Epitaxial perovskite oxide interfaces with different symmetry of the epitaxial layers have attracted considerable attention due to the emergence of novel behaviors and phenomena. In this paper, we show by aberration corrected transmission electron microscopy that orthorhombic $text{LaInO}_text{3}$ films grow in form of three different types of domains on the cubic $text{BaSnO}_text{3}$ pseudosubstrate. Quantitative evaluation of our TEM data shows that $c_{pc}$-oriented and $a_{pc}/b_{pc}$-oriented domains are present with similar probability. While continuum elasticity theory suggests that $c_{pc}$-oriented domains should exhibit a significantly higher strain energy density than $a_{pc}/b_{pc}$-oriented domains, density functional calculations confirm that $c_{pc}$- and $a_{pc}$-oriented domains on $text{BaSnO}_text{3}$ have similar energies.
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