Asymmetric Tilt Grain Boundaries Research Articles

An atomistic survey of shear coupling in asymmetric tilt grain boundaries and interpretation using the disconnections framework

Grain Boundaries (GB) play an important role in determining the behavior of polycrystalline materials. While the mechanisms of motion and associated shear response for symmetric tilt grain boundaries (STGBs) are well studied, the same is not true for asymmetric tilt grain boundaries (ATGBs) despite their greater prevalence in polycrystals. This study aims to investigate the shear response of a large collection of asymmetric tilt grain boundaries (ATGBs) using molecular dynamics (MD) simulations and interpret the data using a discrete disconnections model that works remarkably well for STGBs. MD simulations of shear-driven ATGBs show that the plastic shear (shear coupling factor) in the region swept by a GB exhibits a complex dependence on the inclination angle, and this dependence changes with the misorientation of the GB. In addition, the shear response was observed to be highly sensitive to the applied shear rate and temperature. Recognizing the spatial and temporal scale limitations of MD simulations, we extended the discrete disconnections mesoscale model of Khateret al. (2012) to calculate the nucleation barriers of disconnection modes and predict the effective shear coupling of an ATGB. We observed that the mesoscale model’s predictions of the shear coupling factor of ATGBs do not agree with those observed in MD simulations. Finally, we examine the hypotheses of our mesoscale model that contribute to disagreements between MD simulations and the mesoscale model and propose improvements to the mesoscale model for future work.

Grain-boundary thermodynamics with artificial-neural-network potential: Its ability to predict the atomic structures, energetics, and lattice vibrational properties for Al

An artificial neural network (ANN) potential for Al, trained with density-functional-theory (DFT) data, is constructed to accurately predict lattice vibrational properties and thermodynamics of grain boundaries (GBs) in Al. The ANN potential is demonstrated to accurately predict not only atomic structures and energetics of the GBs at 0 K but also partial phonon densities of states and vibrational entropies, even for GBs absent in the training data sets. In addition, their total potential energies and atomic forces by DFT at elevated temperatures up to 800 K can also be well reproduced by molecular dynamics with the ANN potential. In contrast, a modified embedded atom method (MEAM) potential shows larger errors in phonon frequencies and atomic forces for atoms at GBs, as well as in the bulk, than the ANN potential. The MEAM potential is thus likely to be inadequate to quantitatively predict thermodynamic properties of GBs, particularly at high temperature. The present ANN potential is also applied to systematically examine thermodynamic stability of asymmetric tilt GBs. It is predicted that for the \ensuremath{\Sigma}9 system, the GB free-energy profile as a function of inclination angle exhibits a cusp at elevated temperatures, due to its larger vibrational entropies of asymmetric tilt GBs than those of \ensuremath{\Sigma}9 symmetric tilt GBs.

Formation Energy Profiles of Oxygen Vacancies at Grain Boundaries in Perovskite‐Type Electroceramics

Oxygen vacancy formation energies play a major role in the electric field‐assisted abnormal grain growth of technologically relevant polycrystalline perovskite phases. The underlying effect on the atomic scale is assumed to be a redistribution of cationic and anionic point defects between grain boundaries (GBs) and the bulk interior regions of the grains due to different defect formation energies in the structurally different regions, accompanied by the formation of space charge zones. Using atomistic calculations based on classical interatomic potentials, optimized structures of the symmetric tilt GBs Σ5(210)[001] and Σ5(310)[001], and of the asymmetric tilt GB (430)[001]||(100)[001] in the electroceramic perovskite materials SrTiO3, BaTiO3, and BaZrO3, are derived and discussed. Profiles of oxygen vacancy formation energies across those GBs are presented and their dependence on composition and GB type is discussed.

Standard Deviation Effect of Average Structure Descriptor on Grain Boundary Energy Prediction.

The structural complexities of grain boundaries (GBs) result in their complicated property contributions to polycrystalline metals and alloys. In this study, we propose a GB structure descriptor by linearly combining the average two-point correlation function (PCF) and standard deviation of PCF via a weight parameter, to reveal the standard deviation effect of PCF on energy predictions of Cu, Al and Ni asymmetric tilt GBs (i.e., Σ3, Σ5, Σ9, Σ11, Σ13 and Σ17), using two machine learning (ML) methods; i.e., principal component analysis (PCA)-based linear regression and recurrent neural networks (RNN). It is found that the proposed structure descriptor is capable of improving GB energy prediction for both ML methods. This suggests the discriminatory power of average PCF for different GBs is lifted since the proposed descriptor contains the data dispersion information. Meanwhile, we also show that GB atom selection methods by which PCF is evaluated also affect predictions.

