Grain Size Boundary Research Articles

Artificial Neural Network Molecular Mechanics of Iron Grain Boundaries

This study reports grain boundary (GB) energy calculations for 46 symmetric-tilt GBs in α-iron using molecular mechanics based on an artificial neural network (ANN) potential and compares the results with calculations based on the density functional theory (DFT), the embedded atom method (EAM), and the modified EAM (MEAM). The results by the ANN potential are in excellent agreement with those of the DFT (5 % on average), while the EAM and MEAM significantly differ from the DFT results (about 27 % on average). In a uniaxial tensile calculation of Σ3(1‾12) GB, the ANN potential reproduced the brittle fracture tendency of the GB observed in the DFT while the EAM and MEAM showed mistakenly showed ductile behaviors. These results demonstrate the effectiveness of the ANN potential in grain boundary calculations of iron as a fast and accurate simulation highly in demand in the modern industrial world.

Segregation of P and S Impurities to A Σ9 Grain Boundary in Cu

The segregation of P and S to grain boundaries (GBs) in fcc Cu has implications in diverse physical-chemical properties of the material and this can be of particular high relevance when the material is employed in high performance applications. Here, we studied the segregation of P and S to the symmetric tilt Σ9 (22¯1¯) [110], 38.9° GB of fcc Cu. This GB is characterized by a variety of segregation sites within and near the GB plane, with considerable differences in both atomic site volume and coordination number and geometry. We found that the segregation energies of P and S vary considerably both with distance from the GB plane and sites within the GB plane. The segregation energy is significantly large at the GB plane but drops to almost zero at a distance of only ≈3.5 Å from this. Additionally, for each impurity there are considerable variations in energy (up to 0.6 eV) between segregation sites in the GB plane. These variations have origins both in differences in coordination number and atomic site volume with the effect of coordination number dominating. For sites with the same coordination number, up to a certain atomic site volume, a larger atomic site volume leads to a stronger segregation. After that limit in volume has been reached, a larger volume leads to weaker segregation. The fact that the segregation energy varies with such magnitude within the Σ9 GB plane may have implications in the accumulation of these impurities at these GBs in the material. Because of this, atomic-scale variations of concentration of P and S are expected to occur at the Σ9 GB center and in other GBs with similar features.

Effects of grain boundary structures on primary radiation damage and radiation-induced segregation in austenitic stainless steel

Grain boundary (GB) engineering is crucial in the austenitic stainless steel (ASS) design for nuclear energy applications. In this work, the influence of different GB structures on radiation defect recombination and radiation-induced segregation (RIS) at different temperatures were investigated using molecular dynamics simulation. Four typical GBs in ASSs were selected as model structures. Results showed that GBs remained stable at various temperatures and they all exhibited better self-healing performance than single crystals in terms of radiation defects. However, except Σ3(112) GB, other three GBs cannot inhibit the radiation induced segregation, while promoting the radiation defect recombination. Calculation results showed that the higher Σ value of GBs can lead to a greater lattice mismatch near GBs, which not only results in stronger sink strength for radiation induced defects, but also provides more sites for solute atoms and causes greater segregations eventually. Owing to the intrinsic low Σ and large inclination angle characteristic, Σ3(112) GB achieves an excellent balance between the defect-absorption and RIS. This phenomenon provides a feasible route for the future GB design in ultra-high radiation tolerant materials.

The Mechanism of Grain Boundary Serration and Fan-Type Structure Formation in Ni-Based Superalloys

A model of discontinuous precipitation of γ′ phase at grain boundaries (GBs) in polycrystalline Ni-based superalloys during continuous cooling from supersolvus temperature was developed. The model calculates the size and γ′ phase fraction in GB precipitates as a function of cooling rate and GB mobility. The model is based on the classical mechanism of diffusion-controlled precipitation. It considers fast diffusion of γ′-forming elements along the GB and the motion of the GBs under driving force induced by alloy decomposition. The model predicts either discrete GB gamma-prime particles and GB serration or the growth of fan-type structures depending on the cooling rate and GB mobility. We conclude from the model predictions that the GB mobility is the key factor controlling the type and morphology of GB precipitates. High GB mobility results in formation of fan-type structures, while the lower GB mobility leads to GB serration. The predicted dependence of the size of GB precipitates on the cooling rate is in good agreement with the experimental observations.

