  Most perovskite oxides belong to the Pbnm space group, composed by an
anisotropic unit cell, A-site antipolar displacements and oxygen octahedral
tilts. Mapping the orientation of the orthorhombic unit cell in epitaxial
heterostructures that consist of at least one Pbnm compound is often required
to understand and control the different degrees of coupling established at
their coherent interfaces and, therefore, their resulting physical properties.
However, retrieving this information from the strain maps generated with
high-resolution scanning transmission electron microscopy can be challenging,
because the three pseudocubic lattice parameters are very similar in these
systems. Here, we present a novel methodology for mapping the crystallographic
orientation in Pbnm systems. It makes use of the geometrical phase analysis
algorithm, as applied to aberration-corrected scanning transition electron
microscopy images, but in an unconventional way. The method is fast and robust,
giving real-space maps of the lattice orientations in Pbnm systems, from both
cross-sectional and plan-view geometries and across large fields of view. As an
example, we apply our methodology to rare-earth nickelate heterostructures, in
order to investigate how the crystallographic orientation of these films
depends on various structural constraints that are imposed by the underlying
single crystal substrates. We observe that the resulting domain distributions
and associated defect landscapes mainly depend on a competition between the
epitaxial compressive/tensile and shear strains, together with the matching of
atomic displacements at the substrate/film interface. The results point towards
strategies for controlling these characteristics by appropriate substrate
choice.
