The formation and migration of disconnections (line defects constrained to the grain boundary (GB) plane with both dislocation and step character) control many of the kinetic and dynamical properties of GBs and the polycrystalline materials of which they are central constituents. We demonstrate that GBs undergo a finite-temperature topological phase transition of the Kosterlitz-Thouless (KT) type. This phase transition corresponds to the screening of long-range interactions between (and unbinding of) disconnections. This phase transition leads to abrupt change in the behavior of GB migration, GB sliding, and roughening. We analyze this KT transition through mean-field theory, renormalization group theory, and kinetic Monte Carlo simulations, and examine how this transition affects microstructure-scale phenomena such as grain growth stagnation, abnormal grain growth and superplasticity.
Shear coupling implies that all grain boundary (GB) migration necessarily creates mechanical stresses/strains and is a key component to the evolution of all polycrystalline microstructures. We present MD simulation data and theoretical analyses that demonstrate the GB shear coupling is not an intrinsic GB property, but rather strongly depends on the type and magnitude of the driving force for migration and temperature. We resolve this apparent paradox by proposing a microscopic theory for GB migration that is based upon a statistical ensemble of line defects (disconnections) that are constrain…
We investigate the diffusion of a grain boundary in a crystalline material. We consider in particular the case of a regularly spaced low-angle grain boundary schematized as an array of dislocations that interact with each other through long-range stress fields and with the crystalline Peierls-Nabarro potential. The methodology employed to analyze the dynamics of the center of mass of the grain boundary and its spatio-temporal fluctuations is based on over-damped Langevin equations. The generality and the efficiency of this technique is proved by the agreement with molecular dynamics simulation…
An open question in studying normal grain growth concerns the asymptotic state to which microstructures converge. In particular, the distribution of grain topologies is unknown. We introduce a thermodynamic-like theory to explain these distributions in two- and three-dimensional systems. In particular, a bending-like energy $E_i$ is associated to each grain topology $t_i$, and the probability of observing that particular topology is proportional to $\frac{1}{s(t_i)}e^{-βE_i}$, where $s(t_i)$ is the order of an associated symmetry group and $β$ is a thermodynamic-like constant. We explain the p…
The thermodynamic theory of dislocation/grain boundary interaction, including dislocation pile-up against, absorption by, and transfer through the grain boundary, is developed for nonuniform plastic deformations in polycrystals. The case study is carried out on the boundary conditions affecting work hardening of a bicrystal subjected to plane constrained shear for three types of grain boundaries: (i) impermeable hard grain boundary, (ii) grain boundary that allows dislocation transfer without absorption, (iii) grain boundary that absorbs dislocations and allows them to pass later.
The effects of micro-alloying element, vanadium, on a bcc Fe Σ3(111)[1-10] symmetric tilt grain boundary strength are studied using density functional theory calculations. The lowest energy configuration of the grain boundary structure are obtained from the first-principles calculations. The substitutional and interstitial point defect formation energies of vanadium in the grain boundary are compared. The substitutional defect is prefered to interstitial one. The segregation energies of vanadium onto the grain boundary and its fractured surfaces are computed. The cohesive energy calculation of…
Grain boundary tracer diffusion of Ni, Fe and Cr was studied in a Ni-base 602CA coarse-grained alloy. A co-existence of several short-circuit contributions was distinguished at higher temperatures in Harrison's B-type regime (773-873 K), which were related to different families of high-angle grain boundaries with distinct coverages by precipitates and segregation levels as revealed by HAADF-STEM combined with EDX measurements. Annealing at 873 K for 18 hours resulted in Cr23C6-type carbides coexisting with an α-Cr-Mn-enriched phase in addition to sequential segregation layers of Al, Fe and Ni …
The phase behavior of grain boundaries can have a strong influence on interfacial properties. Little is known about the emergence of grain boundary phases in elemental metal systems and how they transform. Here, we observe the nanoscale patterning of a grain boundary by two alternating grain boundary phases with distinct atomic structures in elemental copper by atomic resolution imaging. The same grain boundary phases are found by grain boundary structure search indicating a first-order transformation. Finite temperature atomistic simulations reveal a congruent, diffusionless transition betwee…
