Defect Core Research Articles

Coupling Phase Field Crystal and Field Dislocation Mechanics for a consistent description of dislocation structure and elasticity

This work addresses differences in predicted elastic fields created by dislocations either by the Phase Field Crystal (PFC) model, or by static Field Dislocation Mechanics (FDM). The PFC order parameter describes the topological content of the lattice, but it fails to correctly capture the elastic distortion. In contrast, static FDM correctly captures the latter but requires input about defect cores. The case of a dislocation dipole in two dimensional, isotropic, elastic medium is studied, and a weak coupling is introduced between the two models. The PFC model produces compact and stable dislocation cores, free of any singularity, i.e., diffuse. The PFC predicted dislocation density field (a measure of the topological defect content) is used as the source (input) for the static FDM problem. This coupling allows a critical analysis of the relative role played by configurational (from PFC) and elastic (from static FDM) fields in the theory, and of the consequences of the lack of elastic relaxation in the diffusive evolution of the PFC order parameter.

Ultra-high spatial resolutions in photopatterning molecular orientations

Accurately aligning liquid crystal molecules into predetermined spatially variant orientations is crucial for fabricating devices such as flat optical elements, soft actuators and robots. Despite the developments of various photopatterning techniques for this purpose, the limits of their spatial resolutions have been rarely addressed. In this study, we delve into the physical constraints governing the spatial resolutions of two prominent photopatterning methods: single exposure to light fields with structured polarizations and multi-exposures to light fields with structured intensities. Theoretical analyses show that the minimal grating period of the first method is only half of the Abbe limit of an intensity imaging system, and that the minimal grating period for the second system can surpass the Rayleigh limit. Experimental studies demonstrate unprecedent high spatial resolution with minimal grating periods of 1 µm. We further establish that the minimal core size in photopatterned singular topological defects is linearly proportional to the minimal grating period and the topological charge and that these photopatterning techniques can yield less than 1 µm defect cores that are in high demand for applications such as coronagraphs.

Trapping of isotropic droplets by disclinations in nematic liquid crystals controlled by surface anchoring and elastic constant disparity.

Linear defects such as dislocations and disclinations in ordered materials attract foreign particles since they replace strong elastic distortions at the defect cores. In this work, we explore the behavior of isotropic droplets nucleating at singular disclinations in a nematic liquid crystal, predesigned by surface photopatterning. Experiments show that in the biphasic nematic-isotropic region, although the droplets are attracted to the disclination cores, their centers of mass shift away from the core centers as the temperature increases. The shift is not random, being deterministically defined by the surrounding director field. The effect is explained by the balance of interfacial anchoring and bulk elasticity. An agreement with the experiment can be achieved only if the model accounts for the disparity of the nematic elastic constants; the so-called one-constant approximation, often used in the theoretical analysis of liquid crystals, produces qualitatively wrong predictions. In particular, the experimentally observed shift towards the bend region around a +1/2 disclination core can be explained only when the bend constant is larger than the splay constant. The described dependence of the precise location of a foreign inclusion at defect cores on the elastic and surface anchoring properties can be used in rational design of microscale architectures.

Development of an innovative diffraction scattering theory of X-rays and electrons in imperfect crystals.

Fundamental equations describing the X-ray and electron diffraction scattering in imperfect crystals have been derived in the form of the matrix Fredholm-Volterra integral equation of the second kind. A theoretical approach has been developed using the perfect-crystal Green function formalism. In contrast, another approach utilizes the wavefield eigenfunctions related to the diagonalized matrix propagators of the conventional Takagi-Taupin and Howie-Whelan equations. Using the Liouville-Neumann-type series formalism for building up the matrix Fredholm-Volterra integral equation solutions, the general resolvent function solutions of the X-ray and electron diffraction boundary-valued Cauchy problems have been obtained. Based on the resolvent-type solutions, the aim is to reveal the features of the diffraction scattering onto the crystal lattice defects, including the mechanisms of intra- and interbranch wave scattering in the strongly deformed regions in the vicinity of crystal lattice defect cores. Using the two-stage resolvent solution of the second order, this approach has been supported by straightforward calculation of the electron bright- and dark-field contrasts of an edge dislocation in a thick foil. The results obtained for the bright- and dark-field profiles of the edge dislocation are discussed and compared with analogous ones numerically calculated by Howie & Whelan [Proc. R. Soc. A (1962), 267, 206].

