Dislocation Structure Of Boundaries Research Articles

Predicting grain boundary dislocation structures through multidimensional neural networks and high-throughput phase-field calculations

Phase-field modeling has been a useful method for describing crystal defects (such as dislocations and grain boundaries) at the continuous level. However, energy functional based on the crystallography and elasticity, as well as the kinetic governing equations for seeking the equilibrium state, may prevent it from widespread application. Therefore, surrogate models that directly map material properties (i.e., the γ-surfaces) to the equilibrium dislocation configurations are highly necessary from the view of improving both practical usability and computing efficiency. Using output data from phase-field calculation, the current work trains a simple neural network (NN) to investigate the geometrical outline of GB dislocations. Moreover, a deep NN concerning complex input and output is constructed to predict the whole configuration of the dislocation networks and stacking faults. The two NNs build up the relationship between the γ-surface and the GB dislocation configurations, which are validated through phase-field simulation in this work and atomic simulation reported previously. This work provides an important framework that bridges the physics-based model and machine learning techniques through data generation and transmission.

1 0 0] Dislocation core extension and decomposition in BCC bicrystal under biaxial loading

The evolution of grain boundary dislocation structure under biaxial tension–compression loading is simulated by the phase field crystal (PFC) method for small angle symmetric tilt grain boundary (STGB) of body center cubic (BCC) bi-crystal. Extension of the STGB dislocation core under the strain and the extended width of the core with the strain increasing are studied. In the elastic deformation process under the loading, the extension of the grain boundary dislocation core is accompanied by increasing the strain energy of the system. When the extension of the dislocation core reaches maximum critical width, the extended dislocation core occurs to decompose into three dislocation cores, in which two cores is in no-extended state, the Burgers vector direction of which is in the same direction of the original extended dislocation. The other dislocation core is of the extended type which Burgers vector direction is opposite to the Burgers vector direction of the original extended dislocation core. By establishing the macroscopic energy equation of the extended dislocation core system, it can be well revealed that the elastic strain energy is mainly stored in the extended dislocation defects and the complete lattice of the matrix. At the same time, it also reveals the function relationship between the energy of the extended dislocation core and the width of the extended dislocation during the biaxial loading process of the bi-crystal, as well as the critical condition of energy instability and the change of the energy barrier of the system for the dislocation extension core decomposition.

Energy of low angle grain boundaries based on continuum dislocation structure

In this paper, we present a continuum model to compute the energy of low angle grain boundaries for any given degrees of freedom (arbitrary rotation axis, rotation angle and boundary plane orientation) based on a continuum dislocation structure. In our continuum model, we minimize the grain boundary energy associated with the dislocation structure subject to the constraint of Frank's formula for dislocations with all possible Burgers vectors. This constrained minimization problem is solved by the penalty method by which it is turned into an unconstrained minimization problem. The grain boundary dislocation structure is approximated by a network of straight dislocations that predicts the energy and dislocation densities of the grain boundaries. The grain boundary energy based on the calculated dislocation structure is able to incorporate its anisotropic nature. We use our continuum model to systematically study the energy of <111> low angle grain boundaries in fcc Al with any boundary plane orientation and all six possible Burgers vectors. Comparisons with atomistic simulation results show that our continuum model is able to give excellent predictions of the energy and dislocation densities of low angle grain boundaries. We also study the energy of low angle grain boundaries in fcc Al with varying rotation axis while the remaining degrees of freedom are fixed. With modifications, our model can also apply to dislocation structures and energy of heterogeneous interfaces.

Dislocation Structure of Grain Boundaries in Single Crystals Deforming in Simple Shear

AbstractA model for the formation of grain boundaries in single crystals having a single active slip system for the case of plane strain simple shear is proposed. It is shown that non‐convexity of the condensed energy gives rise to the formation of a laminate structure, where sharp interfaces between laminate layers are interpreted as grain boundaries. Based on these results the dislocation structure of the boundaries is determined introducing a transition zone between laminate layers, where smooth functions of displacement and plastic slip connect adjacent layers. (© 2015 Wiley‐VCH Verlag GmbH &amp; Co. KGaA, Weinheim)

Carrier Recombination Activity and Structural Properties of Small-Angle Grain Boundaries in Multicrystalline Silicon

The carrier recombination activity and structural properties of small-angle (SA) grain boundaries (GBs) in multicrystalline Si (mc-Si) were systematically investigated by electron-beam-induced current (EBIC) and by transmission electron microscopy (TEM). At 300 K, SA-GBs with a tilt angle from 0 to 10° generally showed weak EBIC contrast (0–10%) with a maximum contrast appearing at 2°, while some special SA-GBs with a tilt angle of 2–3° showed particularly strong contrast (∼30%). At a low temperature (100 K), all the SA-GBs showed strong EBIC contrast despite the tilt angle. Possible explanations for the variation of the EBIC contrast are discussed in terms of the interaction and reconstruction of the boundary dislocations. When decorated with a metal impurity such as Fe, the SA-GBs showed much stronger EBIC contrast than the large-angle GBs, indicating that SA-GBs are effective gettering sites for impurities due to their particular boundary dislocation structures.

