Anisotropic Grain Research Articles

A triple junction energy study using an inclination-dependent anisotropic Monte Carlo Potts grain growth model

This work presents a Monte Carlo Potts grain growth model in which the grain boundary (GB) energies depend on the GB inclination. The inclination is calculated using a linear smoothing approach developed by the authors. In bicrystal simulations with a shrinking grain, the grain changes shape to prefer low energy GB inclinations. However, in polycrystal simulations the preferred inclinations depend on the approach used to assign the triple junction (TJ) energies. Approaches that produce unimodal TJ energy distributions result in the expected behavior of preferring low energy GB inclinations. However, approaches that produce bimodal TJ energy distributions result in medium energy or even high energy inclinations being preferred. Overall, this study underscores the importance of TJs in anisotropic grain growth.

Highly tailorable thermomechanical properties of nanograined silicon: Importance of grain size and grain anisotropy

Nanocrystalline silicon can have unique thermal transport and mechanical properties governed by its constituent grain microstructure. Here, we use phonon ray-tracing and molecular dynamics simulations to demonstrate the largely tunable thermomechanical behaviors with varying grain sizes (a0) and aspect ratios (ξ). Our work shows that, by selectively increasing the grain size along the heat transfer direction while keeping the grain area constant, the in-plane lattice thermal conductivity (kx) increases more significantly than the cross-plane lattice thermal conductivity (ky) due to anisotropic phonon–grain boundary scattering. While kx generally increases with increasing ξ, a critical value exists for ξ at which kx reaches its maximum. Beyond this transition point, further increases in ξ result in a decrease in kx due to substantial scattering of low-frequency phonons with anisotropic grain boundaries. Moreover, we observe reductions in the elastic and shear modulus with decreasing grain size, and this lattice softening leads to significant reductions in phonon group velocity and thermal conductivity. By considering both thermal and mechanical size effects, we identify two distinct regimes of thermal transport, in which anisotropic phonon–grain boundary scattering becomes more appreciable at low temperatures and lattice softening becomes more pronounced at high temperatures. Through phonon spectral analysis, we attribute the significant thermal conductivity anisotropy in nanograined silicon to grain boundary scattering of low-frequency phonons and the softening-driven thermal conductivity reduction to Umklapp scattering of high-frequency phonons. These findings offer insights into the manipulation of thermomechanical properties of nanocrystalline silicon via microstructure engineering, carrying profound implications for the development of future nanomaterials.

Microstructure evolution in 439 stainless steels under tensile: phase field simulation and experiment

A combination of phase-field simulations and experimental validation is utilized to examine the effect of annealing tension on the microstructure evolution of 439 ferrite stainless steel (FSS). The study reveals the competing mechanisms of texture under tensile stress. Furthermore, a phase field model that incorporates anisotropic grain boundary (GB) energy and elastic energy is established. The microstructure of 439 FSS is created using a 3D reconstruction strategy based on the 2D electron backscatter diffraction characterization proposed in this work. Elastic constants are calibrated using actual alloy data and determined through molecular dynamics simulations. Finally, simulations of the grain coarsening process in 439 FSS are successfully achieved, considering both tensile stress and anisotropic GB energy effects. The results reveal that the presence of low-angle GBs deviates from Hillert model predictions in terms of grain size distribution and slows down the average grain size evolution over time. A significant deviation in the grain size distribution, compared to Hillert predictions, is observed in the textured system under tensile stress. The results of growth kinetics indicate that tensile stress promotes grain growth more than GB energy anisotropy retards microstructure evolution. Both experiment and simulation results consistently demonstrate that grains with <111>//ND orientation experience a better growth proficiency compared to grains of other orientations under tensile stress. This investigation offers fresh insights into managing the ferritic microstructure of FSS to enhance its formability capabilities.

