Full Pattern Fitting Research Articles

Electron diffraction characterization of nanocrystalline materials using a Rietveld-based approach. Part II. Application to microstructural analysis

This is the second in a two-paper series concerning the quantitative characterization of nanocrystalline materials using an electron-diffraction-based approach, in which a full-pattern fitting Rietveld-based refinement is applied to electron powder diffraction data in transmission electron microscopy (TEM). Part I [Sinha et al. (2022). J. Appl. Cryst. 55, 953–965] established a standard calibration protocol to determine the instrumental effects, with special emphasis on the camera length and the diameter of the selected area apertures. Possible application cases are now considered to demonstrate the capabilities of the approach, including the evaluation of the phase composition of TEM specimens, an operation that reveals new application fields for this powerful materials characterization technique. In this regard, different types of material specimen are examined: nanocrystalline yttrium oxide, silicon, titanium dioxide and debris from disc brake wear, each one featuring specific aspects to be tackled with the proposed methodology. To demonstrate the limits of the proposed approach as concerns the material characteristics, an analysis of a hematite sample obtained from the heat treatment of natural goethite, displaying a relatively coarse crystallite size, is performed and a critical discussion of the results is given.

Electron diffraction characterization of nanocrystalline materials using a Rietveld-based approach. Part I. Methodology.

Transmission electron microscopy is a powerful experimental tool, very effective for the complete characterization of nanocrystalline materials by employing a combination of imaging, spectroscopy and diffraction techniques. Electron powder diffraction (EPD) pattern fingerprinting in association with chemical information from spectroscopy can be used to deduce the identity of the crystalline phases. Furthermore, EPD has similar potential to X-ray powder diffraction (XRPD) for extracting additional information regarding material specimens, such as microstructural features and defect structures. The aim of this paper is to extend a full-pattern fitting procedure, broadly used for analysing XRPD patterns, to EPD. The interest of this approach is twofold: in the first place, the relatively short times involved with data acquisition allow one to speed up the characterization procedures. This is a particularly interesting aspect in the case of metastable structures or kinetics studies. Moreover, the reduced sampling volumes involved with electron diffraction analyses can better reveal surface alteration layers in the analysed specimen which might be completely overlooked by conventional bulk techniques. The first step forward to have an effective application of the proposed methodology concerns establishing a reliable calibration protocol to take into correct account the instrumental effects and thus separate them from those determined by the structure, microstructure and texture of the analysed samples. In this paper, the methodology for determining the instrumental broadening of the diffraction lines is demonstrated through a full quantitative analysis based on the Rietveld refinement of the EPD. In this regard, a CeO2 nanopowder reference specimen has been used. The results provide indications also on the specific features that a good calibration standard should have.

Low-loss characteristics and sustained magneto-dielectric behaviour of cobalt ferrite nanoparticles over 1–6 GHz frequency range

Cobalt ferrite (CoFe2O4) nanoparticles were synthesized through the citrate precursor route. The XRD pattern confirmed the formation of a homogeneous single-phase spinel structure with an Fd3m space group. No impurities or unreacted constituents in the sample were observed. Analysis of the most prominent (311) peak of the XRD pattern revealed the crystallite size to be ~39 nm with lattice constant and interplanar spacing as ~8.374 Å and ~2.525 Å, respectively. Other key structural parameters, such as dislocation density, strain, X-ray density, and hopping lengths, were also obtained from XRD data. Structural parameters were refined by applying the full pattern fitting of the Rietveld method using the Pseudo-Voigt function. High-resolution images obtained from SEM and TEM confirmed the morphological characteristics and crystallite size of the CoFe2O4 nanoparticles. The hysteresis loop recorded over the applied external magnetizing field of −10 kOe to +10 kOe revealed a specific saturation magnetization, specific remanent magnetization, and coercivity value of ~64 emu/g, ~24 emu/g, and ~565 Oe, respectively. A remanence ratio ~0.374 signified magnetostatic interaction between CoFe2O4 nanoparticles and confirmed their multi-domain structure and soft magnetic nature. Investigations were carried out to obtain the variations in complex dielectric permittivity, complex magnetic permeability, dielectric and magnetic loss tangents, AC conductivity, and quality factor in 1–6 GHz frequency range. The CoFe2O4 nanoparticles exhibited low dielectric and magnetic loss tangents of 10−2 and 10−3 order, along with moderate values of relative permittivity and refractive index, i.e., 4.801 and 2.3, respectively. The sustained magneto-dielectric behaviour and low-loss characteristics suggest that CoFe2O4 nanoparticles can be suitably dispersed in a dielectric matrix and used to develop efficient substrate material for improved telemetry, telecommunications and radar systems of aerospace systems operating over the 1–6 GHz frequency range.

