Low Energy Dislocation Structures Research Articles

Dislocation motion and formation of dislocation structures during in situ deformation in a high voltage electron microscope

Complex dislocation structures develop during in situ deformation of MgO single crystals in a high voltage electron microscope. In ionic crystals, slip usually starts at a few widely separated places. The slip bands broaden by cross-slip, which also controls the dislocation multiplication. Later on, oblique slip systems are activated. A great amount of dislocation debris is produced in the course of deformation. Most probably, the debris is responsible for a great part of the work hardening. Many details of the dislocation arrangement correspond to low energy dislocation structures. It is argued, however, that the deformation process is governed by a principle which keeps the flow stress as low as possible.

Theory of plastic deformation: - properties of low energy dislocation structures

Work-hardening phenomena are based on the very fundamental principles (i) that at the position of every dislocation axis the respective resolved shear stress cannot exceed the friction stress, including the self-stress of bowing dislocations, and (ii) that always that structure forms which among those accessible by the dislocations minimizes stored energy per unit length of dislocation line. Such dislocation structures have been named LEDSs. The corresponding work-hardening theory, the mesh length theory, is applicable to all materials deforming via gliding dislocations and to all types of deformation. Results previously achieved with the mesh length theory are summarized, and a number of new developments are discussed. Depending on the dislocation structures formed, the work-hardening behavior differs. Easily intersecting glide causes dislocation cell structures with almost dislocation-free cell interiors delineated by dislocation rotation boundaries. Pronounced planar glide causes Taylor lattices characterized by local planar order parallel to the one or perhaps two most highly stressed glide plane(s), no systematic lattice rotations, and overall uniform dislocation density. The most widely observed basic features of work hardening are explained in general terms. Specific applications are indicated for layer-type crystals, h.c.p. single crystals, single-crystal and polycrystalline pure f.c.c. metals and α-brass-type alloys, precipitation-hardened materials and steels. Included are the different stages of work hardening, dynamical effects in low temperature plasticity, the general characteristics of grain boundary strengthening and the Hall-Petch relationship. In addition, proposed explanations for (i) glide system interactions in polyslip resulting in microbands and affecting texture formation, and (ii) creep without stress dependence of dislocation density, are discussed.

Energy minimization of dislocations in low-energy dislocation structures

LEDS is the acronym for low-energy dislocation structures. LEDS are those structures in which the energy per unit length of participating dislocations is minimized through mutual stress-screening. They are characterized by the (virtual) absence of long-range stresses and by an alternation between areas with high and low dislocation densities. By means of a number of examples it is shown that the considerable majority of actually occurring dislocation structures are LEDS. LEDS ist das Akronym für low-energy dislocation structures (i.e. energiearme Versetzungsstrukturen). Das sind alle Strukturen, in denen die freie Energie pro Längeneinheit der beteiligten Versetzungen durch gegenseitige Spannungsabschirmung minimalisiert ist. Sie sind charakterisiert einmal dadurch, daß sie (praktisch) frei von langreichenden Spannungen sind, und zweitens durch Gebiete mit abwechselnd kleiner und hoher Versetzungsdichte. An Hand einer Reihe von Beispielen wird gezeigt, daß die große Mehrheit aller beobachteten Versetzungsstrukturen LEDS sind.

