a bulk perovskite a b g c b a b c a b c d e g perovskite  film substrate b a compressive strain tensile strain 2 d 2 d Figure 1: The available structural distortions afforded in perovskite oxides through heteroepi- taxial thin film growth. a, Rotations of the oxygen octahedra are pervasive in bulk perovskites and commonly decomposed into components α, β and γ about each of the Cartesian axes. In coherently strained perovskite films, the B O$_{6}$ octahedra can distort through a contraction ( b ) or elongation ( c ) of the in-plane B -O bond lengths ( d ) under compressive or tensile strain, respectively. Simultaneously, the octahedra can accommodate the substrate-induced in-plane lattice parameters by rotating perpendicular to the substrate ( d ), and/or rotating along the axes parallel to the substrate plane ( e ). diffraction and the calculation of structure factors, makes this a promising strategy for determining the full atomic structure of a broad range of strained perovskite films. We chose to study LaNiO$_{3}$ (LNO) as an example because it exhibits octahedral rotations along each Cartesian axis. Bulk LNO has an a $^{−}$a$^{−}$a− rotation pattern ( α = β = γ = 5 . 2 $^{◦}$) with a R ¯ 3 c symmetry and a pseudocubic lattice parameter of 3.838 ˚ A [22]. This results in uniform Ni-O-Ni bond angles of 165.2 ◦ and Ni-O bond lengths of 1.935 ˚ A. The isotropic nature of bulk LNO is ideally suited to exploring how strain alters bond lengths and angles in an anisotropic manner. Additionally, LNO has garnered interest due to its novel properties such as electric-field control of conductivity [23], correlated Fermi liquid behavior [24], and recent predictions of superconductivity [25]. Our epitaxial LNO films were deposited on SrTiO$_{3}$ ( a = 3.905 ˚ A) and LaAlO$_{3}$ ( a = 3.795 ˚ A) substrates by molecular beam epitaxy [26] in order to probe how both tensile (1.7 % on STO) and compressive (-1.1% on LAO) strain are accommodated by changes in the bond angles and lengths in the perovskite structure. The films grown on SrTiO$_{3}$ (STO) and 3