Model-based simulation of normal grain growth in a two-phase nanostructured system

Abstract

To systematically study normal grain growth in a two-phase volume-conserved system, a modified Potts model is proposed, in which the driving forces for grain boundary migration are the interfacial energy between two phases and the boundary energy inside each phase. Model-based simulation results show that the grain growth kinetics follows a power law with a temperature-independent exponent and that the normalized grain size distribution is lognormal and time invariant. Also, a simple theoretical model is used to predict the potential microstructure in a two-phase system due to the competition between interfacial and grain boundary energies. A critical ratio (~2.6) of the grain boundary energy to the interfacial energy is found for a common two-phase system.     

Modeling nano-scale grain growth of intermetallics

The Monte Carlo simulation is utilized to model the nano-scale grain growth of two nano-crystalline materials, Pd₈₁Zr₁₉ and RuAl. In this regard, the relationship between the real time and the time unit of simulation, i.e. Monte Carlo step (MCS), is determined. The results of modeling show that with increasing time of heating, the grain sizes of both nano-crystalline materials increased as in the case of conventional materials. Moreover, it is found that for both nano-crystalline materials the relationship between the real time and MCS is in power law form, which is linear for the conventional materials.     

On the quasi-stationary grain size distribution from two Gamma size distributions in three-dimensional grain growth

Two different grain structures of which the grain size distribution could be well described by the Gamma distribution were generated by the combination of the Laguerre tessellation and Monte Carlo technique. Monte Carlo simulation shows that the three-dimensional grain growth process can evolve to the quasi-stationary state. The quasi-stationary grain size distribution could be well fit by the Gamma distribution with different parameters. The results in literature from various simulation methods support this point.     

HAZ microstructure simulation in welding of a ultra fine grain steel

In the present work the evolution of grain structure in the weld HAZ (heat affected zone) under welding thermal cycle was simulated. Especially the grain growth in the HAZ of a SS400 ultra fine grain steel was investigated. An integrated 3-D Monte Carlo (MC) simulation system for grain growth of the weld HAZ was developed based on Microsoft Windows. The results indicate that MC simulation is an effective way to investigate the grain growth in weld HAZ. The method not only simulates the non-isothermal dynamics process of the grain growth in the weld HAZ, but also visualizes the austenite grains realistically. Moreover, the thermal pinning effect can be easily included in the simulation process. The grain sizes of the CGHAZ (coarse grain heat affected zone) obtained from MC simulation are basically in agreement with the experimental measurement of the real welded joints under different heat input. Furthermore, the simulation indicates that the grain growth degree is higher for the SS400 ultra fine grain steel compared to conventional steel. With the increase in the heat input, the grain growth of the CGHAZ rapidly increases. Because the activation energy of the grain growth is lower for the SS400 ultra fine grain steel, austenite grains can grow at a relatively lower temperature, hence the range of the CGHAZ becomes wider.     

Combined atomistic and mesoscale simulation of grain growth in nanocrystalline thin films

We have combined molecular-dynamics (MD) simulations with mesoscale simulations to elucidate the mechanism and kinetics of grain growth in nanocrystalline palladium with a columnar grain structure. The conventional picture of grain growth assumes that the process is governed by curvature-driven grain-boundary (GB) migration. Our MD simulations demonstrate that, at least in a nanocrystalline material, grain growth can also be triggered by the coordinated rotations of neighboring grains so as to eliminate the common GB between them. Such rotation–coalescence events result in the formation of highly elongated, unstable grains which then grow via the GB migration mechanism. These insights can be incorporated into mesoscale simulations in which, instead of the atoms, the objects that evolve in space and time are discretized GBs, grain junctions and the grain orientations, with a time scale controlled by that associated with grain rotation and GB migration and with a length scale given by the grain size. These mesoscale simulations, with physical insight and input materials parameters obtained by MD simulation, enable the investigation of the topology and long-time grain-growth behavior in a physically more realistic manner than via mesoscale simulations alone.     

