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Interface Mobility from Interface Random Walk
Abstract
Computational studies aimed at extracting interface mobilities require driving forces orders of magnitude higher than those occurring experimentally. We present a computational methodology that extracts the absolute interface mobility in the zero driving force limit by monitoring the one-dimensional random walk of the mean interface position along the interface normal. The method exploits a fluctuation-dissipation relation similar to the Stokes-Einstein relation, which relates the diffusion coefficient of this Brownian-like random walk to the interface mobility. Atomic-scale simulations of grain boundaries in model crystalline systems validate the theoretical predictions and highlight the profound effect of impurities. The generality of this technique, combined with its inherent spatiotemporal efficiency, should allow computational studies to effectively complement experiments in understanding interface kinetics in diverse material systems.
... Gain boundary (GB) mobility, which describes how fast a GB moves under an applied driving force, is one of the most dominating properties that influence the microstructural evolution in materials. Despite the relatively straightforward physical meaning of GB mobility and decades of investigation on it from both experiments [1][2][3][4] and atomistic simulations [5][6][7][8][9][10][11][12][13][14], GB migration behavior is still hard to predict due to the vast 5-parameter space of GBs. While many theoretical models, such as those based on the conventional concepts of the structural unit [15,16] and the more recent ones based on machine learning and the various types of local atomic descriptors [17,18], have been developed to successfully predict other fundamental properties of GBs, such as GB energy [18] and the energy spectrum for solute segregation [17], no such model can be applied to predict the GB migration behavior accurately even for special GB structures of high symmetry. ...
... However, previous studies based on molecular dynamics (MD) simulations have shown that by applying different driving forces, the mobility [12], as well as the thermal behavior of GBs, could change dramatically [11]. For example, according to [11], when the synthetic driving force changes from 0.005eV to 0.025eV, the Ni Σ7 Trautt et al. [9] have proposed a way to calculate GB mobility at the zero-driving force limit through the random walk of the GB. Deng and Schuh [33] further improved the accuracy of this method in capturing the subtle movement of the GBs. ...
... Deng and Schuh [33] further improved the accuracy of this method in capturing the subtle movement of the GBs. Based on this method, the GB mobility can be computed based on the Einstein relation [9]: ...
Grain boundaries (GBs) that show higher mobility at lower temperatures (i.e., the so-called nonthermally activated or non-Arrhenius GBs) have attracted significant interest in recent years. In this study, we use atomistic simulations to systematically investigate the effect of driving force on GB mobility based on a set of bicrystalline models in Ni. It is found that the thermal behavior of GB migration strongly depends on the temperature and the magnitude of driving forces. When the driving force is small, e.g., GB migration at the zero-driving force limit as induced solely by thermal fluctuations, the mobility of all GBs investigated in the current study shows a transition from thermally activated to non-thermally activated behavior when the temperature is increased. As the driving force increases, the transition temperature at which the mobility peaks would gradually decrease so that for some GBs only the non-thermally activated behavior would be detected. It is further revealed based on nudged elastic band (NEB) analysis that the transition temperature is linearly related to the energy barrier for migration in each GB, and the energy barrier is lowered as the driving force increases. Our work supports the previous theoretical model for GB migration based on both disconnection nucleation and the more recent one based on classical thermal activation. Furthermore, the current study can be used to improve both models by taking into account the influence of driving force with a simple fix to how the energy barrier for GB migration should be considered. It is expected that this work advances the current understanding of general GB migration and sheds some light on a unified theoretical framework in the near future.
... As examples, segregation-based changes in the interfacial free energy can lead to transitions in its structure and morphology [9][10][11][12][13][14], in turn modifying the driving force for coarsening [15,16]. Drag forces exerted by the usually sluggish solute cloud [17][18][19][20][21][22][23][24][25] lead to a dramatic decrease in the interface kinetics [3,26]. The coupled evolution of the interfacial microstructure leads to changes in the final grain size, texture and distribution of interface types that directly impact their material properties [27][28][29]. ...
... 3). Experimentally this is challenging since the level of sample purity and the solute excess at the interfaces required to estimate the drag forces are unknown, and there is growing evidence that even minute quantities of solutes (of the order of a few ppm) can modify the migration rates of grain boundaries [3,26,[41][42][43]. Finally, both continuum and discrete frameworks breakdown at low driving forces (and therefore low velocities) where the transients driven by local solute-interface interactions become important [17,22]. ...
... This value is slightly larger than past studies on segregation of individual carbon atoms with grain boundaries in α-Fe [58], likely due to co-segregation effects. In the absence of solutes, the MSD of the boundary in α-Fe increases linearly with time [26,59], and the slope yields the diffusivity and mobility the grain boundary, D i = 5.1 ± 0.08 × 10 −11 m 2 /s and M i = D i A/k B T = 1.28 ± 0.02 × 10 −7 m 4 /J s respectively (Fig. 8c). Under these conditions, interface diffusivity is the almost twice the bulk diffusivity of interstitial carbon in this model system [57,60], D B s ≈ 3 × 10 −11 m 2 /s. ...
The design of polycrystalline alloys hinges on a predictive understanding of the interaction between the diffusing solutes and the motion of the constituent crystalline interfaces. Existing frameworks ignore the dynamic multiplicity of and transitions between the interfacial structures and phases. Here, we develop a computationally-accessible theoretical framework based on short-time equilibrium fluctuations to extract the drag force exerted by the segregating solute cloud. Using three distinct classes of computational techniques, we show that the random walk of a solute-loaded interface is necessarily non-classical at short time-scales as it occurs within a confining solute cloud. The much slower stochastic evolution of the cloud allows us to approximate the short-time behavior as an exponentially sub-diffusive Brownian motion in an external trapping potential with a stiffness set by the average drag force. At longer time-scales, the interfacial and bulk forces lead to a gradual recovery of classical random walk of the interface with a diffusivity set by the extrinsic mobility. The short-time response is accessible via {\it ab-initio} computations, offering a firm foundation for high throughput, rational design of alloys for controlling microstructural evolution in polycrystals, and in particular for nanocrystalline alloys-by-design.
... Grain boundaries (GBs) are key players in the plasticity, damage, and failure of polycrystalline materials [1][2][3]. A quantitative description of GB-mediated processes, such as migration, sliding, and defect interactions, is hence vital for optimizing the properties of the polycrystal through mechanical processing and has been the subject of long-standing interest [4][5][6][7][8][9][10][11][12][13][14][15][16][17][18][19]. ...
... In order to accurately extract the average GB displacement for each time interval, we dynamically capture the GB profile based on the coordination number of each atom. A similar method was utilized in other works [7,8,10]. Figure 16 shows the shear-coupled GB migration at room temperature in 2D and 3D simulation cells without and with a monovacancy. For the 2D simulation cell, it is observed that GB migration in the presence of a monovacancy is almost one order faster than that GB without a vacancy under shear stress τ = 116 MPa. ...
Mechanical behavior of polycrystalline materials is intimately connected to migration of grain boundaries, which in turn is dramatically impacted by the presence of defects. In this paper, we present atomistic simulations to elucidate the elementary mechanism that dictates the role of vacancies in enhancing grain boundary migration via shear-coupled normal motion. The minimum energy pathway and the associated energy barriers are calculated using the nudged elastic band method. Fully three-dimensional atomistic simulations provide excellent verification of the three-dimensional disconnection model and furnish quantitative evidence that vacancies facilitate grain boundary migration by weakening the line tension of a disconnection loop. It is also revealed that vacancies serve as energetically favorable sites for the nucleation of grain boundary disconnections, thereby inducing shear-coupled grain boundary migration.
... It has also been used to calculate the mobility of particles [85,199] and ions [187,200] in bulk fluids and near or trapped within fluid-fluid interfaces [85,187,199,200]. However, while interfacial mobility has been calculated for solid-solid interfaces such as grain boundaries [201][202][203], it has not yet been calculated for fluid-fluid interfaces. ...
... The interfacial mobility M is related to the mean square displacement (MSD) of the interface given by [85,201] ...
Condensation is of central importance in a broad range of areas in nature and industry. Aerosol-cloud interactions, a currently a significant open question in climate modeling, and water harvesting mechanisms on organisms such as cacti, beetles, and spiders, are natural processes that are rely on condensation. Condensation is an effective method for transferring heat due to the latent heat required for a fluid to change phase from a gas to a liquid. Improvements in condensation processes would have an impact in a variety of industrial areas such as thermal management, environmental control, microelectronics, desalination, and power generation. Dropwise condensation is preferable over filmwise condensation because it has a significantly higher heat transfer coefficient. Nanopatterned surfaces are of interest because they have experimentally demonstrated higher heat transfer than their smooth counterparts, but recent heat transfer measurements on individual droplets have revealed discrepancies between theoretical predictions and experimental measurements for the smallest droplets. Interfacial properties on small length scales are often difficult to measure experimentally and are often used as fitting parameters in condensation models. The common assumptions used when modeling dropwise condensation are that (1) the condensing droplets are thermodynamically quasi-static and that (2) the heat and mass transport are uncoupled, that is, droplet motion and heat transfer are modeled independently of one another. In this dissertation, several continuum properties including the mass accommodation coefficient and interfacial mobility are computed allowing for the physical parameters to be known a priori for continuum scale models such as the Navier-Stokes-Cahn-Hilliard equations or interfacial resistances in condensation models. Furthermore, the two fundamental assumptions used in condensation models are examined in an attempt to resolve the theoretical and experimental discrepancies. This will be done by leveraging microscopic and nonequilibrium thermodynamic approaches to determine the validity of the condensation assumptions for planar and highly curved systems.
