Grain growth controlled by triple junctions: Effect of number of topological elements

In addition to driving forces due to curvature of grain boundaries there are driving forces acting on triple junctions which also contribute to grain growth. Equations are derived for the rate of change, due to the triple junction forces, of the average area or average volume of 2D and 3D grains, respectively, with a fixed number of topological elements (edges in 2D and faces in 3D). The equations derived are compared with the von Neumann-Mullins equation for 2D curvature driven grain growth and to the extension of that equation to 3D grain growth. In triple junction controlled grain growth, the effect ofn orF is qualitatively the same as in curvature driven growth, with a threshold atn or –F between shrinkage and growth. However, the rates are in general not linear onn orF, and there is a size effect which has a repercursion on the overall growth kinetics.     

The Effect of Triple Junctions on Grain Boundary Motion and Grain Microstructure Evolution

The theory of steady state motion of grain boundary sytems with triple junctions and the main features of such systems are considered. A special technique of in-situ observations and recording of triple junction motion is introduced, and the results of experimental measurements on Zn tricrystals are discussed. It is shown, in particular, that the described method makes it possible to measure the triple junction mobility. It was found that the measured shape of a moving half-loop with a triple junction agrees with theoretical predictions. A transition from triple junction kinetics to grain boundary kinetics was observed. This means that triple junctions can drag boundary motion. It is demonstrated that the microstructural (granular) evolution is slowed down by triple junction drag for any n-sided grain. The second consequence pertains to six-sided grains. For a boundary system with dragging triple junctions there is no unique dividing line between vanishing and growing grains with respect to their topological class anymore, like n = 6 in the Von Neumann-Mullins relation.     

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.     

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.     

Mean width and caliper characteristics of network polyhedra

The kinetic modelling of space-filling grain networks has been approached traditionally by representing the grains as spheres of equivalent volume. A spherical approximation used to describe polyhedral grains, unfortunately, relinquishes most geometrical and all topological details of the grain structure. Techniques developed by Hilgenfeldt et al., and by Glicksman, describe network structures comprised of space-filling irregular polyhedra and their kinetics with regular polyhedra, which act as ‘proxies’ that preserve both local topology and network constraints. Analytical formulas based on regular polyhedra and Surface Evolver simulations are used in this study to calculate the average caliper width and mean width for extended sets of polyhedra that vary systematically from convex to concave objects. Of importance, caliper width and mean width measures allow estimation of the growth rates of grains. Comparison of these calculations and simulations, however, reveal a weak dependence between average caliper width and mean width measures and the detailed shapes of polyhedra, especially their face curvatures. This finding might, in fact, affect the application and use of linear measures as kinetic tools in quantitative microstructure measurements.     

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.     

Dependence of grain boundary character distribution on the initial grain size of 304 austenitic stainless steel

Abstract

In order to study the dependence of the grain boundary character distributions (GBCD) on the grain size, annealing treatment was carried out on 304 austenitic stainless steel with different initial grain sizes. The evolution of the GBCD was analysed by electron backscatter diffraction. The experimental results showed that abnormal grain growth (AGG) occurred when grain size was small. With a smaller initial grain size, the number density of abnormally large grains and the fraction of low-Σ CSL boundaries increased but the size of abnormally large grains decreased and the random boundaries presented a continuous network. With a larger initial grain size, the fraction of low-Σ CSL boundaries also increased as well as the size of abnormally large grains but the number density of abnormally large grains decreased and the connectivity of random boundary network was disrupted by low-Σ CSL boundaries, especially Σ3ⁿ (n = 1, 2, 3) boundaries. However, with a very large initial grain size, normal grain growth (NGG) occurred, which had no effect on the fraction of low-Σ CSL boundaries and the connectivity of random boundary network.     

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 growth and phason-strain field in quasicrystalline Al-Li-Cu

We report on grain growth and related structure change in single phased Al-Li-Cu quasicrystals. The icosahedral phase grains have been investigated using scanning ion microscopy and transmission electron microscopy. Regular boundaries between large grains have been observed both before and after high temperature annealing. The electron diffraction study shows that the grain growth is accompanied by a reduction of the phason-strains. The orientation relation between grains sets the 2-fold icosahedral axes parallel, and the coincidence of the planes depends on the phason strain-field. The effect of phason-strain field on these boundaries is discussed. It is proposed that the phason strain elimination can play a role in the grain growth. Received 1 February 1999 and Received in final form 12 May 1999     

晶粒棱长、尺寸与拓扑学特征之间关系的Monte Carlo仿真研究

采用Potts模型Monte Carlo方法研究了晶粒棱长、尺寸与拓扑学特征之间的统计关系.结果表明,晶粒棱长与晶粒面数之间呈线性统计关系,并且平均N面体晶粒模型和Poisson-Voronoi组织均支持该结论.不同时刻的晶粒长大仿真数据表明,在准稳态晶粒长大阶段晶粒棱长的分布具有自相似性.个体晶粒的平均棱长随晶粒面数（或晶粒尺寸）的增加而逐渐增大,这说明一些理论模型中采用的“不同面数的晶粒平均棱长均相等”的假设具有局限性.仿真数据和纯铁实验数据均表明,晶粒尺寸与晶粒面数之间的统计关系表现为一条单调递增的凸曲线. 关键词： 晶粒棱长 晶粒尺寸 拓扑学 Monte Carlo仿真     

