained in terms of only excluded volume effects, has gained important interest. This kind of phenomenon is known as depletion forces. In this paper, the contribution of these two mechanisms is investigated. In order to analyze the effect that repulsions and attractions have on chiral segregation we study a two-dimensional model, bent hard needles model. In one case only infinitely repulsive interactions are considered while in the second case, one and two Lennard-Jones (LJ) sites are added to model the complete van der Waals forces. In the first case, because of the nature of the model, the cause for chiral segregation is due to excluded volume effects that appear when the density of the system is sufficiently high. In the second case, the model proposed is more complex and besides the density the temperature also affects the phase separation. Monte Carlo simulations in the Gibbs ensemble (GMC) are used to perform this comparison. As a result, the segregation phase diagram is obtained for the infinitely repulsive model and that with two LJ sites. The important conclusions are that for some particular molecular geometries, repulsions are not able to produce chiral segregation at all, independently of density. However, when attractions are included the effect of repulsion is complemented and phase separation can be achieved even for those molecular geometries where infinitely repulsions were not able.     

Generalized statistical description of adsorption of polyatomics

Multisite-occupancy adsorption is described as a fractional statistic problem, based on Haldane’s statistics. Site exclusion is characterized by a statistical exclusion parameter, g, which relates to the molecular size and lattice geometry. A general adsorption isotherm is obtained and comparisons with experiments indicate that the spatial configuration of adsorbed molecules and lateral interactions may accurately be assessed from this theory. In addition, the theoretical framework developed in this paper allows to describe orientational transitions occurring in adlayers of polyatomics.     

Ni/Ni3Al interface: A density functional theory study

The optimal geometries, mechanical and thermal properties, and electronic structures of the three low index (0 0 1), (1 1 0), (1 1 1) Ni/Ni₃Al thin film were studied using first principle calculations. Simulated results indicated that Ni and Al atoms in γ^′ phase preferred to place in the hollow site of Ni atoms in γ phase. In hollow site models, electronic states affected by interface localize within 2 atomic layers. While the top site model, electronic states localize within 3 atomic layers. It is also found that hollow site (1 1 0) interface has the best mechanical properties. Hollow site (0 0 1) interface is the most easily formed interface, which has the best thermodynamic properties.     

Anisotropic surface melting in lyotropic cubic crystals

From experiments with metal crystals, in the vicinity of their crystal/liquid/vapor triple points, it is known that melting of crystals starts on their surfaces and is anisotropic. Recently, we have shown that anisotropic surface melting occurs also in lyotropic systems. In our previous paper (Eur. Phys. J. E 19, 223 (2006)), we have focused on the case of poor faceting at the Pn3m/L1 interface in C12EO2/water binary mixtures. There anisotropic melting occurs in the vicinity of a Pn3m/L3/L1 triple point. In the present paper, we focus on the opposite case of a rich devil's-staircase-type faceting at Ia3d/vapor interfaces in monoolein/water and phytantriol/water mixtures. We show that anisotropic surface melting takes place in these systems in a narrow humidity range close to the Ia3d-L2 transition. As whole (hkl) sets of facets disappear one after another when the transition is approached, surface melting occurs in a facet-by-facet type.     

A kinetic approach to the calculation of surface tension of a spherical drop

In literature, surface tension has been investigated mainly from a Thermodynamics standpoint, more rarely with kinetic methods. In the present work, surface tension of drops is studied in the framework of kinetic theory, starting from the Sutherland approximation to Van Der Waals interaction between molecules. Surface tension is calculated as a function of drop radius: it is found that it approaches swiftly an asymptotic value, for radii of several times the distance of minimum approach D of the Sutherland potential. This theoretical asymptotic value is compared to experimental values of surface tension in plane surfaces of a few liquids, and is found in reasonable agreement.     

