Grain Boundary Model Research Articles

Ion Migration at Metal Halide Perovskite Grain Boundaries Elucidated with a Machine Learning Force Field.

Metal halide perovskites are promising optoelectronic materials with excellent defect tolerance in carrier recombination, believed to arise largely from their unique soft lattices. However, weak lattice interactions also promote ion migration, leading to serious stability issues. Grain boundaries (GBs) have been experimentally identified as the primary migration channels, but the relevant mechanism remains elusive. Using molecular dynamics with a machine learning force field, we directly model ion migration at a common CsPbBr3 GB. We demonstrate that the as-built GB model, containing 6400 atoms, experiences structural reconstruction over several nanoseconds, and only Br atoms diffuse after that. A fraction of Br atoms near the GB either migrate toward the GB center or along the GB through different migration channels. Increasing the temperature not only accelerates the ion migration via the Arrhenius activation but also allows more Br atoms to migrate. The activation energies are much lower at the GB than in the bulk due to large-scale structural distortions and favorable non-stoichiometric local environments available at GBs. Making the local GB composition more stoichiometric by doping or annealing can suppress the ion migration. The reported results provide valuable atomistic insights into the GB properties and ion migration in metal halide perovskites.

Microscopic examination of rf-cavity-quality niobium films through local nonlinear microwave response

The performance of superconducting radio-frequency (SRF) cavities is sometimes limited by local defects. To investigate the rf properties of these local defects, especially those that nucleate rf magnetic vortices, a near-field magnetic microwave microscope is employed. Local third-harmonic response (P3f) and its temperature dependence and rf power dependence are measured for one Nb/Cu film grown by direct current magnetron sputtering (DCMS) and six Nb/Cu films grown by high-power impulse magnetron sputtering (HiPIMS) with systematic variation of deposition conditions. Five out of the six HiPIMS Nb/Cu films show a strong third-harmonic response that is likely coming from rf vortex nucleation due to a low-Tc surface defect with a transition temperature between 6.3 and 6.8 K, suggesting that this defect is a generic feature of air-exposed HiPIMS Nb/Cu films. A phenomenological model of surface-defect grain boundaries hosting a low-Tc impurity phase is introduced and studied with time-dependent Ginzburg-Landau (TDGL) simulations of probe-sample interaction to better understand the measured third-harmonic response. The simulation results show that the third-harmonic response of rf vortex nucleation caused by surface defects exhibits the same general features as the data, including peaks in third-harmonic response with temperature, and their shift and broadening with higher microwave amplitude. We find that the parameters of the phenomenological model (the density of surface defects that nucleate rf vortices and the depth an rf vortex travels through these surface defects) vary systematically with film deposition conditions. From the point of view of these two properties, the Nb/Cu film that is most effective at reducing the nucleation of rf vortices associated with surface defects can be identified. Published by the American Physical Society 2024

Revealing the intergranular corrosion mechanism of AA5083 alloys through experiments and atomic-scale computation

Continuously exposure to elevated temperature, known as sensitization, can accelerate the precipitation of the electrochemically active β phase (Al3Mg2) at grain boundaries (GBs) in Al-Mg alloys. This results in intergranular corrosion (IGC), which seriously affects the application of Al-Mg alloys in marine environments. Low-angle GBs (< 15°) are considered to restrict the nucleation and growth of the β phase, while high-angle GBs (> 15°) can promote these processes. However, the quantitative relationship between GB misorientation and IGC sensitivity at atomic scale is unknown. Herein, the underlying mechanism of IGC in AA5083 alloys with β phase and GB misorientation is investigated by experiments and simulation. The experimental results show that after sensitization when the misorientation angle exceeded 22.6°, the density of the β phase at GBs reaches up to 50 %–60 %. The hybrid molecular dynamics/Monte Carlo algorithm was utilized to simulate the diffusion of Mg and cluster formation in Al-5Mg alloy with 11 different GB models at 300 and 425 K. The maximum GB misorientation angle insensitive to IGC is about 18.9° to 22.6°. However, at 425 K, this angle decreases to 16.3°, increasing the IGC risk of Al-5Mg alloys. The calculation results provide valuable quantitative guidance for the corrosion resistance design of Al-Mg alloys.

