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On intrinsic secondary grain boundary dislocation arrays in high angle symmetrical tilt grain boundaries
Abstract
The results of atomistic calculations indicate that the boundary structures change in a strictly continuous manner with small changes in misorientation. If the assumption is made that the boundary structures in this range vary continuously at all misorientations then one may construct predictively the atomic structure of any boundary lying this misorientation range. It is shown how this construction is performed. A SGBD structure can always be assigned to a boundary containing two types of structural unit once the sequence of units is known. It is shown that this SGBD structure is not necessarily that observed experimentally in the trasmission electron microscopy.
... Moreover, the most common method to obtain GBE microstructures in most metallic materials is thermo-mechanical processing (TMP) [26]. In the context of ceramics with more complex crystal structures, CSL theory fails and hence, the existence of low-energy CSL boundaries is hard to visualise [27]- [29]. Furthermore, the techniques used (especially TMP) to obtain GBE microstructures in metallic materials cannot be used in ceramics owing to their low deformability both at room and elevated temperatures. ...
... Moreover, the most common method to obtain GBE microstructures in most metallic materials is thermo-mechanical processing (TMP) [26]. In the context of ceramics with more complex crystal structures, CSL theory fails and hence, the existence of low-energy CSL boundaries is hard to visualise [27]- [29]. Furthermore, the techniques used (especially TMP) to obtain GBE microstructures in metallic materials cannot be used in ceramics owing to their low deformability both at room and elevated temperatures. ...
... Moreover, the most common method to obtain GBE microstructures in most metallic materials is thermo-mechanical processing (TMP) [26]. In the context of ceramics with more complex crystal structures, CSL theory fails and hence, the existence of low-energy CSL boundaries is hard to visualise [27]- [29]. Furthermore, the techniques used (especially TMP) to obtain GBE microstructures in metallic materials cannot be used in ceramics owing to their low deformability both at room and elevated temperatures. ...
Recently, there have been a number of reports on the fabrication of Alumina-Zirconia (Al2O3-ZrO2 (AZ))-based eutectic ceramics using laser additive manufacturing (AM) techniques owing to the exceptional creep and oxidation resistance coupled with excellent microstructural stability in these materials. Moreover, a number of interesting microstructural features (in these materials) have been reported to be formed by the variation of process parameters (especially, laser scanning speed) associated with the aforementioned AM techniques. The present review provides an overview of the present state of research in the area of laser AM AZ-based eutectic ceramics and highlights the challenges and future outlooks in this avenue of research. In addition, the requirement of employing correlative microstructural characterisation in these materials has been highlighted in the outlooks section.
... (29) and (30) also show that the rotation elements in the image of the dimensional raising map cannot be both unitary and commute with the Hamiltonian. Upon raising the dimension by an even number, Eq. (37) shows that the anticommutation of the chiral antisymmetry with the representation of (unitary) rotation symmetry remains preserved. Antiunitary symmetry elements remain antiunitary under the dimensional raising map. ...
We study a link between the ground-state topology and the topology of the lattice via the presence of anomalous states at disclinations -- topological lattice defects that violate a rotation symmetry only locally. We first show the existence of anomalous disclination states, such as Majorana zero-modes or helical electronic states, in second-order topological phases by means of Volterra processes. Using the framework of topological crystals to construct d-dimensional crystalline topological phases with rotation and translation symmetry, we then identify all contributions to (d−2)-dimensional anomalous disclination states from weak and first-order topological phases. We perform this procedure for all Cartan symmetry classes of topological insulators and superconductors in two and three dimensions and determine whether the correspondence between bulk topology, boundary signatures, and disclination anomaly is unique.
... GBs at such unique misorientations can be referred to as the reference structures (or favored GBs [25][26][27][28] or delimiting GBs [29] ) if any GBs between the adjacent reference structures can be interpolated by a combination of those structural units. It has been shown both experimentally and numerically that the symmetrical tilt GBs are composed of two types of 2D reference structural units [19][20][21][22][23][24][30][31][32][33][34][35][36][37][38][39][40][41][42] . Recently, randomly arranged structural units have been discovered around the triple junctions of the insulating oxide thin film, showing the properties of a wide-band-gap semiconductor [43] . ...
