Symmetric 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.

Competitive segregation to grain boundaries between Cr and Co in FeNiCrCo alloy

Alloying elements segregating to grain boundaries (GBs) is vital in determining structural stability and mechanical properties of alloys, especially in high‐entropy alloys (HEAs) that consist of multiple elements. However, some details remain unclear, such as the process of varied atoms (Cr and Co) cosegregation to GBs in FeNiCrCo alloy. Therefore, the competition and cooperation between Fe, Ni, Cr, and Co atoms segregating to GBs of FeNiCrCo alloy were investigated via molecular dynamic (MD) simulation. Five [110] symmetric tilt GBs of FeNiCrCo were applied to study the relation between the tendency of atomic segregation especially Cr and Co and GB characters including GB energy and GB excess free volume (GB excess volume). A competitive segregation phenomenon between Cr and Co atoms was discovered, which could be dominated by GB excess volume and different atomic radii among components.

Grain boundary effects on defect production and damage cascade evolution in SiC/PyC interface: A molecular dynamics study

In this study, molecular dynamics simulations were employed to investigate the effect of symmetrical tilt grain boundaries (STGBs) on the cascade collision evolution at the SiC/PyC interface. We observed that the tilt angle size of grain boundary (GB) spatial structures significantly influences both the type and number of defects caused by primary knock-on atom (PKA) collisions at the interface, altering the cascade damage morphology. Under the PKA range from 1.5[Formula: see text]keV to 15[Formula: see text]keV at 1000[Formula: see text]K, the interplay between GB and interface damage throughout various cascade collision stages impacts defect generation and PKA efficiency. Integrating the analyses of displacement cascade morphology, threshold displacement energy (TDE), and Frenkel pairs (FPs) evolution, it is evident that GBs introduced into the SiC/PyC interface with single crystals exhibit reduced defect absorption efficiency. This implies the existence of competing mechanisms of GB damage and interfacial damage. Notably, the GB plane near the interface exhibits enhanced irradiation resistance and atomic arrangement stability compared to areas without GB. Overall, our results offer crucial insights into the irradiation resistance mechanics of ceramic composite interfaces, laying the groundwork for future studies.

The Pt, Hf dopants in aluminide coating against S impurity: Dependence on grain boundary cohesion and energetic properties

The Pt and Hf additions in aluminide coating can pronouncedly change corrosion resistance against sulfur attack. To provide a comprehensive picture of this issue, by first-principles simulations we study the sulfur-induced embrittlement of ∑5(310)[001] symmetrical tilt grain boundary (STGB) in NiAl, with a focus on roles of Pt, Hf dopants played in sulfur-attacked grain boundary cohesion. The results show that the Hf-doping tends to increase GB combination with larger pre-breaker strength and theoretical tensile strength after sulfur introduction, while Pt-doping hardly makes contribution to the GB mechanical properties. The sulfur-induced embrittlement can be attributed to the charge density depletion and breaking of chemical bonding during stretching process, evaluated by the charge density distributions and bond length analysis. By analyzing the sulfur formation energy at NiAl bulk and NiAl(110) surface, we find that the presence of Pt enhances the energy criterion forming S impurity, while the significant reduction in adsorption energy after Hf-doping results from HfS strong atomic bonding. Alternatively, the existence of Pt decreases probability of S occurrence and becomes the barrier against S invasion. Instead, Hf tightly ‘embraces’ S impurity and impedes its diffusion into depth.

Mobility of screw dislocations absorbed in  symmetric tilt grain boundaries in Al

ABSTRACT The strength and ductility of polycrystalline metals are influenced by the interactions between dislocations and grain boundaries, particularly when the grain size is small. One possible reaction is the absorption of dislocations into the grain boundary structure; however, the mobility of the resulting grain boundary dislocations (GBDs) remains largely unexplored. Thus, the objective of this work is to determine the mobility of GBDs arising from the absorption of lattice screw dislocations into Σ3{111} and Σ11{113} <110> symmetric tilt grain boundaries (STGBs) in Al. Atomistic simulations reveal a reduction in Peierls stress of ∼80% and phonon damping coefficient of ∼65% for GBDs in the {111}<110> STGB compared to lattice screw dislocations. This significant mobility increase is caused by the complete dissociation of the absorbed dislocation. The Peierls stress of GBDs in the {113}<110> STGB is increased to almost 8 times that of the lattice screw dislocation due to the smaller interplanar spacing between slip planes. This work provides a structural justification for the absorption reactions and demonstrates that the mobility of an absorbed dislocation is highly sensitive to the structure of the host grain boundary. Ultimately, mobility laws are provided which can be used to model GBD motion in mesoscale simulations.

