The basic principles and concepts underlying the present understandings of heteroepitaxy are critically reviewed, based on the observations of regular intergrowths of mineral crystals, which include twinning, co-axial intergrowth, oriented overgrowth, exsolution, topotaxy, etc. The concepts of twin lattice by Friedel. CSL by Kronberg and Wilson, misfit ratio by Royer, PBC misfit by Hartman, misfit dislocation, epitaxial temperature, Frank-van der Merve mechanism, Volmer-Weber mechanism, and Stranski-Krastanov mechanism are explained, leading to a conclusion that the interface energy and driving force are essential in forming regular intergrowths of not only crystals of the same kind but also different kinds. Chernov's summary is also introduced. As a future direction of heteroepitaxy researchs, understanding of biocrystallization in the light of growth mehanism involved in epitaxy is suggested.
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