Log-normal Grain Research Articles

Quantitative Indicators of Microstructure and Texture Heterogeneity in Polycrystalline System.

The microstructural features of polycrystals determine numerous properties, whereas the evolution of crystallographic texture is responsible for the anisotropy of particular properties. Therefore, it is of crucial importance to find proper quantitative indicators, which reflect the nature of microstructure and texture characteristics. This is partially performed by the assessment of the average grain size and texture intensity that provide basic information on the microstructural features evolved; however, often, the basic quantitative indicators are not capable of revealing the complete microstructural state especially when the system is highly heterogeneous. This contribution presents various methods to assess the degree of microstructural heterogeneity, while the crystallographic aspect of microstructure evolution is characterized by several indicators of texture heterogeneity. Numerous synthetic microstructures with normal, lognormal, and bimodal grain size distributions as well as their combinations are analyzed to evaluate the applicability of the methods presented in this study. The quantitative indicators described in the frame of this contribution are likewise tested on experimentally observed microstructures. It is shown that the derived coefficients of microstructure heterogeneity correlate well with the standard deviation in grain size distribution, Gini, and Hoover coefficients, while the quantitative measures of texture heterogeneity are capable of revealing hidden aspects of microstructure evolution.

Investigation on Surface Integrity in Milling of Inconel X750: A Comprehensive analysis of Cutting Edges and Machining Parameters

For over a century, machining has been a crucial manufacturing method, with milling standing out as a versatile and effective process for various engineering materials. Ni-based superalloys, renowned for their exceptional properties, present challenges in machining, causing excessive tool wear and surface quality issues. Techniques such as heat treatments, environmental adjustments, and tool geometry alterations are employed to mitigate tool wear and affect surface integrity, crucial for determining the quality of machined work materials, especially in high-strength superalloys where shear deformation induces grain misorientation. In this research article, an experimental study was carried out to find the impact of the different cutting edges on surface integrity while milling Inconel X750. Response Surface Methodology was employed using a central composite rotatable design of experiments to investigate the surface roughness of the machined sample under various cutting conditions. A thorough analysis was undertaken to explore the surface integrity of Inconel X750, involving variations in milling machining parameters (i.e., low, mid, and high) and the utilization of diverse cutting tool inserts. The investigation centred on analysing the sub-surface microstructure, texture, and residual stresses of the machined surface, aiming to achieve a comprehensive understanding of the material's surface characteristics. The double-coated cutting tool T2, with a diameter of 0.8 mm, exhibited superior performance in surface quality and grain distribution, particularly at low cutting parameters (feed rate: 0.15 mm/rev, cutting speed: 35 mm/min, depth of cut: 0.1 mm), showing fine equiaxed and lognormal grain distribution alongside low residual stresses (−36.8 MPa compressive, maximum shear residual stresses: 7.2 MPa) and a surface roughness of 0.17 μm.

Multiscale stress and strain statistics in the deformation of polycrystalline alloys

Multiscale stresses and strains in polycrystalline metals are always inhomogeneous. In this study, a rate-independent crystal plasticity formulation was implemented for a cubic representative volume element (RVE) of an fcc polycrystal generated by 3D Delaunay tessellation. Multiple realizations were generated with crystallographic orientation permutations and different grain morphologies in order to investigate the statistical distribution of stress, elastic lattice strain and total strain at the macro-, meso- and micro-scale. Macroscopically, at 1.55% total strain (elasto-plastic deformation), the overall stress statistics among different RVEs were observed to follow a normal distribution, whose profile shape is affected by the parameters that describes the lognormal grain size distribution. On the mesoscale, the orientation-specific elastic strains were accurately reproduced via the use of diffraction post-processing and validated by neutron diffraction data for a polycrystalline alloy. Microscopically, the local elastic strains (and hence stresses) universally follow a normal distribution, while plastic strains follow a lognormal probability distribution. Reliable knowledge of the statistical distributions of stresses and strains give new guidance for the determination of the minimum RVE size. The above finding reveals the nature of stress and strain inhomogeneity at multiple scales and emphasizes the fact that the dispersion of local stress and strain is much larger than that of the macroscopic average. The statistical analysis of stress and strain distribution at multiple scales provide further rich insights into the connection between microstructure and mechanical properties under monotonic and cyclic loading.

