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Published online by Cambridge University Press: 25 February 2011
An algorithm has been discovered that greatly simplifies the exhaustive search for all orientations of all known crystals that have a lattice match with crystal film to be epitaxially deposited. It is based on the observations that (1) a two-dimensional lattice match of necessity entails an integer-ratio match between the areas of the unit parallelograms of the substrate and deposit planes and (2) that the unit area A (hkl) is equal to the unit cell volume divided by d(hkl). Using this algorithm, we are currently verifying the area-match tolerances for known cases of epitaxy and developing database-generating and searchprogram software.