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

The results of single-site and many-site measurements of cell dimensions fr om single crystals are compared for Bond and four-circle diffractometers us ing samples of corundum (essentially pure rhombohedral alpha-Al2O3, aluminu m 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 diffra ctometer measurements on ruby (alpha-Al2O3, with 0.46 wt % Cr in solid solu tion). The precisions are some parts in 10(5). 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 diffract ometer measurements are less than those for many-site measurements by facto rs of 5 for cell lengths and 2.5 for cell angles. For organic crystals, ind ependent repetitions of adequate quality for comparison and analysis of rou tine four-circle diffractometer measurements are available only for alpha-o xalic acid dihydrate and anthracene. The experimental standard uncertaintie s given for these two crystals agree reasonably well with the sample s.u.s at room temperature, but appreciably less well at similar to 100 K, again g iving partial support to the Taylor-Kennard dictum. The relation between sp ecimen characteristics and attainable precision is emphasized; the precisio ns for routine measurements on good quality organic crystals are some parts in 10(4). Area-detector measurements of cell dimensions have also been app raised; currently published s.u.s from such measurements appear to be highl y unreliable, and this is supported by a recent analysis of the operation o f such diffractometers [Paciorek et al. (1999). Acta Cryst. A55, 543-557]. Formulation of a standard protocol for such measurements is badly needed. T he dangers inherent in high degrees of replication are illustrated by recou nting Kapteyn's Parable of the Chinese Emperor. Attention is drawn to the f act that there has been little improvement in claimed precisions over the p ast 40-60 years.