Rietveld Approach Research Articles

β-Tricalcium Phosphate Interferes with the Assessment of Crystallinity in Burned Skeletal Remains

The analysis of burned remains is a highly complex process, and a better insight can be gained with advanced technologies. The main goal of this paper is to apply X-ray diffraction, partially supported by infrared attenuated total reflectance spectroscopy to determine changes in burned human bones and teeth in terms of mineral phase transformations. Samples of 36 bones and 12 teeth were heated at 1050°C and afterwards subjected to XRD and ATR-IR. The crystallinity index was calculated for every sample. A quantitative evaluation of phases was documented by using the Rietveld approach. In addition to bioapatite, the following mineralogical phases were found in the bone: β-tricalcium phosphate (β-TCP) (Ca3(PO4)2), lime (CaO), portlandite (Ca(OH)2), calcite (CaCO3), and buchwaldite (NaCaPO4). In the case of bone, besides bioapatite, only the first two mineralogical phases and magnesium oxide were present. We also observed that the formation of β-TCP affects the phosphate peaks used for CI calculation. Therefore, caution is needed when its occurrence and evaluation are carried out. This is an important warning for tracking heat-induced changes in human bone, in terms of physicochemical properties related to structure, which is expected to impact in forensic, bioanthropological, and archaeological contexts.

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.

Averaging the intensity of many-layered structures for accurate stacking-fault analysis using Rietveld refinement

Many technologically important synthetic and natural materials display stacking faults which lead to complex peak broadenings, asymmetries and shifts in their powder diffraction patterns. The patterns can be described using an enlarged unit cell (called a supercell) containing an explicit description of the layers. Since the supercell can contain hundreds of thousands of atoms with hundreds of thousands ofhklreflections, a Rietveld approach has been too computationally demanding for all but the simplest systems. This article describes the implementation of the speed-ups necessary to allow Rietveld refinement in the computer programTOPASVersion 6 (Bruker AXS, Karlsruhe, Germany). Techniques implemented include: a peaks buffer that allows hundreds of thousands ofhkl-dependent peak shapes to be automatically approximated by a few hundred peaks; an averaging process for hundreds of large supercells with minimum impact on computational time; a smoothing technique that allows for the use of small supercells which approximate supercells ten to 20 times larger; and efficient algorithms for stacking sequence generation. The result is Rietveld refinement of supercells operating at speeds several thousand times faster than traditional Rietveld refinements. This allows quantitative and simultaneous analysis of structure and microstructure in complex stacking-faulted samples.

Insights into the structural, microstructural and physical properties of multiphase powder mixtures

In recent years, research interests on structural and microstructural properties of materials have gained enormous impetus owing to their absolute necessity in many fields (e.g., chemistry, physics, synthetic and materials science). Herein, we present an insight into comprehensive ascertainment of the general structural, microstructural and physical properties of multiphase powder mixtures. We systematically explored the properties of the multiphase samples to disclose their structure and chemical composition features using a series of techniques, such as X-ray diffraction, and energy dispersive X-ray spectroscopy. The Rietveld approach based on structure and microstructure refinement analysis was adopted for precise determination of several microstructural parameters as well as phase contents of individual phases in the multiphase materials. The X-ray diffraction results confirms that the samples are multiphase and crystallize in the monoclinic baddeleyite structure with P 1 21/c 1 space group, orthorhombic mullite structure with P b a m space group, and cubic molybdenum structure with I m –3 m space group, respectively. The morphology features of the samples were observed by using scanning electron microscopy. The actual elemental distributions can be easily observed in energy dispersive X-ray spectrometry elemental mappings. To shed more light on the properties of the multiphase powder mixtures, their physical features (e.g., dislocation density, unit cell volume, X-ray density, porosity) were researched in detail. Moreover, the residual stresses of the multiphase samples were investigated by utilizing the sin2ψ approach.

