Grain Boundary Motion Research Articles

Molecular dynamic simulations of the mechanical properties of crystalline/crystalline and crystalline/amorphous nanolayered pillars

By properly introducing interfaces and boundaries to nanomaterials, good plasticity can be obtained without sacrificing the strength. Nanolayered crystalline/crystalline (C/C) Cu/Zr and crystalline/amorphous (C/A) Cu/CuZr with and without twin boundaries (TBs) are investigated by large scale molecular dynamic simulations. By characterizing the plastic deformation on atomic scale, the simulation results show that the C/C interfaces, C/A interfaces, grain boundaries (GBs) and TBs have different effects on the deformation behaviors of nanolayered pillars. In C/C pillars, partial dislocations slip in the columnar nano-crystals of Cu layers and diffusion and motion of GBs take place in Zr layers. The dislocations entrapped within the C/C interfaces and the diffusion and motion of GBs in Zr layers lead to strain softening. TBs can effectively improve the yield stress of C/C pillars but not that of C/A pillars. The dominant deformation mechanisms in C/A pillars are the activations of the shear transformation zones (STZs) and the interplay of dislocations and STZs at the interfaces, which, in conjunction with the strain compatibility of the amorphous layers, contribute the less strain softening responses in C/A pillars.

Superplastic deformation mechanism of nanocrystalline copper: a molecular dynamics study

In the process of the generation of jet formed by the shaped charge explosive compression, the grain of the metal liner is refined from 30-80 μm down to sub-micron or nanometer level. There is a strong scientific significance for studying the mechanism of grain refinement and dynamic superplastic deformation at a micro level. The main contents of this study are as follows. Firstly, the models of nanocrystalline copper with the grain sizes of 7.17, 9.11, 12.55, 14.85, 18.38 and 22.48 nm are established using the Voronoi geometrical construction method, and these models are relaxed in 100 ps to the equilibrium state at 293 K. Then, the tensile deformation processes of nanocrystalline copper at various grain sizes are simulated by using the molecular dynamics method. The strain increases to 0.2 gradually at a strain rate of 2×109/s. Based on the data output, the stress-strain curves at different grain sizes are gained and the corresponding values of the averaged flow stress are calculated. The results show that the average flow stress exhibits the maximum at a grain size of 14.85 nm. Finally, the primary deformation process of nanocrystalline copper is displayed by analyzing the atomic configuration evolvement. When the grain size is 22.48 nm, the typical dislocation motion is found and there are a huge number of dislocations in the deformation process. However, the number of dislocations decreases sharply at the grain sizes of 14.85 nm and 9.11 nm, and the grain-boundary motion is visible at these small grain sizes. The most significant work is that the deformation mechanisms of nanocrystalline copper at different grain sizes are analyzed in detail. The results indicate that the dislocation motion dominates the deformation process when the grain sizes of nanocrystalline copper are larger than 14.85 nm. As the grain sizes decrease below 14.85 nm, the grain-boundary sliding and rotation become a dominant deformation mechanism. This change of deformation mechanism is the fundamental reason for softening, which is so-called reverse Hall-Petch relationship. On the basis of previous study and this molecular dynamics simulation, combining the grain coalition and the grain-boundary rotation, an ideal deformation mechanism model is established at small grain sizes, which provides the microcosmic deformation mechanism reference for the large strain deformation of the jet.

Atomic-scale mechanism of grain boundary motion in graphene

Grain boundaries (GBs) in graphene can migrate when irradiated by electron beams from a transmission electron microscope (TEM). Here, we present an ab initio study on the atomic scale-mechanism for motion of GB with misorientation angle of ∼30° in graphene. From total energy calculations and energy barrier calculations, we find that a Stone–Wales (SW)-type transformation can occur more easily near GBs than in pristine graphene due to a reduced energy barrier of 7.23eV; thus, this transformation is responsible for the motion of GBs. More interestingly, we find that a mismatch in the crystalline orientation at GBs can drive the evaporation of a carbon dimer by greatly reducing the corresponding overall energy barrier to 11.38eV. After evaporation of the carbon dimer, the GBs can be stabilized through a series of SW-type transformations that result in GB motion. The GB motion induced by evaporation of the dimer is in excellent agreement with recent TEM experiments. Our findings elucidate the mechanism for the dynamics of GBs during TEM experiments and enhance the controllability of GBs in graphene.

