Symmetric Boundary Research Articles

Comparing Five and Lower-Dimensional Grain Boundary Character and Energy Distributions in Copper: Experiment and Molecular Statics Simulation

The misorientation of 515 grain boundaries has been determined using electron backscatter diffraction data from an 18 μm thick copper foil with columnar grain structure and a preferential {110} surface orientation. The energy of the grain boundaries was determined from the dihedral angles in the vicinity of grain boundary thermal grooves. The experimental grain boundary energy vs. misorientation angle shows deep minima for the low-angle grain boundaries and small minima corresponding to the Σ3 and Σ9 grain boundaries. Only a small fraction of the coincidence site lattice grain boundaries demonstrate an increased occurrence frequency (compared to a random orientation distribution) and low energy. In parallel, the grain boundary energy for a subset of 400 symmetrical tilt grain boundaries was calculated using molecular statics simulations. There is a good agreement between the experiment and molecular statics modeling.

Weakly Singular Symmetric Galerkin Boundary Element Method for Fracture Analysis of Three-Dimensional Structures Considering Rotational Inertia and Gravitational Forces

The Symmetric Galerkin Boundary Element Method is advantageous for the linear elastic fracture and crackgrowth analysis of solid structures, because only boundary and crack-surface elements are needed. However, for engineering structures subjected to body forces such as rotational inertia and gravitational loads, additional domain integral terms in the Galerkin boundary integral equation will necessitate meshing of the interior of the domain. In this study, weakly-singular SGBEM for fracture analysis of three-dimensional structures considering rotational inertia and gravitational forces are developed. By using divergence theorem or alternatively the radial integration method, the domain integral terms caused by body forces are transformed into boundary integrals. And due to the weak singularity of the formulated boundary integral equations, a simple Gauss-Legendre quadrature with a few integral points is suffcient for numerically evaluating the SGBEM equations. Some numerical examples are presented to verify this approach and results are compared with benchmark solutions.

Nonmetallic Trace Elements X (X = H, C, N, O, B and S) Induced Rhenium Co-Segregation in Nickel Σ5 [001](210) Symmetrical Tilt Grain Boundary

Nonmetallic Trace Elements X (X = H, C, N, O, B and S) Induced Rhenium Co-Segregation in Nickel Σ5 [001](210) Symmetrical Tilt Grain Boundary

Phase field crystal simulation of strain-induced square phase low-angle symmetric tilt grain boundary dislocation reaction

In this paper, the phase field crystal method is used to study the dislocation motion and reaction of the square phase symmetric tilt low-angle grain boundaries, and the dislocation configurations with different misorientation angles are analyzed under the action of applied strain. The geometric phase approach is used to characterize the strain field around the dislocations. The results show that after the solidification relaxation, the interfacial dislocations on both sides of the grain are distributed in parallel but opposite direction. With the increase of misorientation angle between grains, the number of dislocations increases, the spacing between them decreases, and the free energy of the system increases. Imposed by the applied strain, the grain boundary dislocations undergo climbing, launching, and reactive annihilation, with the free energy fluctuating. When the misorientation increases, the dislocation motion mode changes from climbing to climbing-sliping, resulting in more dislocation group configurations, and more reactions between dislocations and dislocation groups. For the dislocation reactions of different configurations, positive shear strain drives dislocations to approach, and negative shear strain drives dislocations to annihilate.

ЛИМОЛОГИЧЕСКИЕ ЭТЮДЫ (РЕЗУЛЬТАТЫ АВТОРСКИХ ИССЛЕДОВАНИЙ В ОБЩЕЙ И ГЕОГРАФИЧЕСКОЙ ЛИМОЛОГИИ ЗА 40 ЛЕТ)

