Ensemble Of Grains Research Articles

Investigation of diffusive grain interactions during equiaxed dendritic solidification

Grain growth during the solidification of an alloy is accompanied by the enrichment of the surrounding liquid phase in chemical species. The resulting diffusion fields induce interactions between the grains that are strongly dependent on their spatial arrangement. The influence of these diffusive interactions is not limited to the shapes and sizes of grains but also controls the overall kinetics of the transformation. In this study we investigate the role of the spatial arrangement of equiaxed grains in the average growth kinetics of an ensemble of grains. We perform full-field simulations of different grain ensembles using the mesoscopic grain envelope model (GEM). We show that the growth kinetics of randomly arranged ensembles is fundamentally different from that of periodic arrangements. We provide an explanation of this difference through analyses of the behaviour of individual grains in their local neighbourhood, defined by a Voronoi tessellation. Finally, we compare the full-field GEM simulations to state-of-the-art mean-field models and we point out the limitations of the latter in the prediction of dendritic growth.

Atomistic Theory of Thermally Activated Magnetization Processes in Nd<sub>2</sub>Fe<sub>14</sub>B Permanent Magnet

For the practical use of magnets, particularly at high temperatures, the temperature dependence of magnetic properties is an important ingredient. To study the temperature dependence, methods of treating the thermal fluctuation causing the so-called activation phenomena must be established. To study finite-temperature properties quantitatively, we need atomistic energy information to calculate the canonical distribution. In the present review, we report our recent studies on the thermal properties of the Nd2Fe14B magnet and the methods of studying them. We first propose an atomistic Hamiltonian and show various thermodynamic properties, e.g., the temperature dependences of the magnetization showing a spin reorientation transition, the magnetic anisotropy energy, the domain wall profiles, the anisotropy of the exchange stiffness constant, and the spectrum of ferromagnetic resonance. The effects of the dipole-dipole interaction (DDI) in large grains are also presented. In addition to these equilibrium properties, we also study coercivity, which is the most important issue for magnets. The temperature dependence of the coercivity of a single grain was studied using the stochastic Landau-Lifshitz-Gilbert equation and also by the analysis of the free energy landscape, which was obtained by Monte Carlo simulation. It was found that the upper limit of coercivity at room temperature is about 3 T, which is significantly lower than the so-called theoretical coercivity given by a simple coherent rotation model. The coercivity of a polycrystalline magnet, i.e., an ensemble of grains, is expected to be reduced further by the effects of the grain boundary phase, which is also studied. Surface nucleation is a key ingredient in the domain wall depinning process. Finally, we study the effect of DDI among grains and also discuss the distribution of properties of grains from the viewpoint of first order reversal curve.

High-Energy Coherent X-Ray Diffraction Microscopy of Polycrystal Grains: Steps Toward a Multiscale Approach

We present proof-of-concept imaging measurements of a polycrystalline material that integrate the elements of conventional high-energy X-ray diffraction microscopy with coherent diffraction imaging techniques, and that can enable in-situ strain-sensitive imaging of lattice structure in ensembles of deeply embedded crystals over five decades of length scale upon full realization. Such multi-scale imaging capabilities are critical to addressing important questions in a variety of research areas such as materials science and engineering, chemistry, and solid state physics. Towards this eventual goal, the following key aspects are demonstrated: 1) high-energy Bragg coherent diffraction imaging (HE-BCDI) of sub-micron-scale crystallites at 52 keV at current third-generation synchrotron light sources, 2) HE-BCDI performed in conjunction with far-field high-energy diffraction microscopy (ff-HEDM) on the grains of a polycrystalline sample in an smoothly integrated manner, and 3) the orientation information of an ensemble of grains obtained via ff-HEDM used to perform complementary HE-BCDI on multiple Bragg reflections of a single targeted grain. These steps lay the foundation for integration of HE-BCDI, which typically provides a spatial resolution tens of nanometers, into a broad suite of well-established HEDM methods, extending HEDM beyond the few-micrometer resolution bound and into the nanoscale, and positioning the approach to take full advantage of the orders-of-magnitude improvement of X-ray coherence expected at fourth generation light sources presently being built and commissioned worldwide.

