Modelling of austenite grain growth kinetics in a microalloyed steel (30MSV6) in the presence of carbonitride precipitates

Austenite grain growth kinetics in the presence of secondary precipitates of a microalloyed steel (30MSV6) was studied employing quantitative metallographic techniques. Austenitizing experiments were carried out at 1,000, 1,100 and 1,200?°C. According to the experimental data, abnormal grain growth behaviour is observed at 1,100?°C while it is normal at 1,000 and 1,200?°C. TEM observation represents multicomponent carbonitride precipitate, (Ti,V)(C,N), in the as-received steel with a mean radius of 35?nm. A mathematical model is proposed considering austenite grain growth along with dissolution and coarsening kinetics of the multicomponent precipitates. The austenite grain growth model for short-term non-isothermal and subsequent long-term isothermal heating stages was developed using a statistical approach. The model includes an algorithm to estimate the size distribution of austenite grains. Precipitate mean field dissolution and Lifshitz–Slyozov–Wagner coarsening models were integrated in the proposed model to calculate the pinning pressure retarding the grain boundary movement. The mean austenite grain size and the grain size distribution (normal and abnormal) calculated by the model are in good agreement with experimental data.     

Three-dimensional finite-element simulation of Zener pinning dynamics

The Zener pinning dynamics of a moving boundary interacting with one or more particles is described by a three-dimensional (3D) finite-element model. The model, based upon a variational formulation for boundary motion by viscous drag, is solved by a finite-element method to obtain the velocity at each node of triangular linear elements on the grain boundary. It is first applied to relatively simple and validated cases, for which analytical and numerical results are available. These cases correspond to an axisymmetrical geometry, in which the grain boundary interacts with a centred particle. A simple analytical pinning criterion is derived from these simulations. The model is then applied to general 3D cases, in which the grain boundary interacts with arbitrarily localized and sized particles. The aim of these 3D simulations is to quantify the influence of the position and the number of particles on the average grain-boundary velocity. It is shown, for example, that the drag effect is enhanced when the particle, or the cluster of particles, is off-centre and that pinning is less efficient with several particles than with a single particle producing the same Zener force.     

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.     

Effect of thermal fluctuations on the coarsening dynamics of 2D hexagonal system

The dynamics of ordering in a 2D hexagonal system was investigated through the Cahn-Hilliard-Cook model. At low thermal noise amplitudes, pinning forces acting on grain boundaries dominate the dynamics and the coarsening evolves logarithmically in time. As noise amplitude increases, fluctuations becomes large enough to unlock dislocations located along grain boundaries and the grain boundary motion is driven by curvature. The grain boundary relaxation leads to a grain structure with Lifshitz's configurations. In this case the dynamic is also logarithmic as a consequence of the pinning of triple points.     

Pinning effect of different shape second-phase particles on grain growth in polycrystalline: numerical and analytical investigations

The pinning effect of different shape second-phase particles on the grain growth in polycrystalline structures is numerical simulated by the phase-field method. Simulation results indicate that the average grain size is highly dependent on the shape and distribution of the second-phase particles, and the shape effect of particles on grain growth restraining is enhanced with increasing numbers of particles. In order to discuss the relation between the constraint grain growth and the second-phase particles, pinning forces induced by different shape particles are theoretically calculated via the Zener pinning theory. The calculated pining forces indicate that the maximum pinning force is highly dependent on the contact mode between grains and particles, and the distance between particles has a significantly influence on the pinning forces. Therefore, controlling the shape and distributions of second-phase particles in polycrystalline metals or ceramics might be an efficient way to achieve materials with specified microstructures.     

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.     

Three dimensional analyses of flux pinning centers in Dy-doped YBa2Cu3O7−x coated superconductors by STEM tomography

