March-type models for the description of texture in granular materials.
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Texture in crystalline materials, i.e. preferred orientation (PO), is of interest in terms of texture-property relationships and also in X-ray diffraction science because PO can cause serious systematic errors in quantitative phase analysis using diffraction data. The single- parameter, pole-density distribution function (PDDF), proposed by March (1932) to represent PO in diffraction analysis, is used widely it Rietveld pattern-fitting following a suggestion by Dollase (1986). While the March model is an excellent descriptor of PO for gibbsite [AI(OH)3] x-ray powder diffraction (XRPD) data (O'Connor, Li and Sitepu, 1991), the model has proved to be deficient for Rietveld modelling with molybdite [Mo03], calcite [CaCO3] and kaolinite [A12O3.2SiO2.2H2O] XRPD data (Sitepu, 1991; O'Connor, Li and Sitepu, 1992; and Sitepu, O'Connor and Li, 1996). Therefore, the March model should not be regarded as a general-purpose PDDF descriptor.This study has examined the validity of the March model using XRPD and neutron powder diffraction (NPD) instruments operated, respectively, by the Curtin Materials Research Group in Perth and by the Australian Nuclear Science and Technology Organisation at the HIFAR reactor facility at Lucas Heights near Sydney. Extensive suites of XRPD and NPD data were measured for uniaxially-pressed powders of molybdite and calcite, for which the compression was systematically varied. It is clear from the various Rietveld refinements that the March model becomes increasingly unsatisfactory as the uniaxial pressure (and, therefore, the level of PO) increases.The March model has been tested with a physical relationship developed by the author which links the March r-parameter to the uniaxial pressure via the powder bulk modulus, B. The agreement between the results obtained from directly measured values of B and from Rietveld analysis with the March model are promising in terms of deducing the powder bulk modulus from the March r-parameter.An additional test of the March model was made with NPD data for specimens mounted, first, parallel to the instrument rotation axis and, then, normal to the axis. The results have provided some further indication that the March model is deficient for the materials considered in the study.During the course of the study, it was found that there are distinct differences between the direction of the near-surface texture in calcite, as measured by XRPD, and bulk texture characterised by NPD. The NPD-derived textures appear to be correct descriptions for the bulk material in uniaxially-pressed powders, whereas the XRPD textures are heavily influenced by the pressing procedure.An additional outcome of the NPD work has been the discovery, made jointly with Dr Brett Hunter of ANSTO, that the popular LHPM Rietveld code did not allow for inclusion of PO contributions from symmetry-equivalent reflections. Revision of the code by Dr Hunter showed that there is substantial bias in Rietveld-March r-parameters if these reflections are not factored correctly into the calculations.Finally, examination of pole-figure data has underlined the extent to which the March model oversimplifies the true distributions. It is concluded that spherical harmonics modelling should be used rather than the March model as a general PO modelling tool.
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