Symmetric Tilt Grain Research Articles

First-principles study of the interplay between grain boundaries and domain walls in ferroelectric PbTiO3

Structures and energies of stoichiometric $\ensuremath{\Sigma}$3(111)[$\overline{1}$10], $\ensuremath{\Sigma}$3(112)[$\overline{1}$10], $\ensuremath{\Sigma}$5(201)[010], and $\ensuremath{\Sigma}$5(301)[010] symmetrical tilt grain boundaries are determined in the tetragonal ferroelectric PbTiO${}_{3}$ using a combination of first-principles electronic-structure calculations and atomistic shell-model-potential simulations. The focus is on grain boundaries, which are ferroelectric domain walls at the same time. A main result is that it is energetically preferential for a 180${}^{\ifmmode^\circ\else\textdegree\fi{}}$ domain wall to reside in the region of a $\ensuremath{\Sigma}$5 grain boundary. This is interpreted as a more general mechanism for domain-wall pinning in polycrystalline ferroelectric materials.

Impurity and vacancy segregation at symmetric tilt grain boundaries in Y2O3-doped ZrO2

Segregation energies of impurity ions and oxygen vacancies at grain boundaries in Y2O3-doped ZrO2 as calculated from atomistic simulations using energy minimization and Monte Carlo methods are reported. Based on these energies, local defect equilibrium concentrations have been estimated. It is found that it is more energetically favorable for an yttrium ion to be accompanied by an oxygen vacancy at grain boundaries, although decrease in energy when associated with an oxygen vacancy differs from boundary to boundary. The segregation energy for a neutral defect complex consisting of a two yttrium ions and an oxygen vacancy at infinitely dilute concentration is highly correlated with the coordination environment of each site in the vicinity of the grain boundary (GB), and, in turn, GB energy. Although the estimated local equilibrium concentrations of these defects are similar, detailed analysis of the atomic coordination and defect distributions in the vicinity of a GB reveal that defect distributions, especially of oxygen vacancies, are dependent on the characteristics of the particular GB and that segregation in effect reduces lattice strains at the GB. Equilibrium concentration distributions of yttrium at grain boundaries are also given as a function of spatial resolution, and are useful for interpretation of experimental results.

Structure, energy, and structural transformations of graphene grain boundaries from atomistic simulations

Domain/grain boundaries are often introduced into graphene during chemical vapor deposition growth processes. Here, we performed a series of hybrid molecular dynamics simulations to study the structures, energies, and structural transformations of symmetric tilt grain boundaries of graphene. The grain boundary comprises an array of edge dislocations, with the dislocation density increasing upon increasing the grain boundary misorientation angle. The dislocation in the zigzag-oriented grain boundary contains an edge-sharing pentagon/heptagon defect, whereas the dislocation in the armchair-oriented grain boundary contains two paired pentagon/heptagon defects. In some grain boundaries, out-of-plane buckling exists due to the presence of dislocations. In the transition region (the region between the zigzag- and armchair-oriented grain boundaries), the grain boundary structures feature complex mixtures of both zigzag and armchair grain boundaries. We also discuss the grain boundary transformations and migrations that occur upon adding or removing carbon atoms at the grain boundaries for all of our investigated types of grain boundaries.

First-principles calculation of grain boundary energy and grain boundary excess free volume in aluminum: role of grain boundary elastic energy

We examined the grain boundary energy (GBE) and grain boundary excess free volume (BFV) by applying the first-principles calculation for six [110] symmetric tilt grain boundaries in aluminum to clarify the origin of GBE. The GBE increased linearly as BFV increased. The elastic energy associated with BFV, namely the grain boundary elastic energy, was estimated as a function of BFV and the shear modulus. The grain boundary elastic energies were close in value to the GBEs. The charge density distributions indicated that the bonding in the grain boundary region is significantly different from the bonding in the bulk. The grain boundary elastic energies were 15–32% higher than the GBEs. This overestimation of the grain boundary elastic energy is caused by the characteristics of the electronic bonding at the grain boundary, which is different from bonding in the bulk. We have concluded that GBE results mainly from the grain boundary elastic energy.

Structures of a Σ = 9, [110]/{221} symmetrical tilt grain boundary in SrTiO3

In this study, we fabricated a bicrystal of SrTiO3 containing a Σ = 9, [110]/{221} symmetric tilt grain boundary (GB) and its atomistic structure was directly observed by transmission electron microscopy (TEM) and scanning TEM (STEM). We theoretically estimated the most stable structure by first principles calculations, and by combining this with TEM images determined the atomistic structure of the Σ = 9 grain boundary. We found that when the grain boundary is slightly tilted from the coincident site lattice (CSL) orientation, displacement shift complete (DSC) dislocations are introduced at the grain boundary to accommodate the misorientation between the two adjacent crystals while the most stable atomic structure remains unchanged.

