Determination of the point and space groups for hydroxyapatite by computer simulation of CBED electron diffraction patterns

Abstract

The structure of natural hydroxyapatite $n$HAP (i.e. the hydroxyapatite found in teeth and bones) has not been completely characterized experimentally until now. This involves the study of the structural characteristics of synthetic hydroxyapatite sHAP (i.e. one whose stoichiometric formula is Ca$_{10}$ (PO$_{4})_{6}$ (OH)$_{2})$ using many techniques, in particular electron diffraction computer simulation. Thus, any variation presented in its structure will be easily detected. In this work we comment on the crystallographic elements presented in simulated convergent beam electron diffraction (CBED) patterns for $s$HAP, in its versions of Laue Zones of Zero Order (ZOLZ), First Order (FOLZ), Second Order (SOLZ) and Higher Order (HOLZ), and the deduction of its space group P6$_{3}$/m. These results are compared with those reported experimentally.