Prediction of apatite lattice constants from their constituent elemental radii and artificial intelligence methods

Lattice constants (LCs) of all possible 96 apatite compounds, A5(BO4)3C, constituted by A=Ba2+, Ca2+, Cd2+, Pb2+, Sr2+, Mn2+; B=As5+, Cr5+, P5+, V5+; and C=F1−, Cl1−, Br1−, OH1−, are predicted from their elemental ionic radii, using pattern recognition (PR) and artificial neural networks (ANN) techniques. In particular, by a PR study it is demonstrated that ionic radii predominantly govern the LCs of apatites. Furthermore, by using ANN techniques, prediction models of LCs a and c are developed, which reproduce well the measured LCs (R2=0.98). All the literature reported on 30 pure and 22 mixed apatite compounds are collected and used in the present work. LCs of all possible 66 new apatites (assuming they exist) are estimated by the developed ANN models. These proposed new apatites may be of interest to biomedical research especially in the design of new apatite biomaterials for bone remodeling. Similarly these techniques may also be applied in the study of interface growth behaviors involving other biomaterials.