Anisotropic Boundary Research Articles

Domain Engineering Enabled Giant Linear Electro‐Optic Effect and High Transparency in Ferroelectric KTa1−xNbxO3 Single Crystals

A giant linear electro‐optic (EO) effect and high transparency in ferroelectric potassium tantalate niobate [(), KTN] crystal is achieved via a thermally controlled domain engineering method. It involves a two‐step thermal annealing process: 1) a rapid cooling process that forms polar nano‐regions (PNRs), i.e., a cooling rate of from to where is the Curie temperature; and 2) a slow cooling process that facilitates abnormal domain growth (AGG) i.e., a cooling rate of from to . Since PNR can have a faceted boundary and high anisotropy, it can promote AGG within single crystals to realize solid‐state domain conversion macroscopically from a multi‐domain to single‐domain crystal within a slow cooling process. The resultant KTN crystal offers high transparency that is equivalent to its paraelectric phase; and a linear EO coefficient () as large as , which is five times the value of conventional KTN crystals with similar composition. This giant linear EO coefficient represents a major technical advance in EO materials and significantly reduces the driving voltage, power, and footprint of many types of EO devices.

Comparison of simulated and measured grain volume changes during grain growth

The three-dimensional microstructure of Ni, observed after five annealing intervals, was compared to simulations of grain growth using the threshold dynamics method with the assumption of capillarity as the only driving force. A grain-by-grain comparison made it possible to identify the sources of differences between the simulation and experiment. The most significant difference was for grains of the smallest sizes, which the simulation predicted would lose volume and disappear at a greater rate than observed in the experiment. The loss of grains created errors in the numbers of neighbors of the remaining grains, and it was found that errors in the simulated grain volume were correlated to errors in the number of near neighbors. While anisotropic grain boundary properties likely play a role in the differences, the size dependence of the errors suggest that it might be necessary to include a size dependence in the model for grain boundary migration kinetics.

Co-Circular Polarization Reflector Revisited: Reflection Properties, Polarization Transformations, and Matched Waves

The variety of electromagnetic impedance boundaries is wide since the impedance boundary condition can have a two-dimensional matrix nature. In this article, a particular class of impedance boundary conditions is treated: a boundary condition that produces the so-called co-circular polarization reflector (CCPR). The analysis focuses on the possibilities of manipulating the polarization of the electromagnetic wave reflected from the CCPR surface as well as the so-called matched waves associated with it. The characteristics of CCPR and its special cases (perfectly anisotropic boundary (PAB) and soft-and-hard surface (SHS)) are compared against more classical lossless boundaries: perfect electric, perfect magnetic, and perfect electromagnetic conductors (PEC, PMC, and PEMC).

Kinetic Monte Carlo Simulation of Abnormal Grain Growth in Textured Systems with Anisotropic Grain Boundary Energy and Mobility

The abnormal grain growth behavior of an individual grain in the textured system was simulated by kinetic Monte Carlo method with focusing on the effect of anisotropy configuration and texture intensity. The mobility anisotropy and the energy anisotropy of grain boundary were derived based on the theoretical and experimental data in Fe-Si alloy. The results indicated that the single configured system with anisotropic grain boundary mobility or energy led to apparently unreasonable abnormal growth kinetic and boundary evolution at the growing front of the candidate grains. The composite configured system with anisotropic grain boundary mobility and energy accurately reproduced the microstructure evolution during abnormal grain growth. The 20°− 45° boundaries at the growing front varied with a certain range in the textured systems. The diameter of the abnormal grain increased linearly with the time, and the growth rate decreased with the weakening of matrix texture intensity. It is found that the grain boundary energy anisotropy plays the key role in the system with relatively strong matrix texture, while the grain boundary mobility anisotropy plays the key role in the system with random matrix texture. By converting the simulation time to the real time, the abnormal grain growth rate is estimated to be ∼1188.5–996.5 µm/min, which is roughly consistent with the actual secondary recrystallization. The present simulation is helpful to understand the abnormal grain growth phenomenon, especially the Goss grain growth in grain-oriented electrical steel. Data availabilityThe data required to reproduce these findings cannot be shared at this time since the data forms part of an ongoing study.

