Ian C. Madsen

Outcomes of the International Union of Crystallography Commission on Powder Diffraction Round Robin on Quantitative Phase Analysis: samples 1a to 1h

The International Union of Crystallography (IUCr) Commission on Powder Diffraction (CPD) has sponsored a round robin on the determination of quantitative phase abundance from diffraction data. Specifically, the aims of the round robin were (i) to document the methods and strategies commonly employed in quantitative phase analysis (QPA), especially those involving powder diffraction, (ii) to assess levels of accuracy, precision and lower limits of detection, (iii) to identify specific problem areas and develop practical solutions, (iv) to formulate recommended procedures for QPA using diffraction data, and (v) to create a standard set of samples for future reference. Some of the analytical issues which have been addressed include (a) the type of analysis (integrated intensities or full-profile, Rietveld or full-profile, database of observed patterns) and (b) the type of instrument used, including geometry and radiation (X-ray, neutron or synchrotron). While the samples used in the round robin covered a wide range of analytical complexity, this paper reports the results for only the sample 1 mixtures. Sample 1 is a simple three-phase system prepared with eight different compositions covering a wide range of abundance for each phase. The component phases were chosen to minimize sample-related problems, such as the degree of crystallinity, preferred orientation and microabsorption. However, these were still issues that needed to be addressed by the analysts. The results returned indicate a great deal of variation in the ability of the participating laboratories to perform QPA of this simple three-component system. These differences result from such problems as (i) use of unsuitable reference intensity ratios, (ii) errors in whole-pattern refinement software operation and in interpretation of results, (iii) operator errors in the use of the Rietveld method, often arising from a lack of crystallographic understanding, and (iv) application of excessive microabsorption correction. Another major area for concern is the calculation of errors in phase abundance determination, with wide variations in reported values between participants. Few details of methodology used to derive these errors were supplied and many participants provided no measure of error at all.

Quantification of phases with partial or no known crystal structures

Quantification of mixtures via the Rietveld method is generally restricted to crystalline phases for which structures are well known. Phases that have not been identified or fully characterized may be easily quantified as a group, along with any amorphous material in the sample, by the addition of an internal standard to the mixture. However, quantification of individual phases that have only partial or unknown structures is carried out less routinely. This paper presents methodology for quantification of such phases. It outlines the procedure for calibration of the method and gives detailed examples from both synthetic and mineralogical systems. While the method should, in principle, be generally applicable, its implementation in the TOPAS program from Bruker AXS is demonstrated here.

Outcomes of the International Union of Crystallography Commission on Powder Diffraction Round Robin on Quantitative Phase Analysis: samples 2, 3, 4, synthetic bauxite, natural granodiorite and pharmaceuticals

The International Union of Crystallography (IUCr) Commission on Powder Diffraction (CPD) has sponsored a round robin on the determination of quantitative phase abundance from diffraction data. The aims of the round robin have been detailed by Madsen et al. [J. Appl. Cryst. (2001), 34, 409–426]. In summary, they were (i) to document the methods and strategies commonly employed in quantitative phases analysis (QPA), especially those involving powder diffraction, (ii) to assess levels of accuracy, precision and lower limits of detection, (iii) to identify specific problem areas and develop practical solutions, (iv) to formulate recommended procedures for QPA using diffraction data, and (v) to create a standard set of samples for future reference. The first paper (Madsen et al., 2001) covered the results of sample 1 (a simple three-phase mixture of corundum, fluorite and zincite). The remaining samples used in the round robin covered a wide range of analytical complexity, and presented a series of different problems to the analysts. These problems included preferred orientation (sample 2), the analysis of amorphous content (sample 3), microabsorption (sample 4), complex synthetic and natural mineral suites, along with pharmaceutical mixtures with and without an amorphous component. This paper forms the second part of the round-robin study and reports the results of samples 2 (corundum, fluorite, zincite, brucite), 3 (corundum, fluorite, zincite, silica flour) and 4 (corundum, magnetite, zircon), synthetic bauxite, natural granodiorite and the synthetic pharmaceutical mixtures (mannitol, nizatidine, valine, sucrose, starch). The outcomes of this second part of the round robin support the findings of the initial study. The presence of increased analytical problems within these samples has only served to exacerbate the difficulties experienced by many operators with the sample 1 suite. The major difficulties are caused by lack of operator expertise, which becomes more apparent with these more complex samples. Some of these samples also introduced the requirement for skill and judgement in sample preparation techniques. This second part of the round robin concluded that the greatest physical obstacle to accurate QPA for X-ray based methods is the presence of absorption contrast between phases (microabsorption), which may prove to be insurmountable in some circumstances.

