Disclination Dipole Research Articles

Numerical analysis of the fungibility of disclination dipole by dislocation array or dislocation monopole

Disclinations have been discovered and applied to a wide variety of materials, underscoring the importance of their analysis. Previous studies have demonstrated that a disclination dipole can be represented by a dislocation array in a deformation schematic and by a dislocation monopole in a stress state. Based on these observations, we propose that the elastic field of a disclination dipole can be substituted with that of a dislocation array or dislocation monopole, allowing the development of the disclination theory grounded in dislocation theory. In this study, we conducted a quantitative analysis of the elastic strain–energy of disclination dipoles, dislocation arrays, and dislocation monopoles using linear elasticity theory and molecular dynamics (MD) simulation. While linear elasticity theory facilitates a quantitative evaluation of the elastic field, it fails to account for out-of-plane deformation of the material. Therefore, MD analysis, which considers out-of-plane deformation, was employed to obtain versatile results applicable to a broader range of materials. Our findings from both theoretical analyses indicate that, in terms of strain–energy, a disclination dipole with a large separation can be represented by a dislocation array, whereas a dipole with a small separation can be represented by a dislocation monopole. This study newly performs strain–energy analysis of dislocations and disclinations using these two theoretical approaches.

A computational study of nematic core structure and disclination interactions in elastically anisotropic nematics.

A singular potential method in the Q tensor order parameter representation of a nematic liquid crystal is used to study the equilibrium configuration of a disclination dipole. Unlike the well studied isotropic limit (the so called one constant approximation), we focus on the case of anisotropic Frank elasticity (bend/splay elastic constant contrast). Prior research has established that the singular potential method provides an accurate description of the tensor order parameter profile in the vicinity of a disclination core of a highly anisotropic lyotropic chromonic liquid crystal. This research is extended here to two interacting disclinations forming a dipole configuration. The director angle is shown to decay in the far field inversely with distance to the dipole as is the case in the isotropic limit, but with a different angular dependence. Therefore elastic constant anisotropy modifies the elastic screening between disclinations, with implications for the study of ensembles of defects as seen, for example, in active matter in the extended system limit.

On the nucleation of cracks near stress sources with weak singularities

Analytical expressions are obtained for the configuration force and the value of elastic energy relaxation at the nucleation of a microcrack in a small neighborhood of an arbitrary singular stress source. When analyzing the conditions of crack nucleation at sources with weak divergences of the stress fields, ideas about the instantaneous nucleation of a crack of finite length are used. Simultaneous fulfillment of stress and energy conditions is considered as a criterion for the nucleation of such a crack. Within the framework of these representations, in the configuration space of the system parameters (geometric characteristics and strength of mesodefects, the value of external stress), the regions in which crack nucleation is possible in the case of a combined mesodefect, which is a superposition of the dipole of wedge disclinations and planar shear mesodefect, are determined. It is shown that the nucleation of the crack is significantly facilitated by the instability of the shear mesodefect.

Atomic-scale study of the {[formula omitted]} twinning and {[formula omitted]}-{[formula omitted]} double twinning mechanisms in pure titanium