An atomistically informed kinetic Monte Carlo model of grain boundary motion coupled to shear deformation

The shear coupled motion of grain boundaries (GBs) is modelled by using two different atomistic simulation techniques: molecular dynamics (MD) and kinetic Monte Carlo (KMC). MD simulations are conducted to identify the elementary mechanisms that take place during the coupled motion of GBs. This process is described on the one hand, in terms of the geometrical approach of the dislocation content in the boundary; and on the other hand, by the thermodynamics of the dislocation passage, shown as a thermal activated process. Relevant MD output is extended into a KMC model that considers the GB migration as a result of a sequence of discrete rare events. The independent motion of each structural unit forming the boundary conforms a single event, having a rate per unit of time to move to the next stable position computed according to the transition state theory. The limited time scale of classical MD is overcome by KMC, that allows to impose realistic deformation velocities up to 10μm/s.

Development of microstructure in submicron particles reinforced magnesium matrix composite processed by room temperature deformation

Magnesium matrix composite reinforced with submicron SiC particles was subjected to room temperature deformation. A stepped tensile method was adopted to observe the development of microstructure at different tensile strain state. The microstructure evolution determined by transmission electron microscopy showed that the existence of submicron SiC particles could promote dislocation multiplication as well as impede dislocation motion. Dislocation density around SiC particles increased with the increase of tensile strain. Compared with the matrix alloy, the composite could withstand greater external loads, which can be related to the pinning effect caused by the submicron SiC particles on the movement of grain and twin boundaries. The study of the interface between the submicron SiC particles and matrix in the composite suggested that single submicron SiC particle bonded well with the matrix alloy after tensile process. Initiation of micro-cracks usually generated in the submicron particle dense zone during tensile process, which could lead to the fracture of composite.

Uniaxial stress-driven coupled grain boundary motion in hexagonal close-packed metals: A molecular dynamics study

Stress-driven grain boundary (GB) migration has been evident as a dominant mechanism accounting for plastic deformation in crystalline solids. Using molecular dynamics (MD) simulations on a Ti bicrystal model, we show that a uniaxial stress-driven coupling is associated with the recently observed 90°GB reorientation in shock simulations and nanopillar compression measurements. This is not consistent with the theory of shear-induced coupled GB migration. In situ atomic configuration analysis reveals that this GB motion is accompanied by the glide of two sets of parallel dislocation arrays, and the uniaxial stress-driven coupling is explained through a composite action of symmetrically distributed dislocations and deformation twins. In addition, the coupling factor is calculated from MD simulations over a wide range of temperatures. We find that the coupled motion can be thermally damped (i.e., not thermally activated), probably due to the absence of the collective action of interface dislocations. This uniaxial coupled mechanism is believed to apply to other hexagonal close-packed metals.

Growth competition of columnar dendritic grains: A phase-field study

We report the results of an extensive phase-field study of the growth competition of columnar dendritic grains in two dimensions. We investigate the influence of the temperature gradient and grain bicrystallography on the selection of both grain and microstructure, focusing on a geometry with two grains with principal crystal axes oriented parallel and at a finite misorientation angle with respect to the axis of the temperature gradient. Our first main finding is that, for well-developed dendritic structures forming at a low-temperature gradient, the rate of elimination of the misoriented grain is a non-monotonic function of the difference in undercooling between the dendrite tips of the two grains. Hence this rate cannot be predicted even qualitatively by the common assumption that the elimination rate increases with this undercooling difference. The breakdown of this assumption is particularly striking for highly misoriented dendritic and degenerate structures that persist for very long times despite growing at a substantially larger undercooling than the well-oriented neighboring grains. Our second main finding is that microscopic thermal fluctuations at the origin of sidebranching can induce significant variations in the macroscopic trajectories of grain boundaries (GBs), thereby making grain selection a stochastic process, while yielding limited variations in the selected primary spacings. In contrast, in the absence of fluctuations, GB motion becomes essentially deterministic and grain elimination is suppressed. In addition, our simulations reproduce quantitatively scaling laws deduced from experiments for both the primary dendritic spacing and the dendrite growth direction of misoriented grains. They further reveal that the “intergrain” primary spacing selected by tertiary branching events at GBs is systematically larger than the “intragrain” primary spacing selected by the transient growth competition between primary branches within a single grain, while obeying the same scaling laws. Finally, the fact that the rate of grain elimination is slower in our 2-D simulations than in experiments suggests that the 3-D grain bicrystallography plays a key role in grain selection. This role is interpreted in the light of 2-D simulations that hinder sidebranching on the misoriented grain.

