Profile fitting and the two-stage method in neutron powder diffractometry for structure and texture analysis

An outline and an application of the two-stage method in neutron powder diffractometry are presented. Stage (1): Individual reflection data like position, half-width and integrated intensity are analysed by profile fitting. The profile analysis is based on an experimentally determined instrument function and can be applied without prior knowledge of a structural model. A mathematical procedure is described which results in a variance-covariance matrix containing standard deviations and correlations of the refined reflection parameters. Stage (2): The individual reflection data derived from the profile fitting procedure can be used for appropriate purposes either in structure determination or in texture and strain or stress analysis. The integrated intensities are used in the non-diagonal weighted least-squares routine POWLS for structure refinement. The weight matrix is given by the inverted variance-covariance matrix of stage (1). This procedure is the basis for reliable and real Bragg R values and for a realistic estimation of standard deviations of structural parameters. In the case of texture analysis the integrated intensities are compiled into pole figures representing the intensity distribution for all sample orientations of individual hkl. Various examples for the wide application of the two-stage method in structure and texture analysis are given: structure refinement of a standard quartz specimen, magnetic ordering in the system Tb_xY_1-xAg, preferred orientation effects in deformed marble and texture investigations of a triclinic plagioclase.