LEDS: Properties and effects of low energy dislocation structures

Not only epitaxy and phenomena in connection with solid transformations, but also the static mechanical properties of crystalline materials can be understood via Low Energy Dislocation Structures (LEDS). They are characterized by areas of high dislocation density embedded in, or interspersed with, almost dislocation-free areas. LEDS include misfit boundaries, low angle dislocation boundaries, the Taylor lattice (formed either from interacting pile-ups of alternating sign or from accumulations of dipolar dislocation loops), dipolar dislocation walls (as in “deformation bands” formed in unidirectional deformation, or in the “ladder structure” as well as in the “maze structure” formed in fatigue) and the “mosaic block” structure of old, now recognized to be indentical with the dislocation cell structure. By means of LEDS the empirical rules of (1) the parabolic dependence of shear stress on dislocation density and (2) the decrease of the dislocation cell size with increasing stress are readily understood, as is (3) the three-stage work-hardening curve. The quoted inverse dependence of dislocation cell diameter on flow stress can be used to deduce the stress distribution which caused the cell structure, e.g. after shock loading, about crack tips or underneath wear scars. “Recovery” is the removal of jogs and kinks in LEDS, while the mild stress dependence of flow stress on strain rate is explained through the increase in the fraction of the dislocations which move at any given moment.

Low energy dislocation structures in highly deformed materials

Gross low temperature plastic deformation of metals results from the movement of large numbers of dislocations. This movement is characterized by dislocation-dislocation interaction events statistically distributed in time and space and by the continuing trend of the dislocation density to rearrange into low energy configurations. The various approaches proposed to link flow stress and strain hardening with the evolving substructure may be grouped into families, emphasizing one or the other of those aspects. The first examines possible low energy dislocation configurations and derives the observed flow stress and strain hardening from the characteristics of the proposed dislocation architecture. The second phase relates flow stress evolution to the kinetics of dislocation movement, i.e. the build-up of the substructure as resulting from successive interaction events. The two approaches have been developed independently. It is the aim of the present paper to examine to what extent experimental observations fit into the framework of the existing models (the “kinetic” model being somewhat modified by an addition proposed in this paper) and to what extent the models are complementary in covering different aspects of the one same truth or are mutually exclusive.

Low energy dislocation structures in interfaces

Characterization of interface structure involves describing and determining the manner in which misfit is distributed. Theories based on crystallography and elasticity are used to discover both minimum misfit lattice misorientations and interface planes. With the crystallographic variables defined the Frankvan der Merwe analysis seeks to determine how the misfit is distributed. Computer modelling embodies an explicitly atomistic approach and has provided a bridge between experiment and other analytical methods. Observations validate many of the theoretical concepts. The facetted TiMn parent martensite interface can be understood in terms of Burger's vector density minimization as can the orientation relationships found between b.c.c. deposits and single-crystal f.c.c. substrates. High resolution transmission electron microscopy confirms the extension of the dislocation wall model for low angle boundaries to rotation angles as high as 26°, which had been suggested by computer modelling. We know that the dislocation structure of an interface does not necessarily lead to a complete understanding of the interface core structure because of complications resulting from relative lattice translations and other sources of multiplicity of structure which are evidenced through observations of imperfect interface dislocations and directly through measurement of not necessarily crystallographically equivalent lattice translations. In simple cases high resolution transmission microscopy, ion channelling and UV photoelectron spectroscopy sometimes in combination have permitted a full determination of the atomic structure of interfaces and revealed the physical nature and reality of low energy dislocation structures.

Dislocation structures in a ferrite steel

Using electron microscopy, the dislocation structure in annealed and in fatigued 12CrMo ferrite steel has been studied. Some types of low energy dislocation structure have been observed in the annealed steel. The dislocation structure in the annealed steel changes considerably under pulsating tensile stresses. Both low and high energy dislocation structures exist in the fatigued steel. The typical low energy dislocation structure is a hexagonal dislocation network.

