Determining oxygen octahedral rotations in strained perovskite films using x-ray diffraction

While strain is known to alter the octahedral distortions and rotations in perovskite films, the details of how the local atomic structure accommodates strain are poorly understood due to the difficulty of measuring oxygen positions in thin films. Using epitaxial LaNiO$_{3}$ as a model system, we present a general strategy for determining the atomic structure of strained perovskites via x-ray diffraction. The oxygen positions have been determined by comparing the intensities of half-order Bragg peaks, arising from the two unit cell periodicity of the octahedral rotations, with calculated structure factors. The bond angles and lengths have been determined for LaNiO$_{3}$ films grown on SrTiO$_{3}$ (tensile strain) and LaAlO$_{3}$ (compressive strain), respectively, and are found to depend strongly on the strain state. These diffraction-based results are in excellent agreement with \textit{ab initio} density functional calculations.