Crystallite Microstrain Research Articles

Direct nanocrystallite size investigation in microstrained mixed phase TiO2 nanoparticles by PCA of Raman spectra

Mixed phase anatase and rutile TiO2 nanoparticles (30–67% R/A) have been synthesized by single step laser pyrolysis. Parallel studies by XRD and Raman spectroscopy suggested possible deforming microstress inside certain samples, due to boundary interactions between neighbouring nanocrystallites in nanoparticles, phase instabilities and/or O/C contents. Microstress in nanoparticles supports anatase phase stability in competition with rutile phase. Williamson-Hall plot was used to evaluate crystallite size and strain. A tensile global microstrain in anatase crystallites, was observed for elevated C content titania nanoparticles, together with compressive microstrain in crystallites within O deficient TiO2 nanoparticles. XPS and TEM characterization opens insights regarding the processes behind this type of behaviour. Principal Component Analysis of Raman spectra was applied for batch auto-characterization of mixed phase nanoparticles, with emphasis upon the method ability to simultaneously appreciate crystallite size for both anatase and rutile phase. The method focuses on covariational matrix of multiple samples Raman spectra. It provides results in good agreement with XRD calculated crystallite dimensions for unstrained titania, while for samples with microstrains it returns the size closer to the one predicted by Williamson-Hall plot.

Investigation of the crystal and magnetic structures of BaFe12 - x Al x O19 solid solutions (x = 0.1‒1.2)

The structure of barium ferrite BaFe12 - xAlxO19 solid solutions (x = 0.1‒1.2) with iron partially replaced with diamagnetic aluminum ions has been studied by neutron diffraction. Experimental data have been collected at room temperature on a high-resolution diffractometer, which yielded precise information about the changes in the crystal and magnetic structures and data on the behavior of the sample microstructure. Barium hexaferrite retains a magnetoplumbite structure in the entire range of aluminum concentrations under study, and its magnetic structure is described within the Gorter model, with moments orientated along the hexagonal axis. The total magnetic moment per formula unit decreases while diamagnetic aluminum ions substitute for iron ions. Microstrains in crystallites increase with an increase in the diamagnetic ion concentration, which is related to the difference in the ionic radii of iron and aluminum ions.

Effect of the milling energy on the anisotropy of deformation distortions in nanocrystalline powders of nonstoichiometric tantalum carbide TaC y

The effect of the milling energy and nonstoichiometry of cubic tantalum carbide TaCy (0.81 ≤ y ≤ 0.96) on the strain anisotropy of the crystal and the size of particles in nanocrystalline powders has been experimentally investigated using X-ray diffraction. The functional dependence of the reduced broadening of diffraction reflections on the scattering vector, which takes into account the contributions of the size, strain, and inhomogeneous broadenings, has been obtained. The average size of coherent scattering regions and the crystallite microstrain accounting for the anisotropy of deformation distortions have been estimated. It has been shown that a more precise description of the experimental data on the broadening of diffraction reflections is achieved by the inclusion of the microstrain anisotropy and inhomogeneous broadening in the analysis.

Anisotropy of strain distortions in nanopowders of nonstoichiometric vanadium and tantalum carbides

For the first time, the effect of milling energy and nonstoichiometry of vanadium carbide VC0.875 and tantalum carbide TaCy (0.81≤y≤0.96) on microstrains anisotropy and the particle size of nanocrystalline powders has been studied experimentally by the X-ray diffraction method. A functional dependence of reduced broadening of diffraction reflections on the scattering vector has been obtained, which takes into consideration the contributions from size, strain and inhomogeneity broadenings. The average size of coherent scattering regions and the value of microstrains in crystallites accounting for anisotropy of strain distortions have been estimated. It is shown that allowance for anisotropy of microstrains and inhomogeneity broadening gives more accurate description of the experimental results on diffraction reflection broadening and more accurate determination of the nanoparticle size.