Particle pinning during grain growth—A new analytical model for predicting the mean limiting grain size but also grain size heterogeneity in a 2D polycrystalline context

This study proposes a new analytical model for grain boundary pinning by second phase particles in two-dimensional polycrystals. This approach not only considers how particles impede grain growth, but also elucidates their role in preventing grain disappearance, thereby leading to stabilised microstructures characterised by heterogeneous grain size distribution comprising a mixture of small and large grains. By quantifying the number of particles intercepted by grain boundaries during grain growth or shrinkage, we are able to calculate the respective sizes and fractions of large and small grains. Furthermore, we identify ranges of particle surface fractions and particle sizes that maximise the heterogeneity in grain size. Additionally, we demonstrate the significant influence of initial grain size on the limiting grain size in pinned microstructures. Our analytical model’s results are compared with those obtained from full-field level-set simulations conducted in this study and from phase-field calculations reported in the literature, revealing very good agreement. Finally, the differences between the proposed model and existing ones in the literature are discussed.

Investigation on failure characteristics of mode II crack in heat-treated granite specimen subjected to dynamic loading

In order to solve the energy crisis, geothermal energy development has been increasingly valued in recent years. In many geothermal engineering projects, hydraulic fracturing can cause many cracks to appear inside the rock mass during the extraction process of dry hot rock. At present, there have been many studies on mode I cracks and mixed mode I/II cracks. In order to ensure the smooth progress of the project, it is necessary to supplement the research on mode II crack rocks in high-temperature geothermal environments. A series of experiments were conducted using the Split Hopkinson Pressure Bar (SHPB) device and cracked granite specimens treated at different temperatures, the failure modes could be tracked by using a high-speed camera. The dynamic experiment was simulated using software coupling. The Grain Boundary Model (GBM) can well describe the force-thermal coupling damage behavior among various crystal particles. Some analyses were conducted on dynamic fracture toughness, failure mode, strain distribution, thermal damage, and changes in the number of cracks. The research results illustrated that high temperatures lead to a decrease in the mode II fracture toughness of granite, an increase in fracture time, and greater susceptibility to damage. High temperature will increase the maximum strain at the moment of failure. It was also found that the proportion of intra-grain cracks increased with the temperature. After 500 °C, the number of cracks generated during the fracture process is inversely proportional to the temperature.

Effects of grain boundaries and quasi-plastic deformation in shocked bi-crystal boron carbide nanopillars

Grain boundaries (GBs) significantly affect the mechanical properties of ceramics, but they are understudied. Here, we employ three bi-crystal boron carbide nanopillars to investigate the effect of GBs on the shock behaviors and deformation mechanisms of B4C, using molecular dynamics simulations with a reactive force field. The results reveal a strong correlation among the shock behaviors, interfacial energies, and grain orientations. The (11¯02)/(1¯101) model with the highest interfacial energy model shows intragranular amorphization due to the interaction between the softened GB and the unfavorable orientation of the grain, while the other two GB models experience intergranular amorphization. Furthermore, the quasi-plastic behaviors in the three models arise from GB rotation or GB sliding. The US-UP relationships of quasi-plastic waves exhibit a bilinear relationship due to the intergranular amorphization formation. Noteworthy, this bilinear behavior for the (11¯02)/(1¯101) model displays a second kink, corresponding to the formation of intragranular amorphization. This study serves as a reference for designing ceramics with superior properties.

A Conservative and Efficient Model for Grain Boundaries of Solid Electrolytes in a Continuum Model for Solid-State Batteries

Abstract A formulation is presented to model ionic conduction efficiently inside, i.e., across and along grain boundaries. Efficiency and accuracy are achieved by reducing it to a two-dimensional manifold while guaranteeing the conservation of mass and charge at the intersection of multiple grain boundaries. The formulation treats the electric field and the electric current as independent solution variables. We elaborate on the numerical challenges this formulation implies and compare the computed solution with results from an analytical solution by quantifying the convergence towards the exact solution. Towards the end of this work, the model is first applied to setups with extreme values of crucial parameters of grain boundaries to study the influence of the ionic conduction in the grain boundary on the overall battery cell voltage and, secondly, to a realistic microstructure to show the capabilities of the formulation.

