Anisotropic Line Research Articles

Bifurcation prediction of shear banding in sand with non-coaxial critical state model considering inherent anisotropy

In view of phenomenological observations, the anisotropic state variable accounting for the effect of inherent fabric anisotropy, which can describe the microstructural characteristics of sand, is thought to influence the critical state of sand. Based on revised forms of the anisotropic state variable, the form for the anisotropic critical state line function is revised and the non-monotonically anisotropic effects are incorporated into the strength parameter in the re-adjustment of the elements of the model. The anisotropic plasticity model parameters of Toyoura sand are re-calibrated with triaxial compression and extension tests having various deposition directions. In comparison to the experiments on Toyoura sand, it is shown that the model can simulate the anisotropic stress-strain relationship reasonably well. Then, bifurcation analyses are conducted to predict the onset of strain localization with the corresponding non-coaxial anisotropic model. The results show that the modeling of shear band formation based on the non-coaxial model is in agreement with the tests considering the anisotropic characteristic.

EPR studies of the triangular-lattice antiferromagnet Cs2CuBr4

The spin dynamics of the spin-1/2 triangular-lattice antiferromagnet Cs2CuBr4 is probed by means of high-frequency electron paramagnetic resonance (EPR) spectroscopy. Temperature dependences of EPR parameters are studied in a broad temperature range between 1.4 and 200 K for different orientations of the applied magnetic field. In the high-temperature regime (T ≫ J/kB), an unusually broad and anisotropic resonance line is detected, suggesting a sizeable Dzyaloshinskii–Moriya interaction. Employing the theory of exchange narrowing, the ratio of the Dzyaloshinskii–Moriya vector components, Dc/Da ≈ 0.3, is estimated.

Effect of size and shape of crystallites on the optical properties of nanostructured ZnS films

The nanoparticles of ZnS is grown on the glass slide substrates using the thermal evaporation technique. The films are annealed in a vacuum ambient at temperatures between 300 and 550°C. The origin of anisotropic diffraction line broadening is studied using the modified Williamson-Hall plot. The shape and size of crystallites as well as the mean value of strain are studied by applying one of the powerful method of X-ray diffraction analysis i.e. Rietveld refinement procedure. It is found that, with the rise of annealing temperature, not only the size of crystallites increases, but also the shape of them changes from sphere to ellipsoid. The optical band gap are also studied from the transmittance and reflectance spectra of the films. The correlation between the microstructure and optical band gap are reported.

A kinematic hardening and elastic visco-plastic model of saturated cohesive anisotropic soils

Soils have anisotropic kinematic hardening and time-dependent behavior, therefore an anisotropic and kinematic hardening elastic visco-plastic (EVP) model is developed to simulate the anisotropic kinematic hardening and strain rate effects as well as their combined effect. Following the approach of Perzyna’s overstress visco-plasticity and Suklje’s isotaches concept, the anisotropic yield stresses associated with the parameters CΓ and Cvp are used to describe the effect of viscosity on the yield stress. The isotropic and kinematic hardening laws suggested previously by the authors are implemented in the EVP model. With a smart cone-cap connection at critical state points, the EVP model can maintain zero incremental visco-plastic volumetric strains at the intersection points between the Matsuoka-Nakai cone and the associated visco-plastic ellipse cap. Therefore the direction of the visco-plastic strain increment vectors at the cone-cap intersection points is assured unique and numerical calculation is thus convenient. With a deviatoric fabric scalar, zero incremental visco-plastic deviatoric strains can also be kept at the intersection point between the visco-plastic ellipse cap and the anisotropic line. As well, an associated flow rule further assures a smooth transition of the visco-plastic strain increment vectors on the visco-plastic cone-cap limit state surfaces. With the few parameters determined from traditional experiments for the stress element soil sample, numerical analysis is performed to assess the model via CD constant-strain-rate K0 axial and 1/K0 radial triaxial compression, constant-strain-rate traditional CD triaxial compression/extension. Numerical analysis is also performed to validate the model via constant-strain-rate traditional CU triaxial compression tests and constant-strain-rate CD triaxial K = σr′/σa′ = cst compression tests on the anisotropic Berthierville clay. Numerical analysis by the kinematic hardening anisotropic EVP model validates the test results very well, and especially the combined effect is well simulated between strain rate and kinematic hardening on the visco-plastic behavior of the saturated cohesive anisotropic soil. In the future, micro-structure or/and temperature can be further combined with the kinematic hardening anisotropic EVP model introduced in this paper.

