A kinetic Monte Carlo method on super-lattices for the study of the defect formation in the growth of close packed structures

A modified Kinetic Lattice Monte Carlo model has been developed to predict growth rate regimes and defect formation in the case of the homo-epitaxial growth of close packed crystalline structures. The model is an improvement over standard Monte Carlo algorithms, which usually retain fixed atom positions and bond partners indicative of perfect crystal lattices. Indeed, we extend the concepts of Monte Carlo growth simulations on super-lattices containing additional sites (defect sites) with respect to those of the reference material. This extension implies a reconsideration of the energetic mapping, which is extensively presented, and allows to describe a complex phenomenology that is out of accessibility of standard stochastic approaches. Results obtained using the Kawasaki and the Bond-Counting rules for the transition probability of the Monte Carlo event are discussed in details. These results demonstrate how the defect types (local or extended), the formation mechanisms and the defect generation regimes can be characterized using our approach.     

Investigation of nucleation and grain growth in 2-dimensional systems by using generalized Monte Carlo simulations

In this study, nucleation and grain growth was studied by using 2-dimensional generalized Monte Carlo simulations and experiments. As an attempt to improve the JMAK model, we proposed a new differential equation to be able to model nucleation and growth phenomena using nonextensive thermostatistics. One of the reasons that we would like to perform generalized Monte Carlo simulations in studying of nucleation and grain growth phenomena is that the generalized Monte Carlo algorithm was shown to be more effective than the standard Monte Carlo algorithm and also than the standard Molecular Dynamic algorithm in locating the minimum energy configuration. Therefore, for a given temperature, the fact that a configuration of the system with lower energy could be obtained by using the generalized Monte Carlo simulation means that a different textural configuration of grain growth could be also expected. In this respect, it is possible to say that the nonextensive statistics might be an appropriate tool in studying of nucleation and growth phenomena.     

The kinetic process of non-smooth substrate thin film growth via parallel Monte Carlo method

A Monte Carlo simulation model of thin film growth based on parallel algorithm is presented. Non-smooth substrate with special defect mode is introduced in such a model. The method of regionalizing is used to divide the substrate into sub-regions. This method is supposed to be modulated according to the defect mode. The effects of surface defect mode and substrate temperature, such as the nucleation ratio and the average island size, are studied through parallel Monte Carlo method. The kinetic process of thin film growth in the defect mode is also discussed. Results show that surface defect mode contributes to crystal nucleation. Analyzing parallel simulation results we find that density defect points, substrate temperature and the number of processors contribute decisively to the parallel efficiency and speedup. According to defect mode we can obtain large grain size more feasibly and the parallel algorithm of this model can guide the non-smooth substrate simulation work.     

Hydrodynamic simulation of electron transport in n-type Hg<Subscript>0.8</Subscript>Cd<Subscript>0.2</Subscript>Te

A hydrodynamic approach based on concentration, velocity and energy conservation equations is developed and used for the simulation of the electron transport in bulk HgCdTe. Both transient and steady-state regimes are simulated using input parameters calculated with a Monte Carlo simulator. The model is validated through a comparison in excellent agreement with Monte Carlo results.     

碳纳米管对接成异质结器件的计算模拟

基于Stone-Wales缺陷演变理论与分子动力学、Monte Carlo计算方法, 进行了碳纳米管(CNTs)对接成异质结器件的计算模拟.首先, 提出了一种模拟CNTs端帽位置变化的新算法, 并计算模拟了单根CNT的端帽从开口到闭合的过程. Stone-Wales缺陷演变被设计模拟这些端帽变化的跃变过程, 以模拟C–C键的生成与断裂, 而分子动力学则作为跃变后构型弛豫的渐变模拟. 同时, 研究了不同管型CNTs的端帽打开并对接形成异质结的过程.研究结果显示, 对接初期在对接处先产生大量的缺陷, 以促进反应的发生. 这些缺陷趋向于演变成稳定的六元环结构, 或者五元环/七元环的结构, 使异质结趋于稳定. 关键词： 碳纳米管 Monte Carlo Stone-Wales缺陷 分子动力学     

Analysis of communication costs for domain decomposed Monte Carlo methods in nuclear reactor analysis

A domain decomposed Monte Carlo communication kernel is used to carry out performance tests to establish the feasibility of using Monte Carlo techniques for practical Light Water Reactor (LWR) core analyses. The results of the prototype code are interpreted in the context of simplified performance models which elucidate key scaling regimes of the parallel algorithm.     

Formation of cobalt bilayer islands on Cu(100) surface

Physics of the Solid State - The formation and evolution of Co islands on Cu(100) surface are studied using molecular dynamics simulation and kinetic Monte Carlo method. Two regimes of cluster...     

