Table 5.
Second-order elastic moduli of stoichiometric hydroxylapatite theoretically calculated at DFT level with the PBE functional, using Gaussian-type orbitals (GTO) and planewave (PW) basis sets. Experimental results are reported for a comparison.
| Moduli (GPa) | GTO–AE | GTO–ECP | PW | Experimental | ||||||
|---|---|---|---|---|---|---|---|---|---|---|
| PBE a | PBE-D a | PBE a | PBE-D a | PBE a | PBE-D a | PBE b | PBE c | d | e | |
| C 11 | 171.5 | 182.1 | 226.0 | 236.5 | 126.9 | 147.8 | 118.3 | 117.7 | 143.4 | 137 |
| C 12 | 63.6 | 70.1 | 81.6 | 86.4 | 37.6 | 49.7 | 31.6 | 31.1 | 44.5 | 42.5 |
| C 13 | 76.0 | 80.0 | 83.7 | 86.0 | 67.1 | 64.1 | 63.7 | 66.4 | 57.5 | 54.9 |
| C 33 | 207.0 | 222.2 | 262.2 | 278.0 | 170.0 | 186.2 | 156.8 | 165.0 | 180.5 | 172 |
| C 44 | 28.9 | 36.1 | 43.3 | 50.2 | 41.8 | 45.6 | 33.5 | 38.5 | 41.5 | 39.6 |
| C 66 | 53.9 | 56.0 | 72.2 | 75.1 | 44.3 | 48.9 | 43.4 | 43.3 | 49.5 | 47.3 |
| RMSE | 19.9 | 27.3 | 51.8 | 59.8 | 9.6 | 4.8 | 15.8 | 14.2 | − | − |
a–Ref. [68]; b–Ref. [107]; c–Ref. [110]; d–Ref. [108]; e–Ref. [109]. AE and ECP stand for all-electron and effective-core pseudopotentials basis sets for the description of the core electrons of calcium atoms. PBE-D refers to the DFT functional corrected for dispersive forces with the Grimme’s approach [115]. Root mean square errors (RMSEs) with respect to the experimental results of Ref. [109] are also reported.