Grain Growth Model Research Articles

Phase-field model for anisotropic grain growth

Grain boundary properties may depend on the five macroscopic crystallographic degrees of freedom of the boundary, these being the misorientation between crystals and the inclination of the boundary plane. An orientation-field model is developed which uses a single-well potential and allows the grain boundary energy and mobility to depend on all five macroscopic degrees of freedom. The model reproduces the analytical equilibrium dihedral angles at triple junctions, has no anomalous trijunction drag, and Wulff shapes for cubic grain boundary energy anisotropy. Polycrystalline simulations in two dimensions demonstrate a pronounced effect of low angle grain boundaries on the microstructure evolution, demonstrating the importance of accounting for misorientation-dependent energy, particularly in highly textured materials. This model serves as a simple, computationally efficient, and physics-based method for simulating grain growth phenomena. With the ability to tune the grain boundary energy and mobility, the model shows promise for use in large scale simulations of grain coarsening in a wide range of systems.

Engineering grain boundary anisotropy to elucidate grain growth behavior in alumina

Current grain growth models have evolved to account for the relationship between grain boundary energy/mobility anisotropy and the five degrees of grain boundary character. However, the role of grain boundary networks on overall growth kinetics remains poorly understood. To experimentally investigate this problem, a highly textured Al2O3 was fabricated by colloidal casting in a strong magnetic field to engineer a unique spatial distribution of grain boundary character. Microstructural evolution was quantified and compared to an untextured sample. From this comparison, a prevalence of (0001)/(0001) terminated grain boundaries with anisotropic networks were identified in the textured sample. These boundaries and their networks were found to be driving grain growth at a faster rate than predicted by models. These findings will allow better modelling of grain growth in real systems by experimentally exploring the impact thereon of grain boundary plane anisotropy and relative energy/mobility differences between neighboring boundaries.

Modeling Dynamic Recrystallization Behavior in a Novel HIPed P/M Superalloy during High-Temperature Deformation.

The dynamic recrystallization (DRX) features and the evolution of the microstructure of a new hot isostatic pressed (HIPed) powder metallurgy (P/M) superalloy are investigated by hot-compression tests. The sensitivity of grain dimension and DRX behavior to deformation parameters is analyzed. The results reveal that the DRX features and grain-growth behavior are significantly affected by deformation conditions. The DRX process is promoted with a raised temperature/true strain or a reduced strain rate. However, the grains grow up rapidly at relatively high temperatures. At strain rates of o.1 s−1 and 1 s−1, a uniform microstructure and small grains are obtained. Due to the obvious differences in the DRX rate at various temperatures, the piecewise DRX kinetics equations are proposed to predict the DRX behavior. At the same time, a mathematical model for predicting the grain dimension and the grain growth behavior is established. To further analyze the DRX behavior and the changes in grain dimension, the hot deformation process is simulated. The developed grain-growth equation as well as the piecewise DRX kinetics equations are integrated into DEFORM software. The simulated DRX features are consistent with the test results, indicating that the proposed DRX kinetics equations and the established grain-growth model can be well used for describing the microstructure evolution. So, they are very useful for the practical hot forming of P/M superalloy parts.

Molecular dynamics studies of grain boundary mobility and anisotropy in BCC γ-uranium

Grain morphologies such as grain size and aspect ratio in uranium-based metallic fuels are important microstructural features that can impact various fuel performance properties such as fission-gas-induced swelling, thermal transport, high burnup structure formation, and radiation resistance. Accurate prediction of the fuel grain morphologies requires knowledge of critical grain growth parameters such as grain boundary (GB) mobility and anisotropy. In this work, molecular dynamics (MD) simulations were performed to study the GB mobility and its anisotropy in pure body-centered-cubic (BCC) γ uranium. Nine GBs with different combinations of misorientation angles (20°, 30°, 45°) and rotation axes (<100>, <110>, <111>), as well as an additional <111> 38.2° GB were studied using three interatomic potentials. It is found that the GB mobility anisotropy has complex trends, depending on both rotation axis and misorientation. However, in general the <110> rotation axis has the fastest GB mobility at the same misorientation. The results of this work can be used as not only a baseline for future studies of GB mobility in uranium-based alloys such as uranium-molybdenum (U-Mo) fuels, but also input for mesoscale modeling of grain growth in uranium-based alloys.