3D cellular automaton modelling of silicon crystallization including grains in twin relationship

Production of silicon for solar cells in photovoltaic systems is mainly based on directional casting processes. Twin nucleation is favoured during silicon growth due to the low-level twin energy of formation. As a consequence, in all solidification process, a large amount of grain boundaries (GB) are in twin relationship. A 3D cellular automaton (CA) model has been recently developed for the growth of multi-crystalline silicon including facet formation and nucleation of new grains in twin relationship. Activation of facets is based on an undercooling parameter assigned to each grain and for each of the <111> crystal directions. The model also considers nucleation and growth of grains on <111> facets corresponding to Σ3 twin relationships between twin grains. This model is first applied to comparison with experimental observations. It is found that impingement of growing grains that nucleated in Σ3 twin relationships meet during growth and form Σ3, Σ9 and Σ27 GB, in good agreement with experimental observations. Finally, the model is applied at a larger scale to generate grain structures representative of industrial practice. While quantitative experimental data is missing for comparison at such scale, the model is promising and its implementation in heat and mass transfer models should be considered for assistance to production of silicon for solar cells dedicated to photovoltaic systems.

Abnormal growth of columnar grains and formation of Σ3 grain boundaries in non-oriented electrical steels

The remarkably abnormal growth behavior of columnar grains and the formation of Σ3 grain boundaries (GBs) were studied via plastic deformation and annealing based on an electron backscattering diffraction (EBSD) investigation. Driven by the stored energy and GB mobility, coarse austenite columnar grains were formed by the abnormal growth of fine equiaxed grains with higher grain orientation spread (GOS) values in the reducing atmosphere of hydrogen. Moreover, extraordinarily coarse columnar grains with high GOS values and non-{1 1 1} texture were formed by microstructure inheritance during γ → α transformation. In addition, slender ferritic columnar or island grains with Σ3 GBs and low GOS values were generally obtained, and the formation mechanism was strictly associated with the Kurdjumov-Sachs (K-S) relationship, which was induced during variant selection driven by the GB mobility and surface effect in the reducing atmosphere of hydrogen.

A nonlocal method for modeling interfaces: Numerical simulation of decohesion and sliding at grain boundaries

Understanding and modeling the interface behavior is an important task for predicting materials response in various applications. To formulate the behavior of an arbitrary interface, one needs to construct the relation between acting tractions and displacement jumps at the interface. In addition to capturing the correct physics of the interface, the so-called traction–separation relation must also be thermodynamically consistent and satisfy the basic balance laws. Apart from many attempts in the literature to address these issues, a new and simple method to capture the complex mechanical behavior at an arbitrary interface is proposed. The new formulation is based on introducing a new quantity called “traction density”. As a result, the traction–separation relation for any arbitrary interface is automatically computed by integrating the traction density over the interface. The traction density can be formulated based on understandings and observations from lower scales. As will be shown, the mathematical representation of the traction density is relatively simple and therefore its consistency can be verified easily. When it comes to the grain boundary (GB) behavior, the proposed methodology is able to represent not only intergranular fracture but also grain boundary sliding. For calibration and verification of the model, molecular dynamics (MD) simulations for aluminum Σ5 GB are utilized. Interestingly, the calculations from current MD simulations show size-dependent behavior for the GB. By introducing a healing parameter in the new interface model, it is now possible to explain and predict possible GB size-dependent behavior.

Faceting of Twin Grain Boundaries in High‐Purity Copper Subjected to High Pressure Torsion

The microstructure of high‐purity 5N5 copper processed by high pressure torsion (HPT) is studied. Close to the top and bottom surfaces of HPT disk, the 2–10 μm‐thick ultrafine‐grained layers with equiaxial grains and grain size of about 150 nm are formed. This grain size is typical for HPT of copper and its alloys. However, the remaining bulk layer in the HPT disk contained mainly elongated intersecting twins with high aspect ratio and length of up to 1 μm. These twin grain boundaries (GBs) are faceted. The geometry of the GB facets is analyzed using Σ3 coincidence site lattice (CSL). The Σ3 twins after HPT contained (100)CSL, (110)CSL, (010)CSL, and non‐CSL 9R facets, but not (120)CSL and (130)CSL facets. Earlier, the stability diagram for the Σ3 GB facets is experimentally constructed for the same 5N5 high‐purity copper. The comparison of the data with this diagram allows to estimate for the first time the effective temperature of pure copper during HPT processing at room temperature (RT): Teff = 920 ± 50 K. In other words, the HPT at RT results in Σ3 GB facets as if the sample is annealed at Teff = 920 ± 50 K.

