Correction of zero shift in powder diffraction patterns using the reflection-pair method

Zero shifts of 2θ usually represent one of the most serious systematic errors in powder patterns obtained by diffractometers, and they cannot be readily diagnosed and corrected. Frequently, large zero shifts hinder indexing of the patterns. Programs exist to refine the lattice constants and calculate the zero shift, but they need the indexing results. We have derived an equation, based on the reflection-pair method, to calculate and correct the zero shift before indexing. The equation has been tested on many experimental data and the effectiveness of the method has been confirmed. The method is very useful in ab initio crystal structure determination using powder data.