Theory of Triple Junctions Mobility in Crystals with Impurities

We consider the steady state migration of the triple junction in the tricrystal with impurities which segregate strongly at the grain boundaries. If the mobility of impurities inside grain boundaries is much higher than the rate of impurity atoms jumps from the grain boundary into the bulk, the triple junction migration causes the divergence of the impurity content at the triple point. We show that this divergence can be relaxed either by the non-equilibrium segregation at the growing grain boundary or by the formation of the inclusion of the impurity-rich phase at the triple point. In the former case the dihedral angle at the triple point differs considerably from its equilibrium value and is strongly temperature-dependent. However, the triple junction cannot be described as an individual object with its own mobility. In the latter case of the cavity formation at the triple point the triple junction can be characterized by its own mobility. It is shown that the dependence of the triple junction migration rate on the driving force is approximately linear at the low migration rates and highly nonlinear at high migration rates. Moreover, there is the maximal allowable steady-state migration rate of the system triple junction-inclusion. For the higher migration rates the jerky motion of the triple junction occurs. Both models are in a good agreement with the experimental data.     

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.     

Study of the motion of individual triple junctions in aluminum

The mobility of individual triple junctions in aluminum is studied. Triple junctions with 〈111〉, 〈100〉, and 〈110〉 tilt boundaries are studied. The data obtained show that, at low temperatures, the mobility of the system of grain boundaries with a triple junction is controlled by the mobility of the triple junction (the junction kinetics). At high temperatures, the system mobility is determined by the mobility of the grain boundaries (the boundary kinetics). There is a temperature at which the transition from the junction kinetics to the boundary kinetics occurs; this temperature is determined by the crystallographic parameters of the sample.     

Triple Junction Mobility: A Molecular Dynamics Study

We present a molecular dynamics simulation study of the migration of individual grain boundary triple junctions. The simulation cell was designed to achieve steady state migration. Observations of the triple junction angle and grain boundary profiles confirm that steady state was achieved. The static, equilibrium grain boundary triple junction angles and the dynamic triple junction angles were measured as a function of grain size and grain boundary misorientation. In most cases, the static and dynamic triple junction angles are nearly identical, while substantial deviations were observed for low boundary misorientations. The intrinsic, steady-state triple junction mobilities were extracted from measurements of the rate of change of grain boundary area in simulations with and without triple junctions. The triple junction velocity is found to be inversely proportional to the grain size width. The normalized triple junction mobility exhibits strong variations with boundary misorientation, with strong minima at misorientations corresponding to orientations corresponding to low values of . The triple junctions create substantial drag on grain boundary migration at these low mobility misorientations.     

Effects of the triple junction types on the grain boundary carbide precipitation in a nickel-based superalloy,a statistical analysis

The morphology evolution of carbide precipitated on grain boundary nearby different triple junctions in grain boundary engineering (GBE) treated nickel-based Inconel Alloy 690 aged at 715°C for different time was investigated by scanning electron microscopy and electron backscatter diffraction. The results show that, the diversity of triple junction types was increased by GBE significantly. The size and morphology of grain boundary carbide were not only affected by the grain boundary character, but also the nearby grain boundary character at the triple junction. The higher Σ values of the nearby grain boundaries, the larger carbide precipitated on the other grain boundary. Based on the experimental results, the effects of grain boundary characters and triple junction types on the carbide precipitation behaviours are discussed.     

The stability of triple junctions during the grain boundary diffusion process

The grain boundary diffusion in a system with triple junctions is considered in such a geometry, in which the flows of diffusing atoms meet at the triple line. The solutions of the diffusion equation is given in the frameworks of Fisher's model and under the assumption of quasi-stationary distribution of the diffusing atoms along the grain boundaries. The change of the mechanical equilibrium at the triple junction due to the increase of the concentration of solute atoms is considered. It is shown that under some circumstances the triple junction looses its stability with respect to migration in the direction to the diffusion source. The stability diagrams in the segregation-diffusivity parameter space are plotted.     

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.     