The stability and structure of Csx[Ti2−x4□x4]O4, 0.61 < x < 0.65

The stability of the phase Csx[Ti2−x4□x4]O4, □ = vacancy, in the Cs2OTiO2 system has been studied in the temperature range 800−1120°C. The phase has a narrow range of homogeneity with 0.61 < x < 0.65. Structure refinements were carried out for X-ray intensity data from two crystals obtained from melts with TiO2:CsO0.5 molar ratios of 2.0 and 3.2. The crystals have orthorhombic symmetry, Immm, a0 = 3.83, b0 = 17.00, c0 = 2.96 A. The refinements are consistent with the structural model of Hervieu and Raveau (Rev. Chim. Miner. 18, 642 (1981)) in which (010) corrugated layers of titanium-oxygen octahedra, containing disordered titanium vacancies, are separated by planes of cesium ions. Long-exposure precession photographs showed diffuse superlattice diffraction effects in the form of continuous streaks parallel to b∗0. These have been analyzed in terms of models for two-dimensional ordering of the interlayer cesium ions. Annealing of melted samples below 700°C causes a transformation of the I-centered structure to a C-centered structure of the Kx(MyTi2−y)O4 type in which 3-D ordering of cesium occurs.The stability of the phase Cs/sub x/(Ti/sub 2-x/4/square/sub x/4/)O/sub 4/, square = vacancy, in the Cs/sub 2/O-TiO/sub 2/ system has been studied in the temperature range 800-1120/sup 0/C. The phase has a narrow range of homogeneity with 0.61 < x less than or equal to 0.65. Structure refinements were carried out for X-ray intensity data from two crystals obtained from melts with TiO/sub 2/: CsO/sub 0.5/ molar ratios of 2.0 and 3.2. The crystals have orthorhombic symmetry, Immm, a/sub 0/ = 3.83, b/sub 0/ = 17.00, c/sub 0/ = 2.96 A. The refinements are consistent with the structural model of Hervieu and Raveau in which (010) corrugated layers of titanium-oxygen octahedra, containing disordered titanium vacancies, are separated by planes of cesium ions. Long-exposure precession photographs showed diffuse superlattice diffraction effects in the form of continuous streaks parallel to b/sub 0/*. These have been analyzed in terms of models for two-dimensional ordering of the interlayer cesium ions. Annealing of melted samples below 700/sup 0/C causes a transformation of the I-centered structure to a C-centered structure of the K/sub x/(M/sub y/Ti/sub 2-y/)O/sub 4/ type in which 3-D ordering of cesium occurs.

Description and survey of methodologies for the determination of amorphous content via X-ray powder diffraction

Abstract The presence of amorphous materials in crystalline samples is an increasingly important issue for diffractionists. Traditional phase quantification via the Rietveld method fails to take into account the occurrence of amorphous material in the sample and without careful attention on behalf of the operator its presence would remain undetected. Awareness of this issue is increasing in importance with the advent of nanotechnology and the blurring of the boundaries between amorphous and crystalline species. The methodology of a number of different approaches to the determination of amorphous content via X-ray diffraction and an assessment of their performance, is described. Laboratory-based, X-ray diffraction data from a suite of synthetic samples, with amorphous content rangäing from 0.0 to 50 wt%, has been analysed using both direct (in which the contribution of the amorphous component to the pattern is used to obtain an estimate of concentration) and indirect (where the absolute abundances of the crystalline components are used to estimate the amorphous content by difference) methodologies. In addition, both single peak and whole pattern methodologies have been assessed. All methods produce reasonable results, however the study highlights some of the strengths, deficiencies and applicability of each of the approaches.

