Grain Growth In Polycrystals Research Articles

Effect of the atomic structure of complexions on the active disconnection mode during shear-coupled grain boundary motion

The migration of grain boundaries leads to grain growth in polycrystals and is one mechanism of grain-boundary-mediated plasticity, especially in nanocrystalline metals. This migration is due to the movement of dislocationlike defects, called disconnections, which couple to externally applied shear stresses. While this has been studied in detail in recent years, the active disconnection mode was typically associated with specific macroscopic grain boundary parameters. We know, however, that varying microscopic degrees of freedom can lead to different atomic structures without changing the macroscopic parameters. These structures can transition into each other and are called complexions. Here, we investigate [111¯] symmetric tilt boundaries in fcc metals, where two complexions—dubbed domino and pearl—were observed before. We compare these two complexions for two different misorientations: In Σ19b[111¯](178) boundaries, both complexions exhibit the same disconnection mode. The critical stress for nucleation and propagation of disconnections is nevertheless different for domino and pearl. At low temperatures, the Peierls-like barrier for disconnection propagation dominates, while at higher temperatures the nucleation is the limiting factor. For Σ7[111¯](145) boundaries, we observed a larger difference. The domino and pearl complexions migrate in different directions under the same boundary conditions. While both migration directions are possible crystallographically, an analysis of the complexions' structural motifs and the disconnection core structures reveals that the choice of disconnection mode and therefore migration direction is directly due to the atomic structure of the grain boundary. Published by the American Physical Society 2024

Energy dissipation by grain boundary replacement during grain growth

The changes in both the grain boundary area and grain boundary energy that occur during grain growth have been measured in polycrystalline Ni using high energy diffraction microscopy. In addition to the reduction of grain boundary area, the average grain boundary energy decreases as higher energy grain boundaries are replaced by lower energy grain boundaries. This energy dissipation mechanism influences grain boundary migration and might explain the absence of a correlation between grain boundary curvature and migration velocity.Classical studies of isotropic grain growth in polycrystals have been based on the idea that grain boundary (GB) migration is driven by the product of the GB energy and curvature. [1,2] While support for this foundational concept is certainly found in studies of bicrystals [3] and simulations [4], recent experimental evidence contradicts this idea. When measured curvatures and velocities were compared in Ni [5] and SrTiO3, [6] they were found to be uncorrelated. Similar observations were reported for α-Fe, [7] where the measured constant of proportionality between curvature and velocity did not behave in expected ways. The purpose of this letter is to present evidence that, during grain growth, the replacement of higher energy GBs by lower energy boundaries dissipates energy by a mechanism that is not related to curvature. This reduction of the average GB energy represents an additional driving force for grain growth.For a GB network comprised of N triangular mesh elements of area ai, the total free energy (F) is:

A new analytical test case for anisotropic grain growth problems

Grain growth in polycrystals is one of the principal mechanisms that take place during heat treatment of metallic components. This work treats the single boundary simplification of the anisotropic grain growth problem. By applying the first principles of thermodynamics and mechanics, an expression for the velocity field of a migrating grain boundary with an inclination-dependent energy density is expressed. This result is used to generate the first, to the authors’ knowledge, space-time analytical solution to the anisotropic grain growth problem. This new anisotropic benchmark is simulated in order to explore the convergence properties of the proposed level-set finite element numerical model. Convergence of the method being illustrated, another configuration, using a more general grain boundary energy density, is investigated in order to show the added value of the new formulation.

Behaviors of Normal Grain Growth in Polycrystalline Fe–3%Si Alloys

The grain growth processes of model alloys Fe–3%Si–MnS and Fe–3%Si were investigated. The MnS particles did not completely inhibit normal grain growth but drastically reduced growth velocity. Activation enthalpy (57.72 kJ mol−1) and pre‐exponential factor (7.82 × 10−9 m2 s−1) for boundary migration obtained by statistical regressive calculations were significantly lower than those obtained by bicrystal investigations. The observations indicated that atoms should be pre‐activated before they jump over moving boundaries. Activation enthalpy and pre‐exponential factor decreased with increased pre‐activation energy. The predominant migrations of strongly curved boundaries and triple junctions during grain growth in polycrystals increased the pre‐activation energy, which differed from the simplified behaviors of boundary migration in bicrystals.