Polycrystalline materials have been used throughout the recorded history, and their macroscopic properties strongly depend on the defects in their crystalline structures. Unique properties of the grain boundaries (GBs) should result from nearby nano-scale space, leading to the questions regarding the type of atomic polyhedra that pack the GB region as well as the universal set of structural units. It is essential to reveal the underlying mathematical framework for the polyhedral arrangement of GB structures and identify the origin of structure-property relationships in polycrystalline materials, which is a fundamental aspect but important for designing high-performance materials. Herein, 3D atomic structures of [001], [110], and [111] symmetrical tilt GBs are analyzed in the face-centered cubic (fcc) crystals, where the polyhedral units are rigorously defined in contrast to the polygonal arrangement within the 2D structural unit model. It is concluded that the GB region can only be packed by the bulk or GB-type polyhedral units with minor variations. In this study, the 3D arrangement of atomic polyhedra around the GBs is quantitatively determined and systematically described by numerical analysis. Moreover, the GB hierarchy directly follows the distribution of rational numbers that is represented by the modified Farey diagram, which represents the 3D atomic structure of the symmetrical tilt GBs in an fcc crystal. The definition of singular GB is proposed as the GB packed by at the most two types of polyhedral units, and any GB can be packed by the polyhedral units that form the singular GBs.
... For example, atomic defects such as vacancies, substitutions, or atoms at interstitial positions are not associated to a holonomy, and therefore are not considered topological. For grain boundaries separating regions of different lattice orientations, it has been suggested that they can be described as arrays of dislocations [35][36][37] or disclinations [38][39][40][41][42][43]. ...
We establish a link between the ground-state topology and the topology of the lattice via the presence of anomalous states at disclinations -- topological lattice defects that violate a rotation symmetry only locally. We first show the existence of anomalous disclination states, such as Majorana zero-modes or helical electronic states, in second-order topological phases by means of Volterra processes. Using the framework of topological crystals to construct $d$-dimensional crystalline topological phases with rotation and translation symmetry, we then identify all contributions to $(d-2)$-dimensional anomalous disclination states from weak and first-order topological phases. We perform this procedure for all Cartan symmetry classes of topological insulators and superconductors in two and three dimensions and determine whether the correspondence between bulk topology, boundary signatures, and disclination anomaly is unique.
... Une extension du modèle de Read et Shockley basée sur les unités structurelles, introduites par Sutton et Vitek Sutton et al. 1981;Sutton et al. 1982), et sur le modèle de Balluffi ) fut proposée par Wang et al. (Gui-Jin Wang et al. 1986 . Par exemple, on observera dans la Figure ( ) ...
Ce travail de thèse est dédie à l'étude de l'effet de taille dans le comportement élastovisocplatsique des matériaux nanocristallin purs à structure cubique face centrée. Ce dernier ce révèle notamment par le non respect de la loi de Hall de Petch se produisant dans cas de matériau à très faible taille de grain. Dans un premier temps, un état de l'art détaille présente le type de matériau considéré, leur structure, procédé de fabrication et comportement. Les effets des mécanismes de diffusion (fluage de Coble. Glissement de Lifshitz) son quantifier par l'introduction d'un modèle composite biphasé. Dans un second temps. L'effet de l'émission de dislocations par les joints de grains est étudie. Une nouvelle loi de comportement est introduite, traduisant de l'effet du mécanisme combinée d'émission et de pénétration de dislocations sur le comportement élasto-viscoplastique des joints de grains. Le modèle se base sur le formalisme des mécanismes thermiquement active et une méthode d'obtention des paramètres basée sur la dynamique moléculaire est introduite. Le comportement macroscopique du matériau est obtenu suite à l'application d'un schéma sécant autocohérent. Ce second modèle est complète par une analyse par éléments finis
... For example, we could denote the entire structure associated with one period of the q ¼ 22:62 + GB as a single structural unit (replacing "AC"), in which case it would be considered delimiting. Such SUs that can be decomposed into other SUs are termed multiple unit reference structures (MURS) in the literature [34]. The structure of any GB with 0 < q < 22:62 + can be described as composed of A and [AC] units, where ½, denotes MURS (see the structure of the q ¼ 18:92 + GB in Fig. 1, which is ½AC,A½AC). ...
