Random Polycrystals Research Articles

All-optical 3D blue phase photonic crystal switch with photosensitive dopants

Blue phase (BP) liquid crystals (LC) have lately become the focus of extensive research due to their peculiar properties and structure. BPs exhibit a highly organized 3D structure with a lattice period in the hundreds of nm. Owing to such structure, BPs are regarded as 3D photonic crystals. The unique properties of this complex LC phase are achieved by the self-assembly of the LC molecules into periodic cubic structures, producing bright selective Bragg reflections. Novel applications involving 3D photonic crystals would certainly benefit from enhanced ground-breaking functionalities. However, the use of BPs as 3D has been traditionally curtailed by the BP crystals trend to grow as random polycrystals, making it difficult to develop practical BP-based photonic devices. The possibility of generating mm-sized BP monocrystals was recently demonstrated. However, besides increasing the scarce number of 3D photonic structural materials, their applications as 3D photonic crystals do not show apparent advantages over other solid materials or metamaterials. Having a tunable BP monocrystal, where crystals could be switched, modulating simultaneously some of their properties as 3D photonic crystals, they would constitute a new family of materials with superior performance to other existing materials, opening up a plethora of new applications. In this work, an all-optical switchable 3D photonic crystal based on BPs doped with tailored photoactive molecules is demonstrated. Two switching modes have been achieved, one where the BP reversibly transitions between two BP phases, BPI and BPII, (two different cubic crystal systems) while maintaining the monocrystallinity of the whole system. The second mode, again reversible, switches between BPI and isotropic state. None of these modes are related to the regular thermal transitions between LC phases; switching is triggered by light pulses of different wavelengths. This all-optical approach allows for a seamless fast remotely controlled optical switch between two 3D photonic crystals in different cubic crystal systems and between a photonic crystal and an isotropic matrix. Applications of switchable BPs for adaptive optics systems or photonic integrated circuits would make great advances using 3D photonic crystal switches. All-optical photonic systems such as these hold great promise for the development of tunable and efficient photonic devices such as dynamic optical filters and sensors, as they enable light-driven modulation and sensing applications with unprecedented versatility.

A dislocation density-based crystal plasticity constitutive model: comparison of VPSC effective medium predictions with ρ-CP finite element predictions

This work presents a dislocation density-based crystal plasticity constitutive model for glide kinetics, strengthening and dislocation density evolution, implemented in the effective medium-based visco-plastic self consistent (VPSC) framework and the spatially resolved, ρ-CP crystal plasticity finite element framework. Additionally, a distribution of intragranular stresses is introduced in the VPSC framework, instead of the conventionally used mean value of grain stress for effective medium calculations. The ρ-CP model is first calibrated to predict the mechanical response of a bcc ferritic steel with an initial rolled texture. The same set of constitutive model parameters are then used in VPSC to predict the aggregate stress–strain response and total dislocation densities. For these VPSC simulations, the interaction parameter governing the interaction between the grain and the effective medium in the Eshelby inclusion formalism, and a scalar parameter representative of the distribution of intragranular stresses within a grain, are used to calibrate the VPSC predictions in order to match the predictions of the ρ-CP model. A parametric study is performed to understand the effect of these two parameters on the VPSC predictions. Further, simulations are also performed for a random untextured polycrystal to identify the corresponding VPSC simulation parameters for predicting a similar response as the ρ-CP model. The novelty of the work is in the same set of constitutive models and associated parameters have been implemented in VPSC and ρ-CP to predict similar aggregate stress–strain response and total dislocation densities. This finite element-calibrated effective medium crystal plasticity approach reduces the computational time by at least two orders of magnitude and represents an advance towards the development of multiscale crystal plasticity modeling tools.

