Domain epitaxial growth of ferroelectric films of barium strontium titanate on sapphire

A model of the epitaxial growth of crystalline multicomponent films on single-crystal substrates with a domain correspondence is presented using a solid solution of barium strontium titanate on sapphire substrates ($r$ cut). The domain epitaxial growth suggests the matching of the lattice planes of the film and the substrate having similar structures by comparison of domain multiple of an integral number of the interplanar spacings. Variation of the component composition of the solid solution enables changes in the domain size in the range sufficient for epitaxial growth. This method can be used to project the epitaxial growth of films of various solid solutions on single-crystal substrates.