Quantitative Phase Analysis Method Research Articles

Determination of the degree of crystallinity of polyphenylene sulfide composited with crystalline and non-crystalline fillers by applying the direct derivation method

A new procedure for determining the degree of crystallinity (DOC) has been recently proposed, and it has been verified using experimental and computer-generated powder diffractometry data [Toraya (2023). J. Appl. Cryst. 56, 1751–1763]. As an application to real materials like engineering plastics, this procedure is here applied to the DOC determination of plate-like polyphenylene sulfide (PPS) samples, composited with crystalline and non-crystalline fillers. The coexistence of partially crystallized polymer with non-crystalline fillers in target materials makes it difficult to separate the non-crystalline part of the partially crystallized polymer. This problem is here solved by the inverse application of the direct derivation (DD) method for quantitative phase analysis (QPA). The intensity–composition (IC) formula used in the DD method can derive the weight fractions of the individual components from just the total sums of observed intensities and the chemical composition data for these components [Toraya (2016). J. Appl. Cryst. 49, 1508–1516]. For the present purpose, the IC formula has been inversely applied to calculate the relative intensity ratios of individual components under the assumption that the chemical compositions and weight fractions of the respective components are known. The total halo intensity could then be separated into the non-crystalline part of the polymer and the non-crystalline filler. Analyzed results of PPS composites in four different DOCs are reported.

Quantitative phase analysis method of palygorskite based on XRD orientational sample analysis and Rietveld full spectrum fitting

Palygorskite is a kind of water-rich magnesium aluminosilicate mineral with a chain-layered structure. Due to the difference in forming environment, the phase composition of palygorskite clay is various, and chemical compositions of palygorskite of different origins are also significantly different, which leads to a great difference in its application performance. Due to the coexistence of various types of layered and chain-layered minerals, conducting quantitative phase analysis of palygorskite raw ore becomes highly challenging. This significantly restricts the development and utilization of palygorskite. Herein, a new scheme is proposed to solve this problem by combining Rietveld full spectrum fitting based on the XRD patterns from internal standard method and orientational sample analysis. The new scheme was applied to the quantitative phase analysis of palygorskite raw ores from Mingguang, Xuyi, and Linze, three of the most representative places of origin in China. Not only the exact content of palygorskite and other crystalline phases in the raw ore, but also the content of mixed-layer minerals, and amorphous phase in the raw ore were obtained. The contents of palygorskite, quartz, illite-smectite mixed-layer minerals, and amorphous in the raw ore of Mingguang were 70.81%, 6.43%, 18.81%, and 3.98%, respectively; the contents of palygorskite, quartz, calcite, illite-smectite mixed-layer minerals in the raw ore of Xuyi were 36.08%, 16.18%, 27.06%, 18.04%, and 2.64%, respectively; the contents of palygorskite, quartz, illite-smectite mixed-layer minerals, calcite, illite, gypsum, feldspar, dolomite, microcline and amorphous in the raw ore of Linze were 10.11%, 34.82%, 5.77%, 1.07%, 5.57%, 8.06%, 12.38%, 17.05%, 2.21%, and 2.96%, respectively.

A Bogue approach applied to basic oxygen furnace slag

Basic oxygen furnace (BOF) slag is an industrial by-product of the steel industry and has recently been investigated intensively for high-end applications other than road load and land fill. However, to be applied as a high-end raw material BOF slag lacks a quick and simple quantitative phase analysis method compared to the Bogue approach applied to ordinary Portland cement. This study presents a method to calculate the main phases of BOF slag (C2S, C2(A,F), magnetite (Ff), RO-Phase and f-C) based on chemical composition. A quantitative model assessment was performed in order to further improve the model and two approaches were used to validate the Bogue BOF slag model. One approach compared the calculated chemical composition of phases with real data the second one evaluated whether the Bogue BOF slag model gives comparable quantitative model assessment measures compared to the classical cement Bogue approach. Both approaches validated the proposed final model.

Comments on A new method for quantitative phase analysis using X-ray powder diffraction: direct derivation of weight fractions from observed integrated intensities and chemical compositions of individual phases by Toraya (2016)

Comments are made on a paper by Toraya [J. Appl. Cryst. (2016), 49, 1508–1516] regarding two assumptions on the basis of which the intensity–composition formula was derived and the validity of the direct-derivation method in quantitative phase analysis.