Level-Set Modeling of Grain Growth in 316L Stainless Steel under Different Assumptions Regarding Grain Boundary Properties.

Two finite element level-set (FE-LS) formulations are compared for the modeling of grain growth of 316L stainless steel in terms of grain size, mean values, and histograms. Two kinds of microstructures are considered: some are generated statistically from EBSD maps, and the others are generated by the immersion of EBSD data in the FE formulation. Grain boundary (GB) mobility is heterogeneously defined as a function of the GB disorientation. On the other hand, GB energy is considered as heterogeneous or anisotropic, which are, respectively, defined as a function of the disorientation and both the GB misorientation and the GB inclination. In terms of mean grain size value and grain size distribution (GSD), both formulations provide similar responses. However, the anisotropic formulation better respects the experimental disorientation distribution function (DDF) and predicts more realistic grain morphologies. It was also found that the heterogeneous GB mobility described with a sigmoidal function only affects the DDF and the morphology of grains. Thus, a slower evolution of twin boundaries (TBs) is perceived.

Theoretical basis for phase field modeling of polycrystalline grain growth using a spherical-Gaussian-based 5-D computational approach

Using a previously developed phase field modeling method, where interface energies are described by spherical gaussians that allow the modeling of complex anisotropies, a new phase field model was developed to model 5-D anisotropy in polycrystalline grain growth. We present the use of quaternions, assigned to individual grains as orientations and misorientations for grain boundaries, as a means of simulating the ongoing mesoscale changes during anisotropic polycrystalline grain growth. The full 5-D landscape is scanned in MATLAB, and the grain boundary (GB) energy of each grain boundary is calculated from the continuous function developed by Bulatov et al. MATLAB is then used to find all local minima in the GB energy which are stored for use in the phase field model. The methodology of including these minima in the phase field model involves using 2-D gaussian switches, which match the misorientation between grains with misorientations for the GB energy minima. Within a threshold range of the minima misorientation, the switch activates a spherical Gaussian to set the GB energy to the desired value creating in combination a full 5D GB energy space. This creates a GB energy that morphs in real time and space as the GB plane or grain orientations change. Implementation methods of the model are outlined for the Multiphysics Object Oriented Simulation Environment (MOOSE), where reduced order parameters still retain individual grain identification useful for individually assigned quaternions.

Microscale residual stresses in additively manufactured stainless steel: Computational simulation

Metal additive manufacturing (AM) has attracted much attention in recent years due to its ability of producing parts with complex geometry. Unfortunately, the large temperature gradient during fabrication leads to residual stresses which undesirably result in distortion and even crack of as-built parts. A computational framework is used to study how residual stresses form and evolve in AM parts at the length scale of individual grains, including a multi-physics thermal-fluid flow model, a phase field model for grain growth and a crystal plasticity finite element model. First, this framework is validated by comparing the lattice strain with experimental results in different grain families in two samples made of 316L stainless steel, which were produced by laser powder-bed-fusion with two different sets of process parameters. The relationship between residual stress, plastic strain and grain orientation near the top surface of the samples is then investigated. The residual stresses are observed to form during laser scanning due to compression followed by tension around the molten pool, thus the shape of the molten pool has a significant influence on the residual stress distribution. Redistribution of the plastic deformation during cooling stage is predicted and the residual stresses with greater magnitude occur along the laser scanning direction. This work provides useful insight into the mechanism of microscale residual stress generation and evolution in AM parts.

A numerical model of grain growth

Abstract A numerical model for grain growth has been developed. The governing equations for the model are derived from a variational principle that enforces the balance between energy dissipation and changes of internal energy. This approach significantly simplifies previous modelling of grain growth by replacing a curved grain boundary with several straight lines and relaxing constraints on triple point angles. Such simplifications provide a basis for a finite element method by reducing the analysis of a complex network of interconnected curved lines to the motion of interacting points. In the finite element formulation two approaches are used, namely an element based formulation and a node based formulation. In the latter case, the properties of the elements are lumped together at their common nodes. Such an approach allows the nodal velocity to be determined independently of the forces on other nodes in a lumped mobility methodology, leading to a further reduction of computer time. Several planar grain networks of Voronoi polygons have been studied. The evolution of the grain structures determined from these two approaches is found to exhibit the same trends as those obtained using other models published in the literature. Owing to its simplicity, the node based formulation is recommended.

