Boundary Mobility and Energy Anisotropy Effects on Microstructural Evolution During Grain Growth

We have performed mesoscopic simulations of microstructural evolution during curvature driven grain growth in two-dimensions using anisotropic grain boundary properties obtained from atomistic simulations. Molecular dynamics simulations were employed to determine the energies and mobilities of grain boundaries as a function of boundary misorientation. The mesoscopic simulations were performed both with the Monte Carlo Potts model and the phase field model. The Monte Carlo Potts model and phase field model simulation predictions are in excellent agreement. While the atomistic simulations demonstrate strong anisotropies in both the boundary energy and mobility, both types of microstructural evolution simulations demonstrate that anisotropy in boundary mobility plays little role in the stochastic evolution of the microstructure (other than perhaps setting the overall rate of the evolution. On the other hand, anisotropy in the grain boundary energy strongly modifies both the topology of the polycrystalline microstructure the kinetic law that describes the temporal evolution of the mean grain size. The underlying reasons behind the strongly differing effects of the two types of anisotropy considered here can be understood based largely on geometric and topological arguments.     

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.     

Scaling behavior of grain-rotation-induced grain growth

Recent investigations of grain growth in nanocrystalline materials have revealed a new growth mechanism: grain-rotation-induced grain coalescence. Based on a simple model employing a stochastic theory and using computer simulations, here we investigate the coarsening of a polycrystalline microstructure due solely to the grain-rotation coalescence mechanism. Our study demonstrates that this mechanism exhibits power-law growth with a universal scaling exponent. The value of this universal growth exponent is shown to depend on the assumed mechanism by which the grain rotations are accommodated.     

Molecular-Dynamics Simulation of Grain-Boundary Diffusion Creep

Molecular-dynamics (MD) simulations are used, for the first time, to study grain-boundary diffusion creep of a model polycrystalline silicon microstructure. Our fully dense model microstructures, with a grain size of up to 7.5 nm, were grown by MD simulations of a melt into which small, randomly oriented crystalline seeds were inserted. In order to prevent grain growth and thus to enable steady-state diffusion creep to be observed on a time scale accessible to MD simulations (of typically 10^-9s), our input microstructures were tailored to (i) have a uniform grain shape and a uniform grain size of nm dimensions and (ii) contain only high-energy grain boundaries which are known to exhibit rather fast, liquid-like self-diffusion. Our simulations reveal that under relatively high tensile stresses these microstructures, indeed, exhibit steady-state diffusion creep that is homogenous (i.e., involving no grain sliding), with a strain rate that agrees quantitatively with that given by the Coble-creep formula.     

Size distribution evolution equations in space-competing domain growth systems

A model of microstructure development for phase transformations driven by nucleation and growth is presented. The model is based on a set of Fokker-Planck-like equations which allows us to compute the particle grain density distribution at any time during the transformation, provided that the nucleation and growth dependences on time and/or grain radius are known. The model is applicable to any kind of nucleation and growth protocols fulfilling the Johnson–Mehl–Avrami–Kolmogorov conditions, namely spatially random nucleation and isotropic growth. Comparison with stochastic (Monte Carlo) simulations is presented, giving quantitative agreement in all cases. This work shows the relationship between kinetic parameters and microstructure evolution as well as the accuracy of the developed model.     

Two-dimensional normal grain growth: topological aspects

Normal grain growth in polycrystals is an important example of a capillarity driven coarsening phenomenon where topological structure of the system plays a major role. The process is practically important and attracts much interest, in particular in two-dimensional (2D) polycrystals because of the growing technological importance of thin polycrystalline films. In the present paper we discuss various approaches to normal grain growth in 2D polycrystals. We stay mostly within the framework of the uniform boundary model. This model provides a reasonable simplification leading to the Von Neumann-Mullins relation that relates the rate of growth of an individual grain to its local topology. Comparing different approaches—relatively simple mean-field theories, more sophisticated models incorporating real topology, and computer simulations adequately reproducing local equations of motion—we identify the principal factors responsible for different features of the phenomenon.     