Amorphization induced by 60° shuffle dislocation pileup against different grain boundaries in silicon bicrystal under shear

Molecular dynamics (MD) simulations of the amorphous band nucleation and growth ahead of the tip of a shuffle 60o dislocation pileup at different grain boundaries (GBs) in diamond-cubic (dc) silicon (Si) bicrystal under shear are performed. Amorphization initiates when the local resolved shear stress reaches approximately the same value required for amorphization in a perfect single crystal (8.6–9.3 GPa) for the same amorphization plane. Since the local stresses at the tip of a dislocation pileup increase when the number of the dislocations in a pileup is increased, the critical applied shear stress τap for the formation of an amorphous shear band significantly decreases with the dislocation accumulation at the GBs. In particular, when the number of the dislocations in a pileup increases from 3 to 8, the critical shear stress drops from 4.7 GPa to 1.6 GPa for both the Σ9 and Σ19 GBs and from 4.6 GPa to 2.1 GPa for the Σ3 GB, respectively. After the formation of steps and disordered embryos at the GBs, the atomistic mechanisms responsible for the subsequent amorphous shear band formations near different GBs are found to distinct from each other. For a high-angle GB, such as Σ3, an amorphous band propagates through the crystalline phase along the (112) plane. For the Σ9 GB, dislocations disassociate and the stacking faults form, which then precede the formation of an amorphous band along the (110) plane. For the Σ19 GB, the one-layer stacking fault along the (111) plane transforms into an interesting intermediate phase: a two-layer band with the atomic bonds being aligned along the (111) plane (i.e., rotated by 30o with respect to the atomic bonds outside the band). This intermediate phase transforms to the amorphous band along the (111) plane under a further shearing. The obtained results represent an atomic-level confirmation of the effectiveness of dislocation pileup at the nucleation site for various strain-induced phase transformations (PTs), and exhibit some limitations.

Effects of 3-D grain boundary geometrical angles and the net normal stress on intergranular stress corrosion cracking initiation in a 316 stainless steel

The dependence of intergranular stress corrosion cracking (IGSCC) initiation propensity on the grain boundary (GB) characters and geometrical angles was investigated by utilizing a thin sheet 316 stainless steel sample, of which the thickness was approximately equal to the average grain diameter. The low-ΣCSL GBs especially the Σ3 GBs had higher resistance to cracking initiation. The cracking initiation susceptibility (CIS) of a GB increased with the decrease in the GB inclination angle α. The net effective normal stress (Δ*σN) exerted on a GB increased with the Schmid factor mismatch (Δm) between the two-side grains. It was found that the Δ*σN initially slightly increased with Δm when 0≤Δm≤0.04, and then steeply increased with Δm when 0.04<Δm≤0.18. A criterion was proposed to predict the CIS of a GB, which demonstrated that the CIS of a GB with the Δ*σN over 0.06 would be high.

Exploration of the sliding behavior of a Σ11 grain boundary with precipitates in Ni–Al system using molecular dynamics

Molecular dynamics (MD) was used to gain insights into grain boundary (GB) shear mechanisms in alloys that require GB mobility in a field of coherent precipitates. The area fraction of the Σ11 affected by the γ′ was systematically varied to explore how GB shear mechanisms change with increased number of precipitates. Without precipitates, local atomic shuffling accommodates the Σ11 GB shear; above an area-fraction threshold, GB shear required dislocation emission. In addition to precipitate area fraction, the transition in GB shear mechanisms may also depend on precipitate shape/size, temperature, and GB misorientation. These factors will be investigated in future work.

