Prediction of crystal structures and motifs in the Fe-Mg-O system at Earth's core pressures
Renhai Wang, Yang Sun, Renata M. Wentzcovitch, Feng Zheng, Yimei Fang, Shunqing Wu, Zijing Lin, Cai-Zhuang Wang, Kai-Ming Ho
PPrediction of crystal structures and motifs in the Fe-Mg-O system at Earth’s corepressures
Renhai Wang,
1, 2
Yang Sun, ∗ Renata M. Wentzcovitch,
3, 4, 5, † Feng Zheng, Yimei Fang, Shunqing Wu, Zijing Lin, Cai-Zhuang Wang, and Kai-Ming Ho Department of Physics, University of Science and Technology of China, Hefei 230026, China Department of Physics, Iowa State University, Ames, Iowa 50011, USA Department of Applied Physics and Applied Mathematics,Columbia University, New York, NY, 10027, USA Department of Earth and Environmental Sciences,Columbia University, New York, NY, 10027, USA Lamont–Doherty Earth Observatory, Columbia University, Palisades, NY, 10964, USA Department of Physics, Xiamen University, Xiamen 361005, China (Dated: Feb. 4, 2021)Fe, Mg, and O are among the most abundant elements in terrestrial planets. While the behaviorof the Fe-O, Mg-O, and Fe-Mg binary systems under pressure have been investigated, there are stillvery few studies of the Fe-Mg-O ternary system at relevant Earth’s core and super-Earth’s mantlepressures. Here, we use the adaptive genetic algorithm (AGA) to study ternary Fe x Mg y O z phasesin a wide range of stoichiometries at 200 GPa and 350 GPa. We discovered three dynamicallystable phases with stoichiometries FeMg O , Fe MgO , and FeMg O with lower enthalpy than anyknown combination of Fe-Mg-O high-pressure compounds at 350 GPa. With the discovery of thesephases, we construct the Fe-Mg-O ternary convex hull. We further clarify the composition- andpressure-dependence of structural motifs with the analysis of the AGA-found stable and metastablestructures. Analysis of binary and ternary stable phases suggest that O, Mg, or both could stabilizea BCC iron alloy at inner core pressures. I. INTRODUCTION
O, Fe, Si, Mg, Al, and Ca (CMAS+F) are the mostabundant elements in terrestrial planets [1]. Among theseplanets, Earth provides essential general information, yetit is incompletely deciphered. All CMAS+F elements arelithophile (rock-loving) elements and are present in theEarth’s rocky mantle and crust. Fe is the predominantelement in the core and is a siderophile (metal-loving)element as well. Based on current knowledge, this clas-sification is believed to be valid in the pressure and tem-perature (PT) range achieved in Earth’s interior. Seis-mology and high-pressure data on iron shows that theEarth’s core is ∼ ∼ ∼ ∗ Email: [email protected] † Email: [email protected] the most likely light element candidates in the core areSi, and O. O is considered a required element today, aview that has evolved within the last decade [21–24]. Thevolatile elements S, C, and H are also regarded as likelycandidates, but the abundances of C and H on Earth arestill largely unconstrained. Mg, Al, and Ca have beenbranded lithophile elements up to core pressures. Butthe recent computational discovery of Mg-Fe compoundsup to inner core pressures [25] suggests the possibilityof Mg turning siderophile and its presence in the core.The formation of Fe-O [16] and Fe-Si [15] compoundswith variable stoichiometry have been investigated usingmaterials discovery methods. The theoretical predictionof pyrite-type FeO [16] and its experimental confirma-tion [26, 27] has been one of the greatest successes ofthis approach, which rarely explores the possibility ofternary compounds [17]. Given the present understand-ing that O is a required element in the outer core andshould also exist in the inner core, we explore the pos-sible formation of Fe-Mg-O compounds at typical corepressures of ∼
350 GPa. The investigation of solid com-pounds provides the most critical information. Light ele-ments must be present in both solid and liquid phases butmore abundantly in the liquid phase. It is energeticallymore costly to accommodate these elements in the solidphase, a geochemical definition of incompatible elements.Therefore, the discovery of thermodynamically stable Fe-Mg-O solids is essential to investigate Mg’s presence inthe core.Besides being essential for addressing Mg’s presencein the Earth’s core, the present study of Fe-Mg-O solidshas significant ramifications for the mantle of terrestrial a r X i v : . [ c ond - m a t . m t r l - s c i ] F e b planets larger than Earth whose interiors can reach muchhigher pressures and temperatures. The B1-type iso-morphous alloy (Mg − x Fe x )O, ferropericlase (x < > ∼
