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# Formation of large low shear velocity provinces through the decomposition of oxidized mantle

## Abstract

Large Low Shear Velocity Provinces (LLSVPs) in the lowermost mantle are key to understanding the chemical composition and thermal structure of the deep Earth, but their origins have long been debated. Bridgmanite, the most abundant lower-mantle mineral, can incorporate extensive amounts of iron (Fe) with effects on various geophysical properties. Here our high-pressure experiments and ab initio calculations reveal that a ferric-iron-rich bridgmanite coexists with an Fe-poor bridgmanite in the 90 mol% MgSiO3–10 mol% Fe2O3 system, rather than forming a homogeneous single phase. The Fe3+-rich bridgmanite has substantially lower velocities and a higher VP/VS ratio than MgSiO3 bridgmanite under lowermost-mantle conditions. Our modeling shows that the enrichment of Fe3+-rich bridgmanite in a pyrolitic composition can explain the observed features of the LLSVPs. The presence of Fe3+-rich materials within LLSVPs may have profound effects on the deep reservoirs of redox-sensitive elements and their isotopes.

## Introduction

The large low shear velocity provinces (LLSVPs) are two massive and mysterious regions sitting beneath Africa and the Pacific1,2,3 and occupy ~3–9% of the volume of the Earth3,4. They are characterized by their lower-than-average seismic wave velocities4 and extend by thousands of kilometers laterally and up to >1000 km vertically above the core–mantle boundary (CMB)3,4. As the largest seismic heterogeneities in the lower mantle, they may hold the key to understanding the thermal, chemical, and dynamical evolution of the Earth5,6,7. Different shear-wave tomography models4 have reached agreement that the shear-wave velocity anomaly (dlnVS) ranges from −0.5 to −1.0% in the shallow part of LLSVPs, while it could be up to −3.0% in the bottom part6. The compressional-wave tomography models also reveal negative anomalies of compressional-wave velocities (VP) (refs. 8,9), although the amplitude, shape, and geographical location of VP anomaly vary widely among different models5. The VP anomaly generally has a smaller amplitude than the VS anomaly, causing a high dlnVS/dlnVP ratio9. In particular, waveform and travel-time seismic studies1,3,10,11,12 reveal that the LLSVPs have sharp edges along their margins, which is also supported by the large lateral dVS gradients at the boundary of LLSVPs6.

The systematic and discontinuous contrasts in seismic properties indicate that the LLVSPs are likely composed of distinct chemical materials from the surrounding mantle11,13. A chemically distinct origin of the LLSVPs may be implicated by their density anomalies as well; however, large discrepancies for the density anomaly associated with the LLSVPs exist in the literature5. Recent tidal tomography based on body tide displacements14 found that the mean density of the lower two-thirds of the two LLSVPs is ~0.5% higher than that of the surrounding mantle. On the contrary, a study using Stoneley modes suggested an overall negative density anomaly within LLSVPs, without excluding the possibility of a high-density anomaly within the lowermost LLSVPs15. It is still unknown whether the regional differences in density anomaly are caused by the choice of observations used to constrain density models or reflect the nature of LLSVPs associated with their origins.

Hypotheses for the origin of chemically distinct LLSVPs include processes associated with the accumulation of subducted oceanic crust over Earth history16 and the differentiation and solidification of an ancient basal magma ocean6. Sunken piles of subducted oceanic crust, which is compositionally different from and significantly denser than the pyrolitic lower mantle17, was proposed to explain LLSVPs because of the low velocity of calcium silicate perovskite (CaSiO3, CaPv) (ref. 18). However, there are significant discrepancies in the velocity of CaPv between two experimental studies18,19 and between experiments and theoretical results20. Elastic properties from ab initio simulations for the entire MORB assemblage indicate that subducted oceanic crust has relatively higher velocities than the ambient mantle21. Moreover, geodynamic simulations22 suggested that the present-day subducted oceanic crust is too thin to provide enough negative buoyancy to ﻿survive viscous stirring and it hence is difficult to amass coherent thermochemical structures and shapes at the CMB similar to LLSVPs23. Alternatively, LLSVPs may be composed of primordial residues from basal magma ocean crystallization or core–mantle differentiation that have not yet been fully homogenized by the mantle convection24,25,26. These primordial materials would need to be intrinsically more dense than the surrounding mantle to overcome mantle stirring27. Dense Fe–Ni–S liquid, for instance, was proposed to explain the LLSVPs28, but the amount of this liquid remaining in the deep mantle, which depends on the drainage of melt to the core29, is under debate.

Consistent with both efficient drainage of metallic melt and a primordial origin of the LLSVPs is chemical heterogeneity produced by redox reactions in the magma ocean. Ferrous iron (Fe2+) in silicate melts has been observed to disproportionate to ferric iron (Fe3+) plus metallic iron (Fe0) at high pressures30. Segregation of precipitated Fe0 from the magma ocean into the core would enrich Fe3+ in the mantle. Bridgmanite (Bdg), the dominant Fe3+-bearing mantle mineral, hosts Fe3+ through the Fe3+–Fe3+ or Fe3+–Al3+ charge-coupled substitution in the deep mantle31,32,33,34,35. In particular, a Fe3+-rich Bdg with the chemical composition of (Mg0.5Fe0.5)(Si0.5Fe0.5)O3 was recently synthesized by Liu et al.36. Oxidized domains enriched with such Fe3+-rich Bdg would be distinct from a pyrolitic lower mantle in sound velocity and density37,38 and may be responsible for the origins of lower-mantle seismic and geochemical heterogeneities, such as the LLSVPs1,2,3,6. The conditions of formation of such Fe3+-rich Bdg in a mantle phase assemblage and its elastic properties at lower-mantle-relevant temperatures are vital to test this hypothesis, but these questions remain unclear.

