Lower mantle water distribution from ab initio proton diffusivity in bridgmanite

Proton self diffusion coefficients for bridgmanite at lower mantle conditions are calculated from ab initio molecular dynamics simulations. We find that the proton self diffusion coefficient, $D^{\text{self}}$ is nearly constant ∼ 10⁻⁸ m² s⁻¹ along the lower mantle geotherm but increases by nearly one order of magnitude from ∼10⁻¹⁰ m² s⁻¹ to ∼ 10⁻⁹ m² s⁻¹ along a cold slab geotherm to about 1800 km depth. These rates imply that the proton diffusion length scale is less than 10 km in lower mantle peridotite in the 150-200 million years timescale for slab material to sink through the lower mantle. Cold wet slabs probably lose less than one percent of their total water content to the ambient mantle on their journey through the lower mantle, indicating that recycled water is far from homogeneously distributed since slab delivery is highly heterogeneous. We estimate that 0.1 to 0.3 ocean masses (<100 ppm wt%) of recycled water may be currently stored in slab remnant materials within the lower mantle. This water is likely not entrained by plumes but is instead captured by background mantle flow before returning to the mid-ocean ridges. By contrast, deep-rooted mantle plumes may entrain materials containing primordial-like water from the lowermost mantle or the core, and preserve these anomalies in fairly small-scale heterogeneities. Over the age of the Earth, the proton diffusion length scale is a few tens of km, which places constraints on the size of possible primordial water reservoirs isolated from convective mixing, and indicates little flux of water across the core-mantle boundary.