Electronic and atomic structures of vacancies and protons in hydroxyapatite (HAp) are analyzed by using first-principles band structure calculations. From total energies of supercells for monoclinic HAp, defect formation energies and equilibrium concentrations are evaluated, assuming chemical equilibrium between HAp and aqueous solution saturated with respect to HAp. It is found that interstitial and Ca-substitutional protons form H2O groups or acid phosphates of HPO and are stabilized by making hydrogen bonding with adjacent PO groups. Moreover, defect association considerably decreases the defect formation energies, and, in particular, interstitial protons bonded to OH− groups become most stable when associated with Ca-substitutional protons. Due to abundant formation of the associated defect comprising interstitial and Ca-substitutional protons, Ca contents in HAp decrease with lowering pH, which explains pH dependence of Ca/P molar ratios of HAp observed experimentally.
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机译：使用第一性原理带结构计算分析了羟基磷灰石（HAp）中空位和质子的电子和原子结构。假设HAp和相对于HAp饱和的水溶液之间存在化学平衡，则根据单斜晶HAp的超级电池总能量，评估缺陷形成能和平衡浓度。发现间隙质子和Ca取代质子形成H 2 O基团或HPO的酸性磷酸酯，并通过与相邻的PO基团形成氢键而稳定。此外，缺陷缔合大大降低了缺陷形成能，特别是当与Ca取代质子缔合时，键合至OH-基的间隙质子变得最稳定。由于大量形成的包括间隙质子和Ca取代质子的相关缺陷，HAp中的Ca含量随pH降低而降低，这说明了实验观察到的HAp Ca / P摩尔比与pH的关系。
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