In this work, we combine high pressure-temperature (P-T) experiments, ab initio calculations, and geodynamic simulations to study the formation of Fe3+-rich Bdg, its thermoelastic properties, and its dynamics in the mantle, to evaluate whether enrichment in Fe3+-rich Bdg can explain the seismic signatures of LLSVPs.

## Results

### The coexistence of Fe3+ -rich and Fe-poor bridgmanite phases

We conducted a series of multi-anvil experiments with the bulk composition of 90 mol% MgSiO3–10 mol% Fe2O3 from 10-24 GPa along a mantle geotherm (Supplementary Table 1). At 10 GPa and 1573 K (Fig. 1d), the run products consist of separate MgSiO3 and Fe2O3 phases, demonstrating low solubility of Fe2O3 in clinopyroxenes at upper-mantle conditions due to the incompatibility between large Fe3+ and small tetrahedral site. At 15 GPa, an iron-rich akimotoite (Aki) forms with 33 mol% of MgSiO3 and 67 mol% of Fe2O3, coexisting with (Mg1.79Fe0.18)SiO4 wadsleyite and SiO2 stishovite (Fig. 1c). This indicates that the iron-rich Aki coexisting with iron-depleted oxides/silicates are energetically more stable than a single-phase MgSiO3–Fe2O3 solid solution with intermediate iron content. At 24 GPa and 1873 K, which corresponds to the P–T conditions around the uppermost lower mantle, the products consist of Fe-poor Bdg and Fe-rich Aki with 44–49 mol% Fe in both Mg and Si sites (Fig. 1a and Supplementary Table 1), instead of forming a single phase of (Mg0.9Fe0.1)(Si0.9Fe0.1)O3 Bdg. The Fe-rich Aki is evenly distributed in the matrix of the Fe-poor Bdg (Fig. 1a). The run products of experiments running at the same P–T conditions for 8 and 24 h have the same compositions within analytical uncertainty (Supplementary Table 1), confirming that the experiments reached equilibrium. In situ XRD measurements coupled with a diamond anvil cell (DAC) show that this Fe-rich Aki phase transforms to Bdg phase at 23.5 ± 1.0 GPa and 300 K (Supplementary Fig. 1). Moreover, this Fe3+-rich Bdg phase completely transforms back to Aki with the same lattice parameters as the starting Aki phase after the decompression of the DAC (Supplementary Fig. 1). The reversible phase transition of this Fe-rich phase means that for our multi-anvil experiments at the P–T conditions of the uppermost lower mantle, Fe3+-rich Bdg coexists with Fe-pool Bdg.

A previous multi-anvil study39 synthesized Fe3+-only bridgmanite with 2–4 mol% Fe3+ in the cation sites but did not observe the Fe3+-rich Bdg phase, possibly because the bulk Fe content of their experiments is not high enough to enable the formation of such Fe3+-rich Bdg. Moreover, the presence of unreacted MgO and SiO2 in their run products (Fig. 1 in ref. 39) suggests that their starting materials may not be homogenous or their experiments did not reach chemical equilibrium. Another study40 synthesized Fe3+-only Bdg with the starting material of 90 mol% MgSiO3–10 mol% Fe2O3 using laser-heated diamond anvil cell (LH-DAC)40. However, the chemical composition of Fe3+-only Bdg was not reported, possibly because there was a significant loss of Fe and Mg during melting40, and some Fe3+ was reduced through reaction with diamond during laser heating41. In addition, the proportion of the Fe-rich Bdg phase is much smaller than the Fe-poor Bdg (Fig. 1), and therefore it is difficult to detect without a detailed analysis of the run products in ref. 40.

We also performed ab initio calculations (see methods and supplementary materials) to investigate the stability of (Mg0.5Fe0.5)(Si0.5Fe0.5)O3 Bdg under lower-mantle conditions. Our results show that the assemblage of (Mg0.5Fe0.5)(Si0.5Fe0.5)O3 and MgSiO3 Bdg has a lower Gibbs free energy than a single-phase (Mg0.875Fe0.125)(Si0.875Fe0.125)O3 Bdg under the P–T of the whole lower mantle regardless of the spin state (Supplementary Fig. 2), indicating that the mixed two phases are more stable than the single-phase Bdg with a homogeneous composition. The theoretical results support our experimental observations and reveal that this Fe3+-rich Bdg with the chemical composition of approximately (Mg0.5Fe0.5)(Si0.5Fe0.5)O3 should form as a separate phase coexisting with Fe-poor Bdg in the bulk composition of 90 mol% MgSiO3–10 mol% Fe2O3 due to the miscibility gap.

