Periodic Array Of Dislocations Research Articles

Anomalous strain relaxation and its impact on the valence-driven spin-state/metal-insulator transition in epitaxial (Pr1−yYy)1−xCaxCoO3−δ

Pr-based cobaltites exhibit extraordinary phenomena where abrupt valence shifts trigger coupled structural/spin-state/metal-insulator transitions. Recent work achieved strain control of these phenomena in thin films, with epitaxial compression even stabilizing room-temperature transitions. Here, we study the thickness dependence of these effects in the model system compressively strained $\mathrm{YAl}{\mathrm{O}}_{3}(101)/{({\mathrm{Pr}}_{0.85}{\mathrm{Y}}_{0.15})}_{0.7}{\mathrm{Ca}}_{0.3}\mathrm{Co}{\mathrm{O}}_{3\text{\ensuremath{-}}\ensuremath{\delta}}(001)$. Transport data reveal highly unusual behavior where thicker films exhibit two transitions: one at the fully strained temperature $(\ensuremath{\sim}245\phantom{\rule{0.16em}{0ex}}\mathrm{K})$ and one near the bulk $(\ensuremath{\sim}135\phantom{\rule{0.16em}{0ex}}\mathrm{K})$. High-resolution x-ray diffraction confirms that this is due to anomalous strain relaxation where, immediately above the critical thickness $(\ensuremath{\sim}30\phantom{\rule{0.16em}{0ex}}\mathrm{nm})$, a film region with a near-bulk lattice parameter coexists with a fully strained region. Scanning transmission electron microscopy then reveals striking images where periodic arrays of dislocations occur in the film interior, rather than at the film-substrate interface, seeding accompanying lateral modulations in chemical doping. The unusual transport is thus a direct consequence of anomalous strain relaxation, which we discuss in detail. Intriguing behavior also arises in the ultrathin limit, where temperature-dependent transport and x-ray data reveal gradual suppression of the amplitude of the structural/metal-insulator transition but with no change in transition temperature, which we ascribe to effects of disorder in the presence of symmetry matching between the film and substrate. These results establish an unusual strain relaxation mechanism in perovskite oxide films (likely relevant to other systems) and further elucidate the sensitive strain response of these fascinating and potentially useful valence/structural/spin-state/metal-insulator transitions.

Efficient Flexible Boundary Conditions for Long Dislocations

We present a novel efficient implementation of the flexible boundary condition (FBC) method, initially proposed by Sinclair et al., for large single-periodic problems. Efficiency is primarily achieved by constructing a hierarchical matrix ($\mathscr{H}$-matrix) representation of the periodic Green matrix, reducing the complexity for updating the boundary conditions of the atomistic problem from quadratic to almost linear in the number of pad atoms. In addition, our implementation is supported by various other tools from numerical analysis, such as a residual-based transformation of the boundary conditions to accelerate the convergence. We assess the method for a comprehensive set of examples, relevant for predicting mechanical properties, such as yield strength or ductility, including dislocation bow-out, dislocation-precipitate interaction, and dislocation cross-slip. The main result of our analysis is that the FBC method is robust, easy-to-use, and up to two orders of magnitude more efficient than the current state-of-the-art method for this class of problems, the periodic array of dislocations (PAD) method, in terms of the required number of per-atom force computations when both methods give similar accuracy. This opens new prospects for large-scale atomistic simulations - without having to worry about spurious image effects that plague classical boundary conditions.

Fabrication and characterization of tetragonal yttria‐stabilized zirconia single‐crystalline thin film

AbstractTetragonal yttria‐stabilized zirconia thin film was successfully fabricated by a pulsed laser deposition method. The thin film grew heteroepitaxially with the orientation relationship of ZrO2‖Al2O3. Energy dispersive X‐ray spectroscopy mapping revealed that Y3+ ions were distributed homogeneously without local segregations. X‐ray and electron‐diffraction analysis confirmed a single crystalline structural feature of the film. On the other hand, high‐resolution scanning transmission electron microscopy observations show that this film contains small‐angle tilt grain boundaries, which is composed of the periodic array of dislocations with the Burgers vector .

