Investigation of Epitaxy Relationships Between Ca₅(PO₄)₃OH and Other Calcium Ortho-Phosphates

A procedure for generating and quantitatively comparing possible cases of epitaxy and twinning has been devised and applied to the study of epitaxy between Ca₅(PO₄)₃OH and other calcium orthophosphates. For any two given lattices, pairs of nets which match dimensionally within prescribed limits are found and sorted in order of increasing mismatch. The crystal structural parameters are used to generate and match atomic patterns corresponding to each pair of nets. Pattern matching is done by comparing magnitudes of vectors describing the immediate environment of each atom in turn, and does not require orienting the two patterns relative to one another. Atomic charges related by each vector are also considered. Use of the vector sets introduces the limitation that twinning involving reorientation in a contact plane cannot be distinguished from no reorientation (identity match). An additional method which uses these results to match complete patterns is suggested. The procedure is general in nature and has been applied here to the study of possible epitaxies between Ca₅(PO₄)₃OH and Ca₈H₂(PO₄)₆·5H₂O, Ca₄O(PO₄)₂, CaHPO₄, CaHPO₄·2H₂O, Ca(H₂PO₄)₂·H₂O, β-Ca₃(PO₄)₂ and Ca₅(PO₄)₂SiO₄. Of these cases, only the epitaxies Ca₅(PO₄)₃OH/Ca₈H₂(PO4)₆·5H₂O and Ca₅(PO₄)₃OH/Ca₄O(PO₄)₂ appear to have sufficient structural similarity to occur in practice.