Iron-rich carbonates stabilized by magnetic entropy at lower mantle conditions

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Iron-rich carbonates stabilized by magnetic entropy at

lower mantle conditions

Zhi Li, Stephen Stackhouse

To cite this version:

Zhi Li, Stephen Stackhouse.

Iron-rich carbonates stabilized by magnetic entropy at lower

mantle conditions.

Earth and Planetary Science Letters, Elsevier, 2020, 531, pp.115959.

Contents lists available atScienceDirect

Earth

and

Planetary

Science

Letters

www.elsevier.com/locate/epsl

Iron-rich

carbonates

stabilized

by

magnetic

entropy

at

lower

mantle

conditions

Zhi Li

∗

,

1

,

Stephen Stackhouse

∗

SchoolofEarthandEnvironment,UniversityofLeeds,LS29JT,UK

a

r

t

i

c

l

e

i

n

f

o

a

b

s

t

r

a

c

t

Articlehistory: Received6May2019

Receivedinrevisedform29October2019 Accepted6November2019

Availableonline19November2019 Editor: B.Buffett

Keywords: first-principles carbonate mantle

Constraining the flux ofcarbon in and outof the interior of the Earthdue to long-term geological processesisimportant,becauseoftheinfluencethatithasonclimatechange.Ontimescalesofbillions ofyears,hostmineralssuchascarbonatephasescouldplayasignificantroleintheglobalcarboncycle, transportingcarbonintothelowermantleasacomponentofsubductingslabs.Weusedensityfunctional theorybasedcalculationstostudy thehigh-pressure,high-temperaturephasestabilityofMg1-xFexCO3.

Ourresultsshowthat iron-richphases, wherecarbonisintetrahedralcoordination,areonlystableat lowermantleconditionsduetotheirmagneticentropy,whichisalsoresponsiblefortheunusualshape oftheirphaseboundary.Low-pressurecarbonate phasesarefound tobehighlyanisotropic,but high-pressurecarbonatephasesarenot,whichhasimportantimplicationsfortheirseismicdetectability.Our workconfirmsthatfuturediscussionsoftheglobalcarboncycleshouldincludethedeepEarth.

©2019TheAuthors.PublishedbyElsevierB.V.ThisisanopenaccessarticleundertheCCBYlicense (http://creativecommons.org/licenses/by/4.0/).

1. Introduction

The globalcarbon cycleis of great importance, dueto its in-fluence on climate change (Dasgupta and Hirschmann, 2010). It describesthe distributionandexchangeofcarbonbetweenmajor reservoirs,such asthe atmosphere, crust, mantleandcore. Stud-iesoftheglobalcarboncyclehaveoftenfocusedprimarilyonthe atmosphere,oceans,andshallowcrustalenvironments,referredto asthe“near-surfacecycle”(HazenandSchiffries,2013).Whilethis workswellforshorttime scales, topredict long-termchangesin theconcentrationofCO2 intheatmosphereit isnecessaryto

in-cludeexchangebetweenthesurfaceandinterioroftheEarth. Car-bonenters theinterior oftheEarth viasubduction of carbonate-bearing slabs (Dasgupta and Hirschmann, 2010). Carbonates are believedto persist into the mantle, provided that a slab follows a very cold subduction geotherm (Syracuse et al., 2010), which precludes their melting (Kakizawa et al., 2015; Thomson et al., 2016) or reaction with SiO2 (Drewitt et al., 2019; Kakizawa et

al., 2015; Maeda et al., 2017). Low solubility of carbon in man-tleminerals,suggeststhat,onceinthemantle,carbonisstoredas eithercarbonatesordiamond(Panero andKabbes, 2008;Shcheka etal., 2006), depending on the local oxidation state (e.g. Stagno

*

Correspondingauthors.

E-mailaddresses:zhi.li@ens-lyon.fr(Z. Li),s.stackhouse@leeds.ac.uk

(S. Stackhouse).

1 _{Presentaddress:CNRS,ÉcoleNormaleSupérieuredeLyon,Laboratoirede}

Géolo-giedeLyonUMR5276,CentreBlaisePascal,69007,Lyon,France.

etal., 2011). Supportforthisidea comesfromreportsof carbon-atesasinclusionsinnaturaldiamonds originatingfromthelower mantle(Brenkeretal.,2007).Inviewofthis,constrainingthe high-pressure stabilityof carbonatesisessential forunderstanding the globalcarboncycle.

The most common carbonate minerals on the surface of the Earth are calcite (CaCO3), dolomite (CaMg(CO3)2), magnesite

(MgCO3) and siderite (FeCO3), which adopt the R3c structure at

ambientconditions, exceptfordolomite which hasthe R3

struc-ture. Theoreticalstudiesindicatethat MgCO3 istheprobablehost

ofcarboninthemantle,sinceMgCO3

+

CaSiO3ismorestablethan

CaCO3

+

MgSiO3 to lower mantle pressures (Oganov et al., 2008;

PickardandNeeds,2015; Santosetal., 2019; Zhangetal., 2018). The high-pressurephase stability ofMgCO3,has beenwell

stud-ied (Boulardet al.,2011; Isshiki etal., 2004; Maeda etal., 2017; Oganovetal.,2008;PickardandNeeds,2015;Santosetal., 2019; Zhang et al., 2018) with the general consensus that the C 2/m

structureisstableatlowermantleconditions.

In nature, MgCO3 exists as a solid solution with FeCO3, with

Mg1-xFexCO3 in eclogite (in the upper mantle) expected to have

about 0.16

<

x

<

0.21, while that in peridotite (in the lower mantle) expectedto haveaboutx

=

0.07 (Dasgupta etal., 2004; DasguptaandHirschmann,2006;Sanchez-Valleetal.,2011).Most previous experimental investigations of Mg1-xFexCO3 have

con-centrated oniron-richcompositions,whichexhibit complex high-pressure chemistry (Boulard et al., 2015, 2012, 2011; Liu et al., 2015; Merlini et al., 2015). Common features of the main high-pressurephasesobservedinthesestudiesare:iron existsasFe3+ https://doi.org/10.1016/j.epsl.2019.115959

and carbon is in tetrahedral coordination (Boulard et al., 2015, 2012,2011;Merlini etal., 2015).Threeout offourstudiesreport (C3O9)6− rings(Boulardetal.,2015,2012,2011).

