Grain Boundary Facets Research Articles

Σ3 grain boundary dynamics studied by atomistic spherical bicrystal modeling

In this study, we propose an atomistic spherical bicrystal model that employs the synthetic driving force method to investigate the dynamics of curved interfaces. The model allows tracking the migration and faceting of spherical grain boundaries. As a demonstration case, a simulation for a grain boundary with Σ3 misorientation is performed. A subsequent analysis of interface energy and stiffness is performed, whereby it is found that the dynamics of [111] and segments in the Σ3 boundary plane fundamental zone follow energy and stiffness trends, while others, e.g., the segment, do not.

Shape functions and kinetics of migrating grain boundaries in nanocrystalline materials

Grain boundary (GB) shapes determine driving force of curvature-driven GB migration and therefore is critical to grain growth kinetics. GB shape functions in nanocrystalline materials are hardly known due to experimental difficulties. This study represents the first one with regard to investigating shape functions of steadily migrating GBs at nanometer scale by using molecular dynamics. It is found that two types of GB migration kinetics occur depending on grain size and temperature, both differing from the one in coarse grain counterparts. The two kinetics correspond to different GB shapes. For the grains in a range of about 10–25 nm (the upper limit is expected to extend to sub-micron) at relatively low temperature, new shape functions have been successfully derived, while for the finest nanograins of around several nm at relatively high temperature their shape functions coincide with the ones developed for coarse grains. In addition, GB faceting occur for some GBs, which causes deviation of boundary shape from the functions proposed. The findings in the present study imply that the boundary shapes and migration kinetics may contribute to the specific grain growth kinetics in nanocrystalline materials.

Atomic-scale observation of dynamic grain boundary structural transformation during shear-mediated migration.

Grain boundary (GB) structural change is commonly observed during and after stress-driven GB migration in nanocrystalline materials, but its exact atomic scale transformation has not been explored experimentally. Here, using in situ high-resolution transmission electron microscopy combined with molecular dynamics simulations, we observed the dynamic GB structural transformation stemming from reversible facet transformation and GB dissociation during the shear-mediated migration of faceted GBs in gold nanocrystals. A reversible transformation was found to occur between (002)/(111) and Σ11(113) GB facets, accomplished by the coalescence and detachment of [Formula: see text]-type GB steps or disconnections that mediated the GB migration. In comparison, the dissociation of (002)/(111) GB into Σ11(113) and Σ3(111) GBs occurred via the reaction of [Formula: see text]-type steps that involved the emission of partial dislocations. Furthermore, these transformations were loading dependent and could be accommodated by GB junctions. This work provides atomistic insights into the dynamic structural transformation during GB migration.

Influence of faceting-roughening on triple-junction migration in zinc

Abstract The faceting and migration of individual triple junctions in Zn tricrystals under a constant driving force was investigated. The triple junction (TJ) was formed by three [101̅0] tilt grain boundaries (GBs) with misorientation angles θ of 43°, 37° and 6°. The stationary shape of the migrating triple junction was studied, and the migration rate was measured in-situ between 670 and 688 K using polarized light. In some experimental runs, a facet was formed on the θ = 37° [101̅0] tilt GB. This facet was parallel to the close-packed plane in the constrained coincidence site lattice (CCSL). The length of this facet decreases with increasing temperature and becomes zero at 688 K. The temperature dependence of the facet length is better described by the mean-field Andreev approximation than by the solid-on-solid model. The step energy estimated in the framework of the Bonzel approximation is about 0.1 eV/atom. In other experimental runs, the θ = 37° [101̅0] tilt GB did not facet and remained rough in the same temperature interval. This fact allowed us to compare the stationary migration of the same TJ with faceted and rough GBs. ATJ formed by faceted GBs migrates one to two orders of magnitude more slowly in comparison with a rough TJ. An unrealistically high value of the apparent migration activation enthalpy of faceted TJs can appear due to the changing geometry of faceted GBs, similar to the case of migration of faceted twin tips.

