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.     

Grain Boundary Migration in Metals: Recent Developments

Current research on grain boundary migration in metals is reviewed. For individual grain boundaries the dependence of grain boundary migration on misorientation and impurity content are addressed. Impurity drag theory, extended to include the interaction of adsorbed impurities in the boundary, reasonably accounts quantitatively for the observed concentration dependence of grain boundary mobility. For the first time an experimental study of triple junction motion is presented. The kinetics are quantitatively discussed in terms of a triple junction mobility. Their impact on the kinetics of microstructure evolution during grain growth is outlined.     

Grain boundaries of nanocrystalline materials – their widths, compositions, and internal structures

Nanocrystalline materials contain many atoms at and near grain boundaries. Sufficient numbers of Mössbauer probe atoms can be situated in grain boundary environments to make a clear contribution to the measured Mössbauer spectrum. Three types of measurements on nanocrystalline materials are reported here, all using Mössbauer spectrometry in conjunction with X-ray diffractometry, transmission electron microscopy, or small angle neutron scattering. By measuring the fraction of atoms contributing to the grain boundary component in a Mössbauer spectrum, and by knowing the grain size of the material, it is possible to deduce the average width of grain boundaries in metallic alloys. It is found that these widths are approximately 0.5 nm for fcc alloys and slightly larger than 1.0 nm for bcc alloys. Chemical segregation to grain boundaries can be measured by Mössbauer spectrometry, especially in conjunction with small angle neutron scattering. Such measurements on Fe-Cu and Fe₃Si-Nb were used to study how nanocrystalline materials could be stabilized against grain growth by the segregation of Cu and Nb to grain boundaries. The segregation of Cu to grain boundaries did not stabilize the Fe-Cu alloys against grain growth, since the grain boundaries were found to widen and accept more Cu atoms during annealing. The Nb additions to Fe₃Si did suppress grain growth, perhaps because of the low mobility of Nb atoms, but also perhaps because Nb atoms altered the chemical ordering in the alloy. The internal structure of grain boundaries in nanocrystalline materials prepared by high-energy ball milling is found to be unstable against internal relaxations at low temperatures. The Mössbauer spectra of the nanocrystalline samples showed changes in the hyperfine fields attributable to movements of grain boundary atoms. In conjunction with SANS measurements, the changes in grain boundary structure induced by cryogenic exposure and annealing at low temperature were found to be somewhat different. Both were consistent with a sharper density gradient between the crystalline region and the grain boundary region.     

Effect of grain boundary on the mechanical behaviors of irradiated metals: a review

The design of high irradiation-resistant materials is very important for the development of next-generation nuclear reactors. Grain boundaries acting as effective defect sinks are thought to be able to moderate the deterioration of mechanical behaviors of irradiated materials, and have drawn increasing attention in recent years. The study of the effect of grain boundaries on the mechanical behaviors of irradiated materials is a multi-scale problem. At the atomic level, grain boundaries can effectively affect the production and formation of irradiation-induced point defects in grain interiors, which leads to the change of density, size distribution and evolution of defect clusters at grain level. The change of microstructure would influence the macroscopic mechanical properties of the irradiated polycrystal. Here we give a brief review about the effect of grain boundaries on the mechanical behaviors of irradiated metals from three scales: microscopic scale, mesoscopic scale and macroscopic scale.     

Grain Boundary Kinetics in Oxide Ceramics with the Cubic Fluorite Crystal Structure and its Derivatives

Kinetics of grain boundaries in oxides with the cubic fluorite structure and its derivatives has been investigated using fine grain ceramics that are fully dense. Grain growth measurements in these materials have provided information on grain boundary diffusivity over a diffusion distance of the order of the initial grain size. With the addition of solute cations, grain boundary mobility can be varied over many orders of magnitude, often with very different activation energies. This is caused by the variation of defect population and the defect-solute association. Definitive evidence for solute drag has also been observed in some cases, but solute drag can not be confirmed as a general mechanism in solid solutions. Lastly, while grain boundary at low temperature may continue to serve as a fast diffusion path, it may not be able to migrate because of additional pinning mechanisms such as those exerted by grain boundary nodal points or lines. This means that sintering without grain growth is possible, opening up an avenue for obtaining ultrafine ceramics by pressureless sintering.     

