Equations are given which allow an analyst to obtain a correct absolute quantitative phase analysis via the internal standard method when a reference material with a known crystallinity of less than 100% is used. Comparisons are made with previous equations, and a numerical example is given.

Fifty-two Bidi-Koum bauxites from Guinea, Africa, of diversified chemical composition were characterized for their mineral composition. First, 14 element oxide concentrations were determined by X-ray fluorescence (XRF) using a fusion sample preparation technique. Loss of Mass (LOM) and organic carbon (OC) concentrations were also determined. The initial X-ray diffraction (XRD) phase quantification was carried out employing XDB software. This software allows for full interpretation of a sample diffractogram and helps generate initial concentrations of identified minerals based on a standardless approach. In the stage that followed, the mass balance procedure on the XDB software helped refine the final phase composition. Then, gibbsitic Al2O3 concentrations obtained by wet chemistry for all samples and kaolinitic SiO2 concentrations obtained for selected samples were compared with the concentrations obtained using the XDB software. Phases that were quantified are: gibbsite, boehmite, kaolinite, wavellite, goethite, hematite, quartz, anatase, rutile and illite. Phase concentrations were obtained for illite from K2O and for wavellite from P2O5 concentrations. The alumina substitution in the goethite lattice was also estimated.

In X-ray diffraction (XRD) analysis, preparation of oriented clay specimens enhances their 00l reflections by arranging basal surfaces parallel to the specimen surface. In one-dimensional modeling of XRD intensities, degree of preferred orientation is one of the variable parameters and a user may choose different σ* values for different minerals. The usual assumption is, however, that the layers of all clay minerals that are present exhibit a similar degree of preferred orientation to that of the clay mineral flakes parallel to the basal plane. If the orientation of individual clay minerals is significantly different, and if this is not taken into account, the relative proportions of the constituent minerals cannot be modeled accurately. The actual or so-called ‘preferred’ orientation is a potentially large source of error in any attempt at quantitative XRD analysis because it cannot be assumed to be constant among different minerals and may also vary as a result of pretreatment. In the present study the influence of sample composition and sample pretreatment on the degree of preferred orientation was determined using the parameter σ*. A statistical parameter was calculated to determine and ensure the reproducibility of σ* measurements. The most important result was that, when mixed together, clay minerals influence each other in terms of the degree of preferred orientation. Among individual samples, the degree of preferred orientation can be different for each clay mineral. The power of sonication used in sample pretreatment of a pure kaolinite and a pure illite had no significant influence on the degree of preferred orientation. The changes in intensities upon variation of the tilting angle (χ) allowed for calculation of σ* of smectites in pure samples, in admixtures, and in samples treated in two different ways (air-dried and glycerol-intercalated), which is reported here for the first time. Smectites are very fine grained with flexible morphology which is believed to be the reason for their tendency to exhibit poor orientation (σ* = 22°); further research is required to establish whether this is a general feature of smectites. After glycerol treatment a soil smectite showed a slightly better orientation compared to the air-dried pattern. The results of the study illustrate the difficulty of predicting changes in preferred orientation of clay mineral admixtures, even if non-platy minerals such as clay-sized quartz are added. In general, σ* decreased when non-platy minerals were added, which is explained by changes in geometry of the specimen. Not all clay minerals, however, showed simultaneous changes in their orientation behavior.

We studied a set of 15 reference clays from The Clay Minerals Society (CMS) Source Clays repository. Our aim was to use them as reference materials in our version of the QUAX mineral database. The QUAX software (Quantitative Phase-Analysis with X-ray Powder Diffraction) has been used successfully at the KTB site (German Continental Deep Drillling) to determine mineral assemblages quickly, in an automatic fashion, on a large number of samples (∼40,000). It was also applied to Quaternary marine sediments of the Japan Sea. Our current research focuses on marine and lacrustrine sediments from the Arctic Ocean and Siberia.

