Refined Prediction and Observation of Dislocation Structures in Low Σ Symmetric Grain Boundaries

The grain boundary dislocation structures of three Fe–4at.% Si bicrystals with an additional misorientation of the order of 2° were studied by transmission electron microscopy (TEM), one S5 [001] (310) and two S9 [110] (1 [`1]\overline 1 4). It was found that in the S5 case two Burgers vectors of the structure are not simple basic complete displacement shift lattice (DSC) vectors and are larger than any one of them. This enabled formation of the preferred grain boundary dislocation (GBD) structure with a hexagonal net composed of three screw dislocations and an independent set of parallel edge dislocations. In the S9 case the GBD structure comprises three apparently independent sets of parallel dislocations. The Burgers vectors of two sets could be established as basic DSC vectors in screw and edge orientation, respectively, with respect to the GB plane. For the third set formed by separated groups of four dislocations no corresponding basic DSC vector exists. This case needs further investigation. The previously published table of predicted GBD structures for symmetrical coincidence boundaries up to S11 was refined according to the new results.     

Interaction of dislocation pile-up with a low-angle tilt boundary: a discrete dislocation dynamics study

Abstract

The pile-up of dislocations between two low-angle tilt boundaries (LATB) in an fcc crystal was simulated using three-dimensional discrete dislocation dynamics. The LATB was constructed using glissile edge dislocations stacked on each other. The dislocations in the pile-up were chosen such that their reactions with the dislocations in the LATB resulted in glissile junctions. Parallel pairs of dislocations were inserted to a maximum allowable value estimated from theoretical expressions. A resolved shear stress was applied and increased in steps so as to move the dislocations in the pile-up towards the boundaries. The shear stress required to break the lead dislocation from the wall was determined for varying spacings between the two boundaries. The shear stress and boundary spacing followed the Hall–Petch type relation. Dislocation pile-ups without a LATB were also simulated. The spacing of the dislocations in the pile-up with LATB was found to be closer (ie higher dislocation density) than that without LATB. It was shown through analytical expressions that LATB exerts an attractive force on the dislocations in the pile-up thereby creating a denser pile-up.     

Atomistic simulations of interactions between the 1 / 2⟨111⟩ edge dislocation and symmetric tilt grain boundaries in tungsten

The strength of polycrystals is largely controlled by the interaction between lattice dislocations and grain boundaries. The atomistic details of these interactions are difficult to discern even by advanced high-resolution microscopy methods. In this paper we present results of atomistic simulations of interactions between an edge dislocation and three symmetric tilt grain boundaries in body-centred cubic tungsten. Our simulations reveal that the outcome of the dislocation–grain-boundary interaction depends sensitively on the grain boundary structure, the geometry of the slip systems in neighbouring grains, and the precise location of the interaction within the grain boundary. A detailed analysis of the evolution of the grain boundary structures and local stress fields during dislocation absorption and transmission is provided.     

Periodic image effects in dislocation modelling

The use of periodic boundary conditions for modelling crystal dislocations is predicated on one's ability to handle the inevitable image effects. This communication deals with an often overlooked mathematical subtlety involved in dealing with the periodic dislocation arrays, that is conditional convergence of the lattice sums of image fields. By analysing the origin of conditional convergence and the numerical artefacts associated with it, we establish a mathematically consistent and numerically efficient procedure for regularization of the lattice sums and the corresponding image fields. The regularized solutions are free from the artefacts caused by conditional convergence and regain periodicity and translational invariance of the periodic supercells. Unlike the other existing methods, our approach is applicable to general anisotropic elasticity and arbitrary dislocation arrangements. The capabilities of this general methodology are demonstrated by application to a variety of situations encountered in atomistic and continuum modelling of crystal dislocations. The applications include introduction of dislocations in the periodic supercell for subsequent atomistic simulations, atomistic calculations of the core energies and the Peierls stress and continuum dislocation dynamics simulations in three dimensions.     