Mechanism of associative oxygen desorption from Pt(111) surface

Mechanism of the associative desorption of oxygen from the Pt(111) surface has been studied on atomic level by means of DFT/GGA calculations and kinetic Monte Carlo simulations. It has been found that two oxygen adatoms can occur, with sufficient probability, in neighboring on-top sites, which is essential for formation and subsequent evaporation of the oxygen molecule. Monte Carlo simulations have demonstrated effectiveness of this channel for O₂ formation on Pt(111) and strongly support the suggested model of associative desorption from transition metal surfaces.     

Tracer diffusion in the presence of segregating obstacles

Tracer diffusion in an alloy in which the trajectories of one of the species is biased is examined as a model of mass transport with attendant segregation to extended defects (e.g., dynamic strain ageing, grain-boundary segregation). More specifically, we employ Monte Carlo simulation to describe the nonequilibrium diffusive behavior of the components of a two-dimensional lattice gas comprising A and B atoms wherein one of the species (B) interacts with randomly distributed line defects to create equilibrium atmospheres at late times. Various kinetic assumptions and defect densities are explored to highlight the role of B-atom mobility and defect interaction strength on the transport behavior of the A atoms. From the calculated instantaneous diffusivity, several diffusive regimes are then identified and related to evolving segregation profiles and, in particular, to the free area available for diffusion.     

Real-time path integral approach to nonequilibrium many-body quantum systems

A real-time path-integral Monte Carlo approach is developed to study the dynamics in a many-body quantum system coupled to a phonon background until reaching a nonequilibrium stationary state. The approach is based on augmenting an exact reduced equation for the evolution of the system in the interaction picture which is amenable to an efficient path integral (worldline) Monte Carlo approach. Results obtained for a model of inelastic tunneling spectroscopy reveal the applicability of the approach to a wide range of physically important regimes, including high (classical) and low (quantum) temperatures, and weak (perturbative) and strong electron-phonon couplings.     

Nonequilibrium dynamics of the Bose-Hubbard model: a projection-operator approach

We study the phase diagram and nonequilibrium dynamics involving ramp of the hopping amplitude J(t)=Jt/τ with ramp time τ of the Bose-Hubbard model at zero temperature using a projection-operator formalism which allows us to incorporate the effects of quantum fluctuations beyond mean-field approximations in the strong-coupling regime. Our formalism yields a phase diagram which provides a near exact match with quantum Monte Carlo results in three dimensions. We also compute the residual energy Q, the superfluid order parameter Δ(t), the equal-time order parameter correlation function C(t), and the wave function overlap F which yields the defect formation probability P during nonequilibrium dynamics of the model. We find that Q, F, and P do not exhibit the expected universal scaling. We explain this absence of universality and show that our results compare well with recent experiments.     

Monte Carlo Method in Scanning Electron Microscopy. 3. Modern Condition of the Problem

The applicability of the Monte Carlo method for modeling images obtained in a scanning electron microscope is assessed. It is shown that in the Monte Carlo method, it is impossible to take into account all the mechanisms of the interaction of electrons with matter that affect image formation. Modern random-number generators create an insufficient amount of random numbers necessary for modeling the scattering of electrons in matter. The time it takes to modeling images using contemporary personal computers is too long: it takes years of continuous computer operation. There is no evidence of correctness of the results of the Monte Carlo method when generating images. These factors prove the impossibility of using the Monte Carlo method to modeling the scattering of electrons in a solid, which is used in image formation in a scanning electron microscope.     

Finite-size scaling study of the Laplacian roughening model

We perform further Monte Carlo simulations of the Laplacian roughening model on a triangular lattice to decide whether two-dimensional defect melting proceeds in a single first-order or two successive continuous transitions, as predicted by two conflicting theories. Of the two alternatives, the new high-statistics Monte Carlo data favor the single first-order transition.     

Quantum Monte Carlo study of the optical and diffusive properties of the vacancy defect in diamond

Fixed-node diffusion quantum Monte Carlo (DMC) calculations of the ground and excited state energetics of the neutral vacancy defect in diamond are reported. The multiplet structure of the defect is modeled using guiding wave functions of the Slater-Jastrow type with symmetrized multideterminant Slater parts. For the ground state we obtain the 1E state in agreement with experiment. The calculated energy of the lowest dipole allowed transition is consistent with the experimentally observed GR1 band, which has long been identified with the neutral vacancy in diamond, although no previous first-principles ab initio calculation of this transition exists. The calculated multiplet splitting of over 2 eV indicates the importance of a proper treatment of electron exchange and correlation in this system. DMC calculations of the formation and migration energy of the vacancy defect are presented.     