Properties of grain boundaries (GBs) and their underlying structures are key to understanding polycrystalline material phenomena. The most widely used model for GB structure is the structural unit model (SUM), introduced ∼ 50 years ago. The SUM represents GB structure as a combination of structural units (SUs); this combination evolves systematically with GB misorientation. Despite its successes, many observations suggest the SUM does not completely describe the GB structure; its utility for predicting GB properties is limited. There has been a growing realization that, even for fixed misorientation, multiple stable/metastable structures are common (corresponding to different microscopic degrees of freedom). We generalize the SUM by considering the effect of such metastable structures. While the SUM can describe GB structure evolution between a pair of delimiting boundaries, there will be many such evolutionary paths, corresponding to SUs associated with the metastable structure of the delimiting boundaries. The equilibrium GB energy vs. misorientation does not necessarily correspond to one of these paths, but will have contributions from many. Recognizing this, we propose a new approach to predict GB structure and energy, allowing for accurate determination of the GB energy vs. misorientation based on a very small number of atomistic simulations. For example, we predict the GB energy vs. misorientation for and symmetric tilt boundaries in BCC tungsten over the entire misorientation range to a mean error of % based on atomistic simulations at only three or four misorientations. Our approach allows for the trade-off between computational cost and prediction accuracy.
... Comparison with experimental measurements revealed the periodic nature of atomic arrangements in equilibrium twist grain boundaries. A similar approach was later taken to investigate symmetric tilt grain boundaries (Sutton et al., 1981). ...
This study introduces a numerical tool to generate virtual diffraction peaks from known elastic displacement or strain fields arising in the presence of discrete straight or curved dislocations in continuous media. The tool allows for the generation of diffraction peaks according to three methods: the displacement-based Fourier method of Warren, the Stokes–Wilson approximate method and a new average-strain-based Fourier method. The trade-off between the accuracy and the demand for computational power of the three methods is discussed. The work is applied to the cases of single-crystal microstructures containing (i) straight dislocations, (ii) low-angle symmetric tilt grain boundaries, (iii) a restrictedly random distribution of dislocations and (iv) complex microstructures generated by discrete dislocation dynamics, to illustrate the differences and domains of validity of the aforementioned methods. Dissimilar diffraction profiles reveal that peak broadening from dislocated crystals has additional contributions coming from strain gradients – a feature that is rejected in the Stokes–Wilson approximation. The problem of dealing with multi-valued displacement fields faced in the displacement-based Fourier method is overcome by the new average-strain-based Fourier method.
Solute decoration at grain boundaries (GB) leads to a number of phenomenon such as changes in interface structure, mobility, cohesion etc. Recent experimental investigations on interfacial segregation in steels are based on microstructural characterisation using two correlative methodologies, namely, Transmission Electron Microscopy-Atom Probe Tomography (APT) and Electron Backscatter Diffraction-APT. Considering the growing interest in this avenue, the present review is aimed at addressing the common adsorption isotherms used for quantifying interfacial segregation and providing an overview of the present state of experimental research in the area of GB segregation in steels. The areas where an understanding of GB segregation may be utilised have also been highlighted with a focus on the experimental challenges associated with understanding GB segregation in steels.
Polycrystalline ZnO is used in a wide variety of electrical applications, and its properties are largely influenced by crystalline defects, such as grain boundaries (GBs). Therefore, in this study, the atomic structures of [0001]-symmetrical tilt GBs in ZnO have been characterized by scanning transmission electron microscopy, and the misorientation dependence of the atomic structures around GBs is thoroughly discussed based on the polyhedral-unit model. In addition to theoretical calculations, the polyhedral-unit arrangements for arbitrary tilt angles are described and predicted by a number-theory-based approach. The predicted structural-unit arrangements agreed well with those experimentally observed, indicating that geometrical restrictions determine the ZnO GB structures. Owing to the crystallographic relationship between the structural-unit Burgers vector and the GB-plane normal, the structural-unit arrangement was transformed at approximately 30∘, which is associated with a rigid-body translation from one grain to another.
Equilibrated interfaces between Ni and yttrium stabilized zirconia (YSZ) were formed by solid-state dewetting of thin Ni films on the (111) surface of YSZ single crystals at 1350 °C and an oxygen partial pressure of P(O2) = 10⁻²⁰ atm. The atomistic structure of the equilibrated solid-solid Ni[1¯10]111∥YSZ[11¯0]111 interface was determined by monochromated and aberration-corrected scanning transmission electron microscopy, using different techniques. It was found that due to the large lattice mismatch between Ni and YSZ the interface reconstructs, and adopts a unique structure which consists of a high density of misfit dislocations. However, despite the large lattice mismatch, this interface is not incoherent. The interface was confirmed to be cation terminated, which is probably due to the low oxygen partial pressure used to reach equilibrium.