The {112¯1} twinning and {112¯2}-{112¯1} double twinning mechanisms in pure Ti are systematically investigated using molecular dynamics (MD) simulations. MD simulation results indicate that a {112¯1} twin embryo is composed of a group of pyramidal stacking faults (PSFs) with 6d{112¯1} or 8d{112¯1}, caused by the successive slip of partial dislocations with the Burgers vector of 136〈112¯6¯〉M. The migration of {112¯1} twin boundaries (TBs) is mainly carried out by the slip of twinning dislocations (TDs) b⇀1 = 16(4γ2+1)<1¯1¯26> ±12<11¯00>. Two {112¯2}-{112¯1} double twinning mechanisms are discovered. One is that a {112¯1} twin forms and grows at the {112¯2} twin tip through the dissociation of the TD b⇀1(112¯2) at the {112¯2} twin tip, forming the {112¯2}-{112¯1} double twin structure. The other is that a basal <a>T dislocation interacts with a {112¯2} TB, forming a twin embryo composing of a group of PSF with the 6d{112¯1¯} and leaving a step at the {112¯2} TB, eventually forming the {112¯2}-{112¯1} double twin structure. The interfacial structures of {112¯1} twins have the terraced character with short coherent (112¯2)||(112¯0) facets and coherent twin boundary (CTB) segments. In addition, (0001)||(112¯4) facets with a disclination dipoles feature can form at twin tips. The coherent twin interfaces form at their intersected interfaces during the {112¯2}-{112¯1} double twinning process. Our present findings may provide clues for designing Ti alloys with excellent strength–ductility properties through obtaining a high-volume fraction of coherent interfaces in terms of {112¯2}-{112¯1} double twins.

Strength criterion of graphene GBs combining discrete bond strength and varied bond stretch

The strength criterion of graphene grain boundaries (GBs) under complex stress states plays an important role in guiding the design of high-performance graphene-related materials and devices under severe mechanical environments like ultrastrong structural materials or flexible electronics. However, finding a unified strength criterion that can adapt to different GB angles and loading states is still a challenge. In this work, we proposed a general method to construct the strength criterion of graphene GBs that includes the atomic details of defect. Firstly, systematic molecular dynamics (MD) simulations were carried out to explore the fracture behaviors of graphene GBs with different GB angles and loading states. Then, bond strength of heptagon ring σ t h R was obtained by projecting the applied stress field to the fractured bond direction, which gives the same value for the same type of C-C bond of same GB angle under different loading states. Besides, to further unify the bond strength of different GB angles, the residual stress caused by other pentagon–heptagon defects was considered by using the disclination dipole theory, in which the intrinsic bond strength σ t h 0 for different GB angles collapses to the same value. With this scenario, the strength criterion of graphene GBs is presented as the bond stretch stress generated by external load exceeds any bond strength of the hexagon–heptagon defect. Furthermore, a unified bond strength is found, linearly decreasing with the equilibrium bond length, which can further be applied to the strength criterion of other defective structures like two types of SW defects (without analytical solution of residual stress) and even pristine graphene. The present results provide a comprehensive understanding of the failure of graphene by considering the balance of bond strength of defective structure and bond stretch stress generated by external load, which may pave the way to construct the atomic structure based strength criterion of other two-dimensional materials.

Electrical resistivity of polycrystalline graphene: effect of grain-boundary-induced strain fields

We have revealed the decisive role of grain-boundary-induced strain fields in electron scattering in polycrystalline graphene. To this end, we have formulated the model based on Boltzmann transport theory which properly takes into account the microscopic structure of grain boundaries (GB) as a repeated sequence of heptagon–pentagon pairs. We show that at naturally low GB charges the strain field scattering dominates and leads to physically reasonable and, what is important, experimentally observable values of the electrical resistivity. It ranges from 0.1 to 10 kOmegaupmu m for different types of symmetric GBs with a size of 1 upmum and has a strong dependence on misorientation angle. For low-angle highly charged GBs, two scattering mechanisms may compete. The resistivity increases markedly with decreasing GB size and reaches values of 60 kOmegaupmum and more. It is also very sensitive to the presence of irregularities modeled by embedding of partial disclination dipoles. With significant distortion, we found an increase in resistance by more than an order of magnitude, which is directly related to the destruction of diffraction on the GB. Our findings may be of interest both in the interpretation of experimental data and in the design of electronic devices based on poly- and nanocrystalline graphene.

