Comparison of X-ray and neutron diffraction structural results: a study in methods of error analysis

A number of crystal structures have been precisely analyzed by both X-ray and neutron diffraction. Comparison between the results can lead to some understanding of the type and magnitude of error present in one or both methods. We discuss here the nature of systematic error in crystallographic experiments and in crystal structure refinement models. Statistical methods are presented for testing the significance of the difference between the parameters derived in two crystallographic experiments. These methods are applied to existing neutron and X-ray diffraction data on oxalic acid dihydrate, hydroxyapatite, s-triazine, potassium hydrogen diaspirinate and methylglyoxal bisguanylhydrazone. These tests show that there are strong systematic differences in thermal parameters for heavy atoms and in all parameters for hydrogen atoms. Differences in positional parameters for heavy atoms are marginal. The pattern of results strongly suggests that the differences between neutron and X-ray experiments have some physical bases rather than being due entirely to systematic error in one or both experiments. The results may also be interpreted as indicating that both position parameters and root-mean-square amplitudes of vibration may with care be determined to a precision of 0.001 Å in structures with a moderate number of atoms in the asymmetric unit.