LaAlO$_{3}$ (LAO) are 173 ˚ A and 95 ˚ A thick, respectively, and coherently strained with c -axis parameters of 3.807 and 3.895 ˚ A as confirmed through reciprocal space maps and (00 L ) scans. All x-ray diffraction measurements were performed at room temperature. In addition to exploring how strain modifies the octahedral distortions, growing on the two substrates, STO and LAO, enables us to investigate how the substrates’ structural properties interact with the octahedral rotations of the LNO films through heteroepitaxy. For example, STO is cubic at room temperature and lacks octahedral rotations, whereas LAO is rhombohedral with the a $^{−}$a$^{−}$a− rotation pattern. Thus, by measuring the structural distortions in the LNO/STO films, we can determine whether octahedral rotations are suppressed when growing on a cubic substrate. Similar analysis of the distortions in the LNO films on LAO enables us to determine if the rotational pattern present in the substrate couples to that found in the film. The rotation pattern of the LNO films is identified by observing the presence and absence of specific half-order Bragg peaks. We find half-order peaks in the films grown on both substrates (Fig. 2a,b), which confirms that heteroepitaxial growth on a cubic substrate does not suppress octahedral rotations by forcing atomic registry between the film and the substrate; the epitaxial relationship is not simply “cube-on-cube.” Both films exhibit half-order peaks when the following conditions are met: 1) h , k , and l are equal to n /2, where n is an odd integer and 2) h = k = l , k = l = h , and h = l = k . Peaks are not observed where h = k = l , such as ( 1 / 2 1 / 2 1 / 2 ), or where one of the indices is equal to an integer, such as ( 1 / 2 1 3 / 2 ). This reciprocal lattice indicates the presence of an a $^{−}$a$^{−}$c− tilt pattern within both films [17], with α = β due to the biaxial strain state of the films ( a = b ). The intensities of the half-order peaks can be compared to calculated peak intensities in order to quantify the octahedral rotation angles. The calculated peak intensities are determined from Eq. (1): I = I$_{0}$ 1 sin( η ) 1 sin(2Θ) ( 4 ∑ j =1 D$_{j}$ | F$_{hkl}$ | $^{2}$) , (1) where I$_{0}$ is the incident photon flux, 1/sin( η ) is a correction for the beam footprint, 1/sin(2Θ) is the Lorentz polarization correction, F$_{hkl}$ is the structure factor for the oxygen atoms, and D$_{j}$ is the relative volume fraction of structural domains discussed below. The incident photon angle is η , while the scattering angle is Θ. The structure factor for each Bragg peak 4