Tilt Grain Research Articles

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.

STUDY OF THE TEMPERATURE DEPENDENCE OF THE SYMMETRICAL GRAIN BOUNDARY ENERGIES ON THE PLANE (110) IN ALUMINUM

In this work the energy of symmetric tilt and twist grain boundaries in the range of grain misorientation angles from 0 to 180◦ and temperatures from 100 to 700 K in pure aluminum is investigated. The bicrystal systems with different grain tilt/twist angles are maintained at constant temperatures of 100, 400, or 700 K by molecular dynamic method and the energy of each grain boundary is calculated. The results show that the minimum grain boundary energy decreases as the temperature increases from 100 to 400 K; but the energy may decrease, remain practically unchanged, or even increase with further heating to 700 K. The average grain boundary energy obtained by averaging the energies of the resulting grain boundary structure variations at constant temperature grows with increasing temperature from 100 to 700 K for random boundaries with initially high energies. In the case of special grain boundaries with small Σ values, the average energy will be practically unchanged. To describe the continuous energy dependence of symmetric tilt and twist boundaries on temperature, an approximation by an forward propagation of artificial neural network is proposed. The neural network is trained and tested on atomistic simulation data and shows high predictive ability on test data and to describe the boundary energy in the temperature range from 100 to 700 K.

Mechanics and Energetics of Kink Deformation Studied by Nonlinear Continuum Mechanics Based on Differential Geometry

This study conducts dislocation-based modeling and numerical analysis for kink deformation using the theory of nonlinear continuum mechanics based on differential geometry. The kinematics of the continuum is represented by the reference, intermediate, and current states, which are related to the multiplicative decomposition of the deformation gradient into plasticity and elasticity. The intermediate state is determined by the Cartan first structure equation, whereas the current state is obtained from the stress equilibrium equation. Kink deformation is modeled by a planar array of edge dislocations, and the governing equations are solved numerically using the finite element method. Quantitative verification of the model is conducted by comparing the bending angle at a kink interface and the theoretical prediction given for the tilt grain boundary. We construct two types of ortho-type kink models for several interface lengths to understand the energetics and mechanics of the kink growth process. The present numerical analysis demonstrates the significant stress concentration at the growth front due to the formation of wedge disclination. We also discuss the material strengthening mechanism from elastic strain energy, nonsingular stress fields, and nonlinear elastic interaction between the disclinations.

Revealing the influence of solute segregation on the stability and strength of Cu Σ11 [110](113) symmetrical tilt grain boundary via first-principles investigation

The stability and strength of the grain boundary (GB) structure are critical for the practical application of nanocrystals. This study systematically calculates the impact of the segregation of 26 transitional alloy elements on Cu Σ11 [110](113) GB using the first-principle theoretical calculation method. The research findings demonstrate that there is a parabolic connection between atomic number and segregation energy of TM elements in the same period. In addition to Fe, Co, and Ni, all other 23 elements have the potential to segregate to Cu GB, with Zr exhibiting the strongest segregation tendency. The difference in atomic radius and electronegativity between solute atoms and copper atoms strongly affects the segregation tendency, the greater the difference, the greater the tendency for segregation. The segregation energy of solute segregation has strong linear correlation with its GB energy, and the stronger the segregation ability, the more stable the GB. Except for Zn, Ag, Cd, and Au, other 19 alloying elements can increase the strength of GB. Electronic analysis indicates that the strengthening and embrittlement of solutes are primarily related to the accumulation and consumption of electrons near GB and the bonding between atoms.

