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Yang Sun, Mikhail I. Mendelev, Feng Zhang, Xun Liu, [Bo Da](https://orcid.org/0000-0002-0785-8662), Cai-Zhuang Wang, Renata M. Wentzcovitch, Kai-Ming Ho

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[Unveiling the effect of Ni on the formation and structure of Earth’s inner core](https://mdr.nims.go.jp/datasets/aca70769-93fd-4d9f-a384-cc9b96c98ad9)

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Unveiling the effect of Ni on the formation and structure of Earth’s inner coreYang Sun,1, 2, 3, ∗ Mikhail I. Mendelev,3, † Feng Zhang,3, 4 Xun Liu,5 Bo Da,5Cai-Zhuang Wang,4, 3 Renata M. Wentzcovitch,2, 6, 7, ‡ and Kai-Ming Ho31Department of Physics, Xiamen University, Xiamen, Fujian 361005, China2Department of Applied Physics and Applied Mathematics,Columbia University, New York, NY 10027, USA3Department of Physics, Iowa State University, Ames, IA 50011, USA4Ames Laboratory, US Department of Energy, Ames, IA 50011, USA5Research and Services Division of Materials Data and Integrated System,National Institute for Materials Science, Ibaraki 305-0044, Japan6Department of Earth and Environmental Sciences,Columbia University, New York, NY 10027, USA7Lamont–Doherty Earth Observatory, Columbia University, Palisades, NY 10964, USA(Dated: Sep. 15, 2023)Ni is the second most abundant element in the Earth’s core. Yet, its effects on theinner core’s structure and formation process are usually disregarded because of itselectronic and size similarity with Fe. Using ab initio molecular dynamics simulations,we find that the bcc phase can spontaneously crystallize in liquid Ni at temperaturesabove Fe’s melting point at inner core pressures. The melting temperature of Ni isshown to be 700-800 K higher than that of Fe at 323-360 GPa. hcp, bcc, and liquidphase relation differ for Fe and Ni. Ni can be a bcc stabilizer for Fe at high temperaturesand inner core pressures. A small amount of Ni can accelerate Fe’s crystallization atcore pressures. These results suggest Ni may substantially impact the structure andformation process of the solid inner core.The Earth has a liquid outer core and a solid innercore composed of Fe with a small amount of Ni and lightelements. The solid phase’s chemical composition andstructure are fundamental for understanding the core,but there are still uncertainties [1–3]. Fe alloys in theinner core are often believed to have the hexagonal close-packed (hcp) lattice[4, 5], while the body-centered cubic(bcc) phase is also under consideration[6, 7]. Thermo-dynamic calculations indicate that hcp Fe is the stablesolid phase at inner core pressures. Still, the Gibbs freeenergy difference between the hcp and bcc phases may bemuch smaller than previously thought [8–10]. The pres-ence of other elements diluted in Fe may significantlychange the bcc and hcp stability fields [11, 12]. Thegrowth of the present inner core provides the primarypower source to sustain the outer core convection, whichgenerates the Earth’s magnetic field [13]. Despite its im-portance, significant gaps exist in understanding the in-ner core’s age and nucleation process [14–17]. Recentsimulations showed that the hcp Fe nucleation requiresmuch larger supercooling than the liquid core can reach,leading to the ”inner core nucleation paradox.” [18–21]Metastable bcc Fe was found to nucleate at smaller su-percooling than hcp Fe at core pressures, which may helpresolve the paradox [21].Cosmochemical models estimated 5-15 wt.% Ni con-tent in the core [1]. Iron meteorites can contain even∼35 wt.