912 余分な粒界転位の放出現象における粒界自由体積の関係(OS2-3計算固体力学の新展開一ナノからマクロまで一)

912 余分な粒界転位の放出現象における粒界自由体積の関係(OS2-3計算固体力学の新展開一ナノからマクロまで一)

Atomic structural variations of [0 0 0 1]-tilt grain boundaries during ZnO grain growth occurred by thermal treatments

ZnO thin films were deposited on n-Si substrates by using plasma-assisted molecular beam epitaxy. Plane-view zero-loss energy filtered transmission electron microscopy (TEM) images showed that the grain boundaries between large and small grains changed from the curve to the straight shape during ZnO grain growth. The [0 0 0 1]-tilt grain boundary of as-grown ZnO thin films changed from the zigzag facet planes into the symmetric tilt grain boundary through the asymmetric tilt grain boundary with periodic { 0 1 1 ¯ 0 } / { 3 5 8 ¯ 0 } flat planes. Such an atomic structural variation of grain boundary changes from curved grain boundaries to flat shape was due to decrease of total boundary energy during grain growth. The atomic structural variations of the [0 0 0 1]-tilt grain boundaries during ZnO grain growth occurred by thermal treatments are described on the basis of the TEM images.

Shear response of theΣ9⟨110⟩{221}symmetric tilt grain boundary in fcc metals studied by atomistic simulation methods

The shear response of the Sigma 9 {221} symmetric tilt grain boundary (GB) in three fcc metals Cu, Al, and Ni has been studied by atomistic simulation methods with the embedded atom method for interatomic potentials and with a bicrystal model. By applying an energy minimization procedure, it was found that there are two optimized structures of this particular GB at zero temperature for all the three metals studied. Shear of bicrystals at room temperature has been studied by the molecular-dynamics simulation method. Various kinds of structure evolution behavior have been found for this GB depending on the shear direction: (1) pure GB sliding; (2) GB atomic shuffling accompanied by lattice dislocation emission from the GB; and (3) GB migration coupled with GB sliding, namely, GB coupling motion. The GB coupling motions can differ in the direction and distance of the GB migration depending on the shear direction. An analysis with the aid of the coincidence site lattice theory indicates that the structure evolution behavior can be attributed to several elementary structure transformations inherent to this particular GB. A pair parameter (lambda, kappa) is proposed to describe the GB coupling motions.

Solubility of carbon in α-iron under volumetric strain and close to the Σ5(3 1 0)[0 0 1] grain boundary: Comparison of DFT and empirical potential methods

The solubility of carbon in α-Fe as a function of lattice strain and in the vicinity of the ∑5(310)[001] symmetrical tilt grain boundary is calculated with ab initio methods based on density-functional theory (DFT). The results are compared to four different empirical potentials: the embedded-atom method (EAM) potentials of Lau et al. [1], Ruda et al. [2] and Hepburn et al. [3], and the modified embedded-atom method (MEAM) potential of Lee [4]. The results confirm that the solubility of carbon in body-centered-cubic (bcc) Fe increases under local volume expansion and provide quantitative data for the excess enthalpy to be used in thermodynamic databases. According to our study the excess enthalpy obtained from DFT is more strain-sensitive than the ones obtained from the tested empirical potentials. The comparison of the applied methods furthermore reveals that among the empirical potentials the MEAM is most appropriate to describe the solubility of C in bcc Fe under strain. The differences between the four empirical potentials stem from different parameterizations of the EAM potentials and, in the case of the MEAM, from the altogether different formalism that also includes angular dependent terms in the binding energy.

Trapping of oxygen vacancy at grain boundary and its correlation with local atomic configuration and resultant excess energy in barium titanate: A systematic computational analysis