Interaction between crack and grain boundary in magnesium

In polycrystalline materials, grain boundaries (GBs) play an important role in resisting crack growth. In this study, the interaction of a crack on basal plane with GBs in magnesium was investigated by molecular statics simulations. Three types of GBs with different mis-orientation angles were considered, i.e., [21¯1¯0] asymmetric tilt GB, (011¯0) twist GB and [0001] asymmetric tilt GB. Simulation results show that, for [21¯1¯0] asymmetric tilt GBs, the crack always penetrates through the GBs but the crack growth path in neighboring grain changes from (0001) basal plane to (01¯11) pyramidal plane as the tilt mis-orientation angle increases. For (011¯0) twist GBs, the crack propagation mechanism changes from trans-granular fracture into inter-granular fracture with the increasing twist mis-orientation angle. For [0001] asymmetric tilt GBs, trans-granular fracture happens at small and high tilt mis-orientation angles, while inter-granular fracture occurs at intermedium mis-orientation angles. The critical stress intensity factor (SIF) for crack propagation across or along GB is correlated with the corresponding GB energy. Trans-granular fracture occurs when the GB energy is low, and the critical SIF also increases with the increasing GB energy. For high energy GBs, inter-granular fracture occurs and the critical SIF changes hardly with the increasing GB energy. The current work provides insights into understanding the behavior of cracks and ductility enhancement in magnesium.

Interface dislocations and grain boundary disconnections using Smith normal bicrystallography

The CSL/DSCL model for interfaces in crystalline materials offers a unified framework to study interface dislocations in phase boundaries and disconnections in grain boundaries. The model relies on the existence of a coincidence relation between the two lattices that meet at an interface. The model’s ability to quantitatively predict the thermodynamics and kinetics of interfaces has been demonstrated for a limited set of symmetric tilt grain boundaries (STGBs) in cubic materials and twin boundaries. However, the lack of a general framework of interface defects prevents its applicability to arbitrary rational boundaries. In this paper, we present a mathematical framework based on the Smith normal form (SNF) for integer matrices to study the bicrystallography of rational phase and grain boundaries. One of the main results of the paper is a constructive proof of the invariance of the coincident site lattice (CSL) under discrete relative displacements of the parent lattices (of possibly different kind) by a displacement shift complete lattice (DSCL) vector. In addition, we obtain necessary and sufficient conditions on two lattices, related by not only rotations but also lattice distortions, for the existence of a coincidence relation. We first apply these results to explore coincidence relations in arbitrary phase boundaries, and study interface dislocations. In particular, we demonstrate the framework for a phase boundary formed by a strained hexagonal lattice and a square lattice. As a second application, we show how to enumerate all possible (geometric) disconnection modes in arbitrary rational grain boundaries, including glide and non-glide modes in both STGBs and asymmetric-tilt grain boundaries (ATGBs). The constructive nature of the framework lends itself to an algorithmic implementation based exclusively on integer matrix algebra to construct all interfaces that admit CSLs up to a prescribed size, and determine disconnection modes in grain boundaries. We demonstrate the use of SNF bicrystallography on selected bicrystal misorientation axes/angles in face-centered cubic (fcc), body-centered cubic (bcc), and hexagonal (hex) lattices.

Shear direction induced transition mechanism from grain boundary migration to sliding in a cylindrical copper bicrystal

Control over grain boundary (GB) motion ways provides an effective mean for tailoring the mechanical and physical properties of nanocrystalline metals. However, shear direction induced transition from GB migration to sliding in nanocrystalline metals has remained elusive. In this work, we used molecular dynamics (MD) simulations to track the dynamic process of a representative Σ11(113) high-angle GB in a cylindrical copper bicrystal under controllable shear directions parallel to the GB plane. When the shear direction changed from the [332¯] direction to the [11¯0] direction (the shear angle θ increased from 0° to 90°), the dominant GB deformation mechanism switched from GB migration to sliding. The critical orientation (critical shear angle) of the transition was [85¯1¯] (75°). Atomistic observations indicated that the disconnection and the surface step nucleation provoked the GB migration and sliding, respectively. This shear direction induced transition was also found in other 〈110〉 symmetrical and asymmetric tilt GBs, as well as nano polycrystalline metals. Analytical models revealed that the transition mechanism originated from the competition between the nucleation energies of the disconnection and surface step. These insights may contribute to the ongoing search for favoring manageable design of nanocrystalline metals by GB-mediated plastic deformation.

