How precise are measurements of unit-cell ­dimensions from single crystals?

The results of single-site and many-site measurements of cell dimensions from single crystals are compared for Bond and four-circle diffractometers using samples of corundum (essentially pure rhombohedral α-Al₂O₃, aluminum oxide) of high diffraction quality, where the effects of small changes in temperature and composition (Cr₂O₃, chromium oxide, in solid solution) can be taken into account. Similar comparisons are made for four-circle diffractometer measurements on ruby (α-Al₂O₃, with 0.46 wt % Cr in solid solution). The precisions are some parts in 10⁵. There is partial support for the Taylor–Kennard [Acta Cryst. (1986), B42, 112–120] dictum that standard uncertainties (s.u.s) of cell parameters from routine four-circle diffractometer measurements are less than those for many-site measurements by factors of 5 for cell lengths and 2.5 for cell angles. For organic crystals, independent repetitions of adequate quality for comparison and analysis of routine four-circle diffractometer measurements are available only for α-oxalic acid dihydrate and anthracene. The experimental standard uncertainties given for these two crystals agree reasonably well with the sample s.u.s at room temperature, but appreciably less well at ∼100 K, again giving partial support to the Taylor–Kennard dictum. The relation between specimen characteristics and attainable precision is emphasized; the precisions for routine measurements on good quality organic crystals are some parts in 10⁴. Area-detector measurements of cell dimensions have also been appraised; currently published s.u.s from such measurements appear to be highly unreliable, and this is supported by a recent analysis of the operation of such diffractometers [Paciorek et al. (1999). Acta Cryst. A55, 543–557]. Formulation of a standard protocol for such measurements is badly needed. The dangers inherent in high degrees of replication are illustrated by recounting Kapteyn's Parable of the Chinese Emperor. Attention is drawn to the fact that there has been little improvement in claimed precisions over the past 40–60 years.