Advances in the deep tectonics and seismic anisotropy of the Lijiang-Xiaojinhe fault zone in the Sichuan-Yunnan Block, Southwestern China

The Sichuan-Yunnan Block (SYB) is located at the SE margin of the Qinghai-Tibetan Plateau (TP). Under the influence of the southeastward movement of material originated from the TP, intense crustal deformation, frequent seismic activity, and complex geological structures are observed in the SYB. The Lijiang-Xiaojinhe fault (LXF) goes through the central part of the SYB, dividing it into two blocks from north to south, and forming an intersecting fault system with the surrounding faults. This paper firstly introduces the morphology and the nature of the LXF, the distribution of the regional surface displacements and the focal mechanisms, and then analyzes the medium deformation and the effects of faults. Moreover, according to the regional tectonics and geophysical patterns, the paper discusses the characteristics of the north-south blocks of the SYB and the abrupt change of deep structure along the LXF zone. Since seismic anisotropy is an essential property for detecting crustal stress, deep structures and dynamical mechanisms, this paper is dedicated to the advances in seismic anisotropy at different depths and different scales in the study area. There are noteworthy differences in the anisotropic features between the north part and the south part of the SYB, possibly associated with a clear boundary adjacent to the LXF. Such phenomenon suggests some close correlation between anisotropic zoning boundary and the LXF, although this boundary is not consistent with the LXF in strike. The results from the deformation of the crust and the upper mantle elucidate the distribution patterns of the crust-mantle coupling in the north part and the crust-mantle decoupling in the south part, even though this conclusion needs to be further verified by more studies. Presently, the scientific understanding of the deep tectonics and the media deformation around the “generalized” LXF i.e. the LXF with the Jinpingshan fault on its eastern side, is still insufficient, and related equivocal topics deserve more in-depth studies.

Relative Grain Boundary Energies from Triple Junction Geometry: Limitations to Assuming the Herring Condition in Nanocrystalline Thin Films

Grain boundary character distributions (GBCD) are routinely measured from bulk microcrystalline samples by electron backscatter diffraction (EBSD) and serial sectioning can be used to reconstruct relative grain boundary energy distributions (GBED) based on the 3D geometry of triple lines, assuming that the Herring condition of force balance is satisfied. These GBEDs correlate to those predicted from molecular dynamics (MD); furthermore, the GBCD and GBED are found to be inversely correlated. For nanocrystalline thin films, orientation mapping via precession enhanced electron diffraction (PED) has proven effective in measuring the GBCD, but the GBED has not been extracted. Here, the established relative energy extraction technique is adapted to PED data from four sputter deposited samples: a 40 nm-thick tungsten film and a 100 nm aluminum film as-deposited, after 30 and after 150 minutes annealing at 400{\deg}C. These films have columnar grain structures, so serial sectioning is not required to determine boundary inclination. Excepting the most energetically anisotropic and highest population boundaries, i.e. aluminum {\Sigma}3 boundaries, the relative GBED extracted from these data do not correlate with energies calculated using MD nor do they inversely correlate with the experimentally determined GBCD for either the tungsten or aluminum films. Failure to reproduce predicted energetic trends implies that the conventional Herring equation cannot be applied to determine relative GBEDs and thus geometries at triple junctions in these films are not well described by this condition; additional geometric factors must contribute to determining triple junction geometry and boundary network structure in spatially constrained, polycrystalline materials.

Anisotropic grain boundary area and energy distributions in tungsten

Describing microstructure evolution in tungsten requires a quantitative description of the anisotropic grain boundary energy. We present a grain boundary energy function for tungsten that specifies the energy of an arbitrary boundary given its five macroscopic crystallographic parameters. A comparison of measured grain boundary areas and the grain boundary energies given by the function at the Σ11, Σ17b, and Σ33a misorientations, which are problematic to determine by measurement or atomistic calculations, reveals inverse correlations that are similar to what have been observed in other metals.