Atomistic simulation of interaction of collision cascade with different types of grain boundaries in α-Fe

Presented here are atomistic simulations of the interaction of a collision cascade in α-Fe with different types of grain boundaries (GBs). The collision cascade was generated by a primary knock-on Fe atom of 3 keV kinetic energy. Four different types of symmetric tilt GB configurations (low angle and high angle GBs, Σ3 and Σ11 GBs) with two tilt axes [112¯] and [1¯10] were considered. Difference in potential energy, strength and average displacement of atoms between pristine and irradiated GB configurations were analysed to bring out the effect of irradiation. The vacancy and interstitial formation energies calculated using molecular statics simulations were found to be lower in the GB than in the grain. Collision cascade resulted in defect clusters in and around the GB. Low angle GBs were found to be better sinks for radiation induced defects. Tensile deformation of the irradiated configurations resulted in dislocation loops being nucleated from interstitial clusters. The loss in strength after irradiation was high for Σ3 GBs and negligible for other GBs. It was suggested that materials with low angle GBs and a high dislocation density would be preferred for use in radiation environment.

A Simple Approach to Atomic Structure Characterization for Machine Learning of Grain Boundary Structure-Property Models

Grain boundaries (GBs) have a significant influence on the properties of crystalline materials. Machine learning approaches present an attractive route to develop atomic structure-property models for GBs because of the complexity of their structure. However, the application of such techniques requires an appropriate descriptor of the atomic structure. Unfortunately, common crystal structure identification techniques cannot be applied to characterize the structure of the vast majority of GB atoms (50-98% are classified as other). This suggests a critical need for atomic structure descriptors capable of identifying arbitrary atomic environments. In this work we present a simple procedure that facilitates the identification of arbitrary atomic structures present in GBs. We apply this approach to characterize the atomic structure of the 388 GBs from the Olmsted data set (Olmsted 2009). We show how this approach facilitates visualization of GB atomic structures in a way that reveals important structural information. We test the recently proposed hypothesis that Σ3 GBs contain facets of the GBs that form the corners of the corresponding GB plane fundamental zone. Finally, we briefly demonstrate how the structure descriptors resulting from our approach can be used as inputs to machine learning approaches for the development of atomic structure-property models for GBs.

Effect of misorientation angle of grain boundary on the interaction with Σ3 boundary at crystal/melt interface of multicrystalline silicon

Interactions between Σ3 grain boundaries (GBs), small-angle GBs (SAGBs), and general GBs at a silicon crystal/melt interface are studied by in situ observation during directional solidification. The interactions exhibit a dependence on the misorientation angle. SAGBs can propagate through Σ3 GBs, but this behavior transitions into coalescence with Σ3s when the misorientation approaches the limit of a SAGB, i.e. 15°. On the other hand, general GBs show the ability to terminate Σ3 GBs continuously. The present findings suggest that the presence of intrinsic dislocations in GBs plays a role in GB interactions.

A {112}Σ3 grain boundary generated from the decomposition of a Σ9 grain boundary in multicrystalline silicon during directional solidification

The generation of a {112}Σ3 grain boundary (GB) was observed in situ from the decomposition of a Σ9 GB during directional solidification of multicrystalline Si. A faceted groove formed at the junction of the solid/melt interface and the {112}Σ3 GB. This mechanism is different from that for the growth of {111}Σ3 GBs, for which no groove formed at the interface. If the growth rates for the adjacent facets of the groove are the same, the GB can grow in a straight manner along the {112} plane. The present results suggest that kinetics can give rise to high-energy GBs during solidification.

Ensemble Kalman filter-based data assimilation for three-dimensional multi-phase-field model: Estimation of anisotropic grain boundary properties

Data assimilation (DA) has been used as a machine learning approach to estimate a system's state and the unknown parameters in its numerical model by integrating observed data into model predictions. In this paper, we propose using the DA methodology based on the ensemble Kalman filter (EnKF) to improve the accuracy of microstructure prediction using three-dimensional multi-phase-field (3D-MPF) model and estimate the model parameters simultaneously. To demonstrate the applicability of the DA methodology, we performed numerical experiments in which a priori assumed true parameters related to the grain boundary (GB) energy cusp and GB mobility peak of Σ7 coincidence site lattice GB were estimated from synthetic data of time-evolving polycrystalline microstructure. Four model parameters related to the Σ7 GB properties were successfully estimated by assimilating the synthetic microstructure data to the 3D-MPF model predictions using the EnKF-based DA method. Furthermore, we accurately reproduced the preliminarily assumed true shapes of GB energy cusp and GB mobility peak by using the estimated parameters. The results suggest that implementation of the EnKF-based DA method in the MPF model has great potential for identifying unknown material properties and estimating unmeasurable microstructure evolutions in polycrystalline materials based on real time-series 3D microstructure observation data.

