On the refinement on profile, background and net intensities

The raw data obtained with a single-crystal diffractometer are typically integrated profile and background intensities. All linear combinations of these data items, and in particular net intensities and total backgrounds, are equivalent observations. However, net intensities may be negative, in apparent contradiction with basic physics. Backgrounds are generally discarded from the list of observations once they have been subtracted from the profile intensities. In a crystal structure refinement on all observations, structural parameters including scale, extinction and possibly others, as well as individual background intensities, are refined on the observed profile intensities and on the observed background intensities. It is shown that, in such a refinement, the structural parameters are determined exclusively by the net intensities as in traditional least squares, whereas calculated backgrounds depend on the difference between observed and calculated net intensities. Negative net intensities are therefore not in contradiction with physics or with the structural model, and should be retained unaltered in the data set.