### Elastic properties and sound velocities of (Mg0.5Fe0.5)(Si0.5Fe0.5)O3 bridgmanite

Determining the seismic signature of a separate Fe3+-rich phase in equilibrium with the mantle phase assemblage requires elastic properties of this phase as a function of pressure and temperature conditions in the mantle. The elastic properties of (Mg0.5Fe0.5)(Si0.5Fe0.5)O3 Bdg up to 130 GPa and 3000 K were theoretically obtained from ab initio calculations. Because Bdg may also accommodate Al in the octahedral site31,38,42, we also conducted calculations on an end-member composition (Mg0.5Fe0.5)(Si0.5Al0.5)O3, to quantify the effect of Al on the elasticity of Bdg. In these calculations, the octahedral site (B-site) Fe3+ in (Mg0.5Fe0.5)(Si0.5Fe0.5)O3 Bdg undergoes a high-spin (HS) state to a low-spin (LS) state transition with increasing pressure (Fig. 2a), while the dodecahedral-site (A-site) Fe3+ in both compositions remain in the HS state throughout the lower-mantle conditions43.

Our calculated volumes of HS- and LS-(Mg0.5Fe0.5)(Si0.5Fe0.5)O3 Bdg agree well with experimental measurements at 300 K (ref. 36) (Fig. 2a). The calculated spin transition of the B-site Fe3+ occurs between 49 and 55 GPa at 300 K36, which is slightly higher and narrower than experimental results36. The predicted ﻿volume collapse (ΔVHS-LS) caused by the spin transition of B-site Fe3+ is ~4.3% at 300 K, higher than experimental measurements (2.7%)36 but consistent with previous theoretical calculations44 on (Mg0.5Fe0.125)(Si0.5Fe0.125)O3 Bdg assuming that ΔVHS-LS is linearly dependent on Fe3+ content. The ΔVHS-LS discrepancy between experimental and theoretical studies is probably caused by the difference in the pressure range for the mixed-spin (MS) state. The predicted volumes of (Mg0.5Fe0.5)(Si0.5Al0.5)O3 Bdg also show excellent agreement with experimental results at 300 K42. These comparisons demonstrate the high reliability of our DFT + U calculations in predicting elastic properties, as suggested by previous studies43,44,45.

The spin transition of B-site Fe3+ in (Mg0.5Fe0.5)(Si0.5Fe0.5)O3 Bdg generates a strong effect on bulk modulus (KS) and VP, which both show deep valleys that broaden and decrease in magnitude with increasing temperature (Supplementary Fig. 3). The magnitude and width of the KS and VP anomalies are controlled by the fraction of LS B-site Fe3+ (nLS) and the pressure and temperature dependences of nLS (see Supplementary Materials). Compared to MgSiO3 Bdg46, both (Mg0.5Fe0.5)(Si0.5Fe0.5)O3 and (Mg0.5Fe0.5)(Si0.5Al0.5)O3 Bdg have much lower elastic moduli (KS and G) and velocities (VP and VS) (Supplementary Fig. 4). At lowermost-mantle conditions, the differences in KS, G, VP, and VS between (Mg0.5Fe0.5)(Si0.5Fe0.5)O3 and MgSiO3 Bdg46 are about −5%, −37%, −17%, and −28%, respectively, which in turn causes a higher VP/VS ratio of 2.1 in (Mg0.5Fe0.5)(Si0.5Fe0.5)O3 Bdg (Supplementary Fig. 4). By comparison, the differences in KS, G, VP, and VS between (Mg0.5Fe0.5)(Si0.5Al0.5)O3 and MgSiO3 Bdg are about −4%, −18%, −9%, and −14%, respectively.

## Discussion

Combining elastic data from previous studies20,45,46,47 with our results, we modeled the density and velocity anomalies caused by the presence of Fe3+-rich Bdg relative to the pyrolitic composition, which can effectively reproduce the reference seismic velocities and density of PREM37,38. The modeled chemical assemblage has pyrolitic mineral fractions (15% ferropericlase (Fp) + 78% Bdg + 7% CaPv) in which a portion of Fe2+-bearing Bdg was substituted by (Mg0.5Fe0.5)(Si0.5Fe0.5)O3 Bdg. We find that the enrichment of (Mg0.5Fe0.5)(Si0.5Fe0.5)O3 Bdg in the assemblage can explain the seismic features of the LLSVPs4,6,8,9. The VS anomalies of −1.5% to −3.0% and the large dlnVS/dlnVP ratio >2.0 observed in LLSVPs4,6,8,9 can be reproduced by the enrichment of 10–15% (Mg0.5Fe0.5)(Si0.5Fe0.5)O3 Bdg in pyrolite at 110 GPa (Fig. 3). If LLSVPs are hotter (ΔTLLSVPS > 0), the required proportion of (Mg0.5Fe0.5)(Si0.5Fe0.5)O3 Bdg would accordingly decrease; for example, it will decrease by ~2% if ΔTLLSVPS is +400 K. For a pyrolitic composition, Bdg also contains ~5 mol% Al2O3, which does not significantly change its velocities and density48. When 5 mol% Al2O3 is incorporated into Bdg, the VP and VS anomalies caused by the presence of 15% (Mg0.5Fe0.5)(Si0.5Fe0.4Al0.1)O3 Bdg at ΔTLLSVPS equal to +400 K will be −1.5% and −3.1% (Fig. 3), respectively, which can also reproduce the dlnVS/dlnVP ratio >2.0.