Low energy dislocation structures caused by martensitic transformations

The low energy dislocation structures in microdomains, twin domains and self-accommodating interfaces, causes by martensitic transformations, are evaluated for several B2 alloys with 18R, 9R and 3R martensite structures by the modern theory of martensitic transformations. The transformations are accomplished by two lattice-variant shears and a volume change relaxation and are one dimensional in origin when the order parameter couples linearly with the spontaneous strain. The primary shear, on a system with degenerate stress sense, periodically alternates its direction to minimize long-range stress fields, while the habit plane shear minimizes long-range stress fields by “self-accomodation” between variants. The habit planes and shape strains, computed by this theory, are the same as those for the phenomenological theory; this is discussed. The lattice-variant transformation dislocations originate from the three-dimensional network, where screw dislocation segments dissociate to form fluctuating microdomains (localized soft modes), and these thicken when the transformation dislocations multiply by a cross-slip dissociation mechanism. The computed Schmid factors for variants in self-accommodating groups show opposite signs, indicative of a minimum long-range stress field. The resulting low energy dislocation structure is an interface of primary shear dislocations of alternating signs and habit plane shear dislocations in self-accomodating variants with almost opposite shear strains. The results indicate criteria for high pseudoelasticity and shape memory behavior with a mobile low energy dislocation structure which is highly susceptible to an applied stress.

Low energy dislocation structures produced by cyclic deformation

Cyclic deformation in push-pull straining provides ideal conditions for achieving low energy dislocation structures because large cumulative strains give rise to high dislocation densities and the to-and-fro dislocation motions enhance entrapment probabilities. At low strain amplitudes the structures are dominated by clusters of prismatic loops; evidence for the dislocation content and interaction of the clusters is reviewed and is shown to be consistent with the establishment of low energy arrays. At higher amplitudes the dislocation structures are dominated by dislocation walls which are strongly dipolar. The deformation which occurs in these structures at low numbers of cycles does not seem to be consistent with low energy arrays, or at least only with those of moderately low energy. However, with sufficient cycling, lower energy arrays seem to become established and to promote homogeneity of the strain. At still higher amplitudes, complex cellular structures are observed and the complications of these structures can be interpreted convincingly in terms of low energy dislocation structures.

Low energy dislocation structures in ionic crystals and semiconductors

Low energy dislocation structures in two classes of crystals are discussed according to the results of recent transmission electron microscopy observations and mechanical studies. Special attention is paid to the roles of cross-slip and climb processes at various temperatures in establishing characteristic dislocation structures.

Low energy dislocation structures caused by phase transformation

A review of the theory of Frank and van der Merwe applicable to phase transformations in a variety of systems is presented. This theory recognizes the lattice periodicity by employing an interfacial periodic interaction potential. The two primary defects at interphase boundaries are shown to be lattice-strain- and misfit-compensating dislocations. Although the theory was developed for thin films, its applicability to phase transformations in bulk materials is demonstrated. A comprehensive review of experimental results of interphase structure in various phase transformations follows. The review covers precipitation in metals, ceramics and minerals, directional solidification, lamellar solid-solid phase transformations, and spinodal and martensitic transformations. All these contain a low energy interfacial dislocation structure at partially coherent interphase boundaries.

Geometrical factors influencing the orientations of dipolar dislocation structures produced by cyclic deformation of f.c.c. metals

A recently proposed geometrical model to explain the orientations of labyrinth dipolar walls produced by cyclic deformation of f.c.c. metals is extended to explain the orientations of loop patches, channels within the matrix structure, and dipolar walls within persistent slip bands. The model is based on determining favourable stacking arrangements for dipolar loops involving one or two Burgers vectors and slip systems and on determining the directions in which stacking should be limited. The stacking of dipolar loops into regular networks results evidently in low energy dislocation structures. The dipolar loops are assumed to be swept into the dipolar dislocation arrangements by edge dislocations. When excess dipolar loops of one slip system are present, the ability of the dipolar arrangements to accommodate these becomes important. Good agreement is found between the predictions of this model and the available experimental evidence.

Low energy dislocation structures in epitaxy

The principle of minimum energy was applied to epitaxial interfaces to show the interrelationship between misfit, overgrowth thickness and misfit dislocation configurations were presented for selected interfacial geometries. A review of the interfacial energy calculations was made and a critical assessment of the agreement between theory and experiment was presented. Modes of misfit accomodation were presented with emphasis on the distinction between kinetic effects and equilibrium conditions. Two-dimensional and three-dimensional overgrowths were treated together with interdiffusion-modified interfaces, and several models of interfacial structure were treated including the classical and the current models. The paper is concluded by indicating areas of needed investigations into interfacial structure.