The impact of anisotropic thermal expansion on the isothermal annealing of polycrystalline [formula omitted]-uranium

Although grain growth impacts microstructural evolution in a wide variety of materials systems, the effect of anisotropic thermal expansion on grain boundary mobility and texture evolution has not been widely studied. Anisotropic thermal expansion occurs in multiple non-cubic metals, and the thermomechanical processing behavior of these materials can be better understood with further study into the impact of thermal expansion on grain boundary mobility and texture evolution. In this work, we develop a mesoscale phase field model of grain growth that includes the effect of anisotropic thermal expansion, which is applied to study polycrystalline α-uranium, a highly anisotropic metal. Three-dimensional simulations on polycrystalline α-uranium with and without thermal expansion eigenstrains are performed to study the grain boundary mobility and texture evolution as a function of temperature. A strain-free temperature of 933 K is selected, and the system is studied within the range of 873–933 K at intervals of ten degrees, resulting in increasing thermal eigenstrain with decreasing temperature. We also estimate a grain boundary mobility prefactor and activation energy based on existing experimental data of isothermal annealing of α-uranium. The grain boundary mobility is found to display significant deviation from Arrhenius behavior with the inclusion of thermal expansion eigenstrain as the amount of thermal eigenstrain (and thus elastic strain energy within the system) increases. This result explains an experimentally observed grain boundary mobility deviation from Arrhenius behavior. Furthermore, the texture evolution is affected, such that the grain orientations become less random with increasing thermal eigenstrain, which could explain experimentally observed texture behavior. These results indicate that the effect of thermal expansion should be considered when predicting the thermomechanical processing behavior of α-uranium and other materials with anisotropic thermal expansion.

Study on as-cast microstructure of Fe-15Mn-10Al-5Ni-0.8C low density duplex steel

The microstructure of Fe-15Mn-10Al-5Ni-0.8C low density duplex steel ingots was studied by laser confocal scanning calorimetry , metallographic microscopy and scanning electron microscopy. The results indicated that: the microstructure of Fe-15Mn-10Al-5Ni-0.8C low density steel was mainly composed of coarse austenite dendrites and δ-ferrite phase in dendrite. The δ-ferrite could be completely eliminated by solution treatment. A dynamic model of austenite grain growth was established. Through analysis, it was concluded that the critical temperature for rapid austenite growth was 1250 °C. The activation energy for austenite grain growth was 365 KJ/mol as calculated by Sellars’ model.

Ultrasonic additive manufacturing of nanocrystalline laminated composites

Ultrasonic additive manufacturing has been used to fabricate laminated composites of commercially pure aluminum and a nanocrystalline nickel–cobalt (nc-NiCo) alloy. The nc-NiCo alloy would not weld to itself but readily welded to aluminum. Thus, by alternating between foils of nc-NiCo and Al, we achieved multi-material laminates with strong interlayer bonding. Electron microscopy showed that the nanoscale grain structure of the nc-NiCo was preserved during deposition and that the nc-NiCo/Al weld interface was decorated with comminuted surface oxides as well as Al–Ni–Co intermetallics. These findings are considered in light of process models of junction growth, interdiffusion, and grain growth, which together reveal how the different pressure- and temperature dependences of these phenomena give rise to a range of processing conditions that maximize bonding while minimizing coarsening and intermetallic formation. This analysis quantitatively demonstrates that using a soft, low melting point interlayer material decouples junction growth at the weld interface from grain growth in the nc-NiCo, expanding the range of optimal processing conditions.Graphical abstract

The Characterization of the Dust Content in the Ring Around Sz 91: Indications of Planetesimal Formation?

Abstract One of the most important questions in the field of planet formation is how millimeter- and centimeter-sized dust particles overcome radial drift and fragmentation barriers to form kilometer-sized planetesimals. ALMA observations of protoplanetary disks, in particular transition disks or disks with clear signs of substructures, can provide new constraints on theories of grain growth and planetesimal formation, and therefore represent one possibility for progress on this issue. We here present ALMA band 4 (2.1 mm) observations of the transition disk system Sz 91, and combine them with previously obtained band 6 (1.3 mm) and band 7 (0.9 mm) observations. Sz 91, with its well-defined millimeter ring, more extended gas disk, and evidence of smaller dust particles close to the star, constitutes a clear case of dust filtering and the accumulation of millimeter-sized particles in a gas pressure bump. We compute the spectral index (nearly constant at ∼3.34), optical depth (marginally optically thick), and maximum grain size (∼0.61 mm) in the dust ring from the multi-wavelength ALMA observations, and compare the results with recently published simulations of grain growth in disk substructures. Our observational results are in strong agreement with the predictions of models for grain growth in dust rings that include fragmentation and planetesimal formation through streaming instability.

