Ordered structure of FeGe2 formed during solid-phase epitaxy

${\mathrm{Fe}}_{3}\mathrm{Si}/\mathrm{Ge}(\mathrm{Fe},\mathrm{Si})/{\mathrm{Fe}}_{3}\mathrm{Si}$ thin-film stacks were grown by a combination of molecular beam epitaxy and solid-phase epitaxy (Ge on ${\mathrm{Fe}}_{3}\mathrm{Si}$). The stacks were analyzed using electron microscopy, electron diffraction, and synchrotron x-ray diffraction. The Ge(Fe,Si) films crystallize in the well-oriented, layered tetragonal structure ${\mathrm{FeGe}}_{2}$ with space group $P4mm$. This kind of structure does not exist as a bulk material and is stabilized by the solid-phase epitaxy of Ge on ${\mathrm{Fe}}_{3}\mathrm{Si}$. We interpret this as an ordering phenomenon induced by minimization of the elastic energy of the epitaxial film.