Phase field modeling of domain dynamics and polarization accumulation in ferroelectric HZO

In this work, we investigate the accumulative polarization (P) switching characteristics in ferroelectric (FE) thin films under the influence of sequential sub-coercive electric-field pulses. Performing the dynamic phase-field simulation (based on time-dependent Landau-Ginzburg model) and experimental measurement on Hf0.4Zr0.6O2 (HZO), we analyze the electric field induced domain-wall (DW) motion and the resultant P accumulation process in FE. According to our analysis, even in the absence of an applied electric field, the DW can potentially undergo spontaneous motion. Such a DW instability leads to spontaneous P-excitation and relaxation processes, which play a pivotal role in accumulative P-switching in an FE grain. We show that the extent of such P accumulation increases with the increase in the applied electric field, increase in excitation time and decrease in relaxation time. Finally, by considering an ensemble of grains with local and global coercive field distributions, we model the P-accumulation process in a large area HZO sample. In such a multi-grain scenario, the dependency of P accumulation on the applied electric field pulse attributes follows similar features as that of a single-grain, although the spontaneous processes (excitation/relaxation) are less prominent in large area sample.

Three-dimensional observations of grain volume changes during annealing of polycrystalline Ni

The orientations, locations, and sizes of approximately 2500 grains in a Ni polycrystal were measured at six points in time during an interrupted annealing experiment by synchrotron x-ray based, near field high-energy diffraction microscopy. The volume changes were compared to the geometric characteristics of the grains in both the original microstructures and microstructures in which adjacent twin related domains were merged. Neither the size of a grain nor the number of its nearest neighbors correlates strongly to a grain's volume change over the time scale of this experiment. However, the difference between the number of neighbors a grain has, F, and the average number of neighbors of the neighboring grains have, FNN, is correlated to the volume change. A grain with more (fewer) neighbors than FNN usually grows (shrinks). The correlation between the volume change and F - FNN is obvious only if adjacent twin related domains are merged. The correct sign of the volume change is predicted by F - FNN about two thirds of the time. The results show that the volume change for a given grain is better predicted by comparing a grain's characteristics to its neighbor's characteristics than to the characteristics of the entire ensemble of grains.

Determining Individual Particle Magnetizations in Assemblages of Micrograins

AbstractObtaining reliable information from even the most challenging paleomagnetic recorders, such as the oldest igneous rocks and meteorites, is paramount to open new windows into Earth's history. Currently, such information is acquired by simultaneously sensing millions of particles in small samples or single crystals using superconducting quantum interference device magnetometers. The obtained rock‐magnetic signal is a statistical ensemble of grains potentially differing in reliability as paleomagnetic recorder due to variations in physical dimensions, chemistry, and magnetic behavior. Here we go beyond bulk magnetic measurements and combine computed tomography and scanning magnetometry to uniquely invert for the magnetic moments of individual grains. This enables us to select and consider contributions of subsets of grains as a function of particle‐specific selection criteria and avoid contributions that arise from particles that are altered or contain unreliable magnetic carriers. This new, nondestructive, method unlocks information from complex paleomagnetic recorders that until now goes obscured.

Spread of the dust temperature distribution in circumstellar disks

Accurate temperature calculations for circumstellar disks are particularly important for their chemical evolution. Their temperature distribution is determined by the optical properties of the dust grains, which, among other parameters, depend on their radius. However, in most disk studies, only average optical properties and thus an average temperature is assumed to account for an ensemble of grains with different radii. We investigate the impact of subdividing the grain radius distribution into multiple sub-intervals on the resulting dust temperature distribution and spectral energy distribution (SED). These quantities were computed for two different scenarios: (1) Radius distribution represented by 16 logarithmically distributed radius intervals, and (2) radius distribution represented by a single grain species with averaged optical properties (reference). Within the considered parameter range, i.e., of grain radii between 5 nm and 1 mm and an optically thin and thick disk with a parameterized density distribution, we obtain the following results: In optically thin disk regions, the temperature spread can be as large as ~63% and the relative grain surface below a certain temperature is lower than in the reference disk. With increasing optical depth, the difference in the midplane temperature and the relative grain surface below a certain temperature decreases. Furthermore, below ~20K, this fraction is higher for the reference disk than for the case of multiple grain radii, while it shows the opposite behavior for temperatures above this threshold. The thermal emission in the case of multiple grain radii at short wavelengths is stronger than for the reference disk. The freeze-out radius is a function of grain radius, spanning a radial range between the coldest and warmest grain species of ~30AU.