In addition, we find that the required proportion of (Mg0.5Fe0.5)(Si0.5Fe0.5)O3 Bdg increases with the decreasing of Fe2+ content in the modeled assemblage (noted by the FeO content in Fp, Fe2+Fp) to explain the same VP and VS anomalies (Fig. 4). If there is no Fe2+, the (Mg0.5Fe0.5)(Si0.5Fe0.5)O3 fraction that can reproduce the VS anomaly of −3.0% would be raised to ~17% at ΔTLLSVPS equal to +400 K (Fig. 4 and Supplementary Fig. 5), which corresponds to a VP anomaly of ~−1.0% and a dlnVS/dlnVP ratio of ~3.0. The dlnVS/dlnVP ratio >2.0 tends to be reproduced at relatively low Fe2+ contents (Fig. 4). If Fe2+Fp/Fe2+Fp, NM > 0.9 (Fe2+Fp, NM is the FeO content of Fp in a normal pyrolitic lower mantle, 18 mol%), the dlnVS/dlnVP ratio is less than 2.0. In contrast, when Fe2+Fp/Fe2+Fp, NM is <0.25, the dlnVS/dlnVP ratio >2.0 can be reproduced for different VS anomalies (Fig. 4). Our modeling implies that the enrichment of (Mg0.5Fe0.5)(Si0.5Fe0.5)O3 Bdg in the pyrolite assemblage with relatively lower Fe2+ content can explain the velocity anomalies and the dlnVS/dlnVP ratio observed in LLSVPs4,6,8,9.

In contrast to velocity anomalies, the modeled density anomaly (dlnρ) could be positive, zero, or negative, depending on the (Mg0.5Fe0.5)(Si0.5Fe0.5)O3 abundance, temperature anomaly, and the fraction of Fe2+ in Fp. To produce a VS anomaly of −3.0% for the assemblage enriched in (Mg0.5Fe0.5)(Si0.5Fe0.5)O3 Bdg, the dlnρ decreases from +1.2% at ΔTLLSVPS of 0 K and Fe2+Fp/Fe2+Fp, NM of 0.5 to −0.5% at ΔTLLSVPS of +400 K and Fe2+Fp/Fe2+Fp, NM of 0.0 (Figs. 3, 4 and Supplementary Fig. 5). In general, the density anomaly is correlated with the magnitude of VS anomalies. For dlnVS < −1.0%, the dlnρ could be positive if ΔTLLSVPS is 0 K; however, if ΔTLLSVPS equals to +400 K, the dlnρ could be positive only when dlnVS is <−2.5% (Fig. 4). Our modeling suggests that the lowermost parts of LLSVPs with large negative velocity anomalies (<−3.0%)4,6,8 could be denser than the ambient mantle, while the relatively shallow part of LLSVPs with −0.5 to −1.0% VS anomalies on average likely have slightly lighter density than the ambient mantle. Recent work proposed that the bottom two-thirds of the two LLSVPs are ~0.5% denser than the surrounding mantle14, while Koelemeijer et al.15 argued that the overall density of the LLSVPs is lower than the surrounding mantle. Such different conclusions may be related to different depth sensitivities of the datasets considered49, regardless of the input observations. Also, geodynamic modeling studies50,51 suggested that the density anomalies of the LLSVPs relative to the surrounding mantle could be positive near the top and bottom of the LLSVPs but neutral or slightly negative in the middle of the LLSVPs. The density of LLSVPs could also be laterally inhomogeneous due to their internal convection and the entrainment of multiple compositional components into the LLSVPs52.

The present model for chemical heterogeneities within the LLSVPs is consistent with Fe-rich remnants of a basal magma ocean created early in Earth’s history6,24,25,26. Ferrous Fe in dense silicate melts associated with the basal magma ocean would partially disproportionate to Fe3+ plus Fe0 at high pressures30 and segregation of precipitated Fe0 from the magma ocean into core would enrich silicate melt in Fe2O3 component. A thermodynamic model of magma ocean crystallization53 suggests that the silicate melt fraction would be gradually enriched in iron with Fe/(Fe+Mg) >0.3 in the lower mantle after 60 wt% of the melt has solidified. The Fe/(Fe+Mg) ratio in the residual melt remaining in the lowermost mantle could be up to 0.5 near the end of the crystallization. The amount of Fe3+ in this melt depends on the amount of Fe2+ that would disproportionate into Fe3+ plus Fe0 and the efficiency of Fe0 droplet segregation. The required bulk composition with MgSiO3:Fe2O3 equal to 9:1 could be produced when 40–80% Fe2+ undergoes the disproportionation reaction and all Fe0 migrates into the core. Fe3+ would be incorporated into bridgmanite with further crystallization, and our experiments and ab initio calculations indicate that in these Fe3+-rich regions, a portion of (Mg0.5Fe0.5)(Si0.5Fe0.5)O3 silicate would form as a separate phase, coexisting with Fe3+-poor silicate. Due to the large excess density, (Mg0.5Fe0.5)(Si0.5Fe0.5)O3 silicate could descend to the base of the lower mantle through mantle convection and result in Fe3+-rich bridgmanite piles. Our geodynamic modeling demonstrates that such Fe3+-rich piles with ~18% (Mg0.5Fe0.5)(Si0.5Fe0.5)O3 Bdg, which is ~1.5% intrinsically denser than the ambient mantle (Fig. 4c), could form large-scale thermochemical structures in the lowermost mantle without being mixed into the background mantle throughout Earth’s history (Fig. 5), which may accumulate to form LLSVPs.

