Simulations Of Grain Boundary Migration Research Articles

Atomistic simulation of grain boundary migration induced by non-equilibrium solute distribution

While atomistic simulation is now a widely used method for investigating grain boundary migration, it is usually based on the so-called artificial driving force. In this study, we report a new general atomistic method for simulating grain boundary migration based on a tunable physical driving force that is induced by unbalanced solute distribution. This is motivated by the previous experimental reports that non-equilibrium distribution of solute atoms, e.g., solute atoms are more enriched/depleted in one grain relative to the other, is commonly observed during diffusion induced grain boundary migration. We show that the solute-induced driving force caused by the unbalanced free energy in the two neighboring grains strongly depends on the type of the solute atoms, which can be used to tune both the type (e.g., attraction or repulsion) and magnitude of the driving force. Furthermore, we find that different solute types (with varying atomic size and cohesive energy) interact with the grain boundary in different ways resulting in solute segregation or anti-segregation. Moreover, the lattice strain resulting from atomic size mismatch, which has been proposed to be an important driving force for diffusion induced grain boundary migration, is found to be not always needed to induce the grain boundary migration. We hope that while this study showcases a new atomistic method of simulating grain boundary migration, the results of this investigation also aids the understanding of the phenomenon of diffusion induced grain boundary migration, for which clear physical mechanisms remain elusive after decades of research.

Atomistic Modeling of Grain Boundary Migration in Nickel

Herein, the molecular dynamics (MD) simulations of pure Ni crystallites are performed to show the influence of the grain boundary (GB) geometry on the values of the activation energy of GB migration. The considered systems are bicrystal with Σ5[010] tilt plane boundary, spherical grain with initial curvature radius 5 nm, and polycrystalline 30 nm × 30 nm × 30 nm block. The motion of three types of GBs (flat, spherical, and polycrystalline) at constant temperatures and no applied forces is studied. The obtained values of activation energy are 0.45, 0.11, and 0.57 eV for flat, spherical, and polycrystalline types of GBs, respectively. These values are smaller than those that are reported in experimental works, which is a common issue for atomistic simulations of GB migration. Possible sources of such disagreement and ways to overcome it are discussed. The particular part of this work is devoted to the development of the automated analysis of polycrystalline structure. This analysis provides detailed information on grain size distribution and its evolution in time.

On the temperature dependence of grain boundary mobility

The grain boundary (GB) mobility relates GB velocity to the thermodynamic driving forces and is central to our understanding of microstructure evolution in polycrystals. Recent molecular dynamics (MD) and experimental studies have shown that the temperature-dependence of the GB mobility is much more varied than is commonly thought. GB mobility may increase, decrease, remain constant or show multiple peaks with increasing temperature. We propose a mechanistic model for GB migration, based on the formation and migration of line defects (disconnection) within the GB. We implement this model in a kinetic Monte Carlo and statistical mechanics framework; the results capture all of these observed temperature dependencies and are shown to be in quantitative agreement with each other and direct MD simulations of GB migration for a set of specific grain boundaries. Examination of the dependence of GB mobility on disconnection mode and temperature provides new insight into how GBs migrate in polycrystalline materials.

Atomistic simulations of grain boundary migration under recrystallisation conditions

We present details of an approach to simulating the migration of grain boundaries using classical molecular dynamics (MD) in a regime in which the boundary motion is driven by the presence of dislocation defects resulting from plastic deformation. By simulating the shrinkage of spherical grains of deformed material embedded in a perfect crystal, we create conditions in which grain boundary motion takes place on time scales accessible to MD simulations, in which the defect free energy acts as a driving force additional to the capillary force due to excess grain boundary energy. This approach is particularly flexible in allowing arbitrary choices of misorientation axis and angle and providing an interface in which all grain boundary plane orientations are represented. This flexibility is at the cost of additional complexity in the system under study and we establish an approach suitable for analysing the excess grain boundary energy and the components of the force for boundary motion on a local basis over the surface of the shrinking grain. We demonstrate that this approach is able to resolve variation in the grain boundary energy related to the intrinsic grain boundary dislocation network in lower angle boundaries and to detect local maxima in the driving force due to the dislocation structure within the deformed grain. We show that the variation in measured grain boundary velocities is accounted for by the excess energy of the dislocations. We further show that the presence of dislocations in the shrinking grain has a tendency to reduce the anisotropy in grain boundary behaviour. Indicative evidence is presented that the dislocation network may act as a focal point for mechanisms of grain boundary migration.