135 GPa and ∼ ∼ ∼ (cid:76) terrestrial planet[28], raises the possibility of other compounds and al-loy structures with other compositions. The existence ofother stable ternary phases under pressure may inducedecomposition and recombination reactions between Fe-Mg-O, Fe-O, Mg-O, and Fe-Mg compounds under pres-sure, similar to what has been observed in the Si-Mg-Osystem [17, 18]. Therefore, the current research can alsoprovide the first glimpses on the essential (Mg − x Fe x )Oalloy behavior in these planets.This paper is organized as follows. In the next section,we describe the computational method used in this work.Sec. III presents the crystal structure search results, theternary convex hull, and the predominant structural mo-tifs in low enthalpy structures. Section IV discusses somepotential geophysical implications of these results. Con-clusions are present in Section V. II. METHODS
Crystal structures of Fe-Mg-O at high pressurewere investigated using the adaptive genetic algorithm(AGA)[17, 29]. This method integrates auxiliary inter-atomic potentials and ab initio calculations adaptively.The auxiliary interatomic potentials accelerate crystalstructure searches in the genetic algorithm (GA) loop.At the same time, ab initio calculations are used to adaptthe potentials after several GA generations to ensure ac-curacy. The structure searches were only constrained bythe chemical composition, without any assumption on theBravais lattice type, symmetry, atomic basis, or unit celldimensions. In our AGA searches, the enthalpy was usedas the selection criteria for optimizing the candidate pool.The candidate structure pool size in GA search is 128.At each GA generation, 32 new structures are generatedfrom the parent structure pool via a mating proceduredescribed in [30]. The structures in the pool were up-dated by keeping the lowest-energy 128 structures. Thestructure search with a given auxiliary interatomic po-tential sustained 600 consecutive GA generations. Then,16 structures from the GA search were randomly selectedfor ab initio calculations to re-adjust the interatomic po-tential parameters for the next round of the GA search.This sequence of steps was repeated 40 times. In theAGA search in the Fe-Mg-O system, interatomic poten-tials based on the embedded-atom method (EAM) [31]were chosen as the auxiliary classical potential. In EAM, the total energy of an N-atom system is described by E total = 12 N (cid:88) i,j ( i (cid:54) = j ) ϕ ( r ij ) + (cid:88) i F i ( n i ) , (1)where ϕ ( r ij ) is the pair term for atoms i and j at a dis-tance r ij . F i ( n i ) is the embedded term with electrondensity term n i = (cid:80) j (cid:54) = i ρ j ( r ij ) at the site occupied byatom i . The fitting parameters in the EAM formula arechosen as follows: The parameters for Fe-Fe and Mg-Mginteractions were taken from the literature [32]. Otherpair interactions (O-O, Fe-Mg, Fe-O and Mg-O) weremodeled with the Morse function, ϕ ( r ij ) = D (cid:104) e − α ( r ij − r ) − e − α ( r ij − r ) (cid:105) , (2)where D , α , r are fitting parameters. The density func-tion for O atoms are modeled by an exponentially decay-ing function, ρ ( r ij ) = αe x p [ − β ( r ij − r )] , (3)where α and β are fitting parameters. The form proposedby Benerjea and Smith [33] was used as the embeddingfunction with fitting parameters F , γ as F ( n ) = F [1 − γ In n ] n γ . (4)For Fe and Mg, the parameters of the density func-tion and embedding function were taken from ref.[32] aswell. In the AGA scheme[17], the potential parameterswere adjusted adaptively by fitting to the ab initio en-ergies, forces, and stresses of selected structures. Thefitting process was performed using the force-matchingmethod with a stochastic simulated annealing algorithmimplemented in the POTFIT code[34, 35]. Ab initio calculations were carried out using the pro-jector augmented wave (PAW) method[36] within densityfunctional theory (DFT) as implemented in the VASPcode [37, 38]. The exchange and correlation energy aretreated without the spin-polarized generalized gradientapproximation (GGA) and parameterized by the Perdew-Burke-Ernzerhof formula (PBE) [39]. A plane-wave ba-sis was used with a kinetic energy cutoff of 520 eV,and the convergence criterion for the total energy wasset to 10 − eV. Monkhorst-Pack’s sampling scheme [40]was adopted for Brillouin zone sampling with a k-pointgrid of 2 π × . − , and the unit cell