Neutron diffraction study of nanocrystalline NbC0.93 powders and the anisotropy of deformation distortions

Broadening of the diffraction reflections in nanocrystalline powders of nonstoichiometric niobium carbide NbC0.93 with the average particle size from ∼200 to ∼2000 A has been studied by the neutron diffraction method. The functional dependence of the broadening W 2 on the interplanar distance d 2 has been obtained including size, deformation, and inhomogeneous broadening. The average size of the coherent scattering regions and microstrains in crystallites with allowance for the anisotropy of the deformation distortions have been estimated.

Study of the crystalline and magnetic structures of BaFe11.4Al0.6O19 in a wide temperature range

The structural study of barium hexaferrite (BaFe12O19) whose iron ions are partly replaced by diamagnetic aluminum ions (x = 0.6) is carried out with the help of the neutron-diffraction method. Experimental data are acquired in a wide temperature range of 4–730 K via a high-resolution diffractometer, which makes it possible to obtain both precise information on changes in crystalline and magnetic structures and behavioral data on the sample microstructure. BaFe11.4Al0.6O19 retains the magnetoplumbite structure in the whole temperature range and exhibits the “invar effect,” according to which its bulk thermal-expansion coefficient is close to zero at low temperatures (<150 K). The magnetic structure is defined by the Gorter model with magnetic moments oriented along the hexagonal axis. For all nonequivalent crystallographic positions, the magnetic moment of F3+ is close to 4 μB at 4 K. The total magnetic moment per formula unit is 15.6 μB, i.e., less than the nominal value of 20 μB. This is caused by the fact that diamagnetic Al ions are included in the composition. Crystallite microstrains increase insignificantly with temperature due to increasing influence of the magnetic subsystem.

Quantitative Determination of Lattice Fluoride Effects on the Solubility and Crystallinity of Carbonated Apatites with Incorporated Fluoride

The purpose of this study was to evaluate quantitatively the effects of fluoride on the solubility and crystallinity of carbonated apatites (CAPs) after its incorporation into the crystal lattice using the metastable equilibrium solubility (MES) distribution method. Fluoride-incorporated CAPs (F-CAPs) of two different carbonate levels (3 and 5%) and fluoride contents from 0 to 20,000 µg/g were synthesized. X-ray diffraction experiments and Rietveld analysis were conducted to obtain crystallite microstrain and unit cell parameters. Acetate buffer MES solution media were prepared at two solution fluoride concentrations (0.2 and 2.0 mg/l) and at two pHs (5.0 and 5.7). The unit cell a-axis values of the F-CAPs were found to decrease as the fluoride content increased, consistent with the fluoride being incorporated into the crystal lattice. The fluoride concentrations in the MES solution media were high enough to provide a ‘swamping’ effect such that the fluoride released from the F-CAPs during dissolution was minimal in changing the solution fluoride concentration. Employing the MES distribution superposition method, it was shown that the surface complex possessing the fluorapatite (FAP) stoichiometry [Ca₁₀(PO₄)₆F₂] accounted for the MES distribution behavior of all experiments. In addition, the mean pI_FAP [the value of –log(a_Ca¹⁰a_PO_₄⁶a_F²) calculated from the ionic activity product based on FAP stoichiometry of the MES dissolution media in which 50% of the F-CAPs had dissolved] correlated well with the crystallite microstrain parameters of the F-CAPs. The incorporated fluoride in the F-CAPs showed only modest effects on F-CAP crystallinity and solubility.

Influence of crystallite microstrain on surface complexes governing the metastable equilibrium solubility behavior of carbonated apatites