Experimentalinvestigations ofpureFeCO3 reportthat the R3c

structure is stable up to, at least, 130 GPa at 300 K, with a pressure-inducedspintransitionoccurringatabout45GPa (Ceran-tola et al., 2015; Farfan et al., 2012; Lavina et al., 2010b, 2009; Mattilaetal., 2007; Weisetal., 2017). Incontrast,at1500Kand above, Boulard et al. (2012) observed a high-pressure phase co-existing with other run products above about 40 GPa. This was assigneda Fe4C3O12 composition, butthe atomic positions were

unresolved. Liu et al. (2015) observed a high-pressure phase at similar conditions, above about 50 GPa, at 1400K, but reported ittohaveaFeCO3 composition.Structurerefinementshowedthat

thePmm2 spacegroup bestfittheirX-ray diffractionpattern, but theatomicpositions were unresolved.In amore recentstudy by Cerantolaetal.(2017), FeCO3 wasfoundtobreakdownabove 70

GPa at1400K,forminga complexseriesofdecomposition prod-uctsastemperatureandpressureareincreased. Thefirstofthese was foundto havethesame chemicalcomposition (Fe4C3O12) as

the high-pressurephase of Boulard et al.(2012) and a structure consistentwiththe X-raydiffraction patternofthe high-pressure phase reportedby Liu etal. (2015), suggestingthat they are the same. Furthermore, Cerantola et al. (2017) were able to resolve thecrystal structure,finding itto be a tetrairon(III) orthocarbon-ate,containingCO4tetrahedralunits.Despiteapparentobservation

ofthesamehigh-pressurestructure,thephasediagramsofthe in-vestigationsdiffersomewhat.Forexample,Liuetal.(2015) observe theformationoftheirhigh-pressurephaseat50GPa,whileatthis pressureCerantola etal.(2017) stillfindFeCO3 (R3c)tobestable.

Between70–120 GPaand1500–2200K,Liuetal.(2015) only ob-serveFeCO3 (R3c)andtheirhigh-pressurephase,whereasBoulard

etal.(2012) observeFe4C3O12co-existingwithdiamondandiron

oxides,andCerantolaetal.(2017) observevariouscombinationsof co-existingFe4C3O12,Fe4C4O13 andiron oxides. Inthelattertwo

studiesthephaseboundarywasalsopoorlyconstrained.

In the present work, we perform density functional theory (DFT)calculationstoexamine thephaserelations ofMg1-xFexCO3

atlower mantleconditions. Ourresults illustrate the importance ofincludingtemperaturewheninvestigatingphasebehaviour,with significantdifferencesfoundintheresultsof0Kandhigh temper-aturecalculations.Inparticular,ourresultsindicatethatmagnetic entropyplays asignificant role in stabilizingFe4C3O12

+

C

(dia-mond)andisthereasonfortheunusualshapeofitsphase bound-ary. For lower iron concentrations, our results suggest a phase transitionfromtheR3c toC 2/m structureatabout75GPa,witha smallbinaryphaseloopofafewGPa.Inaddition,wefindthe cal-culatedseismicanisotropyofthehigh-pressurephasestobemuch smallerthan thatofthe low-pressure phases,which has implica-tionsfortheirpotentialseismicdetectability.

2. Calculationdetails

2.1. Crystalstructures

Inordertostudy thehigh-pressurephasebehaviourofMgCO3

andFeCO3,we consideredanumberofstructures.ForMgCO3 we

consideredtheR3c,C 2/m,P 212121,P 21/c andP -1structures

pro-posedinprevious investigations(Oganovetal., 2008;Pickardand Needs,2015;Santosetal.,2019;Zhangetal.,2018).ForFeCO3 we

consideredFeCO3 (R3c), FeCO3 (C 2/m)proposedbyBoulardetal.

(2012) andFe4C3O12 recentlyreportedby Cerantola etal.(2017).

CrystalstructuresofallphasesareshowninSupplementary Mate-rialFigs.S1–S6.

2.2. First-principlescalculations

First-principlescalculationswereperformedusingVASP(Kresse and Furthmüller, 1996a, 1996b), employing the projector aug-mented wave (PAW) method (Blöchl, 1994; Kresse and Joubert, 1999), within the framework of density functional theory. For most calculations the PBE exchange-correlation functional was used (Perdewetal., 1996), butwe alsoperformed some calcula-tions usinga modifiedversion oftheHSE06exchange-correlation functional(Krukauetal.,2006),tostudyreactionscontainingboth Fe2+ _{and Fe}3+ _{(discussed below). The valence electron}

config-urations for the potentials were 2p63s2 for Mg, 3d74s1 for Fe, 2s2_2p2 _forC,and2s2_2p4 _{forO.Thekinetic-energycut-offforthe}

plane-wave basis set was set to 850 eV. For calculationsof lat-ticeparametersandinternalenergiesunitcellswereusedandthe Brillouinzone sampledusing thefollowing Monkhorst-Packgrids (MonkhorstandPack,1976):6

×

6

×

6forthe R3c structuresof MgCO3 andFeCO3(10atoms),2

×

2

×

2fortheC 2/m

,

P 212121,

P 21/c and P -1 structures of MgCO3 and FeCO3 (30–60 atoms),

2

×

2

×

2 for Fe4C3O12 (38 atoms (primitive cell)) and 6

×

6

×

6fordiamond(2atoms).Thebreakcondition fortheelectronic self-consistent loopandionic relaxationwere 10−6 and10−5 eV, respectively. These parameters ensured that energies were con-verged to within 1 meV/atom and elastic constants to within a fewpercent.

It is well-known that standard density functional theory can fail topredictthe correctbandstructure oftransitionmetal min-erals and oxides, because of the strongly correlated d electrons

involved (Anisimov et al., 1991). In order to accurately describe the properties of FeCO3 and Fe4C3O12 at highpressure, we

em-ployed the DFT

+

U method (Anisimov et al., 1997), in particular, the simplifiedschemeofDudarev etal.(1998) inwhichonlythe difference between onsite Coulomb interaction parameter U and onsiteexchangeparameterJismeaningful.Throughoutthepresent work,UisusedtomeanU-J.Inthepresentstudy,U

=

2 eVwas foundtogivebestagreementwithexperimentalvaluesforthespin transitionpressureofironandsowasadoptedforproduction cal-culationsofFeCO3 andFe4C3O12.

The DFT

+

U methodimplemented in VASP uses a constant U, which is inappropriate for studyingreactions involving Fe2+ _and

Fe3+,asironindifferentoxidationstatesrequiresadifferentvalue of U, e.g. in (Mg,Fe)SiO3 post-perovskite the value of Ufor Fe3+

isabout1eVhigherthanthatfor(Fe2+_{)(Yuetal.,2012).Hybrid}

exchange-correlationfunctionalsofferanalternative,althoughata higher computational cost. In view of this, forall calculationsof phase boundaries that involved both Mg1-xFexCO3 andFe4C3O12,

we used a modified version of the HSE06 exchange-correlation functional(Krukauetal.,2006)tocomputeinternalenergies.

