Disclination Network Research Articles

Viscosity and transport in a model fragile metallic glass

How thermally activated structural excitations quantitatively mediate transport and microplasticity in a model binary glass at the microsecond timescale is revealed using atomistic simulation. These local excitations, involving a stringlike sequence of atomic displacements, admit a far-field shear-stress signature and underlie the transport of free-volume and bond geometry. Such transport is found to correspond to the evolution of a disclination network describing the spatial connectivity of topologically distinct bonding environments, demonstrating the important role of geometrical frustration in both glass structure and its underlying dynamics.

Nonlinear Rheology and Fracture of Disclination Network in Cholesteric Blue Phase III

Nonlinear rheological properties of chiral crystal cholesteryl oleyl carbonate (COC) in blue phase III (BPIII) were investigated under different shear deformations: large amplitude oscillatory shear, step shear deformation, and continuous shear flow. Rheology of the liquid crystal is significantly affected by structural rearrangement of defects under shear flow. One of the examples on the defect-mediated rheology is the blue phase rheology. Blue phase is characterized by three dimensional network structure of the disclination lines. It has been numerically studied that the rheological behavior of the blue phase is dominated by destruction and creation of the disclination networks. In this study, we find that the nonlinear viscoelasticity of BPIII is characterized by the fracture of the disclination networks. Depending on the degree of the fracture, the nonlinear viscoelasticity is divided into two regimes; the weak nonlinear regime where the disclination network locally fractures but still shows elastic response, and the strong nonlinear regime where the shear deformation breaks up the networks, which results in a loss of the elasticity. Continuous shear deformation reveals that a series of the fracture process delays with shear rate. The shear rate dependence suggests that force balance between the elastic force acting on the disclination lines and the viscous force determines the fracture behavior.

Quasiperiodic Frank–Kasper phases derived from the square–triangle dodecagonal tiling

Frank–Kasper (F-K) phases form an important set of large-cell crystalline structures describing many intermetallic alloys. They are usually described in term of their atomic environments, with atoms having 12, 14, 15 and 16 neighbours, coded into the canonical $$Z_p$$ cells (with p the coordination number), the case $$p=12$$ corresponding to a local icosahedral environment. In addition, the long-range structure is captured by the geometry of a network (called either “major skeleton” or “disclination network”) connecting only the non-icosahedral sites (with $$p\ne 12$$ ). Another interesting description, valid for the so-called layered F-K phases, amounts to give simple rules to decorate specific periodic 2d tilings made of triangles and squares and eventually get the 3d periodic F-K phases. Quasicrystalline phases can sometime be found in the vicinity, in the phase diagram , of the F-K crystalline alloys; it is therefore of interest to understand whether and how the standard F-K construction rules can be generalized on top of an underlying quasiperiodic structure. It is in particular natural to investigate how well square–triangle quasiperiodic tilings with dodecagonal symmetry, made of square and (equilateral) triangles, can be used as building frames to generate some F-K-like quasicrystalline structures . We show here how to produce two types of such structures, which are quasiperiodic in a plane and periodic in the third direction, and containing (or not) $$Z_{16}$$ sites.

Frustration and defects in non-periodic solids

Geometrical frustration arises whenever a local preferred configuration (lower energy for atomic systems, or best packing for hard spheres) cannot be propagated throughout space without defects. A general approach, using unfrustrated templates defined in curved space, have been previously applied to analyse a large number of cases like complex crystals, amorphous materials, liquid crystals, foams, and even biological organizations, with scales ranging from the atomic level up to macroscopic scales. In this paper, we discuss the close sphere packing problem, which has some relevance to the structural problem in amorphous metals, quasicrystals and some periodic complex metallic structures. The role of sets of disclination line defects is addressed, in particular with comparison with the major skeleton occurring in complex large-cell metals (Frank–Kasper phases). An interesting example of 12-fold symmetric quasiperiodic Frank–Kasper phase, and its disclination network, is also described. La frustration géométrique apparaît lorsquʼune configuration préférentielle (par exemple de plus basse énergie pour des systèmes atomiques ou de compacité maximale dans les modèles sphères dures) ne peut se propager dans lʼespace sans engendrer de défauts. Une approche générale a été proposée dès les années 1980, basée sur des modèles non frustrés définis dans des espaces courbes et qui permet dʼanalyser de nombreux cas, comme les intermétalliques complexes, les matériaux amorphes, les cristaux liquides, les mousses et même certains édifices biologiques dans une vision multi-échelle allant du niveau atomique au niveau macroscopique. Nous discutons dans cet article le problème de lʼempilement de sphères en connexion avec le problème structural des amorphes métalliques, quasicristaux et intermétalliques complexes. On sʼintéressera ensuite au rôle des ensembles de disinclinaisons, dont ceux rencontrés dans les grandes mailles des composés métalliques complexes comme les phases de Frank–Kasper. On décrira enfin un exemple intéressant dʼune phase de symétrie locale dodécagonale quasipériodique de type Frank–Kasper, avec son réseau de disinclinaisons.