粒界移動と粒回転のフェーズフィールドクリスタルシミュレーション

粒界移動と粒回転のフェーズフィールドクリスタルシミュレーション

A modified synthetic driving force method for molecular dynamics simulation of grain boundary migration

Abstract The synthetic driving force (SDF) molecular dynamics method, which imposes crystalline orientation-dependent driving forces for grain boundary (GB) migration, has been considered deficient in many cases. In this work, we revealed the cause of the deficiency and proposed a modified method by introducing a new technique to distinguish atoms in grains and GB such that the driving forces can be imposed properly. This technique utilizes cross-reference order parameter (CROP) to characterize local lattice orientations in a bicrystal and introduces a CROP-based definition of interface region to minimize interference from thermal fluctuations in distinguishing atoms. A validation of the modified method was conducted by applying it to simulate the migration behavior of Ni 〈1 0 0〉 and Al 〈1 1 2〉 symmetrical tilt GBs, in comparison with the original method. The discrepancies between the migration velocities predicted by the two methods are found to be proportional to their differences in distinguishing atoms. For the Al 〈1 1 2〉 GBs, the modified method predicts a negative misorientation dependency for both the driving pressure threshold for initiating GB movement and the mobility, which agree with experimental findings and other molecular dynamics computations but contradict those predicted using the original method. Last, the modified method was applied to evaluate the mobility of Ni Σ5 〈1 0 0〉 symmetrical tilt GB under different driving pressure and temperature conditions. The results reveal a strong driving pressure dependency of the mobility at relatively low temperatures and suggest that the driving pressure should be as low as possible but large enough to trigger continuous migration.

Quantifying uncertainty in molecular dynamics simulations of grain boundary migration

Molecular dynamics simulations of simple bicrystal systems have been much used as a tool to explore how the migration of grain boundaries varies with their structure and with experimental conditions. In order to permit the exploration of a large parameter space, many studies are forced to rely on a small number of simulations (often a single simulation) for each configuration. The motion of a grain boundary is inherently statistical and any variability in the measured grain boundary velocity should be taken into account in subsequent analysis of trends in grain boundary mobility. Here we present the results of large numbers of simulations of equivalent boundaries, which show that this variability can be large, particularly when small systems are simulated. We show how a bootstrap resampling approach can be used to characterise the statistical uncertainty in boundary velocity using the information present in a single simulation. We show that the approach is robust across a variety of system sizes, temperatures and driving force strengths and types, and provides a good order-of-magnitude measure of the population standard deviation across multiple equivalent simulations.

Molecular dynamics simulations of grain boundary migration during recrystallization employing tilt and twist dislocation boundaries to provide the driving pressure

Molecular dynamics simulations of grain boundary migration, where the driving pressure P is the excess stored energy due to dislocation structures, have been performed. This represents recrystallization in metals. Two types of dislocation structures have been simulated: (a) tilt dislocation boundaries, where edge dislocations are arranged as parallel arrays, (b) twist dislocation boundaries, where screw dislocations are arranged in interconnected dislocation networks. The velocity v and mobility M of the migrating grain boundaries have been calculated from the simulations. v and M are higher in twist-type simulations than in tilt-type simulations, although the activation energies are similar in the two cases. v ∝ P is observed for tilt simulations where the driving pressure is changed by varying the density of dislocation boundaries and for twist simulations where the driving pressure is changed by varying the misorientation across dislocation boundaries. When the misorientations across edge dislocation boundaries are varied, however, the simulations show v ∝ P2. It is suggested that this deviation from the usual v ∝ P-relationship is due to local interactions between the grain boundary and nearby individual dislocations. Misorientation variations across grain boundaries have also been simulated, but the mobilities show little dependence on this. The present simulations result in mobilities and activation energies that are, respectively, significantly higher and somewhat lower than experimental values. A direct mimic of experimental observations is, however not the purpose of this study. Rather the present simulations are based on idealized dislocation structures and suggest that variations in the dislocation structures may play a dominant role in recrystallization dynamics and that local effects are very important phenomena, essential for the interpretation of recrystallization mechanisms.