Crystallography and anisotropy of crystals shape in dense aluminum titanate ceramics

This study investigates the anisotropic grain growth of Fe-doped aluminum titanate ceramics using Electron Backscatter Diffraction (EBSD). Three grades of materials exhibiting various grain size distributions were prepared on the basis of different sintering conditions. The crystal structure of the raw powder was first refined using X-ray diffraction. Then the microstructure variation of sintered polycrystalline aluminum titanate associated to anisotropic grain coarsening was accurately studied. Due to the orthorhombic structure of β-Al2TiO5, the crystal shape is prismatic and elongated along the [100] direction. This specific grain shape is analyzed in relation with crystallographic axes in the frame work of the Wulff approach. The obtained results provide valuable information regarding the microstructure of such flexible ceramics made off anisotropic grains.

A new efficient grain growth model using a random Gaussian-sampled mode filter

This paper presents the use of a Gaussian neighborhood mode filter for predicting grain growth in a manner similar to the solutions obtained by a Monte Carlo Potts model. This flexible grain growth model can quickly utilize modern, computationally optimized data science strategies on graphics processing units to simulate grain growth up to 100 times faster than the state-of-the-art, publicly available Monte Carlo Potts model. We show that, given the correct neighborhood, the mode filter can replicate normal grain growth in two or three dimensions. In addition, the paper briefly demonstrates the ability to model limited anisotropic in grain boundary energy and mobility. Anisotropic grain boundary energy is modeled by defining a weighted mode filter operation. Anisotropic grain boundary mobility is modeled by scaling and orienting the Gaussian neighborhood in a particular direction.

Microstructure and properties of silicon nitride ceramics fabricated by vat photopolymerization in combination with pressureless sintering

Silicon nitride (Si3N4) ceramics have been successfully manufactured using vat photopolymerization (VPP) technology. The formulated photocurable paste achieved a high solid loading (48 vol%) while maintaining low viscosity (3.2 Pa s at a shear rate of 30 s−1). Si3N4 ceramics doped with Al2O3–Y2O3 sintering aids were prepared using pressureless sintering at different temperatures (1650 °C, 1700 °C and 1750 °C) for 2 h. The resultant material exhibited a flexural strength of 613.3 ± 53.1 MPa, Vickers hardness of 12.6 ± 0.4 GPa, and a fracture toughness of 7.5 ± 0.3 MPa m1/2. X-ray diffraction (XRD) analysis has demonstrated a complete transformation from α-Si3N4 to β-Si3N4 at a sintering temperature of 1750 °C, where the resultant ceramic exhibited distinctive grain growth anisotropy. By investigating the shrinkage at different sintering temperatures, the sample at 1750 °C has a larger shrinkage in the Z-direction, which is also related to its anisotropic grain growth. Scanning electron microscopy (SEM) images have revealed the presence of elongated grains at a sintering temperature of 1750 °C. The combined effect of elongated grains and growth anisotropy serves to significantly enhance the overall mechanical properties of the material. This study advances current research on the preparation of high-performance Si3N4 ceramics by combining VPP technology with pressureless sintering.

Phase field modeling of anisotropic bicrystal grain growth using a spherical-Gaussian-based 5-D computational approach

A previously developed Spherical-Gaussian method is used to incorporate 5-D anisotropy in two phase field models originally published by Moelans, here named epsilon and gamma models. Quaternions are used for representing both grains orientations and misorientations. A slice of fundamental zone for Σ3 grain boundaries with given orientations and misorientations from Olmsted, are used to verify the outputted grain boundary energies under different cases. Local minima selected from the slice are kept as minima library and used in both models. 2-D gaussian switches are used to compare the studied system misorientations between pair of grains to the list of minima misorientations. The switch causes a reduction from the assigned base energy to that of the minima library energy, depending on the computed value. Using only 3 minima from the corners of the Σ3 fundamental zone, the models are shown to reproduce energies in the full fundamental zone with a maximum error of around 30%. The Multiphysics Object Oriented Simulation Environment (MOOSE) is used to perform bicrystal simulations using both models; with variations in settings yielding close to accurate values as well as physical behaviors like faceting.