Twin interaction with [formula omitted] tilt grain boundaries in BCC Fe : Formation of new grain boundaries

It is well known that the twinning is an important mode of plastic deformation in nanocrystalline materials. As a result, it is expected that the twin can interact with different grain boundaries (GBs) during the plastic deformation. Understanding these twin–GB interactions is crucial for our understanding of mechanical behavior of materials. In this work, the twin interaction with different Σ11 symmetric and asymmetric tilt GBs has been investigated in BCC Fe using molecular dynamics (MD) simulations. The results indicate that twin nucleate from the crack or GB and, its interaction with Σ11 asymmetric tilt GBs leads to the formation of a new GB. This new GB consist of 〈100〉 Cottrell type immobile dislocations. The detailed atomistic mechanisms responsible for this new GB formation have been revealed using atomistic simulations. Interestingly, the new GB formation has not been observed in the case of twin interaction with Σ11 symmetric tilt GBs.

Molecular dynamics investigation on tilt grain boundary energies of beta-titanium and tungsten at high temperature

The grain boundary energies (GBEs) of symmetric tilt grain boundaries (STGBs) and asymmetric tilt grain boundaries (ATGBs) for W at 0 and 2400 K and β-Ti at 1300 K were calculated by means of molecular statics and dynamics simulations to investigate the effects of temperature on GBE and the relationships between GBEs and grain boundary (GB) planes. Generally, the variation trends of GBE with the tilt angle are similar for the three cases, when the tilt axis is specified. It is of course that these similarities result from their similar GB microstructures in most cases. However, the variation trends of GBE with tilt angle are somewhat different between β-Ti at 1300 K and W at 2400 K for STGBs with <100> and <110> tilt axes. This difference mainly stems from the following two reasons: firstly, the GB microstructures of W at 2400 K and β-Ti at 1300 K are different for some STGBs; secondly, the atoms at the STGB of β-Ti at 1300 K tend to evolve into the local ω- or α-like structures distributed at the STGB for some STGBs with <110> tilt axis, which makes the corresponding STGBs more stable, thereby decreasing the GBEs. Furthermore, a geometric parameter θ, the angle between the misorientation axis and the GB plane, was defined to explore the relationships between GBEs and GB planes. It was found that the relationships between GBEs and GB planes can be described by some simple functions of sin(θ) for the GBs with definite lattice misorientation, which can well explain and predict the preferred GB planes for the GBs having the same lattice misorientation. Our calculations not only extend the investigation of GBs to higher temperature, but also deepen the understanding on the temperature contributions to the microstructure evolution at GBs and on the relationships between GBEs and possible geometric parameters.

Atomistic and phase field simulations of three dimensional interactions of [formula omitted] twins with grain boundaries in Mg: Twin transmission and dislocation emission

In polycrystals, the interaction of dislocations and twins with grain boundaries (GBs) plays a role in hardening and formability during plastic deformation. While dislocation-GB interactions are relatively well-understood, twin-GB interactions remain mostly unknown. Here, an approach using molecular dynamics and phase-field simulations is followed to study the forward and lateral interactions between {101¯2} twins and tilt grain boundaries in Mg. Molecular dynamics results show that the resolved shear stress on slip/twinning modes of the neighboring grain, not the geometric alignment, is the dominant factor in determining the outcome of the twin-GB interactions. For some lateral interaction configurations, as the misorientation angle increases, the resolved shear stress on the same {101¯2} twin variant of the neighboring grain reduces while it increases for slip or I2 stacking fault emissions or other twin modes such as {112¯1} and {101¯1}, explaining why twin transmission is not seen at high misorientation angles. Furthermore, lateral and forward interactions of the twin with tilt grain boundaries whose misorientation axes are normal to the coherent twin boundary show significantly different outcomes. For the forward interaction, the twin is absorbed and stacking faults are emitted when interacting for low misorientation angles (up to 30°) while the lateral interaction results in twin transmission, nucleation of a {112¯1} twin, and emission of I2 stacking faults. Finally, comparisons between twin interactions with symmetric and asymmetric tilt GBs with different GB structures show similar outcomes.

