Reverse chemistry of iron under high pressure and the distribution of elements in the deep Earth


 We demonstrate a remarkable change of chemical trend of iron under high pressure that is of great importance for understanding the distribution of elements in the Earth’s mantle and core. Using a massive-scale first principles study, we show that while reacting with p-block elements under increasing pressure from ambient to that of Erath’s core, iron tends to reverse its chemical nature, changing from an electron donor (reductant) to an electron acceptor, and oxidizes p-block elements. Such reverse chemistry significantly impacts the stoichiometries, bond types and strengths, structures and properties of iron compounds under deep planetary conditions, making many p-block elements that are conventionally labeled lithophile or chalcophile to highly siderophile. The chemical binding strengths with iron show an inverse correlation with the depletion of p-block elements in silicate Earth. Furthermore, silicon shows a distinct anomaly in its bonding to iron, which suggests silicon may readily be incorporated into Earth’s core.

many p-block elements that are conventionally labeled lithophile or chalcophile to highly siderophile. The chemical binding strengths with iron show an inverse correlation with the depletion of p-block elements in silicate Earth. Furthermore, silicon shows a distinct anomaly in its bonding to iron, which suggests silicon may readily be incorporated into Earth's core.
The distribution and abundance of both major and trace elements in the Earth's interior provide a record of its formation and evolution 1,2 . An understanding of this record demands knowledge of the chemical affinity of the elements and their compounds under the high-pressure conditions of Earth's interior. For many years, our understanding of such affinities has been predominantly biased by low-pressure observations that are of dubious applicability to Earth's deep mantle and core 3 . Many trace elements are found to have greatly reduced concentrations on Earth relative to their solar abundance 4,5 . This is usually explained in terms of either the escape of elements to space due to volatility during the high-energy conditions of terrestrial accretion 3 , or the incorporation into the Earth's core 6 . The core sequestration model relies on the reactivity of trace elements with Fe (and Ni) under high pressure, which is problematic to assess due to the difficulty of experimentally achieving terrestrial core pressures (135-367 GPa).
Thanks to improvements in computational power and methods, the high-pressure chemistry of Fe has become accessible, leading to the discovery of a number of new Fe compounds with trace elements that supports the argument that they are incorporated in the core. For example, recent work showed that iron may actually bind strongly with xenon to form an Fe 3 Xe compound at the pressures of Earth's core, suggesting that core sequestration is the cause of the 'missing xenon paradox' 7,8 . A similar mechanism was suggested for the depletion of iodine in Earth 9 , although the volatility of the iodine renders this explanation ambiguous. The reactions of Fe with major elements such as O also become quite unusual at very high pressure. As revealed by both computer simulation and diamond anvil cell (DAC) experiments, iron can form an oxygen-rich FeO 2 compound at the pressures of Earth's lower mantle, even if it remains in the low oxidation state of +2 [10][11][12] . We show here that these striking phenomena are all related to dramatic changes in 'iron chemistry' under high-pressure. The broad-ranging chemical trends of iron can only be revealed by a large-scale study of iron reactivity across the periodic table, a task that cannot be performed experimentally with reasonable resources and time.
Many recent studies show that first principles structure predictions are sufficiently advanced that enthalpies of compound formation at high pressure can be accurately calculated and the nature of the chemical bond elucidated [7][8][9][12][13][14][15][16][17] . Using this approach, we have systematically explored the bonding of iron with p-block elements in the periodic table. High pressure greatly enhances bonding to iron for many p-block elements that are conventionally labeled as lithophile or chalcophile 1,18 , making them highly siderophile. However, the depletion of the p-block elements in silicate Earth correlates inversely with Fe binding strength. This striking result suggests that although the Earth's core can host large quantities of the p elements, it is not the cause of their depletion. Instead, cosmochemical accretion models that call on elemental loss by volatility during high-energy conditions of terrestrial accretion may be more relevant 19 . Furthermore, silicon shows a distinct anomaly in its bonding to iron, such that it becomes one of the strongest under high pressure, which suggests silicon may readily be incorporated into Earth's core, corroborating recent perspectives on the composition of Earth's core based on sound speed measurements, experimental petrology and seismology 20,21 .