Scattering of elastic waves by a sphere with orthorhombic anisotropy and application to polycrystalline material characterization

Scattering of elastic waves by an anisotropic sphere with orthorhombic symmetry inside an isotropic medium is studied and applied to characterization of polycrystalline materials with anisotropic grains. For a single sphere the waves in the isotropic surrounding are expanded in the spherical vector wave functions. Inside the sphere, the elastodynamic equations are first transformed to spherical coordinates and the displacement field is expanded in terms of the vector spherical harmonics in the angular directions and power series in the radial direction. The governing equations inside the sphere give recursion relations among the expansion coefficients in the power series. The boundary conditions on the sphere then determine the relation among the scattered wave expansion coefficients and those of the incident wave, expressed as the transition (T) matrix. For low frequencies the elements of the T matrix are obtained in explicit form. According to the theory of Foldy the T matrix elements of a single sphere are used to study attenuation and phase velocity of polycrystalline materials, explicitly for low frequencies. Comparisons of the present method with previously published results and recent FEM results show a good correspondence for low frequencies. The present approach shows a better agreement with FEM for strongly anisotropic materials in comparison with other published methods.

The anisotropic grain size effect on the mechanical response of polycrystals: The role of columnar grain morphology in additively manufactured metals

Additively manufactured (AM) metals exhibit highly complex microstructures, particularly in terms of grain morphology which typically features heterogeneous grain size distribution, irregular and anisotropic grain shapes, and the so-called columnar grains. The conventional morphological descriptors based on grain shape idealization are generally inadequate for representing complex and anisotropic grain morphology of AM microstructures. The primary aspect of microstructural grain morphology is the state of grain boundary spacing or grain size whose effect on the mechanical response is known to be crucial. In this paper, we formally introduce the notion of axial grain size from which we derive mean axial grain size, effective grain size, and grain size anisotropy as robust morphological descriptors capable of effectively representing highly complex grain morphologies. We instantiated a discrete sample of polycrystalline aggregate as a representative volume element (RVE) featuring random crystallographic orientation and misorientation distributions. However, the instantiated RVE incorporates the typical morphological features of AM microstructures including distinctive grain size heterogeneity and anisotropic grain size owing to its pronounced columnar grain morphology. We ensured that any anisotropy observed in the macroscopic mechanical response of the instantiated sample primarily originates from its underlying anisotropic grain size. The RVE was then employed for mesoscale full-field crystal plasticity simulations corresponding to uniaxial tensile deformation along various axes via a spectral solver and a physics-based crystal plasticity constitutive model which was developed, calibrated, and validated in earlier studies. Through the numerical analyses, we isolated the contribution of anisotropic grain size to the anisotropy in the mechanical response of polycrystalline aggregates, particularly those with the characteristic complex grain morphology of AM metals. This contribution can be described by an inverse square relation.

Phase Structure, Microstructure, and Electrical Properties of Bi0.47Na0.47Ba0.06TiO3 Ceramics with (LiNb)4+ Substituted into B-Sites

Due to the substitution of complex ions into B-sites is very interesting in recent, lead-free Bi0.47Na0.47Ba0.06Ti1− x (LiNb) x O3 (BNBT1− x LN x ) ceramics (with x = 0–0.04) were fabricated by the solid-state combustion method. The influence of (LiNb)4+ (x) on the phase structure, microstructure, and electrical properties was investigated. The X-ray diffraction (XRD) patterns exhibited a pure perovskite structure for all specimens. Coexisting rhombohedral and tetragonal phases were observed in all samples and the tetragonal phase increased with increased x, as analyzed by the Rietveld refinement method. The morphology of the BNBT1− x LN x ceramics, obtained by scanning electron microscopy (SEM), revealed almost-round grain shapes and anisotropic grain growth. The density and average grain sizes decreased from 5.84 to 5.54 g/cm3 and 1.7 to 0.9 µm, respectively, when x increased from 0 to 0.04. The grain size distribution decreased with increased (LiNb)4+ content. A reduction in the dielectric properties was observed, due to the phase ratio changing away from a morphotropic phase boundary (MPB), an inferior microstructure, and low density caused by (LiNb)4+ substitution. The (LiNb)4+ substitution induced the transition from non-ergodic relaxor to ergodic relaxor ferroelectric state.

