Ba2Bi0.572TeO6±δ and SrLa2NiFeNbO9 ceramics were prepared in polycrystalline form by conventional solid-state reaction techniques in air. The crystal structures of the title compounds were determined at room temperature from X-ray powder diffraction (XRPD) data using the Rietveld method. The Ba2Bi0.572TeO6±δ structure crystallizes in a triclinic space group I–1 with unit-cell parameters a = 6.0272(2) Å, b = 6.0367(1) Å, c = 8.5273(3) Å, α = 90.007(7)°, β = 90.061(2)°, and γ = 90.015(4)°. The tilt system of the BiO6 and TeO6 octahedra corresponds to the notation a–b–c–. The crystal structure of the SrLa2NiFeNbO9 compound adopts an orthorhombic Pbnm space group with lattice parameters a = 5.6038(5) Å, b = 5.5988(4) Å, and c = 7.9124(6) Å. The BO6 octahedra (B = Ni/Fe/Nb) sharing the corners in 3D. Along the c-axis, the octahedra are connected by O(1) atoms of (x,y,1/4) positions; while in the ab-plane, they are linked by O(2) atoms of (x,y,z) positions. The bond angle of B–O1–B is 168.7° and that of B–O2–B is 156.3°. The octahedral lattice corresponds to the tilt pattern a–a–c+; it indicates that the octahedra tilt out-of-phase along the a,b-axes and in phase along the c-axis.

X-ray diffraction (XRD) characterization of Si powder was carried out using synchrotron and laboratory sources. Microstructural (size-strain) analyses of XRD patterns were carried out using the Rietveld refinement method. Experimentally observed super-Lorentzian shapes of the XRD peaks of Si powder were examined using multimodal profile fitting and bimodal model was found to be adequate. The two components obtained using a bimodal approach are referred as narrow and broad profiles based on their estimated relative peak widths. Peak shapes of crystallite size-dependent parts of narrow and broad profiles were found to be almost Gaussian and Lorentzian in nature, respectively. The simultaneous presence of such peak shapes corresponding to a bimodal microstructure is uncommon in literature. Therefore, in order to explore the role of different natures of XRD peak shapes (size dependent) of the bimodal profiles of Si, detailed microstructural analysis was carried out using the complementary method of whole powder pattern modeling (WPPM) and found to be related to the variance of crystallites' size distribution. Additionally, the effect of instrument resolution (laboratory and synchrotron sources) on the microstructural parameters was also studied. Scanning and transmission electron microscopy were used to characterize the morphology of Si powder and correlate with the microstructural findings of XRD methods.

The crystal structure of kaolinite(Pl, a = 5.153(1), b = 8.941 (1), c = 7.403 (1)Å, α = 91.692(3)°, β = 104.860(3)°, γ = 89.822(3)°, specimens from Keokuk geodes) has been refined in detail and that of dickite (Cc, a = 5.1460(3), b = 8.9376(5), c = 14.4244(6) Å, β = 96.761(5)°) has been re-refined, both from powder diffraction data with the Rietveld method. Except for the hydrogen atoms, the layer structures in both clays are very similar and are much as inferred or determined previously by others. The rotation in the tetrahedral sheet is 7(1)°. The two inner hydroxyl O-H bonds in kaolinite are differently oriented; one points into an octahedral vacancy and the other somewhat away from the octahedral sheet and toward the unoccupied center of an oxygen triangle formed by the two apical oxygens and shared basal oxygen of two adjacent SiO4 tetrahedra. All six of the inner surface hydrogen atoms appear to be nearly equally involved in the hydrogen bonding between kaolinite layers in kaolinite.

A structure refinement of kaolinite made using the Rietveld neutron profile refinement technique has given non-hydrogen atom positions which were not significantly different from those given by B. B. Zvyagin in 1960. All of the hydrogen atoms have been located; the three inner-surface hydrogen atoms are involved in interlayer hydrogen bonds with lengths of 2.95(4), 2.95(4), and 3.06(4) Å with O-H ... O angles of 168(4)°, 144(4)°, and 146(4)° respectively. The inner hydrogen atom is located in a position consistent with that found earlier in dickite and muscovite which are the only dioctahedral layer silicates studied by neutron diffraction to date. The O-H vector makes an angle of 34° with the (001) plane, away from the octahedral sheet, and the projection of the vector on to (001) is at ~30° to the b axis.