Brittle and ductile behavior in monolayer MoS2

Using first-principles calculations, we study the response of monolayer MoS2 with pentagon–heptagon (5|7) pair defect-dominated grain boundary (GB) to an in-plane tension. Brittle or ductile behaviors can occur depending on the GB tilt angle (θ). Brittle failure is dominated by step-by-step dissociation of bonds at GBs, while ductile failure is characterized by a series of reaction and glide events of dislocations. Surprisingly, as θ = 9.40°, 5|7 dislocation defects are annihilated by stretching to form defect-free MoS2. Moreover, the failure strength increases with increasing 5|7 dislocation defect and can be explained by the continuum disclination dipole theory.

Dislocation Equilibrium Positions on Either Side of a Grain Boundary

Abstract The equilibrium positions of two edge dislocations located on either side of a grain boundary have been determined when a disclination dipole is lying in the boundary. It is found that a configuration where the dislocations are distributed symmetrically with respect to the center of symmetry of the grain boundary is selected. This configuration depends on the disclination strength and the dislocation distance from the boundary.

Between microscopic and mesoscopic descriptions of twin–twin interaction

Abstract On a microscopic scale, deformation twinning is carried by the motion of twinning disconnections. A disconnection is an interfacial line defect characterized by a Burgers vector, a line vector, and a step vector. The Burgers vector (dislocation component of the disconnection) carries the deformation while the step vector (ledge component) carries the transformation from one twin variant to the other. On a mesoscopic scale, the deformation produced by twinning is a simple shear. A moving disclination dipole provides a mesoscopic model accounting for the twinning shear. Twin – twin interaction processes including the intersection of twins, the formation of structured twins, and the nucleation of cracks, may feature very complex mechanisms when analyzed on a microscopic scale. It turns out, however, that these mechanisms are controlled by the properties of large disconnection groups containing up to 10 000 disconnections and more. These properties are sufficiently well approximated in the disclination dipole model. The disclination model for twin – twin interaction predicts orientation and volume fractions of secondary twins. The model also predicts the nucleation of cracks and crack growth. The disclination model was used to analyze the ductile-to-brittle transition of austenitic steel deformed at low temperature. The mesoscopic disclination model for twinning is successful because it accounts for the properties and mechanisms of disconnection groups.

Strengthening and Weakening by Dislocations in Monolayer MoS2

Dislocations govern the properties of crystals. Yet, how pentagon–heptagon (5|7) pairs in grain boundaries (GBs) affect the mechanical properties of MoS2 remains poorly known. Using atomistic simulations and the continuum disclination dipole model, we show that depending on the tilt angle and 5|7 dislocation arrangement, MoS2 GB strength can be enhanced or reduced with the tilt angle. For zigzag-tilt GBs primarily composed of Mo5|7 + S5|7 dislocations, GB strength monotonically increases as the square of the tilt angle. For armchair-tilt GBs with Mo5|7 or S5|7 dislocations, however, the trend of GB strength breaks down, as dislocations are unevenly spaced. Moreover, mechanical failure initiates at the bond shared by 5|7 rings, in contrast to graphene in which failure occurs at the bond shared by 6|7 rings. This work provides new insights into the mechanical design of synthetic transition metal dichalcogenide crystals via dislocation engineering.

On the Effect of External Stress on the Stability of a Crack Located near a Wedge Disclination Dipole

On the Effect of External Stress on the Stability of a Crack Located near a Wedge Disclination Dipole

Formation of Two Edge Dislocations in a Grain Due to Interface Disclination Dipoles

Abstract The formation of a dipole of edge dislocations inside one grain separated from the adjacent grains by two interfaces in which are lying disclination dipoles (one in each interface) has been theoretically investigated from an energy variation calculation. Critical grain sizes associated with the formation of the edge dislocation dipole have been determined as well as an activation energy. The effects of the inclination angle of the gliding plane of the dislocations and the characteristic parameters of the disclination dipoles have been finally analyzed.