Absence of hyperscaling violations for phase transitions with positive specific heat exponent

Finite size scaling theory and hyperscaling are analyzed in the ensemble limit which differs from the finite size scaling limit. Different scaling limits are discussed. Hyperscaling relations are related to the identification of thermodynamics as the infinite volume limit of statistical mechanics. This identification combined with finite ensemble scaling leads to the conclusion that hyperscaling relations cannot be violated for phase transitions with strictly positive specific heat exponent. The ensemble limit allows to derive analytical expressions for the universal part of the finite size scaling functions at the critical point. The analytical expressions are given in terms of generalH-functions, scaling dimensions and a new universal shape parameter. The universal shape parameter is found to characterize the type of boundary conditions, symmetry and other universal influences on critical behaviour. The critical finite size scaling functions for the order parameter distribution are evaluated numerically for the cases =3, =5 and =15 where is the equation of state exponent. Using a tentative assignment of periodic boundary conditions to the universal shape parameter yields good agreement between the analytical prediction and Monte-Carlo simulations for the two dimensional Ising model. Analytical expressions for critical amplitude ratios are derived in terms of critical exponents and the universal shape parameters. The paper offers an explanation for the numerical discrepancies and the pathological behaviour of the renormalized coupling constant in mean field theory. Low order moment ratios of difference variables are proposed and calculated which are independent of boundary conditions, and allow to extract estimates for a critical exponent.     

Two velocity difference model for a car following theory

In the light of the optimal velocity model, a two velocity difference model for a car-following theory is put forward considering navigation in modern traffic. To our knowledge, the model is an improvement over the previous ones theoretically, because it considers more aspects in the car-following process than others. Then we investigate the property of the model using linear and nonlinear analyses. The Korteweg-de Vries equation (for short, the KdV equation) near the neutral stability line and the modified Korteweg-de Vries equation (for short, the mKdV equation) around the critical point are derived by applying the reductive perturbation method. The traffic jam could be thus described by the KdV soliton and the kink-anti-kink soliton for the KdV equation and mKdV equation, respectively. Numerical simulations are made to verify the model, and good results are obtained with the new model.     

Complete wetting of pits and grooves

For one-component volatile fluids governed by dispersion forces an effective interface Hamiltonian, derived from a microscopic density functional theory, is used to study complete wetting of geometrically structured substrates. Also the long range of substrate potentials is explicitly taken into account. Four types of geometrical patterns are considered: i) one-dimensional periodic arrays of rectangular or parabolic grooves and ii) two-dimensional lattices of cylindrical or parabolic pits. We present numerical evidence that at the centers of the cavity regions the thicknesses of the adsorbed films obey precisely the same geometrical covariance relation, which has been recently reported for complete cone and wedge filling. However, this covariance does not hold for the laterally averaged wetting film thicknesses. For sufficiently deep cavities with vertical walls and close to liquid-gas phase coexistence in the bulk, the film thicknesses exhibit an effective planar scaling regime, which as a function of undersaturation is characterized by a power law with the common critical exponent -1/3 as for a flat substrate, but with the amplitude depending on the geometrical features.     

Thermal step bunching on the restricted solid-on-solid model with point contact inter-step attractions

We present the restricted solid-on-solid (RSOS) model with the inter-ledge interaction of the point contact type (p-RSOS model). We have made detailed calculation of the Andreev free energy , which is similar to the equilibrium crystal shape (ECS) z=z(x,y), and the surface gradient as the function of the Andreev field . From the calculated and , we have obtained the vicinal surface free energy . The inter-ledge attraction between adjacent steps affects the surface free energies in the equilibrium, and causes the first-order transition on the profile of ECS at low temperature. The inter-ledge attraction also destabilizes the regular train of steps. We also have obtained the thermal step bunching.     