We examine the interaction between precipitates and grain boundaries, which undergo shear-coupled motion. The elastic problem, emerging from grain boundary perturbations and an elastic mismatch strain induced by the precipitates, is analysed. The resulting free elastic energy contains interaction terms, which are derived numerically via the integration of the elastic energy density. The interaction of the shear-coupled grain boundary and the coherent precipitates leads to potential elastic energy reductions. Such a decrease of the elastic energy has implications on the grain boundary shape and…
We introduce a method to visualize dislocations along grain boundaries at the atomic level. It uses an atomic-level Nye tensor, representing the dislocation density. To calculate the Nye tensor at grain boundaries, we extend the Hartley-Mishin strain gradient calculation to the displacement shift complete lattice. We show that the method is effective in visualizing disconnections and the dislocation content of grain boundary phase junctions in body-centered cubic tungsten, as well as face-centered cubic copper. In addition, we use the method to characterize the morphology of a two-dimensional …
Grain boundaries dramatically affect the properties of polycrystalline materials because of differences in atomic configuration. To fully understand the relationship between grain boundaries and materials properties, systematic studies of the grain boundary atomic structure are crucial. However, such studies are limited by the extensive computation necessary to determine the structure of a single grain boundary. If the structure could be predicted with more efficient computation, the understanding of the grain boundary would be accelerated significantly. Here, we predict grain boundary structu…
A detailed theoretical and numerical investigation of the infinitesimal single-crystal gradient plasticity and grain-boundary theory of Gurtin (2008) "A theory of grain boundaries that accounts automatically for grain misorientation and grain-boundary orientation". Journal of the Mechanics and Physics of Solids 56 (2), 640-662, is performed. The governing equations and flow laws are recast in variational form. The associated incremental problem is formulated in minimization form and provides the basis for the subsequent finite element formulation. Various choices of the kinematic measure used …
With the increasing availability of experimental and computational data concerning the properties and distribution of grain boundaries in polycrystalline materials, there is a corresponding need to efficiently and systematically express functions on the grain boundary space. A grain boundary can be described by the rotations applied to two grains on either side of a fixed boundary plane, suggesting that the grain boundary space is related to the space of rotations. This observation is used to construct an orthornormal function basis, allowing effectively arbitrary functions on the grain bounda…
We study the mechanisms of slip transfer at a grain boundary, in titanium, using Differential Aperture X-ray Laue Micro-diffraction (DAXM). This 3D characterization tool enables measurement of the full (9-component) Nye lattice curvature tensor and calculation of the density of geometrically necessary dislocations (GNDs). We observe dislocation pile-ups at a grain boundary, as the neighbor grain prohibits easy passage for dislocation transmission. This incompatibility results in local micro-plasticity within the slipping grain, near to where the slip planes intersect the grain boundary, and we…
Grain boundary embrittlement occurs when a solute enriches at a grain boundary and lowers its cohesive energy. While grain boundary enrichment is often attributed to equilibrium segregation effects, most models of embrittlement consider either the energetics of decohesion or the equilibrium adsorption at the boundary, but not both phenomena together. We develop a model for the change in cohesive energy of a grain boundary of a pure metal upon introduction of solute under conditions of equilibrium segregation prior to fracture. A heuristic grain boundary cohesion map is presented to delineate w…
We present a detailed numerical study on structure and local magnetic properties of $\langle 100 \rangle$ symmetric tilt grain boundaries in bcc-iron. Particular attention is paid to connection between type of grain boundary relaxation and local magnetic properties. Results from first principles calculation showed that grain boundary reconstruction leads to non-uniform distribution of local magnetic moments in grain boundary plane. This is in contrast with the result obtained in grain boundary plane, where simple relaxation is observed. Well optimized atomic configurations in the vicinity of t…
Investigating the grain boundary energies of pure fcc metals and their surface energies obtained from ab initio modeling, we introduce a robust method to estimate the grain boundary energies for complex multicomponent alloys. The input parameter is the surface energy of the alloy, which can easily be accessed by modern ab initio calculations based on density functional theory. The method is demonstrated in the case of paramagnetic Fe-Cr-Ni alloys for which reliable grain boundary data is available.
