Prospects for kinematical least-squares refinement in polymer electron crystallography.

Abstract

Least-squares refinement is unusual in the context of electron crystallography because of the sparsity of the measured intensity data set and the problems of systematic errors due to multiple dynamical scattering. With 120 unique hkl electron diffraction intensities measured from polymorphic form III of isotactic poly(1-butene), conditions for improving an existing structural model derived from initial direct structure analysis have been evaluated. The polymer crystallizes in space group P2(1)2(1)2(1) with a = 12.38, b = 8.88, c = 7.56 A and there are 8 unique atoms in the asymmetric unit. Starting with atomic positions resulting from Fourier refinement, four cycles of least-squares refinement, where the positional shifts of atomic positions were constrained, produced better bonding parameters than found before while lowering the conventional crystallographic residual, based on absolute value(F), from an overall value of R = 0.26 to R = 0.185 for the 58 most intense reflections where magnitude of absolute value(Fh(obs)) > or = 4sigma (Fh(obs)) or 0.216 for the complete data set of 120 reflections. The weighted residuals based on magnitude of absolute value(F)2 fell from 0.50 to 0.41 for the complete data set. This refinement was not improved however when attempts were made to fill in very weak intensities by default values. Also, effects of multiple-scattering perturbations were found in the irregularity of the final isotropic thermal parameters.