Lattice Monte Carlo Model Research Articles

Oxidation dynamics of soot or carbon black accounting for its core-shell structure and pore network

Internal oxidation is most important for removal of soot in diesel particulate filters. Furthermore, it enhances the porosity of carbon blacks (CBs), increases their specific surface area, SSA, determining their performance in batteries, inks and tires, as well as their environmental and health impact. Current models for oxidation of soot or CB neglect its fractal-like pore network during internal oxidation and underestimate its SSA by 60 % on average! Here, a lattice Monte Carlo (LMC) model elucidates both external and internal oxidation dynamics of soot (or CB) accounting for its fractal-like pore structure, for the first time to the best of our knowledge. Random internal oxidation takes place at the bulk soot (or CB), expanding its pore network and increasing the pore fractal dimension, Dfp, up to 3, in good agreement with data. This increases the SSA up to a factor of ten at 75 % conversion. In the presence of a less reactive shell though, internal oxidation stops after the reactive core is consumed. Thus the SSA levels off at large conversions (>50 %). Hence, accounting for the realistic core-shell, fractal-like pore structure during simultaneous external and internal oxidation nicely explains several measurements of soot and CB Dfp, SSA and particle diameter. So the LMC-derived oxidation dynamics of soot or CB presented here can be used to assist the design of highly porous CB grades from first principles, as well as the mitigation of soot emissions by enhancing their oxidation.

Size distribution of clusters and nucleation preference of trimers during SiC (0001) surface epitaxial growth under low coverage

In order to better understand the microscopic nucleation behavior during the epitaxial growth of a SiC crystal, a lattice kinetic Monte Carlo model is developed, in which Si and C particles are set as the basic elements. The events list is built up to implement group search and binary search, which can improve the efficiency of the algorithm. In addition, the Hoshen–Kopelman algorithm is also used to calculate the statistics of the properties of clusters. Then, the cluster size distribution function and the nucleation preference of trimers are analyzed. The results show that the cluster size distribution function obeys the Gauss distribution, and the proportion of crystal nuclei close to the average size gradually increases. Moreover, the growth temperature mainly affects the trapping rate of adatoms by dimers, and the C/Si ratio affects the formation of different types of dimers and the concentration of adatoms.

Computer simulations of melts of ring polymers with nonconserved topology: A dynamic Monte Carlo lattice model.

We present computer simulations of a dynamic Monte Carlo algorithm for polymer chains on a fcc lattice which explicitly takes into account the possibility to overcome topological constraints by controlling the rate at which nearby polymer strands may cross through each other. By applying the method to systems of interacting ring polymers at melt conditions, we characterize their structure and dynamics by measuring, in particular, the amounts of knots and links which are formed during the relaxation process. In comparison with standard melts of unknotted and unconcatenated rings, our simulations demonstrate that the mechanism of strand crossing makes polymer dynamics faster provided the characteristic timescale of the process is smaller than the typical timescale for chain relaxation in the unperturbed state, in agreement with recent experiments employing solutions of DNA rings in the presence of the type II topoisomerase enzyme. In the opposite case of slow rates the melt is shown to become slower, and this prediction may be easily validated experimentally.

Polymer effects on crystallization at the amorphous atazanavir-water interface

Amorphous solid dispersions are a highly relevant pharmaceutical formulation strategy increasingly employed to enhance the dissolution performance of drugs with poor aqueous solubility. Formulation additives are known to play an important role in the phase behavior of such pharmaceutical products, as they can potentially promote or inhibit solid-state crystallization of drug molecules in the dispersion matrix as well as crystallization from supersaturated solutions. Considerably less is known about the potential role of dissolved additives on the fate of amorphous drug-rich interfaces which can arise due to liquid–liquid phase separation during dosing. In this study, amorphous drug films are crystallized in buffer containing various polymeric formulation additives and analyzed via atomic force and scanning electron microscopy methods to explore the effect of additives on the evolution of surface crystals. A 2D lattice Monte Carlo model further examines the polymer systems to determine important modes of polymer action. Results demonstrate adsorbed polymer competitively inhibits crystal growth by preferential interaction with high energy sites.

