Incorporating the direct derivation method and molecular scattering power method into the Rietveld quantitative phase analysis routine in <i>TOPAS</i>

The equations of the direct derivation method (DDM) and the unit-cell scattering power method are reviewed in this report. Their relationships and connections to the conventional Rietveld quantitative phase analysis (QPA) are revealed, leading to the development of the <i>C_k</i> -corrected DDM and the molecular scattering power (MSP) method. Both methods can be seamlessly integrated into the conventional Rietveld QPA routine as hybrid QPA, <i>i.e.</i> they enable fitting phases of partially or no known crystal structure simultaneously with conventional crystal structure modelling of other known crystalline phases. The accuracies of these hybrid QPA methods are evaluated using a calculated X-ray diffraction pattern for a mixture, the IUCr round robin CPD-1 dataset and synthetic mixtures of disordered source clay minerals (kaolinite KGa-2, chlorite CCa-2) with corundum, using both Launch Mode and Graphical User Interface (GUI) Mode of the <i>TOPAS</i> software. Although the accuracies of these hybrid QPA methods are slightly lower than that of conventional Rietveld QPA, their absolute deviations from weighed percentages are scarcely larger than 3 wt%. Compared with the original DDM, the <i>C_k</i> correction enhances QPA accuracy, particularly for mixtures containing phases of large differences in average atomic number. An advantage over the original unit-cell scattering power method is that the proposed MSP method eliminates the need to know the lattice parameters, unit-cell volume or number of molecules in the unit cell.