Effects of local elemental ordering on defect-grain boundary interactions in high-entropy alloys

The way in which defects interact with grain boundaries (GBs) has profound influences on materials performance. In this work, we study defect-GBs interactions in a model CuNiCoFe high-entropy alloy (HEA) based on atomistic simulations. Five representative GBs are considered, namely Σ3 < 101 > {11−1} coherent twin GB, Σ5 < 103 > {010} twist GB, Σ11 < 1–10 > {113} symmetric tilt GB (STGB), Σ11 < 1–10 > {554} asymmetric tilt GB (ATGB), and Σ45 < 1–20 > {001} tilt GB. A particular focus is placed on the role of chemical disorder and local elemental segregation in influencing the defect-GBs interactions. Specifically, we compare the results obtained within an averaged atom model, the random HEA with randomly distributed elements, and the equilibrated HEA with Cu segregation after a combined Monte-Carlo/Molecular statics algorithm. For the pristine CuNiCoFe HEA without GBs, we find chemical occupancy fluctuations tend to lower the formation energies of defects, especially for interstitials because of the larger lattice distortion. For defect-GBs interactions, we find GBs strongly interact with interstitials over vacancies. We further reveal that elemental segregation can enhance the sink strength of GBs towards vacancies, but at the same time, reduce the sink strength toward interstitials. Therefore, the bias effects of GBs toward interstitials and vacancies are suppressed in HEAs due to local ordering, promoting efficient defect annihilation within the grain interiors. We highlight that the local ordering tendency and elemental segregation in HEAs play dominant roles in influencing the defect-GB interactions.

Structures and energies of Σ3 asymmetric tilt grain boundaries in silicon

We optimize 23 silicon Σ3 asymmetric tilt grain boundaries (ATGBs) using Stillinger Weber (SW), Tersoff and the optimized Modified Embedded Atom Method (MEAM) potentials. It is demonstrated that conventional GB optimization via rigid body translations in combination with atom deletions is totally incapable of driving an as-constructed flat Si grain boundary (GB) to its equilibrated state since it may inevitably cause lattice distortions in GB. But it can be easily achieved by initially introducing some pre-designed steps into as-constructed flat GB model. These steps are composed of coherent twin boundary (CTB) and symmetric incoherent twin boundary (SITB) facets. By doing so, energies of all 23 ATGBs are greatly reduced. Meanwhile, some ATGBs may have degenerate states with different structures but same energies. This work not only facilitates the structural characterization of Si Σ3 ATGBs, but may provide new insights into microstructure design in polycrystalline silicon.

Effect of variation in inclination angle of Ʃ5 tilt grain boundary on the shock response of Ni bicrystals

The intensity of damage production during shock wave propagation in polycrystalline metallic systems is mostly dependent on the shock-defect interactions. Traditionally, different coincidence site lattice (CSL) grain boundaries (GBs) are introduced in the polycrystalline structure through various processing techniques to enhance the strength or plasticity. However, their dynamic response to the impulsive loading condition has not been elaborately explored to date, which necessitates a detailed study on the interaction between CSL GBs and shock wave. In this study, we have employed molecular dynamics simulations to investigate the response of both symmetric and asymmetric ∑5[1 0 0] tilt GBs of nickel bicrystal under the influence of shock-wave. We have also analysed the role of piston velocities and inclination angles of the GBs on the shock response and the consequent deformation behaviour. This investigation gives insight into the mechanical response and the underlying mechanisms which are inspected through atomic strain analysis, common neighbour analysis and pressure–time–distance mapping. The results show that the stacking faults formation takes place when specimens are subjected to lower shock velocities, whereas higher velocities facilitate phase transformation along with amorphization. There is a stark contrast between the specimens with symmetric and asymmetric tilt GBs in the manner of plastic deformation behaviour in response to shock-wave and GB failure at lower and higher piston velocities.