An effective mobility approach to solute drag in computer simulations of migrating grain boundaries

An approach for taking solute drag into account in simulations of grain boundary migration in multicomponent systems in two or three dimensions has been developed. The new method is based on an effective mobility which is a function of the thermodynamic properties in the bulk and the grain boundary and the total driving force. Examples from phase-field simulations in Fe–Ni and Ni–Cr–Fe are presented.

Simulation of Recrystallization Using Molecular Dynamics; Effects of the Interatomic Potential

Recrystallization is governed by the migration of high angle grain boundaries traveling through a deformed material driven by the excess energy located primarily in dislocation structures. A method for investigating the interaction between a migrating grain boundary and dislocation boundaries using molecular dynamics (MD) was recently developed. During simulations migrating high angle grain boundaries interact with dislocation boundaries, and individual dislocations from the dislocation boundaries are absorbed into the grain boundaries. Results obtained previously, using a simple Lennard-Jones (LJ) potential, showed surprisingly irregular grain boundary migration compared to simulations of grain boundary migration applying other types of driving forces. Inhomogeneous boundary-dislocation interactions were also observed in which the grain boundaries locally acquired significant cusps during dislocation absorption events. The study presented here makes comparisons between simulations performed using a LJ- and an embedded atom method (EAM) aluminum potential. The results show similarities which indicate that it is the crystallographic features rather than the atomic interactions that determine the details of the migration process.

Stick-slip behavior of grain boundaries studied by accelerated molecular dynamics

We apply parallel-replica molecular-dynamics (MD) simulations to study the peak stress versus velocity relation during stress-driven grain-boundary (GB) migration coupled to shear deformation. Because of the limited time scale of regular MD, all previous atomistic simulations of GB migration were implemented at velocities orders of magnitude higher than experiment. By accelerating MD simulations, the parallel-replica method has allowed us to greatly expand the velocity range and finally approach the experimental velocities. The GB motion observed in this work follows the general stress-velocity relation characteristic of stick-slip dynamics over a wide velocity interval. At the high-velocity end of this interval, the finite damping rate causes a reversal of the stress-velocity curve. At low velocities, we begin to see reverses of GB displacements, indicating the approaching crossover between the stick-slip and driven Brownian regimes. This study points to a close analogy between couple GB motion in crystals and other known cases of stick-slip dynamics, including the tip movements in atomic friction microscopy.

Relation between grain growth and grain-boundary diffusion in a pure material by molecular dynamics simulations

Traditionally, due to the impurities inevitably present in real materials that limit the grain-boundary (GB) mobility, the processes of grain growth and GB diffusion are thought to involve similar activation barriers. However, recent molecular dynamics (MD) simulations of GB migration in bicrystals have suggested that, in pure materials, GB diffusion and GB migration involve distinct mechanisms and, hence, different activation barriers. Here we report MD simulations of grain growth in an impurity-free model nanocrystalline palladium microstructure containing only high-energy GBs. By contrast with the bicrystal simulations, we observe virtually identical activation energies for grain growth and GB diffusion. We discuss several mechanisms that might be responsible for this difference between the bicrystal and polycrystal results, including accommodation of the curvature-driven GB migration by the elimination of GB area and GB excess free volume and a possible finite mobility of the triple junctions. The qualitative agreement of our observations with the general experimental findings is remarkable given the absence of any impurities in our model system. This suggests that a fundamental, intrinsic process may be responsible for the similar activation energies for GB migration and GB diffusion in polycrystals. In our model system this process seems to involve the accommodation of the curvature-driven GB migration by GB diffusion to eliminate the GB area and related GB free volume at the triple junctions.