On the statistical behavior of homogenized properties and ultrasonic phase velocities in random polycrystals

Most theoretical studies on homogenized properties of polycrystals consider infinite textureless media with orientations characterized by independent Euler angles. However, microstructural analyses of polycrystals reveal spatially correlated orientations of grains whose sizes often follow lognormal distributions. Moreover, experimental investigations show that the single-crystal elastic constants (SEC) in the crystallite’s local coordinates could exhibit variabilities. To the best of our knowledge, in the context of our study, these have never been considered in the literature. In this paper, the crystal orientations are simulated using random fields (RFs) with different correlation parameters. A maximum entropy principle is used to simulate realizations of the local stiffness matrices. Numerical results indicate that generating Euler angles using independent random variables is legitimate when correlation lengths of orientations are close enough to the average grain size. Analytical formulas are derived to estimate the statistical behavior of effective elastic moduli and the phase velocities considering either unimodal or bimodal grain size distributions and fluctuations in local tensors for both two- and three-dimensional polycrystals. The former highlight the important roles of the coefficient of variations of the grain sizes and that of the elastic constants. This work contributes to microstructural characterization research associated with ultrasonic phase velocity measurements.

Grain incompatibility determines the local structure of amorphous grain boundary complexions

Amorphous grain boundary complexions lack long-range crystalline order but are not featureless, as distinct gradients in structural short-range order have been reported through their thickness. In this work, we test the hypothesis that the distribution of short-range order is determined by the confining crystals using atomistic simulations of both Cu-Zr bicrystals and a random polycrystal. Voronoi polyhedra with structures similar to that of perfect face-centered cubic serve as signatures of high structural order and are only found at the amorphous-crystalline transition regions. The density of the ordered structural motifs within a specific amorphous-crystalline transition region is found to not be directly determined by the orientation and symmetry of the grain which touches it, but rather by the incompatibility between the two confining grains. Ordered polyhedra density is found to be inversely related to grain incompatibility, meaning that large incompatibilities between the confining crystals lead to less order in the amorphous-crystalline transition region. The finding that the entire grain-film-grain system must be considered to understand local structure unequivocally demonstrates that amorphous complexions are not simply a collection of independent phases which happen to nucleate at a grain boundary. Rather, an amorphous grain boundary complexion is a single entity that finds a local equilibrium configuration.

Ni solute segregation and associated plastic deformation mechanisms into random FCC Ag, BCC Nb and HCP Zr polycrystals

Different types of grain-boundary (GB) solute segregation in nanocrystalline alloys have been described in the literature as being either homogeneous or heterogeneous, which differently impacts their mechanical properties. In heterogeneous segregation, solute atoms tend to cluster along certain GB areas, while other GB regions remain solute-free. This phenomenon is evidenced with the segregation of Ni solute in nanocrystalline FCC Ag. Yet the physical origin for this segregation behavior and its existence in non-FCC alloys are not fully determined. Here, hybrid Monte-Carlo and molecular dynamics simulations were used to study the segregation of Ni solutes (4 at.%) into nanocrystalline FCC Ag, BCC Nb and HCP Zr metals at their solubility limit temperature and the same homologous temperature (0.405·Tm), respectively. A range of segregation configurations was found: Fully heterogeneous segregation in Ag96Ni4 at 500 K, homogeneous segregation with second-phase precipitates in Nb96Ni4 at 1110 K, homogeneous segregation with dispersion of small-scale Ni clusters in Nb96Ni4 at 1564 K and Zr96Ni4 at 464 K, and fully homogeneous segregation with amorphous intergranular films in Zr96Ni4 at 1118 K. We rationalize these changes by quantifying the Ni solute interactions at GBs. Furthermore, significant variations in mechanical behavior and associated plastic deformation mechanisms are shown for each alloy due to their different segregation behaviors. It is found that strain-localized shear banding is the most significant at interfaces with homogeneous solute segregation containing second-phase precipitates and absent with segregation leading to amorphous intergranular films. These findings underscore the importance of solute interactions in profoundly altering segregation and mechanical behavior in stable nanocrystalline alloys.