The modification involved decreasing the fraction of Hartree-Fockexchangefrom25to10percent,sincearecentinvestigation showed that, for FeCO3, this leads to improved agreement with

experimental observations(Sherman, 2009).The internalenergies werecombinedwithvibrationalfreeenergiescalculatedusingthe DFT

+

U method (see below) to determine their Gibbs free ener-gies. Tests showedthat the difference in the vibrationalfree en-ergies calculated using the DFT

+

U method and modified HSE06 exchange-correlationfunctionalwasnomorethan10meV/atom.

2.3. Thermodynamicproperties

The thermodynamic propertiesof each phase were calculated usingthePHONprogram(Alfè,2009),basedonthefinite displace-ment method.Forlatticedynamics calculations,various cellsizes were used.FortheMgCO3 phasesthesewere:R3c (2

×

2

×

2

=

80atoms),C 2/m(1

×

1

×

1

=

60atoms), P -1(2

×

2

×

1

=

120 atoms), P 212121 (1

×

1

×

1

=

60atoms)and P 21

/

c (1

×

2

×

1

=

120atoms).FortheFeCO3 phasesthesewere:R3c (2

×

2

×

2

=

80atoms),C 2/m(1

×

1

×

1

=

60atoms),Fe4C3O12(2

×

2

×

2

=

304atoms)andC(diamond)(4

×

4

×

4

=

128atoms).For super-cells with

<

100atoms, the Brillouinzone was sampled using2

×

2

×

2k-pointsgridsgeneratedbytheMonkhorst-Packscheme (MonkhorstandPack,1976),whileforallothersonlythegamma pointwas considered.Thesesettingsensuredthatcalculated ther-modynamicpropertieswereconvergedtowithin10meVperatom. Ingeneral,thermodynamicvalueswerecalculatedatabout10 vol-umes, in the pressure range from

−

10 to 140 GPa. These were fittedtoaBirch-Murnaghanequationofstate(Birch,1947).

Forminerals containing iron, additional terms need to be in-cludedinthecalculationoftheGibbsfreeenergy(e.g.Tsuchiyaet al.,2006),duetothemagneticandconfigurationalentropy contri-butions.Thefractionofironinthelow-spinstatecanbecomputed as

n

(

P

,

T

)

=

1

1

+

m

(

2S

+

1

)

exp

(

GLS−HS(P,T)

kBT

)

,

(1)

where



GLS–HS

(

P

,

T

)

isthecalculateddifferenceintheGibbsfree

energyofthelow-spinandhigh-spin states,ataparticular pres-sureandtemperature.Thetotalvolumeis

Vtotal

= (

1

−

n

)

VHS

+

nVHS

,

(2)

whereVHSisvolumeofthehigh-spinstateandVLSthevolumeof

thelow-spinstate.

Thecontributionfrommagneticentropyis

Smag

=

kB

(

1

−

n

)

ln



m

(

2S

+

1

)



,

(3) where m is the orbital degeneracy, S is the total spin quantum number and n is the fraction of iron in the low-spin state. For Fe2+_,m

₌

_{3(high-spin)andm}

₌

_{1 (low-spin), whileforFe}3+_,m

=

1(high-spin)andm

=

3(low-spin).ForFe2+_,S

₌

_2(high-spin)

andS

=

0 (low-spin),whileforFe3+, S

=

5/2 (high-spin)andS

=

1

/

2 (low-spin).

In a spin-crossover region, high-spin and low-spin iron is treatedasasolidsolutionwithconfigurationalentropy

Sconf

= −

kB



(

n

)

ln

(

n

)

+ (

1

−

n

)

ln

(

1

−

n

)



,

(4) wherekB isBoltzmann’sconstantandn thefractionofironinthe

low-spinstate.ThetotalGibbsfreeenergyofaphaseisthus

Gtotal

(

P

,

T

)

=

nGLS

(

P

,

T

)

+ (

1

−

n

)

GHS

(

P

,

T

)

−

T

(

Sconf

+

Smag

),

(5) where P is pressure, T istemperature, GHS

(

P

,

T

)

the Gibbs free

energyofthehigh-spinstate, GLS

(

P

,

T

)

theGibbs freeenergyof

low-spinstate, n the fractionof iron in the low-spinstate, Smag

themagneticentropyandSconftheconfigurationalentropy.

Forphase transitionsin pure end-members, phase boundaries were calculated from the difference in their Gibbs free energies, atagivenpressureandtemperature.Forsolidsolutionstheywere determined from the co-tangentof the Gibbs free energies, in a similarmannertothe methodreportedby (MetsueandTsuchiya, 2012),makingtheassumptionthatwehaveidealmixingandthat thespin transitionpressureisindependent ofcomposition (Fuet al., 2017; Hsu and Huang, 2016; Lavina et al., 2010a; Lin et al., 2012; Liu etal., 2014;Merlini and Hanfland,2013; Spivaket al., 2014).

2.4. Elasticandseismicproperties

Inorderto determinethesixindependent elasticconstants of MgCO3 (R3c) and FeCO3 (R3c), one rhombohedral (for c13 and

c33) and two monoclinic strains (for c11, c12, c14 andc44) were

applied to the optimized structures. Correspondingstresses were computedby relaxingatomic positionsin thestrained configura-tions,withthelattice constantskept fixed.Elasticconstants were thencalculatedfromsimplestress-strainrelations,bythefittingof asecond-orderpolynomial.

It should be noted that MgCO3 (R3c) and FeCO3 (R3c) have

two settings. One has 10 atoms in the unit cell (rhombohedral setting)andanotherhas30atoms(conventionalsetting).For com-putationalefficiency,therhombohedralsettingwasusedinall cal-culations. While the total energy is unchanged under coordinate transformations,elastic constants dochange.Forthe convenience of comparingwith previous results,the following cartesian com-ponentsareused:

⎛

⎜

⎜

⎝

0 aRsinθ₂ aRcosθ₂

−

√3

2aRsinθ2

−

12aRsinθ2 aRcosθ2

√ 3 2 aRsin θ 2

−

1 2aRsin θ 2 aRcos θ 2

⎞

⎟

⎟

⎠ ,

(6)

whereaR is thelength ofarbitraryaxis(aR

,

bR orcR) sincethey

areequal,R meansthissettingisrhombohedraland

θ

istheangle betweentwoaxes.