The sink efficiency of symmetric tilt grain boundary under displacement cascade in zirconium

Molecular dynamic (MD) simulation was performed to investigate the sink efficiency of [12¯10]symmetric tilt grain boundaries (STGBs) to irradiation point defects in zirconium (Zr). A total of 15 STGBs with the rotation angle ranged from 0 to 90° were studied during displacement cascade. The results show that the sink efficiency to point defects (especially interstitials) of GB is stronger than that of twin boundary (TB), since the atoms at grain boundary dislocations (GBDs) are loosely arranged with high atomic volume to form channels to absorb interstitials. The higher GB energy indicates the lower coherency of GB including more complex GBD structure, thus the GB has a stronger absorption ability to interstitials. The GB migration induced by displacement cascade is mainly attributed to the cavity formed by the remaining vacancies as the interstitials are absorbed and trapped by GBDs. This work provides new insights of relationship between GB sink efficiency and GB characters, which are important for understanding the irradiation effects in Zr alloys.

Temperature effect on the transition between grain boundary migration and sliding

Grain boundary (GB) dynamics plays an important role in the mechanical and physical properties of nanocrystalline metals. In this study, we investigate the temperature effect on GB deformation transition using molecular dynamics simulations of [100] symmetric tilt GBs in Au bicrystals. Different deformation behaviours were revealed in GBs with the same structures at varied temperatures. GB sliding occurs as the predominant deformation mechanism at elevated temperatures, while GB migration dominates at low temperatures. The temperature-dependent critical stresses for GB migration and GB sliding were compared, revealing that temperature alters the critical GB misorientation at which GB migration transitions to GB sliding. Our study provides new insight into GB-mediated plastic deformation in nanocrystalline materials.

Function of cleavage strength for symmetrical tilt grain boundaries

The cleavage strength for grain boundaries (GBs) plays a crucial role in understanding the GBs' behavior and microstructure evolution during deformation. However, its universal discipline remains uncertain, and a quantitative description is currently unavailable. Here we propose the theoretical models to systematically quantify the strength of symmetrical tilt GBs in the discrete atomic perspectives. Specifically, based on the interaction of metallic atomic pairs, the interaction between the arbitrary parallel planes is expressed by considering the atomic pair distribution on both sides of the separated planes. On this basis, the function of GBs’ cleavage strength is proposed by considering that the interaction at GBs is composed of the interaction of the interfaces that make up GBs and the interaction between mirror atomic pairs at both sides of the symmetry plane. Furthermore, the theoretical prediction of the critical energy release rate Gc for the sharp crack extension is proposed based on the present cleavage strength function. All the theoretical models are validated by the ab initio simulations or citations. This work quantitatively proposes the cleavage strength function of symmetrical tilt GBs, predicts the critical energy release rate for cleavage, and provides a new methodology for studying mechanical properties of materials in the discrete atomic perspectives.

Atomistic simulations and machine learning of solute grain boundary segregation in Mg alloys at finite temperatures

Understanding solute segregation thermodynamics is the first step in investigating grain boundary (GB) properties, such as strong yttrium (Y) effects on grain growth and texture evolution in micro-scale polycrystalline magnesium (Mg) alloys. To estimate the average GB segregation behavior in low-solute-concentration Mg alloys (e.g., 2 at.% Y), a state-of-the-art spectral approach is applied based on a per-site segregation energy spectrum for Y solute atoms at zero K obtained from molecular statistics (MS) simulations of ∼104 GB sites in Mg symmetric tilt GBs (STGBs). Although selected MS simulation results are consistent with verification by density functional theory (DFT) calculations, estimates of average segregation tendency based on the zero-K energy spectrum deviate from experimental observations. To resolve this problem, thermodynamic integration (TI) methods based on molecular dynamics (MD) simulations are used to determine the per-site segregation free energies of Y at representative GB sites, which show contributions beyond harmonic approximations can be important for certain GB sites at high temperatures. A surrogate model of per-site segregation free energy is constructed from a small set of TI data points using stacking cross-validation regressors and physics-informed descriptors. This model is applied to predict the Y segregation free energy spectra for thousands of GB sites in Mg STGBs with uncertainty quantification. The average segregation tendency predicted by the spectral approach based on the free energy spectra agrees well (within the uncertainty range) with experimental observations for micro-scale polycrystalline Mg alloys at typical thermomechanical processing temperatures (500 ∼ 800 K), where thermodynamic equilibrium states are likely to be achieved due to fast diffusion.

