Collection and analysis of powder diffraction data with near-constant counting statistics

The concept of a variable-counting-time (VCT) strategy for use in Rietveld analysis of X-ray powder diffraction data was introduced by Madsen & Hill [Adv. X-ray Anal. (1992), 35, 39-47]. This strategy is based on a function that increases the counting time used at each step in the scan in a manner that is inversely proportional to the decline in reflection intensity that inevitably results from the combined effects of Lp factor, scattering factor and thermal vibration. The present work extends the VCT function to include the effects of reflection multiplicity, cylindrical-sample (capillary) absorption and monochromator polarization. The new algorithm has been incorporated into a PC computer program and applied to the collection of data from samples of LaB₆, tourmaline, forsterite and boehmite. Subsequent analysis of the data using the Rietveld method has shown that VCT data can produce more accurate atomic coordinates and site occupancies, lower residual 'noise' in difference Fourier maps and more stable refinement of `light' atoms.