Softening of hydroxyapatite by vacancies: A first principles investigation

First-principles plane-wave calculations were performed to investigate the influences of intrinsic vacancy on the stability and elastic properties of hydroxyapatite (HA). Five types of vacancies, i.e. H, O, OH, Ca, and Ca2 + vacancy, were considered. Formation energies were evaluated and compared with experimental measurements. It was shown that HA with a Ca2 + vacancy is the most stable one among the considered systems. Elastic constants were estimated via curves of total energy against strain. Bulk, shear and Youngʹs moduli, and Poissonʹs ratio are also evaluated to compare with the experimental value. The elastic properties of HA are significantly affected by the vacancy. Vacancy can soften HA via reducing its elastic moduli. The HA with Ca2 + vacancy is the softest one among the considered systems. Electronic structures of HA with vacancy are also analyzed to explain the softening mechanisms.