... But these fluctuations diminish when either the temperature or the strain rate values are increased. These fluctuations in the GB position are related to the mobility of a GB [124,125]. Thus, the decreased fluctuations in GBs positions with increased temperatures is consistent with previously published works [14,34,37,38,126], confirming this faceted GB's non-Arrhenius (or anti-thermal) migration behavior even under the mechanical loading. It was also inferred from Fig. 8 that the GBs do not just move in one direction; for instance, in the 100 K -10 7 s − 1 (Fig. 8 (e)) and 500 K -10 7 s − 1 (Fig. 8 (c)) cases, the GBs moved in the same and opposite directions, respectively. ...
In this article, molecular dynamics simulations are used to understand how a nickel bicrystal with faceted incoherent Σ3 grain boundaries responds to uniaxial tensile loading. The deformation response is studied over a wide range of temperatures (100 – 900 K) and strain rates (107 – 1010 s−1). The dislocation extraction algorithm and common neighbor analysis are employed to identify the deformation mechanisms. Our results reveal that the yield stress decreases with temperature and increases with strain rate; whereas the elastic modulus decreases with temperature and is independent of strain rate. Furthermore, incipient plasticity is detected ahead of the yield point at lower temperatures and lower strain rates. Interestingly, the incoherent twin grain boundaries are quite mobile under the uniaxial tensile loading at lower temperatures and lower strain rates. But this mobility decreased at higher temperatures and higher strain rates, thereby, confirming this faceted grain boundary's non-Arrhenius (anti-thermal) migration behavior even under mechanical loading. From a deformation perspective, the incoherent twin facet of the grain boundary served as the major source for stacking fault formation at lower temperatures and higher strain rates. However, with the increase in temperature, the stacking faults became shorter and originated from both the incoherent twin facet and the tips of coherent twin facet. These results are in qualitative agreement with the experimental results documented in the literature.
... The grain boundary mobility and excess free energy can be determined using molecular dynamics [24][25][26][27][28]. At the grain boundary center (φ = 0.5), the bulk and reference terms of the density potential difference are zero such that ∆µ φ = −2κ φ ∇ 2 φ. ...
Density-based phase-field (DPF) methods have emerged as a technique for simulating grain boundary thermodynamics and kinetics. Compared to the classical phase-field, DPF gives a more physical description of the grain boundary structure and chemistry, bridging CALPHAD databases and atomistic simulations, with broad applications to grain boundary and segregation engineering. Notwithstanding their notable progress, further advancements are still warranted in DPF methods. Chief among these are the requirements to resolve its performance constraints associated with solving fourth-order partial differential equations (PDEs) and to enable the DPF methods for simulating moving grain boundaries. Presented in this work is a means by which the aforementioned problems are addressed by expressing the density field of a DPF simulation in terms of a traditional order parameter field. A generic DPF free energy functional is derived and used to carry out a series of equilibrium and dynamic simulations of grain boundaries in order to generate trends such as grain boundary width vs. gradient energy coefficient, grain boundary velocity vs. applied driving force, and spherical grain radius vs. time. These trends are compared with analytical solutions and the behavior of physical grain boundaries in order to ascertain the validity of the coupled DPF model. All tested quantities were found to agree with established theories of grain boundary behavior. In addition, the resulting simulations allow for DPF simulations to be carried out by existing phase-field solvers.
... Nevertheless, computational studies [13][14][15] have revealed that the magnitude of driving force can leave significant influences on mobility, owing to the force-induced variation of boundary structure and/or migration mechanism. For example, Deng and Schuh [13] found that for both symmetrical and inclined Ni Σ5 100 tilt GBs, their mobilities agree well with the intrinsic values obtained by the thermal fluctuation method [16] only when the applied driving force is sufficiently low; increasing the driving force will lead to diffusive-to-ballistic transition in the migration mechanism and enlarge the discrepancy between the extracted and intrinsic mobility values. Moreover, for shear-coupling migration GBs (i.e., simultaneous translation in GB plane during the migration along the boundary normal direction), Han and coworkers [7,17,18] demonstrated that both GB mobility and shear-coupling factor (ratio of GB sliding and migration rates) do not only strongly depend on the magnitude but also the source of driving force (stress or a jump in chemical potential across the boundary). ...
Grain boundary (GB) migration is widely believed to maintain a linear relation between its displacement and time under a constant driving force. In this study, we investigated the migration behaviors of a set of GBs in Ni by applying the synthetic driving force and shear stress via atomistic simulations. It was found that the displacements of some shear-coupling GBs do not exhibit a linear or approximately linear relation with the time, as widely assumed, but evidently exhibit an acceleration tendency. Moreover, the boundary velocity significantly decreases when increasing the bicrystal size perpendicular to the GB plane. These behaviors were verified to be independent of the magnitude and type of driving force but closely related to the temperature and revealed to be unique to shear-coupling GBs exhibiting a rise in the kinetic energy component along the shear direction. Moreover, after many attempts, we found that the acceleration in migration and size effect can be largely alleviated by adopting one specific kind of boundary condition. Nevertheless, the continuous rise of kinetic energy still exists and leads to the true driving force for GB migration lower than the nominally applied value. For that reason, a technique is proposed to extract the true driving force based on a quantitative analysis of the work-energy relation in the bicrystal system. Accordingly, the calculated true mobility shows that the recently proposed mobility tensor may not be symmetric at relatively large driving forces.
... Many important properties of GBsincluding diffusion, migration, and strengthare controlled by activation barriers of collective atomic rearrangements inside the boundaries [138,[151][152][153][154][155][156]. Therefore, we probe the distributions of accessible activation barriers for the aboveselected ISs using an energy landscape sampling algorithm [104,112,[157][158][159], as shown in To quantify the kinetic boost factor between the post-processing and pre-processing states (C-0K vs. H-0K), one can compute the Boltzmann factor-weighted integral of the two activation barriers spectra in Figure 5-2.b1 ...
The energetics and kinetics of interactions between microstructural point, line, and planar defects govern the most significant mechanical properties of structural materials, which is crucial in assessing, predicting, and controlling the material behavior in technological applications such as nuclear reactors and additive manufacturing (AM). Modeling microstructural evolutions under extreme conditions with high atomistic fidelity and at experimental time scales has been known as a longstanding challenge in material science. Under some cases, traditional atomistic modeling techniques like molecular dynamics (MD) enable the elucidation of molecular mechanisms of microstructural evolutions. Nevertheless, conventional MD could hardly go beyond nanoseconds and therefore simple extrapolation of MD results from short timescales could undermine the accuracy or even give a misleading prediction of materials performance at realistic environments. To overcome such challenges, advanced atomistic modeling techniques that can directly tackle the long timescale problems are greatly desired. In this thesis, we present a novel computational framework based on the concept of potential energy landscape (PEL), which enables the investigation of microstructural evolutions at long-time scales while fully retaining the atomistic details. To demonstrate its capabilities, we show the application of this framework to some key problems in material science. The following problems are addressed: (i) We investigate a local interaction between dislocation and a vacancy-type obstacle in BCC Fe at room temperature over a wide range of strain rates, from 108s-1 down to 103s-1. Very surprisingly, a non-monotonic correlation is found between the critical resolved shear stress (CRSS) of the system and applied strain rates. We demonstrate that the nSRS is due to the complex interplays between thermal activation and applied strain rate. (ii) We map the kinetic evolution of metastable <100> symmetric tilt grain boundaries (GBs) in copper under non-equilibrium processing, which is significant in determining the strength and ductility of nanocrystalline materials. Our combined study, providing both atomistic simulations and novel experiments employing femtosecond laser-material interactions, demonstrates striking features of the energetics and kinetic pathways to achieve a multiplicity of grain boundary states. Specifically, it can be divided into an ageing regime and a rejuvenating regime over a broad energy—temperature parameter space. We further ascribe the origin of this ageing/rejuvenating behavior to the inherent energy imbalance along with elementary hopping processes in the system’s underlying PEL. (iii) We also investigate the non-equilibrium relaxations of metastable tilted GBs in copper under ultrafast thermal cycles, which is critical in assessing the structural materials’ properties during AM. We demonstrate that the structural evolution of metastable GBs is mainly driven by disorder and rough energy landscape rather than free volume. Most importantly, a universal scaling is observed between the GBs’ inherent structure energies and their structural transition temperatures during the rapid cooling stage. To further assess the applicability of the obtained scaling correlation, we also investigate a group of GBs in Ni. A similar correlation persists, which gives reason to expect the present study may apply to other materials as well. In summary, the PEL-based modeling framework is employed to investigate the microstructural evolution at long time scales, without invoking empirical assumptions or fitting parameters. This framework might shed light on the predictive design of advanced structural materials to be used in complex environments.
... Indeed, domain wall pinning is the main mechanism responsible for the observed magnetic behavior of doped samples. The domain wall motion can be discussed by combining the interface random walk approach and ideas from the Zener pinning model, which describes the interaction between the grain boundary and the pinning particles within the framework of the interface random walk approach [64][65][66]. ...
... Indeed, domain wall pinning is the main mechanism responsible for the observed magnetic behavior of doped samples. The domain wall motion can be discussed by combining the interface random walk approach and ideas from the Zener pinning model, which describes the interaction between the grain boundary and the pinning particles within the framework of the interface random walk approach [64][65][66]. ...