QUAX is a full-pattern method using a reference materials database. The quality of a particular quantification depends on the availability of the relevant mineral phases in the database. Our aim is to extend and improve the database continuously with new data from our current projects, particularly from clay and feldspar minerals.

A reference material in the QUAX software must be monomineralic. Before X-ray diffraction (XRD) patterns of CMS clays could be added to the database, quantification of any impurities was necessary. After measuring the bulk material by XRD, the <2 µm fraction was separated because we assumed it would contain the smallest amount of impurities. Here we present grain-size data, XRD data and X-ray fluorescence (XRF) data for this clay-sized fraction. The results of chemical and mineralogical preparation techniques and (elemental) analysis methods were combined. For XRD, random and oriented clay-aggregate samples as well as pressed pellets for QUAX analysis were prepared. Semi-quantitative clay mineral determinations were run for comparison.

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.

The Reynolds Cup (RC) is a unique round-robin competition that was established by The Clay Minerals Society in 2000 to assess the level of precision and accuracy that is attainable for the mineralogical analysis of a wide range of complex clay-rich materials. Although the Reynolds Cup roundrobin allows any possible analysis methods, X-ray diffraction (XRD) is by far the most frequently used technique. It is not only used to identify components, but also for quantitative phase analysis (QPA). QPA means determination of the relative concentrations of the coexisting phases in a mixture, commonly as a weight percent (wt.%) or mass fraction. Several approaches allow a quantitative determination of mineral contents, such as the Rietveld method (Rietveld, 1967). The successful application of the Rietveld method for QPA requires that all components are correctly identified and that the component diffraction patterns are appropriately described, which is preferably based on structure. In addition, the quality of a Rietveld quantification also depends on suitable sample preparation and measurement conditions, as well as a correct description of instrument configurations. Results from all previous Reynolds Cup contests show that a successful quantification depends strongly on the skill of users. Although the refinement procedure itself is automatic and, therefore, user independent, the results are strongly influenced by the structural models and refinable parameters that are selected and on the limitations of those parameters. Selected examples for the successful application of Rietveld refinement as well as the limitations of the method will be discussed in this article. The goal of the present work was to demonstrate that the Rietveld method is in principle capable of quantifying all Reynolds Cup samples with a high degree of accuracy, but sample specific difficulties and analysts’ inexperience may impede successful application. Incorrect results are often not indicated simply by low residuals or good fits. All refinement results should be validated and corrected using supplementary techniques, even if the results appear acceptable.

X-ray diffraction (XRD) of powdered materials is one of the most common methods used for structural characterization as well as for the quantification of mineral contents in mixtures. The application of the Rietveld method for that purpose requires structure models for each phase. The recursive calculation of structure factors was applied here to the Rietveld refinement of XRD powder patterns of illite-smectite (I-S) minerals. This approach allowed implementation of stacking disorder in structural models. Models for disordered stacking of cis-vacant and trans-vacant dioctahedral 2:1 layers as well as rotational disorder were combined with models for mixed layering of illitic and smectitic layers.

The DIFFaX code was used to simulate non-basal (hk) reflections of illites with different degrees of disorder. Rietveld refinements of these simulated patterns were used to evaluate the application of this new approach. A model describing rotational disorder (n·120° and n·60° rotations) and mixed layering of cis-vacant and trans-vacant dioctahedral layers was tested. Different starting parameters led to identical results within the ranges of standard deviations and confirmed the stability of the automatic refinement procedure. The influence on the refinement result of an incorrect choice of fixed parameters was demonstrated.

The hk model was combined with models describing the basal reflections of disordered I-S and tested on measured data. A glauconitic mineral (Urkut, Hungary), an ordered I-S (ISCz-1, a special clay in the Source Clays Repository of The Clay Minerals Society), and a dioctahedral I-S (F4, Füzérradvány, Hungary) were used as test substances. Parameters describing the mixed layering of illitic and smectitic layers were compared with the results from refinements of oriented mounts and showed good agreement. A pattern of a physical mixture of an I-S mineral and a turbostratically disordered smectite was analyzed in order to test the new approach for application in quantitative phase analysis. The quantitative Rietveld phase analysis results were found to be satisfactory.