Stress determination through diffraction: establishing the link between Kröner and Voigt/Reuss limits

The quantification of stress in polycrystalline materials by diffraction-based methods relies on the proper choice of grain interaction model that links the observed strain to the elastic stress state in the aggregate. X-ray elastic constants (XEC) relate the strain as measured using X-rays to the state of stress in a quasi-isotropic ensemble of grains. However, the corresponding interaction models (e.g., Voigt and Reuss limits) often possess unlikely assumptions as to mechanical response of the individual grains. The Kröner limit, which employs a self-consistent scheme based on the Eshelby inclusion method, is based on a more physical representation of isotropic grain interaction. For polycrystalline aggregates composed of crystals with cubic symmetry, Kröner limit XEC are equal to those calculated from a linear combination of Reuss and Voigt XEC, where the weighting fraction, xKr, is solely a function of the single-crystal elastic constants and scales with the material's elastic anisotropy. This weighting fraction can also be experimentally determined using a linear, least-squares regression of diffraction data from multiple reflections. Data on metallic thin films reveals that this optimal experimental weighting fraction, x*, can vary significantly from xKr, as well as that of the Neerfeld limit (x = 0.5).

A computational study of a model of single-crystal strain-gradient viscoplasticity with an interactive hardening relation

The behavior of a model of single-crystal strain-gradient viscoplasticity is investigated. The model is an extension of a rate-independent version, and includes a new hardening relation that has recently been proposed in the small-deformation context (Gurtin and Reddy, 2014), and which accounts for slip-system interactions due to self and latent hardening. Energetic and dissipative effects, each with its corresponding length scale, are included. Numerical results are presented for a single crystal with single and multiple slip systems, as well as an ensemble of grains. These results provide a clear illustration of the effects of accounting for slip-system interactions.

The Kinetics of Individual Grains in Polycrystalline Materials

Abstract Based on a mean-field approach a 3D grain growth model is presented which predicts the growth history of individual grains of a grain ensemble in terms of linear grain size and time. The analytical results are compared with the results of numerical simulations using the Monte-Carlo-Potts model. In addition, based on a stochastic model of grain growth, the diffusivity of the very discontinuous movements of individual quadruple and triple junctions is set in relation to the rate of growth. This allows the calculation of the average growth law of an ensemble of grains solely from the measurement of the stochastic growth kinetics of individual grains. The results from simulation and theory are compared with experimental results of in-situ scanning electron microscopy observations of grain growth in polycrystalline metals.

Dielectric Response of BaTiO3 Thin Film with Grain Size at Nanometer Scale

In ceramic BaTiO3 thin film prepared by chemical solution deposition, the influence of small grain size (10–150 nm) and grain boundaries on ferroelectric behavior is investigated by the studies of low‐frequency dielectric response. The apparent permittivity is suggested to result from an ensemble of grains possessing different properties and volume fractions, and having a nonferroelectric boundary layer. The effective permittivity of the boundary layer is found to be close to that of an interfacial layer in epitaxial thin‐film ferroelectrics, indicating possible fundamental resemblance of these layers. The maximum effective permittivity of the grain interiors is estimated to be about 1500. The observed small intrinsic grain permittivity, small Curie constant, broad dielectric peaks, and high‐temperature dielectric hysteresis are discussed in terms of size‐induced changes of the phase diagram.

Observation of the condensation of a gas of interacting grains

We consider an ensemble of grains that interact through a dipole-dipole interaction. A granular gas is formed by the vertical motion of a piston at the bottom boundary of the system. The interaction between the grains is controlled by an horizontally applied magnetic field. When the speed of the piston is decreased, we observe a transition from a low density to a high density phase. When the interaction between grains is weak, the transition is continuous. It is discontinuous for stronger interaction. The phase diagram displays strong similarities with the ones observed for usual equilibrium phase transitions.

