Symmetric Tilt Research Articles

Grain Boundary Contributions to Li-Ion Transport in the Solid Electrolyte Li7La3Zr2O12 (LLZO)

The oxide with nominal composition Li7La3Zr2O12 (LLZO) is a promising solid electrolyte thanks to its high (bulk) Li-ion conductivity, negligible electronic transport, chemical stability against Li metal, and wide electrochemical window. Despite these promising characteristics, recent measurements suggest that microstructural features, specifically, grain boundaries (GBs), contribute to undesirable short-circuiting and resistance in polycrystalline LLZO membranes. Toward the goal of understanding GB-related phenomena, the present study characterizes the energetics, composition, and transport properties of three low-energy (Σ3 and Σ5) symmetric tilt GBs in LLZO at the atomic scale. Monte Carlo simulations reveal that the GB planes are enriched with Li, and to a lesser extent with oxygen. Molecular dynamics simulations on these off-stoichiometric boundaries were used to assess Li-ion transport within and across the boundary planes. We find that Li transport is generally reduced in the GB region; however, th...

An intrinsic correlation between driving force and energy barrier upon grain boundary migration

The migration of grain boundary (GB), which plays a key role in the microstructural evolution of polycrystalline materials, remains mysterious due to the unknown relationship between GB mobility associated with specific geometry and external conditions (e.g. temperature, stress, etc., hence the thermodynamic driving force). Combining the rate equation of GB migration with molecular dynamics simulations, an intrinsic correlation between driving force and energy barrier for the migration of various types of GBs (i.e. twist, symmetric tilt, asymmetric tilt, and mixed twist-tilt) is herein explored, showing the decrease of energy barrier with increasing thermodynamic driving force.

Atomistic modeling of grain boundary behavior under shear conditions in magnesium and magnesium-based binary alloys

In this study, the structure, the energetic, and the strength of a 101¯1<112¯0> symmetric tilt grain boundary in magnesium and magnesium binary alloys were analyzed in the framework of (semi-)empirical potentials. Following a systematic investigation of the transferability and accuracy of the interatomic potentials, atomistic calculations of the grain boundary energy, the grain boundary sliding energy, and the grain boundary strength were performed in pure magnesium and in binary MgX alloys (X = Al, Ca, Gd, Li, Sn, Y, Ag, Nd, and Pb). The data gained in this study were analyzed to identify the most critical material parameters controlling the strength of the grain boundary, and their consequence on atomic shuffling motions occurring at the grain boundary. From the methodology perspective, the role of in-plane and out-of plane relaxation on the grain boundary sliding energy curves was investigated. In pure magnesium, the results showed that in-plane relaxation is critical in activating b2{101¯1} twinning dislocation resulting in grain boundary migration. In the alloy systems, however, grain boundary migration was disabled as a consequence of the pinning of the grain boundary by segregated elements. Finally, while the grain boundary energy, the shape of the grain boundary sliding energy curves, and the grain boundary sliding energy are critical parameters controlling the grain boundary strength in pure magnesium, only the grain boundary energy and the segregation energy of the alloying elements at the grain boundary were identified as critical material parameters in the alloys system.

Symmetrical tilt grain boundary engineering of NiTi shape memory alloy: An atomistic insight

The role of austenitic symmetric tilt grain boundaries (STGBs) on the martensitic transformation in NiTi alloy during thermal cycling between 500K and 10K are studied from molecular dynamics simulations. Four austenitic STGBs including Σ3[11¯0](111), Σ3[11¯0](112), Σ9[11¯0](114) and Σ9[11¯0](221) have been considered. Through martensitic transformation, the austenitic STGBs transform to martensitic grain boundaries (GBs) and martensitic twin boundaries form in the interior of the simulation models. After austenitic transformation, the martensitic GBs recover to the austenitic STGBs and the twin boundaries disappear. We find that the roles of STGBs on the martensitic transformation can be divided into three groups based on the martensite start temperature (Ms). (1) The Σ3[11¯0](112) and Σ9[11¯0](221) STGBs retard the martensitic transformation, i.e., decreases Ms, by raising the potential energy of the grain interior. (2) The Σ9[11¯0](114) STGB promotes the martensitic transformation by lowering the potential energy of the grain interior. (3) The effects of the Σ3[11¯0](111) STGB depend on whether twins form during cooling. The evolutions of the microstructures during thermal loadings are analyzed using the von Mise shear strain; insight obtained in this work paves the way for engineering NiTi shape memory alloy through grain boundaries.