Highly reliable and large-scale simulations of promising argyrodite solid-state electrolytes using a machine-learned moment tensor potential

The high ionic conductivity of argyrodite makes it an attractive candidate for solid-state electrolytes (SSEs) in all-solid-state Li-ion batteries (ASSBs). Although great effort has been devoted to using ab initio molecular dynamics (AIMD) to evaluate ionic conductivity and elucidate the Li-ion diffusion mechanism of argyrodite-based SSEs, limitations in system size, simulation temperatures, and time associated with AIMD make accurate predictions and analysis of Li-ion diffusion challenging. Here, we present a reliable, large-scale computational approach to realistic simulation of SSEs in the bulk and at the grain boundary (GB) based on moment tensor potentials (MTPs) trained at the van der Waals optB88 level of theory. MTPs enable sufficiently large-scale and long-time simulations that reflect all possible configurational disorder of experimental crystal structures and provide accurate ionic conductivities that are close to values measured experimentally in halogenated Li-argyrodite (Li6PS5X [X = Cl, Br, I]). Our simulations show that the vibrational motion of a PS4 polyhedron has a positive effect on ionic conductivity. We also developed an accurate MTP using an active-learning approach to exploring Li-ion diffusion at the GB in polycrystalline SSEs. Simulations of the molecular dynamics of large ∑5100021 (>10,000-atom) GB models reveal that Li-ion accumulation around the GB region retards ionic conductivity and extends into an interior region approximately 20 Å from the GB interface. This work provides a practical approach to realistic large-scale and interfacial GB simulations that are otherwise inaccessible through ab initio calculations by developing accurate machine-learned MTPs.

In-situ investigation of tensile anisotropy mechanism in an advanced Ti2AlNb-based alloy associated with CRSS ratio and damage model

Combined with in-situ tensile test and electron backscatter diffraction technology, the critical resolved shear stress (CRSS) ratio of O phase and the damage model of grain boundaries were proposed to reveal the tensile anisotropy mechanism of Ti–22Al–25Nb alloy isothermally forged in B2 phase region. In-situ observation suggests that the single slip mode of lamellar O phase is the major deformation behavior, and its preferential slip dominates the yield of the material. Based on the types, number, Schmid factor (SF) and orientation of slip activation, the CRSS ratio of basal <a>, prism <a>, first-order and second-order pyramidal <c+a> slips for O phase is estimated to be 1.19: 1: 1.37: 1.39. Meanwhile, basal and prism <a> slips mainly appear the radial and axial directions (RD and AD) samples with [012] and [100] texture, while the [001], [010] and [212] texture of OD (45° to RD) sample shows an increase in pyramidal <c+a> slips. Thus, the slip activation of O phase depends on the grain orientation and CRSS, resulting in significant strength anisotropy. Furthermore, the microcracks and secondary cracks at grain boundaries are significantly affected by the slip accumulation of lamellar O phase at the O/O and O/B2 interfaces. Considering the stress state of the grain boundary, a damage model about crack nucleation and propagation is proposed to explain the ductility anisotropy. From this, the RD sample has a higher crack nucleation and propagation resistance than the AD and OD samples due to the flattened morphology of B2 grains.

Pathways of hydrogen atom diffusion at fcc Cu: Σ9 and Σ5 grain boundaries vs single crystal