Density functional study of atomic arrangements in CrMnFeCoNi high-entropy alloy and their impact on vacancy formation energy and segregation

Using the density functional theory-coupled Monte Carlo approach, we explored the chemical short-range order (SRO) and element segregation in equimolar CrMnFeCoNi alloy. We found that state-of-the-art approximation of random element distribution is only applicable at > 1100 K close to the melting temperature, while the Cr-Cr repulsion driving the system stabilization and accompanying the formation of cubic Cr sublattice, and mild Ni-Ni attraction are the most prominent pair interactions at lower temperatures. Chemical potential and vacancy formation energy calculations indicate that Cr is most sensitive to the local chemical environment, making Cr atoms most stabilized when the preferred SRO is introduced. While the vacancy formation is predicted equally probable among five constituting elements in the random solid solution, Cr and Ni atoms show the lowest vacancy formation energies in the structure with SRO. Furthermore, distinct element segregation was predicted in the vicinity of planar defects, including symmetric tilt grain boundary and stacking fault, which we correlated to the site- and chemistry-dependent atomic volume and bond lengths. It suggests that the local mechanical strain and bond energy induce the SRO development and element segregation: Namely, the system takes advantage of segregation of Ni atoms having large atomic volume or Cr-Cr pairs having elongated bond lengths to fill in the excess volume at defects that relaxes the mechanical strain field and optimizes bond energy distribution. The correlation between the SRO and properties of CrMnFeCoNi alloy needs further investigations, which is expected to greatly help understand and control the properties of high-entropy alloys.

The channeling effect of symmetrical tilt grain boundaries on helium bubbles in tungsten

Helium atoms can migrate easily and aggregate at various crystal defects, such as grain boundaries, which promote the nucleation and growth of helium bubbles, ultimately causing severe radiation damage to nuclear materials. Structure characteristics of grain boundaries with low-angle symmetrical tilt of the [100] axle and their channeling effects on helium bubbles in tungsten were investigated by molecular dynamics simulations. The triaxial variation curves of the helium bubble size in each grain boundary model and the relationship of the helium diffusion coefficient of each grain boundary to their intrinsic crystal structures are analyzed. The results indicate that the helium bubbles grow into one-dimensional nanochannels at the selected grain boundaries, and there is a significant difference in the maximum number of helium bubbles these grain boundaries can accommodate before forming one-dimensional nanochannels. Furthermore, the existence of helium nanochannels along the 〈100〉 edge dislocation line in the low-angle symmetrical tilt grain boundaries is well verified by molecular dynamics simulation of the helium bubble growth and helium diffusion equations at the 〈100〉 edge dislocation line. This suggests that releasing helium outside of the tungsten matrix through the nanochannel structures of low-angle symmetrical tilt grain boundaries may be a potential strategy to address the root causes of bubble nucleation and swelling of tungsten material.

Viewpoint: Can symmetric tilt grain boundaries represent polycrystals?

Grain boundaries control a wide variety of bulk properties in polycrystalline materials, so simulation methods like density functional theory are routinely used to study their structure-property relationships. A standard practice for such simulations is to use compact, high-symmetry (coincident site lattice) boundaries as representatives of the much more complex polycrystalline grain boundaries. In this letter, we question this practice by quantitatively comparing the spectra of atomic sites and properties amongst grain boundaries. We show, using solute segregation as an example property, that highly symmetric tilt boundaries (with Σ values less than 10) will fail to capture polycrystalline grain boundary environments, and thus lead to incorrect quantitative and qualitative insights into their behavior.

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.

Dynamic behavior of grain boundaries with misorientations in the vicinity of Σ3 coherent and incoherent twin boundaries in Al bicrystals

The migration behaviour of different grain boundaries with misorientations close to the Σ3 CSL orientation relationship in high purity Al bicrystals under the capillary driving force and applied mechanical stress was investigated. The experiments were performed by an in-situ technique to observe and measure the boundary migration with a scanning electron microscope. The ability of the nearly Σ3 60°〈111〉 incoherent {110} and {112} boundaries to move under capillary driving force was found to depend critically on the initial boundary inclination. While boundaries with inclinations near {112} can easily assume a curved shape and migrate, boundaries with an initial {110} plane remain stationary or form non-mobile facets. This is attributed to the essential anisotropy of the inclination dependence of the energy γ(ψ) of 60°〈111〉 tilt boundaries with differently high torque dγ/dψ around {112} and {110} inclinations, as revealed by atomistic simulations of the respective boundaries. The Σ3 70.5°〈110〉 tilt boundary with the geometry corresponding to the coherent {111} twin boundary, was found to be immobile under both driving forces applied. The 59.2° 〈111〉 tilt grain boundary with geometry near the Σ3 {110} incoherent twin boundary was found to be quite mobile under applied shear stress. The measured migration activation enthalpy H = 0.45 eV for this boundary is the lowest among the values obtained in previous experiments for any other stress driven grain boundary in Al bicrystals of the same purity. Moreover, this boundary migrated with a zero coupling factor, i.e. without producing any measurable shear parallel to the boundary plane.