Bayesian approach applied to the Rietveld method

The application of the Rietveld method for lattice constant and crystal structure refinement has been undertaken with great success. More routinely, this method is used to estimate quantitative phase amounts and to get information on the coherent diffracting length and the lattice defect density. In this paper an innovative combination of the Rietveld method with the Bayes approach is presented, to obtain directly the distribution of the refined parameters from a measured diffractogram, while the conventional Rietveld technique enables only the deduction of the most probable parameter and the estimation of its precision by confidence intervals. Furthermore, the goal of this work is to promote the development of a robust and automatable Rietveld algorithm. A detailed description of the modified algorithm is presented. Such a modified Rietveld approach is applied to anin situhigh-temperature experiment on a steel sample, including the temperature-dependent α → γ phase transformation reaction during heating and the martensitic transformation during the cooling phase.

Quantitative X-ray diffraction analysis of development of Z phase in 12%Cr–Nb–V–N steel

To study the evolution of nitrides (Nb,V)N, (V,Nb)N and Cr2N, and in particular the formation of the Z phase Cr(V, Nb)N, a model alloy with composition similar to that of 12%Cr steels for high temperature applications, microalloyed with Nb and V but with a very low carbon content, has been designed. A quantitative determination of the volume fractions of the extracted nitrides that had formed after aging treatments at 650°C for up to 10 000 h was carried out by an X-ray diffraction procedure, based on the Rietveld approach. The investigation of the Z phase evolution by the Johnson–Mehl–Avrami–Kolmogorov kinetics at 650 and 700°C revealed that, as the kinetic exponent is very close to unity, the formation mechanism of this phase is not associated with a conventional process of nucleation but hints at a gradual diffusion controlled transformation of the pre-existing V and Nb nitrides.

Improving Rietveld‐Based Clay Mineralogic Quantification of Oxisols Using Siroquant

Although mineralogic quantitative phase analysis (QPA) of the soil clay fraction can provide useful information for the improvement of soil management practices, QPA often requires a combination of several analytical techniques, which can be expensive and time consuming. One alternative that involves a single analysis to give accurate QPA of soils is the use of the Rietveld method to analyze powder x‐ray diffraction (XRD) data. In this study, we evaluated the accuracy of the XRD–Rietveld approach for mineralogic quantitative analyses of Oxisol clays when observed structure factors [F(hkl)] of pedogenic minerals (i.e., kaolinite, hematite, and goethite) are used in the Rietveld analyses performed using Siroquant software. The results showed that although the structures of disordered clay minerals are especially difficult to incorporate in standard Rietveld refinement, which relies on ordered three‐dimensional structure models, Mineralogic quantification can be accurately done for complex matrices having a large number of phases and various degrees of structural and compositional disorders when observed F(hkl) values are used. It is also possible to develop observed F(hkl) values for Al‐hematite and Al‐goethite from impure samples of such oxides to use as starting structure models for Rietveld analysis. We believe that this approach can be successfully extended to other geologic materials.

Simulation of layer-faulting in Nb2Co7intermetallic compound using DIFFaX+

The crystal structure and the fault structure of the intermetallic Nb2Co7 phase were determined using DIFFaX+ refinements on the basis of synchrotron powder-diffraction data. The crystal structure was confirmed to be of the monoclinic Zr2Ni7 type. The layer faulting can be understood as partial occurrence of structural features of the Yb2Ag7-type structure, which contains the same “triple layers” as the Zr2Ni7-type structure does, but stacked in a different fashion. Introduction The binary Nb-Co system [1] contains, among other phases, the intermetallic Nb2Co7 compound with the recently identified crystal structure described in ref. [2]. For an intermetallic, Nb2Co7 exhibits an unusually high plastic deformability [3, 4]. Consequently, the question arises, whether there is a relation between the actual crystal structure and the high deformability. The X-ray powder-diffraction patterns used of Nb2Co7 for structural studies exhibit strong line broadening, which can be ascribed to faulting with respect to the layered structure of Nb2Co7. Such defects are expected to play a role in the deformability of this phase, but the traditional Rietveld approach is not able to handle fully the diffraction phenomena associated with faulting. Therefore, DIFFaX+ refinements are provided here, which depart from the layered nature of the material and from previous qualitative considerations concerning the character of the faulting [2]. The results provide useful inside into the defect structure of the material. Crystal structure and faulting model Structure/microstructure analyses were conducted on a Nb2Co7 powder sample containing tiny amounts of the cubic C15-NbCo2 Laves phase (equilibrium phase with Nb2Co7 in a twophases region at the final annealing temperature of 900°C [1]). An X-ray powder-diffraction pattern recorded on the powder diffractometer installed at the ID31 beamline of the ESRF synchrotron (Grenoble, F) using a wavelength of 0.400094 A was available for the specimen. 424 European Powder Diffraction Conference, EPDIC 11 The average (defect free) crystal structure of Nb2Co7 was previously identified [2] to be similar to monoclinic Zr2Ni7 [5, 6], figure 1a. Within the crystal structure one can identify triple-layers parallel to (001) with a complex internal atomic structure: an inner Kagometype layer (KA) of “Co3” sandwiched by two outer “close-packed” layers (CL) “NbCo2” (with Nb-Co ordering), leading to a layer composition of Nb2Co7 corresponding also to the overall phase composition. The triple layers (CL-KA-CL) by themselves ideally exhibit an hexagonal layer symmetry, but in view of the final crystal structure, a centred rectangular unit cell with basis vectors a and b should be considered, identical to the lattice-basis vectors of the monoclinic crystal structure (figure 1b). (a) a tri pl e la ye r