Quantitative phase analysis (QPA) of slags is complex due to the natural richness of phases and variability in sample composition. The number of phases frequently exceeds 10, with certain slag types (EAF, BOF, blends, stainless) having extreme peak overlap, making identification difficult. Another convolution arises from the variable crystallite sizes of phases found in slag, as well as the mixture of crystalline and amorphous components specific to each slag type. Additionally, polymorphs are common because of the complexity of the steelmaking and slag cooling processes, such as the cation-doped calcium aluminum silicate (Ca3Al2O6, C3A, Z = 24) supercell in LMF slag. References for these doped variants may not exist or in many cases are not known in advance, therefore it is incumbent on the analyzer to be aware of such discrepancies and choose the best available reference. All issues can compound to form a highly intricate QPA and have prevented previous methods of QPA from accurately measuring phase components in slag. QPA was performed via the internal standard method using 8 wt% ZnO as the internal standard and JADE Pro's Whole Pattern Fitting analysis. For each phase, five variables (lattice parameters, preferred orientation, scale factor, temperature factor, and crystallite size) must be accounted for during quantitation, with a specific emphasis on not refining crystallite sizes for iron oxides and trace phases as they are inclined to over-broaden and interact with the background to improve the goodness of fit (R/E value). Preliminary investigations show somewhat reliable results with the use of custom file sets created within PDF-4+ specifically targeted toward slag minerals to further regulate and normalize the analysis process. The objective of this research is to provide a standard protocol for collecting data, as well as to update methodologies and databases for QPA, to the slag community for implementation in a conventional laboratory setting. Currently, Whole Pattern Fitting “Modified” Rietveld block refinement coupled with the addition of a ZnO internal standard gives the most accurate QPA results, though further research is needed to improve upon the complex issues found in this study of the QPA of slags.

Although being an old concern, phosphate analysis is still a tremendous challenge. While many different experimental techniques are found in the literature, very few use powder X-ray diffraction (PXRD) patterns for quantitative phase analysis of different phosphate types. Our measurements performed in four commercial samples of diammonium hydrogen phosphate ((NH4)2HPO4) (DAP) show the existence of phosphate contamination mixtures, such as ammonium dihydrogen phosphate (NH4H2PO4) (ADP). The larger the amount of ADP, the larger the microstrain induced in the DAP phase, which impacts both the aggregation of the nanoparticles in solution and the final anticancer activity of the nanostructure. This study shows that PXRD is an excellent technique for quantitative phase analysis to determine the presence and amount of phosphate contamination in diammonium hydrogen phosphate samples.

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.

Quantitative phase analysis is one of the major applications of X-ray powder diffraction. The essential principle of quantitative phase analysis is that the diffraction intensity of a component phase in a mixture is proportional to its abundance. Nevertheless, the diffraction intensities of the component phases cannot be compared with each other directly since the coherent scattering power per unit cell (or chemical formula) of each component phase is usually different. The coherent scattering power per unit cell of a crystal is well represented by the sum of the squared structure factors, which cannot be calculated directly when the crystal structure data is unavailable. Presented here is a way to approximate the coherent scattering power per unit cell based solely on the unit cell parameters and the chemical contents. This approximation is useful when the atomic coordinates for one or more of the phases in a sample are unavailable. An assessment of the accuracy of the approximation is presented. This assessment indicates that the approximation will likely be within 10% when X-ray powder diffraction data is collected over a sufficient portion of the measurable pattern.