Acoustic Backscatter and Attenuation Due to River Fine Sediments: Experimental Evaluation of Models and Inversion Methods

AbstractThe hydroacoustic monitoring of suspended sediment concentration (SSC) in rivers is based on the inversion of backscatter and attenuation models. To evaluate such models, acoustic backscatter and attenuation were measured from a homogeneous suspension of fine river sediments (clay) in a laboratory tank at various concentrations in the range 1–18 g/l. Agreement between the modeled and measured acoustic backscatter and attenuation values was found to be relatively poor. The results are highly sensitive to particle size and shape which come with large measurement uncertainties and they can be significantly improved by adjusting plausible particle parameters. Various inversion methods combining single or multiple frequencies, analysis of backscatter and/or attenuation, spherical or oblate shape hypothesis for particles and fixed or estimated lognormal grain size distribution are tested. The most promising inversion methods using both backscatter and attenuation information led to accurate SSC estimates.

Relevance of processing parameters for grain growth of metal halide perovskites with nanoimprint

The quality and the stability of devices prepared from polycrystalline layers of organic–inorganic perovskites highly depend on the grain sizes prevailing. Tuning of the grain size is either done during layer preparation or in a post-processing step. Our investigation refers to thermal imprint as the post-processing step to induce grain growth in perovskite layers, offering the additional benefit of providing a flat surface for multi-layer devices. The material studied is MAPbBr3; we investigate grain growth at a pressure of 100 bar and temperatures of up to 150 °C, a temperature range where the pressurized stamp is beneficial to avoid thermal degradation. Grain coarsening develops in a self-similar way, featuring a log-normal grain size distribution; categories like ‘normal’ or ‘secondary’ growth are less applicable as the layers feature a preferential orientation already before imprint-induced grain growth. The experiments are simulated with a capillary-based growth law; the respective parameters are determined experimentally, with an activation energy of Q ≈ 0.3 eV. It turns out that with imprint as well the main parameter relevant to grain growth is temperature; to induce grain growth in MAPbBr3 within a reasonable processing time a temperature of 120 °C and beyond is advised. An analysis of the mechanical situation during imprint indicates a dominance of thermal stress. The minimization of elastic energy and surface energy together favours the development of grains with (100)-orientation in MaPbBr3 layers. Furthermore, the experiments indicate that the purity of the materials used for layer preparation is a major factor to achieve large grains; however, a diligent and always similar preparation of the layer is equally important as it defines the pureness of the resulting perovskite layer, intimately connected with its capability to grow. The results are not only of interest to assess the potential of a layer with respect to grain growth when specific temperatures and times are chosen; they also help to rate the long-term stability of a layer under temperature loading, e.g. during the operation of a device.

Can ultrasound attenuation measurement be used to characterise grain statistics in castings?

Industrial inspection protocols are qualified using mock-ups manufactured according to the same procedure as the plant part. For coarse-grained castings, known for their low inspectability, relying on mock-ups becomes particularly challenging owing to the variability of grain properties among components. Consequently, there is a keen interest in the capability to verify whether the grain size of the component under test matches the qualification specification in-situ. This paper investigates the potential of an attenuation measurement for assessing the ultrasonic inspectability of coarse-grained components using qualified procedures in a practical setting. The experimental part of the study focuses on an industrial Inconel 600 mock-up with spatially varying attenuation, measured across the entire sample in an immersion tank. Three zones with distinctly different attenuations were examined using metallography, which allowed for calculating classical grain size histograms and two-point correlation functions. For one of the zones, we synthesised the microstructure with the same statistical properties numerically and simulated the propagation of ultrasound using a grain-scale finite element model. The results showed good agreement with the experiment, and lead to several suggestions for the reasons for the discrepancy, the varying grain size statistics being the most likely. A parametric study, which followed, depicted the effect of the mean and standard deviation-to-mean ratio of the log-normal grain size distribution on the attenuation of ultrasound and its frequency dependence. Most notably, we demonstrated the known non-uniqueness of the relationship between the log-normal grain size distribution parameters and the attenuation. We suggested that the correlation length calculated from a single exponential fit to the two-point correlation function is a more robust metric describing grain statistics for this context, which can be obtained from attenuation. The correlation lengths estimated from measured attenuation using the second-order approximation model for the three zones of the studied mock-up yielded results of acceptable accuracy. We concluded that this metric could replace the average grain size in practical settings, as it retains more statistical information than the mean grain size and allows for linking measurements to the established theoretical attenuation models which this paper demonstrates.