Thermodynamics of microstructure evolution: Grain growth

It is gradually getting clear that the macroscopic description of microstructure evolution requires additional thermodynamic parameters, entropy of microstructure and temperature of microstructure. It was claimed that there is “one more law of thermodynamics”: entropy of microstructure must decay in isolated thermodynamically stable systems. Such behavior is opposite to that of thermodynamic entropy. This paper aims to illustrate the concept of microstructure entropy by one example, the grain growth in polycrystals. The grain growth is treated within the framework of a theory which is a modification of Hillert theory. The modification is made in order to reach simultaneously two goals: to get a coincidence of theoretical predictions with experimentally observed results and to obtain the equations that admit analytical solutions. Due to these features, the modified theory is of independent interest. In the modified Hillert theory one observes the decay of total microstructure entropy when the system approaches the self-similar regime. The microstructure entropy per one grain grows indicating a chaotization of grain sizes. It is shown also that there exits an equation of state of grain boundary microstructure that links entropy of microstructure, energy of microstructure, average grain size and a characteristic of the inhomogeneity of the large grain distribution.

A Stochastic Approach to Coarsening of Cellular Networks

We prove existence for a system of master equations modeling grain growth proposed in [K. Barmak et al., Remarks on a multiscale approach to grain growth in polycrystals, in Variational Problems in Materials Science, Birkhäuser, Basel, 2006, pp. 1–11]. The method used to prove existence for these nonlinear, integro-PDEs employs tools from both functional analysis and probability. The stochastic interpretation for the evolution of the mesoscopic properties of this large scale metastable system we provide here is general enough to apply to other cellular networks. This approach leads to an internally consistent theory and opens a new discussion on asymptotics for the distribution of grains in a two-dimensional network, which is the subject of future work.

Impact of grain boundary junctions on grain growth in polycrystals with different grain sizes

Effect of finite mobility of triple and quadruple grain boundary junctions on grain growth is studied by numerical simulation. They retard the growth process and transform its kinetics from parabolic one into a sequence consisting of exponential, linear and parabolic steps. This relates even to polycrystals with large initial grain sizes. Such junctions can contribute to microstructure stabilization in nanomaterials.

Grain boundary junction engineering

Abstract Under certain circumstances grain growth in polycrystals is controlled by the mobility of grain boundary junctions. The resulting microstructure is distinctly different from the granular assembly in the course of normal grain growth. Also, the structure established under junction control is rather stable even under the conditions characteristic for grain growth governed by grain boundary motion. This provides a means of controlling the grain microstructure evolution, in particular of ultrafine grained and nanocrystalline materials. It is demonstrated that such an effect can be expected not only for 2D arrangements but for 3D microstructures with quadruple junctions as well. The latter statement is supported by an assessment of the mobility of quadruple junctions. We propose to introduce a new branch of grain boundary engineering, namely grain boundary junction engineering.

Grain microstructure evolution and grain boundary junction engineering

The grain microstructure evolution in the course of two dimensional (2D) grain growth is considered in greater detail, taking into account the influence of grain boundary triple junctions. It is shown that there are two limiting regimes of grain growth in polycrystals: the first one is associated with the situation when the kinetics of grain growth are controlled by the motion of grain boundaries, while the second one is defined by the motion of grain boundary triple junctions, i.e. when the mobility of triple junctions determines the kinetics of grain growth. A generalised theory of 2D grain growth including a limited triple junction mobility is presented. The theoretical predictions are compared with results of computer simulations by a virtual vertex model. We introduce a new branch of grain boundary engineering, namely, grain boundary junction engineering that utilises junction properties for microstructure control.

Triple junction motion and grain microstructure evolution

The classical concepts of grain growth in polycrystals are based on the dominant role of grain boundaries. This is reflected by the well known von Neumann–Mullins relation. According to this approach triple junctions do not affect grain boundary motion, and their role in grain growth is reduced to maintaining the thermodynamically prescribed equilibrium angles at the lines where boundaries meet. In the current study the experimental data of triple junction mobility are considered with respect to the process of grain growth in 2D systems, in particular with regard to the controlling kinetics. When boundary kinetics prevails grain growth in a polycrystal complies with the von Neumann–Mullins relation. When grain growth is governed by the mobility of triple junctions the kinetics change, and the von Neumann–Mullins relation does not hold anymore. This is the more pronounced the smaller the triple junction mobility. We present a generalized theory of 2D grain growth including a limited triple junction mobility. In this concept the criterion Λ plays a central role. It reflects the ratio of boundary to triple junction mobility but is proportional to the grain size as well. The generalized von Neumann–Mullins relation can be expressed in terms of Λ. For small values of Λ, conspicuous changes of microstructure evolution during grain growth and of microstructural stability are predicted. The theoretical predictions are compared to results of computer simulations by a virtual vertex model.