Effect of helium on thermal transport properties in single- and bi-crystals of Ni: a study based on molecular dynamics

Nuclear structures are prone to irradiation-induced defects that make them susceptible to alternation in mechanical and thermal properties. The transmutation of Ni to insoluble He atoms is considered to be responsible for the embrittlement of Ni. Helium bubbles are deemed responsible for the deterioration of mechanical and thermal properties of the Ni crystal, and this should be studied in detail to predict the lifespan of ageing nuclear structures. The aim of this article is to study the effect of helium on the thermal transport phenomenon in single- and bi-crystals of Ni. Molecular dynamics-based simulations in conjunction with a hybrid force field are performed to study the effect of a helium bubble on the thermal transport phenomenon in Ni crystals. These simulations are further extended to study the impact of symmetrical tilt grain boundaries (STGB) in conjunction with the doping of helium atoms on the thermal transport phenomenon in bi-crystal Ni. The effect of helium concentration in the bubble significantly alters the thermal transport in single-crystal Ni. The STGB configuration also introduces interfacial thermal resistance as a function of the misorientation angle. The helium-doped grain boundaries further increase the resistance to phonon movement and increase Kapitza resistance. The increase in Kapitza resistance is more dominant in higher misorientation angle grain boundaries.

Imaging of atomic stress at grain boundaries based on machine learning

The mechanical behaviors of crystalline materials, in particular the atomic scale deformation and failure processes, are strongly influenced by the local atomic stress near crystalline defects such as vacancies, dislocations and grain boundaries (GBs). Modern electron microscopy techniques have achieved unprecedented capabilities to image the internal microstructure of crystalline materials with atomic resolution. In comparison, our ability to map the corresponding atomic stress field, especially at grain boundaries with complex atomic structures, remains lagging behind due to the lack of direct experimental methods for stress measurement. Here, we propose a machine learning-based framework to realize atomic structure-stress (Atom-S2) mapping based on in situ transmission electron microscopy images. We demonstrate that, with optimized anti-noise performance and generalization ability, the Atom-S2 framework enables quantitative mapping of atomic stress in symmetrical tilt GBs, twin boundaries (TBs) as well as general GBs with changing curvature in crystalline metals. Moreover, the Atom-S2 can help understand, interpret and predict grain boundary stress evolution and plastic deformation mechanisms based on high-resolution transmission electron microscopy images, which provides a powerful tool to study atomic scale deformation behaviors and holds promises for accelerating materials design through defect engineering.

Atomic insights into the effect of rapid heating pretreatment on the mechanical stability of ⟨100⟩ symmetrical tilt GBs in nanocrystalline materials

Nanograined materials possess ultrahigh strength, while their processing and technological applications are constrained by inherent thermal and mechanical instability. Existing experiments show that the stability of Cu nanograins can be enhanced by performing a rapid heating pretreatment that reduces the grain boundary (GB) energy by changing the GB structure. The variation in the GB structure inevitably affects the migration mechanism of GBs. However, the effect of the pretreatment-induced variation in migration mechanisms on stability remains unclear. Here, the shear deformation of a series of ⟨100⟩ symmetrical tilt GBs after rapid heating pretreatment is systematically investigated by molecular dynamics simulations. The simulations of unheated GBs are also included for comparison. Our results show that the rapid heating pretreatment does not improve the mechanical stability of GBs with tilt angles larger than 36.87° but rather enhances the mechanical stability of those with tilt angles less than 36.87° by the transformation of migration behavior from the normal ⟨110⟩ mode to (i) a ⟨100⟩ mode; (ii) an inhomogeneous mixed one that reconciles the ⟨110⟩ and ⟨100⟩ modes; and (iii) an inhomogeneous ⟨110⟩ mode. The former leads to an increase in the critical shear stress that is required to initiate the migration, whereas the latter two result in a decrease in the migration distance. The variation in the GB migration mechanism is attributed to the change in the GB structure from an ordered kite structure to a disordered one. The research gives an atomic insight into the stabilizing mechanism of nanocrystalline materials with rapid heating pretreatment.