Kapitza thermal resistance across individual grain boundaries in graphene

We study heat transport across individual grain boundaries in suspended monolayer graphene using extensive classical molecular dynamics (MD) simulations. We construct bicrystalline graphene samples containing grain boundaries with symmetric tilt angles using the two-dimensional phase field crystal method and then relax the samples with MD. The corresponding Kapitza resistances are then computed using nonequilibrium MD simulations. We find that the Kapitza resistance depends strongly on the tilt angle and shows a clear correlation with the average density of defects in a given grain boundary, but is not strongly correlated with the grain boundary line tension. We also show that quantum effects are significant in quantitative determination of the Kapitza resistance by applying the mode-by-mode quantum correction to the classical MD data. The corrected data are in good agreement with quantum mechanical Landauer-Bütticker calculations.

Anomalous Nernst and thermal Hall effects in tilted Weyl semimetals

We study the anomalous Nernst and thermal Hall effects in a linearized low-energy model of a tilted Weyl semimetal, with two Weyl nodes separated in momentum space. For inversion symmetric tilt, we give analytic expressions in two opposite limits: for a small tilt, corresponding to a type-I Weyl semimetal, the Nernst conductivity is finite and independent of the Fermi level, while for a large tilt, corresponding to a type-II Weyl semimetal, it acquires a contribution depending logarithmically on the Fermi energy. This result is in a sharp contrast to the nontilted case, where the Nernst response is known to be zero in the linear model. The thermal Hall conductivity similarly acquires Fermi surface contributions, which add to the Fermi level independent, zero tilt result, and is suppressed as one over the tilt parameter at half filling in the Type-II phase. In the case of inversion breaking tilt, with the tilting vector of equal modulus in the two Weyl cones, all Fermi surface contributions to both anomalous responses cancel out, resulting in zero Nernst conductivity. We discuss two possible experimental setups, representing open and closed thermoelectric circuits.

Improvement of Variation Propagation Control in Mechanical Assembly Using Adjustment Assembly Technique

This paper aims to provide an assembly method to improve mechanical assembly quality. In order to improve the variation propagation control in rotationally symmetric cylindrical components assembly, the eccentric and tilt errors of a single rotor stage were taken into account using a connective assembly model and the eccentric deviation in a mechanical assembly was minimized by properly selecting component orientations. Compared to the minimum cumulative error, the maximum cumulative error was reduced by 71 percent, and the average cumulative error was reduced by 57 percent in the assembly of three components. This article provides an assembly method through variation propagation control in rotationally symmetric cylindrical components assembly. The method could be extended to rotationally symmetric cylindrical components assembly, for example in the assembly of aero-engine components.

First principles study on HenV clusters in α-Fe bulk and grain boundaries

Based on the first-principles calculations, we studied the HenV clusters (n=1–9) in α-Fe bulk, and comparatively studied three orthogonal orientations of He2V clusters in the grain boundary (GB) plane of five symmetrical tilt grain boundaries (STGBs). The results of HenV clusters in bulk showed that HenV clusters with larger binding energy (He4V and He6V in this work) are more likely to exhibit a highly symmetrical configuration. Moreover, it is also indicated that the FeHe interatomic potential using an s-band model is more accurate than other potentials to describe the system. The grain boundary region (HenV (0≤n≤2) in a Σ5(310) GB as an example) was effectively used by constructing two simplified GB models (free surface GB model and reconstructed GB model) and the results proved that the free surface GB model is a good approximation by maintaining high precision (−0.09eV to +0.03eV binding energy error) and reducing resources consumption (24–90% computational time of the original GB model) as well. He2V residing in parallel to GB plane with relatively higher binding energies are more stable than the ones that perpendicular to it. He2V perpendicular to GB plane shows shorter HeHe separation distances than in bulk or tend to deviate from the orientation more easily to bind with GBs.

Magnetic structure of [0 0 1] tilt grain boundaries in bcc Fe studied via magnetic potentials

Using magnetic potentials and a molecular statics approach, we study the changes in the magnetic structure of bcc Fe in the vicinity of grain boundaries (GBs). We focus on symmetric tilt GBs around the [0 0 1] axis with a tilt angle between 7 and 53. We find that immediately in the GB plane, the deviations in the magnetic moments from the bulk value are most pronounced. The distribution of moments in the GB plane is modulated according to the periodicity of the coincidence site lattice. In the direction perpendicular to the GB plane, the moments decay exponentially towards the bulk value; the decay length increases with decreasing tilt angle. This dependence can be explained by the well-known stress field around GBs.

Fast and scalable prediction of local energy at grain boundaries: machine-learning based modeling of first-principles calculations

We propose a new scheme based on machine learning for the efficient screening in grain-boundary (GB) engineering. A set of results obtained from first-principles calculations based on density functional theory (DFT) for a small number of GB systems is used as a training data set. In our scheme, by partitioning the total energy into atomic energies using a local-energy analysis scheme, we can increase the training data set significantly. We use atomic radial distribution functions and additional structural features as atom descriptors to predict atomic energies and GB energies simultaneously using the least absolute shrinkage and selection operator, which is a recent standard regression technique in statistical machine learning. In the test study with fcc-Al [110] symmetric tilt GBs, we could achieve enough predictive accuracy to understand energy changes at and near GBs at a glance, even if we collected training data from only 10 GB systems. The present scheme can emulate time-consuming DFT calculations for large GB systems with negligible computational costs, and thus enable the fast screening of possible alternative GB systems.

