No abstract

It is shown that quantitative X‐ray powder diffraction analyses using full profile multiphase refinement should include corrections for the Brindley particle absorption contrast effect. This is demonstrated with synthetic mixtures of the highly contrasting phases LiF and Pb(NO3)2 (μ/ρ = 20 and 231 cm−1 for Co Kα). With contrast corrections, the only parameter which needs to be input is an effective particle radius R for each phase. For mixtures of LiF and Pb(NO3)2 over the whole composition range, quantification is achieved, under the present specimen preparation method, with an effective particle radius of 51 μm for both phases, giving analyses correct to within 1 percentage point. Without Brindley corrections, the analysis is grossly in error.

Crystalline phases present in the three NIST SRM Standard Portland cement clinkers 8486, 8487, and 8488 have been quantified from XRD powder patterns, (CoKα radiation), using the full-profile Rietveld method. Included in the Rietveld refinement are rhombohedral (R), monoclinic (M), and triclinic (T) crystal polymorphic forms of C3S, as well as crystal polymorphs of C2S and C3A. It is necessary to specify the phase crystallography including polymorphs, because of the extreme superposition of alite and belite XRD lines in the clinker patterns. Unsatisfactory results occur when only one or two of the C3S polymorphs are used in the Rietveld quantification; best results occur when all three polymorphs for C3S are included. The latter are called RMT-type refinements. The Rietveld full-profile XRD method is as precise as the microscope point-counting (MPC) method, but much less labor-intensive. The Rietveld method can quantify the C3S phase polymorphs, as well as total C3S. Rietveld and MPC methods give the same phase weight percentages for the three NIST standard clinkers. Calculated oxide weight percentages obtained from Rietveld phase weight percentages agree well with oxide percentages determined by XRF analysis. Bogue mineral weight percentages do not agree with Rietveld or MPC data, while transformation of the Bogue mineral percentages to oxides does not compare well with XRF analysis.

A new method for the quantification of montmorillonite by full-profile Rietveld analysis of the XRD profile is presented. A measured standard XRD pattern of Algerian bentonite was used to construct a universally applicable montmorillonite (hkl) file for use with a P.C. based Rietveld XRD quantitative analysis system, SIROQUANT. “Universal” means that the standard file can be used for montmorillonites from other localities. The validity of the montmorillonite standard profile was tested with weighed mixtures of quartz and different standard montmorillonites. The results show the montmorillonite observed (hkl) file is generally applicable (i.e., universal), and can be used to quantify montmorillonite in any mineral without modification or chemical treatment of the sample. Two halfwidth functions were used for the montmorillonite, corresponding to the sharp (hk0) and broad (hkl) classes of reflections. A March preferred orientation parameter for montmorillonite was also refined.

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.