Atomic structures of \(\langle 110 \rangle \)-symmetrical tilt grain boundaries in yttria-stabilized cubic zirconia are investigated from a mathematical perspective. We predicted the unique arrangement of structural units along the grain boundaries which was confirmed experimentally by atomic-resolution scanning transmission electron microscopy.
Thermal conductivities of polycrystalline thermoelectric materials are satisfactorily calculated by replacing the commonly used Casimir model (freqeuncy-independent) with grain boundary dislocation strain model (frequency-dependent) of Klemens. It is demonstrated that the grain boundaries are better described as a collection of dislocations rather than perfectly scattering interfaces.
The chapter contains sections titles:
In recent years it has become well established that fast diffusion along grain boundaries plays a key role in many important metallurgical processes including cases where net mass is transported along boundaries which act as sources and/or sinks for the fluxes of atoms. In addition, considerable advances have been made in understanding grain boundary structure, and new techniques have become available for studying kinetic phenomena in grain boundaries. This lecture will attempt to review our current knowledge of the atomistic mechanisms responsible for these grain boundary diffusion phenomena. Relevant aspects of the structure of grain boundaries and the point and line defects which may exist in grain boundaries are described first. The important experimental observations are then discussed. Diffusion models are then taken up, and it is concluded that the atomic migration occurs by a point defect exchange mechanism which, in at least the vast majority of boundaries in simple metals, most likely involves grain boundary vacancies. The grain boundary sources and/or sinks required to support divergences in the atomic (vacancy) fluxes are grain boundary dislocations. Phenomena therefore occur which resemblethe Kirkendall Effect in the bulk lattice in certain respects. Additional topics are discussed which include effects of boundary structure on boundary diffusion and the question of whether or not boundary diffusion is faster along migrating than stationary boundaries. © 1982 American society for Metals and the Metallurgical Society of AIME.
The sections in this article areIntroductionGrain Boundary Structure: Concepts and ToolsGrain Boundary DefinitionsGeometrical ConceptsDislocation ModelPrimary Dislocation NetworkSecondary Dislocation NetworkStress Field Associated with Grain BoundariesStructural Unit DescriptionsStick and Ball Structural UnitsEnergetic Structural UnitsAlgebraic Structural UnitsStructural Units and Dislocations/DisclinationsThe Limits of the Structural Unit DescriptionsComputer Simulation TechniquesMethodsBoundary ConditionsInteraction LawsExperimental TechniquesGrain Boundary Structure: Experience and Simulation ResultsSilicon and GermaniumTilt Grain BoundariesTwist Grain BoundariesDiamondSiCGaAsGaNAlNNiOComments on Grain Boundary StructuresElectrical Properties of Grain BoundariesIntroductionElectrical Effects Induced by Grain BoundariesElectronic States Associated with a Grain BoundaryPotential Barrier and Transport PropertiesDynamic Properties and Recombination PropertiesExperimental Methods for Measuring the Grain Boundary Electrical ActivityMethods Based on TransportTransient Methods
Correlation Between Electrical Activity and StructureTransport Experiments in BicrystalsTransient Properties Measured on BicrystalsEmission and Capture Properties of Silicon and Germanium Grain BoundariesPolycrystalline SiliconIntrinsic or Extrinsic Origin of Electrical Activity of Grain BoundariesImpurity Segregation and Precipitation Induced by Grain BoundariesIntroductionDopant ElementsOxygen and SulfurTransition ElementsCopperNickelIronConclusions
Mechanical Properties of Grain Boundaries in SemiconductorsIntroductionInteraction Between Dislocations and Grain BoundariesDislocation AbsorptionDislocation Transmission Across Grain BoundariesGrain Boundaries as a Dislocation SourceGrain Boundary Dislocation MovementPhysical ConsequencesGrain Boundary MigrationRecovery of the Grain Boundary Structure and CavitationDeformation ModellingConclusions
Attention is focused on the interactions which occur when lattice dislocations impinge on interfaces (i.e., grain boundaries, crystal/crystal interphase boundaries and crystal/amorphous boundaries) in solids. The lattice dislocations can generally dissociate into interface dislocations possessing smaller Burgers vectors under a driving force produced by a decrease in the elastic energy. For crystal/crystal interfaces, a wide range of possibilities exists, depending upon the grain boundary type, which extends from dissociation into a discrete number of interface dislocations to dissociations into a distribution consisting of, in the limit, an infinite number of interface dislocations possessing infinitesimal Bur.ers vectors. For crystal/ anorphous interfaces, the latter model is applicable. Examples of dissociations in these various interfaces are presented. The dissociation geometries and kinetics are described briefly. Some of the wider implications of these phenomena are mentioned.