Fatigue behaviour analysis of thermal cyclic loading for through-silicon via structures based on backstress stored energy density

Through-silicon via (TSV) structures are widely used in microelectronic due to the ease of chip interconnection. Few research has focused on investigating the fatigue properties of TSV structures using crystal plasticity finite element (CPFE) simulations. As the process of TSV structures approaches the micron scale, the effects of anisotropic microstructure and grain size on their fatigue behaviours will become necessary. The present work aims to use CPFE simulations to investigate the fatigue properties of TSVs at the microscale. Finite element models with realistic EBSD morphology and orientation are established for four TSV structures with different grain sizes, and CPFE simulations with thermal cyclic loading from −55℃ to 125℃ are performed. From the energy point of view, the stored energy density based on backstress and strain gradient is proposed as a fatigue indicator parameter (FIP). CPFE simulation results show that low-angle grain boundaries (LAGBs) and high-angle grain boundaries (HAGBs) dominate crack initiation at the top, bottom or edges of the TSV structure, which is still mainly due to the thermal mismatch effect caused by the difference in the coefficients of thermal expansion of the materials. The crack initiation in the internal structure is mainly caused by symmetric grains containing twin boundaries (TBs), or trigrain boundaries, and this is different from the macroscopic simulations. Combined with the local FIPs concentration distribution, the backstress stored energy density is able to capture more details than the cumulative plastic strain because of its direct correlation with the strain gradient, and validates its effectiveness as a FIP.

Enhancement of the Dielectric and Energy Storage Properties of Lead-Free BNSLT Ceramics by Zr4+ Substitution into B-Sites

(Bi0.38Na0.30Sr0.28)0.98La0.02Ti1-xZrxO3 (abbreviated as BNSLT1-xZrx, with x = 0 − 0.05) lead free ceramics were fabricated using the solid-state combustion method. The phase structure, microstructure and electrical properties of the ceramics were investigated. The coexistence of the rhombohedral (R) and tetragonal (T) phases was found in all samples. Rietveld refinement confirmed that as x increased from 0 to 0.05, the rhombohedral phase increased from 41 to 60%. A nearly equal R:T phase ratio of 49:51 was obtained for x = 0.01. All ceramics displayed polygonal grain shapes with anisotropic grain growth. The average grain size of the ceramics was in the range of 0.46–0.79 µm. The optimal Zr4+ content resulted in increased grain growth and reduced pores, leading to improved electrical properties. The highest density (5.52 g/cm3), maximum dielectric constant (ε m =2156), maximum polarization (Pmax=15.36 µC/cm2) and high energy storage properties (Wtotal=0.49 J/cm3, Wrec=0.45 J/cm3, Wloss=0.05 J/cm3 and η = 90.54% at 60 kV/cm) were obtained from x = 0.01 caused by a morphotropic phase boundary (MPB) and good morphology.

A simulation study of the role of anisotropic charge transport and grain boundary recombination in thin-film Sb2Se3 photovoltaics

The crystal structure of Sb2Se3, which consists of [001] oriented ribbons held together by weak van der Waals forces, gives rise to unique absorber layer properties different from other more conventional photovoltaic materials, such as Si or CdTe. Charge carrier transport occurs preferentially along the ribbon direction, and grain boundary recombination is minimal provided the ribbons are oriented parallel to the grain boundary plane. For optimum performance the Sb2Se3 absorber layer must have a (001) orientation, although in practice (211) and (221) growth textures are more common. The effect of this non-ideal orientation on anisotropic charge carrier transport and grain boundary recombination has however not been quantified. Here we derive analytical expressions for charge transport along a 1D ribbon under different boundary conditions. The local device properties for a given microstructural feature (e.g. grain boundary) can then be simulated by superposition of all individual ribbon contributions. It is found that anisotropic charge transport has the largest impact on device properties, even in the presence of electrically active grain boundaries (107 cm/s recombination velocity). For example, a 44° ribbon misorientation (i.e. (221) growth texture) resulted in a ∼3% efficiency loss compared to the ideal (001) orientation. This highlights the importance of ribbon misorientation for achieving the highest efficiency Sb2Se3 devices.