Competition Between Generation of Nanovoids and Nanocracksin Bimodal Metal-Graphene Composites

A theoretical model which describes micromechanisms of the deformation-induced formation of nanovoids and the competition between the nanovoid formation and the deformation-induced formation of nanocracks in bimodal metal-graphene composites is presented. In the framework of the model, the formation of nanovoids and nanocracks occurs at the grain boundary (GB) disclination dipoles near the graphene inclusions. It is demonstrated that the formation of nanovoids at the GB disclination dipoles is energetically favorable process in deformed bimodal Ni-graphene composite.

Анализ условий существования стабильных микротрещин в упругом поле напряжений от ротационно-сдвигового мезодефекта

During plastic flow, simultaneously with the formation of junction disclinations, which are linear mesodefects, planar shear mesodefects appear at the grain boundaries and facets of the boundaries, the stress fields from which can significantly affect the orientation and characteristics of a microcrack formed at the junction. The configurational force method is used to analyze the conditions for the existence of stable cracks in the elastic field of a combined mesodefect, which is a superposition of a wedge disclinations dipole and a planar mesodefect. In the configuration space of the parameters of the system under consideration (the strength of the disclinations dipole and the planar mesodefect, the length of the mesodefect, and the angle that specifies the orientation of the crack), the ranges of parameter values are determined at which such cracks can appear. The dependences of the critical strength of the disclination dipole and the length of the nuclear crack arising in the vicinity of the negative disclination of the dipole on the length of the mesodefect are calculated for different values of the strength of the planar mesodefect. It was assumed that the opening of the crack occurs in the direction coinciding with the orientation at which the length of the nuclear crack at fixed values of the strength of the disclinations dipole, the strength of the planar mesodefect and the length of the mesodefect is minimal, and, therefore, the energy for its creation is minimal. It is generally concluded that shear-type mesodefects can significantly facilitate the initiation of microcracks in the vicinity of junction disclinations. In the range of parameter values that allow the existence of stable cracks, the length of the nuclear crack decreases with increasing strength of the planar mesodefect. It is shown that the critical length of the crack is tenths of the length of the disclination dipole.

Revisiting the Application of Field Dislocation and Disclination Mechanics to Grain Boundaries

We review the mechanical theory of dislocation and disclination density fields and its application to grain boundary modeling. The theory accounts for the incompatibility of the elastic strain and curvature tensors due to the presence of dislocations and disclinations. The free energy density is assumed to be quadratic in elastic strain and curvature and has nonlocal character. The balance of loads in the body is described by higher-order equations using the work-conjugates of the strain and curvature tensors, i.e., the stress and couple-stress tensors. Conservation statements for the translational and rotational discontinuities provide a dynamic framework for dislocation and disclination motion in terms of transport relationships. Plasticity of the body is therefore viewed as being mediated by both dislocation and disclination motion. The driving forces for these motions are identified from the mechanical dissipation, which provides guidelines for the admissible constitutive relations. On this basis, the theory is expressed as a set of partial differential equations where the unknowns are the material displacement and the dislocation and disclination density fields. The theory is applied in cases where rotational defects matter in the structure and deformation of the body, such as grain boundaries in polycrystals and grain boundary-mediated plasticity. Characteristic examples are provided for the grain boundary structure in terms of periodic arrays of disclination dipoles and for grain boundary migration under applied shear.

Enhanced ductility of nanomaterials through cooperative dislocation emission from cracks and grain boundaries

An analytical model is established to explore the cooperative mechanism between the dislocation emission from cracks and grain boundaries driven by grain boundary sliding in deformed nanocrystalline materials. In our model, high local stress concentration nearby the crack actives grain boundary sliding which creates a wedge disclination dipole at the grain boundaries’ triple junctions. The grain size-dependent criterions for the dislocation emission from the crack tip and the grain boundary are respectively derived. Influences of grain boundary sliding and grain size on the cooperative mechanism are discussed. The results show that the dislocation emission from the grain boundary is activated ahead of that from the crack tip for small grain sizes. This can explain that grain boundary sliding can toughen the nanocrystalline materials even though it suppresses dislocation emission from cracks when their grain sizes are relative small, which is because the dislocation emission from grain boundaries is activated. With the increasing grain size, the main dislocation source may transform from grain boundaries to crack tips due to grain boundary sliding. Therefore, the ductility of nanomaterials with different grain sizes can be enhanced through the cooperative dislocation emission from cracks and grain boundaries.

