Quantitative texture analysis and combined analysis

Various aspects of crystallographic quantitative texture analysis (QTA) are introduced and the additional information that combined analysis (CA) can yield for the full characterization of real materials (textured, stressed, nanosized, layered etc.) is described. QTA is frequently used because the existence of texture determines the characteristics and properties of the sample. The orientation distribution (OD) of the crystallites is defined, and various ways to resolve the QTA fundamental equation are detailed, including pole-figure measurements and normalization. Methods for resolving the OD (generalized spherical harmonics, vector, WIMV–EWIMV, entropy maximization, components, exponential harmonics, arbitrary defined cells, Radon transform), inverse pole figures, and estimators for OD refinement quality and texture strength are described. Pole figures and OD types are related to the degrees of freedom for the crystallites to orient in the sample. The link between reciprocal-space maps and crystallite orientations is explained. Magnetic QTA is described, using magnetic pole figures and magnetic ODs, characterizing the macroscopic magnetic polarization of the sample. Generalized Rietveld refinement is introduced to physically account for texture presence (as opposed to other texture-correction models, like the March–Dollase model); combined analysis is core to this, and all the various sample characteristics seen by scattering of X-rays are accounted for. Experimental requirements, instrumental contributions and implementations of texture, line broadening, layering, residual stresses etc. are described. An example illustrates the efficiency of CA for characterizing a complex sample made of three thin textured and stressed layers.