Phase-field study of crystallographic texturing in piezoelectric polycrystals

Crystallographic texturing enables the design of piezoelectric polycrystals that outperform traditional random polycrystals by exhibiting outstanding piezoelectric properties. In this work, phase-field modeling and computer simulation were employed to study the effect of crystallographic texture on the piezoelectric properties of ferroelectric polycrystals at the domain level. Domain evolutions for single crystal, random polycrystal, and textured polycrystal are systematically simulated. The simulations reveal that the [001]-textured polycrystal can fully exploit the intrinsic anisotropic properties of piezoelectric materials by exhibiting a piezoelectric coefficient that is as large as that of single crystal while being much larger than that of random polycrystal. To better understand the mechanism of piezoelectricity enhancement by crystallographic texturing, a theoretical analysis based on Landau theory is provided. In comparison with random polycrystal, the textured polycrystal manifests a flatter energy landscape and thus possesses a higher piezoelectric coefficient.

Grain growth kinetics in 2D polycrystals: impact of triple junctions

Abstract Grain growth in random and textured 2D polycrystals is modeled under the supposition that all the triple junctions possess limited mobility. In the random polycrystal, the growth kinetics is at first linear and becomes parabolic at later stages if both the triple-junction mobility and the initial grain size are low. The experimental data on triple-junction mobility are used to show that such an effect could be observed in nanocrystalline materials. In the textured polycrystal, triple junctions with limited mobility are found to shift the evolution of the growth process toward abnormal grain growth.

Microstructural characteristics of 3-d networks

AbstractThe structural characteristics of three-dimensional (3-d) irregular networks, such as random polycrystals, are described using scaling arguments based on the properties of Average N-hedra (ANH’s). ANH’s comprise a special set of highly symmetric polyhedral cells that satisfy topological and geometrical criteria demanded in 3-d space-filling networks. All the geometrical properties of ANH’s may be obtained from exact analytical expressions already derived in [1]. The utility and ease of use of these formulas have been carefully checked against accurate simulations of the excess free energy and evolution kinetics of foams and polycrystals. The vertex-to-vertex distance is chosen in this paper as the consistent gauge to estimate an important microstructure feature set presented here for irregular 3-d networks. In the case of annealed polycrystals this includes the total grain boundary area and its associated stored energy per unit volume, the triple line length per unit volume, and the number density of triple lines and quadra-junctions – all of which may be expressed in terms of the polycrystal's grain number density.

Large and sensitive magnetostriction in ferromagnetic composites with nanodispersive precipitates

Large and sensitive magnetostriction (large strain induced by small magnetic fields) is highly desired for applications of magnetostrictive materials. However, it is difficult to simultaneously improve magnetostriction and reduce the switching field because magnetostriction and the switching field are both proportional to the magnetocrystalline anisotropy. To solve this fundamental challenge, we report that introducing tetragonal nanoprecipitates into a cubic matrix can facilitate large and sensitive magnetostriction even in random polycrystals. As exhibited in a proof-of-principle reference, Fe–Ga alloys, the figure of merit—defined by the saturation magnetostriction over the magnetocrystalline anisotropy constant—can be enhanced by over 5-fold through optimum aging of the solution-treated precursor. On the one hand, the aging-induced nanodispersive face-centered tetragonal (FCT) precipitates create local tetragonal distortion of the body-centered cubic (BCC) matrix, substantially enhancing the saturation magnetostriction to be comparable to that of single crystal materials. On the other hand, these precipitates randomly couple with the matrix at the nanoscale, resulting in the collapse of net magnetocrystalline anisotropy. Our findings not only provide a simple and feasible approach to enhance the magnetostriction performance of random polycrystalline ferromagnets but also provide important insights toward understanding the mechanism of heterogeneous magnetostriction.

On the estimates for the elastic moduli of random Voronoi triclinic polycrystals

Our major new results and the previous ones on the bounds for elastic random polycrystals, and most advanced 3D finite element results for random 3D Voronoi polycrystals are resumed and analysed (together for the first time). Recently obtained numerical Dirichlet and Neumann simulation results for the effective elastic moduli of a large 10000-grain-size random Voronoi polycrystal representative volume element (RVE) for a number of triclinic and monoclinic base crystals (Mursheda and Ranganathan, 2017) are compared critically with the bounds on the moduli. Though major parts within the simulation results fall within the bounds of Pham (2011), some Dirichlet upper estimates still lie outside the bounds. Many more RVEs are needed to represent the Voronoi polycrystal on the same RVE-size-level, and larger RVEs are needed for checking the convergence and comparisons with the bounds.