Emission of dislocations from grain boundaries by grain boundary dissociation

In this article, we examine the conditions that favour the emission of Shockley partial dislocations (SPDs) that standoff from a grain boundary (GB) plane by a few lattice parameters as part of the atomic structure of some GBs. To do so, we consider GBs to be formed by the operation of arrays of intrinsic grain boundary dislocations (GBDs) that create the tilt and twist misorientation, and the lattice mismatch between the two crystal grains adjoining the GB. The conditions to be considered that favour SPDs are the following: (1) Frank’s rule, (2) the proper sequential arrangement of partial dislocations to bound an intrinsic stacking fault and (3) the equilibrium stand-off distance (ESD). We apply an isotropic elasticity analysis to compute the ESD, in the absence of an applied stress, for SPDs emerging from asymmetric tilt GBs in two FCC metals, Cu and Al. The ESD is shown to be dependent on the glide plane orientation relative to the GB plane and on the position of the glide planes, relative to the position of the GBDs. An applied stress increases the ESD up to a critical stress that removes the SPDs without limit from the GB. We examine the effect of the stacking fault energy on the ESD and critical stress. The critical stress is effectively linearly dependent on the stacking fault energy. Finally, we present results of atomistic simulations of asymmetric tilt Σ11[1?0?1]{4?1?4}||{2?5?2} GBs in Cu bicrystal models subject to shock loading that behave in a manner similar to the elasticity predictions. The atomistic simulations reveal additional behaviour associated with elastic incompatibility between the two grains in the bicrystal models.     

In-situ transmission electron microscopy observations and molecular dynamics simulations of dislocation-defect interactions in ion-irradiated copper

An in-situ transmission electron microscopy straining technique has been used to investigate the dynamics of dislocation-defect interactions in ion-irradiated copper and the subsequent formation of defect-free channels. Defect removal frequently required interaction with multiple dislocations, although screw dislocations were more efficient at annihilating defects than edge dislocations were. The defect pinning strength was determined from the dislocation curvature prior to breakaway and exhibited values ranging from 15 to 175 MPa. Pre-existing dislocations percolated through the defect field but did not show long-range motion, indicating that they are not responsible for creating the defect-free channels and have a limited contribution to the total plasticity. Defect-free channels were associated with the movement of many dislocations, which originated from grain boundaries or regions of high stress concentration such as at a crack tip. These experimental results are compared with atomistic simulations of the interaction of partial dislocations with defects in copper and a dispersed-barrier-hardening crystal plasticity model to correlate the observations to bulk mechanical properties.     

Asymptotic expressions for the nearest and furthest dislocations in a pile-up against a grain boundary

In 1965, Armstrong and Head explored the problem of a pile-up of screw dislocations against a grain boundary. They used numerical methods to determine the positions of the dislocations in the pile-up and they were able to fit approximate formulae for the locations of the first and last dislocations. These formulae were used to gain insights into the Hall–Petch relationship. More recently, Voskoboinikov et al. used asymptotic techniques to study the equivalent problem of a pile-up of a large number of screw dislocations against a bimetallic interface. In this paper, we extend the work of Voskoboinikov et al. to construct systematic asymptotic expressions for the formulae proposed by Armstrong and Head. The further extension of these techniques to more general pile-ups is also outlined. As a result of this work, we show that a pile-up against a grain boundary can become equivalent to a pile-up against a locked dislocation in the case where the mismatch across the boundary is small.     

In situ and tomographic analysis of dislocation/grain boundary interactions in α-titanium

In situ straining in the transmission electron microscope and diffraction-contrast electron tomography have been applied to the investigation of dislocation/grain boundary and dislocation/twin boundary interactions in α-Ti. It was found that, similar to FCC materials, the transfer of dislocations across grain boundaries is governed primarily by the minimization of the magnitude of the Burgers vector of the residual grain boundary dislocation. That is, grain boundary strain energy density minimization determines the selection of the emitted slip system.     

Grain boundary sliding during ambient-temperature creep in hexagonal close-packed metals

Even at ambient temperature or less, below their 0.2% proof stresses all hexagonal close-packed metals and alloys show creep behaviour because they have dislocation arrays lying on a single slip system with no tangled dislocation inside each grain. In this case, lattice dislocations move without obstacles and pile-up in front of a grain boundary. Then these dislocations must be accommodated at the grain boundary to continue creep deformation. Atomic force microscopy revealed the occurrence of grain boundary sliding (GBS) in the ambient-temperature creep region. Lattice rotation of 5° was observed near grain boundaries by electron backscatter diffraction pattern analyses. Because of an extra low apparent activation energy of 20 kJ/mol, conventional diffusion processes are not activated. To accommodate these piled-up dislocations without diffusion processes, lattice dislocations must be absorbed by grain boundaries through a slip-induced GBS mechanism.     