Metamictization in zircon: Raman investigation following a Rietveld approach. Part II: Sampling depth implication and experimental data

AbstractProfile line deconvolution following a Rietveld approach is applied to Raman spectra obtained from natural zircon grains from the European Alps. The corrected bandwidths are in perfect agreement with the values obtained from an established correction method (after Irmer) as far as the area of validity of the latter is concerned. For Raman active modes smaller than that, the Rietveld approach also yields accurate values for the true Raman bandwidth. Moreover, changes to instrument parameters are compensated by the correction routine. As for the studied zircon grains, Raman spectroscopy was shown to be a suitable tool for the examination of zoning (i.e. regions which show a variable degree of radiation‐induced damage because of a different amount of incorporated uranium and/or thorium). This is complicated by the fact that the measured Raman signal is not restricted to the depth expected from the axial resolution (several micrometers) but a significant contribution comes from a comparatively large excitation volume (tens of micrometer deep). This sampling volume, however, lies within the same order of magnitude as zoning, which itself is blurred by the range of amorphization‐causing alpha‐particles. Copyright © 2008 John Wiley & Sons, Ltd.

Metamictization in zircon. Part I: Raman investigation following a Rietveld approach: Profile line deconvolution technique.

AbstractThe line profile form of Raman spectra can be analyzed using the very same approach and software used for diffractogram deconvolution via the Rietveld approach. In both cases the ‘true’ profile containing information about the sample must be separated from the instrument's profile function (and potentially from the emission profile) which can be achieved by deconvolution. In this first part of a two‐part study we demonstrate how the instrument's function can be described via a Gaussian function profile (yielding the very same result as several convoluted hat functions) using several examples (diamond, calcite, silicon and silicon carbide) for which true Raman bandwidth values are presented (assuming the true band profile to be Lorentzian). Also, asymmetrical bands can be described and analyzed via the presented deconvolution approach. The second part of this study will discuss and apply this method for studying the radiation‐induced damage in zircon grains (metamictization). Copyright © 2008 John Wiley & Sons, Ltd.

Analysis of crystallization behavior of Fe48Cr15Mo14Y2C15B6 bulk metallic glass by synchrotron radiation

The amorphous-to-crystalline transformation behavior of Fe48Cr15Mo14Y2C15B6 bulk metallic glasses was first investigated by high-temperature differential scanning calorimetry. Three events were detected with onset temperatures at 922, 975, and 1036 K, respectively. In situ synchrotron radiation x-ray diffraction patterns were collected during continuous heating and analyzed with the Rietveld approach. To describe simultaneously the amorphous fraction and crystallization products as a function of temperature, a paracrystalline structure-factor model was developed. It was included for quantitative evaluation of the amorphous phase, together with the structure factor of Cr23C6- and Fe3Mo3C-type phases observed during crystallization. Volume fractions of phases as well as lattice parameters, average lattice disorder, and crystallite size of the crystallized phases have been followed as a function of temperature. In this way, the structure evolution and thermal events have been closely inspected and accounted for by a crystallization mechanism.

