The definitions for important Rietveld error indices are defined and discussed. It is shown that while smaller error index values indicate a better fit of a model to the data, wrong models with poor quality data may exhibit smaller values error index values than some superb models with very high quality data.

The ICDD's Powder Diffraction File™ (PDF®) is a database of inorganic and organic diffraction data used for phase identification and materials characterization by powder diffraction. The PDF has been available for over 75 years and finds application in X-ray, synchrotron, electron, and neutron diffraction analyses. With entries based on powder and single crystal data, the PDF is the only crystallographic database where every entry is editorially reviewed and marked with a quality mark that alerts the user to the reliability/quality of the submitted data. The editorial processes of ICDD's quality management system are unique in that they are ISO 9001:2015 certified. Initially offered as text on paper cards and books, the PDF evolved to a computer-readable database in the 1960s and today is both computer and web accessible. With data mining and phase identification software available in PDF products, and the databases’ compatibility with vendor (third party) software, the 1 000 000+ published PDF entries serve a wide range of disciplines covering academic, industrial, and government laboratories. Details describing the content of database entries are presented to enhance the use of the PDF.

HighScore with the Plus option (HighScore Plus) is the commercial powder diffraction analysis software from PANalytical. It has been in constant development over the last 13 years and has evolved into a very complete and mature product. In this paper, we present a brief overview of the suite focusing on the latest additions and its user-friendliness. The introduction briefly touches some basic ideas behind HighScore and the Plus option.

Methods extracting fast all the peak intensities from a complete powder diffraction pattern are reviewed. The genesis of the modern whole powder pattern decomposition methods (the so-called Pawley and Le Bail methods) is detailed and their importance and domains of application are decoded from the most cited papers citing them. It is concluded that these methods represented a decisive step toward the possibility to solve more easily, if not routinely, a structure solely from a powder sample. The review enlightens the contributions from the Louër’s group during the rising years 1987–1993.

A Fortran 77 computer program has been developed for the quantitative analysis of minerals by multiphase profile analysis of the complete powder diffraction pattern. Featured are full-matrix least-squares refinement of 14 Rietveld “instrumental parameters” (phase scales, asymmetry, preferred orientations (March model), linewidths, instrument zero, lineshapes and unit cell dimensions), Brindley particle absorption contrast factors and amorphicity corrections. The program uses a crystal structure Databank, which contains information on absorption coefficients, unit cell data and crystal structures for some 90 common minerals. New minerals can be easily added. Structure parameters are also refinable by a profile decomposition method using a program called STRUCT. The sum of the calculated patterns, derived from the crystal structure data, is fitted to the observed pattern by a program called TRACSCAL which runs in singlepass multiphase mode and, after the above corrections have been applied, the weight percentages of the component phases are calculated from the Rietveld scaling factors.

The program runs on an IBM-compatible AT computer with 640K of RAM, on an extended memory AT, or a mainframe system. Examples of its use are given with standard mixtures and naturally occurring specimens. On an AT computer with 20MHz clock speed a scaling run, including data input, reading of the pattern, processing of (hkl) files, calculation of the profile and one cycle of least squares fitting takes about 30 seconds for binary standard mixtures and about 2.5 minutes for a 7-phase natural bauxite pattern containing 320 independent (hkl) reflections.

The Reference Intensity Ratio (RIR) is a general, instrument-independent constant for use in quantitative phase analysis by the X-ray powder diffraction internal standard method. When the reference standard is corundum, RIR is known as I/Ic; These constants are collected in the Powder Diffraction File (1987), can be calculated, and can be measured. Recommended methods for accurate measurement of RIR constants are presented, and methods of using these constants for quantitative analysis are discussed. The numerous, complex constants in Copeland and Bragg's method introduced to account for superimposed lines can be simply expressed in terms of RIR constants and relative intensities. This formalism also permits introduction of constraints and supplemental equations based on elemental analysis.

The current report describes the installation and the preliminary commissioning of the Material Science Powder Diffraction (MSPD) beamline at the Spanish synchrotron ALBA-CELLS. The beamline is fully dedicated to powder diffraction techniques and consists of two experimental stations positioned in series: a High Pressure/Microdiffraction station and a High Resolution/High Throughput powder diffraction station.

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.