Effect of symmetrical and asymmetrical tilt grain boundaries with as the tilt axis on the shock response of bi-crystalline Ni

Aim of this article is to study the effect of tilt grain boundaries on the shock response of single and bi-crystalline nickel. Nickel is commonly used in many structural applications, but research on dynamic response is very limited or in an immature stage. In this article, molecular dynamics-based simulations were performed in conjunction with embedded atom method potential to quantify the response of shock in bi-crystalline Ni containing symmetrical or asymmetrical tilt grain boundaries. Simulations were performed under the influence of adiabatic conditions. Compressive ultra-shock pulse of width 2 ps was simulated in the simulation box; stress, particle velocity, dislocation emission and phase transformation were quantified for symmetrical and asymmetrical tilt grain boundaries in bi-crystalline Ni. It was concluded from the simulations that higher mis-orientation angle between the crystals of Ni help in retarding the shock front velocity and stress. The alternation in the shock front behavior was associated with the change in deformation governing mechanism. The emission of dislocations and formation of Lomer Cottrell lock governs deformation in symmetrical tilt grain boundary configurations under shock pulse loading. It was concluded from the set of simulations that plastic deformation blunts the shock front in bi-crystalline Ni, whereas the sharp shock front was observed in single crystal Ni. Radial distribution function in post shock atomistic configurations was performed to capture the stability of the crystal in post shock scenario. Asymmetrical tilt grain boundaries are not as efficient in restricting the shock front as symmetrical tilt grain boundary configurations.

Atomistic Simulation of Symmetric and Asymmetric Tilt Grain Boundaries 5 <001> in Niobium: Structure, Energy, Point Defects, Grain Boundary Self-Diffusion

Symmetric and three asymmetric tilt grain boundaries Ʃ 5 in niobium have been studied by computer simulation methods. The structure and energies of the boundaries under consideration, as well as the energies of the formation of point defects in them, are calculated by the method of molecular-static modeling. The dependences of the formation energies of point defects on the distance from the plane of the grain boundary are analyzed. Using the method of molecular dynamics, the coefficients of grain-boundary self-diffusion for the considered boundaries are calculated.

Atomistic Modeling of Symmetric and Asymmetric Σ5 $$\left\langle {{\text{001}}} \right\rangle $$ Tilt Grain Boundaries in Niobium: Structure, Energy, Point Defects, and Grain-Boundary Self-Diffusion

Atomistic Modeling of Symmetric and Asymmetric Σ5 $$\left\langle {{\text{001}}} \right\rangle $$ Tilt Grain Boundaries in Niobium: Structure, Energy, Point Defects, and Grain-Boundary Self-Diffusion

Mixing enthalpy near grain boundaries in Fe-Cr alloy: The results of atomistic simulation