Flexoelectric switching in cholesteric blue phases

We present computer simulations of the response of a flexoelectric blue phase network, either in bulk or under confinement, to an applied field. We find a transition in the bulk between the blue phase I disclination network and a parallel array of disclinations along the direction of the applied field. Upon switching off the field, the system is unable to reconstruct the original blue phase but gets stuck in a metastable phase. Blue phase II is comparatively much less affected by the field. In confined samples, the anchoring at the walls and the geometry of the device lead to the stabilisation of further structures, including field-aligned disclination loops, splayed nematic patterns, and yet more metastable states. Our results are relevant to the understanding of the switching dynamics for a class of new, "superstable", blue phases which are composed of bimesogenic liquid crystals, as these materials combine anomalously large flexoelectric coefficients, and low or near-zero dielectric anisotropy.

Rheology of cubic blue phases

We study the behaviour of cubic blue phases under shear flow via lattice Boltzmann simulations. We focus on the two experimentally observed phases, Blue Phase I (BPI) and Blue Phase II (BPII). The disclination network of Blue Phase II continuously breaks and reforms under steady shear, leading to an oscillatory stress response in time. For larger shear rates, the structure breaks up into a Grandjean texture with a cholesteric helix lying along the flow gradient direction. Blue Phase I leads to a very different response. Here, oscillations are only possible for intermediate shear rates -- very slow flow causes a transition of the initially ordered structure into an amorphous network with an apparent yield stress. Larger shear rates lead to another amorphous state with different structure of the defect network. For even larger flow rates the same break-up into a Grandjean texture as for Blue Phase II is observed. At the highest imposed flow rates both cubic blue phases adopt a flow-aligned nematic state. Our results provide the first theoretical investigation of sheared blue phases in large systems, and are relevant to understanding the bulk rheology of these materials.

Confined cubic blue phases under shear

We study the behaviour of confined cubic blue phases under shear flow via lattice Boltzmann simulations. We focus on the two experimentally observed phases, blue phase I and blue phase II. The disclination network of blue phase II continuously breaks and reforms under shear, leading to an oscillatory stress response in time. The oscillations are only regular for very thin samples. For thicker samples, the shear leads to a ‘stick–slip’ motion of part of the network along the vorticity direction. Blue phase I responds very differently: its defect network undergoes seemingly chaotic rearrangements under shear, irrespective of system size.

Interpretation of the temperature dependence of the composition distribution in nanostructured alloys under severe plastic deformation

In the work, we analyze experimental data on the temperature dependence of the composition distribution in alloys under severe plastic deformation. The analysis is based on a simple model that combines the concepts of relay-race evolution of ajunction disclination network and structural-kinetic description of brittle fracture in view of quasi-hydrostatic compression. Conditions for a stable homogeneous steady-state plastic flow are considered and temperature-rate modes of plastic flow are determined in the context of deformation controlled by grain boundary diffusion or vacancy diffusion in the grain volume.

Numerical results for the blue phases

We review recent numerical work investigating the equilibrium phase diagram, and the dynamics of the cholesteric blue phases. In equilibrium numerical results confirm the predictions of the classic analytical theories, and extend them to incorporate different values of the elastic constants, or the effects of an applied electric field. There is a striking increase in the stability of blue phase I in systems where the cholesteric undergoes helical sense inversion, and the anomalous electrostriction observed in this phase is reproduced. Solving the equations of motion allows us to present results for the phase transition kinetics of blue phase I under dielectric or flexoelectric coupling to an applied electric field. We also present simulations of the blue phases in a flow field, showing how the disclination network acts to oppose the flow. The results are based on the Landau–de Gennes expansion of the liquid crystal free energy: that such a simple and elegant theory can predict such complex and subtle physical behaviour is remarkable.

Numerical calculations of the phase diagram of cubic blue phases in cholesteric liquid crystals

We study the static properties of cubic blue phases by numerically minimizing the three-dimensional, Landau-de Gennes free energy for a cholesteric liquid crystal close to the isotropic-cholesteric phase transition. Thus we are able to refine the powerful but approximate, semianalytic frameworks that have been used previously. We obtain the equilibrium phase diagram and discuss it in relation to previous results. We find that the value of the chirality above which blue phases appear is shifted by 20% (toward experimentally more accessible regions) with respect to previous estimates. We also find that the region of stability of the O5 structure-which has not been observed experimentally-shrinks, while that of blue phase I ( O-8 ) increases thus giving the correct order of appearance of blue phases at small chirality. We also study the approach to equilibrium starting from the infinite chirality solutions and we find that in some cases the disclination network has to assemble during the equilibration. In these situations disclinations are formed via the merging of isolated aligned defects.

A model of defects in metallic glasses

The disclination network description of the metallic glass structure is discussed. Qualitative predictions concerning point defect stability and mobility in the typical atomic configurations of such a structure are made based on a ball-and-stick simulation.

Evolution of disorder in magnetic stripe domains. II. Hairpins and labyrinth patterns versus branches and comb patterns formed by growing minority component.