Results and discussions
We conducted massive-scale first-principles simulations studying the reactivity of Fe with most of the p-block elements and its dependence with increasing pressure. For each element (X), the structures of a series of compositions (Fe n X m ) are searched by Particle Swarm Optimization (PSO) algorithm and density functional calculations.
The selection of elements includes three major element S (721 K; 50% condensation temperature of 664 K), Si (2628 K; 1310 K) and P (556 K; 1229 K) and a suite of geochemical tracers Ge (3103 K; 883 K), As (886 K; 1065 K), Se (958 K; 697 K), Sn (2543 K; 704 K), Sb (2023 K; 979 K), and Te (1263 K; 709 K) which are critical for understanding planetary accretion and core formation. (The temperatures in parentheses give the 1-bar boiling point and the 50% equilibrium condensation temperature at 10 -4 bar total pressure for solar system abundances of each element, respectively, as a guide to their volatility and reactivity in the condensing solar nebula.) Condensation temperatures are useful to consider when assessing if a particular element is deficient in the silicate mantle relative to chondrites because it suffered volatilization during planetary formation; it is a major task to explore whether such elemental deficiencies relate to elements being "hidden" in the metallic core.
The stability and its relation to element abundance in Earth interior Our calculations reveal that pressure can dramatically increase the stability of iron compounds formed with most p-block elements as evidenced by a significant decrease of formation enthalpy ( Fig. 1). At ambient conditions, although some 2p elements (e.g. C, N, O) can form stable compounds with iron with a ΔH f of approximately -0.5 eV/atom, a subset of 3p (e.g. Si, P, S; Fe -Al compounds are excepted, and will be discussed separately) and 4p (e.g. Ge, As, Se) elements bind only loosely with iron.
This general trend of reactivity is markedly changed upon increasing pressure: most of these elements can form stable compounds with iron with a ΔH f of at least -1eV/atom. For example, Fe and Te are not likely to form a stable compound (with ΔH f = -0.2 eV/atom) at 0 GPa. However, ΔH f decreases by 1 eV/atom under high pressure, making the compound FeTe as stable as FeS at 300 GPa, a pressure similar to that in Earth's inner core of 367 GPa).
This pressure-enhanced Fe reactivity may promote the incorporation of many p-block elements, especially the heavier ones that were previously disregarded due to their weak or absent binding with Fe, into Earth's core. Like the previous works, our results first appear to support the model of core sequestration, i.e. the depletion of certain elements in the silicate Earth is due to their incorporation into Earth's core. This inverse correlation clearly shows that reaction with Fe in Earth's core is unlikely to be the cause of the depletion of trace p-block elements in the silicate Earth, although such reactions may become exceedingly strong under terrestrial core conditions. One reason for the inverse correlations is that the volatility of an element (quantified by its condensation temperature) correlates inversely with its binding strength with Fe, i.e. the higher the volatility the weaker the binding with Fe ( Supplementary Fig. 1). Another factor is that binding of an element with Fe may prevent its evaporation in primordial Earth. Furthermore, our results are in accordance with the fact that moderately siderophile elements (Ni, Co, W etc.) are depleted in silicate Earth whereas the highly siderophile elements (Re, Os, Ir, Ru etc.) are not 22 . The charge redistribution mainly happens between Fe 3d and X np orbitals ( Supplementary Fig. 2), which is the natural result of the energy shifts of the 3d and the np bands ( Supplementary Fig. 3). The Fe 3d bands become lower in energy because they have a smaller radius and are therefore less prone to change under increasing pressure (Supplementary Fig. 4).  (Figs. 3a and 3b). However, at 150 and 300 GPa, iron-rich compounds adopt densely-packed structures, including Fe 2 I adopting Ni 2 In structure (P6 3 /mmc) (Fig. 3c) and Fe 2 I adopting Cu 3 Au structure (Fm3m) (Fig 3d). Correspondingly, the coordination number of iodine increases substantially, to 6 in Fe 2 I and 12 in Fe 3 I, and the lone pairs disappear, in good accordance with the CTR under pressure. Similar structure evolution is also found in other compounds containing lone pair electrons at ambient pressure, including Fe-As and Fe-Te compounds. (See Fig. 3e for ambient phase of both FeAs 2 and FeTe 2 , Figs. 3f and 3g and for high-pressure phases of FeAs and FeTe, respectively.) In contrast, no lone pair is found in the low-pressure structures of FeX where X is a group 13 or 14 element. Furthermore, some compounds contain Fe -Fe bonds in the low-pressure structure that simply vanish as pressure increases (Fig. 3h). For example, FeSn and FeGe are stable in a highly symmetric P6/mmm structure that contains Fe -Fe inter-metallic bonds (Fig 3h). While increasing pressure induces the large charge transfer to iron, Fe -Fe bonds disappear and the compounds become more ionic. At last, it is remarkable that many FeX compounds adopt the simple CsCl structure under high pressure, due to the large charge transfer to Fe. At pressures above 150 GPa, FeSn, FeGe and FeSi transform into the CsCl structure (Pm3m) (Fig 3i) which is a common structure for AB type ionic compounds when the radius of A + and Bions are similar, as stated by Pauling's first rule. Complete structures and structural parameters are shown in Supplementary Fig. 5 Supplementary Fig. 6. This distinctive anomaly is due to the fact that the unoccupied d shells are significantly higher in energy for Si (and Al) and cannot host electrons, in contrast to heavier p-block elements, leaving large charge transfer from Si (and Al) to Fe, especially under high pressure. At 300 GPa, the charge on iron in FeSi is as low as -2e, indicating the very strong ionic nature of the compound. Indeed, the ELF values between Fe and Si decrease dramatically under pressure (Fig. 4a -4b). Consequently, Fe-Si bonding persistently strengthens at increasing pressure. At 0 GPa, the Fe-Si bond strength is similar to Fe-S and Fe-P, all much weaker than Fe-O (Fig. 4c). Under increasing pressure, the Fe-Si binding strengthens most significantly and even surpasses Fe-O at 250 GPa, implying that Si becomes highly siderophile at the pressure of Earth's core 25 . The lower density of FeSi ( Supplementary Fig. 7) under core pressures can also explain the low core density as revealed by the seismic wave measurements.
Ca/Al and Mg/Si ratios are expected to exist in chondritic relative proportions in the silicate Earth, but both ratios are higher than chondritic in the shallower, accessible Earth. This suggests that either volatility controlled fractionation of Mg/Si or the presence of an Al or Si-rich domain in Earth's deep interior [26][27][28] . Si and Al enrichment in the Earth's core may explain the higher-than-chondritic ratios in the shallower, accessible Earth.