Current knowledge of the atomistic mechanisms responsible for grain
boundary diffusion phenomena is reviewed. Relevant aspects of the
structure of grain boundaries and the point and line defects which may
exist in grain boundaries are described first. The important
experimental observations are then discussed. Diffusion models are then
taken up, and it is concluded that the atomic migration occurs by a
point defect exchange mechanism which, in at least the vast majority of
boundaries in simple metals, most likely involves grain boundary
vacancies. The grain boundary sources and/or sinks required to support
divergences in the atomic (vacancy) fluxes are grain boundary
dislocations. Phenomena therefore occur which resemble the Kirkendall
Effect in the bulk lattice in certain respects. Additional topics are
discussed which include effects of boundary structure on boundary
diffusion and the question of whether of not boundary diffusion is
faster along migrating than stationary boundaries.
As the frontier in advanced materials development has shifted into highly disordered systems, concepts of deformation based on crystal lattice dislocations often become too coarse to be of relevance. Therefore, a new deformation process, localized to dimensions smaller than those involved in dislocation mechanisms, was proposed sometime ago. Some of its important features are discussed here to suggest that this mechanism is likely to be of use in understanding the superplastic deformation of metals and alloys, ceramics, metal-matrix- and ceramic-matrix-composites, dispersion hardened materials, intermetallics, geological materials, metallic glasses and poly-glasses of grain sizes in the μm-, sub-μm- or nm-range – a much wider area of application than originally anticipated. This will allow one to define “superplasticity” as due to a unique physical mechanism, rather than by the extreme elongations obtainable in tensile testing or the strain rate sensitivity index being more than ∼0.30.
The relation between two elastic continuum approaches to grain boundary structure, the dislocation and disclination models, is discussed. It is shown that the disclination model has two advantages: a well-behaved expression for the elastic energy of disclination dipole walls, which describes the elastic energy over a wide interval of misorientations, and a continuous misorientation angle dependence of the elastic energy of grain boundaries in an interval between two delimiting boundaries. The elastic energy of the most general, faceted disclination wall is calculated. For cases in which both the energies of delimiting boundaries and elastic constants are available from atomic simulations (〈001〉 and 〈111〉 tilt boundaries in copper and 〈001〉 and 〈011〉 tilt boundaries in diamond) quantitative agreement between the disclination model and simulation results is obtained.
The sources of the multiplicity of metastable structures of grain boundaries are discussed using a recently developed structural unit model of grain boundary structure. Two sets of computer calculations of symmetrical tilt boundaries are presented and it is shown that the calculated multiplicity of metastable structures is readily predicted by the structural unit model. This multiplicity is likely to be very extensive in the case of general grain boundaries. The implications of the structural multiplicity of grain boundaries for various grain boundary phenomena as well as for interpretation of “direct observations” of grain boundary structure are discussed.
The structures of four (001) twist boundaries in f. c. c. metals are re-examined. It is shown that readily identifiable units of the SIGMA equals 5 boundaries are visible in the SIGMA equals 25, 13 and 17 boundaries together with octahedra from the ideal crystal orientation. It follows that localized, distinct stress fields of intrinsic screw dislocations exist in twist boundaries at large (possibly all) angular deviations from the SIGMA equals 5 boundary and the (001) plane of the ideal crystal.
The structural unit model (SUM) has been used to describe the structures of grain boundaries (GBs) in a range of different materials. The validity of this model for all materials has never been proven, however. The structures of Al and Ni <110> symmetric tilt grain boundaries with tilt angles between 0° and 50.5° are investigated. Computer simulations with the lattice statics technique and EAM potentials are used to find the lowest energy structures at a temperature of 0 K. The stability of the structures at elevated temperatures is tested by Monte Carlo annealing simulations. It is found that, while the SUM is applicable to the Al boundaries, it cannot be used to describe the Ni structures. The GB dislocation cores in the Al boundaries are more localized than they are in Ni. The effect of delocalized GB dislocations is discussed. The geometrical and materials dependent limitations of the SUM are summarized.