Analysis and Optimization of Threshold Voltage Variability by Polysilicon Grain Size Simulation in 3D NAND Flash Memory

The impact of linear correlation between lognormal distribution grain size mean and sigma along the polysilicon channel on threshold voltage (Vth) variability has been investigated in three dimensional (3D) NAND flash. The variety of grain size mean and sigma results in the unstable Vth variability. To obtain a stable Vth distribution with various grain size mean, the grain size mean dependent Vth variability sensitivity to the grain size sigma was used to optimize the linear correlation between grain size mean and sigma via TCAD simulation. The optimized linear correlation with stable Vth variability is obtained except for the “unbalance region” affected by the combination of grain boundaries and positions with these grain size mean and sigma values resulting in the slightly shrinking Vth variability. Our results strongly suggest that this approach could guide the direction of polysilicon crystallization optimization to obtain stable Vth distribution with the predicted linear correlation between grain size mean and sigma.

Two-dimensional Monte Carlo–Voronoi simulation of grain growth and nucleation in the heat affected zone of TWIP-Ti welds

The microstructural simulation of grain growth and static recrystallization (SRX) phenomena were simulated in the weld heat-affected zone (HAZ) in Twinning Induced Plasticity (TWIP) steel microalloyed with Ti by means of a 2D Monte Carlo (MC) model combined with Voronoi tessellations (MC-Voronoi) based on experimental data. The simulation considered the effect of different levels of heat input for the Gas Tungsten Arc Welding (GTAW) process in the microstructural field. The MC-Voronoi model estimated the number of grains with annealing twins in TWIP-Ti steel specimens in both as-solution and post-welding conditions. Through the application of modified probabilities for both growth and recrystallization, the proposed microstructural model allowed the simulation of microstructures with lognormal and bimodal grain size distributions. The high microstructure reproducibility and grain morphology predicted by the Voronoi tessellation were improved by means of an image post-processing performed in MATLAB®. A good agreement was obtained between experimental and microstructural simulation results; the validation process was carried out by means of grain size statistical analysis.

Anhysteretic remanent magnetization: model of grain size distribution of spherical magnetite grains

A phenomenological model based on a linear relationship between the magnetic coercivity field and the reciprocal of the grain diameter is applied to explain the anhysteretic remanent magnetization (ARM) imparted to artificial samples with different concentrations of a very well characterized magnetite powder. By analyses of scanning electron microscopy images, the spherically shaped single domain synthetic magnetite is found to follow a lognormal grain size distribution with ~86 nm of mean diameter. The proposed model, fitted to ARM measurements up to a peak alternating field of 100 mT, yields a very good agreement. The coercivity behaviour predicted by micromagnetism theory disagrees with the experimental results of this work. A likely explanation for the discrepancy is that the magnetite particles, which consist of a mixture of grains in coherent rotation and curling modes, produce similar observations as domain processes.

Two-point statistics of synthetic three-dimensional polycrystalline microstructures

The two-point spatial statistics of a heterogeneous material are crucial in ultrasonic attenuation and backscatter calculations. In this presentation, several common assumptions used for modeling polycrystals are examined. In most studies, the spatial and tensorial elements of the covariance function are assumed to be decoupled. Also, two-point correlation models often assume a single effective grain size for polycrystalline materials and a spatial correlation function that has an exponential decay at a rate directly proportional to the average grain diameter. This investigation uses the Dream.3D software platform to generate three-dimensional (3D) realizations of polycrystalline materials in order to study their two-point statistics. Using lognormal distributions with fixed means but different widths, a variety of different polycrystalline microstructures are simulated. The results show that the spatial correlation function is directly influenced by the grain size distribution. For a fixed mean grain size, wider distributions exhibit longer range correlations than narrower ones. The results also show that decoupling of the tensorial and spatial elements of the covariance function may not be valid for all lognormal grain size distributions. These results are anticipated to have an important impact on ultrasonic attenuation and backscatter models. [Research supported by AFRL under prime contract FA8650-15-D-5231.]

A molecular-dynamics study of the tensile deformation and fracture behavior of nanostructured lithium aluminum oxide

Three-dimensional nanocrystalline models of LiAlO2 with the log-normal grain size distribution are constructed with constrained Voronoi tessellation. First, the relaxation procedure of nanostructured LiAlO2 is carried out using molecular dynamics. The results suggest a reduction in the atomic densities after the relaxation process. Next, the tensile deformation and fracture behavior of nanostructured LiAlO2 are studied by using the optimized model. By researching the tensile deformation and fracture behavior of nanostructured LiAlO2, we find some interesting results: on the one hand, the greater the average grain size of the sample is, the stronger its tensile strength. On the other hand, after the strain reaches approximately 3% of the deformation of the sample, the stress of the sample does not change with the increase of the strain, displaying a plastic flow of the plastic material.