Disclination dipoles are the Holy Grail for high temperature superplasticity in ceramics

A model for high-temperature plasticity of polycrystals controlled by disclination dipoles is proposed that predict a parabolic dependence of the strain rate versus the applied stress. The presence of a precise stationary disclination density explains the origin of plasticity without microstructural invariance, commonly known as superplasticity. The disclination mechanism is universal, although other processes, such as dislocation glide, are superposed to this one in many systems such as metals or metallic alloys. While, in ceramics it is likely to be the only operative mechanism. Activation of disclination dipoles is a necessary condition for plasticity and sufficient one for superplastic yielding.

Molecular dynamics simulation of a nonequilibrium grain boundary in titanium under the ultrasonic action

Effect of oscillating tension-compression stresses on a nonequilibrium grain boundary containing a disclination dipole in titanium is studied by means of molecular dynamics simulations. The system with nonequilibrium boundary was constructed by joining two bicrystals with tilt boundaries Ɵ = 36.87 ° and Ɵ = 28.07 °, thus the disclination dipole had a strength ω = 8.8 °. The system was relaxed and equilibrated at temperature T=300 K for 200 ps. Then a sinusoidal stress σ = σ0×sin (2πt / τ) with a period τ = 160 ps was applied along x axis at the same temperature and its effect on the structure of the bicrystal was studied. It is shown that under the action of oscillating stresses the nonequilibrium boundary emits lattice dislocations that sink at appropriate surfaces. This process is irreversible and leads to relaxation of the nonequilibrium structure of the boundary. There is an optimal amplitude at which the nonequilibrium boundary emits a sufficient number of dislocations to relieve internal stresses.

Formation and stability of long basal-prismatic facets in Mg

Long BP facets bounding {101¯2}〈1¯011〉 twins in Mg ( ≥ 4 nm) have been observed experimentally. However, the formation of these long BP facets has not been studied and their contribution/role to the twin growth remains unclear. We observe a long straight BP facet (27 nm) using high-resolution transmission electron microscopy (HRTEM) and investigate its formation, stability, and mobility by atomistic simulations. Experimentally, a serrated twin interface containing short CTBs and short BP facets near a (101¯2) twin tip is observed to transform under the effects of the electron beam into a long straight semi-coherent BP facet that contains disclination dipoles. Molecular dynamics (MD) simulations of the relaxation of a 3D twin domain reveals another process whereby a long partially-relaxed BP interface forms and contains an I2 stacking fault. A comparison between the energy of these configurations as obtained by atomistic simulations suggests that these transformations occur in two steps: (1) serrated interfaces composed of coherent BP segments with lengths less than 2 nm combine and form a long and straight coherent BP facets and (2) these long coherent BP facets quickly transform into relaxed ones with misfit defects. Importantly, it is found that long BP facets are relatively immobile, and upon reloading, decay into more mobile serrated interfaces prior to migrating. The work presented suggests that the atomistic configurations of BP facets during twin growth processes differ significantly from relaxed BP interfaces that would be observed by TEM.

Dislocation emission from a cylindrical circular void separating two disclination dipoles in a high-angle grain boundary

The formation of an edge dislocation from the surface of a cylindrical circular cavity lying in a high-angle grain boundary and separating two disclination dipoles located in the boundary has been investigated from a theoretical point of view. The energy variation due to the dislocation introduction into one grain has been determined, and the equilibrium positions (stable or unstable) of the emitted dislocation have been characterized as a function of the direction of the Burgers vector, the strength and length of the disclination dipoles.