Effects of energy dissipation on anisotropic materials

A model and its simulations are presented to describe the effects of energy dissipation on anisotropic systems. When the current electromigration is constant, energy dissipation depends on lattice constants, resistivity, and the angles along the longitudinal and transversal directions. It is shown that an orientation variation of the grain can significantly influence the energy dissipation for some anisotropic materials. Based on calculations for the grain model, the mechanism of grain growth and microstructure evolution under electromigration is explained. Theoretical implications about material selection and reliability are derived.     

Abnormal grain growth in Ni-5at.%W

The growth of abnormally large grains in textured Ni-5at.%W substrates for high-temperature superconductors deteriorates the sharp texture of these materials and thus has to be avoided. Therefore the growth of abnormal grains is investigated and how it is influenced by the grain orientation and the annealing atmosphere. Texture measurements and grain growth simulations show that the grain orientation only matters so far that a high-angle grain boundary exists between an abnormally growing grain and the Cube-orientated matrix grains. The annealing atmosphere has a large influence on abnormal grain growth which is attributed to the differences in oxygen partial pressure.     

Normal and Abnormal Grain Growth as Transient Phenomena

For the case of uniform grain boundaries the basic equations of the statistical theory of grain growth (GG) of the present authors are shortly reviewed and compared to the classical Hillert model. On the basis of this present theory normal and abnormal 3-D GG is simulated and particularly the effect of the initial grain size distribution function (SDF) on the GG behaviour which may lead to normal or abnormal GG is demonstrated. Finally results of simulations of normal 2-D GG by the statistical method and by a direct model (curvature driven grain boundaries (GBs)) are presented which exhibit good agreement with one another. It is shown by this comparison that the possibility of finding by such direct methods a self similar SDF as long time asymptote can be excluded because, in contrast to the simulations based on the statistical theory, for the direct models the very large computational capacities required for the long simulation times are not available yet. The conclusion repeatedly claimed in literature that the true self similar SDF deviates from the Hillert distribution can thus be shown not to be justified.     

Thin film compressive stresses due to adatom insertion into grain boundaries

Atomic simulations of the growth of polycrystalline Ni demonstrate that deposited atoms incorporate into the film at boundaries, resulting in compressive stress generation. Incorporated atoms can also leave the boundaries and thus relieve compressive stress. This leads to a complex interplay between growth stress, adatom incorporation, and surface structure. A simple, theoretical model that accounts for grain size effects is proposed and is in good agreement with simulation results.     

Experimental and theoretical study of the formation and growth of pearlite colonies in eutectoid steels

Optical and electron-microscopy observations of pearlite structures in eutectoid steels are described. These observations suggest that in such steels the processes of sidewise growth of pearlite colonies along grain boundaries may occur even though they were not observed in noneutectoid steels. A simple theoretical model is proposed to study the thermodynamics and kinetics of pearlite transformations. Simulations of the growth of pearlite colonies carried out on this model reveal that, for the usually assumed mechanism of volume diffusion of carbon, such growth is always unstable, and the steady-state growth can only be realized via interfacial carbon diffusion. A model is proposed for the formation of pearlite colonies near the grain boundaries of austenite. This model is based on the assumption that the diffusion of carbon is strongly enhanced near these boundaries, and it can be applied to plastically deformed steels. The results of simulations with this model qualitatively agree with some microstructural features of the formation of pearlite colonies observed in such steels.     

Theory and simulation of coupled grain boundary migration and grain rotation in low angle grain boundaries

Abstract

Microstructure evolution due to coupled grain boundary migration and grain rotation in low angle grain boundaries is studied through a combination of molecular dynamics and phase field modeling. We have performed two dimensional molecular dynamics simulations on a bicrystal with a circular grain embedded in a larger grain. Both size and orientation of the embedded grain are observed to evolve with time. The shrinking embedded grain is observed to have two regimes: constant dislocation density on the grain boundary followed by constant rate of increase in dislocation density. Based on these observations from the molecular dynamics simulations, a theoretical formulation of the kinetics of coupled grain rotation is developed. The grain rotation rate is derived for the two regimes of constant dislocation density and constant rate of change of dislocation density on the grain boundary during evolution. The theoretical calculation of the grain rotation rate shows strong dependence on the grain size and compares very well with the molecular dynamics simulations. A multi-order parameter based phase field model with coupled grain rotation is developed using the theoretical formulation to model polycrystalline microstructure evolution.     