Egg white-induced auto combustion has been used to synthesize undoped and Fe-doped CuO/Cu2O/Cu4O3 nanocomposites in a soft, secure, and one-pot procedure. X-ray powder diffraction (XRD) and Fourier transform infrared (FTIR) investigations have been used to identify functional groups and the structural properties of crystalline phases present in the as-synthesized composites. Scanning Electron Microscopy/Energy Dispersive Spectrometry (SEM/EDS) elemental mapping analyses and Transmission Electron Microscopy (TEM) techniques were used to explore the morphological and compositional properties of these composites. N2- adsorption/desorption isotherm models have been used to examine the surface variables of the as-prepared systems. Based on the Vibrating Sample Magnetometer (VSM) technique, the magnetic properties of various copper-based nanocomposites were detected due to being Fe-doped. XRD results showed that the undoped system was composed of CuO as a major phase with Cu2O and Cu4O3 as second phases that gradually disappeared by increasing the dopant content. The crystalline phase’s crystallographic properties were determined. The average particle size was reduced when the synthesized systems were doped with Fe. The construction of porous and polycrystalline nanocomposites involving Cu, Fe, O, and C components was confirmed by SEM/EDS and TEM measurements. In terms of the increase in magnetization of the as-manufactured nanocomposites due to Fe-doping, oxygen vacancies at the surface/or interfacial of nanoparticles, while also domain wall pinning mechanisms, were investigated. Finally, employing the investigated production process, Fe doping of CuO/Cu2O/Cu4O3 nanocomposite resulted in the development of a single phase (CuO) exhibiting “pinned” type magnetization. This is the first publication to show that CuO/Cu2O/Cu4O3.
... Many important properties of GBs-including diffusion, migration, and strength-are controlled by activation barriers of collective atomic rearrangements inside the boundaries [27][28][29][30][31][32][33]. Therefore, we probe the distributions of accessible activation barriers for the above-selected ISs using an energy landscape sampling algorithm [34][35][36][37][38], as shown in Figure 2(b). ...
Nonequilibrium relaxations in a multiplicity of tilted grain boundaries (GBs) subjected to ultrafast thermal driving forces are investigated by atomistic modeling. By scrutinizing the intermediate metastable microstates and their assessable activation barriers in the underlying energy landscape, we demonstrate the energetics and atomic diffusions in tilted metastable GBs are disorder-driven rather than free volume-driven. A critical transition temperature is identified, separating the nonequilibrium GBs’ evolution into a fast-varying stage, and a tuning-ineffective stage, respectively. We further discover a universal correlation between such critical temperature and GBs’ inherent structure energy, which enables predicting the tunability of metastable GBs’ kinetic and mechanical properties.
... The atomistic simulations coupled with the low-velocity approximation of the CLS model predicted GB mobilities within the same order of magnitude as observed in GB migration experiments of Al GBs with Fe impurities [22]. Using an interface random-walk method [23,24], Sun and Deng [25] determined the mobility of a Σ5[100] GB in Al with Ni impurities in the low-velocity limit. They highlighted the importance of trans-GB diffusivity and found the GB mobility to be quantitatively consistent with the CLS model in the low-velocity regime. ...
Solute atoms segregate and impose a retarding pressure, also known as solute drag pressure, at the grain boundary (GB) leading to reduced GB migration rates. The solute drag pressure depends critically on the segregation energy and the solute diffusivity across the GB. These parameters are, however, typically used as adjustable parameters to describe experimental observations. Here, we present an approach to analyze solute drag based on density functional theory (DFT) calculations. As an example, we apply the proposed approach to available experimental data for migration rates of the 30∘<111> GB in Au with Fe and Bi impurities at the ppm level. Based on the DFT calculations, Bi is identified as a strongly segregating element while Fe segregation is weak in comparison. The effective segregation energy for Bi is found to vary from -0.59 eV to -0.72 eV in the experimentally investigated temperature range of 500-610 K. Further, the activation energy for trans-GB diffusion of Bi is calculated with DFT to fall into the range of 0.5- 0.6 eV. These DFT based values are consistent with those obtained by the conventional solute drag analysis of the experimental data using the Cahn-Lücke-Stüwe (CLS) model. The proposed approach is discussed in terms of its strengths for trend predictions as well as its quantitative uncertainties.
... The reduced mobilities are lower by an order of magnitude compared to those for simulated HAGBs in pure metals at comparable temperatures (0:9T m ). 25 The activation barrier is larger by at least a factor of two relative to that for HAGBs in a 2D triangular Lennard-Jones (LJ) crystal 26 and is of the order of the activation barriers for motion of boundaries in high purity metals 24 where trace impurities lead to orders of magnitude reduction in their mobilities. 27 The sluggish dynamics is partly due to the fact that this is a binary metalcovalent system, and the reorientation of atoms across the boundary entails interdiffusion of Au and Si to preserve the trilayer structure of the surface crystal. Additionally, unlike 2D crystals on substrates 28 or colloidal crystals stabilized within solvents, 29-32 these liquid supported 2D phases are open systems that are coupled to the underlying liquid. ...
Atomically thin phases that crystallize on the surfaces of liquids above their melting point represent an emerging class of 2D crystals. Using AuSi as a model system, we show that their formation results in polycrystalline patterns that, unlike current generation 2D crystals, naturally coarsen as they form. The dynamics of the low-dimensional grain boundaries and their junctions is strongly coupled to the supporting liquid. The reorientation necessary for curvature driven interfacial kinetics entails diffusional dissipation with the liquid via mobile antisite defects, leading to a scale-independent power law dependence of the coarsening rate. Our study highlights natural thermal evolution of these polycrystals as a viable pathway for engineering the grain boundary networks in 2D surface crystals, motivating the search for a broader set of stable 2D surface crystals in multicomponent liquids and amorphous solids.
... The Janssens implementation [47] of the synthetic driving force was used in this work because of its computational efficiency (an individual 0.2 ns run of the rSDF method takes several hours on a single 32 cpu node in a local cluster) compared to the original ECO method [48] which took several days per simulation run. The Janssens driving force has been shown to give consistent migration mechanism results compared to other techniques, including strain driven motion [23], random walk motion [49] and the ECO implementation of the synthetic driving force [48]. Nevertheless, a deficiency of the Janssens implementation is that nearest neighbor rearrangement events of atoms in the GB core can lead to discontinuous changes in the applied synthetic energy which violate conservation of energy in the simulation. ...
Atomistic simulations provide the most detailed picture of grain boundary (GB) migration currently available. Nevertheless, extracting unit mechanisms from atomistic simulation data is difficult because of the zoo of competing, geometrically complex 3D atomic rearrangement processes. In this work, we introduce the displacement texture characterization framework for analyzing atomic rearrangement events during GB migration, combining ideas from slip vector analysis, bicrystallography and optimal transportation. Two types of decompositions of displacement data are described: the shear-shuffle and min-shuffle decomposition. The former is used to extract shuffling patterns from shear coupled migration trajectories and the latter is used to separate geometrically distinct, temperature dependent shuffling mechanisms. As an application of the displacement texture framework, we characterize the GB geometry dependence of shuffling mechanisms for a crystallographically diverse set of mobile GBs in FCC Ni bicrystals. Two scientific contributions from this analysis include 1) an explanation of the boundary plane dependence of shuffling patterns via metastable GB geometry and 2) a taxonomy of multimodal constrained GB migration mechanisms which may include multiple competing shuffling patterns, period doubling effects, distinct sliding and shear coupling events, and GB self diffusion.
... The GB mobility may be related (Trautt et al., 2006) to fluctuations in the mean GB position ȳ: M = Nȳ 2 (∆t)/2∆tT , where ∆t is the time interval used in the calculation of the time correlationȳ. Figures 20f, g show the GB mobilities versus temperature from the kMC simulations. ...
The grain boundary (GB) mobility relates the GB velocity to the driving force. While the GB velocity is normally associated with motion of the GB normal to the GB plane, there is often a tangential motion of one grain with respect to the other across a GB; i.e., the GB velocity is a vector. Grain boundary motion can be driven by a chemical potential that jumps across a GB or by shear applied parallel to the GB plane; the driving force has three components. Hence, the GB mobility must be a tensor (the off-diagonal components indicate shear coupling). Recent molecular dynamics (MD) and experimental studies show that the GB mobility may abruptly jump, smoothly increase, decrease, remain constant or show multiple peaks with increasing temperature. Performing MD simulations on symmetric tilt GBs in copper, we demonstrate that all six components of the GB mobility tensor are non-zero (the mobility tensor is symmetric, as required by Onsager). We demonstrate that some of these mobility components increase with temperature while, surprisingly, others decrease. We develop a disconnection dynamics-based statistical model that suggests that GB mobilities follow an Arrhenius relation with respect to temperature T below a critical temperature Tc and decrease as 1/T above it. Tc is related to the operative disconnection modes and their energetics. We implement this model in a kinetic Monte Carlo (kMC); 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 GBs. We demonstrate that the abrupt change in GB mobility results from a Kosterlitz-Thouless (KT) topological phase transition. This phase transition corresponds to the screening of the long-range interactions between (and unbinding of) disconnections. This phase transition also leads to abrupt change in GB sliding and roughening. We analyze this KT transition through mean-field theory, renormalization group methods, and kMC simulation. Finally, we examine the impact of the generalization of the mobility and KT transition for grain growth and superplasticity.
... The KT transition theory suggests that ξ → ∞ for T > T KT (Liao et al., 2018). The GB mobility may be related (Trautt et al., 2006) to fluctuations in the mean GB position ȳ: M = Nȳ 2 (∆t)/2∆tT , where ∆t is the time interval used in the calculation of the time correlationȳ. Figures 20f, g show the GB mobilities versus temperature from the kMC simulations. ...
The grain boundary (GB) mobility relates the GB velocity to the driving force. While the GB velocity is normally associated with motion of the GB normal to the GB plane, there is often a tangential motion of one grain with respect to the other across a GB; i.e., the GB velocity is a vector. Grain boundary motion can be driven by a chemical potential that jumps across a GB or by shear applied parallel to the GB plane; the driving force has three components. Hence, the GB mobility must be a tensor (the off-diagonal components indicate shear coupling).
