Softening of hydroxyapatite by vacancies: A first principles investigation

► We investigate the softening effects of hydroxyapatite by vacancies. ► Formation energies are calculated according to density functional theory. ► Five kinds of vacancies were evaluated and Ca2 + vacancy is the stable one. ► Elastic constants for the five considered systems are calculated. ► Vacancy can soften HA and the HA with Ca2 + vacancy is the softest one. ► Electronic mechanisms about the influence were analyzed.