Phase field models for heterogeneous nucleation: Application to inoculation in alpha-solidifying Ti-Al-B alloys

This paper aims at briefly reviewing phase field models applied to the simulation of heterogeneous nucleation and subsequent growth, with special emphasis on grain refinement by inoculation. The spherical cap and free growth model (e.g. A.L. Greer, et al., Acta Mater. 48, 2823 (2000)) has proven its applicability for different metallic systems, e.g. Al or Mg based alloys, by computing the grain refinement effect achieved by inoculation of the melt with inert seeding particles. However, recent experiments with peritectic Ti-Al-B alloys revealed that the grain refinement by TiB₂ is less effective than predicted by the model. Phase field simulations can be applied to validate the approximations of the spherical cap and free growth model, e.g. by computing explicitly the latent heat release associated with different nucleation and growth scenarios. Here, simulation results for point-shaped nucleation, as well as for partially and completely wetted plate-like seed particles will be discussed with respect to recalescence and impact on grain refinement. It will be shown that particularly for large seeding particles (up to 30?μm), the free growth morphology clearly deviates from the assumed spherical cap and the initial growth – until the free growth barrier is reached – significantly contributes to the latent heat release and determines the recalescence temperature.     

SmCo7纳米晶合金晶粒组织热稳定性的热力学分析与计算机模拟

推导出了单相纳米晶合金的晶界过剩体积与晶粒尺寸之间的定量关系, 建立了纳米晶合金的晶界热力学性质随温度和晶粒尺寸发生变化的确定性函数. 针对SmCo₇纳米晶合金, 通过纳米晶界热力学函数计算和分析, 研究了单相纳米晶合金的晶粒组织热稳定性. 研究表明, 当纳米晶合金的晶粒尺寸小于对应于体系中晶界自由能最大值的临界晶粒尺寸时, 纳米晶组织处于相对稳定的热力学状态; 当纳米晶粒尺寸达到和超过临界尺寸时, 纳米晶组织将发生热力学失稳, 导致不连续的快速晶粒长大. 利用纳米晶合金热力学理论与元胞自动机算法相耦合的模型对SmCo₇纳米晶合金在升温过程中的晶粒长大行为进行了计算机模拟, 模拟结果与纳米晶合金热力学模型的计算预测结果一致, 由此证实了关于纳米晶合金晶粒组织热稳定性的研究结论. 关键词： 纳米晶合金热力学 7纳米晶合金')" href="#">SmCo₇纳米晶合金 热稳定性 计算机模拟     

Parallel three-dimensional Monte Carlo simulations for effects of precipitates and sub-boundaries on abnormal grain growth of Goss grains in Fe–3%Si steel

Using parallel three-dimensional Monte Carlo simulations, we investigated the effects of precipitates and sub-boundaries on abnormal grain growth (AGG) of Goss grains based on real orientation data of primary recrystallized Fe–3%Si steel. The simulations showed that AGG occurred in the presence of precipitates which inhibited the grain growth of matrix grains, whereas it did not in the absence of precipitates. The role of precipitates in enhancing AGG is to maintain a relatively high fraction of high energy boundaries between matrix grains, which increases the probability of sub-boundary-enhanced solid-state wetting of an abnormally growing grain. The microstructure evolved by the simulation could reproduce many realistic features of abnormally growing grains, such as the formation of island and peninsular grains and merging of abnormally growing grains which appeared to be separated initially on the cross-section.     

