Single-phase Polycrystalline Materials Research Articles

Crystal plasticity finite element modelling on the influence of grain size and shape parameters on the tensile stiffness and yield strength

A highly parallelised three-dimensional finite element crystal plasticity framework is used to investigate the influence of grain sphericity, number of cross-sectional grains and grain size distribution on the tensile stiffness and yield strength in austenitic stainless steel. Open-source software packages Neper and FEpX were adopted to generate a wide range of synthetic 3D microstructures and to perform crystal plasticity simulations, respectively. Aspects of small-scale simulations with reasonable accuracy and caution in modelling the mechanical properties of thin and/or large grain size specimens are also discussed. This study aims to provide guidelines for estimating mechanical properties in single-phase polycrystalline materials exhibiting wide grain size distributions.

Statistical analysis of the parameters and grain size distribution functions of single-phase polycrystalline materials

A statistical analysis of the grain size distribution is important both for developing theories of the grain growth and microstructure formation, and for describing the size dependences of various characteristics of the physical and mechanical properties of polycrystalline materials. The grain size distribution is also an important characteristic of the structure uniformity and, therefore, stability of the properties of the products during operation. Statistical Monte Carlo modeling of single-phase and equiaxed polycrystalline microstructures was carried out to determine the type of statistically valid distribution function and reliable estimates of the average grain size. Statistical parameters (mean values, variances, variation coefficient) and distribution functions of the characteristics of the grain microstructure were obtained. It is shown that the distribution function of the effective grain sizes for the studied polycrystal model is most adequately described by γ-distribution, which is recommended to be used in analysis of the experimental distribution functions of grain sizes of single-phase polycrystalline materials with equiaxed grains. The general average (mathematical expectation) of the effective grain size (projection diameter) with γ-distribution function (parameters of the distribution function are to be previously determined in analysis of the grain structure of polycrystalline materials) should be taken as a statistically valid and reliable estimate of the average grain size. The results of statistical modeling are proved by the experimental data of metallographic study of the microstructures of single-phase model and industrial materials with different degree of the grain structure heterogeneity.

Phase-field simulations of microstructure evolution during physical vapor deposition of single-phase thin films

Physical vapor deposition (PVD) simulations are performed using a phase-field model to study microstructure evolution in single-phase polycrystalline materials as a function of deposition conditions. Specifically, this work focuses on the influence of (i) polycrystalline substrate microstructure with low-angle and high-angle grain boundaries (GBs), (ii) incident vapor flux rate, and (iii) model parameters controlling grain evolution dynamics. Simulation results show that low-angle and high-angle GBs in the substrate promote the formation of low-angle and high-angle GBs within the deposited thin film, in qualitative agreement with experimental reports. Changing the vapor flux rate has a significant influence on the deposited microstructure. A relatively low flux rate is found to provide a thin film with no subsurface porosity, smoothed surface roughness, and a mixture of grain sizes. With an increased vapor flux rate, uniformly distributed surface columnar features are observed with subsurface porosity. The GBs migrate during growth to align with these surface features. At the largest flux rate studied, a dendritic style microstructure is formed where the GBs tend to align with and grow along the regions of low phase density within the thin film. Finally, a parametric study is performed on the phase-field model grain evolution parameters to elucidate their role on grain boundary thickness, internal grain variations and grain rotation during simulated PVD.

Lattice Boltzmann models for the grain growth in polycrystalline systems

In the present work, lattice Boltzmann models are proposed for the computer simulation of normal grain growth in two-dimensional systems with/without immobile dispersed second-phase particles and involving the temperature gradient effect. These models are demonstrated theoretically to be equivalent to the phase field models based on the multiscale expansion. Simulation results of several representative examples show that the proposed models can effectively and accurately simulate the grain growth in various single- and two-phase systems. It is found that the grain growth in single-phase polycrystalline materials follows the power-law kinetics and the immobile second-phase particles can inhibit the grain growth in two-phase systems. It is further demonstrated that the grain growth can be tuned by the second-phase particles and the introduction of temperature gradient is also an effective way for the fabrication of polycrystalline materials with grained gradient microstructures. The proposed models are useful for the numerical design of the microstructure of materials and provide effective tools to guide the experiments. Moreover, these models can be easily extended to simulate two- and three-dimensional grain growth with considering the mobile second-phase particles, transient heat transfer, melt convection, etc.

