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MULTIPLICITY OF GRAIN BOUNDARY STRUCTURES : VACANCIES IN BOUNDARIES AND TRANSFORMATIONS OF THE BOUNDARY STRUCTURE
Abstract
Un nombre de structures non-équivalentes ont été trouvées dans les études atomistiques des joints de grains périodiques. Ces structures peuvent se transformer mutuellement en ôtant, ou en ajoutant des lamelles d'atomes qui sont parallèles aux joints [19]. Cette multiplicité résultante des structures est très extensive pour des joints de grains généraux avec de longues périodes. On montre ici que les configurations de lacune d'énergie plus basse dans les joints de grain correspondent à la présence locale des unités de structures alternatives, alors que l'absorption ou l'émission des lacunes à un joint peuvent être regardées comme des transformations structurelles locales. Alors, quand la température monte et la concentration équilibre des lacunes monte, on augmente le désordre correspondant à la présence de diverses unités alternatives dans le joint. Ceci peut arriver ou graduellement, ou par une transformation du type ordre-désordre. On montre aussi que l'accumulation de lacunes ou d'impuretés dans le joint peut provoquer des transformations de glissement entre des structures de joint alternatives, conduisant en même temps à la migration des joints. Nous abordons ici l'importance de ces divers genres de transformations structurales pour les phénomènes qui se produisent dans les joints de grain. A number of non-equivalent structures have been found in the atomistic studies of periodic grain boundaries. These can transform into each other by removal or insertion of layers of atoms parallel to the boundary [19]. The ensuing multiplicity of structures is very extensive for long period, general, boundaries. We show here that low energy configurations of vacancies in grain boundaries correspond to the local presence of units of alternative structures so that absorption or emission of vacancies at a boundary can be regarded as local structural transformations. Hence, as the temperature rises and the equilibrium concentration of vacancies increases the disorder corresponding to occurrence of various alternative units in the boundary increases. This may happen either gradually or through an order-disorder transformation. It is further shown that accumulation of vacancies or impurities in the boundary may induce shear transformations between the alternative boundary structures which leads at the same time to the migration of the boundary. The significance of these different structural transformations for various grain boundary phenomena is discussed.
... In opposition, the second school thinks that point defects continue to exist and to diffuse along GBs. In 1985, Vitek et al. [32] wrote that it is generally assumed that vacancies exist in GBs as well defined point defects. They play, in the diffusional processes, a similar role as in the bulk of the crystals. ...
Pure chromium oxidized at 900 °C in synthetic air (p(O 2 ) ~ 0.2 atm) during 30 min gives a chromia scale presenting significant spallation. Contrary to what has recently been observed at lower oxygen partial pressure (10 ⁻¹² atm) Latu-Romain et al. (2018) [1, 2] showing a debonding of the scale localized at the metal/oxide interface, the decohesion in the present conditions occurs inside the oxide. Specifically, the separation of the scale takes place at the interface between an internal equiaxed subscale and an external columnar subscale. Thanks to theirs semiconducting properties (conduction and bandgaps) these subscales have been studied with photoelectrochemical techniques at macro- and micro-scales.
... For example, via MD simulations, Frolov et al. found new GB structures by varying the atomic fraction in the GBs (with fixed macroscopic DOFs) for Σ5 [100] STGBs in FCC metals. This structural change due to the variation of microscopic DOFs is called a "GB structural phase transformation" by Frolov et al. [140] and "GB structural multiplicity" by Vitek et al. [293,294,295] There are many observations of GB structural change for other types of GBs and materials in MD simulations [296,297,298,299,66,300] and experiments [301,302,303,304]. We do not expect that the disconnection model can describe the change of GB atomic structure. ...