Stability and motion of arbitrary grain boundary junctions

The Herring condition is known as the stability condition for a junction line, but the stability conditions for junction points are not readily available. This paper derives stability conditions for arbitrary junction points and allows for anisotropic surface energies and line energies. A junction is considered to be stable when the force on a small neighborhood around the junction vanishes. When the force does not vanish, the junction is expected to move. Equations of motion are derived for the nodes belonging to polygonal curves or triangulated surfaces, and allow for junction lines and junction points to contribute to the drag on a node. The accuracy of the equations of motion is evaluated by the relative error in the rate of volume change of an adjoining grain. They are found to be second-order accurate for nodes on a boundary and first-order accurate for nodes at a junction. A simulation of boundary motion in two dimensions suggests that the equations of motion are of comparable accuracy to alternatives in the literature, and have the advantage of less computational complexity.

A parametric finite element method for solid-state dewetting problems with anisotropic surface energies

We propose an efficient and accurate parametric finite element method (PFEM) for solving sharp-interface continuum models for solid-state dewetting of thin films with anisotropic surface energies. The governing equations of the sharp-interface models belong to a new type of high-order (4th- or 6th-order) geometric evolution partial differential equations about open curve/surface interface tracking problems which include anisotropic surface diffusion flow and contact line migration. Compared to the traditional methods (e.g., marker-particle methods), the proposed PFEM not only has very good accuracy, but also poses very mild restrictions on the numerical stability, and thus it has significant advantages for solving this type of open curve evolution problems with applications in the simulation of solid-state dewetting. Extensive numerical results are reported to demonstrate the accuracy and high efficiency of the proposed PFEM.

Effect of local fields on the Mg acceptor in GaN films and GaN substrates

The electron paramagnetic resonance (EPR) spectrum of the Mg acceptor is studied in a variety of GaN samples, including mm-thick free-standing substrates and sub-micron heteroepitaxial films. The former allows a view of the acceptor unique for EPR—in an environment with less than 107 cm−3 dislocations and doping densities ranging from 4 × 1016 to 6 × 1018 cm−3. By probing Mg in a broad range of samples in one study a new feature of the acceptor emerges. The EPR data reveal an anisotropic line shape that reflects a change in the crystal field in the vicinity of the Mg acceptor. This feature must be accommodated by any of the models proposed for the Mg acceptor. Here, we show that one such previously proposed model agrees well with the EPR data obtained from the wide variety of samples studied. The work implies that Mg-doped GaN contains a common Mg-related defect which can be affected by local crystal fields established during growth.

Stability of the sectored morphology of polymer crystallites.

When an entangled interpenetrating collection of long flexible polymer chains dispersed in a suitable solvent is cooled to low enough temperatures, thin lamellar crystals form. Remarkably, these lamellae are sectored, with several growth sectors that have differing melting temperatures and growth kinetics, eluding so far an understanding of their origins. We present a theoretical model to explain this six-decade-old challenge by addressing the elasticity of fold surfaces of finite-sized lamella in the presence of disclination-type topological defects arising from anisotropic line tension. Entrapment of a disclination defect in a lamella results in sectors separated by walls, which are soliton solutions of a two-dimensional elliptic sine-Gordon equation. For flat square morphologies, exact results show that sectored squares are more stable than plain squares if the dimensionless anisotropic line tension parameter α=γ_{an}/sqrt[h_{4}K_{ϕ}] (γ_{an} = anisotropic line tension, h_{4} = fold energy parameter, K_{ϕ} = elastic constant for two-dimensional orientational deformation) is above a critical value, which depends on the size of the square.

Drops with non-circular footprints

In this paper we study the morphology of drops formed on partially wetting substrates, whose footprint is not circular. These drops are consequence of the breakup processes occurring in thin films when anisotropic contact line motions take place. The anisotropy is basically due to the hysteresis of the contact angle since there is a wetting process in some parts of the contact line, while a dewetting occurs in other parts. Here, we obtain a characteristic drop shape from the rupture of a long liquid filament sitting on a solid substrate. We analyze its shape and contact angles by means of goniometric and refractive techniques. We also find a non-trivial steady state solution for the drop shape within the long wave approximation (lubrication theory), and we compare most of its features with experimental data. This solution is presented both in Cartesian and polar coordinates, whose constants must be determined by a certain group of measured parameters. Besides, we obtain the dynamics of the drop generation from numerical simulations of the full Navier–Stokes equation, where we emulate the hysteretic effects with an appropriate spatial distribution of the static contact angle over the substrate.