Recent molecular dynamics (MD) and experimental studies show that the GB mobility may abruptly jump, smoothly increase, decrease, remain constant or show multiple peaks with increasing temperature.
Performing MD simulations on symmetric tilt GBs in copper, we demonstrate that all six components of the GB mobility tensor are non-zero (the mobility tensor is symmetric, as required by Onsager). We demonstrate that some of these mobility components increase with temperature while, surprisingly, others decrease.
We develop a disconnection dynamics-based statistical model that suggests that GB mobilities follow an Arrhenius relation with respect to temperature $T$ below a critical temperature $T_\text{c}$ and decrease as $1/T$ above it. $T_\text{c}$ is related to the operative disconnection modes and their energetics.
We implement this model in a kinetic Monte Carlo (kMC); 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 GBs.
We demonstrate that the abrupt change in GB mobility results from a Kosterlitz-Thouless (KT) topological phase transition.
This phase transition corresponds to the screening of the long-range interactions between (and unbinding of) disconnections.
This phase transition also leads to abrupt change in GB sliding and roughening.
We analyze this KT transition through mean-field theory, renormalization group methods, and kMC simulation.
Finally, we examine the impact of the generalization of the mobility and KT transition for grain growth and superplasticity.
... The Janssens implementation of the synthetic driving force was used in this work [50]. The Janssens driving force has been shown to give consistent migration mechanism results compared to other techniques, including strain driven motion for equivalent mode selection [51], the random walk method [52] and the ECO implementation of the synthetic driving force [53]. In the case of the Janssens driving force, the actual driving force applied to the bicrystal is often less than the value specified in LAMMPS because of noise in the order parameter at high temperatures and/or small disorientations. ...
It has been hypothesized that the most likely atomic rearrangement mechanism during grain boundary (GB) migration is the one that minimizes the lengths of atomic displacements in the dichromatic pattern. In this work, we recast the problem of atomic displacement minimization during GB migration as an optimal transport (OT) problem. Under the assumption of a small potential energy barrier for atomic rearrangement, the principle of stationary action applied to GB migration is reduced to the determination of the Wasserstein metric for two point sets. In order to test the minimum distance hypothesis, optimal displacement patterns predicted on the basis of a regularized OT based forward model are compared to molecular dynamics (MD) GB migration data for a variety of GB types and temperatures. Limits of applicability of the minimum distance hypothesis and interesting consequences of the OT formulation are discussed in the context of MD data analysis for twist GBs, general {\Sigma}3 twin boundaries and a tilt GB that exhibits shear coupling. The forward model may be used to predict atomic displacement patterns for arbitrary disconnection modes and a variety of metastable states, facilitating the analysis of multimodal GB migration data.
... From this state, the materials are annealed and GB migration occurs to modify the microstructure to a configuration with the desired properties. Generally, most of the solid-state microstructure transformations, such as grain growth, recrystallization and phase transformations, are eventually governed by GB migration 1,[7][8][9][10][11] . At the atomic scale, GB migration is determined by the atomistic mechanism. ...
Grain boundary (GB) migration plays an important role in modifying the microstructures and the related properties of polycrystalline materials, and is governed by the atomistic mechanism by which the atoms are displaced from one grain to another. Although such an atomistic mechanism has been intensively investigated, it is still experimentally unclear as to how the GB migration proceeds at the atomic scale. With the aid of high-energy electron-beam irradiation in atomic-resolution scanning transmission electron microscopy, we controllably triggered the GB migration in α-Al2O3 and directly visualized the atomistic GB migration as a stop motion movie. It was revealed that the GB migration proceeds by the cooperative shuffling of atoms on GB ledges along specific routes, passing through several different stable and metastable GB structures with low energies. We demonstrated that GB migration could be facilitated by the GB structural transformations between these low-energy structures.
... The GB mobility may be related (23) to fluctuations in the mean GB positionȳ: M = Nȳ 2 (∆t)/2∆tT , where ∆t is the time interval used in the calculation of the time correlationȳ. Fig. 3 F and G shows the GB mobilities versus temperature from the kMC simulations. ...
Significance
We reveal the existence of a topological phase transition (Kosterlitz–Thouless type) in grain boundaries (GBs)—important internal surfaces in crystalline materials. GB dynamics are controlled by the formation/migration of line defects (disconnections) with dislocation and step character. Below the GB KT transition, disconnections of opposite signs are bound as pairs, while above it they unbind and proliferate. We demonstrate that GB KT transitions provide a fundamental understanding of many GB properties, the temporal evolution of microstructure, and how it deforms/degrades under stress.
... The GB mobility may be related (23) to fluctuations in the mean GB positionȳ: M = Nȳ 2 (∆t)/2∆tT , where ∆t is the D R A F T time interval used in the calculation of the time correlation y. Figures 3f, g show the GB mobilities versus temperature from the kMC simulations. ...
The formation and migration of disconnections (line defects constrained to the grain boundary (GB) plane with both dislocation and step character) control many of the kinetic and dynamical properties of GBs and the polycrystalline materials of which they are central constituents. We demonstrate that GBs undergo a finite-temperature topological phase transition of the Kosterlitz-Thouless (KT) type. This phase transition corresponds to the screening of long-range interactions between (and unbinding of) disconnections. This phase transition leads to abrupt change in the behavior of GB migration, GB sliding, and roughening. We analyze this KT transition through mean-field theory, renormalization group theory, and kinetic Monte Carlo simulations, and examine how this transition affects microstructure-scale phenomena such as grain growth stagnation, abnormal grain growth and superplasticity.
... For the bicrystal supercell doping solute atoms, the GBs were forced to move by adding an artificial driving force, during which the evolution of GB position as a function of simulation time was recorded. The thermal fluctuation of GBs can be described by, 61 with D GB z , t, <d 2 >, T, and A GB as the diffusion coefficient along the z direction, the time, the mean square displacement, the temperature and the GB area, respectively. M is the GB mobility, which follows an Arrhenius equation with Q, that is, M = M 0 exp(−Q/RT), with M 0 as the pre-exponential factor. ...
Abstract Nanocrystalline (NC) materials exhibit many unique properties over their coarse‐grained counterparts due to the high grain boundary density and the small grain size, but they are too difficult to be used in engineering environment because of the poor thermal stability. With regard of this, two strategies are previously proposed to enhance the thermal stability (or impede the grain growth) of NC materials, that is, the thermodynamic and the kinetic approaches. Recent investigations increasingly support that the two approaches may be physically interacted and acted on each other, and they can be treated together within a unified thermo‐kinetic framework. This paper reviews the progress in the investigation of thermo‐kinetic correlation during grain growth in NC materials. First, the theoretical models to describe the concept of the thermo‐kinetic correlation and the grain growth equations developed based on the thermo‐kinetic correlation are reviewed. Second, experimental and simulated evidences to support the coexistence of thermodynamic and kinetic effects are summarized. Third, the potential application of thermo‐kinetic correlation is analyzed and discussed. This paper shows that the stabilization of NC materials can be tailored by the selection of the suitable strategies. Finally, several directions that require further exploration are identified.
... The asymmetric tilt grain boundary has been chosen because of the method used to initiate GB migration. There are several theoretical methods to study GB mobility [42][43][44][45][46][47][48][49]. In the present research we have chosen the method based on the driving force initiation. ...
... investigate the kinetic properties of GBs typically employ molecular dynamics (MD) methods, such as the synthetic driving force method and the fluctuating boundary method. These approaches usually rely on high driving forces or temperatures to accelerate GB kinetic behavior to a rate which is computationally tractable, but which precludes direct corroboration with experimental results [1][2][3][4][5][6][7]. Kinetic Monte Carlo (KMC), with its stochastically incremented time function, provides a means for accessing experimentally relevant timescales. ...
... The material parameters required to model sintering of silver particles are the surface diffusion coefficient D s eff ; the volume diffusion coefficient D v eff ; the grain boundary diffusion coefficient D gb eff , as required in (3.42); the grain boundary mobility ϑ gb ; the grain boundary energy γ gb ; and the surface energy γ sf . The reported grain boundary mobility data of silver in the literature [121][122][123] reveals a wide range of values with little consistency. The grain boundary mobility for silver is taken from [124], which has a similar order of magnitude compared to other FCC metals like aluminum and copper, although the grain boundary mobility is highly dependent on the grain boundary structure which can vary for different metals. ...
Adhesion and delamination have been pervasive problems hampering the performance and reliability of micro- and nano-electronic devices. In order to understand, predict, and ultimately prevent interface failure in electronic devices, development of accurate, robust, and efficient delamination testing and prediction methods is crucial. Adhesion is essentially a multi-scale phenomenon: at the smallest scale possible, it is defined by the thermodynamic work of adhesion. At larger scales, additional dissipative mechanisms may be active which results in enhanced adhesion at the macroscopic scale and are the main cause for the mode angle dependency of the interface toughness. Undoubtedly, the macroscopic adhesion properties are a complex function of all dissipation mechanisms across the scales. Thorough understanding of the significance of each of these dissipative mechanisms is of utmost importance in order to establish physically correct, unambiguous values of the adhesion properties, which can only be achieved by proper multi-scale techniques.