Induced Polarization of Metal Grains: Simulations of Three‐Dimensional Electric Fields

AbstractInduced polarization (IP) method is one of the geophysical methods that utilizes polarization of subsurface materials. This method is very sensitive to the presence of (semi) conducting materials. Previous studies revealed the underlying mechanisms of metal polarization in simple geometry. However, there is a gap between such studies and the conditions in geological materials. To fill the gap, I have established the simulation method for studying the polarization of metal grains in a three‐dimensional field using the open‐source computational‐fluid‐dynamic software OpenFOAM. The three‐dimensional view of the surface potential distribution on a metal grain clarified how polarization is induced while varying geometrical constrictions. I varied the channel size, the orientation of the anisotropic grain, the elongation of the grain, and the distance of two grains. The results include: (a) a less decay of imaginary potential over distance for shorter or narrower channel, enhanced polarization in narrower channel and reduced polarization in shorter channel, (b) shift of the position of maximum imaginary potential over frequency on the surface of the oriented anisotropic grains, (c) higher peak frequency and larger polarization locally at the edge of the grains for elongated grains, and (d) enhancement of polarization by interaction of nearby grains. The underlying mechanisms were examined for each case. In addition, relationships between each scenario in my simulation and the subsurface environment were discussed. My successful implementation of the simulation for metal grains may be applied to improve the modeling, interpretation, and laboratory experimental setup.

The evolution of grain boundary energy in textured and untextured Ca‐doped alumina during grain growth

AbstractThe role of anisotropic grain boundary energy in grain growth is investigated using textured microstructures that contain a high proportion of special grain boundaries. Textured and untextured Ca‐doped alumina was prepared by slip casting inside and outside a high magnetic field, respectively. At 1600°C, the textured microstructure exhibits faster growth than the untextured microstructure and its population of low‐angle boundaries increases. Atomic force microscopy (AFM) is employed to measure the geometry of thermal grooves to assess the relative grain boundary energy of these systems before and after growth. In the textured microstructure, the grain boundary energy distribution narrows and shifts to a lower average energy. Conversely, the energy distribution broadens for the untextured microstructure as it grows and exhibits abnormal grain growth. Further analysis of the boundary networks neighboring abnormal grains reveals an energy incentive that facilitates their growth. These results suggest that coarsening is not the only dominant grain growth mechanism and that the system can lower its energy effectively by replacing high energy boundaries with those of low energy. The faster growth of lower energy boundaries suggests that isotropic simulations do not adequately account for anisotropic grain growth mechanisms or anisotropic mobility.

Hot rolling deformation behavior of nanocrystalline Nd-Fe-B magnets: One-step powder forming at large size

Anisotropic nanocrystalline Nd-Fe-B magnets were successfully prepared by hot rolling technique. A systematic study of the microstructure, texture, and magnetic properties of hot-rolled (HR) Nd-Fe-B magnets was conducted to gain an insight into the deformation process. The results indicate that: the hot-rolled magnets have good uniformity after one-step rolling of the cold pressed precursors. As the deformation increases, the Br and (BH)max increase from 7.1 kG to 11.9 kG and from 10.9 MGOe to 30.1 MGOe, respectively. Platelet grains were gradually formed and arranged in the fine grain region, resulting in a c-axis texture. During the deformation process, fine grain region of the rare-earth-rich phase was rapidly squeezed into the coarse grain region, which deteriorated the magnetic properties. The microstructural evolution and deformation processes of hot-rolled Nd-Fe-B magnets were analyzed. The conclusion was that the process of deformation involved melt-spun ribbon densification, dissolution-precipitation, anisotropic grain growth, and grain alignment. Additionally, the preparation process and development prospects of hot-rolled magnets were also discussed.