Low energy dislocation structures caused by sliding and by particle impact

Tribological processes cause large plastic strains and plastic strain gradients adjacent to the interface between the interacting materials. For sliding wear and erosion test specimens, the dislocation structures observed in the plastically deformed material are consistent with those expected when energy is minimized. Studies of these structures can contribute to our knowledge of deformation and dislocation substructures produced at large strains under other test conditions. Tribological processes also create patches or layers of mechanically mixed material on one or both of the contacting surfaces. This material is important in the generation of typical wear debris. Studies of the mechanically mixed material may also be helpful in understanding the structure and properties of ultrafine grained two-phase materials.

Low energy dislocation structures associated with cracks in ductile fracture

Ductile fracture in metals and alloys is preceded by work hardening and necking. Microstructural processes, previously explored by in situ transmission electron microscopy, have been re-examined in the context of interactions between glide dislocations and crack tips. In this, the parameters which significantly influence experimental findings have been critically reviewed and theoretical aspects of ductile fracture have been examined including the principle of energy minimization. Consideration was given to the displacement of the stress singularity ahead of the crack tip on account of the plastic zone and the effects of thermal instabilities during crack growth. Crack propagation occurs in ductile materials mostly by void coalescence. This requires the nucleation of microcracks ahead of the crack tip as was observed experimentally in agreement with theoretical expectations. Microcrack initiation was seen to take place at dislocation cell walls which represent the most frequently formed low energy dislocation configurations in work-hardened metals. As a consequence, too, the formation of a plastic crack and its grorth in a virgin crystal are distinctly different from the nucleation and growth of a crack in a crystal with a well-defined cell structure that was formed through prior deformation. Dislocation multiplication is considered to take place by the supercritical bowing of the longest free link lengths present within the cell walls, as also observed experimentally. The microstructural changes that take place in the plastic zone ahead of the crack tip are found to be more important in fracture than the microscopic processes immediately at the tip itself.

Low energy dislocation structures due to unidirectional deformation at low temperatures

The line energy of dislocations is { Gb 2 f( v)/4 π} 1n(R/b) with R range of the dislocation stress field from the axis. This equation implies that quasi-uniform distributions are unstable relative to dislocation clusters in which neighboring dislocations mutually screen their stress fields, correspondingly leaving the major fraction of the volume free of dislocations. The value of R decreases in the following order: pile-ups to dipolar mats, Taylor lattices, tilt and dipolar walls to dislocation cell structures. This is the same order in which dislocation structures tend to develop with increasing dislocation density and hence increased dislocation interactions, leading to the corresponding energy decrease per unit length of dislocation line. Taking into consideration also the longer-range “termination stresses” of finite dislocation boundaries, and minimizing the total energy, explains the size dependence of cells on stress as well as the occasionally observed pattern of rectangular cells with alternating left-right rotation about a common axis. Energy minimization further explains the transition from stage I to II in f.c.c. metals. The following topics which are at the present frontier of research are considered in this paper: (i) the sum of the energy stored in the dislocation line energy and the longer-range stresses is significantly smaller than some recently reported experimental values; (ii) subdivision of cells is discussed on the basis of observations in rolled aluminum showing a “hierarchical” cell structure; (iii) suggestions are made to account for microband formation on the basis of energy minimization. Finally, the relationship between surface markings and the underlying dislocation structure is discussed and related to slip processes taking place during uniaxial deformation.

Low energy dislocation structures due to recovery and creep

The properties of creep subboundaries and dislocation walls which are built up as a result of work-hardening are reviewed. These include the constituent dislocations and their geometry, the associated stress fields, their mobility and the way in which they recover during annealing treatments. The process of cell formation and fragmentation is discussed in terms of these properties. The features of cell walls and subboundaries and their evolution are compared with prominent theoretical models.