Grain boundary chemistry and grain boundary dislocations in bulk YBa2Cu3O7-δ

We report the results of our microchemical analyses of low- large-angle grain boundaries in bulk YBa₂Cu₃O_7- using nanoprobe energy-dispersive-X-ray spectroscopy (EDX) and electron-energy-loss spectroscopy (EELS). We observed periodic variation in the concentration of Cu along the boundaries, and oxygen depletion at the boundaries. We found that the chemistry of the grain boundary is very sensitive to grain boundary dislocations (GBDs), while, in turn, the configuration of the GBDs is very sensitive to the boundary misorientation and the boundary plane normal. The strain field associated with closely spaced GBDs reduced the density of mobile holes at the boundary, which is expected to be detrimental to the superconducting properties of the boundary. The possible structural transition of the grain boundaries from an oxygen-deficient state to a fully oxygenated state near a coincidence orientation is discussed, based on the reduction of the elastic strain energy of the boundaries.     

Strain induced grain boundary premelting in bulk copper bicrystals

In bulk bicrystals strain induced grain boundary premelting (SIGBPM) occurs when heavy screw dislocation pileup can be held up to a certain high temperature, approximately 0.6T _M, where T _M is the melting point of bulk material in Kelvin. SIGBPM occurs at grain boundaries to which new twist component is added due to the rotation of both component crystals toward opposite direction about the axis perpendicular to the grain boundary plane. At the original grain boundary, grain boundary sliding takes place due to this relative rotation. In f.c.c. metals with relatively low stacking fault energies such as copper, nickel, brass(30Zn) and silver, dislocations dissociate into partials. Therefore high density tangled dislocations introduced during plastic deformation hardly loose. If these dislocations can be held to high temperatures, SIGBPM is promoted. Formation of static or dynamic recrystallized grains suppresses SIGBPM itself and the propagation of grain boundary cracks formed by SIGBPM.     

Quantitative HRTEM Investigations of a Symmetrical Tilt Σ11 Grain Boundary with Two Different Grain Boundary Planes in α-Al2O3

High resolution transmission electron microscopy was used for the determination of the Σ11 grain boundary structure in α-Al₂O₃. Two orientations of the Σ11 boundary were investigated, the (101¯1) and the (2¯116) interface planes, respectively. The atomistic structures of the grain boundary core were quantitatively determined by comparing the experimental micrographs with simulated images. Each GB was imaged along two perpendicular directions. 3D models are proposed for each of the grain boundary orientations. For the Σ11 (101¯1) grain boundary an empirical shell model was used as the starting model for the structure refinement, whereas a CSL type model was used for the Σ11 (2¯116) grain boundary. After the quantitative evaluation both Σ11 grain boundaries revealed that the best matching structures were non CSL model structures. Non-mirror symmetry was observed for both configurations for at least one investigated zone axes. For the Σ11 (101¯1) interface a relative shift of one crystal halve with respect to the other was observed perpendicular to the grain boundary plane, where the (101¯1) lattice spacing is reduced by Δy = 0.04 ± 0.01 nm. For the Σ11 (2¯116) interface the resulting atomic structure is shifted by Δx = 0.322 ± 0.035 nm in the [21¯1¯1] direction from the CSL model structure. This corresponds to half of the repeat length of the [21¯1¯1] direction. No relaxation perpendicular to the interface plane was detected.     

Transformation of Slip Dislocations in Σ3 Grain Boundary

Grain boundary processes during plastic deformation of bicrystals were studied by TEM. Two methods were used. In situ straining in the electron microscope followed by post mortem examination and post mortem observation of specimens previously deformed by in situ synchrotron radiation X-ray topography. Two mechanisms governing slip propagation across a coherent twin boundary in a Fe-Si alloy bicrystal were identified. The first mechanism is a dissociation of a slip dislocation with the Burgers vector lying parallel to the boundary into three equal grain boundary dislocations. The second mechanism is a decomposition of a slip dislocation with Burgers vector inclined to the boundary into a dislocation mobile in the other grain and two screw grain boundary dislocations.     

Strongly non-local modelling of dislocation transport and pile-up

The purpose of this work is the continuum modelling of transport and pile-up of infinite discrete dislocation walls driven by non-local interaction and external loading. To this end, the underlying model for dislocation wall interaction is based on the non-singular Peierls–Nabarro (PN) model for the dislocation stress field. For simplicity, attention is restricted to walls consisting of single-sign dislocations and to continuous wall distributions on a single glide plane. In this context, the influence of strongly non-local (SNL; long-range) interaction, and its approximation as weakly non-local (WNL; short-range) are studied in the context of interaction- and external-load-driven wall pile-up at a boundary. The pile-up boundary is modelled via a spatially dependent dislocation mobility which decreases to zero at the boundary. The pile-up behaviour predicted by the current SNL-based continuous wall distribution modelling is consistent with that predicted by discrete wall distribution modelling. Both deviate substantially from the pile-up behaviour predicted by WNL-based continuous wall distribution modelling. As such, it is clearly essential to account in continuum models for the intrinsic SNL character of the interaction between same-sign dislocations ‘close’ to the boundary. Gradient-based WNL ‘approximation’ of this interaction is not justified.     