First-principles study of oxygen segregation and its effect on the embrittlement of molybdenum symmetrical tilt grain boundaries

Elemental segregation can pronouncedly affect the cohesion of grain boundary (GB), which shows tremendous potential in altering the thermal stability and mechanical properties of metals. In this work, we systematically investigate the segregation behavior of oxygen (O) atoms at a series of GBs in molybdenum (Mo), using first principles calculations, to reveal the effect of O segregation on the embrittlement of Mo GBs. It is found that O atoms energetically prefer to segregate at sites in both the GB core and the vicinity of the GB plane. The strengthening energy is strongly associated with the GB structure, and it linearly decreases with the continuous deformation of the GB. O segregation can lead to an increase in the volume of polyhedron sites and a decrease in the charge density among adjacent Mo atoms across the GB plane. The weakened Mo-Mo bonds are believed to disrupt the GB cohesion, thereby increasing the intergranular cleavage tendency of Mo. Interestingly, O segregation does not always trigger GB embrittlement. The Σ5(310)[001] symmetric tilt grain boundary (STGB) with an O atom doped at the cap trigonal prism (CTP) site possesses a strength as strong as the clean GB. O segregation promotes the generation of Mo-O bonds across the GB plane, which counteracts the adverse effect of weakened Mo-Mo bonds. This work deepens the understanding of the possible effect of O segregation on GB cohesion of Mo from the atomic and electronic scales, providing guidance for enhancing the mechanical properties of Mo via GB structure optimization.

Effect of solute atoms segregation on Al grain boundary energy and mechanical properties by first-principles study

First-principles calculations were carried out to study the segregation behavior of Mg, and Cu and their effect on the energy and mechanical properties of different Al grain boundaries (GBs). Four symmetrical tilt GBs were selected for study, namely Σ5[001](210) GB, Σ5[001](310) GB, Σ9[110](221) GB, and Σ11[110](332) GB. The results show that both Mg and Cu have a segregation tendency at the GBs, and the segregation tendency of Cu is stronger than Mg. Mg is prone to form substitutional segregation at the GBs, but Cu is more likely to segregate at the interstitial sites. The segregation of Mg and Cu can reduce GB energy, and the GB energy continues to decrease with the increase of the segregation concentration. First-principles calculation tensile test shows that the segregation of Mg has a negative effect on the strength of GBs, and the GB strength decreases with the increase of the Mg concentration, while the GB strength was gradually enhanced with the increase of the Cu concentration. The strength of Σ5(210) GB and Σ9(221) GB are more sensitive to the segregation of solute atoms than the other two GBs. By calculating the charge density and the density of states of the pristine and the segregated GBs, it was found that the segregation of Mg caused charge depletion and structure expansion at the GBs, while the segregation of Cu increases the charge density of GBs and form new bonds with the surrounding Al atoms. The results provide useful information for improving the mechanical properties of materials by using the concept of GB segregation engineering.

Ab initio calculations and empirical potential assessments of the energy and structure of symmetric tilt grain boundaries in tungsten

Molecular statics/dynamics (MS/MD) based on empirical interatomic potentials (IAPs) is an effective means for conducting grain boundary (GB) related studies. The accuracy of these MS/MD simulations, however, can be greatly affected by the IAP used. Unfortunately, the large discrepancies between the ab-initio values make it difficult to evaluate, improve and further develop IAPs. Motivated by this issue, in the present work we perform a systematic investigation of 〈100〉 and 〈110〉 symmetric tilt GBs in tungsten (W) via atomistic simulations, including the stable structure, GB energy, work of separation, excess volume, and vacancy formation energy. We here use a two-step relaxation process, initially obtaining the candidate structures from MS and then performing DFT validation of these structures to determine the ground state structure, where six empirical IAPs and four exchange–correlation (xc) functionals are used. And the step-like feature is revealed that can be used to reduce the cost of time-consuming optimization processes. Taking the results yielded by PBEsol xc-functional as a benchmark, it is shown that for the same xc-functional, the relative errors of GB energy and work of separation are almost identical, independent of the GB character. The performance of six typical empirical IAPs considered for W is also evaluated by comparing it with the DFT data. The quantities chosen for the comparison include the structure and energetic properties of GBs, as mentioned before. We demonstrate that these empirical IAPs tend to better describe only part of the properties of GBs; for example, some IAPs can predict the energetic properties well, while others can better describe the structure. This suggests that a fully reliable description of GBs remains an elusive objective, requiring further efforts in the development and optimization of the IAP.

