Crystallite Distribution Research Articles

X-ray topographic identification and measurement of plastic strains and elastic stresses in single crystallites of polycrystalline diamond layers

The well-known phenomenon of asterism is used as the basis for the development of an X-ray topographic method to identify and measure plastic strains and residual elastic stresses in single crystallites more than 3 µm in size in polycrystalline diamond layers. The amount of asterism is used as a quantitative measure of plastic strains in crystallites. The distribution of crystallites over the amount of asterism in 40-to 670-µm-thick microwave-plasma-deposited polycrystalline diamond layers is obtained. Shear plastic strains, which cause a misorientation from 0.4′ to 1.5° between different areas of a crystallite, are observed for the first time. The residual elastic stresses calculated in plastically strained crystallites vary between 2.7 kPa and 0.84 GPa.

X‐ray Diffraction Investigations of Microstructure of Calcium Hydroxide Crystallites in the Interfacial Transition Zone of Concrete

This work presents theoretical and experimental X‐ray diffractometry investigations of the morphology and deformation state of calcium hydroxide (Ca(OH)2, CH) crystallites in the interfacial transition zone of concrete. Based on the developed theoretical approach, the distributions of CH crystallites and their coherent domains over strains and sizes are reconstructed. The average amounts of planar defects, cracks, and possible stacking faults within a CH crystallite are estimated. A comparative analysis is conducted for the morphology of CH texture depending on the type of aggregate particles (granite and smoky quartz) used.

Method of platinum-carbon coating of ultrathin sections for transmission and scanning electron microscopy: an application for study of biological composites.

Many biological materials are composites containing two or more components with different mechanical properties. This study is concerned with the application of a method of platinum-carbon coating (Pt/C) of ultrathin sections for TEM and SEM studies of the design of natural composite materials. The changes in profile of the ultrathin resin-embedded sections during different stages of the preparation reflect the material properties of the various components: stiffer regions deform less than softer ones. Such changes in the section profile can be visualized by the Pt/C method and used as evidence of specific material properties in particular regions of composite materials. The method increases the relief contrast, improves the 3D-view of structures, and in combination with standard TEM and SEM procedures can provide clear demonstrations of material design. The distribution of chitin crystallites in the insect cuticle and the ultrastructure of the pore canal system specialized for the transport of epidermal secretions to the cuticle surface were studied here as examples.

Effect of c/a-Ratio on Crystallographic Texture and Mechanical Anisotropy of Hexagonal Close Packed Metals

Hexagonal close packed metals exhibit highly anisotropic mechanical properties, a thorough knowledge of which is a primary requisite for predictability of the dimensional changes in service as well as formability characteristics. We summarize our work on the effects of c/a-ratio on preferred orientations and the resulting anisotropic mechanical properties. Zr and Ti alloys are considered to represent low c/a-ratio while Mg alloy (AZ31B) was chosen as ideal; these materials were available in tubing form. Pure zinc sheet was used to represent high c/a-ratio. Distinct differences are noted in the basal pole distributions, and crystallite orientation distribution functions derived from the pole distributions were combined with crystal slip models to predict the mechanical anisotropy parameters. While in all cases the uniaxial yield stresses were evaluated along the RD and TD, the contractile strain ratios (CSR) were determined using grided tensile samples fabricated from sheets of Zircaloy and Zinc. The experimental results correlated with slip predictions based on predominant prism and basal slip modes respectively in Zicaloy and Zn. For Mg alloy, either pyramidal slip or a combination of basal and prism slip modes exhibited good agreement with the experimental results. In addition, the anisotropic creep behavior of thin-walled Zircaloy tubing is considered. Excellent agreement is noted, in recrystallized Zircaloy tubing, between the experimental creep locus and model predictions based on prism slip dominance. However, distinct deviations are noted in Ti3Al2.5V alloy albeit electron microscopy of deformed tubing revealed dislocations on prism ({10.0}) planes with Burgers vectors along .