Calculation of EPR Spectra of Samples with Anistropic Line Width: A New Efficient Algorithm

Calculation of Electron Paramagnetic Resonance (EPR) spectra is essential part of studying proteins by spin labeling method, and studying metalloenzymes by EPR as well. Solution of inverse EPR problem by fitting model parameters to experimental data involves multiple calculations, so the performance of this elementary step is critical. In case of powder spectrum of disordered samples (like ones frozen at 77K), usual algorithm integrates over the space of orientations, calculating corresponding resonance positions. Resulting ‘stick’ spectrum is then convolved with line shape function (Lorentzian or Gaussian). If the line width does not depend on orientation (i.e., isotropic), Fast Fourier Transform (FFT) can be applied to calculate the convolution efficiently, but in typical case of anisotropic line width it is no more applicable. Program espect presented here uses algorithm that circumvents this limitation, making it possible to use FFT in case of arbitrary anisotropy of line width tensor. This leads to up to 100 times reduction of computational time required to calculate single spectrum. It is achieved by splitting the range of line widths into equal intervals, calculation of sub-spectra in each interval, and then using cubic interpolation to find the target spectrum approximation.

Tissue-Mimicking Geometrical Constraints Stimulate Tissue-Like Constitution and Activity of Mouse Neonatal and Human-Induced Pluripotent Stem Cell-Derived Cardiac Myocytes.

The present work addresses the question of to what extent a geometrical support acts as a physiological determining template in the setup of artificial cardiac tissue. Surface patterns with alternating concave to convex transitions of cell size dimensions were used to organize and orientate human-induced pluripotent stem cell (hIPSC)-derived cardiac myocytes and mouse neonatal cardiac myocytes. The shape of the cells, as well as the organization of the contractile apparatus recapitulates the anisotropic line pattern geometry being derived from tissue geometry motives. The intracellular organization of the contractile apparatus and the cell coupling via gap junctions of cell assemblies growing in a random or organized pattern were examined. Cell spatial and temporal coordinated excitation and contraction has been compared on plain and patterned substrates. While the α-actinin cytoskeletal organization is comparable to terminally-developed native ventricular tissue, connexin-43 expression does not recapitulate gap junction distribution of heart muscle tissue. However, coordinated contractions could be observed. The results of tissue-like cell ensemble organization open new insights into geometry-dependent cell organization, the cultivation of artificial heart tissue from stem cells and the anisotropy-dependent activity of therapeutic compounds.

Proton chemical shift tensors determined by 3D ultrafast MAS double-quantum NMR spectroscopy.

Proton NMR spectroscopy in the solid state has recently attracted much attention owing to the significant enhancement in spectral resolution afforded by the remarkable advances in ultrafast magic angle spinning (MAS) capabilities. In particular, proton chemical shift anisotropy (CSA) has become an important tool for obtaining specific insights into inter/intra-molecular hydrogen bonding. However, even at the highest currently feasible spinning frequencies (110-120 kHz), (1)H MAS NMR spectra of rigid solids still suffer from poor resolution and severe peak overlap caused by the strong (1)H-(1)H homonuclear dipolar couplings and narrow (1)H chemical shift (CS) ranges, which render it difficult to determine the CSA of specific proton sites in the standard CSA/single-quantum (SQ) chemical shift correlation experiment. Herein, we propose a three-dimensional (3D) (1)H double-quantum (DQ) chemical shift/CSA/SQ chemical shift correlation experiment to extract the CS tensors of proton sites whose signals are not well resolved along the single-quantum chemical shift dimension. As extracted from the 3D spectrum, the F1/F3 (DQ/SQ) projection provides valuable information about (1)H-(1)H proximities, which might also reveal the hydrogen-bonding connectivities. In addition, the F2/F3 (CSA/SQ) correlation spectrum, which is similar to the regular 2D CSA/SQ correlation experiment, yields chemical shift anisotropic line shapes at different isotropic chemical shifts. More importantly, since the F2/F1 (CSA/DQ) spectrum correlates the CSA with the DQ signal induced by two neighboring proton sites, the CSA spectrum sliced at a specific DQ chemical shift position contains the CSA information of two neighboring spins indicated by the DQ chemical shift. If these two spins have different CS tensors, both tensors can be extracted by numerical fitting. We believe that this robust and elegant single-channel proton-based 3D experiment provides useful atomistic-level structural and dynamical information for a variety of solid systems that possess high proton density.

