Motion Of Disclinations Research Articles

Active transformations of topological structures in light-driven nematic disclination networks

SignificanceTopological defects are marvels of nature. Understanding their structures is important for their applications in, for example, directed self-assembly, sensing, and photonic devices. There is recent interest in active motion and transformation of topological defects in active nematics. In these nonequilibrium systems, however, the motion and transformation of disclinations are difficult to control, thereby hindering their applications. Here, we propose a surface-patterned system engendering periodic three-dimensional disclinations, which can be excited by light irradiation and undergo a programmable transformation between different topological states. Continuum simulations recapitulating these topological structures characterize the bending, breaking, and relinking events of the disclinations during the nonequilibrium process. Our work provides an alternative dynamic system in which active transformation of topological defects can be engineered.

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.

GD3: generalized discrete defect dynamics

A mesoscale model is introduced to study the dynamics of material defects lying at interface junctions. The proposed framework couples the dynamics of discrete dislocation and disclination lines. Disclinations are expected to be natural defects at interface junctions; their presence serving the purpose of accommodating discontinuities in rotation fields at material interface junctions. Crystallography-based rules are proposed to describe the kinematics of disclination motion. A discrete-continuous couple-stress framework, in which discrete defect lines are introduced as plastic eigenstrains and eigencurvatures, is proposed to explicitly follow the dynamics of interfacial defects. The framework is then applied to study left (10bar {1}2right) twin transverse propagation and thickening in magnesium. Focusing first on the case of a twin domain, It is shown that a disclination based representation of twin domains allows for an appropriate mechanistic description of the kinematics of shear transformations. In what concerns twin thickening, the stability of defects at twin interfaces is further studied. To this end, a 3D crater lying on a twin interface is described as a dipole of disclination loops. Upon self-relaxation, it is found that out of plane motion of disclinations followed by the nucleation of twinning dislocations can be activated; thereby showing that conservative non-planar motion of disclinations can be thermodynamically favorable; mechanism that had been postulated some 50 years ago.

Structural and topological nature of plasticity in sheared granular materials

Upon mechanical loading, granular materials yield and undergo plastic deformation. The nature of plastic deformation is essential for the development of the macroscopic constitutive models and the understanding of shear band formation. However, we still do not fully understand the microscopic nature of plastic deformation in disordered granular materials. Here we used synchrotron X-ray tomography technique to track the structural evolutions of three-dimensional granular materials under shear. We establish that highly distorted coplanar tetrahedra are the structural defects responsible for microscopic plasticity in disordered granular packings. The elementary plastic events occur through flip events which correspond to a neighbor switching process among these coplanar tetrahedra (or equivalently as the rotation motion of 4-ring disclinations). These events are discrete in space and possess specific orientations with the principal stress direction.

Dancing disclinations in confined active nematics.

The spontaneous emergence of collective flows is a generic property of active fluids and often leads to chaotic flow patterns characterised by swirls, jets, and topological disclinations in their orientation field. However, the ability to achieve structured flows and ordered disclinations is of particular importance in the design and control of active systems. By confining an active nematic fluid within a channel, we find a regular motion of disclinations, in conjunction with a well defined and dynamic vortex lattice. As pairs of moving disclinations travel through the channel, they continually exchange partners producing a dynamic ordered state, reminiscent of Ceilidh dancing. We anticipate that this biomimetic ability to self-assemble organised topological disclinations and dynamically structured flow fields in engineered geometries will pave the road towards establishing new active topological microfluidic devices.

Probing the shear viscosity of an active nematic film.

In vitro reconstituted active systems, such as the adenosine triphosphate (ATP)-driven microtubule bundle suspension developed by the Dogic group [T. Sanchez, D. T. Chen, S. J. DeCamp, M. Heymann, and Z. Dogic, Nature (London) 491, 431 (2012)10.1038/nature11591], provide a fertile testing ground for elucidating the phenomenology of active liquid crystalline states. Controlling such novel phases of matter crucially depends on our knowledge of their material and physical properties. In this Rapid Communication, we show that the shear viscosity of an active nematic film can be probed by varying its hydrodynamic coupling to a bounding oil layer. Using the motion of disclinations as intrinsic tracers of the flow field and a hydrodynamic model, we obtain an estimate for the shear viscosity of the nematic film. Knowing this now provides us with an additional handle for robust and precision tunable control of the emergent dynamics of active fluids.

