Relative grain boundary area and energy distributions in nickel

The three-dimensional interfacial network of grain boundaries in polycrystalline nickel has been characterized using a combination of electron backscatter diffraction mapping and focused ion beam serial sectioning. These data have been used to determine the relative areas of different grain boundary types, categorized on the basis of lattice misorientation and grain boundary plane orientation. Using the geometries of the interfaces at triple lines, relative grain boundary energies have also been determined as a function of lattice misorientation and grain boundary plane orientation. Grain boundaries comprising (1 1 1) planes have, on average, lower energies than other boundaries. Asymmetric tilt grain boundaries with the Σ9 misorientation also have relatively low energies. The grain boundary energies and areas are inversely correlated.     

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.     

Molecular dynamics simulations of grain boundary sliding: The effect of stress and boundary misorientation

Molecular dynamics simulations were used to study the effect of applied force and grain boundary misorientation on grain boundary sliding in aluminum at 750 K. Two grains were oriented with their 〈1 1 0〉 axes parallel to their boundary plane and one grain was rotated around its 〈1 1 0〉 axis to various misorientation angles. For any given misorientation, increasing the applied force leads to three sliding behaviors: no sliding, constant velocity sliding and a parabolic sliding over time. The last behavior is associated with disordering of atoms along the grain boundary. For the second sliding behavior, the constant sliding velocity varied linearly with the applied stress. A linear fit of this relationship did not intersect the stress axis at the origin, implying that a threshold stress for sliding exists. This threshold stress was found to decrease with increasing grain boundary energy. The ramifications of this finding for modeling grain boundary sliding in polycrystals are discussed.     

Inclination dependence of grain boundary energy and its impact on the faceting and kinetics of tilt grain boundaries in aluminum

The shape evolution and migration of <1 0 0> and <1 1 1> tilt grain boundaries with rotation angles θ in the range between 6° and 24° were investigated in situ in a scanning electron microscope at elevated temperatures. The results revealed that boundaries with misorientation θ < 15° did not attain a continuously curved shape in the entire temperature range up to the melting point and, thus, did not move under a capillary driving force. Instead, they remained straight or formed several facets which were inclined to the initial boundary orientation. Molecular statics simulations suggest that the observed behavior of low-angle boundaries is due to the anisotropy of grain boundary energy with respect to boundary inclination. This anisotropy diminishes with increasing misorientation angle, and high-angle boundaries assume a continuously curved shape and move steadily under the curvature driving force.     

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 10 K. Grain boundary structures are generated using molecular statics employing an embedded atom method potential, followed by molecular dynamics simulation at a constant 1 × 10⁹ s^?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.     

Low angle tilt boundary migration coupled to shear deformation

The shear stress induced migration of planar 〈1 0 0〉 tilt grain boundaries in Al bicrystals was observed to be perfectly coupled to the lateral translation of grains. Boundaries with misorientations of 10.5° and 12.0° on one side of the misorientation range (0–90°) and 81.0° and 81.1° on its other side move in opposite directions under the same applied external stress. The measured ratios of the normal to the lateral motion comply perfectly with the coupling factors of a recently proposed model of boundary motion.     

Phenomenology of shear-coupled grain boundary motion in symmetric tilt and general grain boundaries

Shear-coupled grain boundary motion is examined for a large number of grain boundaries including 73 〈1 0 0〉, 〈1 1 0〉 and 〈1 1 1〉 symmetric tilt boundaries. In the present work, the grain boundary motion is induced by a synthetic driving force as opposed to prior studies of shear coupling induced by applied shear. For those boundaries that are observed to undergo shear-coupled motion, the results based on the two driving forces agree well, both for experiments and simulations. This agreement also confirms the generality of the shear coupling mechanism over numerous boundaries and boundary types. The examination of boundary structure provides insight into the different trends that are observed. Shear coupling according to modes not predicted by the Frank–Bilby equation are also demonstrated. The temperature dependence of shear coupling is examined, and is consistent with prior work for symmetric tilt boundaries. While prior studies have emphasized symmetric tilt boundaries, some general grain boundaries exhibit shear coupling as well. In these boundaries, it is found that the shear coupling is either temperature independent, decreases in magnitude with increasing temperature or, in some cases, changes direction with temperature.     