Computer algebra removes much of the drudgery from mathematics; it allows users to formulate models by using the language of mathematics and to have those models evaluated with little effort. This symbolic form of representation is often thought of as being separate to dedicated computational programs such as Rietveld refinement. These dedicated programs are often written in low level languages; they are relatively inflexible in what they do and modifying them to change functionality in a small manner is often a major programming task. This paper describes a symbolic system that is integrated into the dedicated Rietveld refinement program called TOPAS. The symbolic component allows large functional changes to be made at run time and with a relatively small amount of effort. In addition, the system as a whole reduces the programming complexity at the developmental stage.

A computer program, Dysnomia, for the maximum-entropy method (MEM) has been tested for the evaluation and advancement of MEM-based pattern fitting (MPF). Dysnomia is a successor to PRIMA, which was the only program integrated with RIETAN-FP for MPF. Two types of MEM algorithms, i.e., 0th-order single-pixel approximation and a variant of the Cambridge algorithm, were implemented in Dysnomia in combination with a linear combination of the “generalized F constraints” and arbitrary weighting factors for them. Dysnomia excels PRIMA in computation speed, memory efficiency, and scalability owing to parallel processing and automatic switching of discrete Fourier transform and fast Fourier transform depending on sizes of grids and observed reflections. These features of Dysnomia were evaluated for MPF analyses from X-ray powder diffraction data of three different types of compounds: taurine, Cu2CO3(OH)2 (malachite), and Sr9In(PO4)7. Reliability indices in MPF analyses proved to have been improved by using multiple F constraints and weighting factors based on lattice-plane spacings, d, in comparison with those obtained with PRIMA.

Results are given of an assessment of a Rietveld-type X-ray powder diffraction pattern fitting structure refinement technique for assaying powdered mixtures as an alternative to conventional discrete peak empirical methods of the type described by Klug and Alexander (1974) and Chung (1974). The values obtained for a mixture of corundum and α-quartz, following calibration of the instrument with a profile of the former, indicate that this technique has excellent potential as an analytical tool.

Crystallite size determined by X-ray line profile analysis is often smaller than the grain or subgrain size obtained by transmission electron microscopy, especially when the material has been produced by plastic deformation. It is shown that besides differences in orientation between grains or subgrains, dipolar dislocation walls without differences in orientation also break down coherency of X-rays scattering. This means that the coherently scattering domain size provided by X-ray line profile analysis provides subgrain or cell size bounded by dislocation boundaries or dipolar walls.

A Monte Carlo code for indexing powder diffraction patterns is presented. Cell parameters are generated randomly and tested against an idealized powder profile generated from the extracted d’s and I’s. Limits with this program in solving problems associated with zeropoint errors and impurity lines are examined. Most problems (V<2000 Å3, cell parameters <20 Å) are solved in less than 1–15 min if the symmetry is as low as monoclinic (with a >2 GHz processor); more time is needed for triclinic cases. Attempts are shown to be successful for the indexation of two-phase samples in simple cases (combining orthorhombic or higher symmetries). © 2004 International Centre for Diffraction Data.

Key words: powder diffraction, indexing, Monte Carlo

The following new or updated patterns are submitted by the JCPDS Research Associateship at the National Bureau of Standards. The patterns are a continuation of the series of standard X-ray diffraction powder patterns published previously in the NBS Circular 539, the NBS Monograph 25, and in this journal. The methods of producing these reference patterns are described in this journal, Vol. 1, No. 1, p. 40 (1986).

The data for each phase apply to the specific sample described. A sample was mixed with one or two internal standards: silicon (SRM640a), silver, tungsten, or fluorophlogopite (SRM675). Expected 2-theta values for these standards are specified in the methods described (ibid.). Data, from which the reported 2-theta values were determined, were measured with a computer controlled diffractometer. Computer programs were used to locate peak positions and calibrate the patterns as well as to perform variable indexing and least squares cell refinement.

A revised structure model of ettringite is presented, in order to provide quantitative X-ray diffraction (QXRD) of this mineral in cement pastes. The model is derived from two different existing structure models, both of which are suitable for restricted use but are inferior to the refined ettringite structure presented. In the first published ettringite structure proposed by Moore and Taylor [Acta Crystallogr. B 26, 386–393 (1970)], none of the 128 positions for H are given in the unit cell, which results in reduced scattering power for use of this model for quantification purposes. For the precise quantification of ettringite in samples together with anhydrous phases, the scattering factors of all atoms including the H positions are indispensable. The revised structure model is based on the data of Moore and Taylor, supplemented by the H positions determined by Berliner (Material Science of Concrete Special Volume, The Sydney Diamond Symposium, American Ceramic, Society, 1998, pp. 127–141) on the basis of a neutron diffraction structural investigation of deuterated ettringite at 20 K. Berliner’s (Material Science of Concrete Special Volume, The Sydney Diamond Symposium, American Ceramic Society, 1998, pp. 127–141) thermal parameter should not, however, be used, since a normal application is at room temperature. In order further to improve the structure model of ettringite, Rietveld refinement with the rigid body approach for OH and H2O molecules and SO4 tetrahedra was employed. The refined and improved ettringite structure model was tested for quantitative phase analysis by the determination of actual ettringite contents in mixtures with an internal standard. Synthesized and orientation-free prepared ettringite powders were investigated by X-ray powder diffraction analysis and quantified in four different blends with zircon. The quantification results with the new structure model demonstrate the superior quality of the revised ettringite structure.