Atomic structures of [001] symmetric tilt grain boundaries (GBs) and their influences on the trapping of oxygen vacancies at GBs in barium titanate $({\text{BaTiO}}_{3})$ were analyzed using static atomistic simulation techniques. It is found that the structures are determined to minimize the deficiency in the coordination numbers of ${\text{Ti}}^{4+}$ ions and to suppress the structural distortion in the vicinity of the GBs. The excess energy of the GB is dependent on the number density of the coordination-deficient ${\text{Ti}}^{4+}$ ions, indicating that the ionic bonds between ${\text{Ti}}^{4+}$ and ${\text{O}}^{2\ensuremath{-}}$ ions are responsible for structural stabilization of GB. It is also found that the GB plays an important role in trapping oxygen vacancies, which acts as a resistance against the oxygen vacancy's diffusion. The trapping originates from the presence of irregular ${\text{O}}^{2\ensuremath{-}}$ sites, where oxygen vacancies energetically prefer to reside, influenced by coordination environment. Based on the detailed analyses on origins of GB energy and the trapping in the vicinity of GB, new physical ground that correlates GB energy and capability of oxygen-vacancy trapping are provided, enabling us to predict how much vacancies can be trapped at GBs on the atomic level by micrometer-order measurement of GB energy. Electrical degradation of the ${\text{BaTiO}}_{3}$ dielectrics used for multilayer ceramic capacitors can be prevented through controlling the characteristics of the GBs to promote oxygen-vacancy trapping at GBs in polycrystalline materials via modifying materials synthesis procedures.

X-ray diffraction study of a Si Σ13 symmetric tilt grain boundary

We present an X-ray diffraction study of a semiconductor symmetric tilt grain boundary. The theory of crystal truncation rod scattering is extended to bicrystal interfaces and compared with experimental data measured at the Diamond Light Source.

Evolution of structure and free volume in symmetric tilt grain boundaries during dislocation nucleation

Grain boundary evolution in copper bicrystals is investigated during uniaxial tension at 10K. Grain boundary structures are generated using molecular statics employing an embedded atom method potential, followed by molecular dynamics simulation at a constant 1×109s−1 strain rate. Interfacial free volume is continuously measured during boundary deformation, and its evolution is investigated both prior to and during grain boundary dislocation nucleation. Free volume provides valuable insight into atomic-scale processes associated with stress-induced grain boundary deformation. Different boundary structures are investigated in this work to analyze the role of interface structure, stress state and initial free volume on dislocation nucleation. The results indicate that the free volume influences interfacial deformation through modified atomic-scale processes, and grain boundaries containing particular free volume distributions show a greater propensity for collective atomic migration during inelastic deformation.

First-Principles Study on the Grain Boundary Embrittlement of Metals by Solute Segregation: Part I. Iron (Fe)-Solute (B, C, P, and S) Systems

The microscopic mechanism of grain boundary (GB) embrittlement in metals by solute segregation has been not well understood for many years. From first-principles calculations, we show here that the calculated cohesive energy (=2·surface energy − GB energy) of bcc Fe Σ3(111) symmetrical tilt grain boundary (STGB) is reduced by the segregation of sulfur (S) and phosphorous (P) while it is increased by the segregation of boron (B) and carbon (C). The rate of the decrease/increase in the cohesive energy is proportional to the experimental shift in the DBTT of high-purity iron with increasing segregation. This indicates that the change in the cohesive energy of GB plays a key role in the GB embrittlement of metals.

Analysis of Oxygen Vacancy Trapping at [001] Symmetric Tilt Grain Boundaries in Barium Titanate by Atomistic Simulations

The role of grain boundaries (GBs) in the diffusion of oxygen vacancies (VO••s) in barium titanate (BaTiO3) and its mechanism were investigated using atomistic simulation techniques. It was found that GBs trapped VO••s at specific sites in the course of the diffusion, and the excess energy reflecting structural distortion of the GB was closely related to the availability of the trapping. GBs therefore act as a resistance of the diffusion of VO••s, suggesting that electrical degradation of multilayer ceramic capacitors (MLCCs), which is derived from vacancy diffusion, enables to be additionally improved by controlling GB structures in BaTiO3-based dielectrics.

Solute Segregation at Σ11(113)[110] Grain Boundary and Effect of the Segregation on Grain Boundary Cohesion in Aluminum from First Principles

We investigate the energy of segregation of solute Ca at symmetric tilt grain boundary in aluminum from the first-principles calculations. As energy of segregation of Ca is negative, Ca atoms tend to segregate at the grain boundary. Furthermore, on basis of the Rice-Wang model, we study the effect of the segregation of Ca on the grain boundary embrittlement of aluminum. Our first-principles calculations of energies of segregation at grain boundary and free surface show that Ca behaves as embrittler.

Dislocation–grain boundary interaction in 〈1 1 1〉 textured thin metal films

The interaction of lattice dislocations with symmetrical and asymmetrical tilt grain boundaries in 〈1 1 1〉 textured thin nickel films was investigated using atomistic simulation methods. It was found that the misorientation angle of the grain boundary, the sign of the Burgers vector of the incoming dislocation and the exact site where the dislocation meets the grain boundary are all important parameters determining the ability of the dislocation to penetrate the boundary. Inclination angle, however, does not make an important difference on the transmission scenario of full dislocations. Only limited partial dislocation nucleation was observed for the investigated high-angle grain boundary. The peculiarities of nucleation of embryonic dislocations and their emission from tilt grain boundaries are discussed.