Grain Growth in Polycrystalline Thin Films of Semiconductors

Grain growth in thin films is usually abnormal, leading not only to an increase in the average grain size, but also to an evolution in the shape of the grain size distribution and to an evolution in the distribution of grain orientations. The latter can be driven by surface, interface or strain energy minimization, depending on film and substrate properties and on deposition conditions, and can lead to different final textures depending on which energy dominates.In semiconductor films, as in other materials, grain growth stagnation coupled with texture-selective driving forces leads to secondary grain growth, the rate of which is higher in thinner films. Self ion-bombardment enhances the rate of pre-stagnation grain growth, and doping of Si with electron donor leads to enhanced pre-stagnation grain growth as well as surface-energy-driven secondary grain growth. The effects of ion-bombardment and dopants on grain growth in Si can be understood in terms of associated increases in point defect concentrations and the effects of point defects on grain boundary mobilities.     

Grain boundary misorientation changes during grain growth in pure aluminium

A new method is described for data-logging large amounts of grain boundary misorientation information from channelling patterns in the scanning electron microscope (SEM). The method relies on producing specimens where the grain size is larger than the specimen thickness and where the grain boundary planes are perpendicular to the specimen plane (the so-called columnar structure). Results for grain growth in pure aluminium at 460 and 500°C are presented. There is an increase in the proportion of low angle boundaries at the expense of high angle boundaries during growth times of up to a few hours. The reasons are thought to be partly connected with lower low angle boundary mobility compared with high angle boundaries. However, the growth kinetics appear to be normal over the entire growth time range.     

Crack–grain boundary interactions in zinc bicrystals

In polycrystalline materials that fail by transgranular cleavage, it is known that crystallographic misorientation of preferred fracture planes across grain boundaries can provide crack growth resistance; despite this, the micromechanisms associated with crack transmission across grain boundaries and their role in determining the overall fracture resistance are not well understood. Recent studies on diverse structural materials such as steels, aluminum alloys and intermetallics have shown a correlation between fracture resistance and the twist component of grain misorientation. However, the lack of control over the degree and type of misorientation in experimental studies, combined with a dearth of analytical and computational investigations that fully account for the three-dimensional nature of the problem, have precluded a systematic analysis of this phenomenon. In this study, this phenomenon was investigated through in situ crack propagation experiments across grain boundaries of controlled twist misorientation in zinc bicrystals. Extrinsic toughening mechanisms that activate upon crack stagnation at the grain boundary deter further crack propagation. The mechanical response and crack growth behavior were observed to be dependent on the twist angle, and several accommodation mechanisms such as twinning, strain localization and slip band blocking contribute to fracture resistance by competing with crack propagation. Three-dimensional finite element analyses incorporating crystal plasticity were performed on a stagnant crack at the grain boundary that provide insight into crack-tip stress and strain fields in the second grain. These analyses qualitatively capture the overall trends in mechanical response as well as strain localization around stagnant crack-tips.     

Linear grain growth kinetics and rotation in nanocrystalline Ni

We report three-dimensional atomistic molecular dynamics studies of grain growth kinetics in nanocrystalline Ni. The results show the grain size increasing linearly with time, contrary to the square root of the time kinetics observed in coarse-grained structures. The average grain boundary energy per unit area decreases simultaneously with the decrease in total grain boundary area associated with grain growth. The average mobility of the boundaries increases as the grain size increases. The results can be explained by a model that considers a size effect in the boundary mobility.     

Grains,growth, and grooving

We report the in situ investigation of grain growth and grain boundary migration, performed with a variable-temperature scanning tunneling microscope (STM) on a polycrystalline gold film. Atomic step resolution allowed us to identify the individual grains and, thus, also the grain boundaries. Our special, thermal-drift-compensated STM design made it possible to follow the same sample area over large temperature intervals. In this way, we have directly observed grain boundary migration and grain growth. In a first quantitative analysis we correlate the observed, unexpected changes in surface roughness with the evolution of the grain and grain boundary configuration.     