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.     

Five-parameter grain boundary distribution of commercially grain boundary engineered nickel and copper

The five-parameter grain boundary distributions of grain boundary engineered nickel and copper specimens have been analyzed in detail. The relative areas of {1 1 1} planes in the entire population did not increase as a result of grain boundary engineering (GBE) and, in the Σ3-excluded population, decreased after GBE. This decrease occurred because the majority of the newly generated Σ3 grain boundaries were not coherent twins with {1 1 1} grain boundary plane orientations. GBE increased the proportion of Σ3 boundary length that was vicinal-to-{1 1 1} and the proportion of asymmetrical 〈1 1 0〉 tilt boundaries. There was a clear propensity for selection of particular planes or plane combinations which were associated with low energy. These plane types were analyzed in some detail, and it was shown that many of these boundaries were asymmetrical tilts comprising (or vicinal to) at least one low-index plane.     

Stress-driven migration of symmetrical 〈1 0 0〉 tilt grain boundaries in Al bicrystals

Stress-induced migration of planar grain boundaries in aluminum bicrystals was measured for both low- and high-angle symmetrical 〈1 0 0〉 tilt grain boundaries across the entire misorientation range (0–90°). Boundary migration under a shear stress was observed to be coupled to a lateral translation of the grains. Boundaries with misorientations smaller than 31° and larger than 36° moved in opposite directions under the same applied external stress. The measured ratios of the normal boundary motion to the lateral displacement of grains are in an excellent agreement with theoretical predictions. The coupled boundary motion was measured in the temperature range between 280 and 400 °C, and the corresponding activation parameters were determined. The results revealed that for mechanically induced grain-boundary motion there is a misorientation dependence of migration activation parameters. The obtained results are discussed with respect of the mechanism of grain-boundary motion.     

Atomic motion during the migration of general [0 0 1] tilt grain boundaries in Ni

We generalize a previous study of the atomic motions governing grain boundary migration to consider arbitrary misorientations of [0 0 1] tilt boundaries. Our examination of the nature of atomic motions employed three statistical measures of atomic motion: the non-Gaussian parameter, the “dynamic entropy” and the van Hove correlation function. These metrics were previously shown to provide a useful characterization of atomic motions both in glass-forming liquids and strained polycrystalline materials. As before, we find highly cooperative, string-like motion of atoms, but the grain boundary migration itself is a longer timescale process in which atoms move across the grain boundary. These observations are consistent with our previous results for Σ5 [0 0 1] tilt boundaries. It is evident from our work that the grain boundary structure and misorientation have a significant influence on the rate of grain boundary migration.     

On the influence of the grain boundary misorientation on the plastic deformation of aluminum bicrystals

Aluminum bicrystals with symmetric 〈1 1 2〉 tilt boundaries and misorientations of 8.7° (small angle), 15.4° (transition), and 31.5° (large angle) were deformed in a channel die experiment in order to study the influence of misorientation on the deformation at grain boundaries. Samples were characterized by strain measurements and microtexture mappings. The experiments were compared to crystal plasticity finite element simulations. We studied strain heterogeneity at the macroscopic and at the microscopic level. Even macroscopically homogeneous areas showed microscopic heterogeneity in the form of bands of different sets of glide systems. We observed clear effects of the grain boundary misorientation on the deformation kinematics close to the boundaries. The 8.7° grain boundary did not show any orientation change which was interpreted in terms of free dislocation penetration. In contrast, the 15.4° and 31.5° bicrystals showed orientation changes which were attributed to dislocation pile-ups.     

