Abstract

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.

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中文翻译：

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羟基磷灰石纳米晶体尺寸的最新预测模型：混合密度泛函理论和人工神经网络

抽象的

这项研究为使用密度泛函理论（DFT）和神经网络（NN）的溶胶-凝胶技术预测制备的羟基磷灰石（HA）的晶粒尺寸提出了一种新方法。在这方面，将各种实际变量，即老化时间，煅烧温度，煅烧时间和使用三种磷光体前体的干燥温度用作输入，并将制备的HA的微晶尺寸用作NN模型的输出。首先，除磷光体前驱体类型外，所有实际变量均直接用作NN模型的输入。为了输入磷光体的前体类型，使用了通过DFT计算的磷光体前体与硝酸钙的相互作用轨道的能级之间的差。这种方法提供了将磷光体前体之间的离散空间转换为连续空间的可能性，₂ HPO ₄作为案例研究。为了验证NN模型的结果，使用X射线衍射（XRD）和场发射扫描电子显微镜（FESEM）对典型的超范围磷光体前驱体Na ₂ HPO ₄表征了制备的HA 。经过训练的神经网络模型的总体均方误差（MSE）为0.2871，线性回归因子为0.9993，证实了该方法有效预测HA晶粒尺寸的预测能力。

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