Our findings imply that the segregation of Fe3+-rich domains may cause heterogeneity in the redox states of the Earth’s mantle, that is, the oxygen fugacity of the lowermost mantle may not be as low as inferred in previous studies54,55. We also expect these Fe3+-rich domains to be enriched in heavy iron isotopes because Fe3+ has a larger Fe force constant than Fe2+ (ref. 56), which may affect the iron isotopic features of the deep Earth57. The presence of lower-mantle oxidizing heterogeneities would have profound effects on the cycles of volatiles30 and the deep reservoirs of redox-sensitive elements. For instance, the dense reduced Fe-C/H/S melts formed at the mantle transition zone and shallow lower mantle by slab/mantle interaction58,59, if they reach the lowermost mantle, could be converted back to an oxidized state instead of sinking into the core. Dynamic cycling with respect to mantle redox heterogeneity could provide new insights into the thermochemical evolution of the bulk silicate Earth and possibly the oxidation of the atmosphere.

## Methods

### High pressure–temperature experiments

The experiments were conducted using the 1000-ton multi-anvil apparatus at the University of Michigan. The COMPRES 8/3 and 10/5 cell assemblies were employed in the experiments. The starting material was a mixture of high purity (>99.99%) MgO, SiO2, and Fe2O3 at a molar ratio of 9:9:1, which corresponds to a bulk composition of (Mg0.9Fe0.1)(Si0.9 Fe0.1)O3. The mixture was heated at 1073 K overnight to remove the moisture and structural water before loading into a platinum capsule. The sample was compressed to target pressure and equilibrated at high temperature for 6–10 h to allow sufficient equilibrium. It was then quenched to room temperature and decompressed to 1 bar.

The recovered sample was polished, coated with carbon, and examined for texture and composition using the JOEL-7800FLV Scanning Electron Microprobe (SEM) and SX-100 Electron Microprobe Analysis (EPMA) at the Electron Microbeam Analysis Laboratory (EMAL) of the University of Michigan. An accelerating voltage of 15 kV and a beam current of 10 nA were employed for imaging and analysis. Forsterite and magnetite were used as standards for Mg, Si, and Fe quantification with EPMA.

### First-principles calculations

Isothermal elastic tensors ($$C_{ijkl}^T$$) of crystals in a Cartesian coordinate system usually can be calculated from Eq. (1) (ref. 60):

$$C_{ijkl}^T = \frac{1}{V}(\frac{{\partial ^2F}}{{\partial e_{ij}\partial e_{kl}}}) + \frac{1}{2}P(2\delta _{ij}\delta _{kl} - \delta _{il}\delta _{kj} - \delta _{ik}\delta _{jl})$$
(1)

where eij(i,j = 1,3) are infinitesimal strains, P is the isotropic pressure, and F is the Helmholtz free energy, which can be expressed in the quasi-harmonic approximation (QHA) as:

$$F\left( {e_{ij},V,T} \right) = U\left( {e_{ij},V} \right) + \frac{1}{2}\mathop {\sum }\limits_{q,m} \hbar \omega _{q,m}\left( {e_{ij},V} \right) + k_BT\mathop {\sum }\limits_{q,m} ln(1 - {\mathrm{exp}}( - \frac{{\hbar \omega _{q,m}\left( {e_{ij},V} \right)}}{{k_BT}}))$$
(2)

where V is the equilibrium volume of the crystal and T is temperature. Subscripts q and m refer to the phonon wave vector and the normal mode index, respectively. $$\hbar$$ and kB are Planck and Boltzmann constants, and ωq,m is the vibrational frequency of the ith mode along with the wave vector q. U is the static energy at the equilibrium volume V. The second and third terms are the zero-point and vibrational energy contributions, respectively. Adiabatic elastic constants ($$C_{ijkl}^S$$) can be derived from:

$$C_{ijkl}^S = C_{ijkl}^T + \frac{T}{{VC_V}}\frac{{\partial S}}{{\partial e_{ij}}}\frac{{\partial S}}{{\partial e_{kl}}}\delta _{ij}\delta _{kl}$$
(3)

where S is the entropy and CV is the constant volume heat capacity. Therefore, calculations of elastic tensors at high pressure and temperature using this usual method require a vibrational density of states (VDoS) of many strained configurations, which demand a tremendous amount of computational power to calculate based on the DFT. Wu and Wentzcovitch61 proposed an analytical approach to calculate the thermal contribution to the elastic tensor, only requiring VDoS for unstrained configurations at different equilibrium volumes. This approach greatly reduces the computation cost to the level of <10% of the usual method without loss of accuracy.