The direct derivation (DD) method is a technique for quantitative phase analysis (QPA). It can be characterized by the use of the total sums of scattered/diffracted intensities from individual components as the observed data. The crystal structure parameters are required when we calculate the intensities of reflections or diffraction patterns. Intensity can, however, be calculated only with the chemical composition data if it is not of individual reflections but of a total sum of diffracted/scattered intensities for that material. Furthermore, it can be given in a form of the scattered intensity per unit weight. Therefore, we can calculate the weight proportion of a component material by dividing the total sum of observed scattered/diffracted intensities by the scattered intensity per unit weight. The chemical composition data of samples under investigation are known in almost all cases at the stage of QPA. Thus, a technical problem is how to separate the observed diffraction pattern of a mixture into individual component patterns. Various pattern decomposition techniques currently available can be used for separating the pattern of a mixture. In this report, the theoretical background of the DD method and various techniques for pattern decompositions are reviewed along with the examples of applications.

Powder X-ray diffraction has become a routine procedure for the quantification of phases in mixtures. The most common method for this measurement is the Rietveld method, which generally returns the relative weight percentages of the crystalline components within the mixture. However, in many instances, it is also desirable to obtain an estimate of the amorphous content of a sample. There are several methods that may be used for this measurement and their accuracy has been assessed previously with a number of ideal, synthetic mixtures. Many samples, especially in the mineralogy sphere, are far from ideal and contain multiple phases of varying absorption contrast. This creates a microabsorption problem which affects the accuracy of the determination of both the crystalline and amorphous components. This paper assesses commonly used methods of amorphous determination with a series of synthetic samples designed to create a considerable microabsorption problem.

The electrochemical behaviour of a number of Pb-based anode alloys, under simulated electrowinning conditions, in a 1.6 M H2SO4 electrolyte at 45 °C was studied. Namely, the evolution of PbO2 and PbSO4 surface layers was investigated by quantitative in situ synchrotron X-ray diffraction (S-XRD) and subsequent Rietveld-based quantitative phase analysis (QPA). In the context of seeking new anode alloys, this research shows that the industry standard Pb-0.08Ca-1.52Sn (wt%) anode, when exposed to a galvanostatic current and intermittent power interruptions, exhibited poor electrochemical performance relative to select custom Pb-based binary alloys; Pb–0.73Mg, Pb–5.05Ag, Pb–0.07Rh, and Pb–1.4Zn (wt%). The in situ S-XRD measurements and subsequent QPA indicated that this was linked to a lower proportion of β-PbO2, relative to PbSO4, on the Pb-0.08Ca-1.52Sn alloy at all stages of the electrochemical cycling. The best performing alloy, in terms of minimisation of overpotential during normal electrowinning operation and minimising the deleterious effects of repeated power interruptions – both of which are significant factors in energy consumption – was determined to be Pb–0.07Rh.

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.

Quantitative phase analysis (QPA) using neutron powder diffraction more often than not involves non-ambient studies where no sample preparation is possible. The larger samples and penetration of neutrons versus X-rays makes neutron diffraction less susceptible to inhomogeneity and large grain sizes, but most well-characterized QPA standard samples do not have these characteristics. Sample #4 from the International Union of Crystallography Commission on Powder Diffraction QPA round robin was one such sample. Data were collected using the POWGEN time-of-flight (TOF) neutron powder diffractometer and analysed together with historical data from the C2 diffractometer at Chalk River. The presence of magnetic reflections from Fe3O4 (magnetite) in the sample was an additional consideration, and given the frequency at which iron-containing and other magnetic compounds are present during in-operando studies their possible impact on the accuracy of QPA is of interest. Additionally, scattering from thermal diffuse scattering in the high-Q region (<0.6 Å) accessible with TOF data could impact QPA results during least-squares because of the extreme peak overlaps present in this region. Refinement of POWGEN data was largely insensitive to the modification of longer d-spacing reflections by magnetic contributions, but the constant-wavelength data were adversely impacted if the magnetic structure was not included. A robust refinement weighting was found to be effective in reducing quantification errors using the constant-wavelength neutron data both where intensities from magnetic reflections were ignored and included. Results from the TOF data were very sensitive to inadequate modelling of the high-Q (low d-spacing) background using simple polynomials.