Self-patterning screw dislocations in pure Mg

In addition to tuning the composition, precipitate, and grain microstructure of an alloy, manipulating dislocation structure provides an additional strategy of designing novel alloys. One promising dislocation structure, in the form of periodic dislocation arrays, conventionally forms in cubic alloys under cyclic loading. In this paper, we demonstrate new possibility of synthesizing periodic dislocation arrays in pure Mg under static loading, a simple processing route. This finding provides insight in advancing dislocation substructures, which promote the performance of engineering alloys.

Grazing-incidence X-ray diffraction investigation of the coincidence site lattice of the Ge/Si(001) system.

The Ge/Si(001) system has been analysed by grazing-incidence X-ray diffraction on a standard laboratory X-ray diffraction tool. A periodic array of interfacial edge dislocations forms a coincidence site lattice (CSL) which yields equidistantly spaced satellite peaks close to Bragg peaks of the Ge layer and Si substrate. The diffraction behaviour of the CSL was analysed using 2θ/φ scans along [100], [110] and [310] directions as well as azimuthal φ scans which revealed a 90° angular symmetry of the CSL. Additionally, different layer thicknesses, from 10 to 580 nm, were analysed, focusing on the dependence of layer thickness on the glancing angles of the satellite peaks. This method provides the ability to analyse whether or not epitaxially grown layers exhibit a periodic array of dislocations, and gain information about the orientation of the interfacial edge dislocations.

Effect of growth temperature on the microstructural properties of 0.95Na0.5Bi0.5TiO3–0.05BaTiO3 films prepared on MgO (0 0 1) substrates

Lead-free 0.95(Na0.5Bi0.5)TiO3–0.05BaTiO3 (NBT-BT) piezoelectric films have been successfully fabricated by high-pressure magnetron sputtering deposition technique on (0 0 1)-oriented MgO substrates at 800 °C and 900 °C, respectively. By advanced electron microscopy techniques, the orientation relationship of (0 0 1)[1 1 0]film//(0 0 1)[1 0 0]MgO and (0 0 1)[1 0 0]film//(0 0 1)[1 0 0]MgO is determined for the NBT-BT/MgO heterostructures prepared at 800 °C and 900 °C, respectively. In comparison, a high density of zigzag-typed planar defects appear in the film prepared at 900 °C. At the semi-coherent interfaces, periodic dislocation arrays form to relax the film-substrate misfit strain. In particular, the formation of both (a/2) 〈0 1 0〉 -type and (a/2) 〈011-〉 -type interfacial dislocations facilitates the growth of NBT-BT films on rough MgO substrates at 900 °C. Our findings indicate that the mode of film growth and microstructure for NBT-BT films prepared on MgO substrates can be tuned by the growth temperature.

Sub-nanometre channels embedded in two-dimensional materials.

Two-dimensional (2D) materials are among the most promising candidates for next-generation electronics due to their atomic thinness, allowing for flexible transparent electronics and ultimate length scaling. Thus far, atomically thin p-n junctions, metal-semiconductor contacts, and metal-insulator barriers have been demonstrated. Although 2D materials achieve the thinnest possible devices, precise nanoscale control over the lateral dimensions is also necessary. Here, we report the direct synthesis of sub-nanometre-wide one-dimensional (1D) MoS2 channels embedded within WSe2 monolayers, using a dislocation-catalysed approach. The 1D channels have edges free of misfit dislocations and dangling bonds, forming a coherent interface with the embedding 2D matrix. Periodic dislocation arrays produce 2D superlattices of coherent MoS2 1D channels in WSe2. Using molecular dynamics simulations, we have identified other combinations of 2D materials where 1D channels can also be formed. The electronic band structure of these 1D channels offers the promise of carrier confinement in a direct-gap material and the charge separation needed to access the ultimate length scales necessary for future electronic applications.

Macroscopic stress and strain in a doubly periodic array of dislocation dipoles.