Fe–(Au,Cu)–B two-phase magnetic microwires with exchange coupled nanosized grains

Results on the magnetic behavior of glass-coated magnetic microwires prepared from the Fe87Au2−xCuxB11 alloy system are reported for the first time. The changes induced in their axial magnetization process by the substitution of Au with Cu have been studied. Hysteresis loops with typical shapes for soft magnetic materials have been observed in all cases except for x=1.5at.% of Cu. Fe87Au0.5Cu1.5B11 microwires display a two-step hysteresis loop with a plateau at zero magnetization. The observed change in the axial magnetization process of Fe–(Au,Cu)–B microwires with Cu content has been explained considering the average distance among adjacent α‐(Fe,Cu) nanosized grains to be smaller than the exchange length. In this way, the ensemble of grains is collectively magnetized and it behaves as a single material from the magnetic point of view. The remainder amorphous matrix is also collectively magnetized, and the resulting stepped loop is the result of the magnetostatic coupling between these two systems: the grain ensemble and the amorphous matrix. The results demonstrate the effectiveness of composition control on the magnetic properties of Fe–(Au,Cu)–B microwires and open up new application opportunities for glass-coated microwires.

A new approach to modelling of non-steady grain growth

Grain coarsening is a phenomenon common to all polycrystalline materials at elevated temperatures. During the last 50 years a number of sophisticated models have been developed for grain-coarsening kinetics. The authors have shown that Onsager’s extremal principle represents a systematic way of deriving evolution equations for parameters characterizing thermodynamic systems. If the grain radii are chosen as those parameters, the application of Onsager’s principle reproduces Hillert’s classical evolution equations for the radii of individual grains (multigrain concept). The observed or calculated ensemble of grains is usually classified by a grain radii distribution function involving a certain number of parameters. The novelty of the paper is represented by the direct application of Onsager’s principle to the radii distribution function by derivation of the evolution equations for its parameters (distribution concept). The kinetics of systems with bimodal and different monomodal starting distribution functions are calculated by means of both multigrain and distribution concepts, and the results of simulations are compared and discussed. The dissipation of the grain coarsening process is evaluated, and it is shown that the width of the distribution function decisively influences the coarsening kinetics.

Nanodiamonds from AGB Stars: A New Type of Presolar Grain in Meteorites

Although the most abundant type of presolar grain found in meteorites is nanometer-sized diamond ("nanodiamond"), the dimensions make study of individual crystallites rather uninformative; instead, laboratory astrophysicists usually work with an ensemble of grains (generally in concentrated form, produced by chemical treatments). This, of course, produces results that are just a measure of average properties, which makes assessing the origin of diamonds quite difficult. An apparently uniform distribution of chemical and physical properties of the grains has been interpreted as their having a single origin. In this paper, however, we demonstrate that slight variations in average grain size can be exploited, using differential centrifugation (followed by analysis using electron microscopy and isotope-ratio mass spectrometry), to produce separates that reflect contributions from specific sources. In this way we identify a contribution from carbon stars, at the asymptotic giant branch stage of evolution, in addition to components already ascribed to supernovae and solar nebular processing. The astrophysical significance of the new discovery is discussed.

Nanoscale polarization relaxation in a polycrystalline ferroelectric thin film: Role of local environments

In this letter, we report on the study of nanoscale polarization relaxation phenomena in polycrystalline PbZr0.4Ti0.6O3 films. Piezoresponse force microscopy (PFM) images of the as-grown sample reveal grains with a range of contrast, from fully white to gray to fully black. It is shown that this local change in the contrast (magnitude) of the piezoresponse from grain to grain can be attributed to the crystallographic orientation within each grain. PFM-based relaxation experiments show that the rate of relaxation is different for each grain, furthermore it is strongly dependent on the tilt of individual crystallographic orientation with respect to the polar axis. Strongly tilted away nonpolar axis grains show a much stronger decay of the polarization compared to polar axis-oriented grains. Therefore, for an ensemble of grains under a common top electrode, the relaxation events would first take place in grains, which are nonpolar axis oriented.

Automatic 3-D simulation and micro-stress distribution of polycrystalline metallic materials

This paper proposes an automatic method to simulate the microstructure of metallic materials and investigates the micro-stress distribution inside the materials. A polycrystalline material is modeled as an ensemble of grains. The response of the polycrystal is the aggregate response of the constituent grains. A software has been developed by combining a tessellation method and the MSC PATRAN/NASTRAN finite element analysis software, and it has the advantage of predicting micro-stress of each grain and their correlation. The shortest distance criterion has been used in the 3-D tessellation software program to determine the grain faces. This information is used with PATRAN to create a 3-D microstructure of a statistical volume element (SVE) with 200 grains. In the SVE model, each grain is assumed to have anisotropic mechanical properties with different orientations. Stress analysis of both single phase and multi-phase alloys are performed using the SVE model, and the statistical micro-stress distribution results show good congruence with this SVE model.