Using the framework of the structural unit model it is argued that tilt grain boundaries are one-dimensional quasicrystals. A classification of irrational tilt boundaries is suggested according to which the simplest irrational tilt boundaries may be described as a quasipenodic sequence of appropriate fundamental structural units. Elementary excitations of the quasipenodic structural unit sequences, diffraction patterns from irrational tilt boundaries, the significance of the quasicrystal concept of local isomorphism for boundary properties and extrinsic grain boundary dislocation Burgers vectors and step heights at irrational tilt boundaries are discussed.
A classification of all symmetrical grain boundaries and their tilt rotation axes based on a geometrical construction expressing the relationship between the interplanar spacing and the orientation of the normal to the boundary plane is introduced for the f.c.c. and b.c.c. lattices. It is shown that the favoured grain boundaries found by computer simulations for different models of interatomic forces are in agreement with the boundaries which belong to low levels of the classification schemes. It is anticipated that this classification, which is different from the classification based on the planar density of atomic sites, is a useful guide-line on the search for symmetrical boundaries that possess special properties.
High resolution electron microscopy (HREM) has been used to investigate the structure of [001] and [011] pure tilt grain boundaries, both near-coincident and coincident, in crystals of Ge and Si. The resolution limit for the detection of the rigid body translation using HREM has been established, and compared with the α-fringe technique. Several structural units for primary and secondary relaxations have been found; it is shown that the core extension of a secondary relaxation covers one primary period. Likewise, a detailed comparison between simulated and experimental images for a σ = 9 grain boundary is presented. Some atomic sites in the period of the grain boundary appear to be preferentially attacked by impurities.
An atomistic study of tilt grain boundary structures in f.c.c. metals has been made. The principal aim of this study is to understand the structure of long-period (`general') tilt boundaries. Boundaries for which Sigma
A new approach to the study of hierarchical grain boundary dislocation structures is proposed. It is shown that the class of primary grain boundary dislocations (GBDs) is wider than that of lattice dislocations and includes GBDs of all favoured boundaries of the same misorientation axis. A simple analysis of the asymptotics of stress fields created by primary dislocation networks obviously shows the nature of higher-level (virtual) dislocations and allows to calculate their Burgers vectors not knowing the geometry of reference structures responsible for each level. An algorithm is presented for constructing the GBD hierarchy and determining the number of its members for any boundary with a given misorientation angle.[Russian Text Ignored].
The Read-Shockley equation describing the dependence of grain boundary energy on misorientation of grains has been reformulated using the recently developed structural unit model of the atomic structure of grain boundaries so that it is applicable to general high angle boundaries. The boundary energy then consists of the energy of a reference structure, and of the core and elastic energies of the corresponding DSC dislocations. While the latter part of the boundary energy is determined using the elastic theory of dislocations the former two parts are determined on the basis of atomistics of grain boundaries employing the structural unit model. In the framework of this analysis the minimum number of reference structures in a give misorientation range as well as the extent of misorientations related to a given reference structure are determined. The positions of cusps in the energy vs misorientation dependence and their relative depths and extent are also determined. The validity of this model is demonstrated for tilt boundaries studied by atomistic computer simulations.
Interfaces are a critical determinant of the full range of materials properties, especially at the nanoscale. Computational and experimental methods developed a comprehensive understanding of nanograin evolution based on a fundamental understanding of internal interfaces in nanocrystalline nickel. It has recently been shown that nanocrystals with a bi-modal grain-size distribution possess a unique combination of high-strength, ductility and wear-resistance. We performed a combined experimental and theoretical investigation of the structure and motion of internal interfaces in nanograined metal and the resulting grain evolution. The properties of grain boundaries are computed for an unprecedented range of boundaries. The presence of roughening transitions in grain boundaries is explored and related to dramatic changes in boundary mobility. Experimental observations show that abnormal grain growth in nanograined materials is unlike conventional scale material in both the level of defects and the formation of unfavored phases. Molecular dynamics simulations address the origins of some of these phenomena.
Any physical property, p, of a grain boundary, which depends primarily on the atomic structure of the core, e.g., boundary diffusivity or core energy. The purpose of the present note is to demonstrate that the recently determined structural unit model for the core structure allows one to estimate p for any boundary in a series of symmetrical tilt boundaries possessing a range of tilt angles if values of p for a few particular boundaries in the series are known. More specifically, that p for all boundaries with misorientations between those of two so-called ''favored boundaries'' can be estimated from a knowledge of the values of p for the two favored boundaries and the intermediate boundary made up of equal numbers of the structural units comprising the two favored boundaries. Applications of the results to measurements of boundary diffusivities and boundary energies are indicated.