Energy characteristics of symmetric tilt (twin) grain boundaries (GBs) Σ5(210) and Σ5(310) with the tilt axis [001] and boundaries Σ3(111) and Σ3(112) with the tilt axis [11¯0] in a bcc random binary FeCr alloy have been studied using atomistic simulation. The simulation has been carried out based on DFT calculations and two-band semi-empirical potential. We have proposed the formula for calculating the mixing enthalpy near GBs. The relationship between the mixing enthalpy and the energy of the boundary in the alloy has been revealed. Both simulation methods have shown a decrease in the mixing enthalpy near a GB compared to the ideal crystal. Moreover, DFT has predicted a stronger decrease in the mixing enthalpy compared to estimates based on semi-empirical interaction. Based on the obtained dependences of the mixing enthalpy on the alloy composition, phase diagrams for the considered GB regions have been constructed. It has been shown that the GB region is characterized by a higher equilibrium concentration of chromium, and the precipitates of the α'-phase have a lower concentration of chromium compared to the bulk. The smallest difference in equilibrium compositions has been observed for the Σ5(310) and Σ3(112) boundaries, and the largest one for the Σ3(111) boundary, which has the highest energy among considered GBs.

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.

Nonmetallic trace elements induced rhenium co-segregation in nickel Σ5 [001](210) symmetrical tilt grain boundary

The thermally/mechanically-driven structural instability of nano- and coarse-grained polycrystalline metals originates from the unstable grain boundaries (GBs). GB segregation of solute elements could not only stabilize but also embrittle GBs. To improve GB stability and cohesion in parallel via solute segregations, in this work the segregation behavior of six non-metallic impurities X at the Σ5 [001](210) GB of nickel-based alloys, their co-segregations with Re element that has no GB segregation tendency, and segregation-induced changes in GB properties were investigated comprehensively from first-principles calculations. We discovered that these nonmetallic elements can segregate to the Ni GB and thus stabilize it, but they are GB embrittlers except B. Annealing temperature and bulk concentration have no effect on the S segregation. With the X pre-segregations, induced GB segregations of Re were observed, which lowers the excess energy and enhances the cohesive strength of all X-segregated GBs. The attractive interactions between C/N/B and Re atoms promote the Re segregation. The stabilizing and strengthening mechanisms of Re segregation were mainly attributed to the changes in Fermi level location and the increased interplanar bonding, respectively. Our findings may gain more insights into the atomic-scale GB co-segregations and stabilization of polycrystalline Ni-based alloys.

Atomistic evaluation of the dislocation transmission across tilt and twist low-angle grain boundaries in body-centered cubic iron

This study systematically and qualitatively evaluates the resistance for dislocation transmission across tilt/twist low-angle grain boundaries (LAGBs), which mainly consist of edge/screw dislocations (“GB dislocations”). The motion of the incident lattice edge dislocation is disturbed by the LAGBs, while the edge dislocation is transmitted to the adjacent grain by applying large shear stress if the tilt and twist angles are sufficiently low. It was observed that the twist LAGB is a stronger obstacle compared to the tilt LAGB for the incident lattice edge segment even though the misorientation angle of both tilt and twist LAGBs is the same because of the reconstruction of the GB-dislocation structures at the twist LAGB owing to the incident lattice dislocation. When we compare the incident lattice edge and screw components, the barrier effect of the GB on the transmission is stronger for the screw component than for the edge component. The stronger barrier effect can be explained mainly by the higher line tension of the screw component based on the dislocation bow-out model. Accordingly, the dominant factors of the GB-strengthening effect in LAGB are the incident lattice dislocation type, the structure of GB dislocations, and dislocation–dislocation reactions. These results indicate that the GB-strengthening factors are dominated by the type of incident lattice dislocation and the GB-dislocation character in addition to the macroscopic misorientation of the GB.

Insights into the interfacial thermal transport properties of in-plane graphene/h-BN heterostructure with grain boundary

The interfacial thermal energy transport ability of graphene (GR)/hexagonal boron nitride (h-BN) heterostructure with different symmetric tilt grain boundaries (GBs) at the interface was explored using molecular dynamics (MD) simulations. The effects of tilt angle and interface atomic connection type on the interfacial thermal conductance (ITC) for the GR/h-BN heterostructure were considered. The results show that the symmetric tilt grain boundaries at the interface reduce the ITC of the GR/h-BN heterostructure, as the symmetric tilt grain boundaries decrease the overlap of in-plane phonon density of states (PDOS) of atoms near the interface. Meanwhile, the interfacial thermal energy transport ability of Model II is superior to Model I. As in the process of heat energy transport, the energy at the interface of model I is higher and more concentrated, which restricts phonons from moving through the interface. For Model II, it is worth noting that at large tilt angles (i.e., 59.04° and 60°) the symmetric tilt grain boundaries have little influence on the ITC.