It is known that in two-dimensional periodic arrays of dislocations the summation of the periodic image fields is conditionally convergent. This is due to the long-range character of the elastic fields of dislocations. As a result, the stress field obtained for a doubly periodic array of dislocation dipoles may contain a spurious constant stress that depends on the adopted summation scheme. In the present work, we provide, based on micromechanical considerations, a simple physical explanation of the origin of the conditional convergence of lattice sums of image interactions. In this context, the spurious stresses are found in a closed form for an arbitrary elastic anisotropy, and this is achieved without using the stress field of an individual dislocation. An alternative procedure is also developed where the macroscopic spurious stresses are determined using the solution of the Eshelby's inclusion problem.

Conductivity of epitaxial and CVD graphene with correlated line defects

Transport properties of single-layer graphene with correlated one-dimensional defects are studied theoretically using the computational model within the time-dependent real-space Kubo–Greenwood formalism. Such defects are present in epitaxial graphene, comprising atomic terraces and steps due to the substrate morphology, and in polycrystalline chemically vapor-deposited (CVD) graphene due to the grain boundaries, composed of a periodic array of dislocations, or quasi-periodic nanoripples originated from the metal substrate. The extended line defects are described by the long-range Lorentzian-type scattering potential. The dc conductivity is calculated numerically for different cases of distribution of line defects. This includes a random (uncorrelated) and a correlated distribution with a prevailing direction in the orientation of lines. The anisotropy of the conductivity along and across the line defects is revealed, which agrees with experimental measurements for epitaxial graphene grown on SiC. We performed a detailed study of the conductivity for different defect correlations, introducing the correlation angle αmax—the maximum possible angle between any two lines. We find that for a given electron density, the relative enhancement of the conductivity for the case of fully correlated line defects in comparison to the case of uncorrelated ones is larger for a higher defect density. Finally, we, for the first time, study the conductivity of realistic samples where both extended line defects and point-like scatterers such as adatoms and charged impurities are presented.

Conditional convergence in two-dimensional dislocation dynamics

For two-dimensional dislocation dynamics simulations under periodic boundary conditions in both directions, the summation of the periodic image stress fields is found to be conditionally convergent. For example, different stress fields are obtained depending on whether the summation in the x-direction is performed before or after the summation in the y-direction. This problem arises because the stress field of a 1D periodic array of dislocations does not necessarily go to zero far away from the dislocation array. The spurious stress fields caused by conditional convergence in the 2D sum are shown to consist of only a linear term and a constant term with no higher order terms. Absolute convergence, and hence self-consistency, is restored by subtracting the spurious stress fields, whose expressions are derived in both isotropic and anisotropic elasticity.

Comparison of phase slippage processes in Josephson junctions and charge-density wave stacked junctions

We discuss a time-space symmetry in phase slippage processes in Josephson junctions and charge density wave (CDW) stacked junctions. In Josephson junctions, above a critical current a phase slip of 2π occurs periodically in time with a period T corresponding to the rate given by the Josephson relation ν = 1/ T= 2eV/h, where V is the voltage on the junction. In CDW stacks, a CDW dislocation appears in the weakest junction of the stack when the voltage on the stack exceeds a threshold value. This phase dislocation corresponds to a local phase slippage of 2π. As the voltage is increased, new dislocations show up and form a periodic array of dislocations with period L. The inverse spacing 1/L obeys an analog of Josephson equation, vF/L = 2eV/h.