An analysis is presented of the role of topological defects in the evolution of disordered stripe-domain phases of ferrimagnetic garnet films. Proliferation by continued nucleation and topologically constrained unbinding of disclination dipoles are identified as the essential mechanisms mediating the strain-induced disordering process. Two distinct classes of metastable, disordered states are distinguished on the basis of the relative predominance of defect-pair proliferation and unbinding, and the fundamentally different corresponding pattern morphologies which accommodate the emerging disclination network. Striking patterns containing linear chains of interdigitated disclination dipoles are representative of the first class, while labyrinthine patterns, exhibiting a robust and well-defined local structure in the form of ``cybotactic'' clusters, are typical of the second class. Results are discussed with reference to defect-mediated melting and the structure of glasses. Comparison is also made with pertinent phenomena in related systems such as ferrofluids and amphiphilic films.

Formation of Quasicrystalline Alloy Powders by Mechanical Alloying.

Mechanical alloying (MA) was used to obtain quasicrystalline; phases Mg3Zn5-xAlx (x=2-4) and i-Mg32Cu8Al4 starting from the elementary metal powders.Mechanical disordering(MD) of cubic Frank-Kasper (F-K) phases such as Mg32(Zn, A1)49 lead to formation of relative quasicrystalline structures as well.The X-ray diffraction patterns of i-phases are identical to those obtained by rapid quenching. SAD patterns of both MA and MD samples demonstrated 2, 3, 6, and 5-fold symmetry pictures.There are ten sets of Bragg spots with angles between them 36°. The values of the interplanar distances in i-Mg32(Zn, Al)49 are d1=0.141nm, d2=0.228nm, d3=0.369nm, d4=0.597nm, dn=dn-1t, where t=(1+51/2)/2.The cubic phases Mg32(Zn, Al)49 and Mg32(Cu, Al)49 are F-K structures with local 5-fold symmetry units.The icosa-hedral structure can be described in terms of cubic F-K phase containing discli-nations.The MD of F-K phases lead to progressive broadering of X-ray peaks due to the structural, defects arising in cubic lattice and the icosahedral phases were formed apparently due to the formation of disclination network during MD.

Mechanochemical synthesis of icosahedral phases in Mg-Zn-Al and Mg-Cu-Al alloys

Mechanical alloying (MA) has been used to obtain the icosahedral phases: i-(Mg-Zn-Al) and i-(Mg-Cu-Al) from metal powders. X-ray diffraction peaks are identical to those of icosahedral obtained by the melt spun technique. SAD patterns from MA samples indicate 2,3,6 and 5-fold symmetry. Annealing of the MA icosahedral phases leads to the formation of related cubic Frank-Kasper phases, that can be transformed into the icosahedral phases by MA. The disclination network which appears in the cubic phase plastically deformed by MA seems to be intrinsic to producing an aperiodic phase with long-range icosahedral order.

On the Screening Length of Disclinations in Amorphous Structures

AbstractDisclinations represent the main defects beside dislocations in topologically disordered structures. The stress field and the energy of a disclination depend strongly on the boundary conditions, mostly the presence of a free surface. Stress field, self‐energy, and pair interactions of disclinations in a finite cylinder are calculated pointing out the relevance of additional interactions of disclinations with the surface, if the disclination is not positioned in the center of the cylinder. The energy of the model system is always diminished by such surface effects. Numerical calculations of the screening length in a disclination network for an amorphous structure show that a cut‐off radius only exists because of the interaction between defects. The screening length is about three times larger than the average distance between disclinations and depends on the disclination density. The cut‐off radius corresponds to the creation of internal surfaces resulting in an additional screening of defects.

Structure disordering in curved space model

Disclination network in an amorphous solid in continuum approximation is considered. The structure corresponds to a curved space with constant curvature K. It is shown that the lattice is unstable with respect to the transition into a space of constant curvature, i.e. into disordered state. The transition temperature is found and shown that it does not depend on metric at K = const. In addition the perturbation of phonon spectrum and its connection to disclination density are found.

Topology of local atomic environments: implications for magnetism and superconductivity

Wigner-Seitz cells have been constructed, as a function of atomic size, for a number of transition-metal alloys, and a disclination network has been obtained from these. Magnetism in these alloys can be related to the disclination lines, much like the superexchange paths familiar in the magnetism of salts.

Disclinations in transversely isotropic media II. Angular and straight disclinations

1. Introduction of the angular disclinations makes it possible to construct stress fields of a disclination network analytically in anisotropic solids. 2. In the case of a highly anisotropic medium (c33≫ c ij ) the disclination dipole and quadrupole are characterized by the strong dependence of the elastic energy on the dipole arm orientation with respect to the basal plane and on the quadrupole shape correspondingly. Thus, the investigation carried out in the present study clearly demonstrates the necessity of anisotropic theory of disclinations development. The generalisation of the theory for the case of disclination with arbitrary Frank vector orientation can be done on the basis of rectangular twist disclination loop elastic fields. We intend to solve this problem in the nearest future.