The relation betweenlattice parameters inrhombohedral and conventionalsettingisexpressedas

ac

=

2

×

aR

×

sin

θ

2

,

(7) cc

=

aR

×

√

3

×

√

1

+

2

×

cos

θ ,

(8)

whereac andccarethelengthsofthea andc axesinthe

conven-tionalsetting,respectively.Thechoicesofcrystalorientationaffects thesignofc14 (Golesorkhtabaretal., 2013).Inthepresentstudy,

the calculated value of c14 is negative, but in order to compare

withpreviousresults,itisreportedpositive.

TheelasticconstantsofMgCO3(C 2/m)werecalculatedfromsix

triclinic strains. The thirteen independent elastic constants were divided into sixgroups (c11,c12,c13,c15; c22, c23, c25; c33, c35;

c44,c46;c55;andc66),witheachgroupbeingcalculatedfromone

strain.

The elastic constants of Fe4C3O12 were calculated using the

samestrainsusedforMgCO3(R3c)andFeCO3(R3c),asithas

sim-ilar R3c symmetry.

TheanisotropyfactorforVP ( AP)isdefinedas

AP

=

2

×

VP,max

−

VP,min VP,max

+

VP,min

×

100%

,

(9)

whereVP

,

max andVP

,

min arethemaximumandminimum

com-pressional wave velocities. The analogous polarization anisotropy factorforVP

(

AS

)

isdefinedas

AS

=

Vs1

−

Vs2 Vs

×

100%

,

(10)

where VS1 and VS2 aretheshearwavevelocitiesand VS the

ag-gregateshear-wavevelocity.

2.5. Pressurecorrection

ItiswellknownthatGGAexchange-correlationfunctionals,like PBE, overestimate pressure. In order, to account for this, an em-pirical pressure correction (Oganov et al., 2001), of a few GPa is applied to all of our results. A single pressure correction was

Fig. 1. PhasediagramofMgCO3.Theexperimentalmeltingcurve(Solopovaetal., 2015)isshownasagreyline,withthedashedportiondepictingitsextrapolation tohighpressure.Solidwhitecirclesindicateconditionswhereexperimental stud-iesreportMgCO3(R3c)tobestable(Isshikietal.,2004).Half-filledcircles(Isshiki

etal.,2004)andsquares(Boulardetal.,2011)indicateconditionswherea high-pressurephasewasobserved.Theblackdashedlineisamantlegeotherm(Stixrude andLithgow-Bertelloni,2011).

calculated forall MgCO3 phases andall FeCO3 phases, based on

experimental data forthe R3c structure. For moredetails please seeSupplementaryMaterialTableS1.

3. Resultsanddiscussion

3.1. PhasediagramofMgCO3

Our computed phase diagram for MgCO3, based on the

cal-culated Gibbs free energies of the R3c, P -1, C 2/m

,

P 21/c and

P 212121 phasesis shownin Fig. 1.In agreement withthe work

of Zhang etal. (2018), we find a direct transition fromthe R3c

structure to the C 2/m structure atabout 75 GPa atall tempera-tures above 1000 K, withthe P -1 structure being stable over a short pressure range at lower temperature. The phase boundary at75 GPa is in agreement withthe predictions of Oganov et al. (2008) andobservationsofBoulardetal.(2011) andMaedaetal. (2017), but conflicts with the work of Isshiki et al.(2004), who found the R3c phase to be stable above 100 GPa at 2000 K.In contrasttoZhangetal.(2018),we findthe P 21/c structuretobe

stable in a small region at about 130 GPa, below about 500 K. However, the difference in the Gibbs free energies of the P 21/c

andC 2/m structuresisonlyafew meV/atomattheseconditions. The P 212121 phaseisfoundtobestableatpressures higherthan

thoseexpectedinthelowermantle,asreportedbyothers(Pickard andNeeds,2015;Zhangetal.,2018).

Comparison of thesequence of phase transitions predicted at lowertemperature,withthatexpectedalongageotherm(Stixrude andLithgow-Bertelloni,2011)revealssome significantdifferences. Inparticular,the P -1and P 21/c structures,whichare stableat0

K,areunstableabove about700K.Thisshowstheimportance of includingtemperatureinstudiesofphasestability.Ourcalculations indicatethatit istheC 2/m phasethat isstableinthelowermost mantle.The C 2/m structure comprises (C3O9)6− rings, similar to

those reportedin high-pressurephases ofiron-rich compositions (Boulardetal.,2015,2012,2011),discussednext.

3.2. SpinstateofironinFeCO3andFe4C3O12

InordertoinvestigatethephasediagramofFeCO3 itis

essen-tialtofirstdeterminethecorrectspinstateofironinthevarious

Fig. 2. Calculatedenthalpydifferencebetweenhigh-spinandlow-spinFeCO3(R3c)

at 0K,usingPBE,DFT+U(U=2 eV) andDFT+U(U= 4eV).Usingthesame approximation, ferromagnetic and antiferromagnetic FeCO3 (R3c) exhibitalmost

identicalspintransitionpressures.InclusionofUshiftsthespintransitiontohigher pressure,asexpected.(Forinterpretationofthecoloursinthefigure(s),thereader isreferredtothewebversionofthisarticle.)

phasesbeingconsidered.Inthepresentwork,we considerFeCO3

(R3c)andtheFe4C3O12phasereportedbyCerantolaetal.(2017).

Inaddition,weconsiderFeCO3(C 2

/

m),astheironend-memberof

themoststableMgCO3 phaseatlowermantleconditions.

Ourcalculated0Kenthalpydifferencesbetweenhigh-spinand low-spinFeCO3 (R3c)are showninFig.2.Calculationswere

per-formed withthe PBE exchange-correlation functional (Perdew et al.,1996)andwiththeadditionofaHubbardUcorrection (Anisi-mov etal., 1997; Dudarev et al., 1998) (DFT

+

U), using effective U values of 2 eV and 4 eV. At 0 GPa, both PBE, and DFT

+

U (U

=

2 eV) predict a ferromagnetic ground state, while DFT

+

U (U

=

4 eV) predicts an antiferromagneticground state. The true ground state isantiferromagnetic (Badautet al., 2010). To obtain an antiferromagnetic ground state using standard DFT function-als,spin-orbitcoupling(SOC)mustbeincludedinthecalculations (Badaut et al., 2010). Since the enthalpy difference between the ferromagnetic andantiferromagnetic statesissmall (3 meV/atom at 0GPa) andphysical propertiesof the ferromagneticand anti-ferromagneticstructuresare almostidentical(Supplementary Ma-terialTableS2),neglectofSOCshouldnotaffectourresultsandis thereforenotincludedinourcalculations.