Effects of Si addition on the microstructural evolution and hardness of Ti–Al–Si–N films prepared by the hybrid system of arc ion plating and sputtering techniques

Ti–Al–Si–N films were deposited on WC–Co substrates by the hybrid coating system of arc ion plating method for Ti–Al sources and dc magnetron sputtering technique for Si incorporation. The synthesized Ti–Al–Si–N films were revealed as composites of solid-solution (Ti,Al,Si)N crystallites and amorphous Si3N4 by instrumental analyses such as x-ray diffraction, high-resolution transmission electron microscopy, and x-ray photoelectron spectroscopy. The Si addition in Ti–Al–N films affected the refinement and uniform distribution of crystallites by percolation phenomenon of amorphous silicon nitride similar to that of the Si effect in TiN film. The solubility limit of Si in the Ti0.76Al0.24N crystal is believed to be about 6 at. %. No free Si was observed due to the very high ionization rate of nitrogen gas in the arc plasma. As the Si content increased up to about 9 at. %, the hardness of Ti–Al–N film steeply increased from 30 GPa to about 50 GPa. Ti–Al–Si–N films having the maximum hardness showed the nanocomposite microstructure consisting of fine (Ti,Al,Si)N crystallites, about 8 nm in size, dispersed uniformly in the amorphous Si3N4 matrix.

A model of continuous dynamic recrystallization

During continuous dynamic recrystallization (CDRX), which occurs in high stacking fault energy metals, new grains are formed by the progressive increase of low-angle boundary misorientations. A simple CDRX model is proposed, that deals with a set of “crystallites” delimited partly by low-angle (LABs) and partly by high-angle (HABs) boundaries. Strain hardening and dynamic recovery are described by the Laasraoui-Jonas equation, which has been modified to take HAB migration into account. Recovery occurs in two ways, viz. by the condensation of dislocations into new LABs, and the absorption of dislocations in the pre-existing boundaries, which leads to the transformation of LABs into HABs. The predictions of the model are presented for both the transient and steady states, including stress-strain curves at various temperatures and strain rates, as well as the associated evolutions of the microstructural parameters such as crystallite sizes, dislocation densities and LAB misorientation distributions. The effect of HAB migration on these parameters is emphasized.

Crystallographic texture induced anisotropy in copper: An approach based on a tensorial Fourier expansion of the CODF

We consider a tensorial Fourier expansion of the crystallite orientation distribution function for aggregates of cubic crystals. The coefficient of rank four is determined explicitly. It is shown that this coefficient governs the anisotropic bounds of the linear elastic behavior of polycrystals. Recently, a phenomenological model has been proposed [4, 6], that describes the evolving elastic anisotropy in copper. The model also reproduces the cyclic Swift effect, which is due to a texture induced plastic anisotropy [7]. In the model the anisotropic part of the effective elastic stiffness tensor is used to define a texture dependent quadratic yield function. The present paper gives a new interpretation of the aforementioned model in terms of an approximation of the crystallographic texture by means of a 4th-order coefficient of the tensorial Fourier expansion of the crystallite orientation distribution function.

3D Monte-Carlo simulation of texture-controlled grain growth

A three-dimensional (3D) Monte-Carlo (MC) routine was developed to quantify the interaction of grain growth and texture development during annealing. The program included special software to enable the input of the initial grain structure and texture and incorporated a description of the misorientation-dependence of the grain-boundary mobility. Outputs from the model quantified the evolving texture in terms of pole figures or crystallite orientation distribution functions and statistics on the grain structure such as the grain-size distribution and boundary-misorientation distribution function. The MC routine was applied to establish grain growth and texture development in materials with random or strongly textured starting conditions and isotropic or anisotropic grain-boundary mobility. Depending on the starting condition and material properties, normal grain growth or a behavior characterized by alternating cycles of fast and slow grain growth was predicted.

