Temperature effects on elastic constants and related properties of apatites

Abstract

The application of apatites, a class of naturally occurring calcium phosphate minerals with the most common forms being hydroxyapatite (HAP), fluorapatite (FAP) and chlorapatite (ClAP), range from primary production of phosphorus, to bone and dental implants, to potential usage in carbon sequestration and nuclear waste immobilization including those that involve exposure to high temperatures. Due to their hexagonal structure, apatites have five independent elastic constants: nevertheless, experimental studies commonly report isotropic properties, and limited computational results available in the literature exhibit a large scatter. Moreover, investigation of temperature dependence of apatite elastic properties which would be essential for designing future applications is yet to be addressed in the current state of the art. In this work, we evaluate the single crystal elastic constants of the three apatite structures using stress–strain relationships: first from density functional theory (DFT) using ultrasoft pseudopotential with PBEsol exchange–correlation functional under generalized gradient approximation (GGA) on a single unit cell , and then with molecular dynamics (MD) with a 5×5×5 unit cell using a core–shell based potential model at temperatures varying from 10K to 1500K. In this temperature range, apatites exhibit the highest stiffness along the ‘c’ axis, and their elastic constants noticeably decrease with increasing temperature. At very high temperatures, C33 becomes greater than C11 for both FAP and ClAP. It is noteworthy that our DFT study exhibits better conformity with experimental findings when compared to other DFT studies reported in literature. Additionally, MD studies have demonstrated favorable consistency in predicting elastic constants, potentially as a result of fitting potential parameters to experimental data. We also calculate various effective isotropic elastic properties from our single crystal MD results and study their temperature dependence as a substitute for first principles modeling of large polycrystalline systems. All the apatites have very comparable bulk, shear, and elastic moduli, but FAP has slightly higher values, and interestingly, HAP’s Poisson’s ratio shows no variation with temperature. This study sets the baseline with which any future studies on high-temperature applications of apatites (such as carbonate or radionuclide rich apatites) can be compared.