Comprehending the mechanical response of materials on an atomic level is pivotal in the optimisation of advanced materials with superior mechanical properties. This research article utilises the atomistic-scale based molecular dynamics simulations to report the uniaxial tensile behaviour of bicrystalline Ni-6Cu (Nickel – 94% and Copper – 6%) alloy incorporated with pre-existing faceted Σ3 [111] 60° {11 8 5} grain boundaries. The primary aim of this investigation is to comprehend the performance of bicrystalline Ni-6Cu alloy under varying thermodynamic conditions and to assess the influence of pre-existing faceted grain boundaries on its tensile behaviour. This work encompasses a range of strain rates (108 to 1010 1/s) and temperatures (spanning from 100 to 900 K) for the uniaxial tensile deformation simulations. The outcomes unveil that the Young’s modulus of Ni-6Cu alloy (with pre-existing faceted grain boundaries embedded in its domain) was inversely proportional to temperature and constant with respect to strain rate. For the same configuration, yield stress was inversely and directly proportional to temperature and strain rate, respectively. Interestingly, incipient plasticity in the tensile stress–strain response was observed at lower temperature and lower strain rate. From the microstructural point of view, at lower temperatures, the incoherent twin boundary served as a source for the nucleation of stacking faults; however, as the temperature increased, both the incoherent twin boundary and the tips of coherent twin boundary function as the source for stacking faults formation. Our simulations also verified the GB’s anti-thermal (or non-Arrhenius) migration behaviour even under tensile load.
Grain boundary (GB) migration exhibits intriguing antithermal behavior (or non-Arrhenius behavior), with the temperature and driving force playing crucial roles. Through atomistic simulations on nickel bicrystals, we investigate the change in GB mobility with variations in both temperature and driving force. Our results reveal that the GB mobility initially increases with temperature and subsequently decreases after reaching the transition temperature (Ttrans), and, notably, Ttrans exhibits a linear relationship with the activation energy (Q) associated with GB migration. By modulating the driving force, we found that the driving force could effectively lower Q, resulting in the shift of Ttrans towards lower temperatures. Additionally, higher driving forces were found to activate more migration modes at lower temperatures, potentially leading to a transition in the thermal behavior of GB migration. Our work supports the existing theoretical models for GB migration based on both classical thermal activation and disconnection nucleation. Furthermore, we refined the existing model by incorporating the influence of the driving force. The modified model can not only describe the effect of driving force on the thermal behavior of GB migration but also accounts for the observed “antidriving force” phenomenon in GB migration. Our research has the potential to offer valuable insights for investigating realistic GB migration under more intricate constraints and environments.
Non-Arrhenius grain boundary migration, sometimes referred to as antithermal migration where temperature and GB velocity values are inversely related to each other, is examined in an incoherent twin Σ3 [111] 60° (11 8 5) nickel grain boundary. Molecular dynamics is used to simulate migration and examine the effect of various factors on the migration, including interatomic potential, system size, driving force, and variation of atomic grain boundary structure. A classical model for grain boundary migration, in its unsimplified form, is used to analyze the results. The grain boundaries exhibit migration mechanisms with very low apparent barrier heights to migration. As a result, the boundaries migrate quickly but exhibit a velocity saturation similar to that of dislocations. The various interatomic potentials exhibit different migration velocities, but their similarities suggest they all predict similar overall behaviors of migration. The variation of atomic structure in the same incoherent twin grain boundary leads to diverse behaviors with barrier heights that vary from non-Arrhenius to Arrhenius migration. Facet nucleation is confirmed not to be a requirement for this boundary based on an examination of simulation cell size; however, the presence and/or interaction between numerous facets does suggest a slowing and increased barrier height to migration for larger boundaries.
Grain boundaries (GBs) are believed as potent defect sinks that contribute to the radiation damage reduction of materials. The defect-GB interaction has been extensively studied in pure metals, but only a few works shed light on the influence of material component such as alloying elements. In this study, the GB-mediated reduction of radiation defects in four W-based alloys (W–Re, W–Ta, W–Mo and W–V) is systematically investigated by atomistic simulations. Quantitative results show that the defect reduction in W-based alloys is significantly decreased comparing with elementary W. The principal reason for this decrease is the presence of various micro configurations where the solute-defect binding interactions are strong. Solutes with high local stress for each atom have a positive effect on the absorption of interstitials by GB. The ability of GB to absorb interstitials is enhanced with the increasing temperature, and also the accumulation of vacancies is increased when the temperature is as high as 1200 K. The findings in this work provide useful information on the design of radiation tolerance materials.
To evaluate the tensile behavior, microstructural evolution, and deformation mechanisms of Ti-45Al-8Nb alloy additively manufactured by electron beam melting, uniaxial tensile experiments were performed at a constant strain rate of 2.5×10⁻⁴ s⁻¹ at various temperatures. The experimental results indicated that the tensile behavior and flow stress are sensitive to temperature. The brittle to ductile transition temperature of Ti-45Al-8Nb alloy additively manufactured by electron beam melting is between 700 and 750 ℃. Below this temperature, the fracture was predominantly trans-granular, resulting in brittle failure. In addition, the brittle failure behavior is related to the localization of deformation within the grains and stress concentrations owing to plastic incompatibility at the interface of the α2+γ phases. However, above this temperature, the fracture transformed from the trans-granular type to the mixed mode of trans-granular and ductile dimples. Dynamic recovery and recrystallization are the primary processes leading to softening behavior. The flow behavior at elevated temperatures results from the competition between work hardening and softening. Furthermore, the Chaboche model was used to describe the tensile inelastic behavior at different temperatures.
High Entropy Alloys (HEAs) are a new broad class of near-random solid solution alloys that can possess some impressive mechanical and physical properties including high stability against grain growth (i.e. low grain boundary (GB) mobility). Here, it is shown that an initially flat GB in an HEA can become spontaneously rough, driven by natural local compositional fluctuations. Roughening lowers the total GB energy and thus can inhibit migration. A parameter-free theoretical framework is developed to demonstrate the energetics and size scales of the roughening in terms of solute/GB interaction energies and GB disconnection energies. Above a critical level of solute/GB interactions, a planar GB is predicted to roughen down to the scale of the GB periodic unit. A similar theory for 1D GBs (minimum periodic length in one direction) is also developed since such geometries are common in atomistic simulations. Specific predictions are made for the [100] symmetric tilt boundaries Σ17[100](530) and Σ5[100](310) in a model CoCuFeNi alloy and atomistic simulations demonstrate roughening consistent with the theory. Analysis of the stresses needed to drive migration shows how migration can be inhibited or enhanced, rationalizing variations in mobility of GBs in HEAs.
Grain morphologies such as grain size and aspect ratio in uranium-based metallic fuels are important microstructural features that can impact various fuel performance properties such as fission-gas-induced swelling, thermal transport, high burnup structure formation, and radiation resistance. Accurate prediction of the fuel grain morphologies requires knowledge of critical grain growth parameters such as grain boundary (GB) mobility and anisotropy. In this work, molecular dynamics (MD) simulations were performed to study the GB mobility of and its anisotropy in pure body-centered-cubic (BCC) γ uranium. Nine GBs with different combinations of misorientation angles (20°, 30°, 45°) and rotation axes (<100>, <110>, <111>), as well as an additional <111> 38.2° GB were studied using three interatomic potentials. It is found that the GB mobility anisotropy has complex trends, depending on both rotation axis and misorientation. However, in general the <110> rotation axis has the fastest GB mobility at the same misorientation. The results of this work can be used as not only a baseline for future studies of GB mobility in uranium-based alloys such as uranium-molybdenum (U-Mo) fuels, but also as input for mesoscale modeling of grain growth in uranium-based alloys.
Improving the room temperature (RT) strength/ductility and hot-working capacity based on lamellar microstructures is of great significance for the practical application of TiAl alloys. However, the microstructure of these alloys has not been clearly identified yet. In this work, two new microstructures, here named triple-phase triple-state (T-T) and triple-phase dual-state (T-D) structures, were developed using a two-step heat treatment process in the Ti-43.5Al-4Nb-1Mo-0.1B (TNM) alloy, which also contains the pearlitic-like microstructure (PM) transformed through triggering a massive cellular response (CR). These two microstructures significantly improved the alloy strength. Furthermore, their ductility at RT and 800 ℃ was enhanced twice and 5∼6 times with respect to that of the lamellar microstructure with nano-scale interlamellar spacing, respectively. It was revealed that the formation of abundant deformation twins and their intersections in PMs during plastic deformation, cause prominent strain hardening and the dynamic Hall-Patch effect. This results in a simultaneous improvement of the RT strength and plasticity and promotes dynamic recrystallization at temperatures lower than 800 ℃; thus, the plasticity is dramatically enhanced at elevated temperatures. This structural design strategy should be extendable to other TiAl systems that can undergo a CR and provides a promising new pathway for solving the severe engineering challenges caused by the low RT plasticity and poor hot-working capacity of TiAl alloys.
Grain boundary migration in magnesium alloys has been studied using quantum mechanical calculations implementing the nudged elastic band method. Four crystallographically different boundaries were examined: two twin boundaries and two general grain boundaries that showed no crystallographic symmetry across the boundary plane. The activation energies for boundary migration were determined from the minimum energy pathways, and these energies were consistent with experimental values. It was found that the activation energy is linearly related to the coordination number of the boundaries. This indicates that boundaries with lower coordination numbers showed smaller activation energies and thus higher mobilities than the more orderly boundaries with larger coordination number and larger activation energies. The effect of solutes at the boundary was also studied, and it was found that most solutes with low co-ordination number decreased the activation energy for boundary migration, but the effect of solutes on boundaries with high coordination number was strongly dependent on the solute chemistry.