Modeling the copper microstructure and elastic anisotropy and studying its impact on reliability in nanoscale interconnects

BackgroundCopper is the primary metal used in integrated circuit manufacturing of today. Even though copper is face centered cubic it has significant mechanical anisotropy depending on the crystallographic orientations. Copper metal lines in integrated circuits are polycrystalline and typically have lognormal grain size distribution. The polycrystalline microstructure is known to impact the reliability and must be considered in modeling for better understanding of the failure mechanisms.MethodsIn this work, we used Voronoi tessellation to model the polycrystalline microstructure with lognormal grainsize distribution for the copper metal lines in test structures. Each of the grains is then assigned an orientation with distinct probabilistic texture and corresponding anisotropic elastic constants based on the assigned orientation. The test structure is then subjected to a thermal stress.ResultsA significant variation in hydrostatic stresses at the grain boundaries is observed by subjecting the test structure to thermal stress due to the elastic anisotropy of copper. This introduces new weak points within the metal interconnects leading to failure.ConclusionsInclusion of microstructures and corresponding anisotropic properties for copper grains is crucial to conduct a realistic study of stress voiding, hillock formation, delamination, and electromigration phenomena, especially at smaller nodes where the anisotropic effects are significant.

A multilevel approach to the evolutionary generation of polycrystalline structures

The Poisson–Voronoi tessellation is commonly used as an approximation to the microstructure of polycrystalline material. Although simple, this approximation fails to respect basic physical properties observed empirically, including the generally lognormal distribution of grain sizes. Stochastic approximations such as genetic algorithms can be used to adjust a Poisson–Voronoi tessellation to better reflect such a distribution. We apply techniques from multilevel optimisation to give a new approach to the evolutionary generation of polycrystalline structures, in a way that allows approximation of a target lognormal grain size distribution with unit mean and arbitrary variance. Results obtained through this method indicate almost perfect distribution fitting, show up to two orders of magnitude improvement in the number of evolutionary steps required for an acceptable fit, and suggest a reduction of the overall problem complexity from Θ(N3) to Θ(N2).

Constructing three-dimensional (3D) nanocrystalline models of Li4SiO4 for numerical modeling and simulation.

The three-dimensional (3D) nanocrystalline models of lithium silicates with the log-normal grain size distribution are constructed by constrained Voronoi tessellation. During evolution process, the algorithm is improved. We proposed a new algorithm idea by combining Genetic Algorithm (GA) with Least Square (LS) method to make up for the disadvantages of traditional genetic algorithm which may be easily trapped in local optimal solution. In the process of modeling, it is the first time, to the best of our knowledge, that we keep the whole sample showing the charge neutrality by deleting the excess atoms on the polyhedron boundary during the modeling. By using the molecular-dynamics method, the relaxation procedure of nanostructured Li4SiO4 is carried out. The results show that the average mass density of the sample is slightly lower than the experimental data of the perfect crystal after relaxation process. In addition, boundary component proportion (BCP) and density reduction proportion (DRP) of the sample is obtained, respectively. The present results display a significantly reduced BCP but an increased DRP when increasing the mean grain size of the sample.

Generalised Voronoi tessellation for generating microstructural finite element models with controllable grain-size distributions and grain aspect ratios

Summary A generalised Voronoi tessellation is proposed to create three-dimensional microstructural finite element model, which can effectively reproduce the grain size distribution and grain aspect ratio obtained from experiments. This new approach consists of two steps. The first step generates the desired lognormal grain size distribution with a given average grain volume and standard deviation. The second step requires grouping meshed elements to create a specific grain aspect ratio, using the Voronoi generators from the first step. A new concept is introduced to describe the transition from the Poisson–Voronoi tessellation to the centroidal Voronoi tessellation. More importantly, instead of using the conventional way where the Voronoi cells are first generated and then meshed into finite elements, this new approach discretises the pre-meshed specimen with the Voronoi generators. This new technique prevents the presence of high density mesh at the vertices of Voronoi cells, and can tessellate irregular geometry much more easily. Examples of microstructures with different size distributions, non-equiaxed grains and complicated specimen geometries further demonstrate that the proposed approach can offer great flexibility to model various specimen geometries while keeping the process simple and efficient. Copyright © 2015 John Wiley & Sons, Ltd.