Illite polytypes are used to elucidate the geological record of formations, such as the timing and provenance of deformations in geological structures and fluids, so the ability to characterize and identify them quantitatively is key. The purpose of the present study was to compare three X-ray powder diffraction (Q-XRPD) methods for illite polytype quantification for practical application to directly date clay-rich fault rocks and constrain the provenance of deformation-related fluids in clay-rich brittle rocks of the upper crust. The methods compared were WILDFIRE© (WF) modeling, End-member Standards Matching (STD), and Rietveld whole-pattern matching (BGMN®). Each technique was applied to a suite of synthetic mixtures of known composition as well as to a sample of natural clay gouge (i.e. the soft material between a vein wall and the solid vein). The analytical uncertainties achieved for these synthetic samples using WF modeling, STD, and Rietveld methods were ±4–5%, ±1%, and ±6%, respectively, with the caveat that the end-member clay mineral used for matching was the same mineral sample used in the test mixture. Various particle size fractions of the gouge were additionally investigated using transmission electron microscopy (TEM) to determine polytypes and laser particle size analysis to determine grain size distributions. The three analytical techniques produced similar 40Ar/39Ar authigenesis ages after unmixing, which indicated that any of the methods can be used to directly date the formation of fault-related authigenic illite. Descriptions were included for pre-calculated WF illite polytype diffractogram libraries, model endmembers were fitted to experimental data using a least-squares algorithm, and mixing spreadsheet programs were used to match end-member natural reference samples.

The degree of preferred orientation of mineral grains in powder X-ray diffraction (XRD) samples prepared by standard techniques has been evaluated by means of a correction model implemented in the Rietveld program, BGMN. It is demonstrated that neither front- nor side-loading of mineral powders obtained by wet grinding in a McCrone micronizing mill yield powder mounts with randomly oriented particles. Despite fine grinding, the primary sizes and shapes of mineral grains contained in multi-phase samples influence the degree of preferred orientation in XRD powder mounts. Two minerals, both of platy habit, were found to show different degrees of preferred orientation in front- and side-loaded samples. In contrast to these methods of sample preparation, the spray-drying technique yielded perfect randomness of the particles. The experiments on artificial mineral mixtures demonstrate that the model applied can effectively correct for preferred orientation allowing reliable Rietveld quantitative phase analysis of moderately textured samples prepared by standard techniques.

Anisotropy in clay-rich sedimentary rocks is receiving increasing attention. Seismic anisotropy is essential in the prospecting for petroleum deposits. Anisotropy of diffusion has become relevant for environmental contaminants, including nuclear waste. In both cases, the orientation of component minerals is a critical ingredient and, largely because of small grain size and poor crystallinity, the orientation distribution of clay minerals has been difficult to quantify. A method is demonstrated that relies on hard synchrotron X-rays to obtain diffraction images of shales and applies the crystallographic Rietveld method to deconvolute the images and extract quantitative information about phase fractions and preferred orientation that can then be used to model macroscopic physical properties. The method is applied to shales from European studies which investigate the suitability of shales as potential nuclear waste repositories (Meuse/Haute-Marne Underground Research Laboratory near Bure, France, and Benken borehole and Mont Terri Rock Laboratory, Switzerland). A Callovo-Oxfordian shale from Meuse/Haute-Marne shows a relatively weak alignment of clay minerals and a random distribution for calcite. Opalinus shales from Benken and Mont Terri show strong alignment of illite-smectite, kaolinite, chlorite, and calcite. This intrinsic contribution to anisotropy is consistent with macroscopic physical properties where anisotropy is caused both by the orientation distribution of crystallites and high-aspect-ratio pores. Polycrystal elastic properties are obtained by averaging single crystal properties over the orientation distribution and polyphase properties by averaging over all phases. From elastic properties we obtain anisotropies for p waves ranging from 7 to 22%.