Anomalous Kinetics and Regimes of Growth of Intermetallic Phases during Solid State Reactions in Nanosystems

Two interesting features of formation and growth of intermetallic phases in nanoscale solid state reactions will be discussed:Linear-parabolic “normal” growth: it will be summarized that at the very early stages of the growth of an already existing new phase (i.e. when nucleation problems can be neglected) the linear kinetics can be observed due to the so-called diffusion asymmetry. Indeed, it was shown that if the ratio of the diffusion coefficients differ by orders of magnitude in the parent materials (and so also in the new phase), during the growth of a phase bordered by parallel interfaces from the parent phases (normal growth geometry), the shift of the individual interfaces can be linear at the beginning and a transition to the parabolic regime can take place even after a shift of several tens of nanometres. In addition, an AB compound in contact with the pure A and B phases can be dissolved if the diffusion in B is much faster than in either A and AB. This means that the thickness of this phase should decrease, or even can be fully dissolved, at the beginning and only after some time—when the composition in B will be high enough allowing the re-nucleation of this AB phase—will the AB phase grow further.The common problem of two stages of solid state reactions will be revisited: usually the growth can be divided into two stages: a) the formation (nucleation) and lateral growth of the new phases and b) the “normal” growth of the already continuous phase. It was concluded in different previous reviews that in stage b) in the majority of cases the parabolic growth was observed in accordance with the above i) point: the linear-parabolic transition length was typically below 1 μm, which was the lower limit of detection in many previous investigations. On the other hand recently the application of the linear-parabolic growth law for the analysis of experimental data obtained in nanoscale reactions became very popular, not making a clear distinction between a) and b) stages. It will be emphasized here that care should be taken in all cases when the experimental methods applied provide information only about the increase of the amount of the reaction product and there is no information where and how the new phase (s) grow. We have illustrated in a series of low temperature experiments - where the bulk diffusion processes are frozen - that even in this case a full homogeneous phase can be formed by cold homogenization called Grain Boundary Diffusion Induced Solid State Reaction (GBDIREAC). In this case first the reaction starts by grain-boundary (GB) diffusion and nucleation of the new phase at GBs or their triple junctions, then the growth of the new phase happens by the shift of the new interfaces perpendicular to the original GB. This is a process similar to the diffusion induced grain-boundary motion (DIGM) or diffusion induced recrystallization (DIR) phenomena and in this case the interface shift, at least in the first stage of the reaction until the parent phases have been consumed, can be considered constant. This means that the amount of the phase increases linearly with time, giving a plausible explanation for the linear kinetics frequently observed in stage a).

Properties of two dimensional materials obtained from experiments in a low-voltage aberration-corrected TEM