A multi-scale MCCPFEM framework: Modeling of thermal interface grooving and deformation anisotropy of titanium alloy with lamellar colony

Micro-scale thermal interface grooving (TIG), as an important breakdown mechanism of single lamella and the key to spheroidization of lamellar colony, does significant influence on the mechanical response and microstructural evolution of titanium alloy with lamellar colony during hot working. This influence may become remarkable by coupling with meso-scale deformation anisotropy of the colony. The coupled effect across different scales is crucial to the spheroidization of lamellar colony, while rare related research is reported due to the difficulty in experiment. In this work, a multi-scale MCCPFEM framework was proposed to model on the micro-scale TIG and meso-scale deformation anisotropy through the fully coupling of lattice kinetic Monte Carlo (MC) model and crystal plasticity finite element model (CPFEM). During the modeling, the modified MC algorithm was established based on the multiple-integral method (MIM) solution with Mullin's theory, which accounts for the TIG's microstructural evolution. In addition, the deformation anisotropy at different length scales including strain localization at lamella, and strain partitioning at colony was characterized by an explicit CPFEM which includes resistance anisotropy of slip systems, evolution of dislocations and high-fidelity representative lamellar colony. At the same time, geometrically necessary dislocation (GND) was also considered in the CPFEM by developing a new algorithm with mesh-free methodology and re-construct radial basic shape functions. The fully coupling of the multi-scale MCCPFEM was realized through the microstructure-based 2D grids acting as both finite elements and lattice sites. Moreover, re-set ‘zero’ of the deformation gradient of the TIG mesh was proposed to characterize the strain-free state of new TIG nucleation. Then, the TIG-induced changes in the dislocation density, lattice rotation, strain-free state and morphological characteristics were returned to MCCPFEM to determine the heterogeneous deformation and anisotropic mechanical response of the lamellar colony. With this multi-scale model, the coupled effect of the deformation anisotropy (strain localization in beta phase, stress relief in TIG and local internal stress concentration in alpha lamella) and TIG-induced microstructural evolution during the isothermal compression of the IMI834 alloy with lamellar colony is well captured and analyzed.

The role of surface energy heterogeneity on crystal morphology during solid-state crystallization at the amorphous atazanavir–water interface

Solid-state crystallization at the amorphous atazanavir/water interface was studied via a lattice Monte Carlo model and atomic force microscopy.

Влияние температуры на морфологию планарных нанопроволок GaAs (моделирование)

Using a kinetic lattice Monte Carlo model, the self-catalyzed growth of planar GaAs nanowires was analyzed. The nanowire growth via the vapor-liquid-crystal mechanism was considered. The effect of temperature and the catalyst droplet location on the morphology and growth direction of planar GaAs nanowires was studied. For GaAs(111)A and GaAs(111)B substrates, a temperature range corresponding to stable growth of planar GaAs nanowires was revealed. The special asymmetric arrangement of droplets allows the one-directional nanowire growth.

Initial Stages of Planar GaAs Nanowire Growth—Monte Carlo Simulation

The initial stages of planar self-catalyzed GaAs nanowire growth via the vapor-liquid-solid mechanism are considered by a kinetic lattice Monte Carlo model. The shapes of the nanocrystals being formed under a catalyzed droplet are presented for three GaAs substrate orientations (111)A, (111)B, (001). The most stable planar GaAs nanowire growth was observed on GaAs(111)A substrates.

A kinetic lattice Monte Carlo study of post-irradiation annealing of model reactor pressure vessel steels

Significant embrittlement in reactor pressure vessel (RPV) steels can be caused by the formation of nanometer-scale Mn–Ni–Si precipitates (MNSPs) and annealing is a promising technique for reducing embrittlement. To achieve better understanding of the evolution of these precipitates at the atomic scale, a kinetic lattice Monte Carlo (KLMC) model, parameterized using CALPHAD and recent atom probe tomography (APT) data, is used to simulate post-irradiation annealing of MNSPs. The model predicts MNSP volume fractions, number densities and sizes that agree well with the experimental observations. The model also predicts that the initial structure of the precipitates may be B2 bcc phases with one sublattice occupied by Ni and the other sublattice occupied by Mn and Si, as well as shows a modest temperature dependence of the MNSP composition. The results show that the simple approach can be used to model MNSP evolution and supports that these precipitates are stable thermodynamic phases.

Monte Carlo Simulation of Ga Droplet Movement during the GaAs Langmuir Evaporation

A kinetic lattice Monte Carlo model is used to study the Ga droplets self-propelled motion along GaAs(111)A and (111)B surfaces during the initial stage of high-temperature annealing. An estimation of the droplet velocity, running along (111)A and (111)B surfaces, in a wide temperature range, is carried out. The mechanism of small Ga drops movement during high-temperature annealing is suggested. Different directions of droplets motion and the morphology of drop-crystal interface on (111)A and (111)B substrates are determined by a difference in the etching rate of (111)A and (111)B facets by liquid gallium. It is shown that metal droplets can cause step bunching.