A summary of the author’s scientific achievements in general and geographical limology over 40 years is provided. The category “boundary” is placed among categories: dialogue, identity, map, compromise, conflict, landscape, position, space, wayfaring/journey, diversity, reflection, etc. Boundaries span the entire spectrum of “arbitrary lines---active symbols---corporeal/physical edges---active axes.” The logic of boundary-making as partitioning and the novel types of boundaries are examined. Boundary-making as partitioning is distinguished from boundary-making as separation. Symmetric and asymmetric boundaries are also distinguished. The logical status of boundaries is specified from the standpoint of the logic of regioning (as distinct from regionalization). The special character of boundaries and working with boundaries is stated with reference to cultural landscape. The relationship between boundaries, transition zones and ecotones is considered. The fundamental duality of boundaries in research and application is defined as the duality of corporeal/physical edge of place (region) versus sign of place. The status of the problem of borders and the status of the borders themselves in different regionalization practices are clarified. Differences and connections of borders outside the districts and inter-district borders are indicated. The meaning of the border as distinguishing and dismembering is shown. A number of well-known semantic border paradoxes are summarized and new ones are formulated. A new general idea of the map is given. Ideas about nomogenic regions and borders, limogenic and limocentric systems are introduced. Atypology of border zones based on “contact - barrier” is developed. A general typology of borderline identities is given. The ecological and cultural-semiotic meanings and functions of boundaries/ecotones and the meaning and value of boundaries in landscape are defined. A summary of limological analysis of a series of places is given: ribbon (tape) forests, “opolyes— polesyes” (as geographical concepts somewhat related to Opolye and Polesye areas), Inner Periphery, Urals, etc. The scientific field of limology is distinguished from the applied sphere of “limonautics.”

Characterization and Visualization of Grain Boundary Disconnections

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 boundary phase nucleus in a symmetric tilt grain boundary in tungsten. This method can be applied to both bulk dislocations and grain boundary disconnections, which makes it ideal for studying the interactions and reactions of bulk dislocations with grain boundaries, and grain boundary disconnections.

Numerical Simulation for the Comparison of Thermal and Plastic Material Flow Behavior between Symmetrical and Asymmetrical Boundary Conditions During Friction Stir Welding

Numerical Simulation for the Comparison of Thermal and Plastic Material Flow Behavior between Symmetrical and Asymmetrical Boundary Conditions During Friction Stir Welding

Symmetric boundary condition for the MPS method with surface tension model

In order to supplement the investigation of boundary conditions for the MPS method, a general computational algorithm of symmetric boundary condition for MPS is presented to simulate the symmetric problems. By the MPS method with the symmetric boundary condition (the SBC-MPS method), only half or quarter of the full computational domain needs to be set up, thus, the computational cost is able to be slashed dramatically. In the SBC-MPS method, mirror particles are introduced, which will be arranged symmetrically according to the positions of real liquid particles near to the symmetric plane, but not involved in the solution of physical properties. The function of these mirror particles is to compensate the values for the calculation of real liquid particles. As numerical tests, various of problems including two-dimensional Poiseuille Flow, three-dimensional dam-break, and some surface tension dominant problems, such as droplet wetting / impinging to a solid surface and binary droplets collision have been systematically studied by the SBC-MPS method. As a result, the algorithm shows good robustness, stability and accuracy, which demonstrates a great potential to improve the computational efficiency for dealing with symmetric problems.

Three-dimensional modelling of composite frames with ductile connections in fire

Connections are vital to the survival of steel and composite framed structures in fire. To prevent brittle failure of connections at elevated temperatures, a novel connection with high ductility has been proposed previously. In this paper, the fire performance of this ductile connection in composite frames is investigated. In order to consider the influence of the out-of-plane structural behaviour, the 3-D models of a fire compartment of a typical composite framed structure with different connection types, including the ductile connection, idealised rigid and pinned connections, as well as commonly used end-plate and web-cleat connections have been built using Vulcan to compare the performance of ductile connection with other connection types. Comparison results show that the proposed ductile connection can provide additional ductility within composite frame to accommodate the axial deformation of connected beam at high temperatures. To further save computational costs, the 3-D composite frame compartment model has been reduced to a quarter of its original size by using symmetric boundaries. The influence of unconnected length between the slab and beam on the connection performance has also been investigated. It is found that the relative beam end slip is affected by the unconnected length. However, due to the inherent mechanical properties of the ductile connection, the influence of unconnected length on the force of the ductile connection is negligible, which can also reflect the deformation capacity of ductile connection.

Grain boundary energies in yttria‐stabilized zirconia

AbstractThe three‐dimensional microstructure of 8% yttria‐stabilized zirconia (YSZ) was measured by electron backscatter diffraction and focused ion beam serial sectioning. The relative grain boundary energies as a function of all five crystallographic grain boundary parameters were determined based on the assumption of thermodynamic equilibrium at the internal triple junctions. Grain boundaries with (100) orientations have low energies compared to boundaries of other orientations, and all [100] twist boundaries have relatively low energies. Other classes of boundaries with lower than average energies include [100] symmetric tilt boundaries with disorientations less than 40° and [111] twist boundaries with disorientations greater than 20°. At fixed misorientations, the relative areas of boundaries are inversely correlated to the relative grain boundary energy. The results suggest that texturing microstructures to increase the relative areas of [100] twist boundaries might increase the oxygen ion conductivity of YSZ ceramics.