lattice vectors(both the unit cell shape and size) are fully relaxed underfixed pressure (200 GPa and 350 GPa) together with theatomic coordinates until the force on each atom is lessthan 0.01 eV/˚A. The phonon dispersions were computedwith density functional perturbation theory (DFPT) im-plemented in the VASP code and the Phonopy soft-ware [41]. The formation enthalpy (H f ) of compoundFe x Mg y O z was calculated as H f = H (cid:0) Fe x Mg y O z (cid:1) − xH ( F e ) − yH ( M g ) − zH ( O ) x + y + z , (5) FIG. 1. (a) AGA search results for the Fe-Mg-O system at 350 GPa. The dots represent searched ternary compositions.The color bar corresponds to the relative enthalpy above the convex hull. The ground-states ( H d = 0) on the convex hull areconnected. The new phases are indicated by the text. 124, 134, 214 and 113 represents FeMg O , FeMg O , Fe MgO andFeMgO , respectively. (b) Stability range of discovered ternary ground states at T = 0 K . The gray bars indicates the pressurerange of decomposition. where H (cid:0) Fe x Mg y O z (cid:1) is the total enthalpy of theFe x Mg y O z alloy. H ( F e ), H ( M g ) and H ( O ) are theenthalpy of the ground state of Fe, Mg, and O at corre-sponding pressures, i.e., hcp-Fe, bcc-Mg, and ζ -O , re-spectively. III. RESULTS AND DISCUSSIONA. AGA search for ternary Fe-Mg-O phases
In Fig. 1(a) we present the AGA results of Fe-Mg-O at 350 GPa. For the sake of simplicity, all chem-ical formulae are expressed as Fe/Mg/O reduced ra-tios. For example, 123 represents the compound withFeMg O . During the structural search, we select arange of different stoichiometries surrounding 111 com-position (i.e., 211, 121, 112, 311, 131, 113, 411, 141, 114,221, 122, 212, 331, 133, 313, 441, 144, 414, 332, 233,323, 321, 312, 123, 132, 231, 213, 421, 412, 124, 142,241, 214, 431, 413, 134, 143, 341 and 314) with 2 or4 formula units to perform the AGA search (up to 32atoms per primitive cell). After the AGA search, weuse the following method to determine the stability ofcompounds. For a ternary compound A x B y C z , we selectthree existing compounds A x B y C z , A x B y C z , and A x B y C z on the diagram; these can also be elementaryor binary end-members. If A x B y C z can be written as a × A x B y C z + b × A x B y C z + c × A x B y C z with a ≥ b ≥ c ≥
0, we compute its rela-tive enthalpy ∆ H = H ( A x B y C z )– a × H ( A x B y C z )– b × H ( A x B y C z )– c × H ( A x B y C z ). If ∆ H ≤ A x B y C z is determined as an energetic ground state. Theenergetic ground states form the convex hull as shown inFig. 1(a). H d is introduced as the enthalpy above theconvex hull to represent the relative stability on the phasediagram. By definition, all the ground-state phases have H d = 0.The AGA search found three new ternary groundstate compounds at 350 GPa: FeMg O , Fe MgO , andFeMg O . They define the current Fe-Mg-O ternaryphase diagram. The stability of these phases from 200GPa and 350 GPa is shown in Fig. 1(b). This stabilitypressure range is computed by considering the relativestability of these phases against decomposition into allend-members (see Supplementary Fig. 1 for the stabilityrange of all ground-state phases). We will discuss theconstruction of the phase diagram in the next section.We also identify low-enthalpy metastable structures suchas FeMgO with enthalpy very close to the convex hull( H d = 18 meV/atom). Here we first analyze these newground states and low-enthalpy structures.Figure 2 shows the atomic structure, phonon dis-persion, and electronic density of states for tetragonalFeMg O with space group I-42d . Fe and Mg atoms arecoordinated with eight oxygen atoms to form a similarMO (M for metal) polyhedra. Unlike a typical cubicpolyhedron, this MO consists only of triangular faces.These triangular faces form pentagonal caps and are sim-ilar to the Frank-Kasper polyhedra [42]. The Fe- and Mg-centered MO8 polyhedra pack in various edge- andface-sharing arrangements. This structure is the same asthe I-42d -type Mg SiO found previously [17, 43]. Asshown in Fig. 1(b), this phase becomes the ground stateat 349 GPa. Below this pressure, it decomposes into MgOand FeO . As shown in Fig. 2(b), there are no imaginaryphonon mode frequencies, which confirms this phase isdynamically stable. The electronic density of state in FIG. 2. (a) Atomic structure of
I-42d
