Structural refinement of Pbnm-type perovskite films from analysis of half-order diffraction peaks

Engineering structural modifications of epitaxial perovskite thin films is an effective route to induce new functionalities or enhance existing properties due to the close relation of the electronic ground state to the local bonding environment. As such, there is a necessity to systematically refine and precisely quantify these structural displacements, particularly those of the oxygen octahedra, which is a challenge due to the weak scattering factor of oxygen and the small diffraction volume of thin films. In this paper, we present an optimized algorithm to refine the octahedral rotation angles using specific unit-cell-doubling half-order diffraction peaks for the a^-a^-c⁺ Pbnm structure. The oxygen and A-site positions can be obtained by minimizing the squared-error between calculated and experimentally determined peak intensities using the (1/2 1/2 3/2) and (1/2 1/2 5/2) reflections to determine the rotation angle α about in-plane axes and the (1/2 5/2 1), (1/2 3/2 1), and (1/2 3/2 2) reflections to determine the rotation angle γ about the out-of-plane axis, whereas the convoluting A-site displacements associated with the octahedral rotation pattern can be determined using (1 1 1/2) and (1/2 1/2 1/2) reflections to independently determine A-site positions. The validity of the approach is confirmed by applying the refinement procedure to determine the A-site and oxygen displacements in a NdGaO₃ single crystal. Finally, the ability to refine both the oxygen and A-site displacements relative to the undistorted perovskite structure enables a deeper understanding of how structural modifications alter functionality properties in epitaxial films exhibiting this commonly occurring crystal structure.