UsingPBEwecalculateahigh-spintolow-spintransition pres-sureofabout20GPa(Fig.2).InclusionofUshiftsthespin transi-tiontohigherpressures,about40GPaforU

=

2 eVand70GPafor U

=

4 eV,asexpected.The differenceinthespintransition pres-surescalculatedforferromagneticandantiferromagneticstructures is, atmost, 2GPa. Experimentalandtheoretical studies ofFeCO3

(R3c), report a spin transitionpressure of about 45 GPa (Ceran-tolaetal., 2015;Farfanetal.,2012; HsuandHuang,2016;Lavina etal.,2010b,2009;Mattilaetal.,2007;Weisetal.,2017).Studies ofa widerangeofcompositionsofMg1-xFexCO3 (x

=

0.05-1)

re-port similarspin transitionpressures,intherange40-52GPa(Fu etal.,2017;HsuandHuang,2016;Lavinaetal.,2010a;Linetal., 2012; Liuet al., 2014; Merlini andHanfland, 2013; Spivaket al., 2014), confirming suggestions that the concentration of iron has littleeffectonspintransitionpressure.

Shietal.(2008) reportaspintransitionpressureof28GPafor FeCO3(R3c),usingDFT

+

U(U

=

4 eV),whichismuchsmallerthan

ourvalueof70GPa.Thereasonforthisdifferenceisnotclear. Far-fan etal.(2012) reporta spintransitionpressureof44GPausing PBE, whichis muchhigher than ourvalue of 20GPa. Thiscould bebecausetheyallowedspintovaryfreelyduringtheirstructural

relaxations,allowing themagnetic momentto decrease gradually asthespintransitionpressureisreached,beforeundergoing mag-neticcollapse.

Temperature shifts the spin transitionto higher pressure and leads toa mixed-spin region,where high-spinandlow-spin iron co-exist (Hsuand Huang,2016; Liu etal., 2014) (Supplementary MaterialFig.S7).Ourcalculatedspin transitionpressure at300K (definedasthepressure atwhichn

=

0.5, wheren

=

fractionof low-spiniron)isabout44GPa,ingood agreementwithprevious studies(Cerantolaetal.,2015;Farfanetal.,2012;HsuandHuang, 2016; Lavinaetal., 2010b, 2009; Mattilaetal., 2007;Weis etal., 2017). The width ofthe mixed-spin region (definedas the pres-surerangeoverwhich0.05

<

n

<

0.95)isabout4GPa at300K andabout 13 GPa at1200 K, ingood agreement with Liu etal. (2014), who report a widthof about 4 GPa at 300K and about 10GPaat1200K.Since DFT

+

U(U

=

2 eV)leads togood agree-mentwithexperiment,we adoptthisvalueforall calculationsof thermodynamicandelasticandseismicproperties.

Calculated0Kenthalpiesforthehigh-spinandlow-spinstates ofFe4C3O12 [

+

C (diamond)] andFeCO3 (C 2

/

m)(Supplementary

Material Fig. S8 and Table S3), indicate that they are in a high-spinstateatlowermantlepressures.Sincespintransitionpressure onlyincreaseswithtemperature,nospintransitionisexpectedin thesephasesatlowermantleconditions.Thissupportstheresults ofCerantolaetal.(2017) forFe4C3O12,butdisagreeswiththoseof

Liuetal.(2015).ForFe4C3O12, amixed-spinstate ismore stable

thanthe low-spinstate atall pressures. Inthismixed-spin state, ironatomssituatedonthethreefold axisareinahigh-spinstate, whileallothersareinalow-spinstate.

3.3.PhasediagramofFeCO3

Liuetal.(2015) observedatransitionfromFeCO3 (R3c)

struc-turetoa high-pressurephaseat about50GPaand1400K.They were ableto resolve thespace group ofthis newphase,but not atomicpositions.However,morerecentexperimentalwork (Ceran-tolaetal., 2017) indicates that thehighpressurephase ofFeCO3

reportedbyLiuetal.(2015) isFe4C3O12.Cerantolaetal.(2017)

re-porta complexseriesofdecompositionproductsforFeCO3 (R3c)

between 70 GPa and 110 GPa, as temperature is increased. The first of these is Fe4C3O12, observed as a single phase at about

1400K and with other phasesup to about 2250 K. The forma-tionofFe4C3O12canbedescribedbythereaction:FeCO3 (R3c)

=

Fe4C3O12

+

C(diamond),whichweinvestigatehere.

Calculated0Kenthalpiesforthehigh-spinandlow-spinstates ofFeCO3 (R3c),Fe4C3O12

+

C(diamond)andFeCO3(C 2/m)

(Sup-plementary Material Fig. S8 and Table S3), indicate that at 0 K low-spinFeCO3 (R3c) is the most stablephase, at lower mantle

pressures. Below about 20 GPa the Fe4C3O12 structure reported

by Cerantola et al. (2017) is found to undergo an iso-symmetric phasetransitiontoa differentstructure identifiedby using FIND-SYM(StokesandHatch, 2005) (SupplementaryMaterial TableS4), butit is less stable than high-spin FeCO3 (R3c)in this pressure

range.Thesituationisdifferentatlowermantletemperatures. Our calculated phase boundary between FeCO3 (R3c) and

Fe4C3O12

+

C(diamond),indicatesthat Fe4C3O12

+

C(diamond)

ismore stablethanFeCO3 (R3c)atlowermost mantleconditions

(Fig.3).ThephaseboundarywascalculatedusingboththeDFT

+

U methodandamodifiedversionoftheHSE06exchange-correlation functionaltocomputeinternalenergies.Thelattershouldbemore reliableforreactionswherethereisachangeinoxidationstate,as it does not require specification of a U value, which may vary with oxidation state. The phase boundary calculated using the modifiedversionoftheHSE06exchange-correlationfunctionalfits the experimental data well, marking the edge of the pressure-temperature space where high-pressure phases have been

ob-Fig. 3. PhaseboundarybetweenFeCO3 (R3c) andFe4C3O12 + C(diamond). The

solidredlineshowsthephaseboundary calculatedusingamodifiedversionof theHSE06exchange-correlationalfunctional.Thedashedredlineshowsthe anal-ogousphaseboundarycalculatedusingtheDFT+Umethod,forcomparison.Both solidwhitecircles(Liuetal.,2015)and squares(Cerantolaetal.,2017)indicate conditionswhereexperimentalstudiesreportFeCO3(R3c)isstable.Solidblack

cir-clesindicateconditionswhereanunknownhigh-pressurephaseisobserved,while half-filledcirclesindicateconditionswhereFeCO3 (R3c)andthe unknown

high-pressure phasecoexist(Liuet al.,2015).Solidblack squaresindicate conditions whereFe4C3O12 isreported tobestable, whilechequeredsquares (Cerantolaet

al.,2017)anddiamonds(Boulardetal.,2012)indicateconditionswhereFe4C3O12

coexistswithotherrunproducts.Thecolourmapindicatesthefractionoflow-spin ironinthestablephase.Thewhitedashedlineisamantlegeotherm(Stixrudeand Lithgow-Bertelloni,2011).