FeMg O and Fe andMg coordination polyhedra. Blue is Fe, green is Mg and redis O. Red dashed lines indicate a pentagonal cap; (b) phonondispersion; (c) electronic density of states. Fig. 2(c) shows a metallic state with somewhat localizedFe and O states near the Fermi level.Figure 3 shows the atomic structure, phonon dis-persion, and electronic density of states for monoclinicFe MgO with space group Cc . By inspecting the struc-ture, we identify the same type of MgO polyhedra foundin I-42d
FeMg O . However, the Fe-O polyhedra aremore complicated. It contains two polyhedral types,one six-fold and one seven-fold coordinated as shown inFig. 3(a). The FeO is a highly distorted octahedron.The FeO also shows the pentagonal cap similar to theMO polyhedron found in I-42d
FeMg O . As shown inFig. 1(b), this phase’s stability pressure range against thedecomposition into MgO and Fe O starts at 325GPa.Phonon calculations confirm its dynamic stability. Theelectronic density of states also indicates this phase ismetallic in Fig. 3(c).The FeMg O Cmmm structure in Fig. 4 shows Fe-Oand Mg-O octahedral building blocks. Visually it is sim-ilar to ferropericlase (Fe − x Mg x )O, which has a NaCl-type (B1) structure. However, unlike the cubic struc-ture and random Fe/Mg cation site occupancies of fer-ropericlase, FeMg O is an orthorhombic structure withordered Fe/Mg site occupancies. The octahedra in theFeMg O structure are Jahn-Teller distorted because ofthe orthorhombic symmetry. This phase becomes stableagainst decomposition into FeO and MgO at ∼
228 GPa.Phonon calculations in Fig. 4(b) also confirm its dynami-cal stability. Unlike the metallic Fe MgO and FeMg O phases, FeMg O Cmmm is a semiconductor.Besides the ternary ground states, we also analyzea metastable FeMgO Immm structure with H d = 18meV/atom. This enthalpy difference is so small thatthe compound may become stable at high tempera- FIG. 3. (a) Atomic structure Cc Fe MgO and Fe and Mgcoordination polyhedra. Blue is Fe, green is Mg and red isO. Red dashed lines indicate a pentagonal cap; (b) phonondispersion; (c) electronic density of states.FIG. 4. (a) Atomic structure of Cmmm
FeMg O and Feand Mg coordination polyhedral. Blue is Fe, green is Mg,and red is O; (b) phonon dispersion; (c) electronic density ofstates. tures. Structural analysis of FeMgO Immm in Fig. 5shows an interesting combination of various polyhedra.Iron shows three different oxygen coordination pulyhe-dra FeO , FeO and FeO . The FeO is an octahedron.The FeO is a trigonal prism with an extra rectangu-lar face capping neighbor. The FeO is a cube. MgOshows one coordination polyhedron type, MgO , not acube but a triangular prism with two rectangular facecapping oxygens. Such a combination of octahedra andprisms is similar to the building blocks in the complex FIG. 5. (a) Atomic structure of metastable
Immm
FeMgO and Fe and Mg coordination polyhedra. Blue is Fe, green isMg and red is O. Red dashed lines indicate the trigonal prism;(b) phonon dispersion; (c) electronic density of states. Fe O polytypes [44]. The appearance of cubic poly-hedron is consistent with the observation of the CsCl-type (B2) structure of FeO at Earth’s core conditions[11]. This FeMgO Immm structure shows an intermedi-ate packing between NaCl-type FeO/MgO phase to theCsCl-type FeO/MgO phases. This phase is dynamicallystable and metallic, as shown by the phonon dispersionand the electronic density of states in Fig. 5.
B. Construction of the Fe-Mg-O ternary convexhull
In this section, we discuss the construction of theternary phase diagram and convex hull. In a binary sys- tem, the compositional space is one-dimensional so thatthe convex hull is a curve connecting the formation en-thalpies of ground-state phases. In a ternary system,the compositional space is two-dimensional, and the con-vex hull consists of surface segments connecting the for-mation enthalpies of three stable phases, as shown inFig. 1. In a discrete compositional space, these surfacesegments are triangles. Any new structure having for-mation enthalpy below this convex hull surface will bea new ground state. The convex hull surface needs tobe reconstructed after the discovery of any new stablephase.For binary references at 350 GPa, the ground-statephases of Fe-O, Fe-Mg, and Mg-O have been investigatedin Refs. [16], [25] and [45], respectively (see Supplemen-tary Fig. 2 for their crystal structures). Because thesecrystal structure searches have already covered the cur-rent study’s pressure range, we do not perform new AGAsearches for the binary phases. Still, we re-calculate theenergetics of the previously found crystal structures.