Influence of La, Mn and Zn Substitution on the Structure, Magnetic and Absorption Properties of M-Type Barium Ferrites

A series of M-type barium ferrites with chemicals composition BaFe12O19 and Ba0.7La0.3Fe(12-2x)(MnZn)xO19 (with x = 0.0, 0.2, 0.5) were synthesized using a chemical coprecipitation based technique. The sample was then called as BFO and BLF, BLFMZ-02 and BLFMZ-05, respectively. The structural parameters were measured by applying the full pattern fitting of Rietveld method using Fullprof program. The crystallite size was calculated using Scherrer formula and Williamson-Hall analysis method, and also confirmed by scanning electron microscope (SEM) and transmission electron microscope (TEM). The morphology of particle is composed of fine-grained aggregates with particle size distributions in the range of 70nm - 160nm. The lattice parameter (a = b and c), cell volume (Vcell) and density (ρ) of the samples were found to be changed with La, Mn and Zn substitution due to the dissimilar cationic radii of Ba2+ (1.49Å), La3+ (1.22Å), Fe3+ (0.64Å), Mn3+ (0.89Å) and Zn2+ (0.76Å) ions. The results of sample measurements with Vibrating Sample Magetometer (VSM) indicate that the magnetic behaviours showed that the saturation magnetization (Ms) increased gradually with the substitution of La3+, Mn3+ and Zn3+ ions, whereas the coercivity (Hc) was increase with addition of La3+ ions and then decrease significantly with the addition of Mn3+ and Zn2+ ions. The vector network analyzer (VNA) revealed that microwave absorption measured within 7 – 15 GHz frequency range indicated optimum reflection loss (RL) of-21.50dB at 10.5GHz for BLMZ-02 sample.

Rietveld, cation distribution and elastic investigations of nanocrystalline Li0.5+0.5xZrxFe2.5-1.5xO4 synthesized via sol-gel route

The present report deals with the structural and elastic behavior of Li+ and Zr4+ substituted spinel ferrites. Nanocrystalline spinel ferrite system of chemical formula Li0.5+0.5xZrxFe2.5-1.5xO4 (where, x = 0.0, 0.1, 0.2, 0.3, 0.4, 0.5 and 0.6) was synthesized by using sol-gel auto combustion method. The as-prepared powder was annealed at 800 °C for 5 h for better crystallinity. The annealed samples were characterized by X-ray diffraction technique and Fourier transform infrared spectroscopy for structural and elastic studies respectively. By applying the full pattern fitting of Rietveld method the x, y, z coordinates of atoms, unit cell dimensions and occupancy of ions were estimated. The lattice parameter was found to decrease after substitution due to increase in electron affinity. Site preferences of cations were obtained by matching experimental and calculated intensity. The characteristic bands of crystallographic sub-lattice for the cubic structure were observed by FTIR spectra.

Polymorphic Transformation of Indomethacin during Hot Melt Extrusion Granulation: Process and Dissolution Control.

To study and elucidate the effect of the intensity and duration of processing stresses on the possible solid-state changes during a hot melt extrusion granulation process. Blends of α-indomethacin and PEG 3350 (w/w 4:1) were granulated using various screw sizes/designs on the melt extruder under different temperature regimes. Differential Scanning Calorimetry and X-ray Powder Diffraction were employed for characterization. The dissolution behavior of the pure polymorphs and the resulting granules was determined using in-situ fiber optic UV testing system. An XRPD quantitation method using Excel full pattern fitting was developed to determine the concentration of each constituent (amorphous, α and γ indomethacin and PEG) in samples collected from each functioning zone and in granules. Analysis of in-process samples and granules revealed that higher temperature (≥130°C) and shear stress accelerated the process induced phase transitions from amorphous and/or the α form to γ indomethacin during heating stage. However, rapid cooling resulted in an increased percentage of the α form allowing isolation of the meta-stable form. By determining the conditions that either prevent or facilitate process induced transformations of IMC polymorphs during melt granulation, a design space was developed to control the polymorph present in the resulting granules. This represents the conditions necessary to balance the thermodynamic relationships between the polymorphs of the IMC system and the kinetics of the possible transformations as a function of the processing stresses.