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 Σ5 [001] (310) and two Σ9 [110] (1\(\overline 1\)4). It was found that in the Σ5 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 Σ9 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 Σ11 was refined according to the new results.

Grain Boundary Dislocation Structure and Motion in an Aluminum Σ=3 [011] Bicrystal

ABSTRACTHigh-resolution transmission electron microscopy (HRTEM) observations are presented of a/3[111] grain-boundary dislocations in an aluminum Σ=3[011] bicrystal. These dislocations are present on both (111) (coherent twin) and (211) (incoherent twin) facets of the bicrystal boundary. The dislocations on the coherent twin facet migrate by a climb process that increases the thickness of the twinned material. These dislocations originate on a Σ=3 (211) incoherent twin boundary where they are closely spaced and dissociated in a wide core configuration. Atomistic calculations of the defect structure and interaction of multiple a/3[111] grain boundary dislocations are discussed.

Dislocation boundaries and active slip systems

Part of the dislocations which have participated in the plastic deformation of a polycrystalline metal are stored in dislocation boundaries in a two- or three-dimensional arrangement. The dislocations in such boundaries can be analysed by determining the misorientation between neighbouring crystallites and the boundary orientation. Information about the dislocations in the boundaries can also be obtained by an analysis of active slip systems based on the crystallite orientation and the imposed stress or strain state in combination with appropriate constraint conditions. In the present paper an analysis of the boundary dislocation structure and of the slip systems has been conducted for pure aluminium cold-rolled to a von Mises strain of 0.41. The results show that a substantial majority of dislocations in different types of dislocation boundaries are from the primary and conjugate slip system in the adjoining crystallites. A basis is therefore provided for integrating deformation structure observations with plastic deformation behaviour.

Influence of Grain Boundary Morphology on Superconducting Properties in YBa2Cu3Ox Ceramics

The critical current density (Jc) in small-grained YBa2Cu3Ox ceramics with varied sintered densities has been found to show characteristic behavior with a peak around a relative sintered density (R. D.) of 90%. This characteristic behavior of Jc in the materials has been investigated from the view points of the changes of both their grain morphologies and grain boundary dislocation structures (GBD) associated with sintered density. GBD networks occurred to relax the localized strain at the grain boundaries regardless the degree of lattice matching thereof, which was estimated using a coincidence-site-lattice (CSL) model. The GBD networks existing at the boundaries were found to reduce the Jc of the materials. The width (δ) of GBD in the materials, determined by transmission electron microscopy, was found to increase rapidly above 90% R. D. The increase in δ is explained in terms of accumulated internal stresses at the grain boundaries, which are assumed to originate from an increase in the aspect ratio of the ceramic grains.

On the Hierarchy of Dislocation Descriptions of Grain Boundary Structures

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Step Structure of Dislocation Boundaries in White Tin Single Crystals. Part I. Observations

The dislocation structure of boundaries, introduced to crystals by stretching and then annealing, was observed. The boundaries were revealed on the (001) surface by an etch hillock technique. They lay nearly in the [010] direction and the dislocation arrangement in them resembled a set of stairs consisting of a series of treads and steps. Observations led us to the conclusion that the dislocations in the treads belong to the slip system <100>{010} and those in the steps to the (1/2) <111>{11̄0}.

X-ray diffraction by a low-angle twist boundary perpendicular to crystal surface. III. The integral characteristics

For X-ray diffraction by a pure low-angle twist boundary perpendicular to a crystal surface, within the framework of the kinematic and dynamical theories, the following integral characteristics are calculated: (a) the bicrystal reflectivity in the vicinity of the lth reflection; (b) the integrated intensity of the lth reflection; (c) the bicrystal total reflectivity, i.e. the sum of the integrated intensities over all reflections. The case for even h. b (b is the diffraction vector, b is the Burgers vector of the boundary screw dislocations) is considered. In dynamical theory an increase of the total reflectivity of a bicrystal due to the boundary dislocation structure is obtained.

Secondary grain boundary dislocation structures in gold and silver 〈001〉 twist boundaries revisited

Abstract A search was made for the presence of localized secondary grain-boundary dislocations (SGBDs) in selected [001] twist boundaries in gold and silver using transmission electron microscopy Screw SGBD networks were detected in near-Σ5, -Σ13, -Σ17, -Σ25 and -Σ29 boundaries in gold and in near-Σ-5 boundaries in silver. The Σ25 and Σ29 networks were observed for the first time and extend the range of SGBD structures observed in [001] twist boundaries in gold beyond that found in earlier work. The observation of Σ5 SGBDs in silver contradicts an earlier claim that these SGBDs are delocalized in this metal. Extensive tests were carried out to verify that all of the observed SGBD images were indeed due to localized dislocations and were not moire fringe patterns.