A mesoscopic theory of dislocation and disclination fields for grain boundary-mediated crystal plasticity

A coarse-grained extension of a recent nanoscale elasto-plastic model of polar dislocation and disclination density fields is developed to model grain boundary-mediated plasticity in polycrystals. At a small resolution length scale, the polar dislocation/disclination densities render continuously the discontinuities of the elastic displacements/rotations across grain boundaries. When the resolution length scale increases, the net polarities of a crystal defect ensemble decrease, perhaps to the point where no strain/curvature incompatibility is left in the body. The defect densities are then labeled “statistical”. However both polar and statistical dislocation/disclination densities contribute to plastic flow, and a coarse-grained mesoscopic plastic curvature rate needs to be defined. In addition, whereas it is overlooked at nanoscale where grain boundaries are seen as continua, tangential continuity of the elastic/plastic curvature/strain rates across grain boundaries needs to be considered at mesoscale, because the latter are seen as singular discontinuity interfaces. It induces long-range, grain-to-grain, elastic/plastic interactions across interfaces. The mesoscale model allow preserving the essential features of the lower scale approach. In particular, it is shown that it allows accounting for such plastic deformation mechanisms as grain boundary migration and grain boundary misorientation variation by disclination motion and concurrent dislocation nucleation, when plasticity by dislocation glide is unavailable. Accumulation of polar defect densities in the vicinity of the grain boundaries and triple lines, leading to long-range inter-granular activation of slip and grain size effects, are also predicted by the model.

Disclinations provide the missing mechanism for deforming olivine-rich rocks in the mantle

Mantle flow involves large strains of polymineral aggregates. The strongly anisotropic plastic response of each individual grain in the aggregate results from the interactions between neighbouring grains and the continuity of material displacement across the grain boundaries. Orthorhombic olivine, which is the dominant mineral phase of the Earth's upper mantle, does not exhibit enough slip systems to accommodate a general deformation state by intracrystalline slip without inducing damage. Here we show that a more general description of the deformation process that includes the motion of rotational defects referred to as disclinations can solve the olivine deformation paradox. We use high-resolution electron backscattering diffraction (EBSD) maps of deformed olivine aggregates to resolve the disclinations. The disclinations are found to decorate grain boundaries in olivine samples deformed experimentally and in nature. We present a disclination-based model of a high-angle tilt boundary in olivine, which demonstrates that an applied shear induces grain-boundary migration through disclination motion. This new approach clarifies grain-boundary-mediated plasticity in polycrystalline aggregates. By providing the missing mechanism for describing plastic flow in olivine, this work will permit multiscale modelling of the rheology of the upper mantle, from the atomic scale to the scale of the flow.

Missing link in mantle dynamics

The discovery of crystallographic imperfections known as disclinations in the most profuse mineral in Earth's upper mantle has the potential to solve a problem that has vexed mineral physicists for decades. See Article p.51 Olivine is the most abundant upper-mantle mineral — and the weakest under a wide range of thermo-mechanical conditions — so its deformation under stress is an important constraint on mantle behaviour. Patrick Cordier et al. present a model for the deformation of olivine aggregates that includes the motion of rotational defects — referred to as 'disclinations' — a factor neglected in previous studies of mantle rheology. The authors conclude that such disclination motion could provide the missing mechanism for describing plastic flow in olivine, which should enable multiscale modelling of the rheology of the upper mantle, from the atomic scale to large-scale mantle flow.

Grain boundary modeling using an elasto-plastic theory of dislocation and disclination fields

Using a recent elasto-plastic theory of dislocation and disclination fields, a continuous representation of grain boundaries is introduced. Periodic arrays of wedge disclination dipoles, including those defined in the Disclination Structural Unit Model, are set-up as initial configurations in a dynamic model for symmetric tilt boundaries. These configurations are found to be unstable when the transport of disclinations is allowed. Driven by their self couple-stress field, the motion of disclinations leads to relaxation of the initial elastic curvature and stress fields and to nucleation and transport of relaxation dislocations, until an equilibrium configuration of lower energy is reached. Most of the residual elastic energy of grain boundaries is localized in a non-singular nanometric layer. This energy arises from alternative dilatation and contraction of the lattice around disclinations, and from lattice curvature and shear between disclination dipoles. By virtue of its continuous and dynamic character, the present theory allows modeling absolute misorientations and leads to energy density levels comparable to molecular statics findings.

Topology and Geometry of Smectic Order on Compact Curved Substrates

Smectic order on arbitrary curved substrate can be described by a differential form of rank one (1-form), whose geometric meaning is the differential of the local phase field of the density modulation. The exterior derivative of 1-form is the local dislocation density. Elastic deformations are described by superposition of exact differential forms. We use the formalism of differential forms to systematically classify and characterize all low energy smectic states on torus as well as on sphere. A two dimensional smectic order confined on either manifold exhibits many topologically distinct low energy states. Different states are not accessible from each other by local fluctuations. The total number of low energy states scales as the square root of the system area. We also address the energetics of 2D smectic on a curved substrate and calculate the mean field phase diagram of smectic on a thin torus. Finally, we discuss the motion of disclinations for spherical smectics as low energy excitations, and illustrate the interesting connection between spherical smectic and the theory of elliptic functions.

Topology of Smectic Order on Compact Substrates

Smectic orders on curved substrates can be described by differential forms of rank one (1-forms), whose geometric meaning is the differential of the local phase field of density modulation. The exterior derivative of the 1-form is the local dislocation density. Elastic deformations are described by superposition of exact differential forms. Applying this formalism to study smectic order on a torus as well as on a sphere, we find that both systems exhibit many topologically distinct low energy states that can be characterized by two integer topological charges. The total number of low energy states scales as the square root of the substrate area. For a smectic on a sphere, we also explore the motion of disclinations as possible low energy excitations, as well as its topological implications.

