Diffractometric crystal centering

A general formalism for centering a single-crystal on a four-circle diffractometer, based on the setting angles of reflections, is presented. The minimum information for the determination of crystal displacement are the diffractometer setting angles of two reciprocal vectors. The method is independent of the crystallographic system and does not require prior information about the crystal lattice. The size of the radiation source, beam divergence and homogeneity are shown to be significant factors for calculating the crystal displacement from the positions of the reflections. The method is primarily designed for samples enclosed in high-pressure diamond-anvil cells and other environments obscuring visual control of the sample position; however, high accuracy of the method in most cases allows the optical centering of the crystals to be improved, particularly for irregularly shaped samples. A procedure for retrieving true lattice dimensions, by accounting for the effect of the crystal displacement from the diffractometer center, is also presented.