Structural characterization, quantitative phase analysis, and morphological behavior of biomineralized deposits in human pancreas [pancreatic stones (PSs)] have been carried out using infrared (IR)-spectroscopy, scanning electron microscopy (SEM), powder x-ray diffraction, and thermogravimetry - differential scanning calorimetry (TG–DSC). The fourier transform infrared (FT-IR) spectra indicated that the primary composition of PSs was calcium carbonate. An x-ray powder diffraction phase quantification using the Rietveld method revealed that five of the pancreatic calculi were composed exclusively of calcite (CAL) and the remaining four contained small amounts of vaterite and aragonite in addition to the CAL phase. The crystallite size of CAL in the PSs study varied between 104(6) and 181(2) nm. The SEM images of pancreatic calculi showed a variety of crystal morphologies for biogenic CAL crystallites such as, thin plates, spherulites, prisms, and cylindrical laths. Thermogravimetric analysis of PS1 reveals that biogenic CAL is stable up to 910 K, above which temperature CAL transforms into calcium oxide.

The use of high-speed detectors made X-ray diffraction (XRD) become an important tool for process control in mining and metal industries. Decreasing ore qualities and increasing prices for raw materials require a better control of processed ore and a more efficient use of energy. Traditionally quality control of iron ore sinter has relied on time-consuming wet chemistry. The mineralogical composition that defines the physical properties such as hardness or reducibility is not monitored. XRD analysis in combination with Rietveld quantification and statistical data evaluation using partial least-squares regression (PLSR) has been successfully established to determine the mineralogical composition and the Fe2+ content of iron ore sinter within an analysis time of less than 10 min per sample. A total of 35 iron ore sinter samples were measured and evaluated using PLSR and the Rietveld method. The results were compared with wet chemistry data. PLSR results show accuracy for the Fe2+ content of ±0.14%. No pure phases, crystal structures, or complex modeling of peak shapes are required. The Rietveld method was used to quantify the total phase composition of the samples. The Fe2+ content could be calculated from all phases present. Both methods take the full XRD pattern into account and can be simultaneously applied on the same measurement. PLSR was found to be the more robust method if only Fe2+ results are required. The Rietveld method helps predict other parameters such as the compressional strength of the sinter by monitoring all existing phases (e.g., larnite, C2S, or silico-ferrite of calcium and aluminum phases).

We report on the analysis of virtual powder-diffraction patterns from serial femtosecond crystallography (SFX) data collected at an X-ray free-electron laser. Different approaches to binning and normalizing these patterns are discussed with respect to the microstructural characteristics which each highlights. Analysis of SFX data from a powder of Pr0.5Ca0.5MnO3 in this way finds evidence of other trace phases in its microstructure which was not detectable in a standard powder-diffraction measurement. Furthermore, a comparison between two virtual powder pattern integration strategies is shown to yield different diffraction peak broadening, indicating sensitivity to different types of microstrain. This paper is a first step in developing new data analysis methods for microstructure characterization from serial crystallography data.

In the last few decades, X-ray diffraction (XRD) systems have been paramount and irreplaceable in controlling bauxite exploration, as well as Bayer and reduction processes. XRD quantitative phase analysis in the aluminum industry witnessed a steady deployment of the Rietveld method, which at present progressively replaces existing methodologies in research and plant laboratories. Rietveld analysis not only helped to surpass traditional XRD calibration methods, it also opened the door for new applications previously not possible. The use of the Rietveld method to characterize selected materials unique to the aluminum industry, such as bauxite, red mud, and alumina is demonstrated and discussed. This paper also presents how synchrotron-based diffractograms obtained for bauxite and red mud samples allowed a much better understanding of mineralogical representation, and made it possible to leverage their Rietveld quantification. Despite clear advantages, the Rietveld method also has limitations that are revealed. For alumina phase quantification, a dedicated Rietveld analytical program was built with structure data for eight alumina mineralogical phases: alpha, beta (β-Al2O3 = Na2O•11Al2O3), delta, gamma (2), kappa, sigma, and theta. The paper gives unique examples of phase quantification in aluminas of various origins and phase composition.