The diffusion of H-atoms is relevant for innumerous physical–chemical processes in metals. A detailed understanding of diffusion in a polycrystalline material requires the knowledge of the activation energies (ΔEa’s) for diffusion at different defects. Here, we report a study of the diffusion of H-atoms at the Σ9 and Σ5 grain boundaries (GBs) of fcc Cu that are relevant for practical applications of the material. The complete set of possible diffusion pathways was determined for each GB and we compared the ΔEa at bulk fcc Cu with the landscape of ΔEa’s at these defects. We found that while a number of diffusion pathways at the GBs have high tortuosity, there are also many paths with very low tortuosity because of specific structural features of the interstitial GB sites. These data show that the diffusion of H-atoms at these GBs is highly directional but can be fast because at certain paths the ΔEa can be as low as 0.05 eV. The lowest energy paths for diffusion of H-atoms through the whole GB models are ΔEa = 0.05 eV for the Σ9 and ΔEa = 0.20 eV at Σ5 which compare with ΔEa = 0.42 eV for the bulk fcc crystal. This shows that H-atoms will be able to diffuse very fast at these defects. With the Laguerre–Voronoi tessellation method, we studied how the local atomic structure of the interstitial sites of the GBs leads to different ΔEa’s for diffusion of H-atoms. We found that the volume expansions and the coordination numbers alone cannot account for the magnitude of the ΔEa’s. Hence, we developed a symmetry quantifying parameter that measures the deviation of symmetry of the GB sites from that of the bulk octahedral site and hence accounts for the distortion at the GB site. Only when this parameter is introduced together with the volume expansions and the coordination numbers, it is possible to correlate the local structure with the ΔEa’s and to obtain descriptors of diffusion. The complete set of data shows that the extrapolation of diffusion data for H-atoms between different types of GBs is non-trivial and should be done with care.

Going against the Grain: Atomistic Modeling of Grain Boundaries in Solid Electrolytes for Solid-State Batteries.

Atomistic modeling techniques, including density functional theory and molecular dynamics, play a critical role in the understanding, design, discovery, and optimization of bulk solid electrolyte materials for solid-state batteries. In contrast, despite the fact that the atomistic simulation of microstructural inhomogeneities, such as grain boundaries, can reveal essential information regarding the performance of solid electrolytes, such simulations have so far only been limited to a relatively small selection of materials. In this Perspective, the fundamental properties of grain boundaries in solid electrolytes that can be determined and manipulated through state-of-the-art atomistic modeling are illustrated through recent studies in the literature. The insights and examples presented here will inspire future computational studies of grain boundaries with the aim of overcoming their often detrimental impact on ion transport and dendrite growth inhibition in solid electrolytes.

Grain boundaries boost the prelithiation capability of the Li2CO3 cathode additives for high-energy-density lithium-ion batteries

Due to high theoretical capacity, Si anodes have attracted tremendous attention. Nevertheless, huge volume change during cycling together with large lithium loss substantially hinders their large-scale application. Prelithiation has emerged as a highly attractive strategy to compensate for the loss of active lithium. Li2CO3, which is ambient stable and delivers more than 5 times the theoretical capacity of the existing cathode materials, serves as an excellent cathode prelithiation additive. However, the practical application of Li2CO3 is limited by its sluggish charge transport and high critical decomposition potential. Herein, we report a facile route to fabircating nanosized Li2CO3 (N-Li2CO3) materials enriched with grain boundaries (GBs). First-principles investigations reveal that the Li-ion transport behavior is dependent on the concentration of GBs. The Σ(001) GB model exhibits higher Li-ion and electronic conductivities compared to those of the bulk counterpart. As a result, the ∼ 100 % capacity utilization of N-Li2CO3 with a delithiation capacity of 724 mAh/g is obtained, which is much higher than that of commercial Li2CO3 (115 mAh/g), greatly enhancing the reversible capacity, energy density and lifetime of the LiNi0.5Co0.2Mn0.3O2//Si-graphite full cell. These findings provide valuable understanding of the role of GBs and the correlation between microstructure engineering and performance optimization.

Understanding the Effect of Grain Boundaries on the Mechanical Properties of Epoxy/Graphene Composites.

This work presents a molecular dynamics (MD) simulation study on the effect of grain boundaries (GBs) on the mechanical properties of epoxy/graphene composites. Ten types of GB models were constructed and comparisons were made for epoxy/graphene composites containing graphene with GBs. The results showed that the tensile and compressive behaviors, the glass transition temperature (Tg), and the configurations of epoxy/graphene composites were significantly affected by GBs. The tensile yield strength of epoxy/graphene composites could be either enhanced or weakened by GBs under a tensile load parallel to the graphene sheet. The underlying mechanisms may be attributed to multi-factor coupling, including the tensile strength of the reinforcements, the interfacial interaction energy, and the inflection degree of reinforcements. A balance exists among these effect factors, resulting in the diversity in the tensile yield strength of epoxy/graphene composites. The compressive yield strength for epoxy/graphene composites is higher than their counterpart in tension. The tensile/compressive yield strength for the same configuration presents diversity in different directions. Both an excellent interfacial interaction and the appropriate inflection degree of wrinkles for GB configurations restrict the translational and rotational movements of epoxy chains during volume expansion, which eventually improves the overall Tg. Understanding the reinforcing mechanism for graphene with GBs from the atomistic level provides new physical insights to material design for epoxy-based composites containing defective reinforcements.