Novel estimation method for anisotropic grain boundary properties based on Bayesian data assimilation and phase-field simulation

Utilizing the data assimilation and multi-phase-field grain growth model, this study proposes a novel framework of measuring anisotropic (nonuniform) grain boundary energy and mobility. The framework can evaluate a large number of boundary properties from typical observations of grain growth without requiring specifically designed experiments or calculations. In this method, by optimizing the multi-phase-field model parameters such that the simulation results are in good agreement with the observation data, the energies and mobilities of multiple individual boundaries are directly and simultaneously estimated. To validate the method, numerical tests on boundary property estimation were performed using synthetic microstructure dataset generated from grain growth simulations with a priori assumed property values. Systematic tests on simple tricrystal systems confirmed that the proposed method accurately estimates each boundary energy and mobility within an error of only several % of their assumed true values even for conditions with strong property anisotropy and grain rotation. Further numerical tests were conducted on a more general multi-grain system, showing that our method can be successfully applied to complicated polycrystalline grain growth. The obtained results demonstrate the potential of the proposed method in extracting a large dataset of grain boundary properties for arbitrary boundaries from actual grain growth observations.

Fluid Injection Under Differential Confinement

Laboratory studies of cavity initiation and propagation in weak or cohesionless materials rely on post-test observations to assess fracture geometry. The experimental setup in this work is a Hele-Shaw cell, which allows for visualization of cavity initiation and propagation within the sand pack, modified to apply differential confinement to a fully 3D specimen. Injection experiments with glycerine at different concentrations and at varying injection rates were conducted with anisotropic boundary conditions on loose sand. The fracture initiation and evolution were observed under various flow rates and viscosities. Infiltration and dislocation of particles were the main mechanisms observed in the tests. Fracture-like channels initially developed in a circular shape due to cavity expansion but then formed rod shapes (shear bands, material fluidization) where an anisotropic stress was applied. This transition from circular to elongated cavity appeared earlier in the tests with higher viscosity fluids, while higher injection rates produced wider openings as the larger volume of fluid was able to displace more particles. Although the cavity showed directionality in all cases, it became less confined to the propagating plane as the flow rate increased. For higher viscosities, the cavities tended to be more circular, whilst for lower viscosities, the cavities showed more directionality. Article Highlights.

On an anisotropic discrete boundary value problem of Kirchhoff type

ABSTRACT The authors prove the existence of at least one nontrivial solution to an anisotropic discrete boundary value problem of -Kirchhoff type and its associated parametric version. They provide an example to demonstrate the applicability of the main results. Their analysis mainly relies on variational methods and Ricceri's variational principle.

Seismic Anisotropic Layering in the Yilgarn and Superior Cratonic Lithosphere

AbstractLayering within the cratonic lithosphere has been explored and reported in different cratons using a range of techniques. However, whether there exists a common feature in the lithosphere for all the cratons is not clear yet. In this study, we carry out a comparison study between the Yilgarn craton in Western Australia and the Superior craton in North America that have never been in direct contact throughout their tectonic history. To have a detailed description of the lithospheric layering in both cratons, we employ receiver function analysis with harmonic decomposition to characterize the anisotropic seismic structure beneath 4 long‐operating sites in each craton. We can identify multiple unique anisotropic boundaries above 170 km at all sites in both cratons. Properties of the anisotropic boundaries are distinct both within and across the cratons. Our observation agrees with a commonly accepted view of the cratonic lithosphere consisting of at least two layers. Moreover, it adds new details to the previous view and reveals lateral variations of the anisotropic properties over distances of a few hundreds of kilometers. Such variations in anisotropic properties likely reflect the tectonic history predating the final assembly of cratons, and suggest horizontal movements are necessary for the formation of cratonic lithosphere.

A 2D Front-Tracking Lagrangian Model for the Modeling of Anisotropic Grain Growth.