To obtain elastic tensors at static conditions and VDoS for unstrained configurations at different equilibrium volumes, we performed first-principles calculations using Quantum Espresso package62 based on the DFT, plane wave, and pseudopotential. Local density approximation (LDA) was adopted for the exchange-correlation function. The energy cutoff for electronic wave functions was set as 70 Ry. The Mg pseudopotential was generated using the von Barth and Car method for all channels using a 2.5 Bohr cutoff radius and five configurations, 3s23p0, 3s13p1, 3s13p0.53d0.5, 3s13p0.5, 3s13d1, with weights of 1.5, 0.6, 0.3, 0.3, 0.2, respectively. The pseudopotentials for Si and O were generated using the Troullier-Martins method63 with the cutoff radius of 1.47 Bohr for Si and 1.45 Bohr for O. Valence configurations for Si and O are 3s23p43d0 and 2s22p4, respectively. The pseudopotentials for Al and Fe were generated using the Vanderbilt method64 with a valence configuration of 3s23p1 and a cutoff radius of 1.77 Bohr for Al, and a valence configuration of 3s23p63d6.54s14p0 and a cutoff radius of 1.8 Bohr for Fe. To address the large on-site Coulomb interactions among the localized electrons (Fe 3d electrons)65, we introduced a Hubbard U correction to the LDA (LDA+U) for all DFT calculations. U values for Fe3+ on A and B sites in bridgmanite were non-empirically determined using linear response method66 in previous work43 and adopted in this study. The initial structure was constructed by replacing one nearest-neighbor Mg2+–Si4+ pair with one [Fe3+]Mg–[Fe3+]Si pair43,44,45. Crystal structures at variable pressures were well optimized on a 6 × 6 × 4 k-point mesh, and VDoS were calculated using the finite displacement method as implemented in the code PHONOPY67. The elastic tensors at static conditions were calculated from the linear dependence of stress on the small strain. Owing to the enormous computational cost of calculating the vibrational density of state based on LDA+U, we used the 20-atom unit cell for (Mg0.5Fe0.5)(Si0.5Fe0.5)O3 bridgmanite43,44,45. Similar to previous studies on the elastic properties of Fe-bearing bridgmanite45,46, we only report results for aggregate elastic moduli, not individual elastic coefficients. The latter are sensitive to atomic configurations and therefore to supercell size, which can accommodate different configurations for the same composition. The aggregate elastic moduli, KS and G, are quite insensitive to the atomic configuration68,69,70.

The Helmholtz free energy calculated from Eq. (2) within the QHA versus volume was fitted by the isothermal third-order finite strain equation of state, and then we can obtain all thermodynamic properties, such as pressures at different temperatures and volumes. Our results show that (Mg0.5Fe0.5)(Si0.5Fe0.5)O3 bridgmanite has a larger volume than (Mg0.5Fe0.5)(Si0.5Al0.5)O3 bridgmanite (Fig. 2). The substitution of Al3+ for LS Fe3+ in the octahedral site causes a slight decrease of ~1.0% in volume at >80 GPa. Compared to ﻿pristine Bdg (MgSiO3), these two Fe3+- and Al3+-rich species have larger volumes; for example, at 90 GPa and 2000 K, the volumes of (Mg0.5Fe0.5)(Si0.5Al0.5)O3 and (Mg0.5Fe0.5)(Si0.5Fe0.5)O3 are 3.5% and 4.4% larger than that of MgSiO3, respectively.

Using the equation of states, we transferred volume- and temperature-dependent elasticity into pressure- and temperature-dependent elasticity. The adiabatic bulk modulus KS and shear modulus G can be obtained by computing the Voigt–Reuss–Hill averages71 from elastic tensors. Thus, compressional and shear velocities can be calculated from the equations $$V_P = \sqrt {(Ks + \frac{4}{3}G)/\rho }$$ and $$V_S = \sqrt {G/\rho }$$ (ρ is density). Bulk moduli (KS), shear moduli (G), compressional-wave velocity (VP), and shear-wave velocity (VS) are also derived from LDA+U calculations as shown in Supplementary Fig. 3. Compared to (Mg0.5Fe0.5)(Si0.5Fe0.5)O3 Bdg, (Mg0.5Fe0.5)(Si0.5Al0.5)O3 Bdg has a lower density, similar KS but much larger G at >90 GPa, which results in much higher velocities in (Mg0.5Fe0.5)(Si0.5Al0.5)O3 Bdg. At 100 GPa and 2000 K, the differences in density, KS, G, VP, and VS between (Mg0.5Fe0.5)(Si0.5Al0.5)O3 and (Mg0.5Fe0.5)(Si0.5Fe0.5)O3 are −10.4%, −0.9%, 19.2%, 8.1%, and 14.8%, respectively. Elastic moduli and velocities almost linearly depend on pressure and temperature after B-site Fe3+ spin transition and their first pressure and temperature derivatives are comparable to those of MgSiO3 Bdg (Supplementary Table 3).

### Ab initio investigation on the stability of (Mg0.5Fe0.5)(Si0.5Fe0.5)O3 bridgmanite

Through high-pressure and high-temperature experiments, we find the formation of iron-rich bridgmanite (Mg0.5Fe0.5)(Si0.5Fe0.5)O3 coexisting with Fe-poor bridgmanite, instead of forming a single phase of (Mg0.9Fe0.1)(Si0.9Fe0.1)O3 Bdg with homogeneous iron content. In order to check the relative stability of (Mg0.5Fe0.5)(Si0.5Fe0.5)O3 bridgmanite, we also calculated the formation energy of the decomposition reaction:

(Mg0.875Fe0.125)(Si0.875Fe0.125)O3 ↔ 3/4MgSiO3+1/4(Mg0.5Fe0.5)(Si0.5Fe0.5) (4)

