a d b c Figure 2: Half-order peaks of LNO films grown on STO and LAO. a, In LNO on STO, the h = k diffraction peaks are more intense than those with h = k , as α > γ . b, The opposite intensity pattern is observed for the LNO on LAO, as α < γ . Intense half-order peaks from octahedral rotations within the LAO substrate are also present; this intensity from the substrate is less than 10% of the film peak intensity. c, Comparison of the measured and calculated peak intensities for LNO on STO for α = β = 7 . 1 ◦ and γ = 0 . 3 $^{◦}$. d, Comparison of the peak intensities for LNO on LAO for α = β = 1 . 7 ◦ and γ = 7 . 9 $^{◦}$, with a domain ratio of 1:2.15:0:0. is obtained from, where the position of the n th oxygen atom within the unit cell is given by ( u , v , w ), and f$_{O}$ 2 − is the O 2 − form factor [27]. The La and Ni atoms are assumed to reside on the ideal corner and body-centered positions, respectively, and thus we do not consider a rhombohedral distortion of the La positions. Given this assumption, only the oxygen atoms contribute to the half-order peak intensities. We account for the octahedral rotations by doubling the F$_{hkl}$ = f$_{O}$ 2 − 24 ∑ n =1 exp[2 πi ( hu$_{n}$ + kv$_{n}$ + lw$_{n}$ )] , (2) 5