A lattice Monte Carlo model for solid particle erosion: An application to brittle fracture

Erosion caused by repeated impact of solid particles entrained in a moving fluid is relevant for many technical applications like resulting wear and reduced service life of turbine blades, propellers and valves. In this work, a lattice Monte Carlo model for erosion of a class of glass submitted to impact of alumina particles reproduces and enhances experimental and simulation results described in Jafar et al., Wear 303, no. 1 (2013): 302–312. The lattice Monte Carlo model of solid particle erosion (LMC-SPE model) is based on a three dimensional representation of the target surface by a cubic lattice, where each cell embodies a small portion of the material susceptible of damage accumulation (in this case, brittle fracture) and subsequent removal. The simulation is driven by a kinetic Monte Carlo method where individual impacts can be generated according to probability distributions of experimental parameters (for example, size, velocity and spatial distributions of particles). In addition, a phenomenological model of the interaction of impacting particles with an already eroded and rough surface is introduced in order to correct unrealistic large final surface roughness and erosion rates obtained otherwise. In spite of its simplicity, the LMC-SPE model can simulate the main topographic features of individual impacts and reproduce correctly dependencies of the erosion rate on velocity, size, and impact angle of the particles. Consequently roughening regimes due to the accumulative effect of thousands of individual impacts acting on relatively large areas are simulated within reasonable computational times. Due to its three dimensional character, LMC-SPE simulations can be compared directly with channels obtained with abrasive jet micro-machining techniques (AJM) described in literature.

Analysis of the statistical and convergence properties of ionic transport coefficients with application to the solid electrolyte Li2OHCl

The challenge of computing ionic transport coefficients from first principles is to achieve the necessary convergence with respect to system size, simulation time, and configurational sampling. Unfortunately current computer resources are not yet available for such convergence studies at the fully first principles level. In this work, a lattice kinetic Monte Carlo model is used to study the convergence properties of transport coefficients, using the Li sub-lattice of the Li ion electrolyte Li2OHCl as an example system. The specific transport coefficients representing tracer diffusion, effective diffusion, and mobility are carefully studied for their convergence properties. Additionally, ion pair correlations of the effective diffusion are recast as a sum over events which allows for a detailed study of the nature of the correlation in terms of time and spatial separation. This experience suggests a general method of performing simulations by using first a kinetic Monte Carlo model followed by a first principles molecular dynamics study. For the Li2OHCl system, the kinetic Monte Carlo results provide both a reference for the Haven ratio due to purely geometric effects and a measure of the computational effort needed to obtain meaningful molecular dynamics results. The combination of the two methods provides further evidence of anti-correlated Li-ion motion in this system as predicted in a previous study.

Concentric GaAs nanorings formation by droplet epitaxy — Monte Carlo simulation

A kinetic lattice Monte Carlo model is used to study the GaAs nanorings growth by droplet epitaxy. The dependences of GaAs nanoring morphology on temperature, arsenic flux and the surface density of gallium droplets are analyzed. The condition of single, double and triple rings formation is discussed. It is demonstrated that the nanoring shape depends on the relationship between the value of gallium diffusion length along the surface and the distance between Ga droplets. The necessary condition for double ring formation – the distance between the drops should exceed the gallium diffusion double length. The variants of the single ring growth are considered.

Electron Mobility and Trapping in Ferrihydrite Nanoparticles

Iron is the most abundant transition metal in the Earth’s crust, and naturally occurring iron oxide minerals play a commanding role in environmental redox reactions. Although iron oxide redox reactions are well-studied, their precise mechanisms are not fully understood. Recent work has shown that these involve electron transfer pathways within the solid, suggesting that overall reaction rates could be dependent upon electron mobility. Initial ultrafast spectroscopy studies of iron oxide nanoparticles sensitized by fluorescein derivatives supported a model for electron mobility based on polaronic hopping of electron charge carriers between iron sites, but the constitutive relationships between hopping mobilities and interfacial charge transfer processes has remained obscured. We developed a coarse-grained lattice Monte Carlo model to simulate the collective mobilities and lifetimes of these photoinjected electrons with respect to recombination with adsorbed dye molecules for essential nanophase ferrihydrit...