Behavior of a wetting phase near a solid boundary: vapor near a weakly attractive surface

Density profiles of a LJ vapor near a weakly attractive surface with long-range fluid wall potential was studied along the pore coexistence curve. There are two localized density maxima near the pore wall: the first one is caused by localization of the molecules in the minimum of the fluid-wall potential, and the second one reflects adsorption of molecules at the first layer at higher densities. In addition, a third, weak density maximum is observed close to the critical temperature due to the competition between the long-range attractive tail of the fluid-wall potential and the effect of missing neighbors. This maximum separates the region of a gradual density depletion toward the surface due to the missing neighbor effect and the adsorption region further from the surface, where the density gradually increases toward the surface due to the attractive fluid-wall potential. When approaching the bulk critical temperature, this maximum moves away from the surface due to the divergence of the bulk correlation length. Applicability of various equations to describe the vapor density profiles is examined. Excess adsorption of vapor at low temperatures turns into excess depletion at higher temperatures. The crossover temperature increases with increasing pore size and strengthening fluid-wall interaction. The problems of the theory of the surface critical behavior of Ising models in a case of a non vanishing surface field and its mapping on a fluid is discussed.     

Analysis of car-following model considering driver’s physical delay in sensing headway

An extended car-following model is proposed by taking into account the delay of the driver’s response in sensing headway. The stability condition of this model is obtained by using the linear stability theory. The results show that the stability region decreases when the driver’s physical delay in sensing headway increases. The KdV equation and mKdV equation near the neutral stability line and the critical point are respectively derived by applying the reductive perturbation method. The traffic jams could be thus described by soliton solution and kink-antikink soliton solution for the KdV equation and mKdV equation respectively. The numerical results in the form of the space-time evolution of headway show that the stabilization effect is weakened when the driver’s physical delay increases. It confirms the fact that the delay of driver’s response in sensing headway plays an important role in jamming transition, and the numerical results are in good agreement with the theoretical analysis.     

Slow coarsening in a class of driven systems

The coarsening process in a class of driven systems is studied. These systems have previously been shown to exhibit phase separation and slow coarsening in one dimension. We consider generalizations of this class of models to higher dimensions. In particular we study a system of three types of particles that diffuse under local conserving dynamics in two dimensions. Arguments and numerical studies are presented indicating that the coarsening process in any number of dimensions is logarithmically slow in time. A key feature of this behavior is that the interfaces separating the various growing domains are macroscopically smooth (well approximated by a Fermi function). This implies that the coarsening mechanism in one dimension is readily extendible to higher dimensions. Received 3 April 2000     

Origins of interdiffusion, crystallization and layer exchange in crystalline Al/amorphous Si layer systems

Aluminium-induced crystallization of amorphous silicon (a-Si) in Al/a-Si and a-Si/Al bilayers was studied upon annealing at low temperatures between 165 and 250 °C, by X-ray diffraction (XRD) and Auger electron spectroscopy (AES). Upon annealing the inward diffusion of Si along grain boundaries in Al takes place, followed by crystallization of this diffused Si. Continuous annealing leads to (more or less) layer exchange in both types of bilayers. The change in bulk energy of the Al phase (release of macrostress and microstrain, increase of grain size) promotes the occurrence of layer exchange, whereas changes in surface and interface energies counteract the layer exchange.     

The role of the amorphous fraction for the equilibrium shape of polymer single crystals

The equilibrium state of polymer single crystals is considered by explicitly taking into account the amorphous fraction formed by loops and tails of the chains using a statistical model introduced by Muthukumar (Philos. Trans. R. Soc. London, Ser. A 361, 539 (2003)). We show that under realistic conditions below the equilibrium melting temperature, tight loops and close re-entries are favored, and that the amorphous fraction can be mapped into an excess surface free energy. The model is extended to many-chain crystals where it is shown that the lamellar thickness increases with the number of chains in the crystal and extended-chain conformations are thermodynamically favored if the number of chains in the crystal is sufficiently large. The number of chains necessary to form an extended-chain crystal in thermodynamic equilibrium scales with the square of the degree of polymerization of the chains. We discuss the temperature behavior of the equilibrium crystal thickness in the under-cooled state.     

Non-equilibrium wetting transition in a magnetic Eden model

Magnetic Eden clusters (Ausloos et al., Europhys. Lett. 24, 629 (1993)) with ferromagnetic interaction between nearest-neighbor spins are grown in a confined 2d-geometry with short range magnetic fields acting on the surfaces. The change of the growing interface curvature driven by the field and the temperature is identified as a non-equilibrium wetting transition and the corresponding phase diagram is evaluated. Received 27 March 2000