Atomistic simulations provide the most detailed picture of grain boundary (GB) migration currently available. Nevertheless, extracting unit mechanisms from atomistic simulation data is difficult because of the zoo of competing, geometrically complex 3D atomic rearrangement processes. In this work, we introduce the displacement texture characterization framework for analyzing atomic rearrangement events during GB migration, combining ideas from slip vector analysis, bicrystallography and optimal transportation. Two types of decompositions of displacement data are described: the shear-shuffle and min-shuffle decomposition. The former is used to extract shuffling patterns from shear coupled migration trajectories and the latter is used to analyze temperature dependent shuffling mechanisms. As an application of the displacement texture framework, we characterize the GB geometry dependence of shuffling mechanisms for a crystallographically diverse set of mobile GBs in FCC Ni bicrystals. Two scientific contributions from this analysis include 1) an explanation of the boundary plane dependence of shuffling patterns via metastable GB geometry and 2) a taxonomy of multimodal constrained GB migration mechanisms which may include multiple competing shuffling patterns, period doubling effects, distinct sliding and shear coupling events, and GB self diffusion.
Magnesium, the lightest structural metal, has limited industrial application due to its poor formability at room temperature. However, the mechanism for the effect of alloying elements on formability has not yet been clarified. To deduce this effect, we study recrystallization, a phenomenon that occurs in the last stage in the manufacturing process, of Mg-Al-Zn and Mg-Zn-Ca solid solutions, which show recrystallization behaviors similar and different to that of pure Mg, respectively. By developing a new atomistic simulation method of migrating grain boundaries in hcp structure materials, we investigate the representative recrystallization phenomena occurring in solid solutions: grain boundary segregation, solute clustering, and grain boundary migration. It is found that the grain boundary segregation occurring in both ternary Mg alloys is not synergistically stronger than those in their constituent binary Mg alloys, but is sufficient to retard the onset of the grain boundary migration. However, solute clusters are actively formed only in the Mg-Zn-Ca alloys and strongly drag grain boundaries during the migration, which strengthens the dragging effect of the Mg-Zn-Ca alloys compared to that of the Mg-Al-Zn alloys. The strong dragging effect originated from solute clusters could be another cause of the change in the recrystallization behavior of Mg alloys.
It has been hypothesized that the most likely atomic rearrangement mechanism during grain boundary (GB) migration is the one that minimizes the lengths of atomic displacements in the dichromatic pattern. In this work, we recast the problem of atomic displacement minimization during GB migration as an optimal transport (OT) problem. Under the assumption of a small potential energy barrier for atomic rearrangement, the principle of stationary action applied to GB migration is reduced to the determination of the Wasserstein metric for two point sets. In order to test the minimum distance hypothesis, optimal displacement patterns predicted on the basis of a regularized OT based forward model are compared to molecular dynamics (MD) GB migration data for a variety of GB types and temperatures. Limits of applicability of the minimum distance hypothesis and interesting consequences of the OT formulation are discussed in the context of MD data analysis for twist GBs, general Σ3 twin boundaries and a tilt GB that exhibits shear coupling. The forward model may be used to predict atomic displacement patterns for arbitrary disconnection modes and a variety of metastable states, facilitating the analysis of multimodal GB migration data.
In-depth understanding and precise controlling of grain boundary (GB) motion at atomic scale are crucial for grain growth and recrystallization in polycrystalline materials. So far, the reported studies mainly focus on the GB motion in the ideal bicrystal system, while the atomic mechanisms of GB motion in polycrystals remain poorly understood. Herein, taking two-dimensional (2D) hexagonal boron nitride (h-BN) as a model system, we experimentally investigated the atomic-scale mechanisms of the GB motion in 2D polycrystals. Since GB motion is directly related to the GB structures, this article is organized following the configurations of GBs, which can be divided into straight (including symmetric and asymmetric GBs) and curved GBs. We revealed that: (I) For symmetric GBs, the shear-coupled motion alone is insufficient to drive the continuous GB motion in polycrystalline materials, and GB sliding is also needed; (II) For asymmetric GBs, GB motion follows a defaceting-faceting process, in which dislocation reactions are crucial; (III) For curved GBs, shear-coupled GB motion (during grain shrinking) leads to grain rotation, and the rotation direction highly depends on the misorientation angles (all rotate to the range of 22°-38°); (IV) Finally, we'll discuss the characteristics of binary lattice (h-BN), and found that partial dislocations participate in the GB motion at high misorientation angles (>38°). Our results build up the framework of the atomic-scale mechanisms of the GB motion in 2D polycrystalline materials, and will be instructive for the technological applications such as grain growth and GB engineering.
Development of the surface morphology and shape of crystalline nanostructures governs the functionality of various materials, ranging from phonon transport to biocompatibility. However, the kinetic pathways, following which such development occurs, have been largely unexplored due to the lack of real-space imaging at single particle resolution. Here, we use colloidal nanoparticles assembling into supracrystals as a model system, and pinpoint the key role of surface fluctuation in shaping supracrystals. Utilizing liquid-phase transmission electron microscopy, we map the spatiotemporal surface profiles of supracrystals, which follow a capillary wave theory. Based on this theory, we measure otherwise elusive interfacial properties such as interfacial stiffness and mobility, the former of which demonstrates a remarkable dependence on the exposed facet of the supracrystal. The facet of lower surface energy is favored, consistent with the Wulff construction rule. Our imaging–analysis framework can be applicable to other phenomena, such as electrodeposition, nucleation, and membrane deformation.
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.
Diffusion-induced grain boundary migration (DIGM) is the phenomenon of normal grain boundary (GB) migration caused by the lateral diffusion of solutes along it. Despite its technological importance and the fact that DIGM has been first observed and studied since 1970, many aspects of it are still not fully understood. In this study, molecular dynamics simulations are used to investigate the physical origin of DIGM with particular focus on the effects of solute-GB interactions. For this purpose, a few binary alloy systems are deliberately selected, e.g., Al-Ti, Al-Ni, and Ni-Cu, in which strong solute-GB interactions including both solute segregation and anti-segregation occur. The simulation results showed that strong solute segregation and anti-segregation can both influence DIGM, although past experimental and theoretical studies on DIGM mostly focused on systems with segregation. Furthermore, it is shown that the direction of GB migration strongly depends on the solute-GB interaction type, e.g., segregation or anti-segregation, which causes an attraction or repulsion between the GB and solute atoms, respectively. It is thus proved that solute-GB interactions, in general, play an important role in driving DIGM. Furthermore, by combining two atomistic simulation techniques, i.e., the synthetic driving force method and interface random walk method, we are able to quantify the driving forces for DIGM. All observations made during the simulations are supported by atomic configurations and graphical analysis. It is hoped that this study sheds some light on this research area after more than a decade’s stagnation in this field.
The Cahn-Hilliard equation is often used to model the temporospatial evolution of multiphase fluid systems including droplets, bubbles, aerosols, and liquid films. This equation requires knowledge of the fluid-fluid interfacial mobility γ, a parameter that can be difficult to obtain experimentally. In this work, a method to obtain γ from nonequilibrium molecular dynamics is presented. γ is obtained for liquid-liquid and liquid-vapor interfaces by perturbing them from their equilibrium phase fraction spatial distributions, using molecular dynamics simulations to observe their relaxation toward equilibrium, and fitting the Cahn-Hilliard model to the transient molecular simulations at each time step. γ is then compared to a different measure of interfacial mobility, the molecular interfacial mobility M. It is found that γ is proportional to the product of M, the interface thickness, and the ratio of thermal energy to interfacial energy.
Atomistic simulations of radiation damage uncover how grain boundaries (GBs) migrate and coalesce under irradiation in bicrystalline Cu. Planar GB migration biased by defect cluster-mediated attraction first leads to slow and steady motion. Subsequently, adjoining GBs coalesce into curved surfaces, where curvature-driven migration with a velocity three orders of magnitude higher than that of a planar boundary dominates motion, triggering rapid grain growth. This study reveals the atomistic mechanisms of radiation-induced grain growth, and has practical implications towards engineering radiation-tolerant nanostructures.
The motion of tilt and mixed tilt-twist grain boundaries with misorientation angles in the range between 34° and 42° in pure Al bicrystals was measured over the temperature range between 310 and 610°C. The experiments revealed that the change of the set of boundary planes in the curved moving tilt boundary does not affect its motion. The shape of the curved moving part of the mixed tilt-twist boundary was measured and compared with analytically calculated boundary
shape. The results have shown that an increase of the twist component along the curved mixed boundary in studied geometrical configuration does not affect its steady-state motion. Similar to the behaviour of pure tilt boundaries, the mobility of mixed tilt-twist grain boundaries in the vicinity of special misorientation å7 depends on the misorientation angle in a non-monotonic fashion.
The recent development in the field of superhard materials with Vickers hardness of ≥40 GPa is reviewed. Two basic approaches are outlined including the intrinsic superhard materials, such as diamond, cubic boron nitride, C3N4, carbonitrides, etc. and extrinsic, nanostructured materials for which superhardness is achieved by an appropriate design of their microstructure. The theoretically predicted high hardness of C3N4 has not been experimentally documented so far. Ceramics made of cubic boron nitride prepared at high pressure and temperature find many applications whereas thin films prepared by activated deposition from the gas phase are still in the stage of fundamental development. The greatest progress has been achieved in the field of nanostructured materials including superlattices and nanocomposites where superhardness of ≥50 GPa was reported for several systems. More recently, nc-TiN/SiNx nanocomposites with hardness of 105 GPa were prepared, reaching the hardness of diamond. The principles of design for these materials are summarized and some unresolved questions outlined. © 1999 American Vacuum Society.
During recrystallisation, high angle grain boundaries migrate through deformed microstructure containing dislocations arranged, for example, in dislocation boundaries. A simple method for designing geometries suitable for atomistic simulations of migrating boundaries during recrystallisation is developed. Preliminary studies show that the method can be used to generate simulation cells with both high angle grain boundaries and small angle dislocation boundaries.