served(Cerantolaetal.,2017;Liuetal.,2015).Thegoodagreement withthephaseboundaryofLiuetal.(2015),supportstheideathat thephasetheyobservedwasFe4C3O12.Thephaseboundary calcu-latedusingDFT

+

U,alsomatchreasonablywell,butisabout500 K lower than experiments. The spin transitionin FeCO3 (R3c),

cal-culatedusingthemodifiedHSE06exchange-correlationfunctional, is about10GPa lower than that calculatedwith DFT

+

Uand ex-periment(Cerantolaetal., 2015;Farfanetal., 2012; Lavinaetal., 2010b,2009; Mattilaetal., 2007;Weis etal., 2017),highlighting thatitisnotaperfectapproximation.However,bothmethods pre-dict the formationof Fe4C3O12

+

C (diamond) at about50 GPa,

alongthemantlegeotherm.

Theunusualshapeofthephaseboundaryandthedrivingforce fortheformationofFe4C3O12ismagneticentropy(Fig.4).At

pres-suresabovethespintransition,FeCO3 (R3c)isinalow-spinstate,

which means that its magnetic entropyis zero regardless of the temperature. Ontheother hand,Fe4C3O12 isina high-spinstate

atallpressuresconsidered,whichmeansitsmagneticentropy in-creaseswithtemperature,eventually stabilizingitwithrespectto FeCO3 (R3c), even though it has a higher lattice enthalpy. This

is seen at 120 GPa, wherethe formation of Fe4C3O12

+

C

(dia-mond) occursat about1500 K ifmagnetic entropy is accounted for,butdoesnot occurup to3000Kifit isneglected (Fig.4(a)). The samething isalsoobserved forFeCO3 (C 2/m).The magnetic

entropyofFeCO3 (C 2/m)increasesfasterthanthatofFe4C3O12

+

C(diamond),sinceit containsferrousiron ratherthanferriciron, anditbecomesmorestableabove3000K.Thephaseboundary be-tweenFeCO3 (R3c)andFeCO3(C 2/m)hasasimilarformtothatof

Fe4C3O12,butisabout500Khigher.Followingamantlegeotherm,

Fe4C3O12

+

C(diamond)becomesstablefollowingtheonsetofthe

spintransitioninFeCO3(R3c),whereitlosesitsmagneticentropy

(Fig.4(b)).Theunusualimportanceofmagneticentropyarisesdue tothehighconcentrationofironinthephasesandthehigh tem-peraturesinthemantle.

Cerantolaetal.(2017) reporttheco-existenceofFe4C4O13with

Fig. 4. RelativeGibbsfreeenergyofFeCO3(R3c),FeCO3(C 2/m)andFe4C3O12+C(diamond):(a)asafunctionoftemperatureat120GPaand(b)alongamantlegeotherm

(StixrudeandLithgow-Bertelloni,2011).Thedashedlinesshowvalueswithoutthemagneticentropycontribution(shadedregion).FeCO3(R3c)hasnomagneticentropy

at120GPa,sinceironisinalow-spinstate.Followingamantlegeotherm,themagneticentropyofFeCO3(R3c)decreasesasthespintransitionprogresses,reachingzero

atabout80GPa.Incontrast,themagneticentropyofFeCO3(C 2/m)andFe4C3O12+C(diamond)increaseswithtemperature,evenathighpressure,asironremainsina

high-spinstate.ThismeansthatFeCO3(C 2/m)andFe4C3O12+C(diamond)aremorestablethanFeCO3(R3c)athightemperature,atpressuresabovethespintransition.

Fig. 5. Binary phase loop for the R3c to C 2/m phase transition, for a Mg0.81Fe0.19CO3composition.Solidwhitecirclesindicateconditionswhere

exper-imentalstudies reportMgCO3 (R3c) tobestable(Isshikietal.,2004).Half-filled

circles(Isshikietal.,2004)andsquares(Boulardet al.,2011)indicateconditions wherea high-pressurephase was observed.The black dashed lineis amantle geotherm(StixrudeandLithgow-Bertelloni,2011).

3000K,butit was notobserved by Liuetal.(2015), which sug-gests that, perhaps, different starting materials or experimental procedures can lead to the formation of different high-pressure phases.Determining the stabilityofthe Fe4C4O13phase isout of

thescopeofthepresentwork.

3.4. PhasediagramofMg1-xFexCO3

Previousinvestigationsofhigh-pressurephasesofMg1-xFexCO3

havetendedto focusoniron-richcompositions.While thesemay existinsomepartsofthemantlewhereironenrichmenthastaken place,itisexpectedthat ineclogite0.16

<

x

<

0.21andin peri-dotitex

=

0.07(Dasguptaetal.,2004;DasguptaandHirschmann, 2006; Sanchez-Valleetal., 2011).Using ourcalculatedGibbs free energiesforthemagnesiumandironend-membersoftheR3c and C 2/m phases, we determine the binary phase loop for the R3c

toC 2/m transitionfor(Mg0.93Fe0.07)CO3 (SupplementaryMaterial

Fig.S9) and(Mg0.81Fe0.19)CO3 (Fig. 5). Theseshow that iron has

a small effect, reducing the R3c to C 2/m phase transition pres-sureby 3–5GPa andopeningupabinary phaseloopof3–5GPa. Onewould, therefore,expect thephasetransitioninnatural iron-bearingcarbonates,whichhavenotundergoneironenrichment,to

Fig. 6. PhaseboundariesbetweenMg0.35Fe0.65CO3 (R3c),Mg0.35Fe0.65CO3 (C 2/m)

and (0.35 MgCO3 (C 2/m) + 0.1625(Fe4C3O12 + C(diamond))), neglecting the

phaseloop.Solidwhite circlesindicate conditionswhereMg0.35Fe0.65CO3 (R3c)

is stable(Liu etal., 2015),whilesolid white squaresindicate conditionswhere Mg0.6Fe0.4CO3(R3c)isstable(Boulardetal.,2012).Half-filledcirclesindicate

con-ditionswhereahigh-pressurephase,thatwaslateridentifiedasFe4C3O12

(Ceran-tolaet al., 2017)is stable,whilehalf-filled squaresindicate conditionswherea high-pressurephaseofMg0.6Fe0.4CO3 consistentwithaC 2/m structureisstable

(Boulardetal.,2012).Theblackdashedlineisamantlegeotherm (Stixrudeand Lithgow-Bertelloni,2011).

occur ata similar depth in the lower mantle as that forMgCO3

(Fig.1).