Correlation among grain boundary character,carbide precipitation and deformation in Alloy 690

The correlation among grain boundary character, carbide precipitation and deformation in the grain boundary engineering (GBE) treated Alloy 690 samples with and without pre-deformation aged at 715^oC for 15?h was analysed by scanning electron microscopy and electron backscatter diffraction. The fraction of low Σ coincidence site lattice (CSL) grain boundary was enhanced by GBE treatment. The fraction of Σ3 grain boundary decreased, and most of Σ9 and Σ27 grain boundaries disappeared in the deformed GBE samples. After aging treatment, bigger carbide precipitated at coherent Σ3 grain boundary, however, most of plate-like carbide precipitated at incoherent Σ3 grain boundary disappeared in the pre-deformed GBE samples. The larger carbide precipitated on the random grain boundary in the 5% pre-deformed sample, while smaller carbide can be observed in the 15% pre-deformed sample. During the in situ tensile test of the aged GBE samples, grain boundary carbide migrated with the grain boundary migration. The slip bands go across Σ3 grain boundary directly, but cannot go across other grain boundaries. The high density of carbide plate precipitated near incoherent Σ3 and Σ9 grain boundaries can resist the evolution of slip bands. Compared to the Σ3 and Σ9 grain boundaries, Σ27 and random grain boundaries are more easily to form microcrack during deformation. The initiation of grain boundary microcrack not only related to the character of grain boundary but also related to the character of nearby grain boundaries. The phase interface of carbide and matrix is another region to initiate the microcrack.     

Effect of atomic ordering on the role of grain boundaries in the plastic deformation of Ni<Subscript>3</Subscript>Fe alloy

The structure of dislocations and the defect structure of grain boundaries and their parameters in Ni₃Fe alloy with short-range order (SRO) and long–range order (LRO) at different stages of plastic deformation are studied by means of transmission diffraction electron microscopy using thin foils and replicas. It is found that atomic ordering reduces the Σ3 twins plasticizing effect, increases the density of grain boundary defects, slows their annihilation during deformation, and intensifies the microstrains at the triple junctions of grain boundaries.     

Cut-off deviation for CSL boundaries in recrystallized face-centered cubic materials

Abstract

Brandon’s criterion is frequently used to quantify distribution of coincident site lattice (CSL) boundaries in studies related to grain boundary character distribution. This criterion is based on theoretical considerations and is meant to define a range within which special boundaries may exist. Experiments have repeatedly shown that this range includes boundaries which do not show special properties. A broad aim of this study is to explore if there exists a cut-off in deviation which includes only boundaries with special properties. While most other criteria in literature are based on theoretical dependence of secondary dislocation spacing, in this work we find the cut-off deviation through experimental data of recrystallised microstructures from in situ as well as ex-situ heating experiments. Deviation from structure was considered in terms of both, deviation of misorientation axis-angle as well as deviation of the boundary plane from the symmetric tilt orientation. Our results indicate that the deviation in terms of misorientation angle is more important than boundary plane deviation. We also show that the limiting deviation for various orders of twin boundaries (Σ3ⁿ) in a recrystallized microstructure is a constant and approximately 1° which is significantly lower than that defined by Brandon’s criterion. We show that this constant cut-off deviation for various Σ3ⁿ CSL boundaries can also be obtained by assuming that the secondary dislocations are spaced proportional to displacement shift complete lattice vector. Similar analysis was also carried out for non-Σ3ⁿ boundaries but due to limited statistics, no cut-off value could be deduced for these boundaries.     

Twinning structure of M23C6 carbide precipitated at twin-related grain boundaries in Alloy 600

The microstructure features of carbides precipitated at twin boundary and Σ9 grain boundary (GB) in nickel-based Alloy 600 after aging at 715?°C for different time were investigated by high-resolution transmission electron microscopy. The carbides precipitated at incoherent twin boundary and Σ9 GB were identified as M₂₃C₆. The bar-like carbides grow parallel to each other and into each side of grain nearby incoherent twin boundary, while only growth into one side nearby Σ9 GB is observed. The carbides precipitated at incoherent twin and Σ9 GBs contain twins. The carbides have (1?1?1) _matrix // (1?1?1) _M23C6 orientation relationship with the nearby matrix. Based on the experimental results, the formation of twinning microstructure features in the M₂₃C₆ is discussed.