On the Structural Characterization of a Series of Novel Ni-Nb-Sn Refractory Alloy Glasses

ABSTRACTRecently refractory alloy glasses of varying Ni, Nb and Sn concentrations were prepared and studied via several characterization methods, including x-ray diffraction via standard lab and synchrotron radiation sources, SEM, and other complementary techniques. A comparison between x-ray diffraction results obtained from synchrotron sources vs. standard lab sources shows the necessity of a low-divergence source in order to distinguish nanoscale crystallites present within an amorphous matrix. The divergence of both sources was determined by comparing the diffraction patterns of a LaB6standard and noting the deviation from ideal or theoretical Bragg peaks. The crystallites in these glasses comprised between 0 and 7.5 percent by volume, depending upon the specific composition. The results presented here also show a very good sample-to-sample consistency for any given alloy composition. While x-ray diffraction results give information about the average structure, SEM was also performed to understand aspects of individual crystallite size and distribution. By studying results of varying alloy concentrations, it is seen that a very small composition range exists for near-perfect glass formers (as defined by a near zero percentage crystallinity). Radial distribution analysis was also performed for each composition and compared to hard sphere models for each alloy composition. This analysis indicated the presence of intermediate range order beyond the first nearest neighbors as indicated by the divergence of the experimental reduced radial distribution functions from that predicted by the accompanying hard sphere models.

Comparison of Ultrasonic Pole Figures Based upon Ultrasonic Nondestructive Evaluation Method with Pole Figures Based upon Finite Element Polycrystal Model

The ultrasonic wave velocities in a polycrystalline aggregate are sensitively influenced by texture changes due to plastic deformation, and their relationship was systematically analyzed by Sayers [J. Phys. D: Appl. Phys. 15 (1982)]. According to Sayers's proposed model, it is possible to construct ultrasonic pole figures via the crystallite orientation distribution function (CODF), which can be derived by using ultrasonic wave velocity changes. In the previous paper, the theoretical modeling to simulate ultrasonic wave velocities propagating in solid materials under plastic deformation has been proposed by the authors and proved to be in good agreement with experimental results. In the present paper, the proposed theoretical modeling is applied to construct the ultrasonic pole figures based upon Sayers's model under various loading conditions of uniaxial tension, pure torsion, equi-biaxial tension-compression, biaxial compression and biaxial tension, respectively. To examine the accuracy and reliability of the ultrasonic pole figures simulated by the proposed theoretical modeling, the ultrasonic pole figures are compared with those analyzed by the finite element polycrystal model (FEPM). The results show a remarkable qualitative similarity among the two methods.

繊維配向を有するＴｉＮおよびＴｉＣＮ薄膜の熱による残留応力変化にともなう機械的強度への一影響

TiN and TiCN thin films are used as antiwear layer on parts such as metal cutting tools. It is reported that the thin films that are deposited ceramics and metals have preferred orientation, and that the residual stresses generate by the difference in the coefficients of thermal expansion between the thin films and the substrate. Tools coated with TiN and TiCN films are heated to high temperature during service due to the frictional heat. Under this condition, the texture and the residual stress should change due to the heat. In the material engineering, it is well known that the residual stress in the material affects the mechanical strength of the industrial products. The purpose of this study is to examine the effect of the residual stress on the mechanical strength of TiN and TiCN thin films having preferred orientation.In this study, specimens that are deposited TiN and TiCN respectively by Physical Vapor Deposition (PVD) were annealed in a furnace at temperature of 573K, 798K, 843K and 893K. Using X-ray diffraction technique, the crystallite orientation was evaluated by the pole figure and the crystallite orientation distribution function (ODF). The films exhibited {111} fiber texture. After that, the residual stress of thin films was measured using CoKα radiation with the two-exposure method at Ψ=39° and 75°. Since the relationship between the mechanical strength and the residual stress has not been revealed about the thin film materials, the effect of the residual stress on the mechanical strength of the TiN and TiCN thin films having preferred orientation was investigated by the dynamic hardness (DH) and the scratch test.As a result, although the ODF little changed due to the heat treatment, the residual compressive stress relaxed at higher temperatures than 573K. As for the hardness of thin films, the residual stress did not affect the hardness. However, the residual stress influenced the behavior of the scratch test. The abrasive wear and the micro cracks were decreased by highly residual compressive stress.