A discrete model and the regular solution approximation are applied to describe the effect of grain boundary motion on grain boundary phase transformations in a binary alloy. The model predicts all thermodynamic properties of the grain boundary and the solute drag force, and permits a broad exploration of the parameter space and different dynamic regimes. The grain boundary phases continue to exist in the moving grain boundary and show a dynamic hysteresis loop, a dynamic critical line, and other features that are similar to those for equilibrium phases. Grain boundary motion strongly affects …
We apply inline electron holography to investigate the electrostatic potential across an individual BaZr0.9Y0.1O3 grain boundary. With holography, we measure a grain boundary potential of -1.3 V. Electron energy loss spectroscopy analyses indicate that barium vacancies at the grain boundary are the main contributors to the potential well in this sample. Furthermore, geometric phase analysis and density functional theory calculations suggest that reduced atomic density at the grain boundary also contributes to the experimentally measured potential well.
Grain Boundaries govern many properties of polycrystalline materials, including the vast majority of engineering materials. Evolutionary algorithm can be applied to predict the grain boundary structures in different systems. However, the recognition and classification of thousands of predicted structures is a very challenging work for eye detection in terms of efficiency and accuracy. A data pipeline is developed to accelerate the classification and recognition of grain boundary structures predicted by Evolutionary Algorithm. The data pipeline has three main components including feature engine…
Mg grain boundary (GB) segregation and GB diffusion can impact the processing and properties of Al-Mg alloys. Yet, Mg GB diffusion in Al has not been measured experimentally or predicted by simulations. We apply atomistic computer simulations to predict the amount and the free energy of Mg GB segregation, and the impact of segregation on GB diffusion of both alloy components. At low temperatures, Mg atoms segregated to a tilt GB form clusters with highly anisotropic shapes. Mg diffuses in Al GBs slower than Al itself, and both components diffuse slowly in comparison with Al GB self-diffusion. …
We present a theoretical study of the interaction of vacancies with a tilt grain boundary in aluminum based on the density functional theory. The grain boundary volume expansion and vacancy induced contraction are calculated and compared for the nearest-neighbor atoms from the defects, and the former is found to be smaller than the latter. The formation energy of a vacancy placed at various layers in the grain boundary has been calculated and we find that the grain boundary does not always act as sinks for vacancies. In fact, it costs more energy to form a vacancy at the boundary plane than in…
Coupled grain boundary (GB) motion has been studied in a two-dimensional tricrystal where a cylindrical grain is embedded at the center of the planar GB of a large bicrystal. Kinetic relations for GB dynamics, grain orientations, and junctions have been derived within the framework of Gibbs thermodynamics. These are solved numerically to investigate the shrinkage of the embedded grain while emphasizing the role of coupled motion as well as junction mobility in the shape evolution.
Cohesive laws are stress-strain curves used in finite element calculations to describe the debonding of interfaces such as grain boundaries. It would be convenient to describe grain boundary cohesive laws as a function of the parameters needed to describe the grain boundary geometry; two parameters in 2D and 5 parameters in 3D. However, we find that the cohesive law is not a smooth function of these parameters. In fact, it is discontinuous at geometries for which the two grains have repeat distances that are rational with respect to one another. Using atomistic simulations, we extract grain bo…
Nanocrystalline materials are defined by their fine grain size, but details of the grain boundary character distribution should also be important. Grain boundary character distributions are reported for ball milled, sputter deposited, and electrodeposited Ni and Ni-based alloys, all with average grain sizes of ~20 nm, to study the influence of processing route. The two deposited materials had nearly identical grain boundary character distributions, both marked by a Σ3 length percentage of 23-25%. In contrast, the ball milled material had only 3% Σ3-type grain boundaries and a large fraction of…
In this work, we experimentally establish the isothermal nanofacet evolution at an asymmetric tilt grain boundary in the Cu-Ag system using a diffusion couple approach. We investigate the nanofacet formation along the grain boundary in dependence of the Ag solute excess concentration. The initial grain boundary dissociates into asymmetric Ag-lean segments and Ag-rich symmetric (210) segments. Increasing Ag excess leads to an increase in Ag-rich facet segment length, while the length of the asymmetric facets remains constant. From this, we construct a grain boundary nanofaceting diagram deduced…