Structure of Perturbed Twin Boundaries in Silicon

ABSTRACTSilicon bicrystals containing Σ =3(60°/[111]1,2) twin boundaries have been fabricated by sintering together single crystal (IMi) :vafers (which deviated from the exact (111) by upto ±4′). Transmission electron microscopic investigation revealed the boundaries to be near-twin boundaries having a superposed tilt component. The grain boundary dislocation structure of these boundaries has been studied in a transmission electron microscope (TEM) and interpreted as arising from the interaction of a large tilt component with a smaller twist component, to give the observed low energy configuration.

Grain boundary dislocation structures in symmetric [001] tilt boundaries in aluminum

Abstract Grain boundary dislocation (GBD) structures in symmetric [001] tilt boundaries in Al bicrystals of controlled geometry have been studied using transmission electron microscopy. The intrinsic GBD structure of near-Σ1, Σ5 and Σ13 boundaries consisted of families of straight edge GBDs with Burgers vectors b=〈100〉 or 1/2〈110〉, 1/10〈310〉 and 1/26〈510〉, respectively. In each case the system chose GBDs with the smallest perfect Burgers vector perpendicular to the boundary, in agreement with previous computer simulations using the method of molecular statics and a pairwise pseudo-potential model. In addition, the b = 〈100〉 GBDs were straight and not serrated by dissociations into partial GBDs and patches of stacking fault as, according to earlier work, they are in gold. This result is attributed to the higher stacking fault energy of Al. Observations were also made of extrinsic GBD structures produced by the superposition of lattice dislocations on the intrinsic GBD arrays. The results were consistent with structures which could be obtained through a sequence of reactions in which each lattice dislocation dissociated into GBDs, possessing Burgers vectors corresponding to the boundary DSC lattice, which then interacted in various ways with the intrinsic array.

Burgers Vectors in Secondary Grain Boundary Dislocation Structures for near S9, S27 and S81 Boundaries

The Burgers vectors of secondary grain boundary dislocations, forming networks in near ~9, ~27a, ~27b and ~81a grain boundaries in polycrystalline specimens of a Cu +6 at. % Si alloy, have been determined using the technique of image matching, which involves a comparison of experimental and theoretical electron micrographs. In all cases, the Burgers vectors of the secondary grain boundary dislocations were found to be vectors of the DSC lattice corresponding to the appropriate CSL orientation. Further, in most cases, the Burgers vectors were found to be basis DSC vectors.

Steady State and Transient Capacitance Measurements of the Energy Levels of a Low Angle Tilt Boundary in a Germanium Bicrystal

ABSTRACTSteady state and transient capacitance (DLTS) measurements have been performed on a low angle tilt boundary in a germanium bicrystal, in combination with an electron microscope study of the boundary dislocation structure. A characteristic level has been found at 0.42 eV below the bottom of the conduction band, with a density about 109 cm-2 and an electronic capture cross-section about 5 × 10-12 cm2.

Stress-induced absorption and emission of point defects by grain boundaries

AbstractIt is postulated that the emission and absorption of point defects take place by dislocation climb in grain boundaries which contain structural arrays of dislocations accommodating misorientations either from single crystal or perfect coincidence orientations. In the absence of any extrinsic dislocation structure, the climb required will result in perturbations to an equilibrated array and the forces required to stabilize these perturbations are estimated by considering elastic interactions between the dislocations. This leads to a threshold driving force for point defect emission or absorption which may be manifested as a threshold stress for diffusional creep. Effects of the grain boundary dislocation structure on the threshold stress are investigated and the energy associated with an array perturbation is estimated.

Two Investigations into Grain Boundary Structure

There has been sustained interest over the last few years into both the intrinsic (primary and secondary) structure of grain boundaries and the extrinsic structure e.g. the interaction of matrix dislocations with the boundary. Most of the investigations carried out by electron microscopy have involved only the use of information contained in the transmitted image (bright field, dark field, weak beam etc.). Whilst these imaging modes are appropriate to the cases of relatively coarse intrinsic or extrinsic grain boundary dislocation structures, it is apparent that in principle (and indeed in practice, e.g. (1)-(3)) the diffraction patterns from the boundary can give extra independent information about the fine scale periodic intrinsic structure of the boundary.In this paper I shall describe one investigation into each type of structure using the appropriate method of obtaining the necessary information which has been carried out recently at Tribophysics.

On the observation of lattice and grain boundary dislocations in UO 2 deformed at high temperatures

The microstructure of a series of deformed, polycrystalline uranium dioxide specimens has been studied by transmission electron microscopy. The lattice and grain boundary dislocation structures observed correlate with three temperature regimes of deformation. At temperatures below the brittle to ductile transition temperature, T c , the specimen is completely brittle and all grains are essentially free of dislocations. The grain boundary structures observed in these brittle specimens are very regular in appearance. In the temperature range between the high temperature transition, T t , and T c , where small degrees of plastic deformation are recorded prior to fracture, the first evidence of dislocation activity within the grains is noted, while the boundary structures remain regular. Above T t , appreciable plasticity occurs prior to fracture and extensive dislocation network formation occurs in the grains of the polycrystal. In addition, the structures in the grain boundaries become very irregular in appearance. A qualitative discussion of the deformation process in polycrystalline UO 2 is derived from the observations of this study.