Phase-field models for simulating physical vapor deposition and grain evolution of isotropic single-phase polycrystalline thin films

Two models are presented based on the phase-field methodology to simulate thin film growth during physical vapor deposition (PVD), including subsurface microstructure evolution, for isotropic single-phase polycrystalline materials. The first model couples previous phase-field modeling efforts on ballistic deposition of single-phase materials and grain orientation evolution in polycrystalline materials in a sequential simulation algorithm. The second model incorporates both PVD and grain evolution dynamics into a single free energy functional for use in a phase-field model. To illustrate the capability of the proposed models in capturing combined thin film growth and subsurface grain evolution, PVD simulations of a generic single-phase polycrystalline metal are performed on substrates with different grain sizes. In both models, when the initial substrate grain sizes are smaller than the expected surface features, the thin film grains coarsen via grain boundary (GB) migration until the GBs become aligned with the valleys between the columnar surface features. Thus, each columnar feature is associated with a distinct subsurface grain, in qualitative agreement with experimental observations. Differences between the models arise when initial substrate grain sizes are larger than the surface columnar features. For example, when using the single free energy functional approach, grains contain noticeable internal low-angle variations, which are not captured using the coupled model.

Elastic wave scattering in random anisotropic solids

Abstract A general ultrasonic scattering model for a polycrystal with arbitrary macroscopic texture and triclinic ellipsoidal grains is developed allowing the texture and grain orientation frames to be independent and the wave propagation direction arbitrary in those frames. Numerical examples are given for an approximate texture model exhibiting triclinic macroscopic symmetry for triclinic crystallites. The scattering coefficients are obtained from integrands of the attenuation coefficients recently derived elsewhere in the Born approximation for the same problem. The results obtained are reducible to the known scattering/backscattering coefficients for a macroscopically isotropic medium in the limit of negligible macroscopic anisotropy. The model is applicable to most single phase polycrystalline materials that may occur as a result of thermomechanical manufacturing processes leading to different macrotextures and ellipsoidal shaped grains. As in the macroscopically isotropic case, the scattering coefficients are factorized into an elastic factor dependent on the preferred crystallographic orientation of the grains and a frequency dependent geometric factor affected by grain size and shape. A general reciprocity relationship for the scattering coefficients is obtained and discussed. Simulation results are presented to shed light on the effect of texture, grain shape and nondimensional frequency on ultrasonic scattering. An approximation of the quasilongitudinal wave polarization, that neglects the deviation of the polarization vector from the propagation direction, on the backscattering coefficient is investigated and the error of the approximation is estimated.

Propagation and scattering of ultrasonic waves in polycrystals with arbitrary crystallite and macroscopic texture symmetries

A general ultrasonic attenuation model for a polycrystal with arbitrary macroscopic texture and triclinic ellipsoidal grains is described with proper accounting for the anisotropic Green’s function for the reference medium. The texture and the ellipsoidal grain frames in the model are independent and the wave propagation direction is arbitrary. The attenuation coefficients are obtained in the Born approximation accompanied by the Rayleigh and stochastic asymptotes. The scattering model displays statistical anisotropy due to two independent factors: (1) shape of the oriented grains and (2) preferred crystallographic orientation of the grains leading to macroscopic anisotropy of the homogenized reference medium. The model is applicable to most single phase polycrystalline materials that may occur as a result of thermomechanical manufacturing processes leading to different macrotextures and elongated-shaped grains. It predicts the strength of ultrasonic scattering and its dependence on frequency and propagation direction as a function of grain shape, grain crystallographic symmetry and macroscopic texture parameters and provides the texture-induced dependence of macroscopic ultrasonic velocity on propagation angle. It considers proper wave polarizations due to macroscopic anisotropy and scattering-induced transformations of waves with different polarizations. Competing effects of grain shape and texture on the attenuation are observed. In contrast to the macroscopically isotropic case, where in the stochastic regime the attenuation is highest in the direction of the longest ellipsoidal axis of the grain, the wave attenuation in the elongation direction may be suppressed or amplified by the texture with different effects on the quasilongitudinal and quasitransverse waves. The frequency behavior is also interestingly affected by texture: a hump in the total attenuation coefficient is found for the fast quasitransverse wave which is purely the result of macroscopic anisotropy and the existence of two quasitransverse waves; this hump is not observed in the macroscopically isotropic case. Striking differences of the texture effect on the directional dependences of the attenuation coefficients are found at low versus high frequencies.