Grain growth is a well-known and complex phenomenon occurring during annealing of all polycrystalline materials. Its numerical modeling is a complex task when anisotropy sources such as grain orientation and grain boundary inclination have to be taken into account. This article presents the application of a front-tracking methodology to the context of anisotropic grain boundary motion at the mesoscopic scale. The new formulation of boundary migration can take into account any source of anisotropy both at grain boundaries as well as at multiple junctions (MJs) (intersection point of three or more grain boundaries). Special attention is given to the decomposition of high-order MJs for which an algorithm is proposed based on local grain boundary energy minimisation. Numerical tests are provided using highly heterogeneous configurations, and comparisons with a recently developed Finite-Element Level-Set (FE-LS) approach are given. Finally, the computational performance of the model will be studied comparing the CPU-times obtained with the same model but in an isotropic context.

Unraveling the Role of Grain Boundary Anisotropy in Sintering: Implications for Nanoscale Manufacturing

Unraveling the Role of Grain Boundary Anisotropy in Sintering: Implications for Nanoscale Manufacturing

Comparative Study and Limits of Different Level-Set Formulations for the Modeling of Anisotropic Grain Growth.

In this study, four different finite element level-set (FE-LS) formulations are compared for the modeling of grain growth in the context of polycrystalline structures and, moreover, two of them are presented for the first time using anisotropic grain boundary (GB) energy and mobility. Mean values and distributions are compared using the four formulations. First, we present the strong and weak formulations for the different models and the crystallographic parameters used at the mesoscopic scale. Second, some Grim Reaper analytical cases are presented and compared with the simulation results, and the evolutions of individual multiple junctions are followed. Additionally, large-scale simulations are presented. Anisotropic GB energy and mobility are respectively defined as functions of the mis-orientation/inclination and disorientation. The evolution of the disorientation distribution function (DDF) is computed, and its evolution is in accordance with prior works. We found that the formulation called “Anisotropic” is the more physical one, but it could be replaced at the mesoscopic scale by an isotropic formulation for simple microstructures presenting an initial Mackenzie-type DDF.

Multi-phase-field lattice Boltzmann model for polycrystalline equiaxed solidification with motion

The formation process of equiaxed structures during alloy solidification is a complicated multiphysics problem as it includes solid–liquid phase transformations, transport of solute and heat, liquid flow, solid motion, solid–solid interactions, and grain growth after solidification completion. In this study, a multi-phase-field (MPF) model with the double-obstacle (DO) potential is introduced to our previous model [T. Takaki et al., Comput. Mater. Sci., 147 (2018) 124–131] to express the formation process of equiaxed structures accurately and efficiently, from the growth of multiple mobile dendrites to the grain growth with grain boundary anisotropy after solidification. The accuracy of the resulting MPF-lattice Boltzmann (MPF-LB) model with the DO potential is evaluated by comparison with the results obtained using a model with the double-well potential through simulations of purely diffusive dendrite growth, the growth of an immobile dendrite with forced convection, and the growth of a mobile dendrite under shear flow. Finally, the model is applied to both large-scale polycrystalline solidification and semi-solid deformation processes.

Analytical modelling of the trans-scale cutting forces in diamond cutting of polycrystalline metals considering material microstructure and size effect

In diamond cutting of polycrystalline metals, the influence of size effect and microstructure on the cutting force is prominent due to the trans-scale variation of undeformed chip thickness (UDCT) from microscale to nanoscale. This study proposes a trans-scale cutting force model for diamond cutting of polycrystalline metals with the full consideration of microstructure, material elastic recovery, size effect and round-tool-edge effect. Specifically, by corelating micro-forming theory and crystal plastic theory, a hybrid slip-line model (HSLM) is developed to determine the flow stress in the primary deformation zone, which can quantify the influence of size effect and microstructure, such as grain size, grain boundary and crystal anisotropy, on flow stress. Then, the normal cutting force and frictional cutting force are determined by analysing the stress distribution and frictional states at tool-chip interface using a tool-chip contact model. The rubbing force induced by material elastic recovery at very small UDCT is determined based on indentation theory. Through diamond cutting of polycrystalline copper with different grain sizes, it is experimentally demonstrated that the proposed HSLM can capture the cutting mechanism transformation phenomenon from shearing (tensile stress) to ploughing (compressive stress) with increasing size factor. Besides, the proposed force model has the improved estimation accuracy compared with the conventional force models developed based on Johnson-Cook constitutive equation.