We report on structural and electronic properties of two-dimensional materials ob-tained by analytical low-voltage aberration-corrected transmission electron microscopy. Basic crystallographic defects and their peculiarities will be discussed for two-dimensional materials at the atomic level. Thus, we report the atomic structure of point defect and -clusters [1], the full life circle of dislocations [2] and the movements of grain boundaries in grapheme [3]. In addition, we unravel the atomic structure of the amorphous phase (graphene, SiO2) in direct space just from single-atom-based analysis of high-resolution TEM images [5, 6]. As the energetic electron beam is interacting with the specimen via transferring energy to the atoms, structural transformation between different phases can be followed atom-by-atom [7, 8, 9]. In addition, physical properties such as the knock-on damage threshold is determined from controlled direct space experiments and precise measurements of high-resolution TEM images of graphene and MoS2[8, 7]. However beam-electron interactions with the specimen are also restricting imaging the pristine structure of a sample. It can be suppressed by simply limiting the total electron doses on the samples. Limited electron doses, however, result in worse signal to noise ratios. Here, a quantitative approach for estimating the visibility of objects in TEM images with limited doses will be presented [10]. Another traditional approach to suppress electron-induced damage during HRTEM observation is to employ an efficient cleaning procedure [11] and the protective coating of sensitive materials. This old approach will be taken to its extreme, when radiation sensitive materials are enclosed inside carbon nanotubes [12] and between two graphene layers [13]. We show moreover the advantage of lowering the accelerating voltage for imaging the pristine structure of low-dimensional materials [14]. [4] P. Wachsmuth, R. Hambach, M.K. Kinyanjui, et al., Phys. Rev. B B 88, 075433, (2013) [5] P. Y. Huang, S. Kurasch, A. Srivastava, et al. Nano Lett. 12(2), 1081, (2012) [6] P. Y. Huang, S. Kurasch, J.S. Alden, et al., Science 342, 224, (2013) [7] H.-P. Komsa, J. Kotakoski, S. Kurasch, et al., Phys. Rev. Lett. 109, 035503 (2012) [8] C Meyer, F Eder, S Kurasch, et al. Physical Review Letters, 108, 196102. 2012. [9] B. Westenfelder, J. C. Meyer, J. Biskupek, et al., Transformations of Carbon Adsorbates on Graphene Substrates under Extreme Heat, Nano Letters, 11 (12), 5123-5127, 2011 [10] Z. Lee, H. Rose, O. Lehtinen, et al., Ultramicroscopy (2014), DOI 10.1016/j.ultramic.2014.01.010 [11] G. Algara-Siller, S. Kurasch, M. Sedighi, et al., Appl. Phys. Lett. 103 (2013) 203107 [12] T. Zoberbier, T. W. Chamberlain, J. Biskupek, et al., J. Am. Chem. Soc. 134 (2012) 3073-3079 [13] G. Algara-Siller, S. Kurasch, M. Sedighi, et al., Appl. Phys. Lett. 103. 203107, (2013) [14] U. Kaiser et al. Ultramicroscopy, 111, 8, 1239, (2011) [15] Fruitful cooperation within the SALVE project and financial support by the DFG (German Research Foundation) and by the Ministry of Science, Research, and the Arts (MWK) of Baden-Württemberg are gratefully acknowledged.

In situ observation of austenite grain growth behavior in the simulated coarse-grained heat-affected zone of Ti-microalloyed steels

Abstract The austenite grain growth behavior in a simulated coarse-grained heat-affected zone during thermal cycling was investigated via in situ observation. Austenite grains nucleated at ferrite grain boundaries and then grew in different directions through movement of grain boundaries into the ferrite phase. Subsequently, the adjacent austenite grains impinged against each other during the α→γ transformation. After the α→γ transformation, austenite grains coarsened via the coalescence of small grains and via boundary migration between grains. The growth process of austenite grains was a continuous process during heating, isothermal holding, and cooling in simulated thermal cycling. Abundant finely dispersed nanoscale TiN particles in a steel specimen containing 0.012wt% Ti effectively retarded the grain boundary migration, which resulted in refined austenite grains. When the Ti concentration in the steel was increased, the number of TiN particles decreased and their size coarsened. The big particles were not effective in pinning the austenite grain boundary movement and resulted in coarse austenite grains.

Strategies to suppress grain growth of nanocrystalline aluminum

The grain growth behaviors of nanocrystalline aluminum, alloy and composite are compared. First, nanocrystalline aluminum is fabricated by consolidation of ball-milled powder. Second, nanocrystalline aluminum alloy is designed to have elements such as Mn, Zr, and Misch metals, which can form thermally stable second phases at grain boundaries and also drag the movement of grain boundaries. Third, nanocrystalline aluminum-based composites containing multi-walled carbon nanotubes (MWCNTs) are also prepared because MWCNTs are expected to be located at grain boundaries and to suppress the grain growth of nanocrystalline aluminum. These three types of samples are annealed at 550 °C for up to 5 d and the effect of annealing time on Vickers hardness of the samples is compared. As a result, MWCNTs are found to be most effective to impede grain growth of nanocrystalline aluminum.

Threshold Dynamics for Networks with Arbitrary Surface Tensions

We present and study a new algorithm for simulating the N‐phase mean curvature motion for an arbitrary set of (isotropic) surface tensions. The departure point is the threshold dynamics algorithm of Merriman, Bence, and Osher for the two‐phase case.A new energetic interpretation of this algorithm allows us to extend it in a natural way to the case of N phases, for arbitrary surface tensions and arbitrary (isotropic) mobilities. For a large class of surface tensions, the algorithm is shown to be consistent in the sense that at every time step, it decreases an energy functional that is an approximation (in the sense of Gamma convergence) of the interfacial energy. A broad range of numerical tests shows good convergence properties.An important application is the motion of grain boundaries in polycrystalline materials: It is also established that the above‐mentioned large class of surface tensions contains the Read‐Shockley surface tensions, both in the two‐dimensional and three‐dimensional settings.© 2015 Wiley Periodicals, Inc.