Dislocation structure at a $$ \{ {\overline{1} 2\overline{1} 0} \}/ {\langle} 10\overline{1} 0 {\rangle} $$ low-angle tilt grain boundary in LiNbO3

LiNbO3 is a ferroelectric material with a rhombohedral R3c structure at room temperature. A LiNbO3 bicrystal with a $$ \{ {\overline{1} 2\overline{1} 0} \}/ {\langle}10\overline{1} 0{\rangle}$$ 1° low-angle tilt grain boundary was successfully fabricated by diffusion bonding. The resultant boundary was then investigated using high-resolution TEM. The boundary composed a periodic array of dislocations with $$ b = { 1}/ 3{\langle} \overline{1} 2\overline{1} 0{\rangle} $$ . They dissociated into two partial dislocations by climb. A crystallographic consideration suggests that the Burgers vectors of the partial dislocations should be $$ 1/ 3{\langle}01\overline{1} 0{\rangle} $$ and $$ 1/ 3{\langle}\overline{1} 100{\rangle} $$ , and a stacking fault on $$ \{ {\overline{1} 2\overline{1} 0} \} $$ is formed between the two partial dislocations. From the separation distance of a partial dislocation pair, a stacking fault energy on $$ \{ {\overline{1} 2\overline{1} 0} \} $$ was estimated to be 0.25 J/m2 on the basis of isotropic elasticity theory.

Algorithms for the calculation of X-ray diffraction patterns from finite element data

A set of algorithms is presented for the calculation of X-ray diffraction patterns from strained nanostructures. Their development was triggered by novel developments in the recording of scattered intensity distributions as well as in simulation practice. The increasing use of two-dimensional CCD detectors in X-ray diffraction experiments, with which three-dimensional reciprocal-space maps can be recorded in a reasonably short time, requires efficient simulation programs to compute one-, two- and three-dimensional intensity distributions. From the simulation point of view, the finite element method (FEM) has become the standard tool for calculation of the strain and displacement fields in nanostructures. Therefore, X-ray diffraction simulation programs must be able to handle FEM data properly. The algorithms presented here make use of the deformation fields calculated on a mesh, which are directly imported into the calculation of diffraction patterns. To demonstrate the application of the developed algorithms, they were applied to several examples such as diffraction data from a dislocated quantum dot, from a periodic array of dislocations in a PbSe epilayer grown on a PbTe pseudosubstrate, and from ripple structures at the surface of SiGe layers deposited on miscut Si substrates.

Electronic transport in polycrystalline graphene

Most materials in available macroscopic quantities are polycrystalline. Graphene, a recently discovered two-dimensional form of carbon with strong potential for replacing silicon in future electronics, is no exception. There is growing evidence of the polycrystalline nature of graphene samples obtained using various techniques. Grain boundaries, intrinsic topological defects of polycrystalline materials, are expected to dramatically alter the electronic transport in graphene. Here, we develop a theory of charge carrier transmission through grain boundaries composed of a periodic array of dislocations in graphene based on the momentum conservation principle. Depending on the grain boundary structure we find two distinct transport behaviours - either high transparency, or perfect reflection of charge carriers over remarkably large energy ranges. First-principles quantum transport calculations are used to verify and further investigate this striking behaviour. Our study sheds light on the transport properties of large-area graphene samples. Furthermore, purposeful engineering of periodic grain boundaries with tunable transport gaps would allow for controlling charge currents without the need of introducing bulk band gaps in otherwise semimetallic graphene. The proposed approach can be regarded as a means towards building practical graphene electronics.

Bi ordered phases on Cu(100): Periodic arrays of dislocations influence the electronic properties

A single layer of bismuth deposited on the Cu(100) surface forms long range ordered structural phases at various Bi density. A highly ordered c(2 x 2) reconstruction is accomplished at 0.5 ML, further Bi deposition induces a c(9square root of 2 x square root of 2)R45 degrees structure and a subsequent p(10 x 10) phase related to the formation of regular dislocations arrays. The transition from a c(2 x 2) superstructure to the c(9square root of 2 x square root of 2)R45 degrees phase is accompanied by a sudden decrease in the work function. Photoemission measurements reveal that the Bi induced states close to the Fermi level, associated to the c(2 x 2) phase, are strongly quenched when the arrays of dislocations are formed, while at higher binding energies, they undergo an energy shift probably due to a confinement effect. The low-energy single particle excitations and the electron dispersion of the Bi induced states of the c(2 x 2) phase are compared to the electronic states deduced by theoretical band structure obtained by ab initio calculation performed within the embedding method applied to a realistic semi-infinite system.

