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.

A compilation has been made of the X-ray powder diffraction patterns of the high Tc superconductor and related phases in the systems of Ba-R-Cu-O, Sr-R-Cu-O and Ca-R-Cu-O, where R = yttrium and lanthanides. In addition to the patterns of compounds found in these systems, other related compounds included are cation substitution products of the high Tc phases of Ba2RCu2O6+x, potential reaction products with different types of sample containers, and selected thin-film substrates. The International Centre for Diffraction Data/Powder Diffraction file (ICDD/PDF) coverage includes Sets 1 to 41. A cross correlation of these phases with those reported in Phase Diagrams For Ceramists (PDFC), has also been completed. Results of these efforts are tabulated.

In recent years, grazing incidence angle attachments have been shown to be very useful in the phase identification of thin polycrystalline films. These devices are sold commercially as attachments to standard powder diffractometers. The attachment normally consists of a long soller slit assembly and a flat crystal monochromator. The soller slit with or without the monochromator is mounted on the diffracted beam side. In this paper we discuss the effects of different configurations from collimator to monochromator on diffraction data. An understanding of these effects is essential in order to obtain more reliable information on phase transformations, crystallite size, microstrain, and residual stress studies.

High resolution X-ray powder diffraction data have been collected with Bragg-Brentano geometry on samples of MgO using Ni-filtered and graphite-monochromated CuKαradiation. Selection of the characteristic radiation by Ni-filtering produces severe peak asymmetry, truncates the low-angle foot of the peak, lowers the general level of background on the low angle side, and leaves a remnant Kβpeak for all foils of reasonable thickness. When step-scan data produced by this method are used for Rietveld analysis, all of these features cause difficulties in fitting a smooth function to the background and in successfully modelling the detailed profiles of the peaks. On the other hand, Kαradiation from a diffracted-beam monochromator provides inherently more symmetric peaks and a smoothly varying background on both sides of the peak centre, both of which effects can be adequately modelled during Rietveld analysis. The primary disadvantage with monochromation is that, even with very careful setting of the pulse height discrimination, the monochromator may pass a small proportion of the λ/2 component of the incident radiation. In samples containing small quantities (i.e., 2 wt%, or less) of impurity phases, the undesirable features of the diffractometer profile (i.e., asymmetric and truncated background, and Kβand λ/2 peaks) can be of similar intensity to the main peaks arising from the impurities (as well as substructure peaks from the primary phases), thereby leading to difficulties in their identification and quantification. Nevertheless, with due care and long data collection times, the abundances of minor phases can be measured with Rietveld analysis down to levels of the order of 0.1 wt%.

An interactive computer program to display, process and analyze raw powder X-ray diffraction data is described. The program extensively employs graphic means of input and output with the help of “pop-up” windows and menus. In addition to those tasks that are common to most primary raw data analyzing programs, it performs many functions which are generally assigned to separate secondary programs. These functions include on-screen correction of d-spacing with reference to a standard compound, calculation of peak width and crystallite size, subtraction of patterns for differential X-ray diffraction and unrestricted overlay of patterns. The advantages of an integrated single program to process X-ray diffraction data in mineral research are illustrated and discussed.

Legislation in the United States and Canada requires labelling of products containing ≥ 0.1 wt.% crystalline silica. Kaolin clays are used in a variety of industries and usually contain low levels of total (i.e., respirable plus non-respirable) quartz, even after beneficiation. X-ray diffraction procedures have been developed here which are suitable for the quantification of total quartz in commercial kaolins with accuracy sufficient to satisfy the legislation. Separation and analysis of the respirable fraction is not addressed in this paper; however, the procedures described would be applicable to such samples if sufficient were available. Use of the 50.1° 2θrather than the 26.6° 26 (CuKα) quartz peak avoids most of the potential problems of overlap with reflections from other accessory minerals. It is shown that profile fitting techniques and optimised experimental procedures allow the determination of quartz in bulk samples to ± 0.03 wt.% (95% confidence) at the 0.1 wt.% level, and ± 0.1 wt.% at the 1.0 wt.% level, with tolerable data collection times.