The buckling of graphene nano-ribbons containing a grain boundary is studied using atomistic simulations where free and supported boundary conditions are invoked. We found that when graphene contains a small angle grain boundary the buckling strains are larger when the ribbons with free (supported) boundary condition are subjected to compressive tension parallel (perpendicular) to the grain boundary. The shape of the deformations of the buckled graphene nanoribbons depends on the boundary conditions and the presence of the grain boundary and the direction of applied in-plane compressive tensio…
Bismuth segregated to the grain boundary in Cu is known to promote brittle fracture of this material. Recently, Schweinfest et al. reported first-principles quantum mechanical calculations on the electronic and structural properties of a Cu grain boundary with and without segregated Bi and argue that the grain boundary weakening induced by Bi is a simple atomic size effect. But their conclusion is invalid for both Bi and Pb because it fails to distinguish the chemical and mechanical (atomic size) contributions, as obtained with our recently developed first-principles based phenomenological the…
We present quantum-based simulations of single grain boundary reflectivity of electrons in metals, Cu and Ag. We examine twin and non-twin grain boundaries using non-equilibrium Green's function and first principles methods. We also investigate the mechanism of reflectivity in grain boundaries by modeling atomic vacancies, disorder, and orientation and find that the change in grain orientation and disorder in the boundary itself both contribute significantly to reflectivity. We find that grain boundary reflectivity may vary widely depending on the grain boundary structure consistent with exper…
Systematic microstructure design requires reliable thermodynamic descriptions of each and all microstructure elements. While such descriptions are well established for most bulk phases, thermodynamic assessment of crystal defects is challenged because of their individualistic nature. In this paper, a model is devised for assessing grain boundary thermodynamics based on available bulk thermodynamic data. We propose a continuous relative atomic density field and its spatial gradients to describe the grain boundary region with reference to the defect-free, homogeneous bulk and derive the grain bo…
Segregation-induced structural transitions in metallic grain boundaries are studied with hybrid atomistic Monte Carlo/molecular dynamics simulations using Cu-Zr as a model system, with a specific emphasis on understanding the effect of grain boundary character. With increasing global composition, the six grain boundary types chosen for this study first form ordered complexions, with the local segregation pattern depending on the grain boundary core structure, then transform into disordered complexions when the grain boundary composition reaches a critical value that is temperature dependent. T…
Grain boundaries often exhibit ordered atomic structures. Increasing amounts of evidence have been provided by transmission electron microscopy and atomistic computer simulations that different stable and metastable grain boundary structures can occur. Meanwhile, theories to treat them thermodynamically as grain boundary phases have been developed. Whereas atomic structures were identified at particular grain boundaries for particular materials, it remains an open question if these structures and their thermodynamic excess properties are material specific or generalizable to, e.g., all fcc met…
We describe a molecular dynamics framework for the direct calculation of the short-ranged structural forces underlying grain-boundary premelting and grain-coalescence in solidification. The method is applied in a comparative study of (i) a Sigma 9 <115> 120 degress twist and (ii) a Sigma 9 <110> {411} symmetric tilt boundary in a classical embedded-atom model of elemental Ni. Although both boundaries feature highly disordered structures near the melting point, the nature of the temperature dependence of the width of the disordered regions in these boundaries is qualitatively different. The for…
The charge redistribution at grain boundaries determines the applicability of high-Tc superconductors in electronic devices, because the transport across the grains can be hindered considerably. We investigate the local charge transfer and the modification of the electronic states in the vicinity of the grain-grain interface by first principles calculations for a (normal-state) 45^o tilted [001] grain boundary in YBa2Cu3O7. Our results explain the suppressed interface transport and the influence of grain boundary doping in a quantitative manner, in accordance with the experimental situation. T…
Using first-principles density functional theory method, we have investigated the distribution and magnetism of doped Mn atoms in the vicinity of the 3 (112) grain boundary in Ge. We find that at low concentration, the substitutional sites are energetically favorable over the interstitial ones for Mn. The binding energy of Mn varies with lattice sites in the boundary region, and hence a non-uniform distribution of Mn nears the boundary. However, the average of their segregation energy is quite small, thus no remarkable grain boundary segregation of Mn is predicted. Due to volume expansion at t…