This study was on the influence of the mineral phase crystallite microstrain (CM) on the nature of the surface complex (SC) governing the metastable equilibrium solubility (MES) behavior of carbonated apatites (CAPs) in aqueous acidic media (0.10 M acetate buffers, with and without fluoride, 0.50 M ionic strength maintained with NaCl). The MES behavior of a set of four CAPs (synthesized at 85 °C by a precipitation method) of increasing CM and therefore of increasing MES (CAP4 > CAP3 > CAP2 > CAP1) was quantified. The following were the findings. For CAP1 and CAP2, the SCs deduced were Ca 10(PO 4) 6(OH) 2 and Ca 10(PO 4) 6F 2 for the nonfluoride and the fluoride cases, respectively. For CAP3 and CAP4, the SCs deduced were Ca 9.5(PO 4) 6OH or Ca 9.5(HPO 4)(PO 4) 5(OH) 2 and NaCa 9.5(PO 4) 6F 2 for the nonfluoride and the fluoride cases, respectively. These results together with that from an earlier limited study show that the Ca/P ratio of the SC decreases from 1.67 to 1.58 to 1.50 with increasing CM of the CAPs; this relationship inversely correlates with the chemistry of maturation of aqueously precipitated defective apatites. Also the SCs do not appear to exist as a continuous series and only a few SCs may account for the MES behavior over a wide range of CAP preparations.

Determination of the radial crystallite microstrain distribution within an AlMg3 torsion sample using monochromatic synchrotron radiation

A solid torsion sample made from AlMg3 (single phase Al alloy with 3 wt.% Mg) is strongly plastically deformed in three steps of Δ γ 1 = 1.5, Δ γ 2 = 1, and Δ γ 3 = 1 to a total deformation of γ = 3.5. The low speed deformation is carried out at room temperature with free ends. After each deformation step, the residual strain and texture within the sample are characterized non-destructively by a three-dimensional diffraction technique using monochromatic high energy synchrotron radiation. The macrostrain tensor is determined as a function of the radial position and the deformation by fitting the distortion of complete diffraction rings. Systematic deviations of the { h k l} specific diffraction ring distortions from the fit are interpreted as crystallite microstrains. These strains are in the order of (480–1550) × 10 −6. A comparison to results from crystallite microstrain measurements on uni- and bi-axially deformed samples shows that particularly the Al {2 2 0} reflection exhibits dramatically higher crystallite microstrains for tri-axial deformation obtained by solid torsion. This proves that crystallite microstrains cannot be neglected when deformations are bi- or tri-axial. In the deformation-dependent texture development, an increasing dominance of ideal torsion texture orientation A 1 * over A 2 * is observed. No evidence is found for ideal orientation B.

Phase formation and lattice strain in superconducting compoundY1−xLaxBa2Cu3Oy(0&lt;~x&lt;~1)

We study the formation and evolution of phases in the La substituted ${\mathrm{Y}}_{1\ensuremath{-}x}{\mathrm{La}}_{x}{\mathrm{Ba}}_{2}{\mathrm{Cu}}_{3}{\mathrm{O}}_{y}$ [(Y--La)123] superconductors from XRD and Raman measurements. We find characteristic modifications in the interatomic distances, bond valence sum (BVS) values and crystallite microstrains, which correlate with corresponding features of the micro-Raman spectra at nominal La compositions $x=0.2,$ 0.5, and 0.8. Based on the Raman spectra we conclude that two phases appear, an intermediate of chemical formula ${\mathrm{Y}}_{1\ensuremath{-}x}{\mathrm{La}}_{x}{\mathrm{Ba}}_{2}{\mathrm{Cu}}_{3}{\mathrm{O}}_{y}$ with x values less than nominal, and another phase of pure La123 with partial substitution of La for Ba and reduced ${T}_{c}.$ The crystallographic changes and the reduction of ${T}_{c}$ can be interpreted based on the formation of this pure La123 subphase upon La doping.

Relationships involving metastable equilibrium solubility, surface complexes, and crystallite disorder with carbonated apatites.