Investigation of granite fracture under three-point bending using the meso-modeling approach considering the random distribution of poly-crystals

A three-dimensional meso-modeling approach based on Weibull distribution for rock is proposed to study the fracture behavior of rock. And the macro-meso model of granite with random poly-crystals is developed for numerical studies. By controlling the kinetic energy of the model system and combining the erosion criterion, a method for accelerating the calculation of quasi-static problems is presented. Through the comparative analysis of numerical simulation and experimental test, the applicability and reliability of the modeling method in the study of spatial heterogeneity of rock materials are verified. Using finite element analysis, the fracture characteristics of granite at different loading rates are obtained. The effect of loading rate includes the following aspects: (1) the tensile strength and fracture toughness increase with the increase of loading rate; (2) the dynamic damage evolution process varies greatly under different loading speeds; (3) the increase of loading rate accelerates the crack propagation, and some cracks that originally propagate along the poly-crystals surface will propagate along the block. These studies offer a meso-scale strategy to study the fracture growth of rock.

FDEM Simulation of Rocks with Microstructure Generated by Voronoi Grain-Based Model with Particle Growth

Rock strength variation is closely related to its microstructure. With the development of computer technology, the numerical model of rocks can be constructed via computer programming, and the numerical simulation avoids a mass of redundant experimental tests and usually limited by the samples retrieved from the sub-surfaces. In previous studies, the microstructure in the numerical model is generated randomly. In this paper, a novel methodology for generating the polycrystalline rock microstructure by a Voronoi grain-based model with particle growth is proposed. The 3D Voronoi tessellations in this numerical model generation procedure do not consist of random poly-crystals; the distribution of the poly-crystals varies in shapes and sizes, which represent different mineral grains, and is determined by petrographic data with the 3D particle growth method. The uniaxial compression tests and tension tests are simulated via a combined FDEM and cohesive crack propagation model. The results demonstrate that the numerical simulation agrees well with the experimental study. More importantly, the fracture patterns in the micro-scale are gained, similar to the results obtained from laboratory experiments. The novel Voronoi grain-based model with the particle growth method can reconstruct the microstructure of polycrystalline rocks and provide further information in understanding the micro-behaviors of rock materials.

Bounds for shear viscosity in Nabarro–Herring–Coble creep

At high homologous temperature, plastic flow of a polycrystalline material can be mediated by self-diffusion and grain boundary sliding, rather than by dislocation glide. The effective viscosity of the polycrystal depends on the underlying mechanisms as well as on the microstructure. Simple expressions relating the shear viscosity to lattice and grain boundary diffusion coefficients were proposed in pioneering contributions by Nabarro (1948), Herring (1950) and Coble (1963). While these models remain widely used today to deduce the dominant mechanism based on the observed dependence of viscosity on grain size, a number of questions remain open. The present work revisits Nabarro–Herring–Coble creep using a micromechanical approach and variational principles. We focus on a random polycrystal of equiaxed grains deforming by coupled lattice and grain boundary diffusion and grain boundary sliding. We show that the classical results of Herring and Coble correspond to upper bounds on the shear viscosity, and obtain complementary lower bounds. Our results shed new light on these classical results and question the validity of the common interpretation of the dependence of viscosity on grain size.

Dislocation content in random high angle grain boundaries

The dislocation content of high angle grain boundaries in a random FCC polycrystal was determined through large-scale molecular dynamics modeling and the dislocation extraction algorithm for detecting dislocations. This method provides a means of calculating grain boundary dislocation content in atomistic samples from relaxed atomic positions. It was found that a large fraction of the boundaries studied contained significant densities of lattice and partial dislocations as part of their structure. The observed dislocation content varied widely depending on the boundary’s specific geometrical parameters. The average grain boundary dislocation segment length observed is of the order of the grain boundary thickness, as calculated from the simulation data. The dislocation densities changed significantly during virtual tensile straining of the samples, as dislocations are emitted from and absorbed at grain boundaries. These results are discussed in the context of the role of the multiplicity of possible grain boundary structures on the deformation response of polycrystalline materials.