Molecular Dynamics Simulation of Zener Pinning by Differently Shaped and Oriented Particles

Zener pinning between a curved Cu grain boundary (GB) and a differently shaped and oriented Ag particle has been simulated via molecular dynamics. The computed magnitudes of the maximum pinning force agreed with theoretical predictions only when the force was small. As the force increased, discrepancy became obvious. Through careful inspection of the structures of the Cu–Ag interfaces, detailed interaction processes, and variation of the Cu GB during the interaction, the discrepancy is found to correlate with GB faceting, which very likely reduces the maximum pinning force and facilitates boundary passage. GB anisotropy and/or interface characteristics are also found to slightly contribute to the discrepancy. These findings suggest that the assumption of an isotropic GB with constant energy utilized in previous theoretical studies for deriving the maximum pinning force might be inappropriate and that an accurate maximum pinning force could not be predicted without knowing the effects of GB evolution together with detailed properties of both GBs and interfaces.

Effects of Grain Boundary Faceting, Grain Boundary Anisotropy and Interface Natures on the Maximum Pinning Force of a Differently Shaped and Oriented Particle

Zener pinning between a curved Cu grain boundary (GB) and a differently shaped and oriented Ag particle has been simulated via molecular dynamics. The computed magnitudes of the maximum pinning force agreed with theoretical predictions only when the force was small. As the force increased, discrepancy became obvious. Through carefully inspecting structures of the Cu-Ag interfaces, detailed interaction processes and variation of the Cu GB during the interaction, the discrepancy is found to mainly result from GB faceting, which can reduce the maximum pinning force and facilitate boundary passage. GB anisotropy and/or interface natures are also found to slightly contribute to the discrepancy. These findings suggest that the assumption of an isotropic GB with constant energy utilized in previous theoretical works for deriving the maximum pinning force is inappropriate and a correct maximum pinning force could not be predicted without knowing the effects of GB evolution together with detailed properties of both GBs and interfaces.

Phase diagram of grain boundary facet and line junctions in silicon

The presence of facets and line junctions connecting facets on grain boundaries (GBs) has a strong impact on the properties of structural, functional, and optoelectronic materials: They govern the mobility of interfaces, the segregation of impurities, as well the electronic properties. In the present paper, we employ density-functional theory and modified embedded atom method calculations to systematically investigate the energetics and thermodynamic stability of these defects. As a prototype system, we consider $\mathrm{\ensuremath{\Sigma}}3$ tilt GBs in Si. By analyzing the energetics of different faceted GBs, we derive a diagram that describes and predicts the reconstruction of these extended defects as a function of facet length and boundary inclination angle. The phase diagram sheds light upon the fundamental mechanisms causing GB faceting phenomena. It demonstrates that the properties of faceting are not determined solely by anisotropic GB energies but by a complex interplay between geometry and microstructure, boundary energies as well as long-range strain interactions.

Migration Pinning and Roughening Transition of a Ni Grain Boundary

To date, much research has been conducted into the effect of migration pinning on the grain size in polycrystalline materials. However, effects of migration pinning on the grain-boundary structure and its transition have not been illuminated. Here, using transmission electron microscopy (TEM) we have explored the pinning effects for the grain boundary in a Ni bicrystal. During TEM specimen preparation, a hole was intentionally drilled in the middle of the grain boundary as a pinning point against grain-boundary migration. The specimen was heated to 600 °C. The grain boundary is driven to migrate by both the surface energy anisotropy and the total strain energy reduction. Grain-boundary facets with a plane orientation of {0 3 2}//{1 1 1} appear near the hole. The facets undergo a structural transition from atomically flat to rough with increasing distance from the hole. A pinning force exerted by the hole suppresses the migration of the grain boundary near the hole, indicating that the grain-boundary region away from the hole is subjected to a higher driving force. It certainly appears that the phenomenon originates from a change in driving force with the distance from the hole, being a signature of kinetic roughening.

Atomic-Precision Fabrication of Quasi-Full-Space Grain Boundaries in Two-Dimensional Hexagonal Boron Nitride.