The double hydroxide of Li+ and Al3+ is an anionic clay comprising positively charged metal hydroxide layers and intercalated anions. While the structure of the iono-covalently bonded metal hydroxide layer is well known, relatively less knowledge is available regarding the manner in which the anions and water molecules are packed in the interlayer region. The sulfate ion is of special interest as it can potentially intercalate in a multiplicity of orientations and grow an extended hydration sphere. The sulfate-intercalated double hydroxide was synthesized by the imbibition of Li2SO4 into both the gibbsite and bayerite forms of Al(OH)3 to obtain layered double hydroxides with the nominal formula Li2Al4(OH)12SO4·nH2O (n = 4–8). The as-prepared compounds were poorly ordered and did not yield any structural information. Temperature-induced partial dehydration yielded ordered phases of different structures in the two systems. Simulation of the powder patterns of different model structures, followed by structure refinement in both direct and reciprocal spaces, showed that the gibbsite-derived phase yielded a two-layer polytype of hexagonal symmetry (space group P63/m). The local symmetry of the sulfate ion was close to D2d with one of the C2 axes of the SO42− being nearly parallel to the c axis of the crystal. The bayerite-derived phase yielded a one-layer polytype of monoclinic symmetry (space group C2/m). The sulfate ion was oriented with its C3 axes tilted away from the stacking direction. Cooling and rehydration (relative humidity ~70%) resulted in a reversible expansion of the basal spacing due to the ingress of water molecules from the ambient humidity into the interlayer region. Hydration in both cases resulted in turbostratic disorder. The disorder in the bayerite-derived phase was a result of random intergrowth of motifs with rhombohedral and monoclinic symmetries.

In the present work, LaNi0.5Ti0.5O3, LaNi0.5Ti0.45Co0.05O3, and LaNi0.45Co0.05Ti0.5O3 perovskites were synthesized using the modified Pechini method. After reduction, the studied perovskites changed crystal structure from the perovskite crystal structure to a cubic symmetry, with space group $Pm\bar{3}m$. The reduction partially decomposed the samples to Ni0 (Co free perovskite), Ni0–Co0, La2O3, La2TiO5, and non-stoichiometric La2NiO4, depending on H2 content of the reductive gases. The degree of reduction of nickel from LaNi0.5Ti0.5O3 reduced with 1.8% H2/Ar and 10% H2/Ar was equal to 36.5% and 95.3%, respectively, while that from LaNi0.5Ti0.45Co0.05O3 or LaNi0.45Co0.05Ti0.5O3, including cobalt, reduced with 10% H2/Ar, was equal to 71.9% and 93.9%, respectively. LaNi0.5Ti0.45Co0.05O3 showed Ni3+ and Co3+ amounts higher than the other perovskites. By increasing H2 content in the reductive mixture from 1.8% to 10%, sintering of metallic nickel was not observed. Moreover, Ni0 displayed weaker metal–support interaction than that observed for Co0, where the support was composed of La containing oxides. LaNi0.5Ti0.5O3 perovskite was used as a catalyst for steam reforming of methane. Syngas production was attributed to the number of Ni sites determined using Rietveld Refinement of X-ray diffraction pattern of this catalyst after the reaction.

Hydrothermally synthesised K2ZnSi5O12 has a polymerised framework structure with the same topology as leucite (KAlSi2O6, tetragonal I41/a), which has two tetrahedrally coordinated Al3+ cations replaced by Zn2+ and Si4+. At 293 K it has a cation-ordered framework P21/c monoclinic structure with lattice parameters a = 13.1773(2) Å, b = 13.6106(2) Å, c = 13.0248(2) Å and β = 91.6981(9)°. This structure is isostructural with K2MgSi5O12, the first cation-ordered leucite analogue characterised. With increasing temperature, the P21/c structure transforms reversibly to cation-ordered framework orthorhombic Pbca. This transition takes place over the temperature range 848−863 K where both phases coexist; there is an ~1.2% increase in unit cell volume between 843 K (P21/c) and 868 K (Pbca), characteristic of a first-order, displacive, ferroelastic phase transition. Spontaneous strain analysis defines the symmetry- and non-symmetry related changes and shows that the mechanism is weakly first order; the two-phase region is consistent with the mechanism being a strain-related martensitic transition.

An unusual occurrence of palygorskite was found near Montestrutto, lower Val d'Aosta (Italy), within an eclogite-facies leucogneiss of the Sesia-Lanzo zone. Under the optical microscope the mineral appears as a felt of fibres hundreds of μm long and a few μm thick. SEM observation proved each filament to be a bundle of smaller but remarkably long fibres (length mostly 15–20 μm and thickness <1 μm). EDS and TGA showed a water content [zeolitic H2O ( ≅ 6%) + structural OH2 (≅8%) + framework OH (≅2%) ≅l6 wt.%] lower than average (≅20 wt.%). Structure refinement by the Rietveld method confirmed the clay dioctahedral character and coexistence of two polymorphs, monoclinic [77.4(4)%] and orthorhombic [22.6(6)%], the latter showing anomalous variations of some cell parameters [c shortens to 5.138(3) and a lengthens to 12.903(7) Å]. The high crystallinity of this palygorskite suggests that it formed under low-T hydrothermal conditions due to interaction between Mg-rich hydrous fluids, derived from mantle ultramafics, and Al-rich continental rocks. Predominance of unusually long fibres (>5 μm) causes the Montestrutto palygorskite to be potentially carcinogenic.