Surface agglomeration is beneficial for release of magnetic property via research of rare earth (RE) element-substitution

BiFeO3 (BFO) thin films and Rare-Earth (RE) element substitutions were successfully fabricated on silicon substrates by sol–gel technology. Multiferroic properties of BFO had been improved considerably on RE (La, Ho, Er)-substitution at Bi site. The RE-substitution principle was presented in Fig. 1(the simulative images of ions matching). The single phase and the perovskite based rhombohedral structure with R3c space group of BFO and RE-substitution films were confirmed through the full pattern fitting of surface and section XRD profiles. There were obvious agglomeration phenomena for RE-substitution films via FESEM patterns, and the AFM images shown that the RE-substation films possessed smoother surface texture comparing with the BFO. The RE-substitution films showed higher saturation magnetization (Ms) and remanent magnetization (Mr) due to the reduced concentration of defects (oxygen vacancy), RE ions with smaller radii size (size effect) and surface structure of compactness. Fe3+ and O2− ions play an essential role in superexchange interaction, the XPS, surface and vertical EDS images revealed increasing tendency of Fe3+ ions and O2− ions.

Competition between the impact of cation distribution and crystallite size on properties of MnxFe3−xO4 nanoparticles synthesized at room temperature

Abstract In the present study, the effect of Mn doping on the structural, morphological and magnetic properties of MnxFe3−xO4 (0≤x≤1) samples has been investigated. The obtained X-ray diffraction patterns indicate that the crystallite size depends on the cation distribution in the samples. The Rietveld full-pattern fitting by MAUD software determines the cation distribution, ion coordination, ion occupancy, crystallite size, microstrain and unit cell parameter. The magnetic hysteresis measurements show that the saturation magnetization and effective anisotropy constant decrease by increasing the Mn content up to x=0.2, while they increase by further Mn doping. Structural and magnetic properties have been completely described on the basis of the competition between the effects of cation distribution and crystallite size. The obtained results show an increase in the crystallite size and consequently, increase in magnetization for the 0.2

Combining XRD and XRF analysis in one Rietveld-like fitting

X-ray diffraction (XRD) and X-ray fluorescence (XRF) are widely used analytical techniques for materials characterization; the information they provide can be considered complementary, as the former is mostly used to obtain crystallographic information and analyze phase content, whereas the latter is sensitive to elemental composition. Many researchers and technologists working in a variety of application fields already use them together in some sort of a “combined” approach, by separately performing XRD and XRF data collection and analysis on the same sample and then comparing the analytical results obtained to integrate and complement the respective analytical information. In this work, we propose a true combined approach to merge both XRD and XRF data acquisition and analysis. Custom analytical X-ray instrumentation has been developed to perform the simultaneous data acquisition, by using a single X-ray source and dedicated detectors to collect the diffracted and fluorescent X-ray photons from the same sample volume. Additionally, a combined XRD/XRF data analysis methodology has been implemented by extending Rietveld based code to incorporate the full pattern fitting of XRF spectra starting from the phases instead of a simple matrix elemental composition. We report two analytical examples from different application fields to better illustrate the capabilities of the proposed approach.

Characterization of nanograined powder samples using the Rietveld method applied to electron diffraction ring patterns

A full-pattern fitting procedure based on the Rietveld method was applied to electron diffraction ring patterns of a two-phase system, exhibiting the co-presence of zinc sulfide (sphalerite) and zinc oxide (Wurtzite). Bright and dark field (DF) images reveal the presence of micrometric aggregates, composed of quasi-spherical nanosized crystallites. These conventional transmission electron microscopy imaging methods provide a general morphological characterization of the specimens although, in the present case, they are not suitable for a detailed characterization of the microstructural features of the analyzed samples. Owing to the overlap and broadening of the diffraction rings of the two phases, DF images cannot provide a satisfactory picture of the individual crystallites of each single phase. To overcome this limit, the mentioned Rietveld approach was applied to model the electron diffraction data. The crystalline domain size and relevant shapes for both phases were successfully evaluated using the proposed methodological approach. The excellent results obtained in the microstructural characterization of the nanostructured multiphase samples demonstrate the capability of this technique, that may represents a fully quantitative method for the routine characterization of crystalline nanomaterials.

