• supercell modelling;
  • turbostratic disorder;
  • nontronite;
  • clay minerals;
  • quantitative phase analysis;
  • TOPAS;
  • synchrotron radiation

Two calibration-based quantitative X-ray diffraction (XRD) models for turbostratically disordered Bulong nontronite, the PONKCS (partial or no known crystal structure) approach and the supercell structural model, were compared in terms of the accuracy and refinement error from Rietveld quantitative phase analysis. The PONKCS approach achieved improved nontronite quantitative results with synchrotron diffraction patterns compared with those achieved with laboratory XRD data as a result of better data quality and the use of Debye–Scherrer geometry with significantly reduced preferred orientation effects. The introduction of a peak shape modifier (spherical harmonics) to correct the quantification result is mainly useful for laboratory XRD patterns containing nontronite collected from Bragg–Brentano geometry with appreciable preferred orientation effects. A novel calibration approach for the nontronite supercell model was developed, based on the Rietveld quantitative formula in the TOPAS symbolic computation system. The calibrated supercell model achieved better accuracy (deviation within 1 wt%) and lower refinement error than the PONKCS approach because the physically based description of turbostratic disorder requires fewer refinable parameters than the PONKCS approach. The drawbacks and limitations of the supercell approach are also discussed.