On-line X-ray diffraction for quantitative phase analysis: Application in the Portland cement industry

The aim of this work was to design, construct, install, and commission an on-line, X-ray diffraction (XRD) analyzer capable of continuously monitoring phase abundances for use in process plant control. This has been achieved through a joint project between CSIRO Minerals and Fuel & Combustion Technology Pty. Ltd. with an instrument designed for use in a Portland cement manufacturing plant. Key factors in tailoring such an instrument to the cement industry were (i) the handling and presentation of a dry sample and (ii) the development of an analytical method suitable for the complex suite of phases contained within Portland cement. The instrument incorporates continuous flow of sample through the diffractometer using a purpose-built sample presentation stage. The XRD data are collected simultaneously using a wide range (120° 2θ) position sensitive detector, thus enabling rapid collection of the full diffraction pattern. The data are then analyzed using a Rietveld analysis method to obtain a quantitative estimate of each of the phases present. The instrument is controlled by a PC linked to the diffractometer through a purpose built interface. The phase abundance information is then transmitted to the central computer in the cement plant where it can be used for the control of mill parameters such as temperature and retention times as well as gypsum feed rate.

TiO2-II. Ambient pressure preparation and structure refinement

Abstract The ∝-PbO2 form of TiO2 forms as a finely crystalline intermediate phase when Ti3O5 is dissolved in sulphuric acid at elevated temperatures. Its structure has been refined using the Rietveld method applied to X-ray powder data. A structural model is proposed for the oxidation and solid-state transformation of Ti3O5 to TiO2-II, controlled by the close match between (110)Ti3O5 and (101)TiO2 atomic layers.

New cesium titanate layer structures

A phase study of the Cs2OTiO2 system in the composition range 75–100 mole% TiO2 and the temperature range 850–1200°C revealed the existence of two new cesium titanates, with compositions Cs2Ti5O11 and Cs2Ti6O13. The former compound undergoes a reversible hydration reaction below 200°C to form Cs2Ti5O11 · (1 + x)H2O, 0.5 < x < 1. The structures of the three phases have been determined. They are based on corrugated layers of edge-shared octahedra, with cesium ions (and H2O) packing between the layers. In Cs2Ti6O13, the layers are continuous in two dimensions, whereas in Cs2Ti5O11 and Cs2Ti5O11 · (1 + x)H2O, the layers are periodically stepped to give 5-octahedra wide, corner-linked ribbons.

Quantitative Phase Analysis

The most common use of powder diffraction in analytical science is the identification of crystalline components, or phases, present in a sample of interest. The near universal applicability of the method for this purpose is derived from the fact that a diffraction pattern is produced directly from the components’ crystal structure. However, for multi-phase samples, once the nature of phases present has been established, the next question usually asked of the diffractionist is “how much of each phase is there?” This chapter provides an overview of the basis and application of commonly used methods of quantitative phase abundance determination as well as references to the extensive literature on the subject.

In situ X-ray diffraction of the transformation of gibbsite to α-alumina through calcination: effect of particle size and heating rate

A study was conducted on the gibbsite to α-alumina (α-Al2O3) transformation dynamics with particular reference to the influence of particle size and heating rate. Coarse- and fine-grained gibbsites were used to examine the transformation paths for the two materials, with particular reference to the upper and lower branch sequences described by Wefers & Misra [Oxides and Hydroxides of Aluminium, (1987), Alcoa Technical Paper No. 19 Revised, Aluminium Company of America]. The main techniques used to assess gibbsite calcination were thermogravimetric differential scanning calorimetry and in situ X-ray diffraction, which provided complementary information on transformation behaviour. Whilst the quantitative phase analysis results indicated that the coarse- and fine-grained gibbsites followed both the upper and the lower branch sequences, detailed analysis of the results highlighted specific differences in the transformation behaviour for the two materials. With the loss of three molecules of water as gibbsite transformed to transition aluminas and finally α-Al2O3, there was a high degree of disorder in the crystal structure, resulting in broad and diffuse reflections in the diffraction patterns.