An Overview of the Effect of Grain Size on Mechanical Properties of Magnesium and Its Alloys

Recent studies show significant advances in improving the mechanical properties of magnesium and its alloys. While many papers deal with different alloy compositions, it is apparent that grain size plays a key role in the mechanical behavior of these materials. The ability to produce samples with very fine grain sizes leads to observations of high strength and/or high elongations. There are recent reports of exceptional elongations of over 100% in pure magnesium and a few alloys. These recent findings are critically reviewed in the present study. The experimental data from over 300 papers are collected, and trends between flow stress, elongation, strain rate sensitivity, and grain size are identified. The role of alloy content is examined. The data clearly shows a transition in the flow stress vs. grain size relationship which is attributed to a change in deformation mechanism from twinning controlled in coarse grained to slip controlled in fine and ultrafine grained samples. The slip controlled deformation agrees with the model of grain boundary sliding, which has shown good agreement with multiple metallic materials. It is shown that the elongations display a maximum in the grain size range in which there is a transition in the deformation mechanism. Three strategies are described for achieving high strength, high ductility, and good strength-ductility combination.

Theory of Josephson current on a lattice model of grain boundary in d-wave superconductors

Identifying the origins of suppression of the critical current at grain boundaries of high-critical-temperature superconductors, such as cuprates and iron-based superconductors, is a crucial issue to be solved for future applications with polycrystalline materials. Although the dominant factor of current suppression might arise during material fabrication and/or processing, investigating it due to an internal phase change of the pair potential is an important issue in understanding the threshold of the critical current. In this paper, we study the Josephson current on a symmetric [001]-tilt grain boundary (GB) of a d-wave superconductor on a lattice model. In addition to the suppression of the maximum Josephson current associated with the internal phase change of the d-wave pair potential which has been predicted in continuum models, we find a unique phase interference effect due to folding of the Fermi surface in the lattice model. In particular, the resultant maximum Josephson current at low-tilting-angle regions tends to be suppressed more than that in preexisting theories. Because similar suppressions of the critical current at GBs have been reported in several experimental works, the present model can serve as a guide to clarify the complicated transport mechanism in GBs.

Ferroelectric domain switching pathways—From grain boundary to grain body

Grain boundaries (GBs) are one of the main factors influencing the polar domain evolution of polycrystalline ferroelectrics. However, domain switching from GBs to grains remains an unsolved aspect. Previous microscopic GB assumptions hinder such theoretical investigations, assuming that the structure and properties of GB are independent of the misorientation of adjacent grains. This work investigates the competition between the energy densities and domain-switching pathways based on the formation mechanism of the GB model. It is found that the domain-switching pathways in polycrystalline ferroelectrics follow three rules: (1) domain switching occurs near low-energy-density GBs; (2) the development of domain-switching pathway originates near the low-energy-density GBs. This pathway ultimately influences the overall domain-switching process, which follows the energy minimization principle; and (3) the domain-switching trend expands to both sides of the pathways after complete formation. The domain evolution rules for polycrystalline ferroelectric materials proposed in this work are conducive to improving the performance of ferroelectric ceramics via GB engineering.

