Powder Pattern Decomposition with the Aid of Preferred Orientation

A method of decomposition of overlapping reflections in a powder pattern with the aid of preferred orientation is presented. Empirical preferred orientation correction with axial symmetry is used. The method is tested on several sets of simulated powder patterns. Introduction Powder patterns collected at various values of some parameter which influences either the position or the intensity of the reflection can be used for the decomposition of overlapping profiles in the pattern. David et al. [l] used the measurements at several temperatures, exploiting so the thermal expansion. Preferred orientation is another suitable tool. Dahms and Bunge [2] used a complete set of X-ray data from a texture goniometer to determine the ODF of the crystallites and to decompose the overlapping profiles. In the present example, the recently generalized empirical preferred orientation correction [3] is used instead of the ODF. The axially symmetric distribution of the crystallite orientation is a necessary condition which can easily be achieved by spinning the sample. Powder patterns collected with any sample orientation with respect to the diffraction vector can be used thanks to the general expression for the preferred orientation correction. Results on simulated data are presented. Correction for preferred orientation Let the distribution of poles Hail in real space in a Cartesian co-ordinate system of the specimen be described by a fi_mction PHa(r = x,y,z) with one maximum in a general direction. The distribution of poles hkl of any other plane, which makes only one angle $H,h with HKL, is given by Phkl (ro) = (I / 27c sin (lWJJ J PHKY, (r) ds (1) where the integration goes on the closed curve, where are situated all the poles Hm, which make the angle $H,h with the pole hkl lying in the direction ro. If the function PHm(r) is known, Phkl (ro) for any direction re making an angle a0 with the direction of the maximum of PH&r) can be calculated. Regardless of the original shape of P HKL(r), the function can be axially symmetrized by rapid sample spinning around one axis. The function PHa(r) can be as follows: PHKL (a) = A exp (G (I co@ a)) (2) where a is the angle between the spinning axis (preferred orientation axis) and r, G and n are free parameters, and A is the normalisation constant. For more details and the case of inclined texture see [3]. The case of symmetry-equivalent planes making different angles $~,h with treated by partial multiplicity factors 141. HKL can be Pattern decomposition using preferred orientation The diffracted integrated intensity of the reflection hkl in a. powder pattern is given by