In order to enhance the superconductive properties of the high temperature superconductors, nanoparticles acting as pinning centers can be intentionally introduced into the structure by chemical doping. In this study, a Dy-doped YBa₂Cu₃O_7?x (YBCO) coated conductor, prepared by a metal organic decomposition process, was investigated to determine the size, composition and 3D distribution of the nanoparticles. It was found that the addition of Dy results in the formation of a high density of secondary phase nanoparticles of composition (Y_sDy_1?s)₂Cu₂O₅ with s ～ 0.6. A tomographic tilt series was acquired by using a scanning transmission electron microscope to analyze the interaction between the particles and the structural defects and to determine the 3D distribution of nanoparticles. For the investigated sample volume (0.06 μm³), 71 particles were located with a particle size distribution ranging between 13 and 135 nm with an average size of ～30 nm. The distribution uniformity, position and the size of the particles are observed to be dependent on the interaction of the particles with the twin boundaries. It is observed that the larger particles are generally located on more than one twin boundary, moreover, the particle size is smaller on the twin boundaries shared by several particles. This suggests that the growth of the particles is determined by fast twin boundary diffusion and the formation of the large particles might be prevented by altering the temperature–time parameters of the production processing to enhance the flux pinning characteristic of the superconductors by achieving a more uniform size of flux pinning centers.     

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.     

Deformation-induced changes in single-phase Al-0.1Mg alloy

Al-0.1wt.%Mg has been chosen to explore the effects of deformation on the microstructure of nominally single-phase materials. For these materials, the rate of static grain growth is much higher compared to that of Zener pinned systems and dual-phase alloys, where growth is hindered due to the pinning force exerted by second-phase particles on grain boundaries. Therefore, deformation-induced microstructural changes in single-phase alloys occur without any restricting pinning pressure. This paper illustrates the complex effect of deformation on the microstructural changes mainly associated with dynamic recovery. The process affects the initial microstructure due to an intensive substructure development. Dynamic recrystallisation, associated with the formation of new grains, is considered to be a transient phenomenon that quantitatively influences the mean grain size formed during straining. This work also aims to estimate the stored energy of the deformed regions and texture components to explore their contribution to the migration of high-angle grain boundaries.     

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.     

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.     

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.     

冷却速率对温敏聚N-异丙基丙烯酰胺胶体结晶过程的影响

冷却速率对结晶过程具有重要的影响. 本文采用温敏poly-N-isopropylacrylamide (PNIPAM) 胶体晶体体系实时观察了冷却速率对结晶晶粒尺寸的影响. 通过高倍透射明场观察和Bragg衍射观察研究连续冷却下的晶粒形核和生长实时演化过程, 发现随着冷却速率的增加, PNIPAM胶体晶体晶粒尺寸不断减少. 晶粒尺寸与冷却速率符合幂指数关系, 与金属体系具有相似的演化规律.     

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.     

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.     

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.     

Jump kinetics on the Fibonacci quasilattice. Exactly solvable model of the layer growth and dislocation kinetics in quasicrystals

The jump kinetics on a quasiperiodic pinning potential is analyzed under small external force in a 1D Fibonacci quasilattice model. The model describes planar (layer) growth of stable quasicrystals from the melt and is also relevant to the movement of quasicrystal dislocations under small stress. An exact solution is found for the spectrum of jump length as function of the driving force. The solution describes the supercooling dependence of the spectrum of nucleus heights on the growing surface of a quasicrystal. The spectrum appears to be universal and its shape has a periodic dependence on the logarithm of the supercooling. The resulting quasicrystal growth kinetics agrees well with that found in computer simulations and in the analysis of continuous thermodynamic models. Pis’ma Zh. éksp. Teor. Fiz. 69, No. 8, 531–536 (25 April 1999) Published in English in the original Russian journal. Edited by Steve Torstveit. Institute of Crystallography, Russian Academy of Sciences, 117333, Moscow, Russia     

Theory and simulation of coupled grain boundary migration and grain rotation in low angle grain boundaries

Abstract

Microstructure evolution due to coupled grain boundary migration and grain rotation in low angle grain boundaries is studied through a combination of molecular dynamics and phase field modeling. We have performed two dimensional molecular dynamics simulations on a bicrystal with a circular grain embedded in a larger grain. Both size and orientation of the embedded grain are observed to evolve with time. The shrinking embedded grain is observed to have two regimes: constant dislocation density on the grain boundary followed by constant rate of increase in dislocation density. Based on these observations from the molecular dynamics simulations, a theoretical formulation of the kinetics of coupled grain rotation is developed. The grain rotation rate is derived for the two regimes of constant dislocation density and constant rate of change of dislocation density on the grain boundary during evolution. The theoretical calculation of the grain rotation rate shows strong dependence on the grain size and compares very well with the molecular dynamics simulations. A multi-order parameter based phase field model with coupled grain rotation is developed using the theoretical formulation to model polycrystalline microstructure evolution.