Advances in the structure and microstructure determination of yttrium silicates using the Rietveld method

The Y 2O 3–SiO 2 1:1 composition doped with a weak concentration of europium ions was prepared with the sol–gel technique and the products studied by X-ray diffraction as a function of temperature in the range from 900 to 1300 °C, using the method of Rietveld for quantitative evaluation of amorphous and crystalline evolving phases. The amorphous profile of the yttrium oxyorthosilicate glasses has been described following the “Rietveld for Disordered Materials” method and subsequently included in the patterns of semicrystalline samples that have been heat-treated for temperatures above 900 °C at 1000, 1100, 1150, 1200 and 1300 °C. The quantitative evaluation of the amorphous phase is obtainable from the Rietveld approach equivalent to the method after Ruland. This enabled us to study in fine detail the structural rearrangements and growth mechanisms that take place during the crystal-to-amorphous transformation in terms of coordination numbers, average interatomic distances, average crystallite size and microstrain and to identify the polymorphous transformation involving the Y 2SiO 5 phase from low-to-high-temperature forms, as well as some minor quantities of other phases namely α-Y 2Si 2O 7 phase, Y 2O 3 and Y 4.67(SiO 4) 3O.

Chemical analyses and X-ray diffraction investigations of human hydroxyapatite minerals from aortic valve stenoses

Abstract A total of 23 solid, mineral-like samples from calcified aortic valves of human origin have been investigated by means of classic analytical techniques (atomic absorption spectroscopy) and powder X-ray diffraction methods (Rietveld approach). The calcification goes back to hexagonal Ca-deficient hydroxyapatite, and there is a large variance in absolute hydroxyapatite contents as well as in crystalline qualities. The source of the calcium deficiency has been traced back to the 4f calcium site of the crystal structure in P63/m, and the calcium loss is compensated by hydroxy group deficiencies. Despite no correlation between analytically and diffractionally determined calcium contents, the crystallinities of the samples and the sharpnesses of their Bragg peaks seem to be related with the sub-occupancy of the 4f calcium site.

Determination of quartz in bauxite by a combined X-ray diffraction and X-ray fluorescence method

Quartz is one of the important phase constituents of any bauxite and may vary from a small fraction to over 50% of the total SiO 2 concentration. At present, the most practical method of estimating quartz is by wet chemistry or by using conventional X-ray diffraction (XRD) methods. Whether employing a direct or Rietveld approach, the XRD method is difficult and not possible for small quartz concentrations because of severe line overlaps. A new method uses bauxite material calcined at 1000 °C. Major bauxite phases, such as gibbsite, boehmite, kaolinite and goethite are entirely decomposed in the calcination process. The calcination procedure converts SiO 2 containing kaolinite into XRD amorphous material. In addition to the amorphous portion, there are just four major crystalline phases present: corundum, hematite, rutile and quartz. Quartz in the calcined bauxite corresponds to the primary quartz occurring in the initial sample. Rutile is employed as the internal standard. First attempts to quantify quartz in calcined bauxite using XRD based Rietveld analysis will be described. Results are presented for the Sangaredi (Guinea) bauxite deposit.

Micro X-ray diffraction on capillary powder samples: a novel and effective technique for overcoming preferred orientation

In past years, both experimental and analytical approaches have been developed for eliminating preferred orientation effects on powder X-ray diffraction patterns. The state of the art does not allow one to face the problem without difficult sample treatments, mechanical randomization, pole-figure study or pattern fitting based on the Rietveld approach. These methods are time consuming or need the knowledge of all the structural parameters, and, moreover, must be managed by specialized operators. Besides, none of the above techniques can be applied to powder samples of drugs loaded into polymeric carriers, the diffraction patterns of which present a structured amorphous halo from which the crystalline drug peaks rise up. In this paper, it is shown that micro X-ray diffraction on capillary powder samples, combined with a two-dimensional detector, is a promising solution to preferred orientation problems, since it provides easy and rapid preparation of randomly oriented powder samples, fast measurements (acquisition times of a few minutes) and correct powder diffraction patterns.

