State-of-the-art predictive modeling of hydroxyapatite nanocrystallite size: a hybrid density functional theory and artificial neural networks

This study proposes a novel approach for the prediction of crystallite size of prepared hydroxyapatite (HA) by sol–gel technique using density functional theory (DFT) and neural networks (NN). In this regard, various practical variables, viz., aging time, calcination temperature, calcination time, and drying temperature with three phosphor precursors were used as input, and the crystallite size of prepared HA was used as output for NN model. Firstly, exception of phosphor precursor type, all practical variables were directly used as input to NN model. To input the precursor type of phosphor, the difference between energy levels of interacting orbitals of phosphor precursor and calcium nitrate that were calculated by DFT was used. Such approach provides the possibility of conversion of discrete space between phosphor precursors to continuous space, which enables the NN model to predict the crystallite size of HA even for other types of precursors outside the range of investigated by experimental collected data, e.g., Na2HPO4 as case study. To validate the results of NN model, X-ray diffraction (XRD) and field emission scanning electron microscope (FESEM) were used for characterization of prepared HA by typically out range phosphor precursor, Na2HPO4. The trained NN model showed an overall mean square error (MSE) of 0.2871 with a linear regression factor of 0.9993, and confirmed the prediction ability of the proposed method for prediction of HA crystallite size effectively.