Abinitio calculations confirm these reported relative phasestabilities of Fe-O [16], Fe-Mg [25], and Mg-O [45]. Byexploring an experimental database [46], we find twopreviously reported MgFe O stoichiometric compounds[47,48]. However, our calculations indicate these phasesare metastable at Earth’s core pressures. Based on theseground-state binary phases, we established the Fe-Mg-O ternary system’s convex-hull shown in Fig. 6. At 200GPa, all the AGA searched ternary compounds have rel-atively higher enthalpy than the elementary or binaryground-state references. Therefore no Fe-Mg-O stoichio-metric phase can be a ternary ground state at 200 GPa.At 350 GPa three ternary phases become stable groundstates. Detailed energetics and crystallographic informa-tion on these ground-state phases is given in Supplemen-tary Tables S1, Table S2 and Table S3. FIG. 6. Ground-state Fe-Mg-O phases and convex hull at (a) 200 GPa and (b) 350 GPa. The blue text refers to stable ternaryphases.
FIG. 7. Scatter plot of enthalpies above convex-hull (Hd) and volume for both stable and metastable Fe-Mg-O structuresfrom AGA search. The color bar in (a) and (b) represent total oxygen concentration as O % = n ( O ) n ( Fe )+ n ( Mg )+ n ( O ) × F e % = n ( Fe ) n ( Fe )+ n ( Mg ) × C. Analysis of structural motifs under pressure
Since Fig. 6 suggests a strong effect of pressure on thesephases’ stability, we now investigate how the structuralmotifs change under pressure. Because the current cal-culation does not include temperature effects on phaserelations and at finite temperatures, the ground statesmay differ. We now focus on the ground-state phasesand metastable phases with formation enthalpy within0.8 eV/atom ( ∼ − x Fe x )O, i.e. fer-ropericlase (x F e < x F e > O Cmmm at 350GPa shown in Fig. 4. Inspecting the higher energy rangein Fig. 7(a) and (c), one finds that oxygen-rich structuresgenerally have lower enthalpies than oxygen-poor struc-tures. The oxygen-rich structures mainly contain octahe-dral clusters, while the oxygen-poor structures can havea greater variety of motifs, including FCC, BCC, HCP-type clusters. This is mainly because Fe and Mg startto alloy to form closely packed motifs under unsaturatedoxygen conditions.At 350 GPa, structures with 50% oxygen concentra-tions still have the lowest formation enthalpy. A fewoxygen-rich phases become more stable and approach theconvex hull energetically compared to 200 GPa. BCC-type clusters start to appear in these oxygen-rich struc-tures at 350 GPa, indicating that the B2-type Fe-O clus-ters are favored at higher pressures over B1-type clustersat lower pressures. The situation with oxygen-poor struc-tures at 350 GPa is similar to the one at 200 GPa. Wenote that at both 200GPa and 350GPa, several motifs(”other” type) that cannot be classified into the currentsimple cluster templates appear. Some of them are due todistortions, while some indeed form more complex clus-ters, e.g., the ones in Fig. 2 and Fig. 3.
IV. GEOPHYSICAL IMPLICATIONS
Our findings on the Fe-Mg-O system at core pressuresappear to have some straightforward geophysical conse-quences. The Fe-rich side (right corner) of the ternaryphase diagram in Fig. 1 suggests that Fe Mg and Fe Ocan form a continuous isomorphic solid Fe (Mg − x O x )solution. Both end-members are BCC-like structuresat 350 GPa, as shown in Fig. 8. BCC-like Fe Mgand hcp (cid:15) -Fe are likely to inter-alloy and form a eu-tectic system, with two coexisting solid phases for somecomposition-temperature ranges. Small Mg concentra-tions might produce hcp-like