A two-dimensional study of coupled grain boundary motion using the level set method

The coupled motion of a closed non-circular grain boundary (GB) in a bicrystal, with both isotropic and anisotropic GB energies, is studied using the level set method. The kinetic relations, obtained within the framework of linear irreversible thermodynamics, govern the overall dynamics, including normal motion (migration) of the GB, viscous sliding along the GB and tangential motion of the grains which is geometrically coupled with the migration. The shape accommodation necessary to maintain coherency of relatively rotating and non-deforming grains is accomplished by allowing for diffusion along the GB. We solve the governing equations for the coupled motion in order to determine the shape and the misorientation evolution of an isolated GB under various constitutive assumptions. First, assuming both GB energy and kinetic coefficients to be isotropic, we study the interplay between kinetic coefficients for initially circular, near-circular and non-circular GBs, as well as the impact of stress and initial conditions on the GB dynamics. Next, we study the influence of anisotropy in the GB energy, mobility and geometric coupling for various combinations of parameters and initial conditions. Allowing for geometric coupling can in fact lead to shapes distinctly different to those that are usually predicted on the basis of migration alone. Our numerical scheme provides a general framework in which to study these and other related problems of GB motion.

Influences of triple junctions on stress-assisted grain boundary motion in nanocrystalline materials

Stress-assisted grain boundary motion is among the most studied modes of microstructural evolution in crystalline materials. In this study, molecular dynamics simulations were used to systematically investigate the influences of triple junctions on the stress-assisted motion of symmetric tilt grain boundaries in Cu by considering a honeycomb nanocrystalline model. It was found that the grain boundary motion in nanocrystalline models was highly sensitive to the loading mode, and a strong coupling effect which was prevalent in bicrystal models was only observed when simple shear was applied. In addition, the coupling factor extracted from the honeycomb model was found to be larger and more sensitive to temperature change than that from bicrystal models for the same type of grain boundary under the same loading conditions. Furthermore, the triple junctions seemed to exhibit unusual asymmetric pinning effects to the migrating grain boundary and the constraints by the triple junctions and neighboring grains led to remarkable non-linear grain boundary motion in directions both parallel and normal to the applied shear, which was in stark contrast to that observed in bicrystal models. In addition, dislocation nucleation and propagation, which were absent in the bicrystal model, were found to play an important role on shear-induced grain boundary motion when triple junctions were present. In the end, a generalized model for shear-assisted grain boundary motion was proposed based on the findings from this research.

Effect of interfacial structural phase transitions on the coupled motion of grain boundaries: A molecular dynamics study

In this work, the coupled motion of two different phases of Σ 5(210)[001] grain boundaries was investigated by molecular dynamics simulations of fcc Cu. The effect of interfacial structural phase transitions is shown to have a profound effect on both the shear strength and the nature of the coupled motion. Specifically, the motion of the two different phases is described by ideal coupling factors β⟨100⟩ and β⟨110⟩ that have different magnitudes and even signs. Additionally, the shear strength for the two interfacial phases is observed to differ by up to 40% at the lowest temperatures simulated. The study demonstrates that grain boundary phases transitions may have strong effects on the kinetics of microstructural evolution.

On the use of copper-based substrates for YBCO coated conductors

It is well known that the recrystallization texture of heavily cold-rolled pure copperis almost completely cubic. However, one of the main drawbacks concerning the use of purecopper cube-textured substrates for YBCO coated conductor is the reduced secondaryrecrystallization temperature. The onset of secondary recrystallization (i.e., the occurrence ofabnormal grains with unpredictable orientation) in pure copper substrate was observed withinthe typical temperature range required for buffer layer and YBCO processing (600–850 °C). Toavoid the formation of abnormal grains the effect of both grain size adjustment (GSA) andrecrystallization annealing was analyzed. The combined use of a small initial grain size and arecrystallization two-step annealing (TSA) drastically reduced the presence of abnormal grainsin pure copper tapes.Another way to overcome the limitation imposed by the formation of abnormal grains is todeposit a buffer layer at temperatures where secondary recrystallization does not occur. Forexample, La2Zr2O7 (LZO) film with a high degree of epitaxy was grown by metal-organicdecomposition (MOD) at 1000 °C on pure copper substrate. In several samples the substrateunderwent secondary recrystallization. Our experiments indicate that the motion of grainboundaries occurring during secondary recrystallization process does not affect the quality ofLZO film.