Heterogeneous Anisotropy Index and scaling in two-phase random polycrystals

Under consideration is the finite-size scaling of the elastic properties in two-phase random polycrystals with individual grains belonging to any arbitrary crystal class. These polycrystals are generated by Voronoi Tessellations with varying grain sizes and volume fractions. Any given realization of such a microstructure sampled randomly is highly anisotropic and heterogeneous. Using extremum principles in elasticity, we introduce the notion of a ‘Heterogeneous Anisotropy Index $$\left( A^U_H\right) $$ ’ and examine its role in the scaling of elastic properties at finite mesoscales ( $$\delta $$ ). The relationship between $$A^U_H$$ and the Universal Anisotropy Index $$A^U$$ by Ranganathan and Ostoja-Starzewski (Phys Rev Lett 101(5):055504, 2008) is established for special cases. The index $$A^U_H$$ turns out to be a function of 43 variables—21 independent components for each phase and the volume fraction of either phase. The scale-dependent bounds are then obtained by setting up and solving 9250 Dirichlet and Neumann type boundary value problems consistent with the Hill–Mandel homogenization condition. Subsequently, the concept of an elastic scaling function is introduced that takes a power-law form in terms of $$A^U_H$$ and ( $$\delta $$ ). Finally, a material scaling diagram is constructed by employing the elastic scaling function which captures the convergence to the effective properties for any two-phase elastic microstructure.

Estimates for the elastic moduli of d-dimensional random cell polycrystals

Minimum energy principles and generalized polarization trial fields are used to derive bounds on the effective elastic moduli of d-dimensional random cell polycrystals, which are extensions of our earlier 3D (3-dimensional) results. The bounds are specialized to the 2D random aggregates of square-symmetric crystals, with numerical results for a number of particular crystals. Numerical finite element simulations for sufficiently large random aggregate samples of a particular 2D random polycrystal model show convergence toward the possible scatter interval for the effective elastic moduli enveloped by the new bounds, which are tighter than the classical Voigt–Reuss–Hill and Hashin–Shtrikman ones.

Elastic behavior of random polycrystals composed of anisotropic [formula omitted]-quartz (SiO2) under pressure

This work presents several sets of results for granular media all composed of quartz (SiO2) and all having grains with trigonal (six constant) elastic symmetry. In some cases, the samples had significant amounts of external pressure (up to 20GPa) applied to the quartz samples while the elastic constants were being either measured or simulated. In other examples, the temperatures ranged from room temperature down to values approaching absolute zero. In addition to the traditional Voigt and Reuss bounds on effective isotropic bulk and shear moduli, the Hashin–Shtrikman bounds of these elastic moduli have also been computed in all these examples. We find that the Hashin–Shtrikman bounds provide a significant tightening of the traditional bounds on the moduli in most cases. Rarely, the Hashin–Shtrikman upper bounds for shear modulus may coincide with Voigt estimates of the shear modulus. More typically we find the HS bounds on both shear and bulk modulus are so close that their averaged values (called here the “self-consistent average” estimates) for both bulk and shear modulus values are tightly constrained by the HS bounds themselves. In contrast, the traditional VRH (Voigt–Reuss–Hill) estimates of the moduli often lie outside of the HS bounds, thus giving reasons for doubting the accuracy of VRH estimates in general – and especially for pressurized samples. Of the eight scenarios considered in the paper, four have substantial confining pressures (10 or 20GPa), and four have zero confining pressure. One general distinction arising in these particular data sets is observed: when the confining pressure is negligible, the VRH estimates are found always to lie inside the Hashin–Shtrikman bounds. In contrast, when the confining pressure is P=10GPa or higher the VRH estimates of bulk and shear moduli both lie outside the Hashin–Shtrikman bounds.