% Ni [22]. High-pressure experiments of Fe-Nialloys focused mainly on the solid phase relations. Ni isknown to stabilize the fcc phase with respect to hcp un-der low P-T conditions [23–26]. The bcc phase was oncereported in a Fe90Ni10 alloy by experiments at pressuresabove 225 GPa and temperatures over 3400 K [27]. How-ever, experiments with P-T conditions up to 340 GPa and4700 K did not confirm the existence of the bcc phase inFe90Ni10 [28, 29]. Static calculations demonstrated thatNi doping could improve the dynamic stability of bcc Fe[30]. In recent experiments, Ni and FeNi melting curvewas studied up to 120 GPa [31–33]. It was suggested thatNi could strongly modify the hcp/fcc/liquid triple pointsin the Fe1−xNix alloy [33]. So far, the effect of Ni on theinner core’s nucleation process is yet to be considered.Previous ab initio quasiharmonic calculations of Ni andFe-Ni alloys at Earth’s core pressures focused mainly onthe fcc-hcp phase relation and assumed anharmonicity tobe negligible[19]. However, the inner core and outer coreare under a solid-liquid coexistence condition with tem-peratures close to the melting point. Anharmonic effectscan significantly affect the free energies and phase stabili-ties, especially in the bcc phase [21, 34, 35]. One practicalway to determine the stable phase near the melting pointis to compute the melting temperatures of competingcrystalline phases when the stable solid phase is uncer-tain. These melting temperatures define the relative sta-bility of different solid phases for liquid coexistence: thephase with the highest melting temperature is the moststable, while other crystalline phases are metastable. Inthis work, we start with an unexpected simulation re-sult, i.e., the crystallization of liquid Ni at inner coreboundary (ICB) conditions. Then we address Ni’s hcp,fcc, and bcc phase stability near the melting tempera-ture and compare it with the corresponding data for Fe.arXiv:2308.04280v2  [cond-mat.mtrl-sci]  22 Sep 20232FIG. 1. Crystallization from liquid to bcc at 323 GPa and6000 K by the AIMD simulation. a. Enthalpy as a functionof simulation time. b. The fraction of liquid and crystallineatoms as a function of simulation time. c. Initial (upper) andfinal (bottom) atomic configurations with 250 atoms.Combining free energy results and crystallization kinet-ics of FeNi systems, we discuss possible scenarios for theeffect of Ni on the formation and structure of the innercore.Bcc crystallization. Our ab initio calculationsshowed that the melting temperature of hcp Fe is 5848K at 323 GPa [10], which is consistent to previous cal-culations of 5730±200 K with the same pseudopotential(see Methods) [36]. Including more valence electrons inthe pseudopotential systematically increases the meltingpoints but does not significantly change the relative sta-bility between the hcp and bcc phases [10](see Methods).If Ni were similar to Fe, as usually assumed, one wouldexpect a similar melting temperature for Ni at the samepressures. Surprisingly, we found that Ni liquid crystal-lizes spontaneously in an ab initio molecular dynamics(AIMD) simulation at 6000 K and 323 GPa, which is wellabove Fe’s melting point. Figure 1a shows the enthalpychange as a function of time during an AIMD simula-tion. The sharp drop of the enthalpy at ∼30 ps indicatesa clear first-order phase transition. Figure 1b shows thatthe fraction of the bcc phase quickly increases at ∼30 ps,which coincides with the enthalpy change in Fig. 1a. Thefraction of hcp also increases at 30 ps and stays steady to31 ps but quickly decreases after the bcc phase becomesdominant. The fraction of fcc during the crystallizationis insignificant. The phase competition is mainly betweenhcp and bcc during the nucleation process. The initialand final snapshots shown in Fig. 1c confirm the liquidsolidified into the bcc phase during the AIMD simula-tion. The solidification of Ni at T=6000 K was unex-pected because this temperature is well above Fe’s melt-ing temperature. Therefore, the Ni melting temperatureshould be significantly higher than Fe at 323 GPa. Thecrystallization of the bcc phase also indicates bcc has noinstability at 6000 K, which is different from the previ-ously revealed instability in the bcc phase at 0 K [37].Therefore, anharmonicity contributes significantly to thebcc phase stability at high temperatures.Crystallization is a rare event challenging to observespontaneously in simulations. Based on the classicalnucleation theory [38], the nucleation rate depends ex-ponentially on