Goal-oriented Atomistic-Continuum Adaptivity for the Quasicontinuum Approximation

We give a goal-oriented a posteriori error estimator for the atomistic-continuum modeling error in the quasicontinuum method, and we use this estimator to design an adaptive algorithm to compute a quantity of interest to a given tolerance by using a nearly minimal number of atomistic degrees of freedom. We present computational results that demonstrate the effectiveness of our algorithm for a periodic array of dislocations described by a Frenkel-Kontorova type model.

Nanoscale dislocation patterning by ultralow load indentation

The use of nanoindentation as a dislocation patterning technique for self-assembled nanostructures is investigated. In this context we have studied the behavior of GaAs under ultralow load indentation conditions. It is shown that periodic dislocation arrays are formed and can be well controlled by nanoindentation. Transmission electron microscopy (TEM) reveals that the crystal deforms solely by dislocation activity with no evidence of stacking faults, twinning, fracture, or phase transformation. The resulting strain field is highly localized, indicating that ultralow load nanoindentation may provide an excellent means to mechanically bias nanostructure nucleation and patterning during subsequent crystal growth.

First principles determination of the Peierls stress of the shuffle screw dislocation in silicon

The Peierls stress of the a/2⟨110⟩ screw dislocation belonging to the shuffle set is calculated for silicon using density functional theory. We have checked the effect of boundary conditions by using two models, the supercell method where one considers a periodic array of dislocations, and the cluster method where a single dislocation is embedded in a small cluster. The Peierls stress is underestimated with the supercell and overestimated with the cluster. These contributions have been calculated and the Peierls stress is determined in the range between 2.4 × 10−2 and 2.8 × 10−2 eV Å−3. When moving, the dislocation follows the {111} plane going through a low energy metastable configuration and never follows the 100 plane, which includes a higher energy metastable core configuration.

Grain-boundary faceting at a = 3, [110]/{112} grain boundary in a cubic zirconia bicrystal

The atomic structure of a = 3, [110]/{112} grain boundary in a yttria-stabilized cubic zirconia bicrystal has been investigated by high-resolution transmission electron microscopy (HRTEM). It was found that the grain boundary migrated to form periodic facets, although the bicrystal was initially joined so as to have the symmetric boundary plane of {112}. The faceted boundary planes were indexed as {111}/{115}. The structure of the {111}/{115} grain boundary was composed of an alternate array of two types of structure unit: {112}- and {111}-type structure units. HRTEM observations combined with lattice statics calculations verified that both crystals were relatively shifted by (α/4)[110] along the rotation axis to form a stable grain-boundary structure. A weak-beam dark-field image revealed that there was a periodic array of dislocations along the grain boundary. The grain-boundary dislocations were considered to be introduced by the slight misorientation from the perfect = 3 orientation. The fact that the periodicity of the facets corresponded to that of the grain-boundary dislocations must indicate that the introduction of the grain-boundary dislocations is closely related to the periodicity of the facets. An atomic flipping model has been proposed for the facet growth from the initial = 3, {112} grain boundary.

Electrical and Structural Characterization of a Low‐Angle Tilt Grain Boundary in Iron‐Doped Strontium Titanate

The atomistic structure and electrical properties of a symmetrical 5.4° [001] tilt grain boundary in Fe‐doped SrTiO3 have been investigated, respectively, by means of various transmission electron microscopy (TEM) techniques and impedance spectroscopy. In weak‐beam dark‐field images, the grain boundary is revealed to consist of a periodic array of dislocations; high‐resolution TEM images show that the dislocation cores are separated by regions of strained lattice. The impedance response of the bicrystal has been measured in the frequency range 20 Hz ≤f≤ 106 Hz as a function of temperature and oxygen partial pressure. The transport of charge across the array of dislocations that form the grain boundary is strongly hindered. Analysis of the impedance data in terms of a double‐Schottky‐barrier model yields a space‐charge potential that exhibits a weak dependence on temperature and oxygen partial pressure and is ∼0.55 V in the investigated regime.