Coarsening in Sintering: Grain Shape Distribution,Grain Size Distribution,and Grain Growth Kinetics in Solid-Pore Systems

Sintering occurs when packed particles are heated to a temperature where there is sufficient atomic motion to grow bonds between the particles. The conditions that induce sintering depend on the material, its melting temperature, particle size, and a host of processing variables. It is common for sintering to produce a dimensional change, typically shrinkage, where the powder compact densifies, leading to significant strengthening. Microstructure coarsening is inherent to sintering, most evident as grain growth, but it is common for pore growth to occur as density increases. During coarsening, the grain structure converges to a self-similar character seen in both the grain shape distribution and grain size distribution. Coarsening behavior during sintering conforms to classic grain growth kinetics, modified to reflect the evolving microstructure. These modifications involve the grain boundary coverage due to pores, liquid films, or second phases and the altered grain boundary mobility due to these phases. The mass transport rates associated with each of these interfaces are different, with different temperature and composition dependencies. Hence, the coarsening rate during sintering is not constant, but changes with the evolving microstructure. Core aspects treated in this review include models for coarsening, grain shape, grain size distribution, and how pores, liquids, dispersoids, and other phases determine microstructure coarsening during sintering.     

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.     

Diffusion Induced Grain-Boundary Migration and Enhanced Grain Growth in BaTiO3

The effect of diffusion induced grain-boundary migration (DIGM) on grain growth has been studied in a model system of BaTiO₃-PbTiO₃. When sintered BaTiO₃ samples of two different grain sizes were heat-treated in contact with PbTiO₃, DIGM occurred in the coarse-grained samples (200 m in average size) while fast grain growth was observed in the fine-grained samples (4 m). Energy dispersive spectroscopy (EDS) analysis confirmed that the fast growth of BaTiO₃ grains was accompanied by the alloying of Pb and thus related to DIGM. A calculation of coherency strain energy for the BaTiO₃-PbTiO₃ system showed that the coherency strain energy of a coherent (Ba_0.8Pb_0.2)TiO₃ layer on BaTiO₃ was between 2 and 3 MJ/m³ depending on the surface orientation. The calculated coherency strain energy values are much higher than the capillary energy due to the grain boundary curvature of 4 m grains in the fine-grained sample. The observed enhancement of grain growth appears therefore to be a result of DIGM. Such grain growth enhancement by DIGM is thought to occur in materials processing under chemical inhomogeneity or inequilibrium, for example, in the sintering of powder mixtures and in the annealing of chemically inhomogeneous polycrystals.     

The Migration of High Angle Grain Boundaries during Recrystallization

When plastically deformed metallic materials are annealed, new strain free grains emerge from the microstructure and grow by means of grain boundary migration until the deformation microstructure is eliminated. This process is called recrystallization. In this paper the various methods by which grain boundary migration rates are measured stereologically in order to characterize the growth process are described and compared using illustrations from recrystallization experiments on commercial AA1050 aluminum. It seems abundantly clear that during recrystallization of cold-deformed materials, isothermal grain boundary migration rates decrease with time and reasons for such a decrease are discussed. A new methodology whereby migration rates of the individual recrystallization texture components may be quantified by combining stereology and orientation imaging by the electron back scattered pattern analysis is outlined. By illustration, recent experiments on aluminum and copper are summarized documenting the slight growth rate advantage the cube texture component (001)[100] possesses during recrystallization of cold rolled material. The role of orientation pinning effects on grain boundary migration is described briefly. It appears that such pinning effects allow recrystallized grains emerging from the weaker deformation texture components to enjoy an average growth rate advantage over those emerging from the stronger deformation texture components.     

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.     

Grain boundary influence on the mechanical behaviour of oriented bicrystals

It is shown through several experiments centred on dislocation transmission through a GB that relating macroscopic mechanical properties of a bicrystalline specimen to the atomic structure of the GB or to local dislocation reactions is not straightforward. Not only the long and short range stresses and the plastic properties of the two grains must be taken into consideration, but also the kinetics of events has to be taken into account to explain the final result.     

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.     

Diffusion along the Grain Boundaries in Crystals with Dislocations

A generalization of the Fisher model of the grain boundary diffusion is suggested, which takes into account the diffusion along short circuit diffusion paths (i.e., dislocations) in the bulk of crystalline grains. For the B-regime of the grain boundary diffusion, three different penetration modes have been found: at the short times the penetration depth of the element diffusing along the grain boundary is given by the Whipple solution of the Fisher model, but with the pipe diffusion coefficients along the dislocation cores instead of the volume diffusivities; at the intermediate times the penetration depth is a weak function of time, and at the large times the penetration depth again increases with time according to the Whipple solution, however, the rate of this increase is much smaller than in the initial period of time. The applications of the model for diffusion in nanomaterials are discussed.