Atomistic simulations of grain boundary migration in copper

While the motion of twist boundaries can be readily studied by atomistic simulations with molecular dynamics (MD) under the action of an elastic driving force, the approach fails for tilt boundaries. This is due to the interaction of the elastic stress with the grain boundary (GB) structure, which causes plastic strain by GB sliding. A novel concept, the orientation correlated driving force, is introduced to circumvent this problem. It is shown that this concept can be successfully applied to the study of the migration of tilt boundaries. The migration behavior of several twist and tilt GBs was investigated. The transition from low-to high-angle boundaries can be captured, and a structural transition of tilt boundaries was found at high temperatures, which also affected the migration behavior. The results compare well with experimental results of the motion high-angle boundaries, but for low-angle boundaries, the agreement is poor.

Influence of Lattice Anisotropy on Models Formulated by Cellular Automata in Presence of Grain Boundary Movement: A Case Study

This paper continues in the previous research focussed to two simple questions. The first one reads: ”What is the influence of anisotropy of computational lattice on simulations of boundary movement?” where grain boundary movement typically appears in simulations of grain boundary migration and static/dynamic recrystallization. The second question reads: ”How is the computational anisotropy related to natural anisotropy of the material lattice itself?” This study is focussed on the influence of change of the computational algorithm and/or lattice on the grain boundary movement. Two algorithms, the majority rule and the simple modification of the Monte Carlo method for two different lattices – namely square and hexagonal one – are used.

Two-dimensional finite element simulation of grain boundary migration for embedded symmetric grains

The grain boundary migration of embedded symmetric grains is simulated by the two-dimensional finite element method. The equilibrium shape of a grain boundary is predicted at dynamic state and the migration rate is investigated for the predicted grain boundary. The equilibrium shape of a grain boundary at dynamic state is found to be slightly different from the circular arc description which would be the shape at static state. By finding the systematic variation of the boundary shape in the embedded n-sided grains, it is verified that the dynamic effects on the shape appear during the grain boundary migration. A geometrical equation is proposed describing the grain boundary shape at dynamic equilibrium state. The simulated migration behavior of the grain boundary of equilibrium shape shows nearly the same behavior predicted from the circular arc description. The dynamic effects on grain growth rate are considered to be negligible.

Simulations of grain boundary migration in austenitic stainless steel weld metal by vertex dynamics

Summary This paper describes an investigation of SUS310S stainless steel weld metal to clarify the direction of grain boundary migration. A vertex dynamics model is used to calculate the transition process of grain growth in the base metal and grain boundary migration in the weld metal. The results are compared with observations of grain boundary migration in the weld metal. The results obtained may be summarised as follows. 1. When the grain boundary migration behaviour of base metal grains is computer-simulated by vertex dynamics, the growth rule and number of grain sides distribution are found to be consistent with the actually observed growth behaviour. That is to say, when the friction coefficient of grain boundary migration is valued at the third power of the grain boundary length, grain growth is proportional to the 1/4 power of the growth time. The number of grain sides distribution is virtually identical in the grain growth process. 2. The grain boundaries in the weld metal migrate from the heat affected zone (HAZ) towards the weld metal in the welding HAZ near the fusion boundary zone and from the axial crystals towards the columnar crystals at the weld metal centre. This is due to the fact that, at the grain boundary edges, the direction of the unit resultant vector of the grain boundary line extending from the grain boundary triple junctions faces towards the weld metal in the HAZ and towards the columnar crystals at the weld metal centre. The direction of grain boundary migration after solidification is therefore considered to be controlled by the migration of the grain boundary triple junctions on both edges, i.e. by the resultant direction of the unit vector of the grain boundary line extending from the grain boundary triple junctions.

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.

Dynamic simulation of grain boundary migration

Dynamic simulation of grain boundary migration in two dimensions requires the combined movement of grain boundaries and three-junctions. In this work, a method of dynamic simulation is described where the migration is broken down into two steps: I. The grain boundaries migrate with frozen threejunctions. II. The three-junctions are released in order to obtain equilibrium. In principle, the development of any initial two-dimensional grain-structure can be studied. The CPU-time and memory requirements increase with increasing number of grains.