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.     

Molecular dynamics investigation of the diffusion permeability of triple junctions of tilt and mixed-type boundaries in nickel

The diffusion permeability of triple junctions of high-angle tilt boundaries 〈111〉 and 〈100〉 and mixed-type boundaries in nickel has been investigated using the molecular dynamics method. It has been shown that the diffusion permeability of equilibrium triple junctions does not exceed the permeability of the grain boundaries forming them. The effective diffusion radius of the considered triple junctions and the width of the grain boundaries are determined.     

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.     

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.     

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.     

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.     

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.     

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.     

Grain boundary wetting phase transition and analysis of the energy characteristics of grain boundaries in the Sns-(Zn/Sn)l system

Regularities of the interaction of tin grain boundaries (special Σ5 and general Σ17 〈001〉) and a Sn-Zn melt of equilibrium composition were studied. The grain boundary wetting phase transition temperature was determined; for Σ5 and Σ17, it is 216°C. More than 90% of the general grain boundaries were completely wetted by the melt over a range of temperatures, from the eutectic melting temperature to the tin melting temperature. It was shown that the anisotropy of interphase energy at the solid tin-Zn-Sn melt interface is 64 ± 10 mJ m^?2 at 216°C. The energies of the Σ5 and Σ17 grain boundaries in the range of 201–216°C were obtained on the basis of the experimental dependence of the dihedral angle on temperature.     

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.     

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.     

On the Origin and Energy of Triple Junction Defects Due to the Finite Length of Grain Boundaries

King [1] established that due to the discrete nature of their dislocation structure, finite length grain boundaries (GBs) in polycrystalline materials possess discrete values of misorientation angle. For a GB with a length that is not a multiple of the GB period, this leads to the formation of specific disclinations at their junctions with neighboring GBs, which compensate the difference between the misorientations of finite and infinite boundaries. In the present paper the origin of these compensating disclinations within GB triple junctions is elucidated and their strength is calculated using the disclination-structural unit model. It is shown that for a GB with length of about 10 nm the junction disclinations can have a strength value not more than 1°, in contrast to King's calculations that indicate much larger values. Elastic energies of triple junctions due to compensating disclinations are calculated for both equilibrium and non-equilibrium structures of a finite length GB, which differ by the position of the grain boundary dislocation network with respect to the junctions. The calculations show that triple junction energies are comparable to dislocation energies, and that compensating disclinations can play a significant role in the properties of nanocrystalline metals with grain sizes less than about 10 nm.     

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.     

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.     

Effect of atomic ordering on the role of grain boundaries in the plastic deformation of Ni<Subscript>3</Subscript>Fe alloy

The structure of dislocations and the defect structure of grain boundaries and their parameters in Ni₃Fe alloy with short-range order (SRO) and long–range order (LRO) at different stages of plastic deformation are studied by means of transmission diffraction electron microscopy using thin foils and replicas. It is found that atomic ordering reduces the Σ3 twins plasticizing effect, increases the density of grain boundary defects, slows their annihilation during deformation, and intensifies the microstrains at the triple junctions of grain boundaries.     

Stability and dissociation of quadruple junctions in polycrystals

Junctions of four grain boundaries (quadruple junctions) may form during grain growth. An analysis of the stability/unstability of quadruple junctions in 2D polycrystals is presented based on simple thermodynamic arguments. Depending on the angles between the four grain boundaries, their junction may dissociate into two triple junctions or be stable. In the first case there are two possible dissociations, but in general one is favored. A stable quadruple junction moves as a whole to a new position before it dissociates. These alternatives in the behavior of a quadruple junction are conveniently displayed in maps which indicate the regions where each alternative occurs.     

Interdiffusion in two-layer Pd/Ag films III. TEM investigation of diffusion-induced grain boundary migration

Diffusion-induced grain boundary migration (DIGM) is studied by the transmission electron microscopy method in polycrystalline two-layer Pd/Ag thin films with a grain size (100–2000 nm). In addition to the typical features of DIGM known for coarse-grained bulk objects and foils, new features are found which are caused by a quite dense network of triple junctions and by misfit dislocations: fast increase of grain boundary curvature and inclination; back motion of grain boundaries owing to recrystallization forces and termination of DIGM. Homogenization resulted from diffusion-induced migration of misfit dislocations is observed in addition to DIGM.     

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.     

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.