Response to comments on A new method for quantitative phase analysis using X-ray powder diffraction: direct derivation of weight fractions from observed integrated intensities and chemical compositions of individual phases

Response to comments on <i>A new method for quantitative phase analysis using X-ray powder diffraction: direct derivation of weight fractions from observed integrated intensities and chemical compositions of individual phases</i>

Correlation of Phase Composition, Structure, and Mechanical Properties of Natural Basalt Continuous Fibers

This paper presents a study of the influence of basalt rocks’ phase composition, acidity modulus, and structural parameter NBO/T on the tensile strength and elastic modulus of basalt continuous fibers (BCFs) derived from them. A series of BCF samples based on 14 different basalt deposits was obtained under equal conditions. The tensile strength and elastic modulus of the BCFs from different deposits vary in the ranges of 1495–3380 MPa and 58.2–78.7 GPa, respectively. Using the original method of quantitative phase analysis based on the Rietveld method, the phase compositions of the 14 deposits were defined. All deposits can be used to obtain BCFs. In the studied natural rocks, the main component is tectosilicates; the mass content of framework aluminosilicates is in the range of 16.5–3.3 mass percent. The second main component is inosilicates; the mass content of chain aluminosilicates is in the range of 6.0–58.0 mass percent. The correlations among phase composition, acidity modulus, ratio of non-bridging oxygens to tetrahedral cations, tensile strength, and elastic modulus of the BCFs from the 14 different basalt deposits were calculated. There were strong positive correlation between tectosilicate minerals mass content and elastic modulus [Pearson correlation coefficient (PCC) of 0.7] and strong negative correlation between content of chain and layered aluminosilicates and elastic modulus (PCC of − 0.74).

X-ray powder diffraction analysis of a tungsten carbide-based ceramic

The results of the qualitative and quantitative X-ray powder diffraction analysis of the W–C system samples are presented. Powder samples were nanopowders of α-WC/W2C obtained by plasma chemical synthesis. High-density fine-grained structure of ceramics was formed using the method of electro pulse plasma sintering (spark plasma sintering) from the initial powder of the α-WC. The optimal experimental conditions for the X-ray diffraction proceeding of the tungsten carbide based ceramic samples were chosen according to the preliminary experiments. Reference intensity ratio method for quantitative phase analysis was used in this study.

A practical approach to the direct-derivation method for QPA: use of observed powder patterns of individual components without background subtraction in whole-powder-pattern fitting

The direct-derivation (DD) method for quantitative phase analysis (QPA) can be used to derive weight fractions of individual phases in a mixture from the sums of observed intensities along with the chemical composition data [Toraya (2016). J. Appl. Cryst. 49, 1508–1516]. The whole-powder-pattern fitting (WPPF) technique can be used as one of the tools for deriving the observed intensities of individual phases. In WPPF, the observed powder pattern of a single-phase sample after background (BG) subtraction can be used as the fitting function in combination with the fitting functions widely used in Pawley and Rietveld refinements. The direct fitting of the observed pattern is a very useful technique when the target component is a low-crystallinity or amorphous material [Toraya (2018). J. Appl. Cryst. 51, 446–455]. Technical problems in utilizing the BG-subtracted pattern are the uncertainty associated with the determination of BG height and the parameter interaction between the BG function (BGF) and the BG-subtracted pattern in the least-squares fit. In this study, a practical approach in which single-phase observed patterns are used for the direct fitting without subtracting their BG intensities is proposed. In QPA, the contribution of BG intensities can be neutralized by converting the sum of BG-included intensities into the sum of BG-subtracted intensities by multiplying by a conversion factor. When the magnitudes of the conversion factors are almost identical for all components, they can be canceled out under the normalization condition in deriving weight fractions, and they are not required in QPA. The magnitude of the conversion factor for each component can be determined by one of two experimental techniques: using a single-phase powder of the target component or a mixture containing the target component in a known weight ratio. The theoretical basis of the present procedure is given, and the procedure is experimentally verified. In this procedure, the interaction between the BGF and the BG-included observed pattern is negligibly small. Least-squares fitting with a few adjustable parameters is very fast and stable. Accurate QPA could be conducted, as indicated by the average deviation of 0.05% from weighed values in QPA of α-Al2O3 + γ-Al2O3 mixtures with five different weight ratios and 0.4% in QPA of an α-SiO2 + SiO2 glass mixture

The Patterson Function and the Development of a New Method for Quantitative Phase Analysis of Individual Crystalline Phases Using X-ray Powder Diffraction Technique

The Patterson Function and the Development of a New Method for Quantitative Phase Analysis of Individual Crystalline Phases Using X-ray Powder Diffraction Technique

Fundamentals of silico-ferrite of calcium and aluminium (SFCA) and SFCA-I iron ore sinter bonding phase formation: effects of mill scale addition

