ABSTRACT
The strong interaction at an interface between a substrate and thin film leads to epitaxy and provides a means of inducing structural changes in the epitaxial film. These induced material phases often exhibit technologically relevant electronic, magnetic, and functional properties. The 2×1 surface of a Ge(001) substrate applies a unique type of epitaxial constraint on thin films of the perovskite oxide BaTiO_{3} where a change in bonding and symmetry at the interface leads to a non-bulk-like crystal structure of the BaTiO_{3}. While the complex crystal structure is predicted using first-principles theory, it is further shown that the details of the structure are a consequence of hidden phases found in the bulk elastic response of the BaTiO_{3} induced by the symmetry of forces exerted by the germanium substrate.