Water incorporation in Fe-containing wadsleyite from density functional theory at extreme conditions

Using first-principles density functional theory (DFT), we studied the issue of water incorporation in iron bearing wadsleyite (Mg$_2$SiO$_4$)mineral at transition zone pressures and temperature under varying conditions of vacancy concentration and oxygen fugacity. We have considered the effect of varying vacancy concentration by considering single and double vacancy. The affect of varying oxygen fugacity has been modelled through varying ratio of ferric and ferrous ions in the cell. Our first-principles calculations have confirmed that about 30% of the Fe$^{3+}$ can be found at the Si tetrahedral site, which is in accordance with the previous experimental observation by Bolfan-Casanova et al. [2012]. Using different structures of Fe bearing wadsleyite, representing vacancy concentration and oxidizing condition, we calculated elastic properties, such as bulk and shear moduli, phase and shear wave velocity, as a function of pressure and temperature. By comparison of our theoretical prediction with the Preliminary Reference Earth Model (PREM) data, we conclude that the water content of the transition zone decreases with increasing depth, corroborating the previously proposed theories on mantle convection [Bercovici and Karato, 2003].