Structural transitions and multiferrocity in Ba and Co substituted nanosized bismuth ferrite

To investigate the effect of Ba2+ and Co2+ substitution on the multiferroic properties of the BiFeO3 (BFO) ceramic, Bi1-xBaxFe1-yCoyO3 (x = 0,y = 0 and x = 0.2, y = 0,0.015,0.03,0.04,0.05) ceramics were prepared using sol-gel method. Multiferroic properties of BFO have been improved considerably on Ba2+ and Co2+ substitution at Bi and Fe site, respectively. Full pattern fitting of the XRD profile pattern confirmed the structural transition from rhombohedral to pseudo-cubic phase. The magnetisation in BFO rises appreciably and found to be 0.463 emu/g for Bi1-xBaxFe1-yCoyO3 (x = 0.2, y = 0.05) ceramic nanoparticles. The abrupt increase in magnetization for Bi0.8Ba0.2Fe0.95Co0.05O3 is due to anti-ferromagnetic orbital ordering among Fe/Co ions. The orbital ordering among the ions would change the low spin state of the Co2+ ions to high spin state and results in increased magnetization. Beside, the Co substitution is found helpful in reducing the coercivity of the magnetic nanoparticles for their application as magnetic sensors. The Ferroelectric behavior of Ba and Co substituted samples revealed that increase in maximum polarization with increasing Co content is due to interactions among different Jahn-Teller active Co2+ ions. Moreover, the slimmer polarization-electric field (P-E) loops on increasing Co content implying the relaxor ferroelectric behavior of the samples.

Effects of Zn-Cr-substitution on the structural and magnetic properties of Ni1−xZnxFe2−xCrxO4 ferrites

Cr and Zn-substituted nickel ferrites, general formula Ni1−xZnxFe2−xCrxO4 (x=0, 0.1, 0.3, 0.5, 0.7), were prepared using the sol-gel auto-combustion method. For precise analysis, the Ni1−xZnxFe2O4and NiFe2−xCrxO4 (x=0, 0.1, 0.3, 0.5, 0.7) samples were also checked individually. The effects of Cr and Zn doping on the structural, morphological, and magnetic properties of the samples were evaluated by X-ray diffraction (XRD), scanning electron microscopy (SEM), and vibrating sample magnetometer (VSM). The full pattern fitting of Rietveld method using MAUD program was also applied to determine the exact coordinates of the atoms, unit cell dimensions, and ion occupancy. XRD measurement by Rietveld refinement confirmed the crystalline structure and phase purity of all the ferrites. SEM images showed that the particles were in the nanosize range. VSM results revealed that the values of MS in the NiFe2−xCrxO4 samples decreased and that HC had no regular behavior with increasing Cr content. The maximum value of HC=16Oe was obtained for a Cr content of x=0.7. On the other hand, saturation magnetization values initially increased in both the Ni1−xZnxFe2−xCrxO4 and Ni1−xZnxFe2O4 samples, with changing the doping level up to x=0.3, while for further content, MS decreased. In addition, coercivity decreased with increasing doping level.

Multiphase Structure of Tantalum Oxynitride TaOxNy Thin Films Deposited by Reactive Magnetron Sputtering

This work deals with the structure and the microstructure of tantalum oxynitride thin films deposited by reactive magnetron sputtering. The local structures of amorphous as-prepared thin films are investigated using the pair distribution function (PDF) technique based on total X-ray scattering experiments. The corresponding annealed thin films are analyzed using conventional θ–θ X-ray diffraction technique and full-pattern fitting methods. Rutherford backscattering and X-ray photoelectron spectrometries are used in conjunction with X-ray techniques. As-prepared thin films are nanostructured. The PDF signal is coming from small structural units below 10 A in diameter, which only maintain nearest-neighbor order and with a composition changing gradually from TaN to δ-TaON and Ta2O5 as the oxygen content in the reactive gas increases. On the other hand, the annealed thin films consist of a mixture of separate crystalline phases with refined cell parameters consistent with the formation of TaN (Fm–3m), β-TaON ...