One of the advantages of a multidetector neutron time-of-flight diffractometer such as the high pressure preferred orientation diffractometer (HIPPO) at the Los Alamos Neutron Science Center is the capability to measure efficiently preferred orientation of bulk materials. A routine experimental method for measurements, both at ambient conditions, as well as high or low temperatures, has been established. However, only recently has the complex data analysis been streamlined to make it straightforward for a noninitiated user. Here, we describe the Rietveld texture analysis of HIPPO data with the computer code Materials Analysis Using Diffraction (MAUD) as a step-by-step procedure and illustrate it with a metamorphic quartz rock. Postprocessing of the results is described and neutron diffraction results are compared with electron backscatter diffraction measurements on the same sample.

A suitable external standard method which was first described by O’Connor and Raven (1988) (“Application of the Rietveld refinement procedure in assaying powdered mixtures,” Powder Diffr. 3, 2–6) was used to determine the quantitative phase composition of a commonly used Ordinary Portland Cement (OPC). The method was also applied in order to determine amorphous contents in OPC. Also investigated were the impact of atomic displacement parameters and the microstrain on the calculated amorphous content. The investigations yielded evidence that said parameters do indeed exert an influence on the calculated amorphous content. On the basis of the data produced we can conclude that the method used is entirely to be recommended for the examination of OPC. No significant amorphous content could be proven in the OPC used.

A task group of the JCPDS—International Center for Diffraction Data (ICDD) was established with the charge of investigating the use of silver behenate, CH3(CH2)20COO·Ag, as a possible low-angle calibration standard for powder diffraction applications. Utilizing several data collection and analysis techniques, long-period spacing (d001) values with a range of 58.219–58.480 Å were obtained. Using the same collected data and one data analysis refinement calculation method resulted in dm values with a range of 58.303–58.425 Å. Data collected using a silicon internal standard and the same singular data analysis calculation method provided d001 values with a range of 58.363–58.381 Å.

The following new or updated patterns are submitted by the JCPDS Research Associateship at the National Bureau of Standards. The patterns are a continuation of the series of standard X-ray diffraction powder patterns published previously in the NBS Circular 539, the NBS Monograph 25, and in this journal. The methods of producing these reference patterns are described in this journal, Vol. 1, No. 1, p. 40 (1986).

The data for each phase apply to the specific sample described. A sample was mixed with 1 or 2 internal standards: silicon (SRM640a), silver, tungsten, or fluorophlogopite (SRM675). Expected 2-theta values for these standards are specified in the methods described (ibid.). Data from which the reported 2-theta values were determined, were measured with a computer controlled diffractometer. Computer programs were used to locate peak positions and calibrate the patterns as well as to perform variable indexing and least squares cell refinement. A check on the overall internal consistency of the data was also provided by a computer program.

Each of the RIR based methods for carrying out quantitative X-ray powder diffraction analysis are described and a consistent set of notation is developed. The so called “standardless” analysis procedures are shown to be a special case of the internal-standard method of analysis where the normalizing assumption is used. All analytical methods, other than the Rietveld whole pattern matching procedure, require the use of explicitly measured standards, typically in the form of RIR values. However, if only semi-quantitative results can be tolerated, the standards may be obtained by using published RIR and relative intensity values. The exciting new techniques of whole pattern fitting and Rietveld constrained quantitative analysis are also described in RIR notation and shown also to be forms of the internal-standard method with the normalization assumption. The quantitative results obtained from Rietveld quantitative analysis are derived from computed standards in the form of computed, normalized, RIRN values. The normalization assumption in Rietveld analysis allows the exclusive use of computed standards and comes as close to a “standardless” analysis as one can achieve: relying on the absence of amorphous material and on the validity of the structural models. Relationships are given for obtaining quantitative analysis from these RIRN values obtainable from the least-squares scale factors.