The atomic configuration and metallic state of extrinsic defects in Nb-doped BiFeO3 thin films

Defects in ferroelectric materials can cause microscopic strain and electron doping, which opens up new possibilities for unique physical properties in nanoelectronics. However, comprehending the relationship between these deep-buried defect configurations and the resulting physical properties is a long-term challenge. Here, utilizing the integrated differential phase imaging technique equipped in scanning transmission electron microscopy combined with energy dispersive X-ray spectroscopy, we show the full element-resolved atomic configuration of characteristic extrinsic defects in Nb-doped epitaxial BiFeO3 thin films. Atomic-resolution characterization reveals that the Nb doping substitutes Fe at the center of an oxygen octahedron and creates Fe vacancies near the defect core, leading to the formation of one perovskite cell-wide BiNbO3 chain that is expanded by 19 % in perovskite cell volume and rotated by 45° relative to the matrix lattice. Further quantitative analysis of the defect demonstrates that the ferroelectric polarization distribution around the dopant-induced defects displays a “head-to-head” configuration, indicating the accumulation of negative charges. Supported by electron energy loss spectroscopy and density functional theory calculations, the linear defect leads to one-dimensional metallic channels embedded within the ferroelectric BiFeO3 matrix. These atomic-scale findings establish the structure-functionality relationship of extrinsic defect in Nb-doped BiFeO3 thin films, providing new insight into their fundamental understanding and potential use in low-dimensional nanoelectronics devices.

Atomic-level mechanisms of short-circuit diffusion in materials

Abstract This paper reviews the recent progress in understanding the atomic mechanisms of short-circuit diffusion along materials interfaces, such as grain and interphase boundaries, as well as lattice and interfacial dislocations/disconnections. Recent atomistic computer simulations have shown that short-circuit diffusion is dominated by collective atomic rearrangements in the form of strings and rings of mobile atoms. The process is dynamically heterogeneous in space and time and has many features in common with atomic dynamics in supercooled glass-forming liquids. We discuss examples of grain boundary, interphase boundary, and dislocation diffusion in metals and alloys, including the solute effect on the diffusion rates and mechanisms. Interphase boundaries are exemplified by Al–Si interfaces with diverse orientation relationships and atomic structures. The hierarchy of short-circuit diffusion paths in materials is reviewed by comparing the rates of grain boundary, interphase boundary, and dislocation diffusion. Future directions in the field of short-circuit diffusion in defect core regions are discussed.

Emergent metallicity at the grain boundaries of higher-order topological insulators

Topological lattice defects, such as dislocations and grain boundaries (GBs), are ubiquitously present in the bulk of quantum materials and externally tunable in metamaterials. In terms of robust modes, localized near the defect cores, they are instrumental in identifying topological crystals, featuring the hallmark band inversion at a finite momentum (translationally active type). Here we show that the GB superlattices in both two-dimensional and three-dimensional translationally active higher-order topological insulators harbor a myriad of dispersive modes that are typically placed at finite energies, but always well-separated from the bulk states. However, when the Burgers vector of the constituting edge dislocations points toward the gapless corners or hinges, both second-order and third-order topological insulators accommodate self-organized emergent topological metals near the zero energy (half-filling) in the GB mini Brillouin zone. We discuss possible material platforms where our proposed scenarios can be realized through the band-structure and defect engineering.

1782-P: Perinatal Hypoxia Lowers the Glucose Threshold for Insulin Secretion Causing Hypoglycemia and Hyperinsulinism

Perinatal stress-induced hyperinsulinism is a common cause of persistent hypoglycemia in at-risk neonates. The hypoxia-inducible factor-1 (HIF-1) pathway regulates cellular adaptation in hypoxic conditions through hypoxia response elements. We hypothesize that perinatal hypoxia leads to activation of the HIF1 pathway causing increased insulin secretion from neonatal β-cells. We examined glucose homeostasis and insulin secretion in NeuroD1-Cre;VhlLoxp/Loxp(VhlbetaKO) and in hypoxic wild type (WT) mouse pups in the first week of life. In VhlbetaKO pups postnatal day 8 (P8), plasma glucose was significantly lower compared to littermate controls (76 vs 129 mg/dL). Plasma insulin (0.54 vs 0.27 ng/mL) and the insulin to glucose ratio were significantly greater in VhlbetaKO pups indicating a failure to suppress insulin secretion. VhlbetaKO islet perifusion showed the lower plasma glucose level was due to a lower threshold (5 mM) for glucose stimulated insulin secretion (GSIS) compared to controls (10 mM). To assess the consequences of perinatal hypoxia, we exposed WT mouse pups to hypoxia (10% O2) between embryonic day 18 and P6. Islets from the hypoxia exposed pups had a lower GSIS threshold (3 mM) compared to islets from normoxic pups (5 mM) at P6. Hypoxic islets also had a lower insulin secretion threshold when stimulated with BCH, a glutamate dehydrogenase activator, or tolbutamide, a KATP channel inhibitor, suggesting that HIF1 pathway activation leads to a decreased stimulus threshold for secretion at or distal to the KATP channel. Patch clamps revealed that β-cells from hypoxic pups were more depolarized than normoxic controls. Our results show that the HIF1 pathway is critical for setting the GSIS threshold and a potential mediator of PSHI. We posit perinatal hypoxia and the HIF1 pathway at the core of β-cell maturational defects leading to increased risk of diabetes in adult life and the long-sought answer to the cause of perinatal stress-induced hyperinsulinism. Disclosure C.Juliana: Research Support; Crinetics Pharmaceuticals, Inc., Twist Bioscience, AmideBio. D.De leon: Consultant; Zealand Pharma A/S, Crinetics Pharmaceuticals, Inc., Eiger BioPharmaceuticals, Hanmi Pharm. Co., Ltd., Research Support; Ultragenix, Crinetics Pharmaceuticals, Inc., Hanmi Pharm. Co., Ltd., Rezolute, Inc.