Aluminum Σ3 grain boundary sliding enhanced by vacancy diffusion

Grain boundary sliding is an important deformation mechanism for elevated temperature forming processes. Molecular dynamics simulations are used to investigate the effect of vacancies in the grain boundary vicinity on the sliding of Al bi-crystals at 750 K. The threshold stress for grain boundary sliding was computed for a variety of grain boundaries with different structures and energies. These structures included one symmetrical tilt grain boundary and five asymmetrical tilt grain boundaries. Without vacancies, low energy Σ3 grain boundaries exhibited significantly less sliding than other high energy grain boundaries. The addition of vacancies to Σ3 grain boundaries decreased the threshold stress for grain boundary sliding by increasing the grain boundary diffusivity. A higher concentration of vacancies enhanced this effect. The influence of vacancies on grain boundary diffusivity and grain boundary sliding was negligible for high energy grain boundaries, due to the already high atom mobility in these boundaries.

β-Sngrain-boundary structure and self-diffusivity via molecular dynamics simulations

The self-diffusion properties of several $\ensuremath{\beta}\text{-Sn}$ symmetric tilt grain boundaries are examined using molecular dynamics simulations. The boundary types examined---(101), (201), (401), (310)-$\ensuremath{\Sigma}5$, and (410)---are chosen from those observed in experiment and from arbitrary Miller planes, giving a variety of tilt angles and interface properties. Planar structure factor and diffusivity profiles for each boundary are computed and a grain-boundary width, ${\ensuremath{\delta}}_{GB}$, is measured from these profiles. Larger diffusive widths $({\ensuremath{\delta}}_{GB})$ are exhibited by higher excess potential energy grain boundaries. Diffusivities $({D}_{GB})$ in the directions parallel to the interface plane are computed and activation energies are found with the Arrhenius relation. ${D}_{GB}$ (as ${\ensuremath{\delta}}_{GB}{D}_{GB}$ normalized by ${\ensuremath{\delta}}_{GB}$) is shown to agree well with experiment. We also investigate the anisotropic diffusive behavior of the (401) grain boundary and find that the low energy grain boundary exhibits very low activation energy diffusion, due to the development of diffusive channels.

Intrinsic electrostatic effects in nanostructured ceramics

Using atomic-level calculations with empirical potentials, we have found that electrostatic dipoles can be created at grain boundaries formed from nonpolar surfaces of fluorite-structured materials. In particular, the $\ensuremath{\Sigma}5(310)/[001]$ symmetric tilt grain boundary reconstructs to break the symmetry in the atomic structure at the boundary, forming the dipole. This dipole results in an abrupt change in electrostatic potential across the boundary. In multilayered ceramics composed of stacks of grain boundaries, the change in electrostatic potential at the boundary results in profound electrostatic effects within the crystalline layers, the nature of which depends on the electrical boundary conditions. For open-circuit boundary conditions, layers with either high or low electrostatic potential are formed. By contrast, for short-circuit boundary conditions, electric fields can be created within each layer, the strength of which then depend on the thickness of the layers. These electrostatic effects have important consequences for the behavior of defects and dopants within these materials.

On intrinsic brittleness and ductility of intergranular fracture along symmetrical tilt grain boundaries in copper

The intrinsic brittleness and ductility of intergranular fracture along a number of symmetrical [1 1 0] tilt grain boundaries (GBs) in Cu are investigated via combined atomistic and continuum studies of dislocation nucleation from an atomically sharp crack tip. In all cases investigated, the classical model of Rice predicts a directional anisotropy in that, along a given GB, brittle cleavage is favored for crack propagation in one direction while dislocation emission from the crack tip is preferred in the opposite direction. This prediction is validated by atomistic simulations of crack propagation along coherent GBs, including Σ 3 ( 1 1 ¯ 1 ) and Σ 11 ( 1 1 ¯ 3 ) . However, for incoherent GBs such as Σ 9 ( 2 2 ¯ 1 ) , Σ 9 ( 1 1 ¯ 4 ) and Σ 11 ( 3 3 ¯ 2 ) , such directional anisotropy in intrinsic ductility is not observed; instead, we show that dislocation emission is favored in both crack propagation directions. The reason for this discrepancy is shown to be dislocation emission at a distance ahead of the crack tip along an incoherent GB, which violates the assumption in Rice’s model that dislocation emission occurs directly at the crack tip.