Determination of low-strain interfaces via geometric matching

We present a general method for combining two crystals into an interface. The method finds all possible interfaces between the crystals with small coincidence cells and identifies the strain and area of the corresponding two-dimensional cells of the two crystal surfaces. We apply the method to the two semiconductor alloys ${\mathrm{InAs}}_{1\ensuremath{-}x}{\mathrm{Sb}}_{x}$ and ${\mathrm{Ga}}_{x}{\mathrm{In}}_{1\ensuremath{-}x}\mathrm{As}$ combined with a selection of pure metals or with NbTiN to create semiconductor/superconductor interfaces. The lattice constant of the alloy can be tuned by composition and we can extract the alloy lattice parameters corresponding to zero strain in both the metal and the alloy. The results can be used to suggest new epitaxially matched interfaces between two materials.