The effect of pressure on the elastic properties and seismic anisotropy of diopside and jadeite from atomic scale simulation

Abstract

Paper:Walker, AM (2012) AbstractThe full elastic constants tensors of diopside (CaMgSi 2 O 6 ) and jadeite (NaAlSi 2 O 6 ) have been calculated using a planewave and pseudopotentials based implementation of density functional theory within the generalised gradient approximation at pressures between 0 and 20 GPa. Both minerals stiffen over this pressure range with the isotropic average bulk moduli increasing by ∼50 % and the shear moduli by ∼20 %. However, in detail the behaviour of the individual elastic constants varies and this drives changes in the anisotropy. Overall, and in contrast to predictions based on the extrapolation of calculations based on inter-atomic potential models, the elastic anisotropy of diopside decreases with increasing pressure. The elastic anisotropy of jadeite increases slightly at low pressure, exhibits a maximum at around 10 GPa and then begins to slowly decrease. Despite the small changes in the total and maximum anisotropy, the shear-wave anisotropy for certain propagation directions vary dramatically with pressure. For example, the anisotropy experienced by a shear-wave propagating in the [010] direction in diopside doubles between 5 and 15 GPa.

The effect of cation order on the elasticity of omphacite from atomistic calculations

“…While the majority of the elastic constants stiffen as the pressure increases, the 252 pressure derivatives of C 15 , C 25 , C 35 , and C 46 are neg a tive, with the values of C 15 a n d C 46 253 converging on zero at high pressure. This is broadly similar to the reported high pressure behaviour 254 of diopside (Walker 2012;Sang and Bass 2014) although, in the case of P2/n omphacite, the value 255 of C 25 remains positive even at high pressure. 256…”

“…Comparing the calculated and experimental cell volumes (Fig. 2), the necessary pressure 235 correction is found to be 4.47 GPa, very close to the average of the pressure corrections of 4.30 GPa 236 for jadeite and 4.66 GPa for diopside found by Walker (2012) using the PBE exchange correlation 237 functional (Perdew et al 1996), consistent with previous findings that the PSHIFT EEC for a 238 material of intermediate composition can be obtained as a composition weighted average of EECs 239 for end-member compositions (van de Walle and Ceder 1999). The applied pressure minus the 240 calculated pressure correction will be referred to throughout the rest of this paper as the 'nominal 241 pressure,' and it is this value that is most relevant for comparisons with experimental data.…”

“…For monoclinic crystals, symmetry constraints reduce the number of 160 independent elastic constants to just 13, rather than the full set of 21 for a triclinic crystal. These can 161 be calculated using just four distinct strain patterns (Walker 2012). As Hooke's Law breaks down at 162 large strain amplitudes, the magnitude of the applied strain must be relatively small so that stress 163 and strain are linearly related.…”

“…The elastic constants of P2/n omphacite at zero 216 applied pressure calculated in this study are listed in Table 1, together with the zero-pressure elastic 217 constants of diopside and jadeite calculated by Walker (2012), also using plane-wave DFT. All 218 reported uncertainties are fitting errors, and larger, systematic errors are likely to be present, in 219 particular those due to the underbinding of the GGA xc-functional.…”

Structural properties of PbVO3perovskites under hydrostatic pressure conditions up to 10.6 GPa

“…We suggest that the experimentally observed abnormal changes of the a and c constants with pressure in the 2.7-4.7 GPa range, as described above, are produced by the coexistence of the T-phase and the C-phase during the transition process. However, the anomaly in the pressure dependence of the a constant of the T-phase might be essential, as the very same anomaly was also observed in PbTiO 3 perovskite [34,35]. The calculated lattice constants of the C-phase at different pressures are in perfect agreement with the experimental results.…”