两种晶粒长大Monte Carlo方法的比较

比较了两种改进的晶粒生长的Monte Carlo方法。通过比较晶粒形貌演化图和晶粒尺寸随时间的变化，发现这两种方法不仅都能够给出比Metropolis抽样更加改进的晶粒生长指数，且明显加快了模拟速度，而且晶粒大小的分布更加合理。这与正常晶粒拓扑演化和理论分析的生长动力学相符合。最后给出了两种改进的方法和Metropolis方法得到的晶粒尺寸分布曲线。     

Influence of the second-phase particle size on grain growth based on computer simulation

A three-dimensional Monte Carlo simulation method for grain growth in two-phased materials is set up, basing on a micro-physical analysis of the interaction between the second-phase particle and the grain boundary. Two-phased systems containing second-phase particles with the same quantity but different sizes are designed, and the complete processes of grain growth are simulated. The influences of the particle size on grain growth are observed and studied quantitatively.     

Grain boundary migration during abnormal grain growth in nanocrystalline Ni

The transformation mechanisms of abnormal grain growth in nanocrystalline Ni were studied extensively by transmission electron microscopy (TEM). A combination of in situ TEM annealing and ex situ annealing followed by TEM characterization was used. It was observed that grain boundary migration is both spatially and temporally non-uniform; migration occurs in a series of discrete steps, which are followed by periods of stagnation.     

Monte Carlo simulation of nucleation and growth of thin films

We study thin film growth using a lattice-gas, solid-on-solid model employing the Monte Carlo technique. The model is applied to chemical vapour deposition (CVD) by including the rate of arrival of the precursor molecules and their dissociation. We include several types of migration energies including the edge migration energy which allows the diffusive movement of the monomer along the interface of the growing film, as well as a migration energy which allows for motion transverse to the interface. Several well-known features of thin film growth are mimicked by this model, including some features of thin copper films growth by CVD. Other features reproduced are—compact clusters, fractal-like clusters, Frank-van der Merwe layer-by-layer growth and Volmer-Weber island growth. This method is applicable to film growth both by CVD and by physical vapour deposition (PVD).     

Vacancies in selected special tilt grain boundaries in Ni3Al

The structure of selected special (Σ=5) symmetrical tilt grain boundaries in Ni₃Al with tilt axis [1 0 0] was simulated by the Monte Carlo method. Vacancies were generated both in Al and Ni sites in their relaxed structure and the vacancy formation and migration energy was estimated.     

二维晶粒演变过程的模拟及分形研究

以蒙特卡罗随机模拟方法为基础,通过对原有算法进行改进,对二维晶粒的演变过程进行了计算机模拟和分形研究,获得了统计等效组织模型．分析表明,模拟的晶粒在演变过程中具有分形特性,即晶粒形态具有与时间无关的相似性,与晶粒形核和生长的物理机制相一致,证明了模拟过程的合理性．从而为后续热变形显微组织演变的模拟中晶核的空间分布和生长提供较为精确的显微组织基础．     

Microstructural evolution in nanostructured gold films

Thin Au films in the thickness range t = 1.5-126 nm were coated by DC sputtering on SiO_x/Si substrates at room temperature inside a vacuum chamber with a base pressure of about 1 × 10^− 2 mbar (1 Pa). The film structure, nanograin characteristics, and the surface roughness as a function of thickness were analyzed using X-ray diffraction, scanning tunneling microscopy and transmission electron microscopy. The results reflect the microstructural evolution with film thickness. They help us to understand the mode of grain growth, which is monomodal-normal columnar as well as spherical. By determination of the dynamic scaling exponent derived from power law dependence of the mean grain size and film thickness, the prevailed mechanism of grain growth is deduced to be the diffusion of mobile Au atoms in grain boundaries. The surface roughness increases with the film thickness following a power law: R_rms ~ t^b. The linear fitted value for b is 0.60.     

Monte Carlo simulation of polycrystalline microstructures and finite element stress analysis

A two-dimensional numerical model of microstructural effects is presented, with an aim to understand the mechanical performance in polycrystalline materials. The microstructural calculations are firstly carried out on a square lattice by means of a 2-D Monte Carlo (MC) simulation for grain growth, then the conventional finite element method is applied to perform stress analysis of a plane strain problem. The mean grain size and the average stress are calculated during the MC evolution. The simulation result shows that the mean grain size increases with the simulation time, which is about 3.2 at 100 Monte Carlo step (MCS), and about 13.5 at 5000 MCS. The stress distributions are heterogeneous in materials because of the existence of grains. The mechanical property of grain boundary significantly affects the average stress. As the grains grow, the average stress without grain boundary effect slightly decreases as the simulation time, while the one with strengthening effect significantly decreases, and the one with weakening effect increases. The average stress and the grain size agree well with the Hall–Petch relationship.     