the nucleation barrier ∆G∗, as J =κexp(−∆G∗/kBT ), where κ is a kinetic prefactor. Thefast crystallization observed here indicates a significantnucleation rate, thus a small nucleation barrier. The keyfactors that determine the nucleation barrier ∆G∗ are thefree energy difference between the bulk solid and liquidphases and the solid-liquid interface (SLI) free energy.While the bcc phase prevails over hcp in the crystalliza-tion process, it does not necessarily mean that bcc Ni hassignificantly lower free energy than hcp Ni. In the caseof Fe, metastable bcc can have a nucleation rate 10-40orders of magnitude higher than that of the stable hcpphase at 1000-600 K supercooling [21], because the SLIfree energy for Fe’s bcc phase is much smaller than thatfor the hcp phase [21]. Therefore, one needs the free en-ergy relations to determine the relative thermodynamicstability of bcc, hcp, and liquid. As free energy relationsalso define melting temperatures, we use the latter toinfer thermodynamic stability among these phases.Phase relations near the melting temperature.We recently showed that the ab initio melting tempera-ture could be accurately obtained from the AIMD simu-lation with the help of a semi-empirical potential if thepotential provides atomic structures close to those ob-tained in the AIMD simulation [10]. Therefore, we de-veloped a Finnis-Sinclair (FS) type potential [39] for Ni inthe present study. The Supplementary Information con-tains details of potential and accuracy tests. The bcc,hcp, and fcc melting temperatures for this FS potentialare computed by two-phase coexistence simulations withlarge-scale classical MD. While no information about themelting temperatures was included in the potential de-velopment, the FS potential predicts that bcc-Ni has thehighest melting temperature. We calculated the ab ini-tio free energy via thermodynamic integration (TI), usingthe classical system described by the FS potential as thereference state (see Method). Table I shows the ab initiomelting temperatures of the three phases computed at323 GPa and 360 GPa, which are the pressures at theboundary and center of the inner core, respectively. Bcc-Ni indeed shows higher melting temperatures than hcp-Ni and fcc-Ni. The differences are small, ∼ 30 K, but aremore significant than the typical confidence interval of15 K in similar calculations [10]. The difference betweenhcp-Ni and fcc-Ni melting temperatures is smaller, ∼73FIG. 2. Ab initio free energy difference referenced tobcc phase at 323 GPa near the melting temperaturesfor Ni and Fe. a. The open circles are obtained throughTI calculations. The circles are connected to guide the eyes.The two black dots at 6528 K and 6366 K indicate hcp-bccand bcc-liquid phase transitions, respectively. b. The freeenergy data of Fe are from Ref. [10]. The black dot indicatesthe phase transition of hcp-liquid. The uncertainty is ∼ 1meV/atom due to the size effect [10].K. In Table I we compare the melting temperatures ofNi phases to those of Fe phases computed in Ref. [10].Both bcc Ni and hcp Ni’s melting temperatures are sig-nificantly higher than those for Fe phases by 700-800K.Figure 2a shows the relative free energy difference ref-erenced to the bcc phase at 323 GPa. Bcc is the stablephase from 6528 K to 6366 K. For temperatures lowerthan 6366 K, hcp is the stable phase while bcc becomesmetastable. A comparison between Fig. 2a and 2b showsthat the bcc-hcp phase relations are very different be-tween Fe and Ni. The bcc phase is always metastablefor Fe, while it is stable for Ni in a small temperaturerange near the melting point. The free energy differenceTABLE I. Melting temperatures of Fe and Ni phases at 323GPa and 360 GPa obtained from Ab initio calculations. Fedata are taken from Ref. [10]. The uncertainty is 15 K.System P (GPa) T bccm (K) Thcpm (K) T fccm (K)Ni 323 6528 6499 6492Ni 360 6870 6833 6824Fe 323 5632 5848 -Fe 360 5850 6094 -between hcp and bcc is much smaller for Ni than for Fe.Therefore, Ni is likely a bcc stabilizer if mixed with Feat high temperatures