Precise control and in-depth understanding of the interfaces are crucial for the functionality-oriented material design with desired properties. Herein, via modifying the long-standing bicrystal strategy, we proposed a novel nanowelding approach to build up interfaces between two-dimensional (2D) materials with atomic precision. This method enabled us, for the first time, to experimentally achieve the quasi-full-parameter-space grain boundaries (GBs) in 2D hexagonal boron nitride (h-BN). It further helps us unravel the long-term controversy and confusion on the registry of GBs in h-BN, including (i) discriminate the relative contribution of the strain and chemical energy on the registry of GBs; (ii) identify a new dislocation core-Frank partial dislocation and four new antiphase boundaries; and (iii) confirm the universal GB faceting. Our work provides a new paradigm to the exploitation of structural-property correlation of interfaces in 2D materials.

Faceting of Twin Grain Boundaries in High‐Purity Copper Subjected to High Pressure Torsion

The microstructure of high‐purity 5N5 copper processed by high pressure torsion (HPT) is studied. Close to the top and bottom surfaces of HPT disk, the 2–10 μm‐thick ultrafine‐grained layers with equiaxial grains and grain size of about 150 nm are formed. This grain size is typical for HPT of copper and its alloys. However, the remaining bulk layer in the HPT disk contained mainly elongated intersecting twins with high aspect ratio and length of up to 1 μm. These twin grain boundaries (GBs) are faceted. The geometry of the GB facets is analyzed using Σ3 coincidence site lattice (CSL). The Σ3 twins after HPT contained (100)CSL, (110)CSL, (010)CSL, and non‐CSL 9R facets, but not (120)CSL and (130)CSL facets. Earlier, the stability diagram for the Σ3 GB facets is experimentally constructed for the same 5N5 high‐purity copper. The comparison of the data with this diagram allows to estimate for the first time the effective temperature of pure copper during HPT processing at room temperature (RT): Teff = 920 ± 50 K. In other words, the HPT at RT results in Σ3 GB facets as if the sample is annealed at Teff = 920 ± 50 K.

Signature of Kinetic Roughening Revealed by Migration Pinning in a Ni Grain Boundary

To date much research has been conducted into the effect of migration pinning on the grain size in polycrystalline materials. However, effects of migration pinning on the grain-boundary structure and its transition have not been illuminated. Here, using transmission electron microscopy (TEM) we have explored the pinning effects for the grain boundary in a Ni bicrystal. During TEM specimen preparation, a hole was intentionally drilled in the middle of the grain boundary as a pinning point against grain-boundary migration. The specimen was heated to 600oC. The grain boundary is driven to migrate by both the surface energy anisotropy and the total strain energy reduction. Grain-boundary facets with a plane orientation of {0 3 2}//{1 1 1} appear near the hole. The facets undergo a structural transition from atomically flat to rough with increasing distance from the hole. A pinning force exerted by the hole suppresses the migration of the grain boundary near the hole, indicating that the grain-boundary region away from the hole is subjected to a higher driving force. It certainly appears that the phenomenon originates from a change in driving force with the distance from the hole, being a signature of kinetic roughening. The same argument applies to the formation of short (0 1 0)//(1 -1 0) facets developing between {0 3 2}//{1 1 1} facets.

A diffuse interface model of grain boundary faceting

Interfaces, free or internal, greatly influence the physical properties and stability of materials microstructures. Of particular interest are the processes that occur due to anisotropic interfacial properties. In the case of grain boundaries (GBs) in metals, several experimental observations revealed that an initially flat GB may facet into hill-and-valley structures with well defined planes and corners/edges connecting them. Herein, we present a diffuse interface model that is capable of accounting for strongly anisotropic GB properties and capturing the formation of hill-and-valley morphologies. The hallmark of our approach is the ability to independently examine the various factors affecting GB faceting and subsequent facet coarsening. More specifically, our formulation incorporates higher order expansions to account for the excess energy due to facet junctions and their non-local interactions. As a demonstration of the modeling capability, we consider the Σ5 〈001〉 tilt GB in body-centered-cubic iron, where faceting along the {210} and {310} planes was experimentally observed. Atomistic calculations were utilized to determine the inclination-dependent GB energy, which was then used as an input in our model. Linear stability analysis and simulation results highlight the role of junction energy and associated non-local interactions on the resulting facet length scales. Broadly speaking, our modeling approach provides a general framework to examine the microstructural stability of polycrystalline systems with highly anisotropic GBs.