The modulation of the lazurite structure has been determined by X-ray diffraction methods. The indexing of satellites on X-ray diffraction powder patterns has been made by means of single crystal X-ray diffraction patterns. The irrationality of the satellite distance from the basic reflections in some specimens of isotropic lazurite confirms the incommensurability of the wavelength of modulation by an edge magnitude of the sodalite subcell and the necessity of a fractional mineral lattice. X-ray diffraction powder data of lazurites with different periods of incommensurate-modulated structure are established. Modulation structure parameters are 0.217 and 0.175, respectively. Indexing of X-ray diffraction powder data of cubic Baikal lazurite suggested by the PDF editorial staff is considered.

This paper describes a new method for the simultaneous determination of mineral composition, mass thickness and mass absorption coefficient of a thin layer of a crystalline substance deposited on a crystalline substrate.

The samples were deposited on membrane disc filters, consisting of mixtures of cellulose acetate and cellulose nitrate. Quantitative results are achieved by measuring the diffraction intensity of the analyte and the attenuation of a reflection of the crystalline material supporting the deposited sample. The mean accuracy of the analysis was found to be: ≈ 3% for mass thickness, ≈ 1% for mass absorption coefficient and ≈ 4% for quantitative mineralogical determination.

X-ray powder diffraction analysis of samples obtained by thermal treatment of coprecipitated amorphous xCd(II) (1-x)Ni(II)2Fe(III)-hydroxides reveals that intermediate crystalline spinel species with lattice constants less than those for the nominal composition are formed before the designated cadmium-nickel ferrites, CdxNil-xFe2O4, come into existence.

In most of the practical problems of the quantitative X-ray analysis, obtaining working equations including only intensity ratios without the sample mass-absorption coefficient is impossible, unless an internal standard is added to the sample. It is shown that the internal standard may be unnecessary if some chemical data are added to the XRD information used. Experimental results justify this claim.

The importance of surface roughness to the measurement of integrated intensity in X-ray powder diffraction is discussed following studies conducted with materials in both powder and bulk (rolled sheet/billet) forms possessing different absorption characteristics. A simple procedure is described which allows for surface roughness effect.

The results of an international project involving five countries and seven laboratories performing over 400 analyses for testing the interlaboratory reproducibility and accuracy using quantitative powder diffraction are presented in this report. Four natural and four artificial mineral mixtures were examined. The RIR (reference intensity ratio) values for all mineral components were either measured or calculated. The relative standard deviation of the interlaboratory determinations range from 5 to 20 percent (for low concentrations, the relative standard deviations can attain 60% percent). Due to systematic errors, the relative standard deviations of the interlaboratory determinations generally exceed the standard deviations determined by individual laboratories. The best results were obtained when the RIR values were measured independendy in each laboratory.

The beautiful methods of crystal analysis that have been developed by Laue and the Braggs are applicable only to individual crystals of appreciable size, reasonably free from twinning and distortion, and sufficiently developed to allow the determination of the direction of their axes. For the majority of substances, especially the elementary ones, such crystals cannot be found in nature or in ordinary technical products, and their growth is difficult and time-consuming.

The method described below is a modification of the Bragg method, and is applicable to all crystalline substances. The quantity of material required is preferably 0.005 c.c., but one tenth of this amount is sufficient. Extreme purity of material is not required, and a large admixture of (uncombined) foreign material, twenty or even fifty per cent, is allowable provided it is amorphous or of known crystalline structure.

The Debye Scherrer method (1917) of determining a crystal system by observation of X-ray interferences on randomly oriented crystal particles amounts in the mathematical problem to deriving quadratic equations for three variables from unknown integer multiples of these variables. In my opinion it is not only physically, but also mathematically reasonable to treat this problem from a geometrical point of view. Let L,M, and N be three non-parallel vectors. Vectors P can be derived by multiplication with the integers n1, n2 and n3, so that

P = n1L + n2 M + n3 N.

X-ray powder patterns for the phases in the CaO-SrO-CuO ternary system, along with the corresponding crystal structures, were obtained from the literature and from the Powder Diffraction File. Available XRD patterns were compared with each other and with a calculated pattern for each phase, yielding a recommended reference pattern. The simulated powder patterns presented here deal with the phases found within the (Ca,Sr)O, (Ca,Sr)2CuO3, (Ca,Sr)14Cu24O41, (Ca,Sr)CuO2, (Ca,Sr)Cu2O3, and (Ca,Sr)Cu2O2 solid solution series and are recommended for the Powder Diffraction File (PDF).