Intergranular amorphous films and dislocations-promoted grain growth in SrTiO 3

To investigate the effect of dislocations on grain growth in polycrystals, two sets of experiments were performed using SrTiO 3 single crystals and SrTiO 3 powder compacts. In the first set, with single crystals embedded in 2.0-mol%-TiO 2-exess powder compacts, the growth of the single crystal was not affected by dislocations at 1300 °C, below the eutectic temperature, while it was enhanced by dislocations at 1470 °C, above the eutectic temperature, where the grain boundaries are wetted by an amorphous phase. In the second set, with 0.5-mol%-Nb 2O 5-doped powder compacts, the single crystal grew considerably into the SrTiO 3 matrix grains in the presence of an amorphous film between the grains at 1470 °C both in 95N 2-5H 2 and in air, similar to the case of the TiO 2-exess samples. However, when annealed at 1470 °C in 95N 2-5H 2 after pre-annealing at 1250 °C in 95N 2-5H 2, the amorphous phase remained at triple junctions and did not penetrate the grain boundaries, implying that this boundary configuration also is thermodynamically stable above the eutectic temperature. In this case, growth of the embedded single crystal was insignificant in spite of the presence of dislocations. These experimental observations indicate that the growth of SrTiO 3 is promoted by dislocations only when an intergranular amorphous film is present at grain boundaries. The apparent ineffectiveness of dislocations on grain growth promotion without an intergranular amorphous film is discussed in terms of a low fraction of facetted grain boundaries and grain boundary drag by triple junctions.

Triple junction drag and grain growth in 2D polycrystals

The process of grain growth in 2D systems is analyzed with respect to the controlling kinetics: from solely boundary kinetics, when grain growth in a polycrystal is determined by the Von Neumann–Mullins relation, to exclusively triple junction kinetics, when grain growth is governed by the mobility of triple junctions. It is shown that in the “intermediate” case, when the driving force for grain boundary motion and the characteristic mobility are grain boundary curvature and grain boundary mobility, respectively, a limited mobility of triple junctions essentially influences grain boundary motion. The Von Neumann–Mullins relation does not hold anymore, and this is the more pronounced the smaller the triple junction mobility. In the case where grain growth is determined by the mobility of grain boundary triple junctions (triple junction kinetics) all grains are transformed into polygons in the course of grain growth. Grain growth would cease if all grains assumed the shape of regular polygons, not only hexagons like in the Von Neumann–Mullins case. The only exceptions are triangles: they collapse without transforming into a polygon. The respective relation for the rate of a change of grain area under triple junction kinetics is obtained and discussed with regard to microstructure evolution.

Anisotropy of grain growth in polycrystals of α-Fe

Results of studies of grain growth in α-Fe are reported. Grain boundary networks were studied in longitudinal and transverse cross-sections. Geometrical features of grain sections were measured using an image analyser. The concept of vertical sectioning and a system of cycloid test lines were used to estimate grain boundary surface area per unit volume. The results confirm earlier observations that the changes in the mean size of grains are accompanied by variations in the degree of grain size uniformity and the shape of grains. The data show that grain growth proceeds at different speeds in directions perpendicular and parallel to the axis of the specimens.

Texture development during grain growth in polycrystals with strong preferred orientation

Texture alterations accompanying grain growth have been simulated by means of a new statistical model which for the first time takes into account the dependence of both the energy and mobility of grain boundaries on their disorientation. Model polycrystals with a single-component texture are assumed to consist of preferably oriented grains A (the main texture component) and randomly oriented grains B. Therefore, there are three types of grain boundaries in these polycrystals: high-angle A–B and B–B boundaries, and A–A boundaries with a smaller disorientation. A novel map showing the effect of both the scatter and intensity of the main texture component on the character of grain growth is obtained. Abnormal grain growth leads eventually to vanishing of the main texture component. However, the main component enhances at the incubation period of abnormal grain growth, especially in the case when the initial distribution of randomly oriented grains is displaced toward small sizes, as in materials with cube texture. The texture evolution during normal grain growth is strongly affected by the initial position of the size distribution of randomly oriented grains. If this distribution is displaced toward small sizes, the main texture component is enhanced. In contrast, normal grain growth results in vanishing of the main component if the initial size distributions of grains A and B are identical. Various texture evolutions observed in the simulations are shown to be a result of an interplay of the consumption and the growth of randomly oriented grains during the growth process.