Summary
We conducted a massive-scale first principles study on the reactivity of Fe with most of the p-block elements under pressures ranging from ambient to that of the center of the Earth. For each element X, the stability of Fe-X compounds with various compositions under different pressures are studied after searching the most stable structures using PSO algorithm and DFT calculations. While piecing together the results of all the elements, we found a general and solid trend of Fe chemistry, namely, under increasing pressure, Fe tends to become more electron negative and may revert its chemical from a reductant to an oxidant while reacting with many p-block elements. This chemical trend of Fe might have profound effect to the element distribution in Earth interior because it renders that pressure can significantly enhance the binding strength of these elements with Fe. However, while comparing the Fe binding strengths with the depletion of the element in silicate Earth, we found a distinct inverse correlation, which strongly supports the volatile depletion mechanism.
On the other hand, the revealed strong binding with Fe under core condition provides a strong chemical driving force for the incorporation of light p elements in Earth's core. Among them, Si shows an anomaly of exceedingly strong binding with Fe, suggesting it a key component that lowers the density of the Earth's core.
We would like to emphasize that this work does not aim to develop a comprehensive thermodynamic model of Earth's core for which many other important factors need to be included-but is instead focused on identifying new chemistries for Fe at terrestrial core conditions. For example, Earth's core may contain a considerable budget of light elements such as S, O and H that might modify trace element affinities for the core 21 . However, since the Earth's core consists of predominantly Fe (and Ni) that will largely lower the activity of the light elements, the inclusion of these light elements is unlikely to overturn the chemistry of p-block elements in the core that has been examined here. Furthermore, our calculations are performed for crystalline compounds, and are therefore more directly related to Earth's solid inner core. On the other hand, the general trend that the chemical binding with Fe becomes much stronger under pressure can be equally applied to the liquid outer core, because the chemical driving force is irrelevant to the state of the matter. Furthermore, the change of the Fe redox propensity under increasing pressure can also help to understand and perceive the redox state of Earth mantle and its evolution during the accretion of the Earth and the segregation of the core. 29

Methods
Structure searches under pressure. We performed structure predictions through a global minimization of free energy surfaces based on the CALYPSO (Crystal structure AnaLYsis by Particle Swarm Optimization) methodology as implemented in CALYPSO code 30,31 . We searched the structures of stoichiometric