Grain boundary,triple junction and quadruple point mobility controlled normal grain growth

Reduction in stored free energy provides the thermodynamic driving force for grain and bubble growth in polycrystals and foams. Evolution of polycrystalline networks exhibit the additional complication that grain growth may be controlled by several kinetic mechanisms through which the decrease in network energy occurs. Polyhedral boundaries, triple junctions (TJs), and quadruple points (QPs) are the geometrically distinct elements of three dimensional networks that follow Plateau’s rules, provided that grain growth is limited by diffusion through, and motion of, cell boundaries. Shvindlerman and co-workers have long recognized the kinetic influences on polycrystalline grain growth of network TJs and QPs. Moreover, the emergence of interesting polycrystalline nanomaterials underscored that TJs can indeed influence grain growth kinetics. Currently there exist few detailed studies concerned either with network distributions of grain size, number of faces per grain, or with ‘grain trajectories’, when grain growth is limited by the motion of its TJs or QPs. By contrast there exist abundant studies of classical grain growth limited by boundary mobility. This study is focused on a topological/geometrical representation of polycrystals to obtain statistical predictions of the grain size and face number distributions, as well as growth ‘trajectories’ during steady-state grain growth. Three limits to grain growth are considered, with grain growth kinetics controlled by boundary, TJ, and QP mobilities.     

Texture weakening in pure magnesium during grain growth

The microstructure and texture evolution during annealing of rolled pure Mg, at temperatures ranging from 150 to 400°C, was characterised in the present study. A grain growth exponent of n?=?13 was observed and the activation energy for grain growth kinetics was found to be 95.6?kJ?mol^?1. Further, broadening of the normalised grain size distributions, indicating abnormal grain growth, was also observed at all temperatures of annealing. The sample had a dominant basal texture before annealing. However, after annealing up to a temperature of 300°C, the alleviation of basal texture was observed in the samples. On further annealing at a temperature of 400°C, a strong basal texture was developed in the samples. The mobility of high angle grain boundaries, which is proportional to correlated misorientation distribution, was observed to be responsible for texture strengthening of the material. The grain boundary mobility changes during grain growth led to the growth of either small or large grains. It was further observed that the growth of small grains caused the formation of basal fibre and large grains led to the weakening of basal texture.     

Non-planar grain boundary structures in fcc metals and their role in nano-scale deformation mechanisms

This work presents the results of a comparative molecular dynamics study showing that relaxed random grain boundary structures can be significantly non-planar at the nano-scale in fcc metals characterized by low stacking fault values. We studied the relaxed structures of random [1?1?0] tilt boundaries in a polycrystal using interatomic potentials describing Cu and Pd. Grain boundaries presenting non-planar features were observed predominantly for the Cu potential but not for the Pd potential, and we relate these differences to the stacking fault values. We also show that these non-planar structures can have a strong influence on dislocation emission from the grain boundaries as well as on grain boundary strain accommodation processes, such as grain boundary sliding. We studied the loading response in polycrystals of 40 nm grain size to a level of 9% strain and found that the non-planar grain boundaries favour dislocation emission as a deformation mechanism and hinder grain boundary sliding. This has strong implications for the mechanical behaviour of nano-crystalline materials, which is determined by the competition between dislocation activity and grain boundary accommodation of the strain. Thus, the two interatomic potentials for Cu and Pd considered in this work resulted in the same overall stress–strain curve, but significantly different fractions of the strain accommodated by the intergranular versus intragranular deformation mechanisms. Strain localization patterns are also influenced by the non-planarity of the grain boundary structures.     

Grain growth and static recrystallization kinetics in Co–20Cr–15W–10Ni (L-605) cobalt-base superalloy

The grain size evolution of cold-rolled L-605 cobalt-base superalloy during ultra-rapid annealing is investigated in this paper. Cold-worked specimens undergo static recrystallization, leading to grain refinement or grain coarsening depending on the annealing time and temperature. The kinetics of grain growth is found to be independent of the initial deformation. The evolution of grain size can be simply described by a grain growth model for high temperatures and long annealing times, and the mobility of interfaces is estimated by modelling. Fast annealing treatment process is a very promising technique to customize grain size and enhance mechanical strength. In particular, the reduction of annealing time is an efficient method to produce a refined microstructure through static recrystallization.     

