The evaluation of transmission factors and their first derivatives with respect to crystal shape parameters

Methods, implemented into a computer program (LSABS), are described which calculate transmission factors and their first derivatives with respect to the positions of the faces of a convex polyhedral monocrystal. Both Gaussian and analytical integration procedures are considered in detail. LSABS has been implemented as a module of the Xtal system of programs. It functions independently of the instrument used to collect the intensity data. Test results obtained with this program are compared with standard literature values. Correlation coefficients of an absorption-corrected intensity data set of calcite, CaCO₃ are reported. The need for transmission factor derivatives in the refinement of crystal shape and in the elimination of correlated absorption-corrected structure amplitudes is explained.