Quantitative Phase‐Composition Analysis of Liquid‐Phase‐Sintered Silicon Carbide Using the Rietveld Method

Accurate quantitative X‐ray diffraction analysis of SiC‐based ceramics is difficult because of the significant overlap of the Bragg reflections from the different SiC polytypes. In this regard, the Rietveld method is a powerful tool for the accurate and precise analysis of the phase/polytype compositions in these materials. In this study, we have used two different types of Rietveld codes for the quantitative phase/polytype analysis of a liquid‐phase‐sintered SiC specimen: FULLPROF, which is based on the classical Rietveld approach, and BGMN, which is based on the new fundamental parameter approach. In both cases, the effect of texture corrections on the precision of the analysis also was studied. The accuracy of the analysis, in terms of the weight percentage of SiC (all polytypes) and yttrium aluminum garnet liquid phase, as determined from the starting powder composition, is within the standard deviation of the analysis in both cases (FULLPROF and BGMN), with and without the texture corrections. In addition, in the case of the classical code (FULLPROF), inclusion of the texture corrections has been shown to improve the precision. In contrast, the precision of the analysis using the BGMN code without the texture corrections is better. However, inclusion of the texture corrections is expected to improve the accuracy of the analysis.

Determination of alpha and beta alumina in ceramic alumina by X-ray diffraction

Determination of alpha alumina (α-Al 2O 3) content has been one of the oldest X-ray diffraction (XRD) methods of analysis. However, rhombohedral aluminas may have a variety of morphological forms for which there are marked differences in relative intensities of their major XRD reflections (the preferred orientation effect). In addition, a specimen X-ray diffracting power may vary making it difficult or impossible to employ a reference material. Consequently, comparing intensities of selected reflections from a sample with those of a reference material may cause a serious analytical error. A conventional XRD and a Rietveld approach were used to analyze nine commercial ceramic aluminas, three NIST standards and two special grades of alumina for alpha and beta alumina (β-Al 2O 3=Na 2O·11Al 2O 3) content. The samples were also analyzed by scanning electron microscopy (SEM) to assess morphology. Increasing the number of XRD reflections analyzed from two to eight did not improve the reliability of the quantification process. The morphological differences among samples could not have been minimized that way. Conventional XRD (two to eight reflections) indicated alpha alumina values varying from 88 to 106% while the Rietveld analysis (full pattern) attributed 100% for all but two. These two samples were found to contain beta alumina. Initial Rietveld refinements indicate that the beta phase contains only a fraction of the total Na 2O content. The preferred orientation was computed for 14 specimens and assessed using a relative scale. The Rietveld least-square refinements would not only provide relatively quick, but also reliable information on alpha and beta content, as well as unit cell parameters of alpha and beta phases.

Structure refinement of triclinic tungsten trioxide

The thermodynamically stable form of WO 3 at room temperature is triclinic. The structure of this form of WO 3 was for the first time refined from neutron diffraction data. The data were obtained on a new high resolution powder diffractometer. The structure obtained appears to be somewhat more accurate than that obtained from single crystal X-ray diffraction data. Rietveld approach was used to refine the neutron powder diffraction data. Results using the software packages GSAS, Rietan and PROFIL are compared. Using GSAS, an R wp of 7.97 and an R p of 5.87 were obtained. Neutron diffraction data were also collected and analysed on a sample which was a mixture of the monoclinic and triclinic forms of WO 3; Rietveld refinements of this data were stable and yielded reasonable results.

Rietveld Analysis of Ceramic Nuclear Waste Forms

ABSTRACTPowder X-ray diffraction patterns were collected from three titanate waste forms - a calcine powder, a prototype ceramic without waste, and a ceramic containing 10 wt% JW-A simulated waste - and interpreted quantitatively using the Rietveld method. The calcine consisted of fluorite, pyrochlore, rutile, and amorphous material. The prototype waste form contained rutile, hollandite, zirconolite and perovskite. The phase constitution of the JW-A ceramic was freudenbergite, loveringite, hollandite, zirconolite, perovskite and baddeleyite. Procedures for the collection of X-ray data are described, as are assumptions inherent in the Rietveld approach. A selection of refined crystal data are presented.