Thermodynamically Driven Tilt Grain Boundaries of Monolayer Crystals Using Catalytic Liquid Alloys.

We report a method to precisely control the atomic defects at grain boundaries (GBs) of monolayer MoS2 by vapor-liquid-solid (VLS) growth using sodium molybdate liquid alloys, which serve as growth catalysts to guide the formations of the thermodynamically most stable GB structure. The Mo-rich chemical environment of the alloys results in Mo-polar 5|7 defects with a yield exceeding 95%. The photoluminescence (PL) intensity of VLS-grown polycrystalline MoS2 films markedly exceeds that of the films, exhibiting abundant S 5|7 defects, which are kinetically driven by vapor-solid-solid growths. Density functional theory calculations indicate that the enhanced PL intensity is due to the suppression of nonradiative recombination of charged excitons with donor-type defects of adsorbed Na elements on S 5|7 defects. Catalytic liquid alloys can aid in determining a type of atomic defect even in various polycrystalline 2D films, which accordingly provides a technical clue to engineer their properties.

The effects of hydrogen and vacancy on the tensile deformation behavior of Σ3 symmetric tilt grain boundaries in pure fe

The interplay of hydrogen, vacancy and grain boundary plays an important role in hydrogen induced premature fracture in the metallic materials. In this work, two models with the representative high angle grain boundaries with the low and high grain boundary energy have been built according to the coincidence site lattice theory. The effects of hydrogen and hydrogen-vacancy combination on the deformation behaviors of the two models were investigated by means of molecular dynamics simulation with the straining direction vertical to the grain boundary. It is found that in both cases hydrogen tends to segregate and maintain a high local stress state around the grain boundary, and promote the premature fracture compared with the hydrogen-free model. Vacancy enhanced the effects of hydrogen in the model with grain boundary of the lower energy. However, vacancy promoted the dislocation evolution behavior in the model with grain boundary of the higher energy. The simulation results were further explained by considering the effects of hydrogen on the generalized stacking fault energy and the work of separation of the grain boundary.

Molecular Dynamics Study on the Effects of Substrate Grain Boundaries on the Adsorption State of Graphene: Implications for Nanoscale Lubrication

Graphene on polycrystalline surfaces, such as stainless steel, exhibits frictional strengthening properties during nanofriction. The adsorption state of graphene is directly related to the nanofriction behavior, and graphene’s adsorption state is affected by substrate grain boundaries. However, the mechanism of the influence of the substrate grain boundaries on the adsorption state of graphene is not clear. Herein, the adsorption states of graphene on different stainless-steel grain boundary surfaces are analyzed, and the mechanism of the substrate grain boundaries regulating the surface graphene bulge is revealed. The notion that graphene bulges are related to the type of substrate grain boundaries has been confirmed. Moreover, we demonstrate that the difference in the crystal surfaces on both sides of the grain boundaries and the gradient of adsorption energy are the key factors regulating the graphene bulge. Graphene bulging can only be caused by the existence of crystal surface differences in the grain boundary structure; therefore, the tilt grain boundaries are unable to cause graphene bulging. In addition, the adsorption energy distribution within the grain boundary will also influence graphene bulging if there is a grain surface difference in the grain boundary structure. When the direction of the adsorption energy gradient is perpendicular to the grain boundary, such a grain boundary structure favors the appearance of graphene bulges. In contrast, graphene bulging is suppressed when the direction of the adsorption energy gradient is parallel to the grain boundary. It provides a theoretical basis for explaining graphene’s nanofriction on polycrystalline substrates such as stainless steel. It is important for the use of graphene for the nano-lubrication of stainless-steel components in microelectromechanical systems.