Disclination Velocity in Bistable Chiral Splay Nematic Liquid Crystal Device

We investigate how miscellaneous parameters influence the velocity of the disclination line in a bistable chiral splay nematic liquid crystal (BCSN LC) device, using a model derived from the relationship of the free energy loss rate with dissipation energy. The disclination velocity is consistently coupled with the free energy difference between two stable states, rotational viscosity, and damping factor, in which the free energy difference is the most influential. The relationships between the energy difference and the parameters of the BCSN LC device were elucidated by examining the portrait of bistable curves. The calculated velocities of the disclination motion were also confirmed by comparing them with the measured results.

Field-Induced Motion of Nematic Disclinations

An individual defect in a nematic liquid crystal moves not only in response to its interaction with other defects but also in response to external fields. We analyze the motion of a wedge disclination in the presence of an applied field of strength H. We neglect backflow and seek steadily traveling patterns. The stationary picture yields a semi-infinite wall of strength $\pi$, bounded by the defect line. We find that the disclination advances into the region containing the wall at velocity v(H), where v scales as H/|log H| as long as the magnetic coherence length is greater than the core radius. When the external field is applied in the presence of a pair of disclinations, their dynamics is strongly influenced. We compute the expected relative velocity of the disclinations as a function of distance and field. The natural tendency for the disclinations to annihilate each other can be overcome by a sufficiently strong field suitably directed.

Emission of partial dislocations by grain boundaries in nanocrystalline metals

A theoretical model is proposed to describe the emission of partial dislocations by grain boundaries in nanocrystalline materials during plastic deformation. Partial dislocations are assumed to be emitted during the motion of grain-boundary disclinations, which are carriers of rotational plastic deformation. The ranges of the parameters of a defect structure in which the emission of partial dislocations by grain boundaries in nanocrystalline metals are energetically favorable are calculated. It is shown that, as the size of a grain decreases, the emission of partial dislocations by its boundary becomes more favorable as compared to the emission of perfect lattice dislocations.

Disclinations and rotational deformation in fine-grained materials

A theoretical model is presented which describes a new mechanism of plastic deformation in fine-grained materials. In the framework of the model, rotational deformation occurs via motion of dipoles of grain-boundary disclinations and is associated with the emission of lattice dislocations from grain boundaries into adjacent grain interiors. Ranges of defect system parameters are identified in which the disclination motion is energetically favourable. It is shown that the mechanism can contribute to plastic flow in fine-grained materials prepared by highly non-equilibrium methods such as ball milling, severe deformation and high-pressure compaction.

Disclination motion in liquid crystalline films

We theoretically study a single disclination motion in a thin free-standing liquid crystalline film. Backflow effects and the own dynamics of the orientational degree of freedom (bond or director angle) are taken into account. We find the orientation field and the hydrodynamic velocity distribution around the moving disclination, which allows us to relate the disclination velocity to the angle gradient far from the disclination. Different cases are examined depending on the ratio of the rotational and shear viscosity coefficients.

Changes in grain boundary misorientation caused by emission of dislocation pairs

A new geometric micromechanism responsible for changes in the misorientation of grain boundaries in the course of (super)plastic deformation is proposed. According to this, the misorientation changes as a result of the motion of grain-boundary disclinations accompanied by the emission of lattice dislocation pairs. Within the framework of the proposed model, the energy characteristics of the motion of grain-boundary disclinations are calculated.

Transformations of grain boundaries due to disclination motion and emission of dislocation pairs

A theoretical model is suggested which describes changes of grain boundary misorientation parameters in plastically deformed polycrystalline and nanocrystalline materials. In the framework of the model, the changes occur via grain boundary disclination motion associated with emission of dislocation pairs from grain boundaries into adjacent grain interiors. Energetic characteristics of the disclination motion in question are calculated.

Motion, creation, and annihilation of disclinations in multidomain structured nematic liquid crystal cells.

We study dynamical processes in a multidomain (MD) structured nematic liquid crystal cell with a particular emphasis on the motion, creation, and annihilation of disclinations. In the MD cell right- and left-handed director helices alternate due to a special choice of the director pretilt angles at the surfaces. As a result, a net of twist disclinations occurs. We have implemented a numerical algorithm based on a pure rotational dynamics of the director field to monitor the motion of the defect lines during the switching process, i.e., when an electric voltage is applied to or removed from the cell. We demonstrate that the total light transmission vs time is not affected by the presence of the defects compared to a conventional twisted nematic cell. If the pretilt angles at the surfaces are sufficiently small, the twisting sense of one species of helices is reversed and a configuration free of defects occurs. On the other hand, for an applied voltage twist disclinations close to the surface have to exist. Therefore, defect lines are created or they annihilate during the switching process. We investigate these situations in detail and reveal the underlying mechanisms.