High-Q slow light and its localization in a photonic crystal microring

We introduce a photonic crystal ring cavity that resembles an internal gear and unites photonic crystal (PhC) and whispering gallery mode (WGM) concepts. This `microgear' photonic crystal ring (MPhCR) is created by applying a periodic modulation to the inside boundary of a microring resonator to open a large bandgap, as in a PhC cavity, while maintaining the ring's circularly symmetric outside boundary and high quality factor ($Q$), as in a WGM cavity. The MPhCR targets a specific WGM to open a large PhC bandgap up to tens of free spectral ranges, compressing the mode spectrum while maintaining the high-$Q$, angular momenta, and waveguide coupling properties of the WGM modes. In particular, near the dielectric band-edge, we observe modes whose group velocity is slowed down by 10 times relative to conventional microring modes while supporting $Q~=~(1.1\pm0.1)\times10^6$. This $Q$ is $\approx$50$\times$ that of the previous record in slow light devices. Using the slow light design as a starting point, we further demonstrate the ability to localize WGMs into photonic crystal defect (dPhC) modes for the first time, enabling a more than 10$\times$ reduction of mode volume compared to conventional WGMs while maintaining high-$Q$ up to (5.6$\pm$0.1)$\times$10$^5$. Importantly, this additional dPhC localization is achievable without requiring detailed electromagnetic design. Moreover, controlling their frequencies and waveguide coupling is straightforward in the MPhCR, thanks to its WGM heritage. By using a PhC to strongly modify fundamental properties of WGMs, such as group velocity and localization, the MPhCR provides an exciting platform for a broad range of photonics applications, including sensing/metrology, nonlinear optics, and cavity quantum electrodynamics.

Radiation induced segregation near dislocations and symmetric tilt grain boundaries in Fe-Cr alloys: A phase-field study

A phase-field model dedicated to dislocation climb under irradiation has been coupled to point defects and chemical species transport equations. It allows to predict radiation induced segregation in Fe-Cr alloys around dislocations in the isolated or stacking configuration like in symmetric tilt grain boundaries. This work is challenging for several reasons: (i) radiation induced segregation in Fe-Cr is difficult to simulate since Cr depletion or enrichment can occur, depending on the Cr nominal composition and temperature, (ii) dislocations are biased sinks due to their elastic fields which can not be ignored in this case and (iii) other surrounding microstructural defects can interact with dislocations and impact point defect and solute transport. To overcome (iii), a mean-field approach is adopted, in which the influence of the surrounding sinks is taken into account through the introduction of an overall and uniform sink strength in the point defect diffusion equations. Despite the numerous parameters of the model, unknown experimental information and approximations made to make the simulations tractable, the numerical results are in good agreement with the experimental ones. Moreover, the model allows to identify the main physical parameters to correctly quantify radiation induced segregation in the case of dislocations. Among them, the point defect relaxation volumes are of first importance in comparison with the solute relaxation volume or the nature of the slip system.

Evaluation of grain boundary energy, structure and stiffness from phase field crystal simulations

A two-mode phase field crystal (PFC) model is employed to investigate the equilibrium configurations of a range of grain boundaries in fcc-structured materials. A total of 80 different symmetrical tilt grain boundaries are evaluated by PFC simulations in 3D and the results are shown to agree well with data taken from the literature, both regarding the variation of grain boundary energy and also in terms of the resulting grain boundary structures. This verification complements existing PFC studies which are almost exclusively focused either on grain boundaries found in 2D systems or in bcc lattices in 3D. The present work facilitates application of PFC in the analysis of grain boundary mechanics in an extended range of materials, in particular such mechanics that take place at extended time scales not tractable for molecular dynamics (MD) simulations. In addition to the verification of predicted grain boundary energies and structures, wavelet transforms of the density field are used in the present work to obtain phase fields from which it is possible to identify grain boundary fluctuations that provide the means to evaluate grain boundary stiffness based on the capillarity fluctuation method. It is discussed how PFC provides benefits compared to alternative methods, such as MD simulations, for this type of investigations.