Grain boundaries (GBs) are central defects for describing polycrystalline materials, and playing major role in a wide-range of physical properties of polycrystals. Control over GB kinetics provides effective means to tailor polycrystal properties through material processing. While many approaches describe different GB kinetic phenomena, this review provides a unifying concept for a wide range of GB kinetic behavior. Our approach rests on a disconnection description of GB kinetics. Disconnections are topological line defects constrained to crystalline interfaces with both step and dislocation character. These characteristics can be completely specified by GB bicrystallography and the macroscopic degrees of freedom of GBs. GB thermal fluctuations, GB migration and the ability of GBs to absorb/emit other defects from/into the delimiting grains can be modeled via the nucleation, propagation and reaction of disconnections in the GB. We review the fundamentals of bicrystallography and its relationship to disconnections and ultimately to the kinetic behavior of GBs. We then relate disconnection dynamics and GB kinetics to microstructural evolution. While this review of the GB kinetics literature is not exhaustive, we review much of the foundational literature and draw comparisons from a wide swath of the extant experimental, simulation, and theoretical GB kinetics literature.
... A simple and well studied example of GBs is provided by symmetric tilt grain boundaries (STGBs). These have been investigated repeatedly in bcc metals with a focus on GB structure and energetics [18][19][20][21][22][23]. ...
Using magnetic potentials and a molecular statics approach, we study the changes in the magnetic structure of bcc Fe in the vicinity of grain boundaries (GBs). We focus on symmetric tilt GBs around the [0 0 1] axis with a tilt angle between 7(Formula presented.) and 53(Formula presented.). We find that immediately in the GB plane, the deviations in the magnetic moments from the bulk value are most pronounced. The distribution of moments in the GB plane is modulated according to the periodicity of the coincidence site lattice. In the direction perpendicular to the GB plane, the moments decay exponentially towards the bulk value; the decay length increases with decreasing tilt angle. This dependence can be explained by the well-known stress field around GBs.
... При этом диффузионные процессы, протекающие на фоне структурной и морфологической релаксации [4], интенсифицируются и как следствие рост новых фаз осуществляется в результате низкотемпературных (Т≈(0,10÷0,3)) Т пл ) процессов массопереноса [5], характерных для твердофазных процессов роста фаз в пленках [6]. При определенных условиях система границ может эволюционировать, взаимодействуя с диффузионными потоками, что приводит к резким изменениям кинетики роста новых фаз в следствии качественных изменений механизмов диффузии в системах с мигрирующими границами [7]. ...
Applying the hydrothermal reactions for synthesizing whiskers of alkali metal titanates is considered in the paper. Some results of our research in this field are presented. The main purpose of this research is to study the mechanisms of the hydrothermal synthesis process and to obtain kinetic models of whisker growth. The idea of the mechanisms of crystal synthesis is considered and the influence of pressure, temperature, degree of the autoclave filling and other process parameters is estimated. As a result of experimental studies, the possibility of synthesizing potassium titanate whiskers under hydrothermal conditions in obtaining high-quality fibrous crystal structure, corresponding to potassium hexatitanite, the maximum yield of which can be achieved by the degree of filling the reactor by 60% and a pressure of 50 MPa. Based on the studies of the process mechanisms the kinetic models are constructed. They can be used for analyzing the process and selecting the rational parameters of synthesizing potassium hexatitanite crystals. The results of theoretical and experimental studies allow estimating the measurements of the various process properties on the hydrothermal treatment and identifying the factors of controlling either the processes of batch mixture dissolution in the autoclave or the crystal growth processes, which can be applied in the development and design of reactors for performing hydrothermal reactions in obtaining whiskers.
The dependence of grain-boundary (GB) character on its ability to act as a vacancy sink was investigated. For this, vacancy formation energies at different 〈101〉 symmetric-tilt Al GBs were evaluated using atomistic simulations. This information was then used to study the equilibrium segregation of vacancies to the GBs as a function of temperature, grain size, and initial vacancy supersaturation using a multiple-site segregation model. The results show that even though differences in the ability of the GBs to act as a vacancy sink inversely vary with temperature, vacancy supersaturation, and, to a lesser extent, the grain size, such differences are much more sensitive to the GB character. In agreement with previous studies, both low-angle and random high-angle GBs were observed to act as better vacancy sinks than special GBs (such as the coherent twin boundary). More importantly, it was observed that GBs vicinal to the coherent twin boundary (in particular, those with around 10∘ offset about the coherent twin misorientation) also act as very good sinks for vacancies. Upon closer inspection, few sites in these GBs were found to have very low vacancy formation energies, which act as deep traps for the vacancies. In fact, these sites were observed to be clustered around the core of GB dislocations in the low-angle and vicinal boundaries, and these were the precise sites wherein vacancies were observed to delocalize.