The Gibbs free energy of (Mg1-xFex)(Si1-xFex)O3 can be expressed as (see Supplementary Materials):

$$G_{{\mathrm{HS/LS}}}\left( {P,T} \right) = G_{{\mathrm{HS/lS}}}^{{\mathrm{stat}} + {\mathrm{vib}}}\left( {P,T} \right) + G_{{\mathrm{HS/LS}}}^{{\mathrm{mag}}}\left( {P,T} \right) - {\mathrm{TS}}^{{\mathrm{conf}}}$$
(5)

where Sconf is the configurational entropy (Sconf = kBlnM, M is the configuration degeneracy). $$G_{{\mathrm{HS/lS}}}^{{\mathrm{stat}} + {\mathrm{vib}}}\left( {P,T} \right)$$ and $$G_{{\mathrm{HS/LS}}}^{{\mathrm{mag}}}\left( {P,T} \right)$$ can be derived from Eqs. (3–6) in Supplementary Materials. Thus, the Gibbs formation free energy of the decomposition reaction for pure HS/LS state can be expressed as:

$$\Delta G = \frac{1}{4} \ast \left( {G_{x = 0.5}^{{\mathrm{stat}} + {\mathrm{vib}}} - {\mathrm{TS}}_{x = 0.5}^{{\mathrm{conf}}}} \right) + \frac{3}{4} \ast G_{{\mathrm{MgSiO3}}}^{{\mathrm{stat}} + {\mathrm{vib}}} - (G_{x = 0.125}^{{\mathrm{stat}} + {\mathrm{vib}}} - {\mathrm{TS}}_{x = 0.125}^{{\mathrm{conf}}})$$
(6)

We also investigated the disordered substitution of Fe3+ in (Mg0.875Fe0.125)(Si0.875Fe0.125)O3 bridgmanite in a 40-atom cell ($$\sqrt 2 \times \sqrt 2 \times 1$$ supercell). Similar to the case for (Mg0.5Fe0.5)(Si0.5Fe0.5)O3 bridgmanite, the initial structure was constructed by ﻿replacing one nearest-neighbor Mg2+–Si4+ pair with one [Fe3+]Mg–[Fe3+]Si pair. Due to the extremely high computational cost of VDOS calculation using LDA+U functional, we did not calculate the VDOS of (Mg0.875Fe0.125)(Si0.875Fe0.125)O3 bridgmanite. Because (Mg1-xFex)(Si1-xFex)O3 bridgmanite with different Fe3+ contents have similar structures, here we assume that the vibrational contribution to the Gibbs free energy linearly depends on Fe3+ content ($$G_{x = 0.125}^{{\mathrm{vib}}} = \frac{1}{4} \ast G_{x = 0.5}^{{\mathrm{vib}}} + \frac{3}{4} \ast G_{{\mathrm{MgSiO3}}}^{{\mathrm{vib}}}$$). Under this approximation, ΔG can be written as:

$$\Delta G = \frac{1}{4} \ast \left( {H_{x = 0.5}^{{\mathrm{stat}}} - {\mathrm{TS}}_{x = 0.5}^{{\mathrm{conf}}}} \right) + \frac{3}{4} \ast H_{{\mathrm{MgSiO3}}}^{{\mathrm{stat}}} - (H_{x = 0.125}^{{\mathrm{stat}}} - {\mathrm{TS}}_{x = 0.125}^{{\mathrm{conf}}})$$
(7)

where Hstat is the internal energy or the Gibbs free energy without the vibrational contribution.

As shown in Supplementary Fig. 2, ΔG is negative at lower-mantle conditions regardless of the spin state of B-site Fe3+ in (Mg1-xFex)(Si1-xFex)O3 bridgmanite. This implies that the assemblage of (Mg0.5Fe0.5)(Si0.5Fe0.5)O3 and MgSiO3 bridgmanite is more stable than the single-phase (Mg0.875Fe0.125)(Si0.875Fe0.125)O3 bridgmanite, consistent with our experimental results (Fig. 1). In addition, our LDA+U calculations extend the occurrence of this decomposition reaction to the lowermost-mantle conditions, where (Mg0.5Fe0.5)(Si0.5Fe0.5)O3 bridgmanite is still more stable than (Mg0.875Fe0.125)(Si0.875Fe0.125)O3 bridgmanite.

In order to check the effect of the exchange-correlation function on the results, we also calculated the enthalpy change of this reaction using the generalized gradient approximation with Hubbard U correction (GGA+U). U values for Fe3+ on A and B sites in bridgmanite are 3.3 and 4.5 eV, respectively. The ΔH predicted by the GGA+U calculations is similar to that from the LDA+U calculations (Supplementary Fig. 2), both of which favor the mixed phases over the single phase.

### Thermoelastic models for the estimations of velocity and density heterogeneities

Previous studies37 have suggested that the pyrolitic lower mantle that consists of 15% Mg0.82Fe0.18O ferropericlase (Fp), 78% Mg0.92Fe0.08SiO3 bridgmanite (Fe2+-Bdg), and 7% CaSiO3 Ca-perovskite (CaPv)) can admirably reproduce the velocity and density profiles of PREM model72 for the lower mantle. Combining the thermoelastic properties20,46,47 of these three major minerals with our elastic data for LS-(Mg0.5Fe0.5)(Si0.5Fe0.5)O3 and (Mg0.5Fe0.5)(Si0.5Al0.5)O3 bridgmanite, we quantify the dependences of velocity and density anomalies on the amount of Fe3+-rich Bdg by substituting a certain proportion of Fe3+-free Bdg with (Mg0.5Fe0.5)(Si0.5Fe0.5)O3 bridgmanite. Compared to the pyrolitic composition, the modeling chemical assemblage has identical mineral fractions (15% ferropericlase + 78% Bdg + 7% CaPv) in which a portion of Fe2+-bearing Bdg was substituted by (Mg0.5Fe0.5)(Si0.5Fe0.5)O3 or (Mg0.5Fe0.5)(Si0.5Fe0.4Al0.1)O3 Bdg. In other words, the ferropericlase and Ca-perovskite contents are fixed to 15% and 7%, respectively. We also explore the effect of Fe2+ content in the assemblage (noted by the Fe2+ content in Fp, Fe2+Fp) on modeling results because the incorporation of Fe2+ into Fp and Bdg decreases their velocities to some extent46,47. The Fe–Mg partition coefficient between Fp and Bdg73 is used to constrain their Fe2+ contents. The modeled ﻿aggregate with enrichment of Fe3+-rich Bdg is composed of 15% Mg1-xFexO ferropericlase, 7% CaSiO3 Ca-perovskite, Z% (Mg0.5Fe0.5)(Si0.5Fe0.5)O3 or (Mg0.5Fe0.5)(Si0.5Fe0.4Al0.1)O3 bridgmanite, and (78-Z)% Mg1-yFeySiO3 bridgmanite.