Fe − x Mg x alloys, but aBCC-like Fe x Mg − x might precipitate and coexist be-yond a certain concentration threshold. The situationis very similar for the Fe O-Fe system. Therefore, theFe-Mg-O system might contain Mg and O dissolved sub-stitutionally in (cid:15) -Fe for small Mg and O concentrations,but beyond a certain concentration threshold BCC-likeFe x + y (Mg / − x O / − y ) might precipitate. BCC-Fecan be stabilized at inner core pressures by alloying withS [52, 53], and it has been argued, but not confirmed,that BCC iron could be stabilized at inner core con-ditions [54]. Therefore, the precipitation of BCC-likeFe x + y (Mg / − x O / − y ) for non-negligible amounts ofMg, O, or both is not a surprising conclusion.The ternary phases discovered in the O-rich side(left corner) of the phase diagram are relevant for themantle of some Super-Earths. The absence of stable ternary phases at pressures lower than 228 GPa sug-gests that stable phases involving all three elementsare solid-solutions of end-member phases with a smallconcentration of inter-alloying metals. For example,Fig. 7(a) shows that at 200 GPa, the low-energy struc-tures are dominated by structures with octahedral coor-dination, with more Mg than Fe, and approximately 50%O, i.e., ferropericlase or B1-type (Mg − x Fe x )O. At 350GPa, the oxygen-rich ternary phases FeMgO , Fe MgO ,FeMg O , and FeMg O emerge as ground states orlow-enthalpy phases, besides the B1-type phase. Oneof them, I-42d
FeMg O , has the same structure as I-42d Mg SiO , the stable silicate phase predicted toexist in the mantle of Super-Earths above 500 GPa[17, 43]. Here emerges the possibility of an I-42d -type Mg (Si − x Fe x )O phase, with Fe substitutional inthe Si site, or vice-versa, an unusual type of substitu-tion in the Earth’s mantle, unless as a coupled Mg-Si substitution. From the chemistry standpoint, thenewly found phases at 350 GPa can all be viewed ascombinations of binary end-members, e.g., FeMgO as(MgO)(FeO ), Fe MgO as (MgO)(Fe O ), FeMg O as(MgO) (FeO ), and FeMg O as (MgO) (FeO). Suchstable compositions suggest other stable stoichiometricphases might be found by exploring combinations ofsuch end-member compounds, as seen in the Mg-Si-Osystem, i.e., (MgO) n (SiO ) m phases [17, 43]. FurtherAGA searches aiming at these complex compositions areneeded to identify other possible ternary phases in theMg-Fe-O system. Finally, O’s greater intermixing withthe metallic elements at 350 GPa suggests that Mg andO abundances might be non-negligible in the Earth’s in-ner core. Also, core formation by Fe exsolution fromthe oxides might be a more complicated process duringSuper-Earths’ core formation, or O and Mg might bemore abundant light elements in Super-Earths’ cores. (a) Fe O, I4/ mmm (b) Fe Mg, I4/mmm
FIG. 8. Similar BCC-like Fe O and Fe Mg ground states at350GPa.
V. CONCLUSION
We use the AGA combined with ab initio calculationsto identify high-pressure structures in the Fe-Mg-O sys-tem at 0 K across a wide range of stoichiometries. Thisprocedure is a crucial preparatory stage for modeling thesystem at finite temperatures. At 350 GPa, we iden-tify mechanically stable phases with FeMg O , Fe MgO and FeMg O compositions and one low-enthalpy phasewith FeMgO composition. These discoveries lead to theconstruction of the ternary phase diagram and convexhull at 350 GPa. While we have not found any ground-state stoichiometric ternary compound at 200 GPa, themetastable phases’ analysis indicates that ferropericlase-or magnesiumw¨ustite-type phases with 50% oxygen arevery close to the convex hull. Oxygen-rich phases aregenerally closer to the convex hull than the oxygen-poorphases at all pressures. Motif analyses show octahedralclusters are energetically favored at both pressures andBCC-type clusters start to appear in oxygen-rich phasesat 350 GPa. In particular, the nature of iron-rich phases at 350 GPa indicates that Mg, O, or both simultaneouslycould stabilize a BCC-type iron alloy at inner-core pres-sures. VI. ACKNOWLEDGMENTS