Imaging and Manipulating Energy Transfer Among Quantum Dots at Individual Dot Resolution

Many processes of interest in quantum dots involve charge or energy transfer from one dot to another. Energy transfer in films of quantum dots as well as between linked quantum dots has been demonstrated by luminescence shift, and the ultrafast time-dependence of energy transfer processes has been resolved. Bandgap variation among dots (energy disorder) and dot separation are known to play an important role in how energy diffuses. Thus, it would be very useful if energy transfer could be visualized directly on a dot-by-dot basis among small clusters or within films of quantum dots. To that effect, we report single molecule optical absorption detected by scanning tunneling microscopy (SMA-STM) to image energy pooling from donor into acceptor dots on a dot-by-dot basis. We show that we can manipulate groups of quantum dots by pruning away the dominant acceptor dot, and switching the energy transfer path to a different acceptor dot. Our experimental data agrees well with a simple Monte Carlo lattice model of energy transfer, similar to models in the literature, in which excitation energy is transferred preferentially from dots with a larger bandgap to dots with a smaller bandgap.

Influence of molecular shape and interaction anisotropy on the self-assembly of tripod building blocks on solid surfaces

Molecular shape and directionality of intermolecular interactions are important factors which affect structure formation in adsorbed overlayers. In this contribution, using theoretical methods we demonstrate the importance of these factors in the surface-confined self-assembly of tripod-shaped organic molecules with reduced symmetry. To that end a lattice Monte Carlo model is proposed in which the molecules are represented in a coarse grained way, as flat rigid structures comprising a few connected segments adsorbed on a triangular lattice. The calculations are performed for the molecules equipped with terminal active centers providing directional intermolecular interactions. These results are compared with analogous data obtained for C3-symmetric units and Y-shaped molecules whose all composite segments are active. The simulated results show that for the directional interactions, the reduction of molecular symmetry leads to the formation of disordered, glassy, porous networks with hexagonal nanovoids of different shapes. Moreover, it is demonstrated that the interaction mode involving all molecular segments of the asymmetric building blocks is responsible for the formation of compact patterns. Relative thermal stability of the simulated assemblies is also compared, highlighting deciding role of the interaction mode in stabilization of the adsorbed superstructures. The findings of our theoretical investigations can be helpful in designing new molecular blocks and programming their interactions to create 2D molecular superstructures with tunable morphology and functions.

Molecular mobility with respect to accessible volume in Monte Carlo lattice model for polymers

Abstract A three-dimensional cubic Monte Carlo lattice model is considered to test the impact of volume on the molecular mobility of amorphous polymers. Assuming classic polymer chain dynamics, the concept of locked volume limiting the accessible volume around the polymer chains is introduced. The polymer mobility is assessed by its ability to explore the entire lattice thanks to reptation motions. When recording the polymer mobility with respect to the lattice accessible volume, a sharp mobility transition is observed as witnessed during glass transition. The model ability to reproduce known actual trends in terms of glass transition with respect to material parameters, is also tested.

Monte Carlo simulation of the formation of AIIIBV nanostructures with the use of droplet epitaxy

A Monte Carlo lattice model is proposed to describe the formation of semiconductor nanostructures by the vapor–liquid–solid growth mechanism. This model is used to simulate the growth of GaAs nanostructures by the droplet epitaxy technique in the temperature range from 500 to 600 K in As2 fluxes with intensity of 0.005–0.04 ML/s. The morphology of the formed structures is demonstrated to depend on the growth parameters. Etching of the GaAs substrate by a gallium droplet is studied. The ranges of temperature and As flux rates necessary for the formation of GaAs nanorings are determined. The conditions of the formation of single and double concentric rings are analyzed.

Self-catalyzed GaAs and InAs nanowire growth (Monte Carlo simulation)

A new lattice Monte Carlo model of AIIIBV nanowire growth according to the vapor- liquid-solid mechanism is suggested. The peculiarities of this model and the procedure of energy parameters estimation for the InAs system are described. The characteristics of InAs and GaAs self-catalyzed nanowire growth are obtained using the suggested model. A comparison of InAs and GaAs self-catalyzed nanowire growth characteristics using the suggested Monte Carlo model is performed

Simulated growth of GaAs nanowires: Catalytic and self-catalyzed growth

The kinetic lattice Monte Carlo model of GaAs nanowire growth by the vapor-liquid-crystal mechanism is suggested. The catalytic and self-catalyzed growth of nanowires on the GaAs (111)B surface is simulated. The dependence of the morphology of the growing nanowires on the growth parameters is demonstrated. Upon self-catalyzed growth with gallium drops serving as the growth catalyst, the growth rate of the nanowires linearly depends on the arsenic flow in a wide range of arsenic flow rates. The decreasing dependence of the self-catalyzed growth rate of the nanowires on the initial gallium drop diameter is less steep, and the optimal growth temperature is higher than that for catalytic growth. It is shown that self-catalyzed growth is more sensitive to the ratio between the gallium and arsenic flow rates than catalytic growth.