The thermal decomposition of mill scale, and the effect of mill scale addition on the formation and decomposition of Silico-Ferrite of Calcium and Aluminium (SFCA) and SFCA-I iron ore sinter bonding phases, has been investigated usingin situX-ray diffraction. Application of the external standard method of quantitative phase analysis of thein situdata collected during decomposition of the mill scale highlighted the applicability of this method for the determination of the nature and abundance of amorphous material in a mineral sample. Increasing mill scale addition from 2.6 to 10.6 and to 21.2 wt% in an otherwise synthetic sinter mixture composition designed to form SFCA did not significantly affect the thermal stability ranges of SFCA-I or SFCA, nor did it significantly affect the amount of each of SFCA or SFCA-I, which formed. This was attributed to the low impurity (i.e. Mn, Mg) concentration in the mill scale, and also the transformation to hematite during heating of the wüstite and magnetite present in the mill scale, with the hematite available for reaction to form SFCA and SFCA-I.

Application of the Rietveld Method in the Reynolds Cup Contest

AbstractThe 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.

Phase quantification by X-ray photoemission valence band analysis applied to mixed phase TiO2 powders

A method of quantitative phase analysis using valence band X-ray photoelectron spectra is presented and applied to the analysis of TiO2 anatase-rutile mixtures. The valence band spectra of pure TiO2 polymorphs were measured, and these spectral shapes used to fit valence band spectra from mixed phase samples. Given the surface sensitive nature of the technique, this yields a surface phase fraction. Mixed phase samples were prepared from high and low surface area anatase and rutile powders. In the samples studied here, the surface phase fraction of anatase was found to be linearly correlated with photocatalytic activity of the mixed phase samples, even for samples with very different anatase and rutile surface areas. We apply this method to determine the surface phase fraction of P25 powder. This method may be applied to other systems where a surface phase fraction is an important characteristic.

Quantitative phase analysis using observed integrated intensities and chemical composition data of individual crystalline phases: quantification of materials with indefinite chemical compositions

In a previous report, a new method for quantitative phase analysis (QPA) of multi-component mixtures using a conventional X-ray powder diffractometer was proposed. The formula for deriving weight fractions of individual crystalline phases presented therein includes sets of observed integrated intensities measured in a wide 2\theta range, chemical formula weights and sums of squared numbers of electrons belonging to atoms in respective chemical formula units [Toraya (2016).J. Appl. Cryst.49, 1508–1516]. The latter two parameters required to perform QPA could be calculated from only the information of chemical formulae of individual phases. In the present study, these two parameters are replaced with a single parameter in the form new parameter = (chemical formula weight)/(sum of squared numbers of electrons). As will be expected from this definition, the parameter has nearly equal values for groups of materials consisting of similar kinds of atoms, and its value becomes identical for polytypes or polymorphs having the same chemical composition. That characteristic of this parameter makes it possible to estimate the parameter value not only directly from the chemical composition of the target material itself but also from database-stored chemical analysis data sorted on the basis of mineral or chemical composition. The parameter value is also hardly changed as a result of small compositional variations of the target component material. Therefore, the present method can be applied to QPA of materials not only of definite chemical compositions but also of indefinite chemical compositions without degrading the accuracy of the analysis. This is expected to widen the application to QPA of, for example, natural products containing many kinds of trace elements, industrial materials with complex substitutional replacement of atoms, nonstoichiometric compoundsetc. The theory and some examples of applications are presented. A procedure for quantifying unknown material is also proposed.

A new method for quantitative phase analysis using X-ray powder diffraction: direct derivation of weight fractions from observed integrated intensities and chemical compositions of individual phases. Corrigendum

Erroneous equations in the paper by Toraya [J. Appl. Cryst. (2016), 49, 1508–1516] are corrected.

A new method for quantitative phase analysis using X-ray powder diffraction: direct derivation of weight fractions from observed integrated intensities and chemical compositions of individual phases

A new method for the quantitative phase analysis of multi-component polycrystalline materials using the X-ray powder diffraction technique is proposed. A formula for calculating weight fractions of individual crystalline phases has been derived from the intensity formula for powder diffraction in Bragg–Brentano geometry. The integrated intensity of a diffraction line is proportional to the volume fraction of a relevant crystalline phase in an irradiated sample, and the volume fraction, when it is multiplied with the chemical formula weight, can be related to the weight fraction. The structure-factor-related quantity in the intensity formula, when it is summed in an adequate 2θ range, can be replaced with the sum of squared numbers of electrons belonging to composing atoms in the chemical formula. Unit-cell volumes and the number of chemical formula units are all cancelled out in the formula. Therefore, the formula requires only single-measurement integrated intensity datasets for the individual phases and their chemical compositions. No standard reference material, reference intensity ratio or crystal structure parameter is required. A new procedure for partitioning the intensities of unresolved overlapped diffraction lines has also been proposed. It is an iterative procedure which starts from derived weight fractions, converts the weight fractions to volume fractions by utilizing additional information on material densities, and then partitions the intensities in proportion to the volume fractions. Use of the Pawley pattern decomposition method provides more accurate intensity datasets than the individual profile fitting technique, and it expands the applicability of the present method to more complex powder diffraction patterns. Test results using weighed mixture samples showed that the accuracy, evaluated by the root-mean-square error, is comparable to that obtained by Rietveld quantitative phase analysis.