Direct Observation of Crystal−Amorphous Interphase in Lamellar Semicrystalline Poly(ethylene terephthalate)

We report on the direct evidence in real space of the crystal−amorphous interphase in a lamellar semicrystalline polymer, poly(ethylene terephthalate) (PET). This evidence was obtained by the TEM observation of the compositional variation of (stained) PET segments in the boundary of an isolated lamellar stack in a binary blend of semicrystalline PET with amorphous poly(ether imide). The lamellar morphology exhibited by the TEM image of a stained lamellar stack was also investigated in detail, in terms of the thickness distributions of lamellar crystallites and noncrystalline interlamellar layers. The validity of employing our TEM imaging method through differential staining of PET segments was then ascertained by comparing the power spectral density obtained from the TEM data with the measured small-angle X-ray scattering profile from semicrystalline PET samples. Compared with this lamellar morphology, the thickness of the observed crystal−amorphous interphase at the boundary of the lamellar crystallites and (mixed) random melts is even greater than the thickness of the noncrystalline interlamellar layer of PET. This striking result may be attributed to the rigid aromatic groups in the PET chain backbone which prohibit the occurrence of tight chain folding. Accordingly, the entire noncrystalline interlamellar region of aromatic semicrystalline polymers may be regarded as the interphase, devoid of truly random amorphous phase.

Thermomechanical behavior of metallocene ethylene-α-olefin copolymers

The thermal, dynamic mechanical and stress–strain properties of a set of commercial LLDPEs prepared by metallocene catalysts were studied and compared with two LLDPEs obtained with traditional Ziegler–Natta catalysts. The type and amount of comonomer strongly affects the degree of crystallinity and branching, resulting in different material morphology and macroscopic thermomechanical behavior. Within each set of ethylene-α-olefin copolymers a gradual decrease in the percentage crystallinity and position and intensity of β- and γ-transition is observed, with respect to the comonomer content. In addition, the studied materials are characterized by the absence of an α-transition. This behavior is attributed to the high comonomer content (5–24)%. Tensile behavior changes from the typical necking, cold drawing and strain hardening to the uniform elastomeric deformation, as the comonomer content increases. The experimental methods used, in combination with scanning electron microscopy, lead to converged results, while tensile testing proved to be sensitive to the crystallite size and distribution.

Dislocation density and graphitization of diamond crystals

Two sets of diamond specimens compressed at 2 GPa at temperatures varying between 1060 K and 1760 K were prepared; one in which graphitization was promoted by the presence of water and another in which graphitization of diamond was practically absent. X-ray diffraction peak profiles of both sets were analyzed for the microstructure by using the modified Williamson-Hall method and by fitting the Fourier coefficients of the measured profiles by theoretical functions for crystallite size and lattice strain. The procedures determined mean size and size distribution of crystallites as well as the density and the character of the dislocations. The same experimental conditions resulted in different microstructures for the two sets of samples. They were explained in terms of hydrostatic conditions present in the graphitized samples.

High-resolution texture imaging with hard synchrotron radiation in the moving area detector technique

The orientation distribution of crystallites in polycrystalline materials (called texture) is usually measured by polycrystal X-ray diffraction by “step-scanning” the sample in angular intervals in the order of 1°. This technique is not suited to fully exploit the low angular divergence of hard synchrotron radiation in the order of “milliradian”. Hence, step-scanning was replaced by a continuous “sweeping” technique using a continuously shifted area detector. In order to avoid overlapping from different reflections ( hkl) a Bragg-angle slit was introduced. The “moving-detector” technique can be applied to obtain images of orientation as well as of location distributions of crystallites in polycrystalline samples. It is suitable for imaging continuous “orientation density” distribution functions as well as of “grain-resolved” textures. The excellent features of high-energy synchrotron radiation combined with the moving area detector technique will be illustrated with several examples including very sharp deformation textures, fully and partially recrystallized samples and materials with steep texture gradients.

