The oxygen octahedral rotation (OOR) in perovskite oxides is closely related to its physical properties. The recent development of synchrotron radiation three-dimensional diffraction provides opportunities for efficient characterization of the superlattice half-order peaks corresponding to OOR, but quantitative analysis is still difficult.

This study aims to provide guidance for the measurement of OOR half-order peaks and lay a foundation for their quantitative analysis through a theoretical simulation of the half-order peak intensity.

Firstly, a universal calculating formula for coordinates of all the oxygen ions in an OOR super cell was provided. Then, starting from the calculation formula of structure factor of a lattice unit cell, a quantitative formula for calculating the half-order peak intensity of lattice with OOR was deduced according to the basic theory of crystal diffraction kinematics. Subsequently, the half-order peak intensity distribution patterns corresponding to the 27 rotation modes were simulated and exhibited by programming, and the appearance rules were summarized. Finally, two typical examples were used to verify the consistency between the simulation results and the measured results.

Two typical examples show that the simulation results are in good agreement with the measured results. Based on these results, the OOR half-order peak pattern can be predicted beforehand and their origins may be verified after hand for experimental measurement of half-order peak. This work may promote the application of synchrotron radiation diffraction in the characterization of perovskite OOR.