Review: grain boundary faceting–roughening phenomena

Similar to free surfaces, the grain boundaries (GBs) in metals, semiconductors and insulators can contain flat (faceted) and curved (rough) portions. In the majority of cases, facets are parallel to the most densely packed planes of coincidence sites lattice formed by two lattices of abutting grains. Facets disappear with the increasing temperature (faceting–roughening transition) and the increasing angular distance from coincidence misorientation. The temperature of GB faceting–roughening transition T R decreases with the increasing inverse density of coincidence sites Σ. In case of fixed Σ, T R decreases with the decreasing density of coincidence sites in the GB plane. The intersection line (ridge) between facets or between facets and curved (rough) portions of surfaces can be of first order (two different tangents in the contact point) or of second order (common tangent, continuous transitions). The rough (curved) portions of GB can also form the first-order rough-to-rough ridges (with two tangents). GB facets control the transition from normal to abnormal grain growth and strongly influence the GB migration, diffusion, wetting, fracture and electrical conductivity.

Motion of Grain Boundaries: Experiments on Bicrystals

Recent research on grain boundary migration is reviewed. Novel in-situ measuring techniques based on orientation contrast imaging and the experimental results obtained on specially grown bicrystals are presented. Particularly, the investigated faceting and migration behavior of low angle grain boundaries under the curvature force in aluminum bicrystals was addressed. In contrast to the pure tilt boundaries, which remained straight/flat and immobile during annealing at elevated temperatures, mixed tilt-twist boundaries readily assumed a curved shape and steadily moved under the capillary force. Computational analysis revealed that this behavior is due to the inclinational anisotropy of grain boundary energy, which in turn depends on boundary geometry. The migration of planar grain boundaries induced by a magnetic field was measured in bismuth and zinc bicrystals. Various structurally different boundaries were investigated. The results revealed that grain boundary mobility essentially depends on the misorientation angle and the inclination of the boundary plane. Stress driven boundary migration in aluminium bicrystals was observed to be coupled to a tangential translation of the grains. The activation enthalpy of high angle boundary migration was found to vary non-monotonously with misorientation angle, whereas for low angle boundaries the migration activation enthalpy was virtually the same. The motion of the mixed tilt-twist boundaries under stress was observed to be accompanied by both the translation of adjacent grains parallel to the boundary plane and their rotation around the boundary plane normal.

On migration and faceting of low-angle grain boundaries: Experimental and computational study

The motion and faceting behavior of low-angle 〈100〉 tilt and mixed tilt–twist boundaries was investigated. The experiments were conducted on high-purity (99.999%) aluminum bicrystals by utilizing an in situ technique for the observation and continuous recording of boundary migration. In contrast to pure tilt boundaries, the mixed boundaries were found to readily assume a curved shape and steadily move under the capillary driving force. This behavior is associated with the inclination dependence of boundary energy, which was determined for tilt and mixed boundaries by molecular statics simulations. The shape evolution and shrinkage kinetics of cylindrical grains with different tilt and mixed boundaries were studied by molecular dynamics simulations. The mobility of low-angle 〈100〉 boundaries with misorientation angle >10°, obtained by both the experiments and simulations, does not differ from that of the high-angle boundaries, but decreases essentially with the further decrease of misorientation. The shape evolution of the embedded grains was found to relate directly to results of the energy computations. Further simulation results revealed that the shrinkage of grains with pure tilt boundaries is accompanied by grain rotation. In contrast, grains with the tilt–twist boundaries composed of dislocations with the mixed edge–screw character do not rotate as they shrink.

Effect of Grain Boundary Energy Anisotropy on Faceting and Migration of Low Angle Grain Boundaries

The faceting and migration behavior of low angle <100> grain boundaries in high purity aluminum bicrystals was investigated. In-situ technique based on orientation contrast imaging was applied. In contrast to the pure tilt boundaries, which remained straight/flat and immobile during annealing at elevated temperatures, mixed tilt-twist boundaries readily assumed a curved shape and steadily moved under the capillary force. Computational analysis revealed that this behavior is due to the inclinational anisotropy of grain boundary energy, which in turn depends on boundary geometry – the energy of pure tilt low angle <100> boundaries is anisotropic, whereas that of mixed tilt-twist boundaries isotropic with respect to boundary inclination.