Analysis of grain-boundary segregation of hydrogen in bcc-Fe polycrystals via a nano-polycrystalline grain-boundary model

Hydrogen embrittlement caused by hydrogen segregation at grain boundaries (GBs) is the most serious issue in the development of high-strength steels, but the mechanisms behind this process are still not well understood. The GB segregation behavior of hydrogen in body-centered cubic (bcc)-Fe polycrystals was comprehensively analyzed based on the interatomic potentials derived from first-principles calculations. Considering that the atomic structure of GBs is almost independent of the grain size, the GBs in polycrystals were modeled as nano-polycrystalline GBs with random orientations. The segregation energies of hydrogen for ∼17 million interstitial sites in this GB model were calculated. From these segregation energies, the effective segregation energy for the polycrystalline GB at thermal equilibrium under various temperature and hydrogen content conditions were determined, and the validity of the calculation method was verified by comparing the results with experimental data. The relationship between the segregation energy of hydrogen at each segregation site and the surrounding local atomic environment was used to identify the major hydrogen segregation sites at the atomic level, and the changes in the crystal structure near the GB that dominated segregation were clarified. The effective segregation energies at the polycrystalline GBs were in the range of −0.48 to −0.42 eV, which are in good agreement with the experimentally reported binding energy of hydrogen at GBs of bcc-Fe polycrystals (−0.52 eV). The major hydrogen segregation sites were octahedral sites with Voronoi volumes larger than 7.0 Å3, and the segregation energy was mainly due to the uniaxially distorted crystal structure in the short-axis direction of octahedral sites. Our findings and the developed calculation method contribute to the understanding of the hydrogen segregation behavior and hydrogen embrittlement mechanism in polycrystalline metallic materials.

Electromechanical grain boundary model with formation mechanism in polycrystalline ferroelectrics

Grain boundaries (GBs) are transitional, defective, and anisotropic interfaces between adjacent grains with different orientations. However, most models assume that the GB is an isotropic dielectric determined by itself and lacks formation information; these assumptions hinder the theoretical investigation of the effect GBs have on polycrystalline ferroelectrics at the mesoscopic scale. Here, a novel GB model based on the formation mechanism is established for ferroelectric polycrystals. It has been found that the Curie–Weiss temperature range, elastic coefficient, and permittivity of GBs are related to the orientation of adjacent grains and the polarization state. The shielding effect, polarization enhancement, domain continuity, and spontaneous polarization on the GBs are obtained in mesoscopic simulations based on this model. In addition, the proportion of GBs can significantly affect the electric field distribution in grains. It provides a mechanistic explanation for the relationship between the coercive electric field and the proportion of GBs in the previous experiment. By achieving a better mesoscopic description of GBs, the GB model proposed in this work provides an effective investigation tool for electromechanical, electrocaloric, and energy storage of polycrystalline functional materials.

Fatigue crack propagation across grain boundary of Al-Cu-Mg bicrystal based on crystal plasticity XFEM and cohesive zone model

In this paper, a methodology integrating crystal plasticity (CP), the eXtended finite element method (XFEM) and the cohesive zone model (CZM) is developed for an Al-Cu-Mg alloy to predict fatigue crack propagation (FCP) across grain boundary (GB) of Al-Cu-Mg alloy during stage ІІ. One GB model is incorporated into FCP constitutive law to describe grain interaction at GB. A bicrystal containing GB is built up to simulate FCP behavior through L participated GBs. Modelling features including GB characteristic, cumulative plastic strain (CPS) distribution and crystal slipping evidence can be identified. The numerical results are compared with published experimental data to check the accuracy of model. This work demonstrates that the combination of CP containing GB constitutive laws, XFEM and CZM is a promising methodology in predicting twist angle-controlled crack deflection through GBs.

Thermal ridges – Formation of hillock-like structures in deformed bulk nickel

The effect of surface topography on grain boundary migration has been the focus of numerous studies due to its importance for microstructure evolution in thin films. In this work we have studied grain boundaries in samples of pure bulk Ni after mild cold deformation and a subsequent anneal. The surface topography in the vicinity of grain boundaries featured large protrusions formed during the anneal with a striking resemblance to downscaled terrestrial mountains. We coined the term 'thermal ridges' to describe these protrusions. Their size decreases with increasing annealing time and degree of deformation. We developed a kinetic model of ridges based on the original Mullins’ model of mobile grain boundary grooves modified to account for high surface anisotropy. The combination of our experimental and modeling results sheds new light on the phenomenon of hillock formation in thin polycrystalline films.