Twenty-one 〈110〉 symmetric tilt grain boundaries (GB’s) are investigated with atomistic simulations, using an embedded-atom method (EAM) potential for a low stacking-fault energy fcc metal. Lattice statics simulations with a large number of initial configurations are used to identify both the equilibrium and metastable structures at 0 K. The level of difficulty in finding the equilibrium structures is quantitatively assessed. The stability of the structures at an elevated temperature is investigated by Monte Carlo annealing. A form of GB dissociation is identified in a number of the boundaries. These structures are used to develop a dislocation model of GB dissociation by stacking-fault emission. Also, an attempt is made to apply the structural unit model (SUM) to the simulated boundaries and problems that are encountered for GB structures in low stacking-fault energy metals are enumerated and discussed. © 1996 The American Physical Society.
An assessment of the experimental findings leads to the conclusion that optimal structural superplasticity results from grain/interphase boundary sliding–diffusion coupled flow. An analysis of the boundary sliding process is presented first. By suggesting that both regions I and IIa (lower stress range of region II) of superplastic flow result from sliding-diffusion coupled flow, and treating mesoscopic (cooperative) boundary sliding as the rate controlling mechanism for optimal superplasticity, the stress, temperature, and grain size dependences of the strain rate of deformation are predicted. The above equation is then related to the stress exponent n (the inverse of the strain rate sensitivity index m). An analysis for determining the true activation energy for the rate controlling process is presented. Expressions for the distribution of internal stresses arising from sliding and the boundary viscosity are derived, and the presence of an initial unsteady region, predicted in an earlier analysis, is shown to be a natural consequence of this approach.MST/3074
A critique of the structural unit model is presented. It is shown that the predictive capacity of the model is severely limited when it is applied to boundaries with relatively-high-index rotation axes. Recent computer simulations suggest that ‘high index’ means ⟨221⟩ and above. A new approach to grain boundary structure is needed for mixed tilt and twist boundaries.
A contribution to the study of the left bracket 001 right bracket symmetrical tilt boundary structure in diamond-structure materials is presented, based on an examination of a germanium SIGMA equals 5 (13 OVER BAR 0) bicrystal very close to the coincidence orientation relationship. From an alpha fringe contrast analysis and an electron diffraction study, the relative position of the adjacent crystals and the interface are deduced. A structural model of the SIGMA equals 5 (13 OVER BAR 0) boundary is suggested and discussed.
Intrinsic secondary grain boundary dislocation (GBD) structures were observed by weak-beam transmission electron microscopy in a variety of [001] twist boundaries in MgO prepared by a welding technique. Square networks of intrinsic screw GBDs were found in boundaries possessing twist deviations from the exact ∑ = 1, 6, 13, 17, 25, 29 and 53 coincidence site lattice (CSL) misorientations. (∑ ≡ fraction of lattice sites in coincidence.) These GBDs were all perfect GBDs with Burgers vectors given by the primitive vectors of the corresponding DSC lattice except in the case of ∑ = 13 where a square array of apparently partial screw GBDs was observed. Arrays of screws GBDs were not detected in a number of high. ∑ boundaries. Superimposed arrays of edge-type intrinsic GBDs were observed in all boundaries when a small tilt component was present. The structures were similar in many respects to those observed in an earlier study of corresponding [001] twist boundaries in gold. All results appeared consistent, with the CSL model for grain boundaries. suggesting that this model therefore holds for grain boundaries in ionic solids.
A classification of grain boundaries based on the separation of the atomic planes parallel to the boundary plane is presented. The results are compatible with computer simulations of the grain boundary atomistic structure interpreted in the framework of the structural unit model. The classification scheme can be used as a guide-line for the theoretical and experimental investigation of the grain boundaries with special properties.Es wird eine Klassifikation der Korngrenzen dargestellt, welche auf dem Abstand zwischen den zur Korngrenze parallelen Atomebenen aufgebaut ist. Die Ergebnisse sind verträglich mit Computersimulationen der atomistischen Korngrenzenstruktur, die im Rahmen des Modells der strukturellen Einheiten interpretiert werden. Das Klassifikationsschema kann als Leitfaden für theoretische und experimentelle Untersuchungen der Korngrenzen mit speziellen Eigenschaften dienen.