Kinematics and dynamics of disclination lines in three-dimensional nematics

An exact kinematic law for the motion of disclination lines in nematic liquid crystals as a function of the tensor order parameterQis derived. Unlike other order parameter fields that become singular at their respective defect cores, the tensor order parameter remains regular. Following earlier experimental and theoretical work, the disclination core is defined to be the line where the uniaxial and biaxial order parameters are equal, or equivalently, where the two largest eigenvalues ofQcross. This allows an exact expression relating the velocity of the line to spatial and temporal derivatives ofQon the line, to be specified by a dynamical model for the evolution of the nematic. By introducing a linear core approximation forQ, analytical results are given for several prototypical configurations, including line interactions and motion, loop annihilation, and the response to external fields and shear flows. Behaviour that follows from topological constraints or defect geometry is highlighted. The analytic results are shown to be in agreement with three-dimensional numerical calculations based on a singular Maier–Saupe free energy that allows for anisotropic elasticity.

Spiralling defect cores in chromonic hedgehogs

ABSTRACTAn elastic quartic twist theory has recently been proposed for chromonic liquid crystals, intended to overcome the paradoxical conclusions encountered by the classical Oseen-Frank theory when applied to droplets submerged in an isotropic fluid environment. However, available experimental data for chromonics confined to cylindrical cavities with degenerate planar anchoring on their lateral boundary can be explained equally well by both competing theories. This paper identifies a means to differentiate these theories both qualitatively and quantitatively. They are shown to predict quite different core defects for the twisted hedgehogs that chromonics generate when confined to a fixed spherical cavity with homeotropic anchoring. In the quartic twist theory, the defect core is estimated to be nearly one order of magnitude larger (few microns) than in the other and, correspondingly, the director field lines describe Archimedean spirals instead of logarithmic ones.

ВЗАИМОДЕЙСТВИЕ И ДИНАМИКА ТОПОЛОГИЧЕСКИХ ДЕФЕКТОВ В ДОМЕННОЙ СТРУКТУРЕ ЗАКРУЧЕННОГО НЕМАТИКА

The dynamics and interaction of topological defects in the domain structure of π/2 twisted nematic liquid crystal are studied. A feature of Williams domains in twisted nematics is that hydrodynamic flows in them, along with the tangential velocity component, also have an axial component, the direction of which is opposite in neighboring domains. The axial velocity component arises as a result of the strong coupling between the initial twisted director orientation n and the hydrodynamic flow velocity. In domain structures of π/2 twisted nematics, as well as in planar oriented ones, edge dislocations with topological charges S =±1 arise. With increasing applied voltage density of dislocations grows. Dislocations move both along the Williams domains ( climb ) and perpendicular to them ( glide ). At a certain rate of the increasing applied voltage U > U c, distortions of the domain structure begin to propagate on both sides of the defect core. This leads to the formation of a special topological defects - dislocations with a “diffused” core, or linear defects, which are oriented perpendicular to the Williams domains and move mainly along them. The arising linear defect has the same topological charge as the initial dislocation. It is shown that their interaction is qualitatively well described by the perturbed sine-Gordon equation.