The anisotropic line correlation function as a probe of anisotropies in galaxy surveys

We propose an anisotropic generalisation of the line correlation function (ALCF) to separate and quantify phase information in the large-scale structure of galaxies. The line correlation function probes the strictly non-linear regime of structure formation and since phase information drops out of the power spectrum, the line correlation function provides a complementary tool to commonly used techniques based on two-point statistics. Furthermore, it is independent of linear bias as well as the Gaussian variance on the modulus of the density field and thus may also prove to be advantageous compared to the bispectrum or similar higher-order statistics for certain cases. For future applications it is vital, though, to be able to account for observational effects that cause anisotropies in the distribution of galaxies. Based on a number of numerical studies, we find that our ALCF is well suited to accomplish this task and we demonstrate how the Alcock-Paczynski effect and kinematical redshift-space distortions can in principle be measured via the ALCF.

Corrugations of the basal planes in hexagonal boron nitride and their impact on the phase transition to cubic boron nitride

Among the microstructure defects in hexagonal graphitic boron nitride, the basal plane corrugations are of high relevance for the sp2to sp3phase transition under high pressures (HP) and high temperatures (HT). A microstructure model is described, which is capable of quantifying the amplitude of the basal plane corrugations on the basis of the anisotropic X-ray diffraction line broadening. It is illustrated that this model correctly reproduces the specific shape of the diffraction lines from corrugated basal planes, i.e., the characteristic splitting of the 00lpeaks. The results from XRD are verified by direct observation in the transmission electron microscope with high resolution. Subsequent HP/HT experiments were performed in order to highlight the difference in the phase transition kinetics between hexagonal boron nitride samples with different amount of basal plane corrugations. The effect of these microstructure defects on the conversion rate and on the obtained synthesis product is discussed.

Anisotropic interfacial tension, contact angles, and line tensions: a graphics-processing-unit-based Monte Carlo study of the Ising model.

As a generic example for crystals where the crystal-fluid interface tension depends on the orientation of the interface relative to the crystal lattice axes, the nearest-neighbor Ising model on the simple cubic lattice is studied over a wide temperature range, both above and below the roughening transition temperature. Using a thin-film geometry L(x)×L(y)×L(z) with periodic boundary conditions along the z axis and two free L(x)×L(y) surfaces at which opposing surface fields ±H(1) act, under conditions of partial wetting, a single planar interface inclined under a contact angle θ<π/2 relative to the yz plane is stabilized. In the y direction, a generalization of the antiperiodic boundary condition is used that maintains the translational invariance in the y direction despite the inhomogeneity of the magnetization distribution in this system. This geometry allows a simultaneous study of the angle-dependent interface tension, the contact angle, and the line tension (which depends on the contact angle, and on temperature). All these quantities are extracted from suitable thermodynamic integration procedures. In order to keep finite-size effects as well as statistical errors small enough, rather large lattice sizes (of the order of 46 million sites) were found to be necessary, and the availability of very efficient code implementation of graphics processing units was crucial for the feasibility of this study.

Thermal stability of titanate nanorods and titania nanowires formed from titanate nanotubes by heating

The structure of titanate nanowires was studied by a combination of powder X-ray diffraction (XRD) and 3D precession electron diffraction. Titania nanowires and titanate nanorods were prepared by heating of titanate nanotubes. The structure of final product depended on heating conditions. Titanium nanotubes heated in air at a temperature of 850°C decomposed into three phases — Na2Ti6O13 (nanorods) and two phases of TiO2 — anatase and rutile. At higher temperatures the anatase form of TiO2 transforms into rutile and the nanorods change into rutile nanoparticles. By contrast, in the vacuum only anatase phases of TiO2 were obtained by heating at 900°C. The anatase transformation into rutile began only after a longer time of heating at 1000°C. For the description of anisotropic XRD line broadening in the total powder pattern fitting by the program MSTRUCT a model of nanorods with elliptical base was included in the software. The model parameters — rod length, axis size of the elliptical base, the ellipse flattening parameter and twist of the base could be refined. Variation of particle shapes with temperature was found.

