An experimental “primary extinction” correction for electron diffraction intensities: improved phase determination in organic crystal structure analysis

Abstract

An experimental method is described for the ab initio correction of observed electron diffraction intensities for n-beam dynamical scattering. The best possible data | F HV hk |, least perturbed by dynamical effects, are collected at high voltage and are to be corrected by this method. Another data set | F LV hk | from the same material is collected at an appropriate low voltage, and should correspond closely to the convolution of kinematical structure factors | F hk ∗ F hk |. Using the phase grating approximation, the correction to kinematical structure factors | F kin hk | will then be expressed by | F kin hk |⋍(| F HV hk | 2− m| F LV hk | 2) 1 2 , where m is a refineable scale factor. The efficacy of this correction is demonstrated w ith electron diffraction intensities collected from monolayer crystals of n-hexatriacontane at 800 and 20 kV. Normalized structure factors obtained from the corrected intensities are much more useful for direct phase determination than the dynamical intensity data analyzed previously. Further, the data set collected at 20 kV, i.e. | F 20kV hk |, can be used to test the correctness of the phase set since this approximation of | F hk ∗ F hk |, is very similar to the Sayre equation often used for phase refinement in X- ray crystallography. Due to the constraints of the phase grating approximation, this methodology will be most useful for light atom structures where most of the scattered intensity is found within a suitable lower-angle region of reciprocal space.