Faceting of a moving grain boundary and its effect on the kinetic properties of grain boundaries

The motion of an individual half-loop grain boundary in zinc is studied experimentally. A correlation is revealed between the half-loop’s mobility and the change in the shape of its structural elements (curved segments, facets, and grain boundary edges). A hysteresis is observed on the temperature dependence curve of grain boundary mobility. The results from investigating grain boundary migration accompanied by faceting inside zinc bicrystals indicate that unsteady grain boundary motion occurs upon high-temperature isothermal annealing. The unsteady motion is due to the considerable difference between the mobility of a facet and that of the curved part of a grain boundary.     

Grain Boundary Dynamics: A Novel Tool for Microstructure Control

The reaction of grain boundaries to a wide spectrum of forces is reviewed. Curvature, volume energy and mechanical forces are considered. The boundary mobility is strongly dependent on misorientation, which is attributed to both grain boundary structure and segregation. In magnetically anisotropic materials grain boundaries can be moved by magnetic forces. For the first time a directionality of boundary mobility is reported. Flat boundaries can also be moved by mechanical forces, which sheds new light on microstructure evolution during elevated temperature deformation. Curvature driven and mechanically moved boundaries can behave differently. A sharp transition between the small and large angle boundary regime is observed. It is shown that grain boundary triple junctions have a finite mobility and thus, may have a serious impact on grain growth in fine grained materials. The various dependencies can be utilized to influence grain boundary motion and thus, microstructure evolution during recrystallization and grain growth.     

Atomistic Simulation of Curvature Driven Grain Boundary Migration

We present two dimensional molecular dynamics simulations of grain boundary migration using the half-loop bicrystal geometry in the experiments of Shvindlerman et al. We examine the dependence of steady-state grain boundary migration rate on grain boundary curvature by varying the half-loop width at constant temperature. The results confirm the classical result derived by absolute reaction rate theory that grain boundary velocity is proportional to the curvature. We then measure the grain boundary migration rate for fixed half-loop width at varying temperatures. Analysis of this data establishes an Arrhenius relation between the grain boundary mobility and temperature, allowing us to extract the activation energy for grain boundary migration. Since grain boundaries have an excess volume, curvature driven grain boundary migration increases the density of the system during the simulations. In simulations performed at constant pressure, this leads to vacancy generation during the boundary migration, making the whole migration process jerky.     

Reduced Mobility of Triple Nodes and Lines on Grain Growth in Two and Three Dimensions

Vertex dynamics models in two and three dimensions are applied to study grain growth including a limited mobility of triple points (two dimensions) and triple lines (three dimensions). A recent experiment on a triple node is used to validate the proposed model. The reduced triple node/line mobility in the case of a polycrystalline sample is shown to influence both, the grain growth kinetics and the grain size distribution function.     

Size-dependent grain-growth kinetics observed in nanocrystalline Fe

Measurements of grain growth in nanocrystalline Fe reveal a linear dependence of the grain size on annealing time, contradicting studies in coarser-grained materials, which find a parabolic (or power-law) dependence. When the grain size exceeds approximately 150 nm, a smooth transition from linear to nonlinear growth kinetics occurs, suggesting that the rate-controlling mechanism for grain growth depends on the grain size. The linear-stage growth rate agrees quantitatively with a model in which boundary migration is controlled by the redistribution of excess volume localized in the boundary cores.     

To the Question of Forming Geometrically Necessary Disclinations in Triple Junctions of Grain Boundaries in Metals

The Bollman and King models are tested by means of molecular dynamics simulation for the formation of geometrically necessary disclinations in triple junctions of grain boundaries in metals. It is shown that the stresses arising in a triple junction due to the non-multiple lengths of low-angle tilt boundaries to the distance between grain boundary dislocations is not compensated for mainly by the formation of an additional disclination in the junction (the King model) but by the bending of one or several grain boundaries, accompanied by the displacement of grain boundary dislocations. A triple junction of the Bollman U-type (containing a geometrically necessary disclination) is not formed at the conjugation of tilt boundaries with common misorientation along the junction or at the conjugation of mixed-type boundaries.     