Structure of 3 at.% and 9 at.% Si-doped HfO2 from combined refinement of X-ray and neutron diffraction patterns

The crystal structure of 3 at.% and 9 at.% Si-doped HfO2 powder was determined through refinements using X-ray and neutron diffraction patterns. The lattice parameters, atomic positions, dopant occupancy, and the second phase fraction were determined with high precision using a combined full pattern fitting via the Rietveld method. The results show that both 3 at.% and 9 at.% Si-doped HfO2 powder exhibit the monoclinic crystal structure with P 1 21/c 1 space group. Through the combined refinement, the crystal structure parameters, especially for the positions and occupancies of the lighter atoms, were more precisely determined compared to independent X-ray diffraction refinement. Although the ionic radius of Si4+ is smaller than Hf4+, with increasing Si occupancy, the unit cell volume slightly increases; possible mechanisms for this effect are discussed. Moreover, the refined results provide evidence of the existence of a non-equilibrium phase of HfxSi1−xO2. The second phase (SiO2) fraction is determined as 0.17 at.% for 3 at.% Si-doped HfO2 powders and 1.7 at.% for 9 at.% Si-doped HfO2 powders.

Effects of Co-substitution on the structural and magnetic properties of NiCoxFe2−xO4 ferrite nanoparticles

The sol–gel auto-combustion method was used to prepare nanocrystalline powders of Co-substituted nickel ferrite with the general formula NiCoxFe2−xO4 (x=0.0, 0.1, 0.25, and 0.5). The effects of Co-doping on the structural, morphological, and magnetic properties of the samples were subsequently evaluated by X-ray diffraction (XRD), Fourier transform infrared (FTIR), field emission scanning electron microscopy (FE-SEM), and vibrating sample magnetometer (VSM). Using the MAUD program, the full pattern fitting of Rietveld method was employed to determine the exact coordinate of the atoms, unit cell dimensions, and ion occupancy. X-ray diffraction measurements by Rietveld refinement confirmed the crystalline structure and phase purity of all the ferrites prepared. FTIR results also confirmed the formation of a spinel phase and FE-SEM images showed that the particles were in the nanosize range. Moreover, Rietveld analysis and saturation magnetization (Ms) revealed that Co3+ replaced Fe3+ in the tetrahedral A-sites up to x=0.1. then, it replaced Fe3+ in both A- and B-sites for x≥0.25. Finally, VSM results demonstrated that while Ms remained nearly constant with increasing Co3+ substitution, coercivity (Hc) increased significantly. It may be suggested that the larger magneto-crystalline anisotropy of Co3+ ions is responsible for the increased Hc observed in the Co-doped Ni ferrite samples.

Sucrose lyophiles: A semi-quantitative study of residual water content by total X-ray diffraction analysis

Total X-ray Powder Diffraction Analysis (TXRPD) using transmission geometry was able to observe significant variance in measured powder patterns for sucrose lyophilizates with differing residual water contents. Integrated diffraction intensity corresponding to the observed variances was found to be linearly correlated to residual water content as measured by an independent technique. The observed variance was concentrated in two distinct regions of the lyophilizate powder pattern, corresponding to the characteristic sucrose matrix double halo and the high angle diffuse region normally associated with free-water. Full pattern fitting of the lyophilizate powder patterns suggested that the high angle variance was better described by the characteristic diffraction profile of a concentrated sucrose/water system rather than by the free-water diffraction profile. This suggests that the residual water in the sucrose lyophilizates is intimately mixed at the molecular level with sucrose molecules forming a liquid/solid solution. The bound nature of the residual water and its impact on the sucrose matrix gives an enhanced diffraction response between 3.0 and 3.5 beyond that expected for free-water. The enhanced diffraction response allows semi-quantitative analysis of residual water contents within the studied sucrose lyophilizates to levels below 1% by weight.