3D random Voronoi grain-based models for simulation of brittle rock damage and fabric-guided micro-fracturing

A grain-based distinct element model featuring three-dimensional (3D) Voronoi tessellations (random poly-crystals) is proposed for simulation of crack damage development in brittle rocks. The grain boundaries in poly-crystal structure produced by Voronoi tessellations can represent flaws in intact rock and allow for numerical replication of crack damage progression through initiation and propagation of micro-fractures along grain boundaries. The Voronoi modelling scheme has been used widely in the past for brittle fracture simulation of rock materials. However the difficulty of generating 3D Voronoi models has limited its application to two-dimensional (2D) codes. The proposed approach is implemented in Neper, an open-source engine for generation of 3D Voronoi grains, to generate block geometry files that can be read directly into 3DEC. A series of Unconfined Compressive Strength (UCS) tests are simulated in 3DEC to verify the proposed methodology for 3D simulation of brittle fractures and to investigate the relationship between each micro-parameter and the model's macro-response. The possibility of numerical replication of the classical U-shape strength curve for anisotropic rocks is also investigated in numerical UCS tests by using complex-shaped (elongated) grains that are cemented to one another along their adjoining sides. A micro-parameter calibration procedure is established for 3D Voronoi models for accurate replication of the mechanical behaviour of isotropic and anisotropic (containing a fabric) rocks.

Lattice strain distributions due to elastic distortions and GND development in polycrystals

Techniques for the determination of lattice spacing distributions resulting from elastic distortion and from the development of a Burger׳s discontinuity (or equivalently, geometrically necessary dislocation density), are presented within a computational crystal plasticity framework, and a number of validatory analyses discussed.The contributions from both elastic distortions and Burger׳s circuit discontinuity to lattice spacing distributions and corresponding peak widths are evaluated and assessed for an fcc single crystal bearing elastic distortion and a plastic strain gradient. The single crystal analyses show that the elastic distortions lead to peak broadening and that at the initiation of plastic slip in the presence of a plastic strain gradient, the Burger׳s discontinuity (or equivalently GND density) also contributes to the peak broadening and may dominate as the strains become larger. After slip initiation, the contribution from elastic distortion remains largely unchanged. Analyses of random and textured polycrystals under uniaxial (100) straining to 5% show that the Burger׳s discontinuity contribution to peak broadening tends to dominate earlier over that from elastic distortion relative to the single crystal behaviour, because of the higher level of heterogeneity present. The randomly textured polycrystal showed more {100} peak broadening than that for the textured sample as a result of the relatively higher heterogeneity in the former.

Experimental and computational studies of ultrasound wave propagation in hexagonal close-packed polycrystals for texture detection

Texture in hexagonal close-packed (hcp) polycrystalline metals, often developed during thermomechanical processing, affects ultrasonic wave velocity. In this study, the relationship between bulk texture and ultrasonic wave velocity in aggregates of (predominantly) hcp grains is investigated using theoretical, numerical and experimental methods. A representative volume element methodology is presented, enabling the effects of texture on ultrasonic wave speed to be investigated in two-phase polycrystals, and is employed to examine the ultrasonic response of random polycrystals, textured polycrystals and macro-zones often observed in titanium alloys. Numerical results show that ultrasonic wave speed varies progressively with changing texture, over a range of ∼200ms−1, within bounds set by the two extreme single-crystal orientations. Experimental ultrasound studies and full electron backscatter diffraction (EBSD) characterization are conducted on unidirectionally rolled and cross-rolled Ti–6Al–4V samples in three orthogonal directions. In addition, the EBSD-determined textures are incorporated within the polycrystal model and predicted ultrasonic velocities compared directly with ultrasonic experiments. Good quantitative agreement is obtained and both the experimental and computed results demonstrate that ultrasonic velocity profiles exist for random, unidirectionally rolled and cross-rolled textures. The combined results indicate the possibility of the development of a methodology for bulk texture determination within Ti polycrystal components using ultrasound.