To compareour resultswithexperimental studies ofiron-rich compositions, we calculate the Gibbs free energies of Mg0.35Fe0.65CO3 (R3c) and Mg0.35Fe0.65CO3 (C 2/m) and consider

their potential transformation to (0.35 MgCO3 (C 2/m)

+

0.1625

(Fe4C3O12

+

C(diamond))).Forsimplicity,thephaseloopbetween

thetwoMg0.35Fe0.65CO3 phases,whichisonlyabout5GPa,is

ne-glected. The calculated boundary between the phases is plotted in Fig.6.Ourresults indicatethat above about60GPa and1800 K, Mg0.35Fe0.65CO3 (R3c) transforms to Mg0.35Fe0.65CO3 (C 2/m),

whereas at lower temperatures it transforms to MgCO3 (C 2/m),

Fe4C3O12 and C (diamond).In their study of an Mg0.35Fe0.65CO3

composition, Liu et al.(2015) reported the presence of Siderite-II, later identified as Fe4C3O12 (Cerantola et al., 2017), close to

our predicted phase boundary. However, they did not observe MgCO3(C 2/m).InanotherexperimentalstudyofanMg0.6Fe0.4CO3

composition, Boulard et al. (2012) detected the formation of HP-(MgFe)CO3 (as well as ferropericlase, a high-pressure

mag-Fig. 7. ElasticpropertiesofMgCO3 (R3c).Experimentalresultsareshownassolidwhiteup-pointingtriangles(Fiquetetal.,2002),down-pointingtriangles(Litasovetal., 2008),squares(Sanchez-Valleetal.,2011)andcircles(Yangetal.,2014).

netite phase and diamond), above about 75 GPa and 2600 K. HP-(MgFe)CO3 is thephase reportedin one oftheir earlier

stud-ies (Boulard et al., 2011), which is consistent with the C 2/m

space group, and fits with our phase diagram. Our results indi-catethat Fe4C3O12 willonlybe presentalong amantlegeotherm

forMg1-xFexCO3 (with x

>

0.7),forminginan intermediatelayer

comprising(1-x)MgCO3(C 2/m)

+

(x/4)(Fe4C3O12

+

C(diamond))

(SupplementaryMaterialFig. S10).

3.5.Elasticandseismicproperties

Theelasticpropertiesofcarbonatephasescanbe usedto pre-dicttheseismicpropertiesof mantleassemblages,whichare im-portantforconstraining the globalcarboncycleand carbon stor-age. In particular, the seismic anisotropy of Mg1-xFexCO3 is

re-portedtobe significant(Marcondes etal., 2016;Sanchez-Valleet al.,2011;Stekieletal.,2017;Yaoetal.,2018)andcouldbeusedas adiagnostictoolinregionsofsubductionoflithosphere.The elas-ticconstantsofMgCO3(R3c)havebeenmeasuredtoabout14GPa

(Yangetal., 2014) andcalculated to150 GPa at0 K(Marcondes etal., 2016; Stekieletal., 2017) andto90GPa athigh tempera-ture(Yaoetal., 2018).Calculated values havealsobeenreported MgCO3 (C 2/m) to 150 GPa at 0 K (Marcondes et al., 2016). In

contrast,much lessisknownabouttheelasticpropertiesof iron-bearingcarbonatephases.TheelasticconstantsofMg0.35Fe0.65CO3

havebeen measured to 70 GPa (Fu et al., 2017), while those of theironend-memberFeCO3 haveonlybeenmeasuredatambient

conditions(Sanchez-Valleetal.,2011).CalculatedvaluesforFeCO3

havebeenreportedto60GPa,withmeasurementsofc33andc44

(Stekieletal.,2017).Theseareinsufficientfordiscussionsontheir seismicdetectabilityinthemantle.

Ourcalculated0 Kelasticconstants of MgCO3 (R3c)are

plot-tedin Fig. 7and listed in Supplementary Material Table S5, and areinexcellentagreementwiththelowpressureexperimental re-sultsofFiquetetal.(2002), Litasovetal.(2008), Sanchez-Valleet al.(2011), Yang etal.(2014) and calculationsofMarcondesetal. (2016), Stekielet al.(2017) and Yao etal. (2018). The electronic

spin transition in FeCO3 leads to unusual pressure-dependence.

Our calculated 0 K elastic constants for FeCO3 (R3c), plotted in

Fig. 8and listed inSupplementary Material Table S6, are consis-tentwithmeasurements foraMg0.35Fe0.65CO3 composition(Fuet

al.,2017)andcalculationsandmeasurementsofFeCO3 (Stekielet

al., 2017). c12andc13soften tosuchan extentthat theybecome

negativeabove40GPa.c11andc33arealsobothsignificantly

soft-ened. In contrast,c44 increase by 65% and c14 increasesby 19%.

The elastic constants ofMgCO3 (C 2/m) are listed in

Supplemen-tary MaterialTable S5,withthose ofFe4C3O12 inSupplementary

MaterialTable S6.

Fig.9showsacomparisonoftheVP,VS,anddensityofMgCO3

(R3c), MgCO3 (C 2/m), FeCO3 (R3c), Fe4C3O12 and other major

mantlemineralsasafunctionofpressure,at0K.Atpressures cor-responding to theupper mantleand transitionzone, the seismic velocities of MgCO3 (R3c)are very similar to those offorsterite,

although its densityis much lower. Inclusion of iron reduces its seismicvelocitiesandincreasesdensity,meaningthattheseismic velocities of FeCO3 (R3c) are much lower and its densitymuch

higherthanthoseofforsterite,wadsleyiteandringwoodite.Inthe lowermantle,theseismicvelocitiesanddensityofMgCO3 (C 2/m)

aremostsimilartothosecalculatedforpericlaseandbridgmanite. Inclusionofironreducesvelocitiesandincreasesdensity.