An insight into thermal properties of BC3-graphene hetero-nanosheets: a molecular dynamics study

Simulation of thermal properties of graphene hetero-nanosheets is a key step in understanding their performance in nano-electronics where thermal loads and shocks are highly likely. Herein we combine graphene and boron-carbide nanosheets (BC3N) heterogeneous structures to obtain BC3N-graphene hetero-nanosheet (BC3GrHs) as a model semiconductor with tunable properties. Poor thermal properties of such heterostructures would curb their long-term practice. BC3GrHs may be imperfect with grain boundaries comprising non-hexagonal rings, heptagons, and pentagons as topological defects. Therefore, a realistic picture of the thermal properties of BC3GrHs necessitates consideration of grain boundaries of heptagon-pentagon defect pairs. Herein thermal properties of BC3GrHs with various defects were evaluated applying molecular dynamic (MD) simulation. First, temperature profiles along BC3GrHs interface with symmetric and asymmetric pentagon-heptagon pairs at 300 K, ΔT = 40 K, and zero strain were compared. Next, the effect of temperature, strain, and temperature gradient (ΔT) on Kaptiza resistance (interfacial thermal resistance at the grain boundary) was visualized. It was found that Kapitza resistance increases upon an increase of defect density in the grain boundary. Besides, among symmetric grain boundaries, 5–7–6–6 and 5–7–5–7 defect pairs showed the lowest (2 × 10–10 m2 K W−1) and highest (4.9 × 10–10 m2 K W−1) values of Kapitza resistance, respectively. Regarding parameters affecting Kapitza resistance, increased temperature and strain caused the rise and drop in Kaptiza thermal resistance, respectively. However, lengthier nanosheets had lower Kapitza thermal resistance. Moreover, changes in temperature gradient had a negligible effect on the Kapitza resistance.

Molecular dynamics simulations on the intergranular crack propagation of magnesium bicrystals

As an important micro-structure, grain boundary plays a significant role in the micro-structure evolution and mechanical property of metallic materials. In this study, comprehensive molecular dynamics simulations were performed to investigate the propagation mechanisms of intergranular cracks along [11-00] symmetric tilt grain boundaries in magnesium bicrystals under tensile loading conditions. The effects of grain boundary misorientation angle, temperature and solid solution were considered. The results show: At low temperature, most of the cracks with different misorientation angles propagate by the brittle cleavage mechanism, which generally agrees with the theoretical predictions based on the Rice’s model. With increasing the temperature, the crack propagation mechanism changes, on the one hand, from brittle cleavage to void nucleation, growth and coalescence; on the other hand, the local plastic deformation becomes favorable near the crack tip, due to the dislocation emission and nanograin nucleation via the split of original grain boundary, which relaxes the stress concentration and shields the crack tip. Also, the brittle-to-ductile transition is observed due to the effect of temperature. By adding the alloying elements of Al, Ca, Zn, it is seen that the strength of the grain boundary is enhanced. This work provides insights into the understanding of the ductility of magnesium and its alloys.

First-principles analysis of the grain boundary segregation of transition metal alloying elements in γFe

In this study, first-principles calculations were carried out for the first time to systematically investigate the grain boundary segregation of transition metal alloying elements (Ti, V, Cr, Mn, Co, Ni, Cu, Nb, and Mo) in paramagnetic γFe and its dependence on the grain boundary character. The segregation energies of each element and site were comprehensively calculated for nine [001] symmetric tilt grain boundary models with Σ values from 5 to 41; the paramagnetic state was simulated by the antiferromagnetic double-layer (AFMD). By calculating the effective segregation energy for each grain boundary model from the obtained segregation energies, the grain boundary segregation behavior for each alloying element and its dependence on the grain boundary character were investigated. The segregation energy of transition metal elements is dominated by the Voronoi volume of Fe at the segregation site and arises from the elastic energy derived from the difference in atomic radii between the host and solute metals. Ti, Cu, Nb, and Mo have negative effective segregation energies (indicating a tendency toward segregation) at all investigated grain boundaries, and the absolute values of the effective segregation energy increase in the order of Cu < Mo < Ti < Nb in all of the grain boundary models. In contrast, the sign of the effective segregation energies for V, Ni, and Co changes depending on the grain boundary, and the effective segregation energies for Cr and Mn are positive at all grain boundaries. These results corresponded well with the experimental results. The results obtained in this study provide important basic data for the material design of high-strength steels and are useful for understanding the effects of alloying elements in γFe.