Microstructure characterization via stereological relations — A shortcut for beginners

Stereological relations that can be routinely applied for the quantitative characterization of microstructures of heterogeneous single- and two-phase materials via global microstructural descriptors are reviewed. It is shown that in the case of dense, single-phase polycrystalline materials (e.g., transparent yttrium aluminum garnet ceramics) two quantities have to be determined, the interface density (or, equivalently, the mean chord length of the grains) and the mean curvature integral density (or, equivalently, the Jeffries grain size), while for two-phase materials (e.g., highly porous, cellular alumina ceramics), one additional quantity, the volume fraction (porosity), is required. The Delesse–Rosiwal law is recalled and size measures are discussed. It is shown that the Jeffries grain size is based on the triple junction line length density, while the mean chord length of grains is based on the interface density (grain boundary area density). In contrast to widespread belief, however, these two size measures are not alternative, but independent (and thus complementary), measures of grain size. Concomitant with this fact, a clear distinction between linear and planar grain size numbers is proposed. Finally, based on our concept of phase-specific quantities, it is shown that under certain conditions it is possible to define a Jeffries size also for two-phase materials and that the ratio of the mean chord length and the Jeffries size has to be considered as an invariant number for a certain type of microstructure, i.e., a characteristic value that is independent of the absolute size of the microstructural features (e.g., grains, inclusions or pores).

Electrical and Optical Properties of Nickel- and Molybdenum-Doped Titanium Dioxide Nanoparticle: Improved Performance in Dye-Sensitized Solar Cells

Nanocrystalline undoped and doped TiO2 particles with different concentrations of nickel and molybdenum (1-7%) was synthesized using the hydrothermal method followed by characterization using standard analytical techniques such as x-ray diffraction (XRD), scanning electron microscopy (SEM), transmission electron microscopy (TEM) and UV-Vis spectroscopy. The XRD analysis shows no change in crystal structure of TiO2 after doping with different concentration of Ni and Mo which indicates the single phase polycrystalline material. The SEM analysis shows the partial crystalline nature of undoped and doped TiO2 and TEM analysis shows the particle size were in the range of 7-11 nm for Ni and 9-13 nm for Mo-doped TiO2. The electrical and photovoltaic properties of the undoped and newly synthesized Ni- and Mo-doped TiO2 were studied. The a.c. analysis shows that the dielectric constant e′ and dielectric loss tan δ decreases with increase in frequency and become independent at higher frequency ranges. The dielectric property decreases with increase in dopant concentration which provides the valuable information about conduction process. At low frequency, the mechanism of a.c. conductivity was found to be same as that of d.c. conduction. As the frequency increases, the magnitude of complex impedance decreases indicating the increase in a.c conductivity. It was observed that the impedance increases with the corresponding increase in the dopant concentration. Under simulated solar illumination with an optimum content of Ni and Mo involves in TiO2, the amount of dye absorption increases resulting in the gradual increase in photovoltaic current and hence improvement in the cell efficiency of dye-sensitized solar cell (DSSC) from 6.23 to 6.72% and 6.23 to 7.16% by increasing the dopant concentration of Ni and Mo from 0 to 5%, respectively, was achieved.

Structural analysis and physical properties of Sr2−xLaxVO4−δ

The effects of the oxygen deficiency, δ, on the electrical and magnetic properties of Sr2−xLaxVO4−δ were investigated. For this objective, single-phase polycrystalline materials of Sr2−xLaxVO4−δ (x=0, 0.04, 0.1, 0.2, 0.8 and 1) were synthesized. The value of δ was determined by thermo-gravimetric-analysis. The δ of Sr2−xLaxVO4−δ (x⩽0.2) was almost the same value, ∼0.2. The δ of x=0.8 was 0.05 and that of x=1 was ∼0. Electrical resistivity measurement showed that all the samples were semiconductive. For the low magnetic field (∼0.002T) measurement, the spin-glass-like behavior was clearly observed for larger δ samples (x=0.04, 0.1 and 0.2). This behavior became weak for smaller δ samples (x=0.8 and 1). It is considered that the random distribution of the oxygen vacancies in the two-dimensional VO2 plane lead to this result. From the high magnetic field (1T) measurement, it was found that the Curie–Weiss term, χcw, dominated in the magnetic susceptibility, χ, of Sr2−xLaxVO4−δ (x⩽0.2, δ∼0.2). The χcw considerably reduced for x=0.8 (δ=0.05) and almost disappeared for x=1 (δ∼0) i.e., SrLaVO4. Thus, the χcw is considered to be originated from oxygen vacancies. Hence, it is revealed that the δ is critical to the properties of Sr2−xLaxVO4−δ, in addition to x. It is worthy to note that almost temperature independent χ of SrLaVO4 is anomalous, because in this material, all the V are V3+ with S=1. The almost temperature independent susceptibility may be due to the spin fluctuation enhanced by the strong two-dimensionality of the crystal structure, quantum fluctuation or the spin frustration in VO2 square lattice.