Grain boundary ridges slow dawn grain boundary motion: In-situ observation

The impact of grain boundary (GB) ridge on motion of high-angle GB in Zn was studied. The steady-state motion of faceted GB half-loop with [101¯0] tilt GB and GB ridge was recorded in-situ. The temperatures of faceting–roughening transition were experimentally defined for three GB half-loops. Above the transition temperature GB half-loops had GB “rough-to-rough” ridge with continuously curved GB segments. Below the transition temperature a facet appeared and coexisted with two “facet-to-rough” ridges. For the first time we could extract mobility of “rough-to-rough” and “rough-to-facet” ridges and bring out clearly that GB ridge slows down GB motion. Present removes contradiction between high facet mobility and the low mobility of faceted GB.

Shear responses of -tilt {1 1 5}/{1 1 1} asymmetric tilt grain boundaries in fcc metals by atomistic simulations

The shear response of the -tilt and -tilt (1 1 5)/(1 1 1) asymmetric tilt grain boundaries (GBs) in fcc metals Cu and Al has been studied by atomistic simulation methods with the embedded atom method interatomic potentials and with a bicrystal model. It is found that the structure of the GBs studied can be well described by the coincidence site lattice (CSL) theory. Shear of these GBs at room temperature along eight different directions within the GB plane shows that these two types of GBs can transform between each other by the formation of a coherent twin boundary. The structure transformation of the GBs can also take the form of GB sliding, GB sliding–migration coupled motion, GB faceting, GB 9R structure formation, etc, depending on the shear directions adopted and the material involved (Cu or Al). The detailed structure transformation mechanisms have been analyzed with the aid of the CSL–DSC (displacement shift complete) theory. Several structure transformation paths adherent to these two types of GBs have been identified for the activation of the GB sliding–migration coupled motion. It is concluded that, although CSL–DSC theory can be applied to describe the sliding–migration coupled motion of the GBs studied, some other effects such as the shear direction within the GB plane and the bonding characteristics of the materials should also play a significant role in the shear response of these GBs.

A creep model for austenitic stainless steels incorporating cavitation and wedge cracking

A model of damage evolution in austenitic stainless steels under creep loading at elevated temperatures is proposed. The initial microstructure is idealized as a space-tiling aggregate of identical rhombic dodecahedral grains, which undergo power-law creep deformation. Damage evolution in the form of cavitation and wedge cracking on grain-boundary facets is considered. Both diffusion- and deformation-driven grain-boundary cavity growth are treated. Cavity and wedge-crack length evolution are derived from an energy balance argument that combines and extends the models of Cottrell (1961 Trans. AIME 212 191–203), Williams (1967 Phil. Mag. 15 1289–91) and Evans (1971 Phil Mag. 23 1101–12). The time to rupture predicted by the model is in good agreement with published experimental data for a type 316 austenitic stainless steel under uniaxial creep loading. Deformation and damage evolution at the microscale predicted by the present model are also discussed.

New method to characterise grain boundary plane orientations based on EBSD orientation microscopy for serial sectioned surfaces

A new 'elementary facet' method has been developed to measure grain boundary (GB) plane orientations using three-dimensional electron backscattered diffraction on serial sectioned surfaces in a sample. The method defines different types of elementary facets in an orthogonal coordinate system in the sample. These elementary facets are used to pave GBs. For a flat GB, its projected areas on the orthogonal coordinate planes in the sample are obtained from the numbers of different facets paved in the GB. From the projected areas of the GB plane in the three coordinate planes, the GB plane normal is derived. For uneven GBs, a convolution method has been developed to obtain the GB plane orientations at different GB locations. In essence, this new method measures the GB orientations at every elementary facet that is used to pave the GBs in the sample. Together with the measured crystal orientations of different grains, the GB five parameters at all facets can be obtained readily. The distribution of GB five parameters for the whole GB population in a sample can be derived from the collection of properties of individual GB facets in the sample.