Microstructure, Stress and Texture in Sputter Deposited TiN Thin Films: Effect of Substrate Bias

Titanium nitride thin films deposited by reactive dc magnetron sputtering under various substrate bias voltages have been investigated by X-ray diffraction. TiN thin films exhibits lattice parameter anisotropy for all bias voltages. Preferential entrapment of argon atoms in TiN lattice has been identified as the major cause of lattice parameter anisotropy. Bombardment of argon ions during film growth has produced stacking faults on {111} planes of TiN crystal. Stacking fault probability increases with increasing substrate bias voltages. X-ray diffraction line profile analysis indicates strain anisotropy in TiN thin films. Diffraction stress analysis byd-sin2ψmethod reveals pronounced curvature in the plot of inter-planar spacing (d) (or corresponding lattice parameter (a)) versussin2ψ. Direction dependent elastic grain interaction has been considered as possible source of the observed anisotropic line broadening.

Charge Separation in P3HT:SWCNT Blends Studied by EPR: Spin Signature of the Photoinduced Charged State in SWCNT.

Single-wall carbon nanotubes (SWCNTs) could be employed in organic photovoltaic (OPV) devices as a replacement or additive for currently used fullerene derivatives, but significant research remains to explain fundamental aspects of charge generation. Electron paramagnetic resonance (EPR) spectroscopy, which is sensitive only to unpaired electrons, was applied to explore charge separation in P3HT:SWCNT blends. The EPR signal of the P3HT positive polaron increases as the concentration of SWCNT acceptors in a photoexcited P3HT:SWCNT blend is increased, demonstrating long-lived charge separation induced by electron transfer from P3HT to SWCNTs. An EPR signal from reduced SWCNTs was not identified in blends due to the free and fast-relaxing nature of unpaired SWCNT electrons as well as spectral overlap of this EPR signal with the signal from positive P3HT polarons. However, a weak EPR signal was observed in chemically reduced SWNTs, and the g values of this signal are close to those of C70-PCBM anion radical. The anisotropic line shape indicates that these unpaired electrons are not free but instead localized.

The effect of clustering of VO2+ ions in sub- and supercritical water. An in situ EPR study

Temperature variations of the EPR spectra of VO2+ ions in sub- and supercritical water under isothermal and temperature gradient conditions are investigated using an in situ EPR. Broadening of the hyperfine structure at increasing temperature and the appearance of an unresolved broad low-intensity line (ΔHpp ≈ 300 Oe) in the supercritical state are observed in the absence of temperature gradients, indicating an increase of exchange interaction between VO2+ ions in supercritical water. An exchange-narrowed anisotropic absorption line is observed under the temperature-gradient conditions in the subcritical water near the transition to a supercritical state. The shape of this line is close to that observed in the solid salt VOSO4 · 3H2O. It is shown that in situ EPR allows us to investigate the effects of changing the local environment of paramagnetic ions, which precedes the well-known process of clustering and formation of amorphous oxide particles in sub- and supercritical conditions.

Towards understanding the influence of data-richness on interpretational confidence in image interpretation

Geological interpretations of aeromagnetic and gravity images are highly subjective but are rarely accompanied by a quantitative confidence assessment, which is a key limitation on the usefulness of the results. This paper outlines a method with which the relative level of data richness can be assessed quantitatively, leading to an improved understanding of spatial variations in interpretational confidence. Simple rules were used to quantify the likely influence of several major sources of uncertainty. These were: 1) the level of geological constraint, using the local abundance of outcropping rock and the quality of geological mapping; 2) the interpretability of the data, considering the strength of edge-like features and the degree of directionality of these features, a proxy for structural complexity; 3) data collection and processing errors, including gridding errors, derived from the statistical error returned during kriging, and the influence of anisotropic line data collection on the detection of gradients. From these individual sources of uncertainty an overall data richness map was generated through a weighted summation of these grids. Weightings were assigned so as to best match the result to the interpreter's perception of interpretational confidence. This method produced a map of data richness, which reflects the opportunity that the data provided to the interpreter to make a correct interpretation. An example from central Australia indicated that the data influences were preserved over a moderate range of weighting factors, and that strong bias was required to override these. In addition to providing a confidence assessment, this method also provides a way to test the potential benefits of additional data collection.