  We report the relationship between epitaxial strain and the crystallographic
orientation of the in-phase rotation axis and A-site displacements in Pbnm-type
perovskite films. Synchrotron diffraction measurements of EuFeO3 films under
strain states ranging from 2% compressive to 0.9% tensile on cubic or
rhombohedral substrates exhibit a combination of a-a+c- and a+a-c- rotational
patterns. We compare the EuFeO3 behavior with previously reported experimental
and theoretical work on strained Pbnm-type films on non-orthorhombic
substrates, as well as additional measurements from LaGaO3, LaFeO3, and
Eu0.7Sr0.3MnO3 films on SrTiO3. Compiling the results from various material
systems reveals a general strain dependence in which compressive strain
strongly favors a-a+c- and a+a-c- rotation patterns and tensile strain weakly
favors a-a-c+ structures. In contrast, EuFeO3 films grown on Pbnm-type GdScO3
under 2.3% tensile strain take on a uniform a-a+c- rotation pattern imprinted
from the substrate, despite strain energy considerations that favor the a-a-c+
pattern. These results point to the use of substrate imprinting as a more
robust route than strain for tuning the crystallographic orientations of the
octahedral rotations and A-site displacements needed to realize
rotation-induced hybrid improper ferroelectricity in oxide heterostructures.