Anisotropic Grain Growth of Al-Si Wire Under Electromigration Tests in Power Devices

Anisotropic Grain Growth of Al-Si Wire Under Electromigration Tests in Power Devices

Insights into microstructural evolution of tungsten-tungsten carbide plasma facing composite materials prepared by field assisted sintering technique

Combining a stable, resilient W-W2C or WC as plasma-facing material, with thermally more conductive and ductile W as a structural material, may provide a solution for the demanding environment in the fusion reactor chamber. In order to ensure the structural stability of such layered composite, their phase composition and thermal stability at elevated temperatures and cyclic heat loads needs to be evaluated.In situ densification and joining of W and W-xWC materials have been performed by field-assisted sintering technique. Microstructural analysis revealed that the interface layer formed between W and pure WC consists primarily of large W2C grains. Initially, equiaxed W2C grains are formed following the decarburisation of WC due to the large C concentration gradient. Further C diffusion results in the formation of larger anisotropic grains growing preferentially in the 〈0001〉 direction. A similar microstructure was observed when joining WC-reinforced W (W-xWC, x = 7, 17, 28, 33 at. % C) with WC. On the other hand, the joining of W with WC-reinforced W resulted in a sound joint with no observable grain growth at the interface, even at large C concentrations (e.g. 28 at. %). As formed, microstructures were stable after thermal ageing at 1600 °C for 24 h with no observable change in major microstructural features.The combination of WC-reinforced W as high strength plasma facing armour material and W-structural material offers a promising composite solution for improved thermal stability under high cyclic heat loads expected in future fusion power plants.

The Modeling and Simulation of Austenite Grain Growth in 25Cr2Ni4MoV Nuclear-Power Rotor Steel

The modeling of austenite grain growth of 25Cr2Ni4MoV steel for super-large nuclear-power rotors was investigated during the common heating process including the continuous heating and isothermal heating process. Based on the isothermal grain growth model considering the steady-state grain size and the rule of additivity, a new grain growth model during the continuous heating process was established. The comparison between experimental and predicted results indicates the model has good predictability. To describe the anisotropic and isotropic grain growth during the different isothermal heating stages of the super-large nuclear-power rotor, a cellular automaton model considering anisotropic grain boundary energy for grain growth of 25Cr2Ni4MoV steel was developed. It is found that the anisotropic grain boundary energy mainly exists in the early isothermal heating stage at lower temperatures, and the normal grain growth occurs under anisotropic grain boundary energy conditions. When the temperature is not less than 1273 K and the cellular automaton step is not less than 15, the normal grain growth containing only isotropic grain boundary energy occurs. The analysis of the morphology, energy variance, topology and growth kinetics further indicates that normal grain growth of 25Cr2Ni4MoV steel can be simulated fairly well by the present CA model.

Laser-Induced Melting and Crystal Growth of Sodium Ion Conductive β-NaFeO&lt;sub&gt;2&lt;/sub&gt;

Laser irradiation of β-NaFeO2 shows local melting and crystal growth from the melt pool and sodium ion conductivity. Local melting, densification, and crystal growth were confirmed on the β-NaFeO2 surface through laser irradiation with a wavelength of 1 µm. Scanning electron microscopy and electron backscatter diffraction analysis confirmed anisotropic grain growth and grain boundary shrinkage in the laser-irradiated area. X-ray diffraction results suggested that the laser-irradiated area was in a low crystalline state. In addition, the precipitation of Fe3O4 in laser-irradiated β-NaFeO2 indicates a reduction reaction, suggesting that the laser-irradiated area is heated to 1500°C or higher. We confirmed that the structure change region could be controlled down to a thickness of about 10 µm by laser irradiation with varying laser power to β-NaFeO2.