The effect of profile-step counting time on the determination of crystal structure parameters by X-ray Rietveld analysis

Crystal structure parameters have been obtained for α-Al₂O₃, β-PbO₂ and (Mg, Fe)₂SiO₄ by Rietveld analysis of Cu Kα X-ray powder diffraction data collected on a conventional diffractometer using counting times ranging from 0.01 to 5 s per step. For all but the 0.01 s data collected on (Mg, Fe)₂SiO₄ the structural parameters obtained at different counting times are statistically identical at the 3 σ level, and the spread in the values is essentially the same as that obtained by sample repacking at a fixed counting time of 1 s per step. The parameter e.s.d.'s and conventional agreement indices R_wp and R_B decrease to values limited by residual model errors as the counting time increases, but the goodness-of-fit parameter becomes unacceptably larger than its ideal value of unity. When more than a few thousand counts are accumulated for the maximum step intensity in the diffraction profile a weighting scheme based solely on counting variance is inappropriate and the parameter e.s.d.'s are no longer a reflection of their accuracy.