Partitioning of FeSiO 3 and FeAlO 3, Fe-spin state and elasticity for bridgmanite and post-bridgmanite C.E. Mohn 1 R.G. Trønnes 1,2 1 Centre for Earth Evolution and Dynamics (CEED), Univ. Oslo 2 Natural History Museum, Univ. Oslo

ABO 3 -compounds bridgmanite (bm) and post-bridgmanite (pbm) Site occupacy A: divalent, Mg 2+, Fe 2+ B: quadrovalent, Si 4+ Additional trivalent cations, mostly: Fe 3+ A Al B System MSAF (Fe 3+ ) trivalent substitution vectors

i  V i exp(  G i / k B T)  exp(  G i / k B T) i V = Methods DFT and Boltzmann statistics, VASP software V, axis-lengths and H: averaged over many configurations Gibbs free energy: G i = H i + E i -TS i for configuration i. H i : static enthalpy, S i : vibr. entropy (quasiharmonic lattice dyn.), E i : zero point motion Phase relations (incl. element partitioning), crystal chemistry and mineral physics of bm and pbm Two compositional joins: MS-FS: MgSiO 3  FeSiO 3 MS-FA: MgSiO 3  FeAlO 3 - G i and spin-polarisations of Fe are calculated at the GGA + U level U: 5eV for FA, 3eV for FS - Elastic constants are calculated directly from the force constants. - Simulation box: 80 atoms,16 fmu, energy cut-off: 700 eV, k-mesh grid:2*2*2 - Computations (static limit) for MS-FS and MS-FA joins are at 100 and 120 GPa, respectively, to be with in the two-phase loops - Configurational Boltzmann avaraging at 3000 K

Partitioning Well established partitioning of: FS to pbm FA to bm The energy differences are small, rendering DFT-based phase loops uncertain (work in progress)

Two examples of experimentally based phase loops, contrasting compositions - broadly consistent with our DFT-results Mao et al. (2004, PNAS): MS-FS join Andrault et al. (2010, EPSL): approx.MS-FA join

Deviations (%) from fully ionic character (GGA +U) Mg 2+ A : 14 Si 4+ B : 19 Fe 3+ A-HS : 38 Al 3+ B : 18 O Fe A-HS : 18 Al 3+ A : 17 Fe 3+ B-LS : 49 O Fe B-LS : 18 Bader radius Mg 2+ A : 0.77 Si 4+ B : 0.65 V 80-atom cell (FA 6.25% ) Fe 3+ A-HS : 0.92 Al 3+ B : 0.68 O Fe A-HS : Al 3+ A : 0.72 Fe 3+ B-LS : 0.90 O Fe B-LS : Considerable charge transfer and covalency of flexible Fe-O bonds Therefore, the large Fe A-HS fits well in the irregular A site

Enthalpy-volume relations for various MS-FA configurations in bridgmanite

Net chemical reaction: 2 FeAlO MgSiO 3 + Fe = 3 FeSiO 3 + Al 2 O MgO bm pbm The bm-pbm transition in peridotitic and basaltic lithologies Peridotite MgO may increase the proportion and MgO-component of ferropericlase Al 2 O 3 may dissove in pbm  if pbm becomes Al-saturated: MgAl 2 O 4 -component of an Al-rich phase (Ca-ferrite or Ca-tit. struct.) mineralogical distribution according to lithology, peridotite - basalt FeNiS- alloy Basalt (picrite and komatiite) MgO and Al 2 O 3 : may increase the proportion and MgAl 2 O 4 -component of an Al-rich phase, CF-CT Additional MgO: combines with SiO 2 to increase the MgSiO 3 -component of pbm  if no free silica phase (e.g komatiite): ferropericlase will form

Stixrude and Lithgow-Bertelloni (2011, GJI) Mohn and Trønnes (2015) Main partitioning result - possible phase relations Important geophysical implications: - pbm in LLSVPs or not - thermal conductivity, diffusion - elasticity, density

Crystal chemistry of MgSiO 3 -dominated bridgmanite Incorporation of trivalent cations: - Stoichiometric: A 2+ B 4+ = A 3+ B 3+ - Non-stoichiometric: B 4+ = B 3+ with loss of 0.5O 2- Cation "sizes" (bond lengths): Fe 2+ > Mg 2+ > Fe 3+ > Al 3+ > Si 4+ ideal A-site ideal B-site A 2+ : Mg B 4+ : Si Trivalent A- and B-cations: Al, Fe 3+

Experiments on natural compositions: Al / Fe tot > 1 Bridgmanite (bm) with 200 cations (normalization) Very roughly: Peridotite: (Mg,etc.) 92 Fe tot 8 Al 9 Si 92 O 300 Basalt: (Mg,etc.) 65 Fe tot 30 Al 40 Si 65 O 300 Conclusion 1: the FeAlO 3 -component may be very dominant in bm Conclusion 2: No spin pairing transition of Fe 3+ in A-position in bm (or in post-bm) [ If some Fe 3+ is in B-position → spin pairing ] Conclusion 3: Spin pairing transition of Fe 2+ in A-position in bm (and in post-bm) Cation "sizes" (bond lengths): Fe 2+ > Mg 2+ > Fe 3+ > Al 3+ > Si 4+ ~ ideal A-site ~ ideal B-site