Simulation of Liquid Film Migration during Melting

Melting of a single-phase polycrystalline material is known to start by the formation of liquid films at the surface and at grain boundaries. The internal liquid films are not necessarily quiescent, but can migrate to avoid/reduce supersaturation in the solid phase. The migration is discussed in the literature to be governed by coherency strains of the solid/liquid interface, by concentration gradients in the liquid or by concentration gradients in the solid phase. A phase transformation model for diffusional phase transformations considering interface thermodynamics (possible deviations from local deviations) has been put up to describe the migration of the solid/liquid (trailing) and the liquid/solid (leading) interfaces of the liquid film. New experimental results on melting in a temperature gradient in combination with simulation calculations reveal that concentration fluctuations in the liquid phase trigger the liquid film migration and determine the migration direction, until after a short time in the order of microseconds the process is governed by diffusion in the solid phase.

Influence of Ce Doping on the Electrical and Optical Properties of TiO2and Its Photocatalytic Activity for the Degradation of Remazol Brilliant Blue R

Nanocrystalline TiO2particles doped with different concentrations of Cerium (Ce, 1–10%) have been synthesized using sol-gel method. The prepared particles were characterized by standard analytical techniques such as X-ray diffraction (XRD), FTIR and Scanning Electron Microscopy (SEM), and Transmission Electron Microscopy (TEM). The XRD analysis shows no change in crystal structure of TiO2after doping with different concentrations of Ce, which indicates the single-phase polycrystalline material. The SEM analysis shows the partial crystalline nature of undoped, and doped TiO2and TEM analysis shows the particle sizes were in the range of 9–14 nm in size. The a.c. analysis shows that the dielectric constantεand dielectric loss tanδdecrease with the increase in frequency. The dielectric property decreases with the increase in dopant concentration. It is also observed that the impedance increases with an increase in dopant concentration. The photocatalytic activity of the synthesized particles (Ce-doped TiO2) with dopant concentration of 9% (Ce) showed the highest photocatalytic activity for the degradation of the dye derivative Remazol Brilliant Blue R in an immersion well photochemical reactor with 500 W halogen linear lamp in the presence of atmospheric oxygen.

A combined stochastic diffusion and mean-field model for grain growth

A combined stochastic diffusion and mean-field model is developed for a systematic study of the grain growth in a pure single-phase polycrystalline material. A corresponding Fokker-Planck continuity equation is formulated, and the interplay/competition of stochastic and curvature-driven mechanisms is investigated. Finite difference results show that the stochastic diffusion coefficient has a strong effect on the growth of small grains in the early stage in both two-dimensional columnar and three-dimensional grain systems, and the corresponding growth exponents are ~0.33 and ~0.25, respectively. With the increase in grain size, the deterministic curvature-driven mechanism becomes dominant and the growth exponent is close to 0.5. The transition ranges between these two mechanisms are about 2-26 and 2-15 nm with boundary energy of 0.01-1 J <TEX>$m^{-2}$</TEX> in two- and three-dimensional systems, respectively. The grain size distribution of a three-dimensional system changes dramatically with increasing time, while it changes a little in a two-dimensional system. The grain size distribution from the combined model is consistent with experimental data available.

Impact of domain anisotropy on CTE of isotropic microcrystalline material

An analytical, phenomenology-based model is proposed for thermal expansion of isotropic single-phase polycrystalline materials. Standard rules of mixing fail to predict correctly the coefficient of thermal expansion (CTE) of such materials. The model introduced in this paper explains and accurately reproduces the U-shaped thermal expansion curve of low-CTE ceramics (cordierite and β-eucryptite) quantitatively. The integrity function of a material is introduced as a measure of microcracking as a function of temperature. This function can be useful for analysis of different bulk properties of isotropic polycrystalline materials that depend on domain microcracking.