The grain boundary-mediated mechanisms that control plastic deformation of nanocrystalline metals should cause evolution of the grain boundary network, since they directly alter misorientation relationships between crystals. Unfortunately, current experimental techniques are unable to track such evolution, due to limits on both spatial and temporal resolution. In this work, molecular dynamics simulations are used to study grain boundary restructuring in nanocrystalline Al during both monotonic tension and cyclic loading. This task is enabled by the creation of new analysis tools for atomistic …
An algorithm implemented in an open-source python library was developed for building periodic coincidence site lattice (CSL) grain boundary models in a universal fashion. The software framework aims to generate tilt and twist grain boundaries from cubic and tetragonal crystals for ab-initio and classical atomistic simulation. This framework has two useful features: i) it can calculate all the CSL matrices for generating CSL from a given Sigma (Σ) value and rotation axis, allowing the users to build the specific CSL and grain boundary models; ii) it provides a convenient command line tool to en…
This paper studies how solute segregation and its relationship to grain boundary energy in binary alloys is captured in the phase field crystal (PFC) formalism, a continuum method that incorporates atomic scale elasto-plastic effects on diffusional time scales. Grain boundaries are simulated using two binary alloy PFC models --- the original binary model by Elder et al (2007) and the XPFC model by Greenwood et al (2011). In both cases, grain boundary energy versus misorientation data is shown to be well described by Read-Shockley theory. The Gibbs Adsorption Theorem is then used to derive a se…
It is believed that grain boundary segregation of light interstitials can serve as possible mechanism of thermal stability in commercially pure nanostructured titanium alloys. In this paper, using first-principles calculations, we show that independent segregation of C, N and O atoms at Σ7 high angle grain boundary in α-Ti is energetically unfavourable. The presence of interstitial elements near and at the grain boundary interface results in the increase of the grain boundary width and specific formation energy.
Faceted grain boundaries, where grain boundary area is increased in the name of producing low-energy segments, can exhibit new and unexpected migration trends. For example, several faceted $Σ$3 boundaries have demonstrated anti-thermal and thermally damped mobility. $Σ$11 <110> tilt boundaries represent another promising but relatively unexplored set of interfaces, with a (113) low-energy plane that can lead to faceting. In this study, molecular dynamics simulations are used to study grain boundary migration of an asymmetric $Σ$11 <110> grain boundary in two face centered cubic metals. Mobilit…
Recent grain growth experiments have revealed that the same type of grain boundary can have very different mobilities depending on its local microstructure. In this work, we use molecular dynamics simulations to quantify uncertainty in the reduced mobility of curved grain boundaries for different types of boundary conditions and over a range of initial velocity seeds. We consider cylindrical island grains in Ni with a [001] tilt axis as a model system. Unexpectedly, we find large variation in the reduced mobility of curved grain boundaries depending on both the imposed constraints and the init…
Grain boundary networks should play a dominant role in determining the mechanical properties of nanocrystalline metals. However, these networks are difficult to characterize and their response to deformation is incompletely understood. In this work, we study the grain boundary network of nanocrystalline Ni and explore whether it can be modified by plastic deformation. Mechanical cycling at room temperature did not lead to structural evolution, but elevated temperature cycling did alter the grain boundary network. In addition to mechanically-driven grain growth, mechanical cycling at 100 $°$C l…
An age-hardenable Al-Cu-Mg alloy (A2024) was processed by high-pressure torsion (HPT) for producing an ultrafine-grained structure. The alloy was further aged for extra strengthening. The tensile strength then reached a value as high as ~1 GPa. The microstructures were analyzed by transmission electron microscopy and atom probe tomography. The mechanism for the high strength was clarified in terms of solid-solution hardening, cluster hardening, work hardening, dispersion hardening and grain boundary hardening. It is shown that the segregation of solute atoms at grain boundaries including subgr…
Energetics of Cs defects at Sigma3 grain boundaries of 3C-SiC has been studied using density functional theory to understand the role of the grain boundaries in Cs diffusion and its eventual release from the tristructural isotropic fuel particles (TRISO). Cs is shown to be much more stable at the Sigma3 grain boundary than in bulk of SiC with a significant decrease (7-17eV) in the formation energies at the grain boundaries than in bulk. It is found to have even lower formation energies than those of Ag at the Sigma3 grain boundaries, while this trend was opposite in the bulk SiC as demonstrate…