Most real solid materials are used in the form of polycrystals, high-angle grain boundaries (GB's) being a necessary ingredient of their structure. The paper deals with the results of investigations of GB structural rearrangements under thermal and mechanical influences as well as with their role in deformation and recrystallization processes.
In case of germanium, the atomic structure of σ = 33{144} (θ = 20.05°) tilt grain boundary was analyzed. It was found that it contained a glide mirror symmetry and not a mirror plane symmetry. The high resolution transmission electron microscopy images were combined with energy calculations of relaxed structures described using semi-emprical potentials to show the glide mirror symmetry. Results showed that the atomic structure at grain boundary was better described by the model consisting of a tetracoordinated structure made up of L+, L- and C structural units. This structure was more stable than the purely symmetrical one.
The structure of intrinsic ledges at interphase boundaries has been interpreted with extended O-lattice/DSC-lattice approaches.
The distribution of structural ledges can be predicted if the spacing difference between parallel matrix and product planes
is treated as a measure of the relaxed coincidence condition. A small rotation away from the low-index planar parallelism
introduces a series of interfacial dislocations that cancels the spacing difference, resulting in a lattice invariant line.
Misfit-compensating ledges at bcc: hcp interfaces are produced as a ledged interface intersects additional O-points that are
recognized with the incorporation of previously omitted bcc atom positions into the O-lattice construction. Energetic consideration
suggests that structural interfacial energy may decrease when a flat interface becomes ledged with misfit-compensating ledges.
Burgers vectors associated with structural ledges and misfit-compensating ledges are displacement shift complete (DSC) lattice
vectors. Precipitate and martensite crystallography may both include a lattice invariant line, but they are involved in different
interphase boundary characteristics. Assumptions and implications in precipitate and martensite crystallography are discussed
in the framework of the O-lattice theory and phenomenological theory of martensite crystallography.
A model that was proposed originally to account for optimal superplasticity in metals and alloys with grain size in the micrometer
range and later extended in a few subsequent papers to cover optimal superplastic deformation in ceramics, sub-micrometer-grained
and nanostructured materials and intermetallics is described, with an emphasis on the current ideas used in this model and
the mathematical procedure used at present (yet to be published in detail) for validating the proposals. The central assumption
is that the rate controlling deformation process is confined to high-angle grain/interphase boundary regions that are essential
for grain boundary sliding developing to a mesoscopic scale (defined to be of the order of a grain diameter or more) and for
superplastic flow setting in. The strain rate equation was validated against experimental observations concerning metals,
alloys and ceramics of micrometer- and sub-micrometer grain sizes, nanostructured materials and intermetallics.
A definition of structural defects in amorphous solids in terms of the distribution of the internal stresses on the atomic level and of the symmetry of the environment of individual atoms is introduced. This definition does not require an ideal reference structure. The concept of the internal stresses on the atomic scale has been previously applied to describe the core structure of crystalline dislocations. In this paper it has been applied to the model amorphous structure generated by a computer simulation. It was found that there is a significant variation in the magnitude and direction of internal stresses, and that there are regions of 10 to 20 atoms over which the stresses remain either high or low. A method of calculating the symmetry coefficients at atomic sites has been proposed, and applied to the same system. It has been shown that there are significant correlations between the internal stresses and the local symmetry. The low-stress, high-symmetry regions resemble microcrystalline clusters, while the high-stress, low-symmetry regions show a stress-distribution pattern and symmetry similar to the crystalline defects. The structural defects in amorphous structures are defined as the latter regions, and the significance of such a definition in elucidating the properties of amorphous solids is discussed.
We present nonlinear self-consistent calculations of the charge density induced by isolated Li+, K+, Mg++, Al+++, and Ca++ ions when placed in an electron gas of the appropriate metallic density. By comparison with linear-response theory we show that in the first four metals nonlinear effects in the response of the conduction electrons to the ionic perturbations play an important role in determining the charge density and the interionic potential. However as in the case of Na studied in the previous paper these nonlinear effects can be simulated by using a suitably adjusted model potential. The calculated phonon dispersion curves for Li, K, and Al agree very well with experiment. Nonlinear effects are also very likely to be important in Ca but further work is necessary before conclusions can be drawn.
Theory of Dislocations
- Hirth