Why does skin stay smooth? The dynamics of tissues in statistical equilibrium

Abstract The ‘molecular dynamics’ of cells in the epidermis of mammals is presented by generalizing a model of grain growth in polycrystals or coarsening foams due to Telley. The tissue remains in statistical equilibrium in spite of and because of constant renewal through local elementary topological transformations, which are division (mitosis), neighbour exchange and detachment of the cells. The global evolution and response of tissues can now be described realistically, geometrically with very few parameters and little biological input. The dynamics of cell division is modelled for the first time.

Two-dimensional normal grain growth: topological aspects

Abstract 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.

Topological events in two-dimensional grain growth: Experiments and simulations

Grain growth in polycrystals is a process that occurs as a result of the vanishing of small grains. The mean topological class of vanishing two-dimensional (2-D) grains was found experimentally to be about 4.5. This result suggests that most vanishing grains are either 4- or 5-sided. A recent theory of 2-D grain growth is explicitly based on this fact, treating the switchings as random events. The process of shrinking of 4- and 5-sided two-dimensional grains was observed experimentally on polycrystalline films of transparent, pure succinonitrile (SCN). Grain shrinking was studied theoretically and simulated by computer (both dynamic and Monte Carlo). It was found that most shrinking grains are topologically stable and remain within their topological class until they are much smaller than their neighbors. We discuss differences which were found with respect to the behavior of 2-D polycrystals, a 2-D ideal soap froth, and a 2-D section of a 3-D grain structure.

Topological rearrangements during 2D normal grain growth

Topological rearrangements during grain growth in polycrystals provide an example of the strongest possible non-linearity in the grain population evolution dynamics. For a 2D grain the equation of growth is linear (von Neumann-Mullins law) until there is a topological change. The inevitable occurence of a topological rearrangement makes the system intrinsically non-linear, and the non-linearity effects are critical to understanding grain growth dynamics. In situ experimental investigation of topological rearrangements in thin polycrystalline films of succinonitrile (SCN) show that according to theoretical considerations (and contrary to conventional wisdom) small 4- and 5-sided quasi-2D grains usually shrink almost to the vanishing limit, without losing sides through the expected topological cascade of neighbor switchings. Vanishing grains generally do not create multiple vertices in the system. They do not shrink to a point as 2D soap froth bubbles do, but rather shrink to a line, with 2 vertices (in the case of 4-sided grains) or to two lines with 3 vertices (in the case of 5-sided grains). The experimental results are compared with those of direct computer simulation of 2D grain shrinking. The simulation shows also that the main topological results remain valid both in systems with uniform and anisotropic boundaries.

Grain geometry evolution in the process of grain growth induced by temperature and plastic deformation - problem of the incubation period

Grains in polycrystalline materials form a population characterized by a stochastic distribution of geometrical features. The grains differ in their size as well as in their shape. Grain growth in polycrystals is defined as a process leading to an increase in the mean size of grains. The process take place via migration of the grain boundaries and is a complex phenomenon that involves simultaneous changes in the size and shape of grains. Migration of the grain boundaries in polycrystals is driven by a tendency to lower energy of the system. Depending on the micro-structural details, movement of grain boundaries is controlled by such effects as: a) surface tension of the grain boundaries, b) anisotropy and non-homogeneity of their energy, c) energy release due to annihilation of the lattice dislocations. For each of these, one can define a field of forces acting on the grain boundary segments. The action of this field leads to migration of the grain boundaries and in turn to growth of the grains. It should be pointed out, however, that grain boundary migration by itself does not need to result in grain growth. Growth takes place only if the migration results in a constant annihilation of grains. In steady-state conditions developed under the action of a given driving-force field, a fraction of grains systematically shrink and the remainder of the grains grow at the expense of their neighbors. Since the volume of the material remains constant during rate of grain annihilation. d