![]() Our goal is to explore the causes of this transition and its intrinsic mechanism. We are particularly interested in a transition numerically observed in these defects, whereby dislocations appear at the core of grain boundaries when the angle made by the rolls on each side is decreased. In what follows, we focus on symmetric grain boundaries, which are invariant under reflection across their core, the latter then taking the form of a straight line. The existence of the latter is due to the almost invariably present rotational symmetry of the system before rolls emerge, resulting in a degeneracy associated with the orientation of the pattern.Īs a consequence, in a spatially extended system, regions of rolls of different orientations are likely to appear, thereby giving rise to grain boundaries, which are curves separating these regions. This article is concerned with two-dimensional stationary stripe patterns and their line defects, which are grain boundaries. Particularly fascinating is the role played by nonlinearities and symmetries in defining the properties of emerging patterns and of their defects. Pattern-forming systems, their solutions, defects and instabilities, have driven the field of nonlinear phenomena for more than 100 years (see as well as for instance and references therein). This article is part of the theme issue ‘Stability of nonlinear waves and patterns and related topics’. Outcomes of this work regarding the role played by phase derivatives in the creation of defects in pattern-forming systems, about the role of harmonic analysis in understanding the phase structure in such systems, and future research directions are also discussed. These observations are then connected to properties of the associated phase diffusion equation. Numerical results of the SH equation that aim to analyse the phase structure of far-from-threshold grain boundaries are presented. Our goal is to shed some light on this transition, which provides an example of defect formation in a system that is variational. It is well known that, as the angle made by the rolls on each side of a grain boundary is decreased, dislocations appear at the core of the defect. The work is set in the context of a canonical pattern-forming system, the Swift–Hohenberg (SH) equation, and of its phase diffusion equation, the regularized Cross–Newell equation. In under-deposit corrosion and hydrogen damage, grain boundaries are the site at which the methane collects that leads to the intergranular cracking characteristic of hydrogen damage.This article discusses numerical and analytical results on grain boundaries, which are line defects that separate roll patterns oriented in different directions. Grain boundaries will oxidize or corrode more rapidly, usually referred to as grain-boundary penetration or intergranular attack. The grain-boundary atoms are more easily and rapidly dissolved, or corroded, than the atoms within the grains. Both low- and high-angle boundaries are retarded by grain refinement, to minimize or prevent recrystallization or grain growth during heat treatment. The mobility of low-angle boundaries is much lower than that of high-angle boundaries. High-angle boundaries are considerably more disordered, with large areas of poor fit and a comparatively open structure. High-angle grain boundaries are whose misorientation is greater than about 11 degrees.Low-angle grain boundaries are those with a misorientation less than about 11 degrees.Grain boundaries have two types, as per their orientation: The properties of grain boundaries often determine the grains': Where there is a disturbance in the atomic packingĬharacterization of grain boundaries is of critical importance in materials studies.Transition regions between the neighboring crystals.The grain boundary is a transition region in which some atoms are not exactly aligned with either grain. The juncture between adjacent grains is called a grain boundary. Corrosionpedia Explains Grain Boundary (GB)
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