Defect interaction summary between edge dislocations and -axis symmetric tilt grain boundaries in copper on activation barriers and critical stresses

The interactions between edge dislocations and <112>-axis symmetric tilt grain boundaries (GBs) in copper have been investigated by atomistic simulations. Molecular dynamics simulations and the nudged elastic band method were implemented to investigate the atomistic reaction between the two defects and the activation energy required to trigger such an event in various stress or strain states. The results showed that although different GBs were introduced, the most common scenarios were dislocation absorption into the GB and transmission through the GB. In most cases, the leading partial dislocation was absorbed into the GB once these two crystallographic defects impacted. In contrast, the trailing partial dislocation played a crucial role in determination of the threshold reaction stress. From transition state theory, the reaction energy barriers showed a linear relationship with the resolved shear stress or strain state. The constant activation volume was in the range 22–53b3, where b is the Burgers vector. Furthermore, the corresponding strain rate sensitivities obtained through the activation volumes showed good agreement with the experiment data.

Orientation effect on intergranular fracture behaviors along symmetrical tilt grain boundaries in bcc iron

The fracture of crystalline metals preferentially occurs in intergranular way. This work investigates orientation effect on intergranular fracture behaviors along symmetrical tilt coherent and incoherent Σ3 grain boundaries (GBs) in bcc iron. The analytical results obtained based on Rice concept and numerical results obtained based on molecular dynamics theory are presented. The two inconsistencies observed between the analytical and numerical results achieved for stacking fault formation on the plane coincident with crack plane and twinning formation on the plane not coincident with crack plane are fully discussed. The results in this work show that intergranular cracks on coherent Σ3 GB prefer to propagate in a ductile way, while those on incoherent Σ3 GB prefer to propagate in a brittle way. Along both symmetrical tilt coherent and incoherent Σ3 GBs, intergranular crack propagation depends on advance direction and usually presents directional anisotropy due to non-mirror symmetrical atomic distribution along the plane vertical to crack advance direction. Intergranular crack propagation also depends on front direction. On account of the differences in the type and nucleation ability of plastic behavior, intergranular cracks with different front directions have different ductile-brittle levels and corresponding models have different maximum tensile stresses. Investigation on orientation effect can provide a good reference to improve material reliability.

Molecular dynamics investigation on tilt grain boundary energies of beta-titanium and tungsten at high temperature

The grain boundary energies (GBEs) of symmetric tilt grain boundaries (STGBs) and asymmetric tilt grain boundaries (ATGBs) for W at 0 and 2400 K and β-Ti at 1300 K were calculated by means of molecular statics and dynamics simulations to investigate the effects of temperature on GBE and the relationships between GBEs and grain boundary (GB) planes. Generally, the variation trends of GBE with the tilt angle are similar for the three cases, when the tilt axis is specified. It is of course that these similarities result from their similar GB microstructures in most cases. However, the variation trends of GBE with tilt angle are somewhat different between β-Ti at 1300 K and W at 2400 K for STGBs with <100> and <110> tilt axes. This difference mainly stems from the following two reasons: firstly, the GB microstructures of W at 2400 K and β-Ti at 1300 K are different for some STGBs; secondly, the atoms at the STGB of β-Ti at 1300 K tend to evolve into the local ω- or α-like structures distributed at the STGB for some STGBs with <110> tilt axis, which makes the corresponding STGBs more stable, thereby decreasing the GBEs. Furthermore, a geometric parameter θ, the angle between the misorientation axis and the GB plane, was defined to explore the relationships between GBEs and GB planes. It was found that the relationships between GBEs and GB planes can be described by some simple functions of sin(θ) for the GBs with definite lattice misorientation, which can well explain and predict the preferred GB planes for the GBs having the same lattice misorientation. Our calculations not only extend the investigation of GBs to higher temperature, but also deepen the understanding on the temperature contributions to the microstructure evolution at GBs and on the relationships between GBEs and possible geometric parameters.

Gauging anomalous unitary operators

Boundary theories of static bulk topological phases of matter are obstructed in the sense that they cannot be realized on their own as isolated systems. The obstruction can be quantified/characterized by quantum anomalies, in particular when there is a global symmetry. Similarly, topological Floquet evolutions can realize obstructed unitary operators at their boundaries. In this paper, we discuss the characterization of such obstructions by using quantum anomalies. As a particular example, we discuss time-reversal symmetric boundary unitary operators in one and two spatial dimensions, where the anomaly emerges as we gauge the so-called Kubo-Martin-Schwinger (KMS) symmetry. We also discuss mixed anomalies between particle number conserving U(1) symmetry and discrete symmetries, such as $C$ and $\mathit{CP}$, for unitary operators in odd spatial dimensions that can be realized at the boundaries of topological Floquet systems in even spatial dimensions.