under core pressures.Crystallization of Fe-Ni mixture. The compar-isons between Fe and Ni suggest the effect of Ni on thecore’s structure and formation should be carefully con-sidered. Previous studies have found liquid Fe at corepressures requires an unrealistically large undercoolingto nucleate the solid inner core phase, which is unlikelyto be reached under Earth’s core conditions and age[18, 20, 21]. Since Ni’s melting temperature is consid-erably higher than Fe’s at the same pressures, the Fe-Ni mixture could have an increased liquidus temperaturecompared to Fe’s melting temperature. Because Fe andNi liquids nucleate the bcc phase first [21], we shouldconsider a simple metastable bcc-liquid phase diagramschematically shown in Fig. 3a. It demonstrates thatmixing Ni in Fe can effectively change the supercooling(∆T ) and might accelerate the nucleation process. Weperformed AIMD simulations of Fe and Fe85Ni15 liquidsat large supercooling temperatures under core pressuresto examine this mechanism. At ∼310 GPa and 5000 K,the Fe85Ni15 liquid crystallizes within 50 ps, as shown inFig. 3b. In contrast, no crystallization was observed forthe Fe liquid up to 76 ps under the same P-T condition.Crystallization is a stochastic process; consequently, thenucleation incubation time can fluctuate. We performedthree additional AIMD simulations for Fe85Ni15 and Feto counteract this stochastic effect. The results are pre-sented in Supplementary Figure S3. We found the aver-aged crystallization time for Fe85Ni15 is ∼ 40 ps, whileno crystallization can be observed with pure Fe up to 80ps at 5000 K and 310 GPa. This suggests that Fe85Ni15alloy has a higher nucleation rate than pure Fe. The Ni’seffect on accelerating Fe’s crystallization process can alsobe observed from large-scale classical MD simulations bycooling the melts with ultrahigh cooling rates (Supple-mentary Note 2). It shows that 15% Ni reduces the re-quired supercooling by ∼400 K under a cooling rate of1011 K/s. While this cooling rate is far from Earth’score condition, it validates Ni’s effect on Fe’s crystalliza-tion revealed by the AIMD simulations. We note thatFig. 3a may be changed with the inclusion of light ele-ments, while the effect of Ni should always be consideredto study the nucleation of the core.4The crystallization process of Fe85Ni15 liquid in theAIMD simulations is analyzed based on its local atomicstructure change in Fig. 3c. Interestingly, the liquidshows two attempts to nucleate: first at ∼25 ps, thenat 47 ps. In the first attempt, an hcp nucleus emergesbut only grows to a small size and then remelts. Thisindicates that the nucleus cannot overcome the nucle-ation barrier to reach the critical size. In the secondattempt, a bcc nucleus emerges and successfully crys-tallizes. During the bcc growth, ∼20% of liquid atomstransform to hcp. It forms a bcc-hcp coexisting systemin the as-crystallized solid, shown in Fig. 3d. The par-tial pair correlation functions of Fe and Ni are almostindistinguishable, suggesting Fe and Ni atoms randomlydistribute in the as-crystallized solid. This is consistentwith previous calculations that Fe and Ni do not formstoichiometric compounds but only form completely dis-ordered solid solutions under core conditions [40, 41]. Ad-ditional three AIMD simulations of Fe85Ni15 crystalliza-tion in Supplementary Figure S3 also show minor hcpphases in the as-crystallized bcc phases.Discussion. The current results demonstrate that Nistrongly stabilizes the bcc phase and accelerates the crys-tallization of Fe under Earth’s core conditions. Moreover,our simulation showed that bcc and hcp can coexist dur-ing the crystallization of Fe85Ni15 alloy. These resultssuggest a potential coexistence of hcp and bcc phasesunder Earth’s inner core. Using this study’s minimalfree energy data, one can propose a binary Fe-Ni phasediagram, as illustrated in Fig. 3d. On the Ni side, thebcc phase has a stability field close to the melting curve.This bcc stability field can extend into the Fe-rich do-main, posing a challenge to