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Prediction of hexagonal lattice parameters of stoichiometric and non-stoichiometric apatites by artificial neural networks

Koçkan, Ümit
Apatite group of minerals have been widely used in applications like detoxification of wastes, disposal of nuclear wastes and energy applications in addition to biomedical applications like bone repair, substitution, and coatings for metal implants due to its resemblance to the mineral part of the bone and teeth. X-ray diffraction patterns of bone are similar to mineral apatites such as hydroxyapatite and fluorapatite. Formation and physicochemical properties of apatites can be understood better by computer modeling. For this reason, lattice parameters of possible apatite compounds (A10(BO4)6C2), constituted by A: Na+, Ca2+, Ba2+, Cd2+, Pb2+, Sr2+, Mn2+, Zn2+, Eu2+, Nd3+, La3+, Y3+; B: As+5, Cr+5, P5+, V5+, Si+4; and C: F-, Cl-, OH-, Br-1 were predicted from their elemental ionic radii by artificial neural networks techniques. Using artificial neural network techniques, prediction models of lattice parameters a, c and hexagonal lattice volumes were developed. Various learning methods, neuron numbers and activation functions were used to predict lattice parameters of apatites. Best results were obtained with Bayesian regularization method with four neurons in the hidden layer with ‘tansig’ activation function and one neuron in the output layer with ‘purelin’ function. Accuracy of prediction was higher than 98% for the training dataset and average errors for outputs were less than 1% for dataset with multiple substitutions and different ionic charges at each site. Non-stoichiometric apatites were predicted with decreased accuracy. Formulas were derived by using ionic radii of apatites for lattice parameters a and c.