Millimeter-sized Dust Grains Surviving the Water-sublimating Temperature in the Inner 10 au of the FU Ori Disk

Abstract Previous observations have shown that the ≲10 au, ≳400 K hot inner disk of the archetypal accretion outburst young stellar object, FU Ori, is dominated by viscous heating. To constrain dust properties in this region, we have performed radio observations toward this disk using the Karl G. Jansky Very Large Array in 2020 June–July, September, and November. We also performed complementary optical photometric monitoring observations. We found that the dust thermal emission from the hot inner disk mid-plane of FU Ori has been approximately stationary and the maximum dust grain size is ≳1.6 mm in this region. If the hot inner disk of FU Ori, which is inward of the 150–170 K water snowline, is turbulent (e.g., corresponding to a Sunyaev &amp; Shakura viscous α t ≳ 0.1), or if the actual maximum grain size is still larger than the lower limit we presently constrain, then as suggested by the recent analytical calculations and the laboratory measurements, water-ice-free dust grains may be stickier than water-ice-coated dust grains in protoplanetary disks. Additionally, we find that the free–free emission and the Johnson B- and V-band magnitudes of these binary stars were brightening in 2016–2020. The optical and radio variability might be related to the dynamically evolving protostellar- or disk-accretion activities. Our results highlight that the hot inner disks of outbursting objects are important laboratories for testing models of dust grain growth. Given the active nature of such systems, to robustly diagnose the maximum dust grain sizes, it is important to carry out coordinated multiwavelength radio observations.

Modeling of abnormal grain growth in (111) oriented and nanotwinned copper

Uni-modal, not bi-modal, of abnormal grain growth has been observed in (111) oriented and nano-twinned Cu films. Because of the highly anisotropic microstructure, our kinetic analysis and calculation showed that it is the mobility which dominates the uni-modal growth, in which the lateral growth rate can be two orders of magnitude higher than the vertical growth rate. As a consequence, the abnormal grain growth has been converted from bi-modal to uni-modal.

Grain Growth in Escaping Atmospheres: Implications for the Radius Inflation of Super-Puffs

Abstract Super-puffs—low-mass exoplanets with extremely low bulk density—are attractive targets for exploring their atmospheres and formation processes. Recent studies suggested that the large radii of super-puffs may be caused by atmospheric dust entrained in the escaping atmospheres. In this study, we investigate how the dust grows in escaping atmospheres and influences the transit radii using a microphysical model of grain growth. Collision growth is efficient in many cases, hindering the upward transport of dust via enhanced gravitational settling. We find that the dust abundance in the outflow hardly exceeds the Mach number at the dust production region. Thus, dust formed in the upper atmospheres, say at P ≲ 10−5 bar, is needed to launch a dusty outflow with a high dust abundance. With sufficiently high dust production altitudes and rates, the dusty outflow can enhance the observable radius by a factor of ∼2 or even more. We suggest that photochemical haze is a promising candidate of high-altitude dust that can be entrained in the outflow. We also compute the synthetic transmission spectra of super-puff atmospheres and demonstrate that the dusty outflow produces a broad spectral slope and obscures molecular features, in agreement with featureless spectra recently reported for several super-puffs. Lastly, using an interior structure model, we suggest that the atmospheric dust could drastically enhance the observable radius only for planets in a narrow mass range of ∼2–5 M ⊕, in which the boil-off tends to cause total atmospheric loss. This may explain why super-puffs are uncommon despite the suggested universality of photochemical hazes.