Stable and metastable structures and their energetics of asymmetric tilt grain boundaries in MgO: a simulated annealing approach

A simulated annealing (SA) method based on molecular dynamics is employed to reveal atomic structures of asymmetric tilt grain boundaries (ATGBs) in MgO. Σ5 and Σ13 ATGBs with the [001] tilt axis are systematically investigated. The ATGBs after SA simulations dissociate into saw-toothed nanofacets composed of multiple structural units. These nanofacets are lower in GB energy than those obtained from a γ-surface method with structural optimization, demonstrating the importance of SA-based methods for obtaining low-energy structures of ATGBs. For most of the Σ5 ATGBs, the nanofacets consist of only structural units of Σ5 symmetric tilt GBs (STGBs). For the Σ13 ATGBs studied, their nanofacets do not consist of only Σ13 STGBs but always contain non-Σ13 structural units, which probably results from a large difference between the excess volume of Σ13(510) and Σ13(320) STGBs. It is also found that ATGBs have a larger number of metastable structures whose GB energies are close to the lowest energy structure than STGBs, due to the fact that ATGB nanofacets are more tolerant of variation in facet junction, structural units and their arrangement. Consequently, the lowest energy structures have low probabilities of being formed than metastable structures.

A Comparison between ∑3 Asymmetrical Tilt Grain Boundary Energies in Niobium Obtained Analytically and through Molecular Dynamics Based Simulations

Niobium is an important constituent of Zr-Nb alloys being used widely in the nuclear industries as fuel claddings and pressure tubes. In this article, MD based simulations are performed to obtain grain boundary (GB) energies in ∑3 symmetrical and asymmetrical tilt grain boundaries (ATGBs) along &lt;110&gt; tilt axis. Grain boundary energies are also obtained analytically by utilizing the equation establishing the relationship between inclination angle and grain boundary energy for ATGBs. It is observed that in both the cases the GB energies increase with the increase in inclination angle of the ATGBs. The increase in the GB energy follows the same trend with a little offset between the results obtained analytically and MD based simulations. The offset between both the results can be attributed to the limitations of the potentials employed for the simulations. MD based simulations thus provide an accurate method to calculate the GB energies.

Plastic deformation mechanisms of hierarchical double contraction nanotwins in Mg

Recent experiments demonstrated that hierarchical double contraction nanotwins (DCTWs), i.e., $$ \left\{ {10\bar{1}1} \right\} - \left\{ {10\bar{1}1} \right\} $$ nanotwinned structures, can simultaneously improve the strength and ductility of Mg–Li alloys. With Mg as model material using atomistic simulations and interface defect analysis, we characterize structural characteristics of boundaries associated with DCTWs and investigate plastic deformation mechanisms of double contraction nanotwinned structures. It is revealed that the boundaries associated with DCTWs are composed of $$ \left\{ {10\bar{1}1} \right\} $$ coherent twin boundaries (CTBs), symmetrical tilt grain boundaries (STGBs), and asymmetrical tilt grain boundaries (ASTGBs). Under mechanical loadings, the corresponding grain boundary defects along STGBs and ASTGBs act as sources for nucleating and emitting basal and pyramidal dislocations, enhancing the plasticity. Meanwhile, the densely distributed CTBs in DCTWs act as strong barriers for dislocation motion, strengthening the material.

Interaction between a [formula omitted] twin boundary and grain boundaries in magnesium