Grain boundaries are thermodynamically unstable. Hence, their properties should be path-dependent: grain boundaries in nanocrystals prepared using different methods might exhibit different properties. Using molecular dynamics simulations, we investigated grain boundaries of nanocrystals formed by quenching,solidification with pre-induced nucleation sites, and Voronoi tessellation. Some properties were found to be path depend: the quenched model has lower boundary energy per atom, smaller boundary excess free volume per atom, and slower grain growth than the Voronoi model. We surmise that these…
It is a conventional wisdom that symmetry breakdown at grain boundaries in crystals introduces volume expansion and there has been no confirmed evidence of volume contraction at a grain boundary in any kind of crystals. We report surprising volume contraction at the Sigma3(111) grain boundary in vanadium. The lattice distortion near this grain boundary is found to drive the local structure toward a hypothetical ω phase, which is only slightly less stable than the bcc phase. Compressing lattice constant a of the ω-phase down to the value of bcc, as is the case at the Sigma3(111) grain boundary,…
A quantitative phase-field model for grain boundary trapping and diffusion of hydrogen
KU Leuven（荷语鲁汶大学）；Department of Materials Engineering, Faculty of Engineering, KU Leuven（荷语鲁汶大学工程学院材料工程系）；Department of Computer Science, Faculty of Engineering Science, KU Leuven（荷语鲁汶大学工程科学学院计算机科学系）
While it is known that alloy components can segregate to grain boundaries (GBs), and that the atomic mobility in GBs greatly exceeds the atomic mobility in the lattice, little is known about the effect of GB segregation on GB diffusion. Atomistic computer simulations offer a means of gaining insights into the segregation-diffusion relationship by computing the GB diffusion coefficients of the alloy components as a function of their segregated amounts. In such simulations, thermodynamically equilibrium GB segregation is prepared by a semi-grand canonical Monte Carlo method, followed by calculat…
Nanocrystalline metals contain a large fraction of high-energy grain boundaries, which may be considered as glassy phases. Consequently, with decreasing grain size, a crossover in the deformation behaviour of nanocrystals to that of metallic glasses has been proposed. Here, we study this crossover using molecular dynamics simulations on bulk glasses, glass-crystal nanocomposites, and nanocrystals of Cu64Zr36 with varying crystalline volume fractions induced by long-time thermal annealing. We find that the grain boundary phase behaves like a metallic glass under constraint from the abutting cry…
Needle-shaped atom probe specimens containing a single grain boundary were produced using the focused ion beam (FIB) of a dual-beam FIB/SEM (scanning electron microscope) system. The presented specimen preparation approach allows the unprecedented study of a grain boundary which is well characterised in its crystallographic orientation by means of the field ion microscope (FIM) and the tomographic atom probe (TAP). The analysis of such specimens allows in particular the determination of solute excess atoms at this specific grain boundary and hence the investigation of the segregation behaviour…
Thermal stability of nanocrystalline multilayer thin film is of paramount importance as the applications often involve high temperature. Here we report on the layer instability phenomenon in binary polycrystalline thin film initiating from the grain boundary migrations at higher temperatures using phase-field simulations. Effect of layer thickness, bilayer spacing and the absence of grain boundary are also investigated along with the grain boundary mobility of individual phases on the layer stability. Layer instability in the polycrystalline film is shown to arise from the grain boundary groov…
Atomistic simulations are employed to demonstrate the existence of a well-defined thermodynamic phase transformation between grain boundary (GB) phases with different atomic structures. The free energy of different interface structures for an embedded-atom-method model of the $Σ5 (310) [001]$ symmetric tilt boundary in elemental Cu is computed using the nonequilibrium Frenkel-Ladd thermodynamic integration method through molecular dynamics simulations. It is shown that the free-energy curves predict a temperature-induced first-order interfacial phase transition in the GB structure in agreement…
We have studied the fundamental process of hydrogen binding at interstitial, vacancy and grain boundary (GB) in palladium crystals using Density-Functional Theory. It showed that hydrogen prefers to occupy the octahedral interstitial site in Pd matrix, however a stable H-vacancy complex with most H occupations would contain up to eight hydrogen atoms surrounding the vacancy at tetrahedral sites. Furthermore, H presence assists the pairing or formation of nearby vacancies, which in agreement with previous suggestions by both experiment and theory investigation. Also, this observation could impl…