Texture and Microstructure Analysis with High-Energy Synchrotron Radiation

High-energy synchrotron radiation with wavelengths in the range of 0.1 A is an excellent tool to measure the orientational and spatial distribution of crystallites in polycrystalline materials of any kind. A particular sweeping method for continuous imaging of texture and microstructure with high resolving power is described. In grain-resolved structures, the orientation stereology of the grains can thus be obtained. High-energy synchrotron radiation has penetration depths in most materials comparable with that of neutrons. It is thus very well suited for the study of big samples and for non-destructive testing of complex technological components.

X-Ray Stress Measurements of TiCN Thin Films

TiCN thin films deposited by Physical Vapor Deposition (PVD) were heated to various temperatures. Using X-ray diffraction technique, the preferred orientation of the crystallites was evaluated from pole figures and the crystallite Orientation Distribution Function (ODF) was calculated from the pole figures. After that, the residual stress was analyzed using the X-ray elastic constant obtained from the ODF. As a result of the heat treatment, the residual compressive stress relaxed at temperatures higher than 573K.

Residual Stress Dependent Optical Properties of ZnI2 Films

The optical absorption measurements are reported for stoichiometic, tetragonally structured ZnI 2 films. The optical band gap was found to be of the direct type. Structural analysis shows a random orientation of crystallites and the presence of internal residual stress in the film. Non-uniform compressive residual stress shows an initial increase followed by saturation with film thickness and a linear increase with treatment temperature. Both these behaviors correlate well with the variation of packing density and size distribution of crystallites as a function of film thickness and treatment temperature as seen by morphological studies. The decreasing optical band gap (Eg) with either film thickness or treatment temperature can be explained by residual compressive stress. The thickness and treatment temperature data dependences together show quite a good linear relationship between Eg and the residual stress yielding a band gap of 4.75 eV for a stress free perfect crystal.

Crystallization of Sol–Gel Boehmite via Hydrothermal Annealing

Thin crystallites of boehmite were synthesized by annealing a sol–gel precursor under hydrothermal conditions. Samples were characterized with X-ray powder diffraction, thermogravimetry, transmission electron microscopy, and by refining the crystalline phases. Fresh samples consisted of boehmite sheets forming folded paper-like “crystallites,” which were transformed into thin flat crystalline plates perpendicular to crystallographic b-axis when they were annealed under hydrothermal conditions using water as mineralizer. Boehmite's crystallite size increased with the annealing time. The rhombic boehmite crystallites had their shortest diagonal parallel to crystallographic a-axis, and their lateral faces parallel to {101} planes forming an angle of 104.32° between each other; these planes contained active aluminum atoms responsible for the crystallites growing along them. The hydrogen bonding length, which decreased as crystallite size increased, determined the variation of boehmite's transition temperature into γ-alumina. Since this transformation is pseudo-morphic, both particle morphology and sample porosity of alumina were determined by the arrangement of crystallites in boehmite. γ-Alumina crystallite distribution had memory about boehmite crystallite dimensions and atomic arrangement: crystallites were oriented parallel to boehmite’s a axis, and were confined by boehmite's crystallite dimensions.

An analytical approximation for a size-broadened profile given by the lognormal and gamma distributions

The size-broadened profile given by the lognormal and gamma size distributions of spherical crystallites is considered. An analytical approximation for the size-broadened profile is derived that can be analytically convolved with the strain-broadened and instrumental-broadened profiles. The method is tested on two CeO2powders; one shows `super-Lorentzian' profiles that were successfully modelled under the assumption of a broad lognormal size distribution. It is shown that the Voigt function, as a common model for a size-broadened profile, fails for both very narrow and broad size distributions. It is argued that the size-broadened line profile is not very sensitive to variations in size distribution and that an apparent domain size or even column-length distribution function can correspond to significantly different size distributions.