Limitations in powder diffractometry imposed by scatter slits and/or a diffracted-beam monochromator, which have been ignored in the past, are discussed and mapped quantitatively. These limitations become manifest especially with ωoffsets, i.e.in stress measurements and with ωoscillation to improve the reproducibility of intensities in the presence of too coarse grains. The limitations can only be established with knowledge of slit sizes and with precise alignment of all slits, their holders and the diffracted-beam monochromator. To that end, concise, accurate procedures for obtaining these measurements in-situare proposed.

The crystal structure of Tl4V2O7 is solved ab-initio from powder diffraction data collected in Debye-Scherrer geometry using an Inel X-ray Position Sensitive Detector. The structure has been determined from Rietveld analysis in space group ml, Z = 1, with a = 5.9388(2)Å and c = 7.7322(3)Å. The structure of Tl4V2O7 is built up from isolated V2O7 groups aligned along the trigonal c axis. Thallium atoms alternate along a 3-fold axis. The presence of stereochemically active lone pairs is demonstrated and their positions are calculated using a self-consistent electrostatic model. The influence of sample absorption is briefly discussed and the results are compared with those obtained in Bragg-Brentano geometry using flat-plate specimen.

X-ray powder diffraction data for the three title compounds are reported. The crystals of all three compounds are monoclinic and the space group is P21 (No. 4) in each case. (1R, 2R)-(−)- norpseudoephedrine hydrochloride has a = 5.4422(8) Å, b = 8.071(1) Å, c = 11.839(1) Å and P= 101.803(9)°. For (1S,2R)-(+)-nqrephedrine hydrochloride a = 8.457(1) Å, b = 10.337(2) Å, c = 12.575(3) Å, and β = 107.46(1)° and for(±)-norephedrine hydrochloride a = 7.4406(6) Å, b = 9.4557(6) Å, c = 14.5799(8) Å and β= 103.446(7)°.

In many experiments on X-ray stress analysis, the tilt angle Ψ shows that for a given peak the integrated intensity function of Ψ is not a constant. In this paper a geometric factor is described which corrects the integrated intensity in asymmetric X-ray diffraction. The defocussing effect, always present in asymmetric X-ray diffraction, reduces the number of diffracted X-ray photons registered by the detector. For a θ/2θ diffractometer, the new correction was found to be dependent on the divergence angle of source and detector slit, the tilt angle Ψ and the Bragg angle θ.

The experimental results corrected with the proposed factor are in good agreement with the theory in limits of acceptable errors.

An algorithm has been derived, forming the basis of a computer program called BBCCURV, which calculates a Bragg-Brentano X-ray diffractometer intensity correction curve (intensity correction factor Kivs. 2θi) given the diffractometer and sample dimensions, and the effective (not theoretical) linear absorption coefficient of the sample. Use of this calibration curve gives a set of intensity data free from aberrations, which are caused mainly by sample transparency, curvature of the diffraction cones passing through the receiving slit and possible beam overflow past the specimen at low angles.

The algorithm was confirmed with a full-profile Rietveld refinement of Bragg-Brentano X-ray diffraction data from a H+-ZSM5 zeolite sample. On introducing a BBCCURV correction curve, the profile R-factor over the pattern points dropped from 30.8% to 16.5%, a significantly better fit when the data were corrected with a BBCCURV curve.

BBCCURV intensity calibration curves from LiF (μ= 1.5 mm−1) through zeolites, clays, ZnO, rutile, Pb(NO3)2and finally solid metal (μ= 1000 mm−1) (CoKα) indicate upward revision of the measured diffractometer intensities by factors of between 2 and 10 at 2θ= 5° for these sample types, normalised to a correction factor of 1.0 at 2θ= 44°. Corrections of this magnitude to Bragg-Brentano data are thus significant in full-profile structure refinement and quantitative analysis with Bragg-Brentano data. Use of a variable divergence slit (VDS) is not appropriate in full-profile refinements as the intensity aberrations are magnified, and conversion from VDS data to aberration-free data is sample- and transparency-dependent, and not the simple area (sinθ)−1function generally assumed. Use of a fixed divergence slit with a BBCCURV-type calibration is recommended.