Grain growth, anomalous scaling, and grain boundary grooving in polycrystalline CdTe thin films

We examine the evolution of the surface morphology as well as the dynamics of grain growth and grain boundary (GB) grooving in polycrystalline CdTe films sputter deposited on CdS/glass substrates. Anomalous scaling behavior is found with local roughness exponent αloc = 1 and global (local) growth exponent β = 0.36 (βloc = 0.14). In good agreement with the scaling relation, βloc = β − nαloc, we obtain the correlation length exponent n=1/z≃0.23. We also find that the grain size coarsening exponent p and GB groove growth exponent βg are both equal to β, while the grain size distribution is well described by a log-normal distribution. These results suggest that GB grooving is responsible for the enhanced anomalous scaling and a deviation from the theoretical prediction of p = 1/2, along with the observed log-normal grain size distribution.

Microstructure Evolution of nc-TiN/a-(C, CNX) Nanocomposite Films with Different Amorphous Phase Amounts

The microstructure evolution of two-phase nanocomposite Ti-C-N thin films grown by reactive close-field unbalanced magnetron sputtering in an Ar-N2 gas mixture with microstructures comprising of nanocrystalline (nc-) Ti(N,C) phase surrounded by amorphous (a-) (C,CNx) matrix under different a-phase amounts have been investigated by using high-resolution transmission electron microscopy and Monte Carlo simulation. The results show that with the a-phase amounts increasing, the grain size decreasing and a size-dependent lognormal grain size distribution have been found in nanocomposite films. The formation mechanism of this microstructure evolution is attributed to the transformation of grain growth mode from the nc/nc-boundary-curvature-driven growth to the a/nc-boundary-curvature-driven growth accompanied with a convergence of energy on per grain boundary with grain size decreasing (i.e. a-phase amount increasing), leading to the tendency from the off-lognormal size distribution to the lognormal one. When a-phase amount increases to about 28% with grain size reducing to let per grain boundary covered by one monolayer a-phase, the uniform diffusion-controlled growth is dominant, resulting in the lognormal grain size distribution. This study suggests an important implication to prepare the nanocomposite films with a well-controlled nanostructure.

Size dependence of the Curie temperature of L1o-FePt nanoparticles

Monte Carlo simulations using the single histogram method are performed to study the effects of finite size and Cu doping on the Curie temperature of a single FePt nanoparticle. An atomistic model is used with an effective classical spin Hamiltonian constructed on the basis of first-principles calculations for L1o FePt. The Curie temperature, evaluated from the peak in the temperature variation of the magnetic susceptibility, is consistent with the finite-size scaling relation Tc(L)=Tc(∞)(1−xoL−1/ν), where L is the in-plane grain size, xo is found to depend on the grain aspect ratio, and the critical exponent of the correlation length is ν=1.06±0.06. A theoretical relation is obtained for the Tc dispersion arising from a lognormal grain size distribution. Addition of Cu results in reduction of the Curie temperature proportional to the dopant content.

Grain Coarsening – Insights from Curvature Modeling Cyril Stanley Smith Lecture

Normal and abnormal grain coarsening, NGC and AGC, are briefly reviewed and discussed in the light of grain curvature and kinetic models - notably those of Mullins. The critical importance of the log-normal grain size distribution determined by Hull and the grain shapes measured by Rhines and Craig are reviewed. It is shown that in NGC, as in particle coarsening, the largest grains or particles in their respective distributions grow at the rates, larger by a factor of the ratio of the largest to average size, required to maintain the size distributions during coarsening. The particle curvature removal model for NGC anchorage, giving = 0.2 r/f, developed here, matches surprisingly well the data reviewed by Manohar et al. Finally the need is indicated for further experimental and modeling studies to test the current ideas and to answer the many remaining questions.

Effect of grain size distribution and texture on the cold extrusion behavior and mechanical properties of AZ31 Mg alloy

An experimental investigation into the cold extrusion and the subsequent annealing processes of an Mg–2.8%Al–0.83%Zn (AZ31) Mg alloy was studied. Microstructures, grain size distribution and texture evolution of the as-extruded and as-annealed specimens were investigated by optical microscopy and electronic backscattered diffraction (EBSD). Tensile tests along the extrusion direction were carried out at room temperature. It is found that firstly, the uniform microstructure with log-normal grain size distribution led to homogeneous cold deformation and good appearance without cracks for the as-extruded rods; secondly, texture was able to soften the yield strength induced by grain refinement and even overcame the refined grain size effect; thirdly, well-distributed microstructure reduced the absolute difference of yield strength for the sub-micrometer-grain Mg alloys.