Grain growth and stabilisation of nanostructured aluminium at high temperatures: review

Nanostructured (NS) materials have a large stored energy due to their large grain boundary area and thus tend to be unstable with respect to grain growth during high temperature annealing or deformation. This problem can limit the application of NS materials at high temperatures (>0·5T_m, absolute melting temperature), especially Al alloys owing to their low melting points. Restoration processes and grain growth in NS Al based materials are critically reviewed, with emphasis on nanostructure grain stabilisation at high temperatures. The mechanisms of normal and abnormal grain growth during isothermal annealing are presented, followed by consideration of thermal stabilisation by the addition of solute atoms/impurities and/or dispersion of second phase particles. Grain growth is significantly facilitated by applying deformation at elevated temperatures during preparation or further processing of semifinished NS materials. The dynamic restoration processes, dynamic grain growth and dynamic particle coarsening are addressed in NS Al. Finally, grain growth during consolidation of nanocrystalline powders (one of the principal methods to fabricate bulk NS Al) is presented, and the effects of processing parameters on grain size stabilisation are discussed.     

蒙特卡罗方法模拟陶瓷晶粒生长研究进展

概述了蒙特卡罗模拟方法的基本原理和思想,介绍了陶瓷烧结过程中,蒙特卡罗分别模拟单相系统和二相系统中晶粒生长的模型,综述了国内外蒙特卡罗方法模拟陶瓷烧结过程中晶粒生长的研究进展,指出了当前该研究领域中存在的问题,提出了今后发展的主要方向:将模型与具体材料和实际工艺联系起来,模拟定量化,并向三维模拟发展,以解决实际问题.     

Impact of grain boundary junctions on grain growth in polycrystals with different grain sizes

Effect of finite mobility of triple and quadruple grain boundary junctions on grain growth is studied by numerical simulation. They retard the growth process and transform its kinetics from parabolic one into a sequence consisting of exponential, linear and parabolic steps. This relates even to polycrystals with large initial grain sizes. Such junctions can contribute to microstructure stabilization in nanomaterials.     

磁性多层膜系统自旋重取向行为的Monte Carlo模拟

依据Heisenberg模型,利用Monte　Carlo方法模拟了磁性多层膜系统的自旋重取向行为,研究了各向异性、偶极相互作用以及外磁场对系统自旋取向的影响。通过模拟计算,获得了系统组态、磁分量等随偶极相互作用、外加磁场和温度的变化规律,重点研究了磁性多层膜系统在外磁场作用下的磁滞现象。     

Grain growth simulation of {1 1 1} and {1 1 0} oriented CVD–SiC film by Potts Monte Carlo

In analyzing microstructure evolution of material, study for the process of grain growth is both theoretically and practically significant. On (1 1 1) and (1 1 0) facets, the process of CVD–SiC film in two-dimension is simulated with Potts Monte Carlo method. The relationship between the microstructure morphology and growth rate, nucleating density is analyzed. The simulation result is given as the following. Both competitive growth and coarsening effect have been found in the growth process. The increase of nucleation density results in thinning of the grain size in SiC film. The grain size distribution is found to be self-similar, not differed with the corresponding growth parameter. The fitted result of Weibull and Louat function is better than that of lognormal function obviously. The result is in agreement with the corresponding theory and experiment conclusion well.     

Comparative study of two phase-field models for grain growth

There exist different phase-field models for the simulation of grain growth in polycrystalline structures. In this paper, the model formulation, application and simulation results are compared for two of these approaches. First, we derive relations between the parameters in both models that represent the same set of grain boundary energies and mobilities. Then, simulation results obtained with both models, using equivalent model parameters, are compared for grain structures in 2D and 3D. The evolution of the individual grains, grain boundaries and triple junction angles is followed in detail. Moreover, the simulation results obtained with both approaches are compared using analytical theories and previous simulation results as benchmarks. We find that both models give essentially the same results, except for differences in the structure near small shrinking grains which are most often locally and temporary for large grain structures.