The basic dynamic behavior of martensitic interfaces has been analyzed within the framework of lattice dislocation dynamics. Two limiting cases of the martensitic interface structure have been considered: (a) the case when the interface can be appropriately described in terms of an array of non-interacting (well-spaced) interfacial dislocations and; (b) the case when the interfacial dislocations are so closely spaced that the interface can be approximated by a continuous distribution of dislocations. In the first case, it was demonstrated that, after the inclusion of a chemical driving force in the equation of motion, the dynamics of lattice dislocations can be directly applied to analyze the interfacial dynamics. In the second case, on the other hand, while the lattice dislocation dynamics is still quite relevant, several parameters in the equation of motion have to be redefined to reflect the fact that the interface now acts as a planar defect. For both of the cases of interfacial dislocation structure, we have analyzed the two basic modes of interfacial motion: (a) the continuous mode in which the motion is controlled by various energy-dissipative processes (e.g., phonon and electron drag) and; (b) the discontinuous or jerky mode in which the motion is controlled by the thermal activation of the interface/obstacle interactions.
As current experimental and simulation methods cannot determine the mobility of flat boundaries across the large misorientation phase space, we have developed a computational method for imposing an artificial driving force on boundaries. In a molecular dynamics simulation, this allows us to go beyond the inherent timescale restrictions of the technique and induce non-negligible motion in flat boundaries of arbitrary misorientation. For different series of symmetric boundaries, we find both expected and unexpected results. In general, mobility increases as the grain boundary plane deviates from (111), but high-coincidence and low-angle boundaries represent special cases. These results agree with and enrich experimental observations.
The recrystallization textures that develop when deformed metals are annealed have been the subject of extensive study. These textures are largely responsible for the directionality of properties observed in many finished products. Recrystallization textures are related to the nature of the nucleation event, the orientation dependence of the rate of nucleation in inhomogeneities of various type and orientation environment, and to the nature, energy and mobility of the boundaries among grains of various orientations. The determination of microtextures by Electron Backscatter Diffraction (EBSD), which enables a correlation to be made between local orientation and microstructure, is now enabling some advances in this field. The development of an annealing texture does not cease when recrystallization is complete. It continues during grain growth and the final texture is not necessarily representative of the texture present when primary recrystallization is complete. There is increasing evidence that the orientation of the material before deformation plays a significant role in determining the recrystallization texture. The purity of a particular metal may strongly influence the recrystallization texture. In many cases very small amounts of second elements may, by affecting the boundary mobility, change the annealing texture completely.
The process of primary recrystallization and the subsequent grain growth were investigated in high purity zone melted nickel after 60 and 80% cold work.The formation of nuclei occurred predominantly at original grain boundaries by growth of subgrains which had already been formed during the deformation process.The rate of grain growth during and after primary recrystallization was determined by observing the time dependence of the largest and of the average grain diameters. The results may be interpreted in terms of the concept that the elementary process of grain boundary motion consists of a diffusion of single atoms across the grain boundary. Then the rate determining process is the grain boundary diffusion. The activation energy of grain growth was about 28–30 kcal/Mol and was equal to the activation energy of nuclei formation for large degrees of deformation.During the primary recrystallization the time dependence of the isothermally recrystallized fraction XR of the matrix may be described by the equation xr = 1 − exp(−Btκ). The K-value of 1.38 suggests a predominantly one-dimensional grain growth.The experimental data for the rate of grain growth after primary recrystallization indicate an influence of residual impurities still present in the crystal.RésuméLe mécanisme de recristallisation et la croissance des grains recristallisés dans le nickel pur élaboré par fusion zonaire, sont étudiés après des déformations à froid de 60 à 80%. La germination apparaît principalement aux anciens joints de grains par croissance des sous-grains, qui se sont déjà formés pendant la déformation. La vitesse de croissance des grains a été déterminée pendant et après la recristallisation primaire, par la détermination de l'influence du temps sur le diamètre des grains respectivement, le plus grand et le moyen.Les résultats des mesures peuvent s'expliquer par l'hypothèse que le mécanisme élémentaire du mouvement des joints de grains consiste en une diffusion des différents atomes au-delà du joint de grain. Le processus déterminant la vitesse est alors la diffusion dans le joint de grains. L'énergie d'activation de la croissance des joints de grains se situe vers 28–30 kcal/mole; pour des taux de déformation élevés, elle est égale à l'énergie d'activation de la formation des germes.Pendant la recristallisation primaire l'influence du temps sur la quantité xR de la structure recristallisée par un traitement isotherme peut être exprimée par la formule suivante: xR = 1 − exp (− Btk). La valeur de 1,38 pour le facteur exponentiel κ indique qu'il s'agit principalement d'une croissance en une direction.Les mesures obtenues pour la vitesse de croissance des grains après la recristallisation primaire mon-trent l'influence des impuretés résiduelles qui sont encore présentes.
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High angle grain boundaries have been artificially introduced into (110) [1–12] oriented, 97 % rolled gold single crystals and their movement has been isothermally examined under the influence of a constant driving force over a temperature range between 230 and 340°C.The temperature dependence of the migration velocity G of the 30° 〈111〉-tilt boundaries can be described by an exponential expression of the form . At temperatures below 290° and above 330°C G0, is found to be 3 · 108 and 3.5 · 104 mm/min, respectively; the Q-values are 30.5 and 19.1 kcal/mol, respectively. The range between these temperatures is a transition range with no defined activation energy.The results are discussed in terms of the Cahn-Detert-Lücke-Stüwe theory. The transition from the high to the low temperature range is ascribed to the fact that the grain boundary movement is hindered by solute iron (20 ppm).RésuméLes auteurs ont suivi le mouvement, sous l'influence d'une force directrice constante, de joints de grains à fortes désorientations introduits artificiellement dans des monocristaux d'or laminés à 97 % orientés suivant (110)[11̄2], au cours d'isothermes entre 230 et 340°C.La variation de la vitesse de déplacement G avec la température peut être décrite par une loi exponentielle de la forme . Pour les températures inférieures à 290°C et supérieures à 330°C, on obtient respectivement G0 = 3 · 108 et 3,5 ·. 104 mm/min., et Q = 30,5 et 19,1 kcal/mol. Dans le domaine de températures intermédiaires on observe une zone de transition où aucune énergie d'activation ne peut être déterminée. Les résultats sont discutés dans le cadre de la théorie de Stüwe, Lücke, Detert et Cahn. Le passage entre le domaine des températures élevées et le domaine des températures basses est interprété par l'idée suivant laquelle le fer dissous (20 ppm) empêche le déplacement du joint de grains.
Although the interpretation of experiments in such fields as the shapes of small particles and the thermal etching of surfaces usually involves problems of kinetics rather than mere equilibrium considerations, it is suggested that a knowledge of the relative free energies of different shapes or surface configurations may provide a useful perspective. This paper presents some theorems on these relative free energies which follow from the Wulff construction for the equilibrium shape of a small particle, and some relations between atomic models of crystal surfaces and the surface free energy function used in this construction. Equilibrium shapes of crystals and of noncrystalline anisotropic media are classified, and it is pointed out that the possibilities for crystals include smoothly rounded as well as sharp-cornered forms. The condition is formulated for thermodynamic stability of a flat crystal face with respect to formation of a hill-and-valley structure. A discussion is presented of the limitations on the applicability of the results imposed by the dependence of surface free energy on curvature; and it is concluded that these limitations are not likely to be serious for most real substances, though they are serious for certain idealized theoretical models.
Experiments show that the impurities can drastically change grain boundary mobilities in a non-trivial manner. The most widely used type of theoretical model for impurity effects on boundary migration is a one-dimensional, continuum model, based upon several simplifying assumptions. Although several of these assumptions can be relaxed, these models cannot adequately describe realistic situations and are not quantitative. Since grain boundary mobility depends on several atomic-scale properties that are difficult to reliably extract from experiments (or calculate from a first principles method), it is not currently possible to make a quantitative comparison between theoretical models and experiment. Dynamic atomistic (MD) simulations do not provide a practical alternative because of the need to include such slow processes as long range diffusion and boundary migration. An alternative approach is based upon simple spin (extended Ising) models and kinetic Monte Carlo. This provides a concrete model against which the prediction of the continuum theory can be compared in a situation where all microscopic physical properties are known. Such simulations show that the key deficiencies of the continuum models are the assumption that intrinsic and impurity drag effects can be superimposed and not considering the mechanism of grain boundary migration. Analytical theories that address these two deficiencies are capable of reproducing the effects of impurities on boundary mobility seen in the simulations. Simple simulations provide rigorous tests against which new theories should be compared.
Grain boundary character distribution is a relatively new microstructural feature that describes the proportions of random
and special grain boundaries as defined by the coincident site lattice model. The combination of the availability of a new
experimental technique based on the automatic indexing of backscatter Kikuchi electron diffraction patterns in the scanning
electron microscope (orientation imaging microscopy) and reports in the literature describing the optimization of the grain
boundary character distribution through thermomechanical processing are making the potential for enhanced materials properties
in commercial metals and alloys a reality. Although the effects of optimizing the grain boundary character distribution in
the cost-effective improvement of properties have been documented, the potential for commercialization has limited the disclosure
of processing details. In this article, two separate approaches to the optimization of the grain boundary character distribution
in oxygen-free electronic copper at Lawrence Livermore National Laboratory are discussed.
Average grain boundary migration rates during recrystallization of cold-deformed copper were estimated from stereological
measurements. In the same material, the instantaneous driving forces for boundary migration during recrystallization were
calculated from calorimetric measurements of the release of the stored energy of cold work. The migration rate dependence
on driving force was analyzed in the context of grain boundary migration rate theory, and within experimental error, a linear
dependence was observed. The average mobility of grain boundaries migrating during recrystallization of cold-worked copper
at 121 °C was calculated to be 6.31×10−10 (m4 s−1 MJ−1). This result was found to be consistent with single boundary, curvature-driven grain boundary mobilities measured in copper
at higher temperatures. It was also demonstrated that the average grain boundary mobility was reasonably within the expectation
(order of magnitude uncertainty) of the Turnbull single process model of boundary migration with a process akin to grain boundary
self-diffusivity as the rate-controlling atomic mechanism.