The sodium-magnesium hydrated double salt konyaite, Na2Mg(SO4)2·5H2O, has been studied by single-crystal X-ray diffraction and thermogravimetry on synthetic samples and by quantitative X-ray diffraction utilizing the Rietveld method on natural samples from the Mount Keith mine, Western Australia. Konyaite crystallizes in space group P21/c, with the cell parameters: a = 5.7594(10), b = 23.914(4), c = 8.0250(13) Å, β = 95.288(9)°, V = 1100.6(3) Å3 and Z = 4. The crystal structure has been refined to R1 = 3.41% for 2155 reflections [Fo>4σ(Fo)] and 6.44% for all 3061 reflections, with all atoms located.

Quantitative phase analysis utilizing the Rietveld method was undertaken on five samples of konyaite-bearing mine tailings from the Mount Keith Nickel Mine, Western Australia. Konyaite was found to decompose over time and after 22 months had transformed to other sulphate and amorphous phases. Blödite did not increase in any ofthe samples indicating that konyaite may not always transform to blödite. Over the same time frame, synthetic konyaite completely decomposed to a mixture of thenardite (Na2SO4), hexahydrite (MgSO4·6H2O), blödite (Na2Mg(SO4)2·4H2O) and löweite (Na12Mg7(SO4)13). Detection of konyaite and other Mg-rich sulphates is important in terms of CO2 fixation. Magnesium bound to sulphate mineral phases reduces the overall potential of tailings piles to lock up atmospheric carbon in Mg carbonates, such as hydromagnesite. Amorphous sulphates are also highly reactive and may contribute to acid mine drainage ifpresent in large quantities, and may dissolve carbonate phases which have already sequestered carbon.

The present work analyses the thermal behaviour of alum-(K), KAl(SO4)2·12H2O, by in situ laboratory high-temperature powder X-ray diffraction data from 303 K to melting, which starts at 355 K and is completed, due to kinetics, at 359 K. The calculated a0 linear thermal expansion coefficient is of 14.68(11) × 10–6 K–1 within the investigated thermal range. The k disorder parameter, describing the extension of the orientational disorder of the sulfate group, has been found to decrease from ∼0.70 to ∼0.65 just before melting. It has been demonstrated that the occurrence of the disorder implies the coexistence of K+ ions in both six- and seven-fold coordination. This is necessary for assigning a reasonable bond-valence sum of 0.81 valence units (vu) to the 'average' K+ ion a instead of 0.66 vu, which is obtained in the case of six-fold coordination alone. We can describe the temperature dependence of k from 93–355 K by means of the empirical equation k = 0.798(12) + 2.5(11) × 10–4 T – 1.9(2) × 10–6T2, which includes reference low-temperature data. Bond-valence analysis has shown that, on cooling, an increase of the k disorder parameter and shortening of the K–O2 bond distance act together to maintain constancy in the bond-valence sum at the K site, stabilizing the structure. Therefore, the need for keeping the 'average' K+ ion at a reasonable bond-valence sum appears to be the driving force for the ordering process involving the sulfate group.

X-ray diffraction is one of the most effective tools for the characterization of the stacking defects which occur frequently in clay minerals. Modelling of the diffraction patterns of oriented mounts is often used for obtaining structural information about the nature of stacking order. Manual matching of calculated and observed patterns is time consuming and the results are user dependent and especially troublesome if a consistent model of the same mineral measured under different conditions needs to be obtained. It was shown recently that the Rietveld method could be applied successfully for the evaluation of the X-ray patterns of oriented mounts. Nevertheless, this automatic refinement procedure can also lead to inconsistent results if independent refinements are performed that describe the same sample measured under different conditions. One way to solve this problem is the application of parametric Rietveld refinement. For this approach a set of different measurements of the same sample was collected and fitted in one combined refinement by the connection of the structural models via external parameters. These conditions may involve different pre-treatments (e.g. different intercalations), different temperatures or relative humidities and/or different experimental setup (powder or oriented samples). All patterns were fitted in one overall refinement process by the BGMN software.