Convection-Induced Compositional Patterning at Grain Boundaries in Irradiated Alloys.

We consider the stability of precipitates formed at grain boundaries (GBs) by radiation-induced segregation in dilute alloys subjected to irradiation. The effects of grain size and misorientation of symmetric-tilt GBs are quantified using phase field modeling. A novel regime is identified where, at long times, GBs are decorated by precipitate patterns that resist coarsening. Maps of the chemical Péclet number indicate that arrested coarsening takes place when solute advection dominates over thermal diffusion right up to the precipitate-matrix interface, preventing interfacial local equilibrium and overriding capillary effects. This contrasts with liquid-solid mixtures where convection always accelerates coarsening.

Anharmonicity in grain boundary energy for Al: Thermodynamic integration with artificial-neural-network potential

Anharmonicity in grain boundary (GB) energies for Al is elucidated by employing a thermodynamic integration method with a high-accuracy artificial-neural-network potential. Symmetric tilt GBs with the [001] and [11¯0] rotational axes are examined. It is found that anharmonic components tend to be small at low temperatures and increasingly contribute to reduction of GB free energies at elevated temperatures. The magnitude of anharmonicity is roughly correlated with excess volume at GBs. This is presumably because GB atoms tend to have longer bond lengths than the bulk atom, and hence the inclination of the potential energy surface at GBs is more moderate than in the bulk. On the other hand, the Σ13(510) GB takes non-negligible values of the anharmonic component even at intermediate temperatures. This GB contains a distinct atom around which the potential-energy curve significantly deviates from that of the harmonic approximation. Similar trends are also observed for other [001] GBs.

The surface and grain boundary properties of uranium boride: A DFT calculation

Uranium borides are currently being investigated as an accident tolerance fuel or advanced technology fuels (ATFs) to replace conventional UO2 fuel due to their high uranium density and high thermal conductivity. The surface properties of diverse facets of a crystal are pivotal for understanding different corrosion behaviors, fission gas bubble behaviors, and equilibrium morphologies. In this study, we employ density functional theory (DFT) calculations to investigate the surface properties of uranium borides. The surface orientations with maximum miller index up to 4, 1, and 2 for UB2, UB4 and UB12 were analyzed, respectively. Based on the calculated surface energies, the other surface properties of uranium borides were obtained through Wulff construction, including equilibrium morphology, dominant surface orientations, area-weighted surface energy and work function. Additionally, grain boundaries (GBs) have a significant impact on material properties, such as mechanical properties, corrosion behavior, and resistance to irradiation. Therefore, we use DFT calculations to determine the GB energies and work of separation for three low-Σ (7) symmetrical tilt GBs (STGB) and two twist GBs (TGB).

Interactions between displacement cascades and grain boundaries in NiFe single-phase concentrated solid solution alloys

Single-phase concentrated solid solution alloys (SP-CSAs) are promising structural materials with excellent irradiation resistance. It is very important for their application in nuclear reactor structures to understand the interactions between their grain boundaries (GBs) and irradiation-induced defects. With molecular dynamics (MD) simulations, the displacement cascades in NiFe SP-CSAs with Σ5(210) symmetrical tilt GB were studied. Compared with pure Ni, NiFe has higher sink strength of GB for vacancies but has little effect on the interstitial absorption of GB. The formation energies of interstitials and vacancies near the GB are more dispersed, so that the point defects are more difficult to aggregate, which is beneficial for the recombination of interstitials and vacancies near the GB. Both the formation energies of point defects and the sink strengths of GB for point defects could be changed with the SP-CSA compositions. When the Fe atom concentration is higher than 30 at.%, the point defects are easier to annihilate. Both the effects of the PKA energy and the PKA-GB distance on the displacement cascades damage can be explained with the size of overlapping region between the cascade region and GB. In addition, the formation of SP-CSAs helps to annihilate the vacancies in NiFe with Σ37(750) symmetrical tilt GB and Σ5 twist GB.

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.