Microstructural evolution and grain-growth kinetics of Al0.2CoCrFeNi high-entropy alloy

ABSTRACT Grain-growth kinetics of high-entropy, single-phase, face-centred cubic (FCC) Al0.2CoCrFeNi alloy was studied by isothermal annealing over a wide temperature range for different time intervals. Both optical and EBSD studies show a significant amount of annealing twins. Data were analysed using classical grain-growth models and the activation energy was estimated using the Arrhenius type equation. The grain-growth exponent was found to be n = 3 and the measured activation energy for grain growth was 190 ± 15 kJ mol−1. Significant resistance to grain growth was observed at 1100°C. Microstructural characterisation tools like EBSD, along with nanoindentation, was used to understand the observed behaviour.

Phase-field modeling of magnetic field-induced grain growth in polycrystalline metals

A constitutive model for diffuse interface description of magnetic field-induced grain boundary migration in polycrystalline metals is developed based on the laws of thermodynamics. Within this phase field modeling framework, simultaneous minimization of the total grain boundary energy and the stored magnetic energy within grains provides the driving force for grain growth in a polycrystal material exposure to a magnetic field. Using the available experimental data, phase field simulations of magnetic field induced grain growth in bicrystalline zinc and polycrystalline titanium with two-dimensional columnar microstructure are performed and the model is validated by demonstrating a qualitative and quantitative match with experimental data. Using the validated constitutive model, the effects of magnetic field intensity and direction on evolution of microstructure and polycrystalline texture in titanium are investigated. Quantitative simulation results show that under certain magnetic field directions and sufficient magnetic field intensity, the magnetic energy minimizing driving force can overcome the curvature driving force and cause texture evolution towards less magnetic energy grain orientations during annealing. However, magnetic fields with insufficient intensity or improper direction have negligible effect on grain coarsening by nearly normal grain growth. The desired magnetic field direction and intensity are quantitatively presented for cold-rolled and annealed sheet titanium samples.

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.

Modelling of Microstructure Evolution during Laser Processing of Intermetallic Containing Ni-Al Alloys

There is a growing interest in laser melting processes, e.g., for metal additive manufacturing. Modelling and numerical simulation can help to understand and control microstructure evolution in these processes. However, standard methods of microstructure simulation are generally not suited to model the kinetic effects associated with rapid solidification in laser processing, especially for material systems that contain intermetallic phases. In this paper, we present and employ a tailored phase-field model to demonstrate unique features of microstructure evolution in such systems. Initially, the problem of anomalous partitioning during rapid solidification of intermetallics is revisited using the tailored phase-field model, and the model predictions are assessed against the existing experimental data for the B2 phase in the Ni-Al binary system. The model is subsequently combined with a Potts model of grain growth to simulate laser processing of polycrystalline alloys containing intermetallic phases. Examples of simulations are presented for laser processing of a nickel-rich Ni-Al alloy, to demonstrate the application of the method in studying the effect of processing conditions on various microstructural features, such as distribution of intermetallic phases in the melt pool and the heat-affected zone. The computational framework used in this study is envisaged to provide additional insight into the evolution of microstructure in laser processing of industrially relevant materials, e.g., in laser welding or additive manufacturing of Ni-based superalloys.

Investigating the Calcination and Sintering of Li7La3Zr2O12 (LLZO) Solid Electrolytes Using Operando Synchrotron X-ray Characterization and Mesoscale Modeling

The crystallographic structure and microstructure of solid electrolytes, such as Li7La3Zr2O12 (LLZO), have a profound impact on their reactivity, conductivity, and stability toward dendrites in solid-state batteries. Controlling the material’s structure and morphology requires fine control during the synthesis process, where multiple conditions (precursor particle size/distribution, calcination/sintering temperature, ramp rate, etc.) influence performance. This paper describes, for the first time, the operando characterization of the calcination process using synchrotron X-ray diffraction combined with a mesoscale model of grain growth during the calcination and densification of LLZO. The model is then used to guide synthesis conditions to enhance the densification process. The X-ray data reveal significant coarsening of the initial nanophase lanthanum zirconate precursors during conversion to LLZO. The mesoscale model shows that the activation energy for diffusion during calcination is lower than that during sintering, indicating the inherent coupling between the chemical reaction and grain growth processes. Simulations suggest that particles with small and bimodal size distribution experience better densification, as does precise grading (smaller particles near the surface and larger particles at the center) of different-sized particles. The approach described here can be adapted to understand and guide the synthesis of other materials that undergo calcination and sintering (e.g., transition metal oxide cathodes).