晶体相场法模拟纳米晶材料反霍尔-佩奇效应的微观变形机理

采用晶体相场模型模拟获得了平均晶粒尺寸从11.61–31.32 nm的纳米晶组织, 研究了单向拉伸过程纳米晶组织的强化规律的微观变形机理. 模拟结果表明: 晶粒转动、晶界迁移等晶间变形行为是纳米晶材料的主要微观变形方式, 纳米晶尺寸减小, 有利于晶粒转动, 使屈服强度降低, 显示出反霍尔-佩奇效应.当纳米晶较小时, 变形量超过屈服点达到4%, 位错运动开启, 其对变形的直接贡献有限, 主要通过改变晶界结构而影响变形行为, 位错运动破坏三叉晶界, 引发晶界弯曲, 促进晶界迁移. 随纳米晶增大, 晶粒转动困难, 出现晶界锯齿化并发射位错的现象. 关键词： 晶体相场 纳米晶 反霍尔-佩奇效应 微观变形     

Effect of hydrostatic pressure on the migration of tilt grain boundaries in Sn- and Al-bicrystals

Abstract

The use of hydrostatic pressure as an intensive parameter for investigation of grain boundaries (GBs) migration in bicrystals is potentially important in gaining additional information on the mechanism of GB migration. This is because an analysis of the pressure dependence of the GB mobility yields a new activation parameter of the migration process, namely the activation volume V* which quantitatively is the difference between the volumes of the system in the ground and activated states. Only a few experiments to study the pressure dependence of GB mobility are known [1,2]. These experiments were made on polycrystalline materials. They provide the average data for all GBs in polycrystal and do not permit the determination of the connection between GB structure and value of activation volume V* of GB migration. In studying the mobility of single boundaries of a given type, there is the possibility of connecting the activation volume with the GB structural peculiarities, in particular, of determining the misorientation dependence of the activation volume, that is, of determining V* for GBs having various degrees of ordering.     

Grain boundary sliding and lattice dislocation emission in nanocrystalline materials under plastic deformation

A theoretical model is proposed to describe the physical mechanisms of hardening and softening of nanocrystalline materials during superplastic deformation. According to this model, triple interface junctions are obstacles to glide motion of grain boundary dislocations, which are carriers of grain boundary glide deformation. Transformations of an ensemble of grain boundary dislocations that occur at triple interface junctions bring about the formation of partial dislocations and the local migration of triple junctions. The energy characteristics of these transformations are considered. Pileups of partial dislocations at triple junctions cause hardening and initiate intragrain lattice sliding. When the Burgers vectors of partial dislocations reach a critical value, lattice dislocations are emitted and glide into adjacent grains, thereby smoothing the hardening effect. The local migration of triple interface junctions (caused by grain boundary sliding) and the emission of lattice dislocations bring about softening of a nanocrystalline material. The flow stress is found as a function of the total plastic strain, and the result agrees well with experimental data.     

Orientation dependence of void growth at triple junction of grain boundaries in nanoscale tricrystal nickel film subjected to uniaxial tensile loading

Molecular dynamics simulation was performed in order to investigate the dependence of void growth on crystallographic orientation at the triple junction of grain boundaries in nanoscale tricrystal nickel film subjected to uniaxial tensile loading. The nucleation, the emission and the transmission of Shockley partial dislocations play a predominant role in the growth of void at the triple junction of grain boundaries. The orientation factors of various slip systems are calculated according to Schmid law. The slip systems activated in a grain of tricrystal nickel film basically conform to Schmid law which is completely suitable for a single crystal. The activated slip systems play an important role in plastic deformation of nanoscale tricrystal nickel film subjected to uniaxial tensile loading. The slip directions exhibit great difference among the activated slip systems such that the void is caused to be subjected to various stress conditions, which further leads to the difference in void growth among the tricrystal nickel films with different orientation distributions. It can be concluded that the grain orientation distribution has a significant influence on void growth at the triple junction of grain boundaries.     

The formation of α at triple junctions of parent β phase in titanium alloys

We have examined the formation of α phase at grain boundary triple junctions of parent β in a metastable β titanium alloy with orientation imaging microscopy based on electron backscattered diffraction (EBSD). As in the case of α formed at grain boundaries of parent β grains, α at a triple junction also forms with the Burgers orientation relationship with one of the three neighbouring β grains. The experimental results are analyzed in terms of the deviation of the 36 possible α variants that can form at a triple junction from the Burgers orientation relationship with neighbouring grains.     

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.