Motion of a grain boundary facet in aluminum

The shape and migration of a capillary-driven 20.8°〈1 0 0〉 tilt grain boundary in aluminum bicrystals were investigated in situ in a scanning electron microscope at elevated temperatures. The moving boundary assumed a semi-faceted configuration composed of a singular facet connected to a curved boundary section joined at a distinct edge. At constant temperature the boundary with a facet moved steadily and its shape remained self-similar. Both the facet length and the connecting angle between the facet and the curved boundary section did not change over the investigated temperature range. The capillary-driven migration of the semi-faceted grain boundary in “quarter-loop” geometry was analyzed. The obtained results revealed that the major factor responsible for the formation of the mobile facet was the energy difference between the facet and the curved boundary. The temperature dependence of the facet mobility was determined. The migration activation enthalpy of the investigated capillary-driven planar boundary/facet was a factor of two higher than the activation enthalpy for migration of a geometrically similar boundary driven by an applied stress.     

Atomistic simulation of grain boundary sliding in pure and magnesium doped aluminum bicrystals

Molecular dynamics and statics simulations are used to study grain boundary sliding and energy in bicrystals with symmetric tilt grain boundaries of Al and Mg doped Al. There is an increase in grain boundary energy in Al bicrystals with the presence of Mg depending on the position of Mg atom. Simulations of sliding show a clear dependence of magnitude of sliding on grain boundary energy.     

Structure and free volume of 〈1 1 0〉 symmetric tilt grain boundaries with the E structural unit

Atomistic simulations are used to investigate the structure and interfacial free volume of 〈1 1 0〉 symmetric tilt grain boundaries in copper containing the E structural unit from the Σ9(2 2 1)θ = 141.1° grain boundary. In this work, a stereologically-based methodology is used to calculate the grain boundary free volume along with the spacing and connectivity of free volume. After generating the minimum energy equilibrium grain boundary, we examine (i) the grain boundary structure, (ii) a measure of free volume associated with the grain boundary, (iii) spatial correlation functions of the distribution of free volume, and (iv) images of grain boundary free volume distribution. Using the results from these calculations, the influence of free volume spatial distribution and grain boundary structure on dislocation dissociation and nucleation is briefly discussed for boundaries with the E structural unit subjected to tensile loading normal to the interface along with the potential implications of free volume connectivity.     

Kinetics of diffusion induced grain boundary migration of [100] twist boundaries in the Cu(Zn) system

The kinetics of diffusion induced grain boundary migration (DIGM) in the Cu(Zn) system was experimentally studied for [100] twist boundaries using Cu bicrystals annealed at 693 K for various times between 5.4×10⁴ and 1.73×10⁵ s. The experiment was carried out for bicrystal specimens with misorientation angles of 15, 20, 23 (Σ13), 25, 28 (Σ17), 32, 37 (Σ5), 40, 44 (Σ29) and 45°. During DIGM, the grain boundary migrates rather unidirectionally towards one of the crystal grains for most of the specimens and becomes wavy with increasing annealing time. The migration distance at 5.4×10⁴ s is smaller for coincidence site lattice (CSL) boundaries with low energy than for random boundaries with high energy. The migration rate of the moving boundary was observed to be almost constant independent of the annealing time between 5.4×10⁴ and 1.73×10⁵ s. The steady state migration rate is larger for low-energy CSL boundaries than for high-energy random boundaries. The experimental results were quantitatively analyzed using the energy balance model proposed by Kajihara and Gust. In this analysis, the effective driving force for DIGM was calculated as a function of the migration rate. The calculation indicates that 75–93% of the chemical driving force is consumed by the volume diffusion of Zn in the untransformed Cu matrix ahead of the moving boundary under the given experimental conditions. Considering the energy consumption, the mobility M of the moving boundary was evaluated for the steady state stage. The evaluation yields M=6.6×10⁻¹⁷ m⁴/J s as the mobility of the random boundary for DIGM in the Cu(Zn) system at 693 K.     

