Anisotropy in the variation of serially-measured integrated intensities

The variation (often decline) in intensity standards measured during a typical X-ray diffraction structure determination is commonly corrected by means of an isotropic polynomial expression of the form I_t = I₀(1 - Σ_n A_ntⁿ), where t is the exposure time in hours, I₀ is the integrated intensity at zero exposure and 1 ≤ n ≤ 7. A linear decline corresponding to n = 1 is reported in many studies. In the simplest (linear) anisotropic case, the variation may be represented by I_t = I₀[1 - t(α₁₁h² + α₂₂k² + α₃₃l² + 2α₁₂hk + 2α₁₃hl + 2α₂₃kl)/(h² + k² + l²)] where the α_ij are coefficients of a radiation-damage-effect ellipsoid. Higher-order and exponential time dependences have also been investigated. The results of applying the anisotropy relation both to an organometallic and an inorganic structure, as evaluated by the method of least squares, are presented. For each case the linear anisotropic correction leads to significant reductions in R_int and wR_int, with additional improvement resulting from inclusion of quadratic decline correction terms. The smallest number of experimental data required to evaluate the radiation damage anisotropy consists of two sets of symmetry-equivalent reflections.