First-Principles Investigation of Intergranular Fracture in Copper by Grain Boundary Segregation of Sulfur

Grain boundary (GB) embrittlement by sulfur in fcc CuΣ5(012)[100] symmetrical tilt grain boundary (STGB) is simulated by first-principles calculations. The surface and grain boundary segregation energies are estimated by progressively placing solute atoms in the potential segregation sites in the boundaries. Based on the calculated segregation energies, the cohesive energy of the grain boundary is evaluated as a function of the sulfur atoms concentration. It is found that, when a two atomic layers’ concentration is attained, the cohesive energy is reduced by one order of magnitude compared to its value for the clean grain boundary.

FEATURES OF THE Σ5 AND Σ9 GRAIN BOUNDARIES MIGRATION IN BCC AND FCC METALS UNDER SHEAR LOADING – A MOLECULAR DYNAMICS STUDY

Molecular dynamics simulation of metallic bicrystals has been carried out to investigate the behavior of the symmetrical tilt grain boundaries under shear loading. Σ5 and Σ9 grain boundaries in Ni and α-Fe were analyzed. It is found that behavior of the defect depends not only on the structure of boundaries but also on the type of crystal lattice. In particular it is shown that under external stress the grain boundary (GB) behaves differently in the BCC and FCC metal. A comparison of the values of displacement of various types of GB due to their migration caused by shear deformation is carried out. The results can help us to understand the features of the plastic deformation development in nanoscale polycrystals under shear loading.

Interaction between lattice dislocations and low-angle grain boundaries in Ni via molecular dynamics simulations

Low-angle grain boundaries (LAGBs) may show up frequently as distinct dislocation products such as in the processes of work hardening, recovery and recrystallisation of metals and alloys. To reveal their mechanical behaviours, interactions between lattice dislocation and symmetric tilt and twist LAGBs are studied with molecular dynamics simulations. It is shown that dislocation reaction and slip transmission depend on the structure of LAGB, the character of incident dislocation and the particular glide planes inhabiting the incoming slip. For tilt LAGBs, a free slip-transmission process is identified where dislocations can be forced to penetrate through the boundary without inducing dislocation reaction. Otherwise, the incident slip tends to be trapped or absorbed by those intrinsic grain boundary dislocations. With increasing the applied strain, a number of dislocation reactions can be triggered, which may lead to indirect slip transmission across the boundary.

Atomic bond-breaking behaviour during grain boundary fracture in a C-segregated Fe grain boundary

First-principles fully relaxed tensile tests were performed on a C-segregated Fe Σ3 (1 1 1)/[] symmetrical tilt grain boundary (GB) to investigate the breaking behaviour of C–Fe bonds during tensile straining. Fe atoms around a C atom moved obliquely to the tensile direction, and C–Fe bonds stretched in the tensile direction without premature bond-breaking. Analyses of the electronic states during deformation showed that a variation in the charge density at the bond critical point was much larger for the C–Fe bond than for the P–Fe bond and that the C atom exhibited larger variations of s and p states involved in the covalent-like characteristics than the P atom. It is suggested that these lead to a high mobility of the C–Fe bonds. On the other hand, first-principles shear tests on the Fe GB imply that C-segregated Fe GB toughening is not associated with increased crack blunting by dislocation emission.

Interactions between lattice dislocation and Lomer-type low-angle grain boundary in nickel

Symmetric tilt Lomer-type low-angle grain boundaries (LLAGBs) are distinct grain boundaries formed by Lomer dislocation locks in face-centered cubic (fcc) metals. To reveal their mechanical behaviors, interactions between lattice dislocation and LLAGB are studied with molecular dynamics simulations. Dislocation reaction and slip transmission depend on the tilt angle of LLAGB, the character of incident dislocation and the particular glide planes inhabiting the incoming slip. For LLAGBs with relatively small tilt-angles, a free slip-transmission zone can be identified where dislocations can be forced to penetrate through the LLAGB without inducing dislocation reaction. Otherwise, the incident slip tends to be trapped, triggering a number of dislocation reactions and leading to indirect slip transmission across the boundary in the reaction zone. Critical strains for dislocation reactions are examined. Raising up the temperature will widen the dislocation reaction zone and the free transmission zone tends to disappear.