This work was supported primarily by National ScienceFoundation awards EAR-1918134 and EAR-1918126 andthe Extreme Science and Engineering Discovery Environ-ment (XSEDE), which is supported by National ScienceFoundation grant number ACI-1548562. R.M.W. andY.S. also acknowledge partial support from the Depart-ment of Energy Theoretical Chemistry Program throughgrant DOE-DESC0019759. R.W. and Z.L. were sup-ported by the National Natural Science Foundation ofChina (11774324 & 12074362) and the SupercomputingCenter of USTC. Y.F., F.Z., and S.W. were supportedby the National Natural Science Foundation of China(11874307). [1] A. E. Doyle, E. D. Young, B. Klein, B. Zuckerman, andH. E. Schlichting, Science 366, 356 (2019).[2] K. Hirose, S. Labrosse, and J. Hernlund, Annu. Rev.Earth Planet. Sci. 41, 657 (2013).[3] F. Birch, J. Geophys. Res. 57, 227 (1952).[4] F. Birch, J. Geophys. Res. 69, 4377 (1964).[5] L. S. Dubrovinsky, S. K. Saxena, F. Tutti, S. Rekhi, andT. LeBehan, Phys. Rev. Lett. 84, 1720 (2000).[6] J. Shanker, B. P. Singh, and S. K. Srivastava, Phys. EarthPlanet. Inter. 147, 333 (2004).[7] A. Dewaele, P. Loubeyre, F. Occelli, M. Mezouar, P. I.Dorogokupets, and M. Torrent, Phys. Rev. Lett. 97, 29(2006).[8] Y. Kuwayama, G. Morard, Y. Nakajima, K. Hirose, A.Q. R. Baron, S. I. Kawaguchi, T. Tsuchiya, D. Ishikawa,N. Hirao, and Y. Ohishi, Phys. Rev. Lett. 124, 165701(2020).[9] G. Morard, D. Andrault, D. Antonangeli, and J. Bouchet,Comptes Rendus - Geosci. 346, 130 (2014).[10] D. Alf`e, M. J. Gillan, and G. D. Price, Earth Planet. Sci.Lett. 195, 91 (2002).[11] H. Ozawa, F. Takahashi, K. Hirose, Y. Ohishi, and N.Hirao, Science 334, 792 (2011).[12] S. Tateno, K. Hirose, Y. Ohishi, and Y. Tatsumi, Science330, 359 (2010).[13] M. J. Gillan, D. Alf`e, J. Brodholt, L. Voˇcadlo, and G. D.Price, Reports Prog. Phys. 69, 2365 (2006).[14] F. Zhang and A. R. Oganov, Geophys. Res. Lett. 37, n/a(2010).[15] G. L. Weerasinghe, R. J. Needs, and C. J. Pickard,Phys. Rev. B - Condens. Matter Mater. Phys. 84, 174110(2011).[16] G. L. Weerasinghe, C. J. Pickard, and R. J. Needs, J.Phys. Condens. Matter 27, 455501 (2015).[17] S. Q. Wu, M. Ji, C. Z. Wang, M. C. Nguyen, X. Zhao, K.Umemoto, R. M. Wentzcovitch, and K. M. Ho, J. Phys. Condens. Matter 26, 035402 (2014).[18] K. Umemoto and R. M. Wentzcovitch, Phys. Rev. Mater.3, 123601 (2019).[19] L. Zhang, Y. Wang, J. Lv, and Y. Ma, Nat. Rev. Mater.2, 1 (2017).[20] A. R. Oganov, C. J. Pickard, Q. Zhu, and R. J. Needs,Nat. Rev. Mater. 4, 331 (2019).[21] E. Ohtani and A. E. Ringwood, Earth Planet. Sci. Lett.71, 85 (1984).[22] D. Alf`e, M. J. Gillan, and G. D. Price, J. Chem. Phys.116, 7127 (2002).[23] H. Huang, Y. Fei, L. Cai, F. Jing, X. Hu, H. Xie, L.Zhang, and Z. Gong, Nature 479, 513 (2011).[24] J. Badro, G. Fiquet, F. Guyot, J. P. Rueff, V. V.Struzhkin, G. Vank´o, and G. Monaco, Science 300, 789(2003).[25] P. Gao, C. Su, S. Shao, S. Wang, P. Liu, S. Liu, and J.Lv, New J. Chem. 43, 17403 (2019).[26] Q. Hu, D. Y. Kim, W. Yang, L. Yang, Y. Meng, L. Zhang,and H.-K. Mao, Nature 534, 241 (2016).[27] M. Nishi, Y. Kuwayama, J. Tsuchiya, and T. Tsuchiya,Nature 547, 205 (2017).