Validation of the method of quantitative phase analysis by X-ray diffraction in API: case of Tibolone

In this study, different structural and microstructural models applied to X-ray analysis of powder diffraction data of polymorphic mixtures of known concentrations of Tibolone were investigated. The X-ray data obtained in different diffraction instruments were analysed via Rietveld method using the same analytical models. The results of quantitative phase analysis show that regardless of the instrument used, the values of the calculated concentrations follow the same systematics with respect to the final errors. The strategy to select a specific analytical model that leads to lower measurement errors is here presented.

Quantification of amorphous phases in the silt fraction of Mexican pre-Hispanic adobe earth bricks

This study is focused on quantifying the amorphous phases in soil-related material samples by quantitative phase analysis (QPA) with a carefully designed methodological strategy in the X-ray diffraction sample measurement and in the refinement procedure. The configuration applied was Debye–Scherrer geometry with Mo Kα radiation which, together with meticulous instrumental profile modelling using an LaB6 standard, allowed the refinement of a minimum of sample-related parameters. This method was applied to two micro-samples of adobe earth bricks from The Great Pyramid of Cholula, Mexico, and one local soil micro-sample containing several amorphous and semi-crystalline phases such as allophane, volcanic glass and opal. The results obtained by the QPA method, complemented by elemental particle induced X ray emission (PIXE) spectrometry analysis, were compared with a silicon chemical environment analysis by 29Si MAS-NMR. An average amorphous content of 40 wt% was calculated with the QPA/PIXE results, which is in agreement within 10% with the NMR experiments. Consequently, the methodology proposed could be of interest for further studies of cultural heritage geomaterials, which usually contain amorphous phases in their composition and allow only micro-sampling.

Quantitative Phase Analysis by the Rietveld Method for Forensic Science.

Quantitative phase analysis (QPA) is helpful to determine the type attribute of the object because it could present the content of the constituents. QPA by Rietveld method requires neither measurement of calibration data nor the use of an internal standard; however, the approximate crystal structure of each phase in a mixture is necessary. In this study, 8 synthetic mixtures composed of potassium nitrate and sulfur were analyzed by Rietveld QPA method. The Rietveld refinement was accomplished with a material analysis using diffraction program and evaluated by three agreement indices. Results showed that Rietveld QPA yielded precise results, with errors generally less than 2.0% absolute. In addition, a criminal case which was broken successfully with the help of Rietveld QPA method was also introduced. This method will allow forensic investigators to acquire detailed information of the material evidence, which could point out the direction for case detection and court proceedings.

A Reitveld quantitative XRD phase-analysis of selected composition of the Sr(0.5+x)Sb(1−x)Fe(1+x)(PO4)3(0 &lt; x &lt; 0.50) system

Qualitative XRD phase-analysis of four (x = 0.10, 0.20, 0.30, 0.40) selected compositions of the Sr (0.5+x) Sb (1−x) Fe (1+x) (PO 4 ) 3 (0 0.50 SbFe(PO 4 ) 3 (R space group) and SrSb 0.50 Fe 1.50 (PO 4 ) 3 (R c space group), type-phases. Rietveld refinement method, using the XRPD technique, has been used for a quantitative phase-analysis of these compositions. In order to evaluate the relative errors of this experimental result, a set of standard phase-mixtures of both end compositions of the system was also quantified by the Rietveld method. Obtained results show the usefulness of this method for quantitative phase-analysis, particularly in geology including other classes of materials such clay and cement.

Changes in the structure of plasticized coals caused by extraction with dichloromethane

Changes in the structure of plasticized high, medium, and low volatile bituminous coals caused by dichloromethane extraction were studied using an X-ray method of quantitative phase analysis. The FT-IR and GC–MS methods were used to investigate the differences in composition of the dichloromethane soluble material from the coals studied.It was stated that the removal of dichloromethane soluble material leads to an increase in the amount of the crystallite phase. The contribution of hydrogen bonds and aromatic ring stretching in formation of bands on the FT-IR spectra of the extracts from plasticized coals increases but the contribution of the CO bonds decreases. The ratio of the amount of selected PAHs in extracts of plasticized high, medium, and low volatile bituminous coals to the amount of the same PAHs in extracts of raw coals is 5.7, 20.9, and 0.6 correspondingly.