Effect of grain boundary character on sink efficiency

The dependence of the width of void-denuded zones (VDZs) on grain boundary (GB) characters was investigated in Cu irradiated with He ions at elevated temperature. Dislocation loops and voids formed near GBs during irradiation were characterized by transmission electron microscopy, and GB misorientations and normal planes were determined by electron back-scatter diffraction. The VDZ widths at Σ3〈1 1 0〉 tilt GBs ranged from 0 to 24 nm and increased with the GB plane inclination angle. For non-Σ3 GBs, VDZ widths ranged from 40 to 70 nm and generally increased with misorientation angle. Nevertheless, there is considerable scatter about this general trend, indicating that the remaining crystallographic parameters also play a role in determining the sink efficiencies of these GBs. In addition, the VDZ widths at two sides of a GB show different values for certain asymmetrical GBs. Voids were also observed within GB planes and their density and radius also appeared to depend on GB character. We conclude that GB sink efficiencies depend on the overall GB character, including both misorientation and GB plane orientation.     

Tracer diffusion of Au and Cu in a series of near Σ=5 (310)[001] symmetrical Cu tilt grain boundaries

Grain boundary diffusion of Au and Cu was measured in a series of Cu bicrystals with symmetrical near Σ=5, Θ=36.9° (310)[001] CSL tilt grain boundaries (GBs) using the radiotracer and the serial sectioning technique. The orientations of the bicrystals were very precisely determined with the Kossel technique where all three macroscopic parameters describing the orientations of the grains in the bicrystal were evaluated. The tilt angles ranged from 33.21° to 39.26°. The GB diffusion of the radiotracers ¹⁹⁵Au and ⁶⁴Cu was measured as a function of tilt angle and temperature. In the investigated temperature range 1030–661 K the orientation dependence of both radiotracers shows a characteristic cusp not exactly at but slightly below the ideal Σ=5 CSL GB. The Arrhenius parameters, activation enthalpy and frequency factor, determined from lower temperature data adopt a maximum, again slightly before the ideal Σ=5 CSL GB. These features are discussed with respect to the accidental small twist and second tilt orientations and the corresponding dislocation network inherent in the investigated real GBs. With increasing temperature a negative deviation from a straight Arrhenius behaviour is observed. This result indicates a certain change in the GB structure in the temperature range above 800 K.     

Spatial correlation in grain misorientation distribution

Grain misorientation was studied in relation to the nearest neighbor’s mutual distance using electron back-scattered diffraction measurements. The misorientation correlation function was defined as the probability density for the occurrence of a certain misorientation between pairs of grains separated by a certain distance. Scale-invariant spatial correlation between neighbor grains was manifested by a power law dependence of the preferred misorientation vs. inter-granular distance in various materials after diverse strain paths. The obtained negative scaling exponents were in the range of ?2 ± 0.3 for high-angle grain boundaries. The exponent decreased in the presence of low-angle grain boundaries or dynamic recrystallization, indicating faster decay of correlations. The correlations vanished in annealed materials. The results were interpreted in terms of lattice incompatibility and continuity conditions at the interface between neighboring grains. Grain-size effects on texture development, as well as the implications of such spatial correlations on texture modeling, were discussed.     

General schema for [0 0 1] tilt grain boundaries in dense packing cubic crystals

Atomic resolution Z-contrast images from a series of CeO₂ [0 0 1] tilt grain boundaries at coincident site lattice (CSL) or near-CSL misorientations can all be explained within a structural unit model. These structural units (which cover all boundaries from 0° to 90°) show striking similarities to comparable CSL boundaries observed in cubic crystal structures that are also derived from dense packing (face centered cubic metal; rocksalt, perovskite, etc.). A general model for the structure of grain boundaries in such similarly structured materials systems has been developed that is based on the crystallography of the parent structures. Changes away from these predicted grain boundary symmetries can be interpreted as showing the frustration of symmetry caused by the incorporation of point defects (vacancies and impurities). This general model for grain boundary structures can, in principle, provide a means to infer the structure–property relationships in broad classes of materials.