The elastic moduli and densities of the aggregate are calculated using:

$$\rho = \mathop {\sum}\nolimits_i {f_i\rho _i}$$
(8)
$$M = \frac{1}{2}\left[ {\mathop {\sum }\limits_i f_iM_i + \left( {\mathop {\sum }\limits_i f_iM_i^{ - 1}} \right)^{ - 1}} \right]$$
(9)

where ρi, Mi, and fi are the density, bulk modulus (KS) or shear modulus (G), and the fraction of the ith mineral, respectively. Similarly, the compressional and shear velocities (VP and VS) were derived from $$V_P = \sqrt {(Ks + \frac{4}{3}G)/\rho }$$ and $$V_S = \sqrt {G/\rho }$$, and hence the velocity and density anomalies relative to the pyrolitic lower mantle are estimated with the consideration of temperature anomaly.

### Geodynamic models

We performed thermochemical calculations to study the dynamics of iron-rich materials in the lowermost mantle. The numerical simulations were conducted by solving the nondimensional equations of conservation of mass, momentum, and energy under the Boussinesq approximation. The intrinsic density anomaly is represented by the buoyancy number B, which is defined as the ratio between the intrinsic (compositional) density anomaly and the density anomaly caused by thermal expansion, B = Δρ/(ραΔT), where Δρ is the intrinsic density anomaly for the iron-rich materials compared to the background mantle. We used α = 1 × 10−5 K−1 and ΔT = 2500 K in this study.

The whole-mantle dynamics is simulated in a 2D Cartesian box with an aspect ratio of 3:1. The model domain contains 1536 and 512 elements in the horizontal and vertical directions, respectively. Models are basally heated, with the top and bottom having a fixed temperature at T = 0 and T = 1, respectively. The top and bottom boundaries are both free-flip and the side boundaries are reflective. The viscosity is determined by η = η0exp[0.5−T], where η0 is a viscosity pre-factor, and A is the activation energy. Here, η0 is 1.0 and 30.0 for the upper mantle and the lower mantle, respectively, and A = 9.21 which leads to the viscosity changing four orders of magnitude as temperature increases from 0 to 1. Initially, the whole mantle was assumed to be hot with a temperature of T = 0.72 (or 1800 K) everywhere, and we introduced a global layer of iron-rich materials in the lowermost 300 km of the mantle.

We performed four cases. Case 1 is the reference case in which the iron-rich materials are 1.2% intrinsically denser (with a buoyancy number of B = 0.48) than the background mantle materials and the Rayleigh number, which controls the vigor of mantle convection, is Ra = 1 × 107. Cases 2 and 3 have a Rayleigh number of Ra = 1 × 106 and Ra = 1 × 108, respectively, while other parameters are the same as case 1. In case 4, the iron-rich materials are 1.5% intrinsically denser (with a buoyancy number of B = 0.6) than the background mantle materials, and other parameters are the same as case 1.

## Data availability

The data are available in the main text, the supplementary materials, and from ﻿the corresponding authors.

## Code availability

The open-source Quantum Espresso package used in this study is available at https://www.quantum-espresso.org/.

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## Acknowledgements

This work is supported by the Strategic Priority Research Program (B) of the Chinese Academy of Sciences (XDB41000000 and XDB18000000), Natural Science Foundation of China (41925017 and 41721002), and the Fundamental Research Funds for the Central Universities (WK2080000144). M.M.L. is supported by National Science Foundation (NSF) grants EAR-1849949 and EAR-1855624. S.M.D. acknowledges support from the new faculty startup funding of Michigan State University and NSF EAR-1664332. J. Li acknowledges support from NSF EAR2031149 and NASA NNX15AG54G. Some computations were conducted in the Supercomputing Center of the University of Science and Technology of China.

## Author information

Authors

### Contributions

W.Z.W. and J.C.L. conceived and designed this project. W.Z.W. performed the theoretical calculations. J.C.L., F.Z., S.M.D., and J.L. performed the experiments, M.M.L. conducted the geodynamic simulations. W.Z.W., J.C.L., and Z.F. wrote the paper, and all authors contributed to the discussion of the results and revision of the paper.

### Corresponding authors

Correspondence to Wenzhong Wang, Jiachao Liu or Zhongqing Wu.

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Wang, W., Liu, J., Zhu, F. et al. Formation of large low shear velocity provinces through the decomposition of oxidized mantle. Nat Commun 12, 1911 (2021). https://doi.org/10.1038/s41467-021-22185-1

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• DOI: https://doi.org/10.1038/s41467-021-22185-1