Structure and elasticity of wadsleyite at high pressures

The athermal equilibrium structure, the equation of state, the elastic cons tants, and O atom charges were calculated for Mg2SiO4 wadsleyite over a ran ge of pressures using a plane-wave pseudopotential method. The zero-pressur e volume is 2% lower and the bulk modulus is 4.5% higher than experimentall y observed. After correcting for zero point motion and the 300 K temperatur e difference between theory and experiment, using a Debye model, the calcul ated zero pressure volume is within 1% of experiment and the bulk modulus a grees within experimental error. The structure compresses anisotropically w ith linear moduli for the a, b, and c axes of 610 GPa, 599 GPa, and 454 GPa , respectively. The compression is largely taken up by the Mg octahedra M1, M2, and M3 which are much softer than the Si tetrahedra, with polyhedral b ulk moduli of 161 GPa, 159 GPa, 157 GPa, and 331 GPa, respectively. The M1 and M3 octahedra were found to compress anisotropically which explains the greater compressibility of the c axis. The geometry of the Si2O7 group is c haracterized by a small Si-O-Si angle of 121.2 degrees; compression of this group is largely accommodated by shortening of the Si-O bonds, while the i nter-tetrahedral angle is almost pressure independent. We find that our res ults at ambient pressure are consistent with previously established systema tics relating bulk modulus to volume, and Si-O-Si angle to Si-O bond length . However the variation of these quantities upon the application of pressur e leads to trends that are distinct from the systematics. The calculated ze ro pressure elastic constants agree to within 10% with available Brillouin scattering data, with the exception of C-12 which is 15% higher than experi mentally observed. The calculated isotropically averaged bulk and shear mod ulus and their pressure derivatives are K-o = 182 GPa, K-o' = 4.23, and G(o ) = 116 GPa, G(o)' = 1.10, respectively. Them aggregate velocities and thei r pressure derivatives are V-p = 9.75 km/s, V-p' = 0.056 knVs/GPa, and V-s = 5.72 km/s, V-s = 0.012 km/s/GPa. We find that the elastic anisotropy of w adsleyite is intermediate between the two other Mg2SiO4 polymorphs, forster ite, and ringwoodite. The anisotropy is only weakly pressure dependent and decreases with increasing pressure. The azimuthal and polarization anisotro py for S waves 14.5% and 12.8% respectively, is almost pressure independent , while the azimuthal anisotropy for P waves decreases from 12.5% at ambien t pressure to 10.5% in the upper part of the transition zone (14-17 GPa). O ur calculated O atom charges suggest that O1 is the most likely hydroxyl si te and remains so throughout the stability field of wadsleyite.