Multi-phase field simulation of competitive grain growth for directional solidification

The multi-phase field model of grain competitive growth during directional solidification of alloy is established. Solving multi-phase field models for thin interface layer thickness conditions, the grain boundary evolution and grain elimination during the competitive growth of SCN-0.24-wt% camphor model alloy bi-crystals are investigated. The effects of different crystal orientations and pulling velocities on grain boundary microstructure evolution are quantitatively analyzed. The obtained results are shown below. In the competitive growth of convergent bi-crystals, when favorably oriented dendrites are in the same direction as the heat flow and the pulling speed is too large, the orientation angle of the bi-crystal from small to large size is the normal elimination phenomenon of the favorably oriented dendrite, blocking the unfavorably oriented dendrite, and the grain boundary is along the growth direction of the favorably oriented dendrite. When the pulling speed becomes small, the grain boundary shows the anomalous elimination phenomenon of the unfavorably oriented dendrite, eliminating the favorably oriented dendrite. In the process of competitive growth of divergent bi-crystal, when the growth direction of favorably oriented dendrites is the same as the heat flow direction and the orientation angle of unfavorably oriented grains is small, the frequency of new spindles of favorably oriented grains is significantly higher than that of unfavorably oriented grains, and as the orientation angle of unfavorably oriented dendrites becomes larger, the unfavorably oriented grains are more likely to have stable secondary dendritic arms, which in turn develop new primary dendritic arms to occupy the liquid phase grain boundary space, but the grain boundary direction is still parallel to favorably oriented dendrites. In addition, the tertiary dendritic arms on the developed secondary dendritic arms may also be blocked by the surrounding lateral branches from further developing into nascent main axes, this blocking of the tertiary dendritic arms has a random nature, which can have aninfluence on the generation of nascent primary main axes in the grain boundaries.     

Diffusion generated motion for grain growth in two and three dimensions

An efficient algorithm for accurately simulating curvature flow for large networks of curves in two dimensions and surfaces in three dimensions on uniform grids is proposed. This motion arises in the technologically important problem of simulating grain boundary motion in polycrystalline materials. In this formulation grain boundaries are zero-level sets of signed distance functions. Curvature motion is achieved by first diffusing locally maintained signed distance functions followed by a reinitialization step. A technique is devised to allow a single signed distance function to represent a large subset of spatially separated grains. Hundreds of thousands of grains can be simulated using a small number of signed distance functions (in this work, 32 in two dimensions and 64 in three dimensions are more than sufficient) using modest computational hardware.     

Grain Boundary Migration in Ceramics

During ceramic fabrication, densification processes compete with coarsening processes to determine the path of microstructural evolution. Grain growth is a key coarsening process. This paper examines grain boundary migration in ceramics, and discusses the effects of solutes, pores, and liquid phases on grain boundary migration rates. An effort is made to highlight work in the past decade that has contributed to and advanced our understanding of solute drag effects, pore-boundary interactions, and the role of liquid phases in grain growth and microstructural evolution. Anisotropy of the grain boundary mobility, and its role in the development of anisotropic (anisometric) microstructures is discussed as it is a central issue in recent efforts to produce ceramic materials with new combinations of properties and functionality.     

Mechanical grain growth in nanocrystalline copper

Nanograined materials have some unusual properties. To maintain the small size of the grains, grain growth should be avoided. But recently grain growth has been observed under an indenter at liquid-nitrogen temperatures. Such grain growth has never been reported before. How can this happen and how can it be prevented? These questions are answered here using a simple tilt boundary. It is found that high purity and nonequilibrium structure are necessary conditions for mechanical grain growth. The material must be pure enough so that free dislocations are available to move out of the boundary. But the boundary should not be in the lowest-energy state so that extra dislocations are available to be emitted by stress. Based on these conditions, methods can be devised to avoid low temperature grain growth.     

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.