Second‐order elastic constants of hexagonal hydroxylapatite (P6₃) fromab initioquantum mechanics: Comparison between DFT functionals and basis sets

Abstract

Three very popular Hamiltonians in the density functional theory framework, PBE, PBEsol, and B3LYP, and different basis sets (Gaussian‐type orbitals and plane waves) were employed to simulate the hydroxylapatite unit cell and its second‐order elastic constants. Dispersive interactions were included in the quantum‐mechanical treatment via the DFT‐D2 and Tkatchenko‐Scheffler schemes. The calculated bulk, shear, and Young's moduli were in the range of 82‐117 GPa, 42‐51 GPa, and 107‐134 GPa, respectively. The axial moduli, Ka and Kb, were instead in the range of 277‐322 GPa and 506‐509 GPa. The theoretical data, especially those from plan waves simulations, are in good agreement with available results in literature and further extend the knowledge of the mechanical and vibrational properties of hydroxylapatite.

Study of the variation of the optical properties of calcite with applied stress, useful for specific rock and material mechanics

“…1 ). In this regard, the proposed approach including the dispersive forces correctly describes the Ca 2+ –O 2– attractive interactions, resulting in an optimized distance between the layers, and gives a correct description of the unit cell of a crystal, which is mandatory for obtaining reliable structure-dependent properties, such as vibrational 20 , 21 , elastic 22 and photoelastic ones 23 .…”

Cr concentration driving the structural, mechanical, and thermodynamic properties of Cr‐Al compounds from first‐principles calculations

“…During the process of structural optimization, all atomic position and lattice parameters of Cr-Al compounds were relaxed. [39][40][41] 3 | RESULTS AND DISCUSSIONS…”

“…The k ‐point grids of 14 × 14 × 5, 11 × 11 × 5, 8 × 8 × 8, 17 × 17 × 23, 17 × 17 × 17, 10 × 10 × 12, 17 × 17 × 23, 7 × 7 × 7, and 10 × 10 × 10 for Cr 3 Al 8 with monoclinic structure, Cr 3 Al 5 with hexagonal structure, Cr 5 Al 8 with rhombohedral structure, Cr 2 Al 3 with tetragonal structure, CrAl with cubic structure, Cr 5 Al 3 with tetragonal structure, Cr 2 Al with tetragonal structure, Cr 7 Al 3 with cubic structure, and Cr 3 Al with cubic structure were treated. During the process of structural optimization, all atomic position and lattice parameters of Cr‐Al compounds were relaxed …”

Hydroxylapatite and Related Minerals in Bone and Dental Tissues: Structural, Spectroscopic and Mechanical Properties from a Computational Perspective

“…Recently, Ulian and Valdrè [ 68 ] made a comparison between the elastic moduli of hydroxylapatite obtained by different approaches within the DFT framework (at 0 K). An excerpt of the results is here presented in Table 5 , together with previous theoretical and experimental analyses [ 107 , 108 , 109 , 110 ].…”