Modelling of the Influence of the Grain Size Distribution on the Grain Growth in Nanocrystals

The paper presents results of grain growth modelling in single-phase polycrystalline materials based on the Hillert mean filed theory [1]. For the context of grain growth in nano-polycrystals this theory has been modifiedto take into account transient states and the effect of grain size distribution on the kinetics of the grain growth. Both, global and local mean size of grains as well as effect of spatial fluctuations in the size of grains have been studied. The results show that the structure homogeneity and the mobility of the grain boundaries have a significant impact on the grain growth process. Relevance of the results to the processes taking place in some examples of nano-metals (e.q. [2,3]) is briefly discussed.

A dynamic material library for the representation of single-phase polyhedral microstructures

Quantitative estimation of features from sectional images of microstructures is fundamental to determining the microstructural influences on material behavior. Geometric data extracted from planar materialographic sections through image analysis techniques are primarily lower-order descriptors of the microstructure. Such descriptors do not contain complete morphological information and hence cannot fully describe the material microstructure. This work uses a multi-class support vector machine classification method in conjunction with principal component analysis to build a dynamic and evolving microstructure library that can be used to efficiently describe single-phase polyhedral microstructures. Lower-order descriptors are initially used to associate the material microstructure to classes of microstructures stored in a digital material library. Complete description is obtained by quantifying the microstructure using the coefficients of a continuously updating basis within a class of the library. These techniques are essential towards the development of a dynamic materials library that will be able to analyze, classify and represent microstructures for modeling, accelerating the design and testing of single-phase polycrystalline materials.

Crystal Structure Refinement of CuxAg1‐xInTe2 Bulk Material Determined from X‐Ray Powder Diffraction Data Using the Rietveld Method.

AbstractFor Abstract see ChemInform Abstract in Full Text.

Modelling IR-spectra of single-phase polycrystalline materials with random orientation—a unified approach

Two recently developed formalism, one for the modelling of spectra of randomly oriented polycrystalline bulk materials consisting exclusively of crystallites being small compared to the resolution limit [Appl. Spectrosc. 56 (2002) 1194] and one for polycrystalline bulk materials in the large crystalline limit [J. Opt. A: Pure Appl. Opt. 4 (2002) 540] are combined in a unified approach in order to enable the modelling of spectra of materials consisting of both optically small and large regions of order. Based on this generalized formalism, several model calculations are carried out to demonstrate the influence of different crystallite size distribution on IR-reflectance spectra. The model calculations for a sample consisting of a 3:1 mass mixture of small and large crystallites are compared with the experimental results; the good correspondence between measured and modeled spectra confirms the value of the unified approach.

Modelling IR-spectra of single-phase polycrystalline materials with random orientation – Supplementations and refinements for optically uniaxial crystallites

Summary The IR-reflectance spectra of a bulk sample of randomly oriented polycrystalline fresnoite (Ba2TiSi2O8) are presented. The sample was prepared by Spark Plasma Sintering from a powder consisting of optically large crystallites. The spectra are of notable higher quality than those of conventionally prepared samples, especially those of the cross-polarization terms. The spectra were modelled by a 4 ×4-matrix-formalism [T. G. Mayerhofer, J. Opt. A: Pure Appl. Opt. 4, 540 (2002)], which was refined for optically uniaxial crystals, resulting in a correct prediction of the relative peak-intensities of the cross-polarization terms. The modelling was carried out with two different orientational averaging schemes. The comparison between modelled and measured spectra revealed that the use of any weighing factor is unjustified in case of orientational averaging of the IR-optical properties of solids.

Preparation, crystal and magnetic structure of the double perovskite Ba 2 FeWO 6

Single-phase polycrystalline material of the double perovskite Ba2FeWO6 was prepared and characterized by X-ray and neutron powder diffraction (NPD). The crystal structure was tetragonal with lattice parameters a=b=5.7479(4) A and c=8.1444(9) A at room temperature (295 K). NPD data at 10 K shows the evidence of an antiferromagnetic ordering of the Fe atoms. The reverse Monte Carlo powder (RMCPOW) technique was used to find the magnetic structure, which showed that it is based on a unit cell related to that of the nuclear structure by the propagation vector 0\(\frac\Box1\Box\Box2\Box\)\(\frac\Box1\Box\Box2\Box\) . An ordering of collinear spins was found with alternate layers in the c-direction or in the a-b plane. The model was checked by Rietveld refinement and the magnetic moment of iron was found to be 3.39(2)μB at 10 K.