The atomistic stress state along a grain boundary can be treated as a representation of the Cauchy stress tensor for the calculation of continuum traction fields, which ultimately governs the ability of grain boundaries to generate, absorb, or transmit dislocations. Such quantitative grain boundary descriptors are mostly confined to molecular dynamics (MD) simulations, where the notion of atomistic stress can be defined through virial theorem. Here, we use artificial neural networks for machine learning (ML), fed with a limited training dataset from MD simulations, to predict the local atomistic stresses from atomic position information across a series of equilibrium <110> symmetrical-tilt Cu grain boundary structures. Accuracy of the ML algorithm is found to depend on the type, sequence, and distortion of the grain boundary structural units. Accounting for these characteristics in the training dataset enables accurate predictions of the local atomistic stress distributions across the family of grain boundary structures. This ML-based constitutive modeling paves the way for direct interpretation of the equivalent stress state of atomistic structures beyond the MD domain, including those from high-resolution transmission electron microscopy (HRTEM) imaging and Density Functional Theory (DFT) modeling.
It has been previously proposed that grain boundary can be treated as a two-dimensional phase in materials with possible transformations between its multiple metastable states under external stimuli such as high temperature. In this work, the influences of another type of common external stimuli, i.e. mechanical load, on grain boundary structural phase transformation (GBSPT) are studied by molecular dynamics simulations. Two types of high angle symmetrical grain boundaries in Cu are used as model systems to investigate their structural transformation under both constant and cyclic mechanical loading. While in general GBSPT can be enhanced or weakened under a constant tensile or compressive stress as compared to that caused by temperature only, the influences of tension and compression are not the same. For this reason, cyclic loading consisting of symmetric tensile/compressive half-cycles can significantly influence the overall GBSPT. Furthermore, it is found that the macroscopic strain in the material caused by GBSPT under compression/tension can be well described by Coble creep, which implies that GBSPT could be a grain boundary diffusional process during the creep of polycrystalline materials that has been overlooked before. Additionally, it is shown that together with shear coupled grain boundary motion and sources of free volume such as voids or cracks, cyclic shear loading can also cause GBSPT between its metastable structures of different atomic density, which can be possibly utilized to heal damage or microcracks in engineering materials.
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.
Grain boundaries in polycrystals form a complex interconnected network of intercrystalline interfaces. The crystallographic character of individual grain boundaries and the network structure of the grain boundary ensemble have been experimentally observed to have a strong influence on many materials properties. This observation suggests that if we could control the types of grain boundaries present in a polycrystal and their spatial arrangement then it would be possible to dramatically improve the properties of polycrystalline materials and tailor them to specific engineering applications. However, there are a number of major obstacles that have, until now, precluded the realization of this opportunity: (1) methods capable of simultaneously quantifying the crystallographic and topological structure of grain boundary networks do not exist; (2) theoretical models relating grain boundary network structure to physical properties have not yet been developed; and, consequently, (3) there are no techniques to quantitatively identify grain boundary network structures that would be beneficial for a given property. In this thesis I address these obstacles by first developing a new statistical description of grain boundary network structure called the triple junction distribution function (TJDF), which encodes both crystallographic and topological information. I establish new results regarding the physical symmetries of triple junctions and find a relationship between crystallographic texture and grain boundary network structure. I then use the TJDF to develop a model for the effective diffusivity of a grain boundary network. Finally, using the relationship between texture and grain boundary network structure that I develop, I describe a method for texture-mediated grain boundary network design. This process permits the theoretical design of grain boundary networks with properties tailored to a given engineering application and is applicable to any polycrystalline material. I demonstrate the potential of this technique by application to a specific design problem involving competing design objectives for mechanical and kinetic materials properties. The result is a designed microstructure that is predicted to outperform an isotropic polycrystal by seven orders of magnitude.
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