그래핀 결정입계의 이동 및 결함과의 상호작용

다결정 및 단결정 Cu 시편에 CVD를 이용하여 그래핀을 합성 하였으며, 광학현미경 조직사진을 이미지 조절 및 분석 가능한 소프트웨어를 활용하여 광학현미경 조직사진 상에서는 구분이 어려운 그래핀 합성에 따른 미세한 특성들을 이미지 분석을 통하여 구현하였다. 그래핀이 Cu 시편의 결정입계에서 핵 생성하여 Cu 입내로 성장하는 거동을 보이고, 그래핀 성장 시 그래핀 입계의 이동이 Cu 입계 및 기공과 상호작용하는 현상들에 대하여 설명하고, 결과적으로 야기되는 문제들의 원인과 결과를 논하였다. On poly and single crystalline Cu substrates, the graphene was synthesized by chemical vapor deposition(CVD). Optical microscopic images which were not possible to show the detailed characterization of graphene growth were adjusted and analyzed using image analyzing software. As a result it was possible to show the detailed growth mechanism of graphene by utilizing the image analysis. Nucleation of graphene on Cu grain boundary and its growth behavior into Cu grain are shown. In addition, the movement of graphene grain boundary interacting with Cu grain boundary and pinholes during growth was illustrated in detail, and the cause and result are discussed as a result of those interactions.

Grain boundary ridges slow dawn grain boundary motion: In-situ observation

The impact of grain boundary (GB) ridge on motion of high-angle GB in Zn was studied. The steady-state motion of faceted GB half-loop with [101¯0] tilt GB and GB ridge was recorded in-situ. The temperatures of faceting–roughening transition were experimentally defined for three GB half-loops. Above the transition temperature GB half-loops had GB “rough-to-rough” ridge with continuously curved GB segments. Below the transition temperature a facet appeared and coexisted with two “facet-to-rough” ridges. For the first time we could extract mobility of “rough-to-rough” and “rough-to-facet” ridges and bring out clearly that GB ridge slows down GB motion. Present removes contradiction between high facet mobility and the low mobility of faceted GB.

Phase field crystal simulation of grain boundary movement and dislocation reaction

The phase field crystal (PFC) model is used to simulate the premelting dislocation movement of the symmetric tilt grain boundary (STGB) under strain action when the system temperature is at far from the melting point and close to the melting point, respectively. The results show a local premelting occurs surrounding the dislocations as the premelting temperature is approached to from below temperature. The premelting dislocations of the STGB can glide under strain action, and the premelting region is a companion for dislocation gliding. The process of STGB decay is very similar at the two high temperature conditions. As premelting presents, it diminishes the gliding resistance for the dislocations and leads to a faster movement of dislocations, and also brings about more energy reduction of the system during the decay process of STGB. In spite of applying strain to these premelting samples in whole decay processes of STGB, the premelting dislocation region does not obviously develop and extend. This indicates that the external strain action does not promote the premelting at the high temperature, and cannot induce more premelting dislocation, which can be owed to the premelting phase around the dislocation exhibit fluid-like properties and to the premelting dislocation easily gliding and relaxing the strain energy; this is in agreement with the results of experiments and molecular dynamics.

Capillary-driven grain boundary motion and grain rotation in a tricrystal: A molecular dynamics study

We report on molecular dynamics (MD) simulations of a tricrystal composed of a cylindrical grain embedded at the center of a plane grain boundary (GB). The embedded grain shrinks by capillary forces and eventually vanishes. This process is often accompanied by rotation of the embedded grain in either a clockwise or counter-clockwise direction. Using the geometric theory of coupling between GB motion and grain translations, we propose a model capable of predicting the direction of the grain rotation depending on the crystallographic parameters of the three grains. Full agreement has been found between the model predictions and the MD simulation results for both spontaneous grain shrinkage and in the presence of applied shear stresses. The consequences of these results for grain rotation in polycrystalline materials and possible extensions of the model to multiple grains are discussed.