Complex-tensor theory of simple smectics

Matter self-assembling into layers generates unique properties, including structures of stacked surfaces, directed transport, and compact area maximization that can be highly functionalized in biology and technology. Smectics represent the paradigm of such lamellar materials — they are a state between fluids and solids, characterized by both orientational and partial positional ordering in one layering direction, making them notoriously difficult to model, particularly in confining geometries. We propose a complex tensor order parameter to describe the local degree of lamellar ordering, layer displacement and orientation of the layers for simple, lamellar smectics. The theory accounts for both dislocations and disclinations, by regularizing singularities within defect cores and so remaining continuous everywhere. The ability to describe disclinations and dislocation allows this theory to simulate arrested configurations and inclusion-induced local ordering. This tensorial theory for simple smectics considerably simplifies numerics, facilitating studies on the mesoscopic structure of topologically complex systems.

Spontaneous flows and dynamics of full-integer topological defects in polar active matter.

Polar active matter of self-propelled particles sustain spontaneous flows through the full-integer topological defects. We study theoretically the incompressible flow profiles around ±1 defects induced by polar and dipolar active forces. We show that dipolar forces induce vortical flows around the +1 defect, while the flow around the -1 defect has an 8-fold rotational symmetry. The vortical flow changes its chirality near the +1 defect core in the absence of the friction with a substrate. We show analytically that the flow induced by polar active forces is vortical near the +1 defect and is 4-fold symmetric near the -1 defect, while it becomes uniform in the far-field. For a pair of oppositely charged defects, this polar flow contributes to a mutual interaction force that depends only on the orientation of the defect pair relative to the background polarization, and that enhances defect pair annihilation. This is in contradiction with the effect of dipolar active forces which decay inversely proportional with the defect separation distance. As such, our analyses reveals a long-ranged mechanism for the pairwise interaction between topological defects in polar active matter.

A machine-learned spin-lattice potential for dynamic simulations of defective magnetic iron

A machine-learned spin-lattice interatomic potential (MSLP) for magnetic iron is developed and applied to mesoscopic scale defects. It is achieved by augmenting a spin-lattice Hamiltonian with a neural network term trained to descriptors representing a mix of local atomic configuration and magnetic environments. It reproduces the cohesive energy of BCC and FCC phases with various magnetic states. It predicts the formation energy and complex magnetic structure of point defects in quantitative agreement with density functional theory (DFT) including the reversal and quenching of magnetic moments near the core of defects. The Curie temperature is calculated through spin-lattice dynamics showing good computational stability at high temperature. The potential is applied to study magnetic fluctuations near sizable dislocation loops. The MSLP transcends current treatments using DFT and molecular dynamics, and surpasses other spin-lattice potentials that only treat near-perfect crystal cases.

Applications and Software Developments for Analyzing Crystal Defect Cores

Applications and Software Developments for Analyzing Crystal Defect Cores

Preface to Special Issue on Frontiers in Scientific Research on Crystal Defect Cores

Preface to Special Issue on Frontiers in Scientific Research on Crystal Defect Cores

Crystal Defect Core Studied by Advanced Electron Microscopy

Crystal Defect Core Studied by Advanced Electron Microscopy

Development of Energy Conversion/storage Materials Based on Crystal Defect Cores

Development of Energy Conversion/storage Materials Based on Crystal Defect Cores

Method and Applications for New Material Science on Nanoscale Structures and Functions of Crystal Defect Cores

Method and Applications for New Material Science on Nanoscale Structures and Functions of Crystal Defect Cores

Theory of Layered-Oxide Cathode Degradation in Li-ion Batteries by Oxidation-Induced Cation Disorder

Disorder-driven degradation phenomena, such as structural phase transformations and surface reconstructions, can significantly reduce the lifetime of Li-ion batteries, especially those with nickel-rich layered-oxide cathodes. We develop a general free energy model for layered-oxide ion-intercalation materials as a function of the degree of disorder, which represents the density of defects in the host crystal. The model accounts for defect core energies, long-range dipolar electrostatic forces, and configurational entropy of the solid solution. In the case of nickel-rich oxides, we hypothesize that nickel with a high concentration of defects is driven into the bulk by electrostatic forces as oxidation reactions at the solid-electrolyte interface reduce nickel and either evolve oxygen or oxidize the organic electrolyte at high potentials (>4.4 V vs Li/Li+). The model is used in battery cycling simulations to describe the extent of cathode degradation when using different voltage cutoffs, in agreement with experimental observations that lower-voltage cycling can substantially reduce cathode degradation. The theory provides a framework to guide the development of cathode compositions, coatings and electrolytes to enhance rate capability and enhance battery lifetime. The general theory of cation-disorder formation may also find applications in electrochemical water treatment and ion separations, such as lithium extraction from brines, based on competitive ion intercalation in battery materials.