the stability of hcp, poten-tially leading to the emergence of a liquid-hcp-bcc eutec-tic. Thus, there’s a possibility for a thermodynamicallystable coexistence of bcc and hcp in the solid phase of theinner core. At lower temperatures, when both Fe and Niare in the hcp phase, they might form two distinct hcpphases (H+H’) with varying Ni compositions or a singleone, depending on how different or similar their partialmolar volumes are. The nature of the equilibrium statesin Fig. 3d should be investigated via simulations and ex-periments in future studies. Interestingly, a recent ex-perimental study revealed the coexistence of hcp and B2phases in the Fe93Ni7 alloy at 186 GPa and 2970 K [42].A comprehensive Fe-Ni phase diagram encompassing liq-uidus, solidus, and solvus curves is essential to advanceunderstanding of the Earth’s inner core structure and theassociated seismic velocity anomalies [43, 44].To conclude, we find that the bcc phase crystallizesfrom Ni liquid at a temperature above the melting pointof Fe under inner core pressures. Ab initio free energy cal-culations indicate that Ni’s melting temperature is 700-800 K higher than Fe’s at 323-360 GPa. Bcc is the ther-modynamically stable phase near Ni’s melting point atinner core pressures. Ni accelerates Fe’s crystallizationFIG. 3. Fe and Fe85Ni15 liquid at 310 GPa and 5000K by the AIMD simulation. a. The enthalpy change as afunction of simulation time. The data are referenced to aver-aged liquid enthalpy for Fe and Fe85Ni15, respectively. b. Thefraction of liquid/disordered and crystalline atoms as a func-tion of time in Fe85Ni15 simulation. The arrows mark the twonucleation attempts. c. The partial pair correlation functionof the crystallized Fe85Ni15 phase averaged over the last 10 psof the simulation. The insert shows the final atomic configu-ration. The center atoms of hcp-like clusters are colored redand connected to guide the eyes. Blue are bcc. d. Schematicof a “likely” Fe-Ni liquid-bcc-hcp phase diagram. Ni (TNim )has a higher melting temperature than Fe (TFem ). For pure Fe,hcp is the stable phase, and bcc is metastable. For pure Ni,bcc is the high-tempeature stable phase and transform to hcpat lower temperatures. L stands for liquid phase; B is bccphase and H and H’ are hcp phases. Dashed box indicatesuncertain shape/existence.process at inner core conditions. The Fe-Ni mixture maylead to the coexistence of hcp and bcc phases under coreconditions. These results suggest that Ni can be a keyfactor in modeling the Earth’s inner core formation andpresent structure.METHODSAb initio molecular dynamics simulations. Abinitio molecular dynamics (AIMD) were employed withthe Born Oppenheimer approach to simulate crystal-lization, collect input data to develop semi-empiricalpotential and perform thermodynamic integration cal-culations. The Vienna ab initio simulation package(VASP) [45] was employed for the density-functional the-ory (DFT) calculations. The projected augmented-wave(PAW) potentials shipped with VASP was used to de-scribe the electron-ion interaction with 8 and 10 valenceelectrons for Fe and Ni, respectively. The core radii cut-5off of these PAW potential are 1.2 Å. The effect of thenumber of valence electrons was examined in the calcu-lation of the Fe’s melting temperature of the bcc andhcp phases 10. At 323 GPa, Fe hcp and bcc’s melt-ing temperatures are 5848 K and 5632 K, respectively,with PAW8 potential. They are 6357 K and 6168 K withPAW16 potential, which includes additional 3s23p6 elec-trons. The difference between hcp and bcc Tm was 216 Kand 189 K for PAW8 and PAW16 potentials, respectively.Therefore, including more inner shell electrons as valenceelectrons can systematically increase the melting temper-ature [10, 36]. However, it does not significantly affectthe relative melting temperature differences between bccand hcp phases [10]. To achieve sufficiently long simu-lations of crystallization, we employ the PAW potentialswithout 3s23p6 for both Fe and Ni, which provides aconsistent condition for describing their