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.
During ceramic fabrication, densification processes compete with coarsening processes to determine the path of microstructural evolution. Grain growth is a key coarsening process. This paper examines grain boundary migration in ceramics, and discusses the effects of solutes, pores, and liquid phases on grain boundary migration rates. An effort is made to highlight work in the past decade that has contributed to and advanced our understanding of solute drag effects, pore-boundary interactions, and the role of liquid phases in grain growth and microstructural evolution. Anisotropy of the grain boundary mobility, and its role in the development of anisotropic (anisometric) microstructures is discussed as it is a central issue in recent efforts to produce ceramic materials with new combinations of properties and functionality.
A molecular-dynamics method for the simulation of the intrinsicmigration behavior of individual, flat grain boundaries is introducedand validated. A constant driving force for grain-boundary migrationis generated by imposing an anisotropic elastic strain on a bicrystalsuch that the elastic-energy densities in its two halves aredifferent. For the model case of a large-planar-unit-cell, high-angle(001) twist boundary in Cu we show that an elastic strain of1%–4% is sufficient to drive thecontinuous, viscous movement of the boundary at temperatures wellbelow the melting point. The driving forces thus generated (at thehigh end of the experimentally accessible range) enable aquantitative evaluation of the migration process during the timeframe of 10-9 s typically accessible bymolecular-dynamics simulation. For this model high-angle grainboundary we demonstrate that (a) the drift velocity is, indeed,proportional to the applied driving force thus enabling us todetermine the boundary mobility, (b) the activation energy forgrain-boundary migration is distinctly lower than that forgrain-boundary self-diffusion or even self-diffusion in the melt and(c) in agreement with earlier simulations the migration mechanisminvolves the collective reshuffling during local disordering(melting) of small groups of atoms and subsequentresolidification onto the other crystal.
The kinetic coefficient, , is the constant of proportionality between the velocity of a solid-liquid interface and the interface undercooling. The value of and its anisotropy are critical parameters in phase field modeling of dendritic solidification. In this paper we review several different molecular dynamics simulation methods which have been proposed to compute the kinetic coefficient. Techniques based on forced velocity simulations, free solidification simulations and fluctuation analyses are discussed and compared. In addition, a model of crystalline growth kinetics due to Broughton, Gilmer and Jackson will be compared with available atomistic simulation data.
During sintering in alumina powder compacts, the density has been found to increase linearly with the logarithm of time, and the grain size increases with the one‐third power of time. Incorporation of the time dependence of grain size increase into latestage bulk diffusion sintering models (from Part I) [R. L. Coble, J. Appl. Phys. 32, 787 (1961)] leads to corrected models by which a semilogarithmic behavior is predicted. The presence of density gradients in normally fabricated pellets makes impossible the deduction of whether theoretical density will be achieved from the early stages of the course of densification. Diffusion coefficients calculated from the intermediate and later stages of sintering bear order‐of‐magnitude agreement with those calculated from the initial‐stage sintering measurements in alumina. All diffusion coefficients from sintering data are higher than Kingery's measured diffusion coefficients for oxygen. It is hypothesized that the sintering process must then be controlled by bulk diffusion of aluminum ions while the oxygen transport takes place along the grain boundaries. In controlling the sinterability of alumina to theoretical density, it appears that magnesia does not ``inhibit'' discontinuous grain growth, but instead increases the sintering rate such that discontinuous growth nuclei do not have time to form.
Molecular dynamics simulations have been used to study steady-state, capillarity-driven grain boundary migration in three dimensions for a series of 〈1 1 1〉-tilt boundaries in aluminum. The reduced boundary mobility and boundary enthalpy were determined as a function of misorientation and temperature. For the misorientations examined, the reduced mobility is a maximum and the activation energy for migration is a minimum at the Σ7 misorientation. The reduced mobility is an Arrhenius function of temperature. Excellent agreement between the present three-dimensional simulation results, those obtained earlier in two dimensions and experiment is obtained for a wide variety of features, with the notable exception of the magnitude of the grain boundary mobility. The mobilities from the simulations are much higher than from experiment; the activation energies for migration are much lower. The present results are intrinsic, while the experimental measurements may be limited by extrinsic factors such as impurity drag.
We investigated the motion of planar symmetrical and asymmetrical tilt boundaries in high-purity aluminium with <112>- and <111>-tilt axes under the influence of an external mechanical stress field. It was found that the motion of low-angle grain boundaries as well as high-angle grain boundaries can be induced by the imposed external stress. The observed activation enthalpies allow conclusions on the migration mechanism of the grain boundary motion. The motion of planar low- and high-angle grain boundaries under the influence of a mechanical stress field can be attributed to the movement of the grain boundary dislocations which comprise the structure of the boundary. A sharp transition between low-angle grain boundaries and high-angle grain boundaries was observed at 13.6°, which was apparent from a step of the activation enthalpy for the grain boundary motion. For the investigated boundaries the transition angle was independent of tilt axis, impurity content and tilt boundary plane.
Grain boundary stiffness and mobility determine the kinetics of curvature-driven grain growth. Here the stiffness and mobility are computed using an analysis of fluctuations in the grain boundary position during molecular dynamics simulations. This work represents the first determination of grain boundary stiffness for a realistic three-dimensional system. The results indicate that the boundary stiffness for a given boundary plane has a strong dependence on the direction of the boundary distortion. The mobility deduced is comparable with that determined in previous computer simulation studies. The advantages and limitations of the fluctuation approach are discussed.
This paper describes a strategy for the measurement of boundary mobility using molecular dynamics (MD) simulations and its application to the migration of nominally flat 〈001〉 tilt grain boundaries in nickel, as described using an EAM potential. Determination of the driving force for boundary migration requires proper accounting for non-linear elastic effects for strains of the magnitude needed for MD simulation of stress-driven boundary migration. The grain boundary velocity was found to be a non-linear function of driving force, especially at low temperature. However, extrapolation of the data to small driving force allows for the determination of the mobility at all temperatures. The activation energy for grain boundary migration was found to be 0.26 eV. This demonstrates that boundary migration in pure metals is not athermal, but the activation energy is much smaller than expected based upon experimental measurements. This discrepancy is similar to that found in earlier simulation measurements.
We rederive and explain the paradoxical prediction, confirmed by experiment, that the normal velocity, , of a curved antiphase domain boundary (APB) in an ordered alloy tends to a finite limit at a critical point, where the APB effectively disappears, its surface energy γ tending to 0, and its thickness λ diverging. The prediction is in apparent contradiction to the expectation that the velocity of the APB should tend to 0 based on the notion that should be proportional to γ and inversely proportional to λ. Combining an Allen–Cahn equation for the rate of change of the order parameter, a non-conserved quantity, with a Cahn–Hilliard equation for the diffusion of one of the chemical components of an alloy, a conserved quantity, we obtain a system from which we derive an expression, via formal asymptotics, for of an APB domain boundary in an ordered alloy. The drags from the two types of quantities are found to be additive. We find that the drag from the changes in ordering accompanying the motion of the APB decreases inversely as the thickness. Thus, at the critical temperature where the thickness of an APB diverges and its γ tends to 0, the drag tends to 0. This resolves the paradoxical behavior of APB at the critical point; they continue to move up to the limiting condition where they, and their driving force for motion, disappear. The drag from the conserved component, which moves with the boundary as an adsorbed layer, exerts a drag on the boundary that is similar to what is predicted for impurity drag. In general the drag is given by a compositional integral through the interface that is not simply related to either the thickness or the total adsorption. However, for thick compositional wetting layers the drag indeed varies with thickness. We believe that the distinction we have encountered in the behavior of composition and order parameter is quite general for motion of interfaces, unless strong cross-effects influence the evolution of the system. Our results yield a unification and reconciliation of several diverse theories of interface motion.
Both experimental and atomistic simulation measurements of grain boundary mobility were made as a function of temperature and boundary misorientation using the same geometry that ensures steady-state, curvature-driven boundary migration. Molecular dynamics simulations are performed using Lennard–Jones potentials on a triangular lattice. These simulations represent the first systematic study of the dependence of intrinsic grain boundary mobility on misorientation. The experiments focus on high purity Al, with 〈111〉 tilt boundaries, which are isomorphic to those examined in the simulations. Excellent agreement between simulations and experiments was obtained in almost all aspects of these studies. The boundary velocity is found to be a linear function of the curvature and the mobility is observed to be an Arrhenius function of temperature, as expected. The activation energies for boundary migration varies with misorientation by more than 40% in the simulations and 50% in the experiments. In both the simulations and experiments, the activation energies and the logarithm of the pre-exponential factor in the mobility exhibited very similar variations with misorientation, including the presence of distinct cusps at low Σ misorientations. The activation energy for boundary migration is a logarithmic function of the pre-exponential factor in the mobility, within a small misorientation range around low Σ misorientations.
Abstract Advances in automated electron diffraction techniques, microstructural modeling, and the understanding of structure-property
relationships for grain boundaries have resulted in the emergence of grain boundary engineering as a formidable tool for cost-effectively
achieving enhanced performance in commercial polycrystalline materials (i.e., metals, alloys, and ceramics). In this article,
some applications for grain boundary engineering technology that have been developed during the past several years are presented.
- D Y Yoon
- R A Vandermeer
- D Jensen
- E Woldt