Deformation twinning is a common plastic deformation mode in polycrystalline magnesium (Mg), so the interaction between twin boundary (TB) and grain boundary (GB) plays an important role in the improvement of material strength and ductility. In this work, molecular dynamics (MD) method was employed to study the interaction between {101‾2} TB and GB. Four GB types were considered, i.e., symmetric tilt grain boundary (STGB), asymmetric tilt grain boundary (ATGB), basal twist grain boundary (BTGB, GB coincides with the basal planes of both grains) and prismatic twist grain boundary (PTGB, GB coincides the prismatic planes of both grains). MD simulations show that for both tilt GBs, the twin is able to penetrate through GB at small misorientation angle (<15°). At medium misorientation angle (15°–75°), the TB is absorbed by GB with stacking faults nucleated on the new GB, while at large misorientation angle (>75°), the TB is fully absorbed without any stacking faults. For twist GBs, the TB always penetrates through PTGBs, but is fully absorbed by BTGBs for all considered misorientation angles. All the GBs were observed to have a blocking effect on twinning deformation whether the twin penetrates through GB or not. Based on the interaction mechanisms mentioned above, we proposed an analytical twin thickening model via the Eshelby solutions to describe the GB strengthening effects or grain size effects on twinning, which shows that the material strength dominated by twinning is inversely proportional to the grain size. By comparison with the Hall-Petch model, we can see that the grain size effect on twinning deformation is stronger than that on dislocation slip, which agrees well with previous experimental observations. It is worth noting that this model would be valid for not only HCP (hexagonal close-packed) materials but also FCC (face-centered cubic) and BCC (body-centered cubic) materials. Current work provides new insights into the GB strengthening effects and grain size effects on twinning deformation.

Atomistic investigation of hydrogen embrittlement effect for symmetric and asymmetric grain boundary structures of bcc Fe

An atomistic simulation study has been carried out to understand that the grain boundary hydrogen (H) will have a significant effect on grain boundary (GB) energy, surface (FS) energy and cohesive energy. Molecular statics simulations at zero temperature for pure a-Fe with a single H atom and two H atoms placed at the crystal interfaces of 〈1 0 0〉 symmetric tilt grain boundary (STGB) systems and asymmetric tilt grain boundary (ATGB) systems were performed. Simulation results show that the segregation energy of solute H atom on the GB was greater than zero, i.e. the system energy with H located at the GB is larger than the energy with H at the free surface, which implies that the failure mode should be intergranular. Moreover, only when H is located within the distance of 2a (lattice constant) from the grain boundary will H have a significant effect on grain boundary destruction. Finally, the calculated GB energy, surface energy and cohesive energy of bcc Fe 〈1 0 0〉 STGB and ATGB systems are affected by the hydrogen segregation at the GB structure. Both the surface energy and the grain boundary cohesive energy decrease with the increase of hydrogen coverage. The impacts of H or 2H atoms at the GB plane on the surface energy and the cohesive energy are explored as quadratic polynomial functions. The promoting effect of 2H atoms on the intergranular fracture is more obvious than H atoms’. Both H and 2H have more effect on surface energy than cohesive energy.

Effect of symmetrical and asymmetrical tilt grain boundaries on radiation-induced defects in zirconium

In this article, molecular-dynamics-based simulations were used to study the effect of grain boundaries (GBs) on the formation and spatial distribution of radiation-induced point defects. In order to perform this study, two sets of symmetrical and asymmetrical tilt grain boundaries were constructed along [0 0 0 1] and [0 −1 1 0] as the tilt axis, respectively. Vacancy, interstitial and Frenkel pair formation energies were estimated as a function of the distance from the GB core for both symmetrical as well as asymmetrical tilt GBs. The trend obtained between GB energies and point defect formation energies helps explain the biased absorption of interstitials over vacancies in most cases, as well as the equal absorption of both kinds of point defects in a few of them. It has already been reported from the experimental work that [0 0 0 1] GB structures closely resemble the polycrystalline texture of hcp materials, which motivates us to study the effect of irradiation on these GBs.

Extracting knowledge from molecular mechanics simulations of grain boundaries using machine learning

In this paper, we demonstrate that the “process-structure-property” (PSP) paradigm of materials science can be extended to atomistic grain boundary (GB) simulations through the development of a novel framework that addresses the objective identification of the atoms in the grain boundary regions using the centro-symmetry parameter and local regression, and the quantification of the resulting structure by a pair correlation function (PCF) derived from kernel density estimation (KDE). For asymmetric tilt GBs (ATGBs) in aluminum, models were successfully established connecting the GB macro degrees of freedom (treated as process parameters) and energy (treated as property) to a low-rank GB atomic structure approximation derived from principal component analysis (PCA) of the full ensemble of PCFs aggregated for this study. More specifically, it has been shown that the models produced in this study resulted in average prediction errors less than 13 mJ/m2, which is less than the error associated with the underlying simulations when compared with experiments. This demonstration raises the potential for the development and application of PSP linkages from atomistic simulation datasets, and offers a powerful route for extracting high value actionable and transferrable knowledge from such computations.