An extensive 3D dislocation dynamics investigation of stage-I fatigue crack propagation

Stage-I fatigue crack propagation is investigated using 3D discrete dislocation dynamics (DD) simulations. Slip-based propagation mechanisms and the role of the pre-existing slip band on the crack path are emphasized. Stage-I crack growth is found to be compatible with successive decohesion of the persistent slip band/matrix interface rather than a mere effect of plastic irreversibility. Corresponding crack tip slip displacement magnitude and the associated crack growth rate are evaluated quantitatively at various tip distances from the grain boundary. This shows that grain boundaries systematically amplify slip dispersion ahead of the crack tip and consequently, slow down the stage-I crack growth rate. The results help in developing an original crack propagation model, accounting for the boundary effects relevant to polycrystals. The crack growth trend is then evaluated from calculations of the energy changes due to crack length increments. It is shown that the crack necessarily propagates by increments smaller than 10 nm.     

γ-α相变中不同晶界特征下铁素体生长形貌的相场模拟

利用多相场模型模拟了奥氏体(γ)-铁素体(α)相变过程中不同晶界特征下铁素体晶粒的形貌与生长动力学.模型中通过能量梯度系数和耦合项系数的协同变化定量表达晶界能与晶界迁移率的各向异性,同时固定相场界面宽度来保证计算精度.模拟结果显示:随着原奥氏体晶界能与铁素体-奥氏体晶界能比值σ_(γ,γ)/σ_(α,γ)的增加,三叉相界面处的平衡角β减小,铁素体晶粒沿原奥氏体晶界与垂直于奥氏体晶界方向的生长速率差变大.铁素体与奥氏体晶粒间的晶粒取向越接近,铁素体生长越缓慢.模拟结果可描述铁素体晶粒生长形貌的多样性,与实验结果符合.     

Nonuniform growth of embedded silicon nanocrystals in an amorphous matrix

The phase transformation of a metastable system occurs when islands of a second stable phase form and grow. The growth velocity of the islands controls the kinetics of the phase transformation. In this work we consider the amorphous-to-crystalline transformation in silicon as the prototype of a solid-to-solid transformation. The results of atomistic simulations are fit using an analytic model for the growth of [100]-oriented nanosized crystalline fibers embedded into an amorphous matrix. We demonstrate that the radius of the island does not grow, in general, at constant velocity. On the contrary, we identify a decelerated motion that is due to anisotropic effects of the crystal grain. Such a nonuniform growth should be taken into account in the modeling of solid-to-solid crystallization.     

Effect of finite boundary junction mobility on the growth rate of grains in 3D polycrystals

With decreasing grain size, grain boundary junctions become increasingly important for microstructure evolution. We show that the effect of a limited mobility of triple junctions on the growth rate of polycrystals can be implemented in theories of three-dimensional (3D) grain growth. Respective analytical relations are derived on the basis of the average n-hedra approach introduced by Glicksman to describe the volume rate of change of 3D grains in a polycrystalline aggregate under the impact of a limited triple junction mobility. The theoretical predictions were compared to network-model computer simulations, and good agreement was obtained.     

Effect of High-Temperature Structure and Diffusion on Grain-Boundary Diffusion Creep in fcc Metals

Molecular dynamics simulations of high-energy twist and tilt bicrystals of fcc palladium reveal a universal, liquid-like, isotropic high-temperature diffusion mechanism, characterized by a rather low self-diffusion activation energy that is independent of the boundary type or misorientation. Medium-energy grain boundaries exhibit the same behavior at the highest temperatures; however, at lower temperatures the diffusion mechanism becomes anisotropic, with a higher, misorientation-dependent activation energy. Our simulations demonstrate that the lower activation energy at elevated temperatures is caused by a structural transition, from a solid boundary structure at low temperatures to a liquid-like structure at high temperatures. We demonstrate that the existence of such a transition has important consequences for diffusion creep in nanocrystalline fcc metals. In particular, our simulations reveal that in the absence of grain growth, nanocrystalline microstructures containing only high-energy grain boundaries exhibit steady-state diffusion creep with a creep rate that agrees quantitatively with that given by the Coble-creep formula. Remarkably, the activation energy for the high-temperature creep rate is the same as that characterizing the universal high-temperature diffusion in high-energy energy bicrystalline grain boundaries.