感染生长模型的逾渗模拟

在规则格子点阵中，活跃点逐步动态地以可变概率感染附近空缺点而生成系综.利用感染概率替代系综温度，给粒子划分能级，可以用巨正则系综配分函数表征体系.蒙特卡洛方法模拟验证了该体系在逾渗阈值处的相变行为.提出了一种新的较为普适的估算规则点阵逾渗阈值的方法.对介质基底上金属薄膜的实验研究验证了该感染生长模型的合理性.由此给出了格子点阵的固有属性(逾渗)如何在粒子聚集成团簇这一动态过程中体现出来的物理模型. 关键词： 逾渗 系综 蒙特卡洛方法 生长模型     

Diffusion correlation effects of molybdenum and silicon in molybdenum disilicide

Diffusion data for both principal directions of silicon and molybdenum as well as germanium are briefly summarised. Analysis is performed of the defect formation energies (available from previous ab initio calculations and experimental measurements) for diffusion mechanisms via home and foreign sublattices. The home sublattice mechanism is shown to be the preferred one for both silicon and molybdenum. Tracer correlation factors for silicon and molybdenum diffusion via sublattice vacancies in the respective sublattices of the tetragonal C11_b structure of molybdenum disilicide are calculated by a direct Monte Carlo simulation technique. Correlation factors for Si diffusion on its sublattice are compared with literature values that were calculated using a more complicated Monte Carlo method based on the matrix approach. It is shown that there is no need for this complicated approach and that the direct Monte Carlo simulation technique gives highly accurate correlation factors. Correlation factors and anisotropy ratios of vacancy-mediated diffusion in both sublattices are deduced and compared with experimental data. Tracer correlation in the tetragonal direction is shown to contribute 0.40?eV (i.e. over 55%) of the migration energy of the corresponding Si diffusivity. Two possible jump rates for Si diffusion are separately estimated. Mo diffusion correlation factors are calculated using the direct Monte Carlo technique. A comparison with experiment is made and the ratio of two possible jump rates is also estimated.     

Monte Carlo simulation of grain growth in polycrystalline materials

Understanding the kinetics of grain growth, under the influence of second phase (such as impurities, voids and bubbles) is fundamental to advances in the control of microstructural evolution. As a precursor to this objective, we have investigated the grain growth kinetics in a polycrystalline material using a standard Q-state Potts’ model under Monte Carlo settings. Based on physical reasoning, new modifications are suggested to circumvent some of the disadvantages in the basic Potts model. The efficacy of these modifications vis-à-vis the basic model is verified. The influence of second phase particles on the impurity loaded grain boundaries is investigated for the study of grain growth kinetics.     

A benchmark comparison of Monte Carlo particle transport algorithms for binary stochastic mixtures

We numerically investigate the accuracy of two Monte Carlo algorithms originally proposed by Zimmerman [1] and Zimmerman and Adams [2] for particle transport through binary stochastic mixtures. We assess the accuracy of these algorithms using a standard suite of planar geometry incident angular flux benchmark problems and a new suite of interior source benchmark problems. In addition to comparisons of the ensemble-averaged leakage values, we compare the ensemble-averaged material scalar flux distributions. Both Monte Carlo transport algorithms robustly produce physically realistic scalar flux distributions for the benchmark transport problems examined. The base Monte Carlo algorithm reproduces the standard Levermore-Pomraning model [3] and [4] results. The improved Monte Carlo algorithm generally produces significantly more accurate leakage values and also significantly more accurate material scalar flux distributions. We also present deterministic atomic mix solutions of the benchmark problems for comparison with the benchmark and the Monte Carlo solutions. Both Monte Carlo algorithms are generally significantly more accurate than the atomic mix approximation for the benchmark suites examined.     

Portraits of the flux tube in QED3: A Monte Carlo simulation with external sources

We determine numerically, and display graphically, the electromagnetic energy distribution due to static sources in compact QED₃. Using the polymer formulation of the functional integral, Monte Carlo simulations are performed with external sources included in the lattice action. Both the Wilson and Villain forms of the action are studied, and the string tension is determined in a small range of weak couplings. For the Villain action, our values for the string tension σ are in agreement with Polyakov's formula. For the Wilson action, we are able to detect a string tension in a range of weak couplings 2.1 ? β ? 2.3 below the weak-to-strong coupling cross-over point. In the same range, standard Monte Carlo results for up to 8 × 8 Wilson loops are consistent with ordinary perturation theory (no confinement). A possible explanation of this discrepancy is discussed, and it is suggested that the standard (source-free) Monte Carlo might miss configurations which are important for flux-tube formation.