A Description of Preferential Sites for Vacancy Formation on Grain Boundaries in Copper by Structural Unit Model

The preferential sites for vacancies on a series of symmetric tilt grain boundaries in copper have been investigated by molecular dynamics simulation. The regularity of preferential sites for vacancies on these boundaries can be described by the structural unit model. This is essential because of the correspondence between the geometries of the structural units and the local stress field. The vacancies are energetically preferred at the sites with relatively large tensile stress, and these sites are the corner sites of the structural units. Moreover, these preferential sites are mainly related to the structural unit types irrespective of which grain boundary that the structure units locate in. Therefore, the preferential sites for vacancies on various grain boundaries formed by combinations of certain structural units can be readily described and predicted by the structural unit model.

Ab initio studies of two Al grain boundaries subjected to mixed tension/shear mode loading: how shear may promote breakage

Using the framework of density functional theory, the structural and energetic response of two face-centred cubic (fcc) Al grain boundaries (GBs) to combined tension and shear loadings has been examined. It is shown that tension will serve to inhibit the Σ5 [100] 36.87° twist GB response to shear in a mixed-mode loading scenario, by increasing the difference in structural environments for inequivalent atoms at the GB plane. We propose that the presence of such atoms, rather than the full structural details of the GB structure, is instrumental in triggering this tension–shear interplay. As support for this hypothesis, we compute the Σ3 [-110] (111) 60° symmetric tilt GB mixed-mode loading response. Here, all atoms at the GB plane are equivalent, and the qualitative shear energy variation is unaffected by tension. Our findings indicate that general fcc Al GBs may display a stronger shear energy variation at larger levels of tension, contrasting general expectations. The implications to GB breakage are discussed.

Edge dislocations interacting with a Σ11 symmetrical grain boundary in copper upon mixed loading: A quasicontinuum method study

Using quasicontinuum method (QCM), we study GB migration in the dissociated edge dislocation interacting with a Σ11 symmetrical tilt grain boundary (STGB) upon the mixed-mode of simple shear and tensile loadings. The interaction mechanisms are analyzed with the aid of Burgers vectors conservation equations. It is found that loading state significantly impacts not only the dislocation transmission but also the nucleation of grain boundary dislocations (GBDs). Under mixed loading, GBD dipole nucleation tends to easily occur in comparison to the pure shearing even when some incoming dislocations impinging on GB. Besides, mixed loading could reduce the normal stress resolved on the out-going slip plane in the neighboring grain, which makes the dislocation transmission easier in comparison with the pure shearing loading. Further, a map of the critical shear and normal stresses resolved on the grain boundary (GB) plane at the dislocation-GB interaction site is given to identify dislocation transmission, nucleation of GBD and GBD dipole for the different loading states and the cases of different number of incoming dislocations.

Molecular dynamics simulation of the interaction of a nano-scale crack with grain boundaries in α-Fe

The interaction of nano-scale cracks with grain boundaries in α-Fe were studied using symmetric tilt grain boundaries with [112¯] and [1¯10] tilt axis. For each tilt axis four types of grain boundaries were chosen – low angle, general high angle, Σ3 and Σ11. A crack perpendicular to the boundary plane was introduced between the two boundaries. The grain boundaries were equilibrated using molecular statics simulation and the entire configuration was deformed at constant strain rate using isobaric-isothermal (NPT) ensemble at 0K. The stress strain behaviour of the configurations, variation of dislocation line density with strain and the screening effect of the grain boundaries were studied. The strain field around the crack tip and the dislocations emitted from it interact with the grain boundaries. The configuration with Σ3 grain boundaries showed higher tensile strength while that with Σ11 showed lower tensile strength. This was attributed to the orientation of the dislocations in the {11¯0} boundary plane with 180° tilt angle and the complete coherency with {1¯1¯2} boundary plane with 70.53° tilt angle. Further, in both the Σ3 grain boundary configurations, even the most favourable slip system had a low Schmid factor, thus making slip difficult in the grain too. The configurations with 4.9° and 31.59° tilt angle about the [1¯10] tilt axis showed the most effective stress screening.

Energetics of Hydrogen Segregation to α-Fe Grain Boundaries for Modeling Stress Corrosion Cracking

The physics of embrittlement is dictated by the various interactions between the impurities/defects and the local structure in polycrystalline material systems. In this study, a physically motivated model that describes the degree of interaction of hydrogen (H) defects on the segregation behavior to α-Fe grain boundaries (GBs) is developed. Molecular statics simulations were performed to quantify the segregation behavior of 1–2 H atoms at various interstitial sites around the , , , and symmetric tilt GBs. The results provide insights into the concentration profile of hydrogen defects along different GBs. Furthermore, the model accurately links the intrinsic GB character by quantifying the segregation length scale for the individual GBs based on the segregation behavior of defects. Finally, the metrics provided in this work are essential to comprehensively understanding the effect of hydrogen on the macroscopic behavior of α-Fe.