Modified statistical dynamical diffraction theory: analysis of model SiGe heterostructures

A modified version of the statistical dynamical diffraction theory (mSDDT) permits full-pattern fitting of high-resolution X-ray diffraction scans from thin-film systems across the entire range from fully dynamic to fully kinematic scattering. The mSDDT analysis has been applied to a set of model SiGe/Si thin-film samples in order to define the capabilities of this approach. For defect-free materials that diffract at the dynamic limit, mSDDT analyses return structural information that is consistent with commercial dynamical diffraction simulation software. As defect levels increase and the diffraction characteristics shift towards the kinematic limit, the mSDDT provides new insights into the structural characteristics of these materials.

Acid‐extractable potassium in agricultural soils: Source minerals assessed by differential and quantitative X‐ray diffraction

AbstractDifferent extraction methods are used world‐wide in routine soil analysis to estimate long‐term potassium (K) reserves for plants. In Sweden, K extracted with 2 M HCl at 100°C (KHCl) is frequently used, although with limited understanding of the phases extracted. In the present study, we quantified the effects of this extraction on soil minerals in particle size fractions ranging from clay to sand, and estimated their relative contribution to KHCl. The study included three Swedish long‐term agricultural field experiments with texture ranging from loamy sand to silty clay, as well as mineral specimens of K feldspar. Total weight loss of particle size fractions was determined, and quantitative and differential X‐ray powder diffraction (QXRD, DXRD), applied on solids before and after extraction, was used to quantify the dissolution of individual mineral phases. QXRD and DXRD included spray‐drying of samples, addition of an internal standard and full pattern fitting, where a combination of mineral‐standard XRD traces was matched with the experimental one. Our results show that KHCl was primarily associated with clay minerals concentrated in the two finest fractions (2–20 and < 2 μm). Highly expandable and mixed‐layer phyllosilicates were quantitatively the most important minerals dissolved. The K was released from micaceous layers in mixed‐layer phyllosilicates with a vermiculitic character. Whether di‐ or trioctahedral, a shared property of the dissolved phases was that they were rich in Fe. In the loamy sand, the coarser fractions (20–2000 μm), where feldspars were prominent, accounted for 35% of KHCl. According to DXRD, there was no significant decrease in K feldspars in any of the samples, and KHCl data for the feldspar specimens suggest that clay minerals contributed at least 70% of KHCl also in the loamy sand. Our study provides insights about the soil minerals that contribute to the long‐term K delivery capacity of soils and an explanation for the prior observation that KHCl is a dynamic fraction that can be affected by management.

Fitting Full X-Ray Diffraction Patterns for Quantitative Analysis: A Method for Readily Quantifying Crystalline and Disordered Phases

Fitting of full X-ray diffraction patterns is an effective method for quantifying abundances during X-ray diffraction (XRD) analyses. The method is based on the principal that the observed diffraction pattern is the sum of the individual phases that compose the sample. By adding an internal standard (usually corundum) to both the observed patterns and to those for individual pure phases (standards), all patterns can all be normalized to an equivalent intensity based on the internal standard intensity. Using least-squares refinement, the individual phase proportions are varied until an optimal match is reached. As the fitting of full patterns uses the entire pattern, including background, disordered and amorphous phases are explicitly considered as individual phases, with their individual intensity profiles or “amorphous humps” included in the refinement. The method can be applied not only to samples that contain well-ordered materials, but it is particularly well suited for samples containing amorphous and/or disordered materials. In cases with extremely disordered materials where no crystal structure is available for Rietveld refinement or there is no unique intensity area that can be measured for a traditional RIR analysis, full-pattern fitting may be the best or only way to readily obtain quantitative results. This approach is also applicable in cases where there are several coexisting highly disordered phases. As all phases are considered as discrete individual components, abundances are not constrained to sum to 100%.

Rietveld Structure Refinement and Cation Distribution of Substituted Nanocrystalline Ni-Zn Ferrites

Ferrite nanoparticles of were prepared by a sol-gel autocombustion method. The prepared samples were shown to have a cubic spinel structure by applying the full pattern fitting of the Rietveld method. The unit cell dimension, discrepancy factor, and interatomic distance have been determined. As the Cr3+ content x increases, the unit cell dimensions and crystallite size are decreased. The IR spectra show two absorption bands in the wave number range of 400 to 600 cm−1.