atomic interac-tions. The generalized gradient approximation (GGA) inthe Perdew-Burke-Ernzerhof (PBE) form was employedfor the exchange-correlation energy functional. A plane-wave basis set was used with a kinetic energy cutoff of 400eV. The AIMD simulations were performed for the con-stant number of atoms, volume, and temperature (NVT)canonical ensemble. In the crystallization simulations, Niand Fe85Ni15 liquids are modeled by 250 Ni atoms andFe212Ni38 atoms, respectively. The Γ point was used tosample the Brillouin zone of these supercells for crystal-lization. A time step of 1.5 fs was used to integrate New-ton’s equations of motion. The Nosé-Hoover thermostatwas employed to control the temperature. The electronicentropy at high temperatures was described by the Mer-min functional [46, 47]. The non-magnetic calculationswere performed in AIMD. We tested the spin-polarizedcalculations and found that the magnetic moments of Feand Ni phases are quenched when the electronic temper-ature is more than 4000 K at 323 GPa.Local structure characterization. The clusteralignment (CA) method [48, 49] was employed to rec-ognize bcc, fcc, and hcp short-range orders in the localatomic clusters during crystallization. The CA methodaligns the atomic clusters to the standard bcc, fcc, andhcp templates and computes the root mean square devia-tion (RMSD) between the atomic clusters and templates.Supplementary Figure S4 indicates that CA can distin-guish well crystalline phases from the liquid. To removethe noise caused by thermal fluctuations, the atomic po-sitions were averaged for 0.06 ps to perform the CA anal-ysis.Classical molecular dynamics simulations. Clas-sical molecular dynamics (CMD) simulations were per-formed with LAMMPS (Large-scale Atomic/MolecularMassively Parallel Simulator) code [50]. The interatomicinteraction was modeled using the Finnis-Sinclair (FS)type [39] semi-empirical potential developed in this work.During the MD simulation, the constant number ofatoms, pressure, and temperature (NPT) ensemble wasapplied with the Nosé-Hoover thermostat and barostat.The time step of the simulation was 1.0 fs. The melt-ing temperatures of the classical system, denoted as TmC ,were determined using the solid-liquid coexistence ap-proach [51] with 22,500 atoms. The free energy differencebetween liquid and solid, ∆GL−SC , is determined by theGibbs-Helmholtz equation,∆GL−SC (T ) = −T∫ TTmC∆H(T )/T 2dT, (1)where ∆H is the latent heat which is computed by theenthalpy difference between liquid and solid from classi-cal simulations with 5,000 atoms.Ab initio melting temperature. The ab initiomelting temperature, TmA , was obtained when the abinitio free energy difference between liquid and solidphases is zero, i.e., ∆GL−SA (TmA ) = 0. ∆GL−SA is com-puted by thermodynamic integration (TI) between theclassical system (C) and ab initio system (A) [10]. Itwas performed by exchanging the ab initio and classi-cal atomic information on-the-fly in an MD simulation[10]. Classical molecular dynamics simulations were per-formed with LAMMPS (Large-scale Atomic/MolecularMassively Parallel Simulator) code [50]. During the TI-MD, the NVT ensemble was applied, and the Nosé-Hoover thermostat [52] was employed to control the tem-perature. A time step of 2.0 fs was used to integrateNewton’s equations of motion. Supercells with 288, 256,250, and 250 atoms were used to simulate hcp, fcc, bcc,and liquid, respectively.ACKNOWLEDGMENTSWork at Iowa State University and Columbia Uni-versity was supported by the National Science Founda-tion awards EAR-1918134 and EAR-1918126. We ac-knowledge the computer resources from the Extreme Sci-ence and Engineering Discovery Environment (XSEDE),which is supported by the National Science Foundationgrant number ACI-1548562. X.L. and B.D. are supportedby JSPS KAKENHI Grant Number JP21K14656. Molec-ular dynamics simulations were supported by the Numer-ical Materials Simulator supercomputer at the NationalInstitute for Materials Science (NIMS). S. 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