TESTING OF AN OPTIMIZATION ALGORITHM FOR AVAZ INVERSION ON SYNTHETIC DATASET

In the paper, we study an optimization algorithm for a nonlinear AVAZ inversion of PP reflections from an anisotropic media. The algorithm is based on the exact formulas for PP wave reflection coefficient for an anisotropic HTI medium and could be applied in the case of strong-contrast boundary and various anisotropy degree. Algorithm testing on synthetic dataset for radial survey system shows that estimation of anisotropy parameters γ , δ and HTI medium symmetry axis is robust in the case of signal to noise ratio ≥ 5. For estimation of parameter ε far offset data is needed.

The role of adiabatic and non-adiabatic phenomena in passing waves from a semi-bounded loss-free waveguide to semi-bounded plasma waveguide

Thermal effects have been studied in phenomena of wave transportation from a loss-free isotropic cylindrical metallic waveguide to a semi-bounded warm plasma waveguide. The considered configuration consists of two semi-bounded waveguides which connected to each other. The first part is a dielectric waveguide with loss-free metallic wall and the second part is a cylindrical dielectric waveguide where a warm plasma column is placed on its symmetric axis. An incident wave in a single mode will be inserted from first part toward to second part via transversely anisotropic boundary surface. The incident wave is reflected and transmitted via interface surface of two waveguides. Taking into account the suitable boundary conditions on the interface surface of two waveguides and using warm approximation for the plasma column, the reflection and transmission coefficients of each new modes have been calculated. The reflection and transmission coefficients are function of the geometrical dimensions, the incident wave frequency and the temperature of the plasma. The diagrams of the reflection and transmission coefficients of the reflected and transmitted waves and phase difference of the reflected and transmitted waves respect to the incident wave, in term of the plasma temperature have been investigated.

Anisotropy Gradients in the Middle of the Ross Sea Embayment, West Antarctica: Evidence From QL Scattered Surface Waves

AbstractLong‐period quasi‐Love (QL) waves in West Antarctica were detected using the band‐pass filtering. Rayleigh waves from March 11, 2011 Tohoku Mw 9.1 earthquake and March 9, 2011 Tohoku Mw 7.3 earthquake had evident QL waves in the frequency range of 7–13 mHz when crossing the Ross Sea Embayment (RSE), while exhibiting normal behavior when crossing the Southern Ocean adjacent to the RSE. We located an anisotropic boundary in the upper mantle beneath the RSE according to the QL waves. Surprisingly, the boundary was consistent with the sharp transition zone of magnetic anomalies discovered by the most recent airborne magnetic surveys. Thus, we speculate that the anisotropic boundary was most likely due to vertical mantle flow below the RSE, which may provide evidence of a vertically coherent boundary condition in the RSE. That anisotropic boundary may be an important tectonic imprint for maintaining the stability of the Ross Ice Shelf.

Flow-coupled cohesive interface framework for simulating heterogeneous crack morphology and resolving numerical divergence in hydraulic fracture

A user-friendly and generic finite element framework for simulating hydraulic fracture with a complex crack network in unconventional oil and gas exploitation is developed in this work with the following unique features. While the cohesive zone model (CZM) removes crack singularities, its finite element simulations suffer numerical convergence problem during crack nucleation and growth, which can be regularized by a fictitious viscosity approach. The decoupling of cohesive-cracked solid and fluid into separate free body diagrams allows the development of a weak-form finite element formulation for the former and a finite-difference approach for the transport analysis in the latter. Enforcing the Kirchhoff condition in polycrystalline geomaterials allows the study of the fluid-driven complex fracture propagation process. Our method has been verified by analytical solutions, and then employed to simulate the synergistic roles of confining pressure and grain boundary anisotropy on the fracking morphology. Numerical implementation into a user-defined element (UEL) subroutine in ABAQUS provides easy adaptation and further development for the research community.