Previous studies have shown that the metastable equilibrium solubility (MES) behavior of carbonated apatites (CAPs) may be described by a surface complex with the hydroxyapatite (HAP) stoichiometry in the absence of solution fluoride and by that with the fluorapatite (FAP) stoichiometry when appreciable solution fluoride is present. Studies have also shown that the magnitude of the MES is directly related to the crystallinity of the CAP. The aim of the present investigation was to examine the relationship between the CAP MES determined in the presence of solution fluoride and CAP crystallinity and to examine the effect of the change in the stoichiometry of the surface complex (from that of HAP to that of FAP) upon the relationship of the CAP MES to crystallinity. CAP samples were prepared by methods based on the precipitation of CAP from calcium phosphate solutions and the hydrolysis of dicalcium phosphate dihydrate in bicarbonate solutions. From X-ray diffraction experiments, the crystallite microstrain, and the full width at half maximum (FWHM) of the 002 reflection were determined for the CAPs. From CAP MES experiments conducted in the presence of solu tion fluoride, linear plots of the mean MES (i.e., mean pK(FAP)) values vs the crystallinity parameter (i.e., microstrain and FWHM) were obtained that yielded slopes that were essentially the same as those obtained in the absence of solution fluoride (i.e., mean pK(HAP) values vs crystallinity). This parallel finding suggests that the CAP crystallite disorder affects the energetics of the two surface complexes essentially to the same extent and provides new insight into the nature of CAP surface complexes.

Texture and crystallite microstrain development during tensile deformation of copper - simulation and comparison to experimental results

Textures formed by tensile deformation at ambient temperatures and texture induced crystallite microstrains of pure copper were simulated using the full plastic Taylor-Bishop-Hill theory and an elastic unloading process described by the linear elastic Voigt model. The results of the simulations are compared to inverse pole figures experimentally determined by X-ray diffraction and e φψ vs. sin 2 ψ curves experimentally determined using high energy synchrotron radiation. It is shown that the texture evolution has a strong influence on the crystallite microstrains and produces non-linear strain curves. The microstrain distribution depends on the deformation mode and the lattice plane.

Composition fluctuations in the demixed supercooled liquid state of Zr41Ti14Cu12.5Ni10Be22.5: a combined ASAXS and SANS study

This chapter contains basic concepts and applications of wide-angle X-ray diffraction (XRD) and small-angle X-ray scattering (SAXS) to studies of nanostructured materials. The first part includes an introduction to the technique of X-ray powder diffraction (XPD), which is commonly applied to phase identification of powdered materials, characterization of unit cells, determinations of lattice parameters and, in some cases, also coordinates of atoms inside the unit cells. The main aspect described here is the analysis of the shape of X-ray diffraction peak profiles, which allows one to determine additional and also valuable structural information of nanomaterials, such as average crystallite sizes and crystallite microstrains. Detailed deductions of the equations used for different applications of X-ray diffraction and basic concepts of crystallography (such as those related to symmetries, Bravais and reciprocal lattices, etc.) are not described. The second part presents the basic equations related to the SAXS method and their applications to several biological systems (proteins in solution). Classical SAXS is an experimental procedure that is employed in transmission mode and is also applied to the study of many nanostructured inorganic materials. The third part includes two variants of the classical SAXS procedure, namely grazing incidence small-angle X-ray scattering (GISAXS) and anomalous small-angle X-ray scattering (ASAXS). The basic concepts of the GISAXS method and several applications to studies of nanostructured materials deposited on flat substrates and buried nanostructures are presented. The basic concepts of the ASAXS method are described, together with its applications to complex materials that cannot be properly studied using the classical SAXS technique, such as, for example, materials modeled by three phases with different electron densities. Most of the experiments described in this chapter were performed by the authors using X-ray beam lines of the National Synchrotron Light Laboratory (LNLS), Campinas, Brazil.

Simulation of texture and crystallite microstrain development during compression and tension of an Al alloy and comparison to experimental results

Cold compression textures, tension textures and crystallite microstrains of an AlMg 3 aluminum wrought alloy were simulated using the Taylor–Bishop–Hill theory and an elastic unloading model. The results of the simulations are compared to inverse pole figures determined by X-ray diffraction and ε ϕψ vs sin 2 ψ-curves determined using synchrotron radiation. It is shown that the texture evolution has a strong influence on the crystallite microstrains and produces non-linear microstrain curves, which can be interpreted and evaluated using the results of the simulations.