Nonlinear Dynamics of Grains in a Liquid-Saturated Soil

A new kind of nonlinearity of inertial type caused by accelerated motionof interacting particles is described. The model deals with an ensembleof grains immersed into a vibrating fluid. First, the nonlinearvibration of two connected grains is studied. The temporal behaviours ofdisplacement and velocity, as well as spectrum of vibration, areanalysed. Numerical simulations are performed. Then an infinite chain ofgrains is considered and the corresponding differential-differenceequation is derived. For the continuum limit the inhomogeneous nonlinearwave equation is solved and temporal profiles are calculated. A newresonant phenomenon is described and the resonant curves areconstructed.

Micromagnetic modeling of first-order reversal curve (FORC) diagrams for single-domain and pseudo-single-domain magnetite

First-order reversal curve (FORC) diagrams have been experimentally shown to be a better way of discriminating domain states in a sample compared to the straightforward use of major hysteresis loops. In order to better understand the fundamental behavior of assemblages of single-domain (SD) grains, we used a micromagnetic model with a conjugate gradient algorithm to calculate FORC diagrams for isolated grains of magnetite as well as for arrays of grains. In the case of individual elongated grains, we found that the FORC diagram consists of a single peak centered on the coercive force Hc if the grain is SD. For a pseudo-single-domain (PSD) grain with vortex structure, we observe multiple peaks on the FORC diagram. The modeling of arrays of elongated SD particles reveals two distinct types of patterns depending on the spacing between particles. In a 2×2×2 array of particles, a secondary branch on the reversal curves appears if the spacing between particles is less than about twice the particle length. This feature translates into the appearance of one negative and three positive peaks on the FORC diagram. In the case of a 3×3×3 array of particles, we again observe several secondary branches when the spacing between grains is less than about twice the particle length, leading to the appearance of multiple peaks on the FORC diagram. Splitting of the central peak on the Hu axis when particles interact could explain the vertical spread of FORC distributions of natural interacting samples as an effect of superposition of multiple peaks caused by the random orientation and distributions of particle spacing and switching fields of a large number of grains. The presence of symmetric peaks on a FORC diagram can be an indicator of the presence of either small PSD grains or magnetic interactions in an ensemble of grains.

A photometric-dynamic model to simulate coma and jets from a comet

A model to compute the trajectories of dust grains ejected by comets to simulate intensity and polarization maps on the sky plane is presented. The model is used to constrain the silicate to organic mass ratio, porosity and size distribution of the grains in the shells and coma of comet Hale-Bopp to explain 1) the published polarizations at three continuum wavelengths at 0.6840 μm, 0.4845 μm and 0.3650 μm at different phase angles, 2) higher polarization and bluer colour of the shells compared to the coma, 3) the intensity variation and rapid decline of polarization on the sunward side and 4) higher polarization on the anti-sunward direction. The present results obtained using Mie theory in the model indicate that although it is impossible to determine the nature of the silicate (pyroxenes/olivines or amorphous/crystalline) using the present technique, the porosity, organic fraction and size distribution of the grains can be constrained. The fit to the data set indicates an ensemble of grains in which 60% are silicate grains with a range in silicate to organic mass ratio r m between 1 and 2 and of medium porosity 8 on the shells can explain their bluer colour. A narrow size distribution between 0.08 μm-0.6 μm is inferred for 70% of the grains in the coma and shell. These small grains may not be individual grains but part of loosely bound grains in which larger grains may also be present which may control the dynamics. The narrow size distribution may therefore represent statistically the size range of individual subunits of larger highly porous aggregates of fractal dimension close to two. The polarizations in JHK bands also support the aggregate structure. Despite the availability of an extensive and wide range of data set on this comet, the inclusion of a large parameter space, lack of knowledge on the nature of organic material found in comets and use of Mie theory, which does not adequately represent the polarization phase curves of natural grains, set limitations in getting a unique solution in the present work. The results presented here are open to improvements when more realistic light scattering theories are used in the model and our understanding on the nature of the organic content of the grains improves. However, visibility of up to 8-10 shells in well exposed images implies β < 1 for these grains. As a result of this dynamical constraint which is independent of the assumptions on the scattering characteristics of the grains, the results for the dust grains in the shell may be more robust compared to that of the coma.