Atomistic understanding of helium behaviors at grain boundaries in vanadium

Using first-principles calculations, we systematically investigated the interaction of He (helium) with high-angle grain boundaries (GBs) in vanadium alloy. Three representative grain boundaries were examined: Σ3(1 2 1) GB with a compact structure, Σ3(1 1 1) and Σ5(0 1 2) GBs with open structures. Our results reveal that Σ3(1 2 1) GB has higher resistance to He segregation compared with the other GBs, since the segregation energy of He at Σ3(1 2 1) is high and He atoms are hardly trapped. All three GBs can decrease the He diffusivity along GB compared with bulk diffusion in vanadium and provide obstacles for He migration between the GB cavities. For the effect of He on the theoretical tensile strength of GBs, the cohesive strength of V GBs is weaken significantly, especially for Σ3(1 1 1) and Σ5(0 1 2) GBs, which results from that He can deplete considerably the charge density of GB region and weaken the interlayer bonding strength of GBs. It is worth noting that the low content of He (when one atom segregates at GBs) decrease slightly the cohesive strength of Σ3(1 2 1) GB, indicating that Σ3(1 2 1) exhibits better resistance to He-induced GB embrittlement compared with the other GBs. The physical mechanisms involved in He behaviors in the three distinct GBs are discussed in detail.

Slip of shuffle screw dislocations through tilt grain boundaries in silicon

In this paper, molecular dynamics (MD) simulations of the interaction between tilt grain boundaries (GBs) and a shuffle screw dislocation in silicon are performed. Results show that dislocations transmit into the neighboring grain for all GBs in silicon. For Σ3,Σ9 and Σ19 GBs, when a dislocation interacts with a heptagon site, it transmits the GB directly. In contrast, when interacting with a pentagon site, it first cross slips to a plane on the heptagon site and then transmits the GB. The energy barrier is also quantified using the climbing image nudged elastic band (CINEB) method. Results show that Σ3 GB provides a barrier for dislocation at the same level of the Peierls barrier. For both Σ9 and Σ19 GBs, the barrier from the heptagon sites is much larger than the pentagon sites. Since the energy barrier for crossing all the GBs at the heptagon sites is only slightly larger than the Peierls barrier, perfect screw dislocations cannot pile up against these GBs. Furthermore, the critical shear stress averaged over the whole sample for the transmission through the Σ9 and Σ19 GBs is almost twice on heptagon site for initially equilibrium dislocation comparing with dislocations moving at a constant velocity.

Grain-Boundary Shear-Migration Coupling in Al Bicrystals. Atomistic Modeling

The energy of grain boundary shears is calculated for symmetric grain boundaries (GBs) using ab initio methods and molecular-dynamic modeling in order to elucidate mechanisms that control GB shear-migration coupling in typical symmetric GBs, such as Σ3 (111), Σ5 (012), Σ5 (013) and Σ11 (113) tilt GBs, in Al bicrystal. The energy of generalized grain-boundary stacking faults (GB–SF) is determined, and the preferred directions and the energy barrier are established for grain-boundary slippage. It is shown that the relative slippage of neighboring grains at certain directions of particle shears is accompanied by conservative migration of GB in the direction perpendicular to its plain. The modeling data are comparative to known grain-boundary shear-migration coupling mechanisms in Al.

The role of the interface stiffness tensor on grain boundary dynamics

Grain boundary (GB) properties and associated anisotropies due to the boundary's geometric degrees of freedom (DOF) greatly influence many of the salient features of polycrystalline aggregates, and as a consequence the observable properties of the material. Through theoretical analysis and atomistic simulations, we show that when considering the GB plane normal DOF, the GB interface stiffness tensor plays a paramount role in a wide range of GB dynamical processes. As a demonstration, we examine the interface stiffness tensor of Σ3 GBs in nickel and show that the stiffness can be much larger in magnitude and more anisotropic than the GB energy itself. Moreover, it is found that a wide range of inclinations exhibit negative stiffness values, a signature of a structural instability. This is the first study to consider the complete spatial description of the GB stiffness tensor, where both angular variations describing the interface plane normal are explored. In broad terms, our results highlight the integral role that the stiffness tensor plays in GB interfacial phenomena, such as curvature-driven flow and faceting instabilities.