Model Calculations of the Accuracy of Structure Factor Determination From Textured Powder Samples

Abstract

Crystal structure analysis is based on absolute values of structure factors |Fhkl|. These values can be measured by powder diffraction. In random powder diffraction many superpositions occur in the diffraction diagram over the Bragg angle θ. If non-random (textured) samples are used and intensity measurements are done in the three-dimensional reciprocal space, i.e. over θ and the sample rotation angles αβ then these superpositions can be deconvoluted to a good deal. In order to perform this deconvolution a two-step procedure was developed and was implemented in a computer code. In the first step the texture is determined from a low number of reflections having no or only two-fold overlap. In the second step the deconvolution is done for all reflections. This includes the deconvolution of “systematically” overlapped reflections, e.g. those with the same h2+k2+l2 in cubic symmetry.Model calculations were performed in order to test the reliability and resulting accuracy of the deconvolution procedure depending on various experimental as well as modelling parameters. It is concluded that good resolution for superposed |Fhkl| can be reached up to reasonably high lattice parameters.The decisive accuracy limiting factor is texture determination in the first step of the procedure. It is concluded that it is necessary to employ texture analysis methods with higher angular resolving power and higher statistical accuracy than in conventional routine texture analysis. This is, however, possible with the existing modern texture diffractometers.