This approach was demonstrated on a mixture of two disordered reference materials and on a set of geological samples. Two different states for each sample were refined independently and parametrically and it was shown that this approach leads to consistent results, saves computation time and may even resolve small structural differences.

The alkaline content of mixed transition metal phosphates Li(1−y)·zNay·zM0.5Fe0.5PO4 (M = Mn, Co; 0 ≤ y < 1; 0.5 ≤ z ≤ 1) was determined by powder X-ray diffraction data by means of Rietveld analysis and multi-fraction models. The compounds LiM0.5Fe0.5PO4 were synthesized via solid-state reactions. Chemical extraction of Li with bromine in acetonitrile yielded well-crystalline Li0.5M0.5Fe0.5PO4. Subsequent reduction with Na2S in acetonitrile gave a product with a triphylite-type phase of the average composition Li0.5Na0.5M0.5Fe0.5PO4 showing a broad distribution of Li-to-Na-ratios. For Rietveld refinements a set of 11 fractions Li1−yNayM0.5Fe0.5PO4 was used to represent the triphylite-type phase and its composition fluctuation. To obtain samples with compositions close to NazM0.5Fe0.5PO4 (z = 0.5 or z = 1) up to two additional cycles of chemical oxidation and reduction were required. Because of a complex distribution of Li and Na within the triphylite-type phase a model of 121 fractions of Li(1−y)·zNay·zM0.5Fe0.5PO4 was developed to enable proper Rietveld refinements. The scaling factors of the 121 fractions were constrained by a bimodal bivariate normality. The evaluation of the pattern revealed a type of passivation, preventing the compound from complete oxidation or reduction of Fe for higher cycle numbers. Hence, no completely Li-free samples could be obtained.

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.

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.

The paper describes an approach for automated crystal structure solution from powder diffraction data using the multi-population genetic algorithm (MPGA). The advantage of using co-evolution with the best individual exchange, compared with the using of the evolution with a single genetic algorithm without interpopulation exchange, is shown. As an example, the paper describes the use of MPGA for solving the [Pt(NH3)5Cl]Br3 crystal structure, having the tetragonal I41/a space group [a = 17.2587(5) Å, c = 15.1164(3) Å, Z = 16, unit-cell volume V = 4502.61(10) Å3]. The MPGA convergence charts and the atomic positions distribution maps of the MPGA populations are given. The description of the final structure solution is also shown.

The study presents the results of the influence of high-energy ball-milling time on the structure of the new β-type Ti–Ta–Nb–Zr alloys for biomedical applications. Initial elemental powders were mechanically alloyed in a planetary high-energy ball mill at different milling times (from 10 to 90 h). Observation of the powder morphology after various stages of milling leads to the conclusion that with the increase of the milling time the size of the powder particles as well as the degree of aggregation change. Clear tendency of crystalline size reduction at every stage of the grinding process is clearly observed. The X-ray diffraction results confirmed the formation of β phase during high-energy ball milling of the precursor mixture of Ti, Ta, Nb, and Zr. The Rietveld refinement method has shown that both the production method and the atomic radii of the elements used in the mechanical synthesis have influence on the structure. Furthermore, it was found that a broadening of the diffraction peaks with increase of the milling time results from an increase in the crystallites dispersion and an enlargement in the lattice distortion. The results indicate that this technique is a powerful and high productive process for preparing new β-titanium alloys with nanocrystalline structure and appropriate morphology.

The Rietveld method based on X-ray diffraction (XRD) technology has been commonly applied for the quantitative analysis of crystalline minerals in organic-rich rocks. The presence of organic matter, however, has interference in varying degree to the quantitative result. In this work, the mixed samples of organic matter and crystalline minerals at given proportions were prepared to investigate the effect of organic matter on the Rietveld quantitative analysis of crystalline minerals in coal gangue. The relative standard deviation (RSD) and absolute error (AE) were used to evaluate the precision and accuracy of the quantitative result. The results showed that the presence of organic matter led to a reduction in the precision and accuracy. It was attributed in part to the presence of organic matter, which can produce a background noise in the XRD pattern, especially in the region of 5–30° (2θ). Further results showed that the interference in this region increased with the increase in the organic matter content. The RSD and AE were within the range of 10% and 2%, respectively, when the organic matter content is <30 wt%. Based on this, an approximate method for the Rietveld quantitative analysis of crystalline minerals in coal gangue was established.