[28] A. P. P. Van den Berg, D. A. A. Yuen, K. Umemoto, M.H. G. H. G. Jacobs, and R. M. M. Wentzcovitch, Icarus317, 412 (2019).[29] X. Zhao, M. C. Nguyen, W. Y. Zhang, C. Z. Wang, M. J.Kramer, D. J. Sellmyer, X. Z. Li, F. Zhang, L. Q. Ke, V.P. Antropov, and K. M. Ho, Phys. Rev. Lett. 112, 045502(2014).[30] D. M. Deaven and K. M. Ho, Phys. Rev. Lett. 75, 288(1995).[31] S. M. Foiles, M. I. Baskes, and M. S. Daw, Phys. Rev. B33, 7983 (1986).[32] X. W. Zhou, R. A. Johnson, and H. N. G. Wadley, Phys.Rev. B 69, 144113 (2004).[1] A. E. Doyle, E. D. Young, B. Klein, B. Zuckerman, andH. E. Schlichting, Science 366, 356 (2019).[2] K. Hirose, S. Labrosse, and J. Hernlund, Annu. Rev.Earth Planet. Sci. 41, 657 (2013).[3] F. Birch, J. Geophys. Res. 57, 227 (1952).[4] F. Birch, J. Geophys. Res. 69, 4377 (1964).[5] L. S. Dubrovinsky, S. K. Saxena, F. Tutti, S. Rekhi, andT. LeBehan, Phys. Rev. Lett. 84, 1720 (2000).[6] J. Shanker, B. P. Singh, and S. K. Srivastava, Phys. EarthPlanet. Inter. 147, 333 (2004).[7] A. Dewaele, P. Loubeyre, F. Occelli, M. Mezouar, P. I.Dorogokupets, and M. Torrent, Phys. Rev. Lett. 97, 29(2006).[8] Y. Kuwayama, G. Morard, Y. Nakajima, K. Hirose, A.Q. R. Baron, S. I. Kawaguchi, T. Tsuchiya, D. Ishikawa,N. Hirao, and Y. Ohishi, Phys. Rev. Lett. 124, 165701(2020).[9] G. Morard, D. Andrault, D. Antonangeli, and J. Bouchet,Comptes Rendus - Geosci. 346, 130 (2014).[10] D. Alf`e, M. J. Gillan, and G. D. Price, Earth Planet. Sci.Lett. 195, 91 (2002).[11] H. Ozawa, F. Takahashi, K. Hirose, Y. Ohishi, and N.Hirao, Science 334, 792 (2011).[12] S. Tateno, K. Hirose, Y. Ohishi, and Y. Tatsumi, Science330, 359 (2010).[13] M. J. Gillan, D. Alf`e, J. Brodholt, L. Voˇcadlo, and G. D.Price, Reports Prog. Phys. 69, 2365 (2006).[14] F. Zhang and A. R. Oganov, Geophys. Res. Lett. 37, n/a(2010).[15] G. L. Weerasinghe, R. J. Needs, and C. J. Pickard,Phys. Rev. B - Condens. Matter Mater. Phys. 84, 174110(2011).[16] G. L. Weerasinghe, C. J. Pickard, and R. J. Needs, J.Phys. Condens. Matter 27, 455501 (2015).[17] S. Q. Wu, M. Ji, C. Z. Wang, M. C. Nguyen, X. Zhao, K.Umemoto, R. M. Wentzcovitch, and K. M. Ho, J. Phys. Condens. Matter 26, 035402 (2014).[18] K. Umemoto and R. M. Wentzcovitch, Phys. Rev. Mater.3, 123601 (2019).[19] L. Zhang, Y. Wang, J. Lv, and Y. Ma, Nat. Rev. Mater.2, 1 (2017).[20] A. R. Oganov, C. J. Pickard, Q. Zhu, and R. J. Needs,Nat. Rev. Mater. 4, 331 (2019).[21] E. Ohtani and A. E. Ringwood, Earth Planet. Sci. Lett.71, 85 (1984).[22] D. Alf`e, M. J. Gillan, and G. D. Price, J. Chem. Phys.116, 7127 (2002).[23] H. Huang, Y. Fei, L. Cai, F. Jing, X. Hu, H. Xie, L.Zhang, and Z. Gong, Nature 479, 513 (2011).[24] J. Badro, G. Fiquet, F. Guyot, J. P. Rueff, V. V.Struzhkin, G. Vank´o, and G. Monaco, Science 300, 789(2003).[25] P. Gao, C. Su, S. Shao, S. Wang, P. Liu, S. Liu, and J.Lv, New J. Chem. 43, 17403 (2019).[26] Q. Hu, D. Y. Kim, W. Yang, L. Yang, Y. Meng, L. Zhang,and H.-K. Mao, Nature 534, 241 (2016).[27] M. Nishi, Y. Kuwayama, J. Tsuchiya, and T. Tsuchiya,Nature 547, 205 (2017).[28] A. P. P. Van den Berg, D. A. A. Yuen, K. Umemoto, M.H. G. H. G. Jacobs, and R. M. M. Wentzcovitch, Icarus317, 412 (2019).[29] X. Zhao, M. C. Nguyen, W. Y. Zhang, C. Z. Wang, M. J.Kramer, D. J. Sellmyer, X. Z. Li, F. Zhang, L. Q. Ke, V.P. Antropov, and K. M. Ho, Phys. Rev. Lett. 112, 045502(2014).[30] D. M. Deaven and K. M. Ho, Phys. Rev. Lett. 75, 288(1995).[31] S. M. Foiles, M. I. Baskes, and M. S. Daw, Phys. Rev. B33, 7983 (1986).[32] X. W. Zhou, R. A. Johnson, and H. N. G. Wadley, Phys.Rev. B 69, 144113 (2004).