Using calculations based on low pressure elastic constants of MgCO3 (R3c)andestimatedvolumefractions, previous

investiga-tions(Sanchez-Valleetal.,2011;Yangetal.,2014)showedthatthe differences in velocities of carbonated and non-carbonate eclog-ite and peridotite are about 1% or less, making the detection of carbonated lithologies from seismic velocities difficult. However, they did not consider a possible high-pressure phase transition. Ourcalculations predict aphase transition fromMgCO3 (R3c) to

MgCO3 (C 2/m) at 75 GPa. If we make a first-order

approxima-tionandneglect temperature,basedon our0Kelasticconstants, seismic discontinuities of about

+

4% in VP and

+

9% in VS are

expectedacrossthephasetransition.However, giventhatthe vol-ume fraction of MgCO3 in carbonated eclogite and peridotite is

Fig. 8. ElasticpropertiesofFeCO3(R3c).ExperimentalresultsforFeCO3(R3c)areshownassolidwhitesquares(Sanchez-Valleetal.,2011),whilethoseforMg0.35Fe0.65CO3

(R3c)areshownassolidwhitecircles(Fuetal.,2017).

Fig. 9. Compressionalwavevelocity(VP),shearwavevelocity(VS)anddensityofvariousphasesofMgCO3,FeCO3andFe4C3O12,comparedwiththoseofothermajormantle

minerals.Solidlinesrepresenttheresultsof0Ktheoreticalcalculations:forsterite(da Silvaetal.,1997),ringwoodite(Kieferetal.,1999),wadsleyite(Kieferetal.,2001), MgO(Karkietal.,1997)andMgSiO3(Kiefer,2002).ExperimentalresultsforMgCO3(R3c)areshownassolidwhitesquares(Sanchez-Valleetal.,2011)andcircles(Yanget

al.,2014)witharededge,whilethoseforFeCO3(R3c)areshownassolidwhitesquares(Sanchez-Valleetal.,2011)withablackedgeandthoseforMg0.35Fe0.65CO3(R3c)

assolidwhitecircles(Fuetal.,2017)withablackedge.

andHirschmann,2006;Sanchez-Valleetal.,2011),itislikelythat thesediscontinuitiesareundetectable.

From ourcalculated0K elasticconstants forFeCO3 (R3c), we

predictvelocityanomaliesacrossthespintransitionof45%in VP

and25% in VS. Their magnitudewill decrease withiron-content

andtheir sharpnessdecrease with temperature(Hsu andHuang, 2016).At47GPaand0K, VP ofFeCO3 (R3c)andFe4C3O12 differ

byabout6%,whiletheirVS differbyabout14%.

Usingour0 Kelasticconstants (SupplementaryMaterialTable S5 and S6), we estimate the anisotropy factor for VP ( AP) and

polarizationanisotropyfactorforVS ( AS)forMgCO3(R3c),MgCO3

(C

/

2m),low-spinFeCO3 (R3c)andFe4C3O12(Fig. 10).The centre

ofeachfigureisthedirectionperpendiculartotheab-plane,which isorthogonal tothepage.We notethat our0Kelastic constants

do not account fortemperature. Yang etal. (2014) reported that the influenceoftemperatureon theseismicanisotropy ofMgCO3

isweak,buttheirstudywasperformedoveralimitedtemperature rangeandshouldbeconfirmed.

We find that at 75 GPa, AS has a maximum value of 52%

for MgCO3 (R3c). This supports previous low pressure studies

(Sanchez-Valle etal., 2011; Yang etal., 2014), which report that MgCO3 (R3c)exhibitsgreateranisotropythanother majormantle

minerals.Incontrast,forthehigh-pressurephase,MgCO3 (C 2/m),

AS has a maximum value of 27%. This suggests that the R3c to

C 2/m phasetransition leads to a significant decrease in seismic anisotropy.Forlow-spinFeCO3 (R3c), AS hasamaximumvalueof

Fig. 10. Seismicanisotropy ofMgCO3 (R3c), MgCO3 (C /2m), FeCO3 (R3c), and

Fe4C3O12 at75 GPa.Thecentreofeachfigureis thedirectionperpendicularto

theab-plane,whichisorthogonal tothepage.Maximumandminimumvaluesare markedbysolidblacksquaresandcircles.Low-pressurephases(MgCO3(R3c)and

FeCO3 (R3c))exhibitaveryhighdegreeofseismicanisotropy,comparedtothe

high-pressurephases(MgCO3(C /2m)andFe4C3O12).MadeusingtheMATLAB

Seis-micAnisotropyToolkit(MSAT)(WalkerandWookey,2012).

is 11%. This implies that the transformation of FeCO3 (R3c) to

Fe4C3O12(diamond),willalsoresultinadecreaseinanisotropy.

Previousstudies (Sanchez-Valleetal., 2011;Yang etal., 2014) arguedthatcarbonatescoulddevelopahighdegreeoflattice pre-ferred orientation and the large anisotropy of MgCO3 (R3c) and

FeCO3(R3c),couldbeusedasadiagnosticfeaturetodetecthighly

carbonatedregionsinthe uppermantle.Ourresultssupport this, showing that, the large anisotropy of MgCO3 (R3c) and FeCO3

(R3c),persistsatlowermantlepressures.Incontrast,ourpredicted high-pressurephases, MgCO3 (C 2m) andFe4C3O12, exhibit much

weaker anisotropy, making it likely impossible to detect carbon-atedmineralsinthelowermostmantle.

3.6.Outstandingissues

Experimentalstudies show that carbonatesreact with SiO2 to

producesilicates

+

C

+

O2(Drewittetal.,2019).Theconditionsat

whichthisreactiontakesplaceisdebated.Onestudyindicatesthat thereactionwillnotoccuralongaverycoldslabgeotherm(Maeda et al., 2017), permitting the subduction of carbonates down to thecore-mantle boundary. In contrast,anotherinvestigation sug-geststhatreactionshouldoccurabove1500km,regardlessofslab geotherm(Drewittet al.,2019), meaningno carbonateswill per-sistbelowthisdepth.Ifthe formerstudyis correct,Mg1-xFexCO3

(C 2/m)andFe4C3O12 could be presentinthe lowermostmantle,

withformation ofthe latter providing an alternative explanation forsuper-deep diamonds (Wirth et al., 2014). If the latterstudy iscorrect, Mg1-xFexCO3 (C 2/m) isunlikely to presentinthe

low-ermostmantle.ThereactionbetweenFe4C3O12withSiO2 remains

tobeinvestigatedanditmaybestabletogreaterdepths.

Despite many studies of iron-rich carbonates (Boulard et al., 2015, 2012, 2011; Cerantola et al., 2017; Liu et al., 2015; Mer-lini et al., 2015), none have demonstrated that iron-enrichment willoccur,sincethestartingmaterialsfortheexperimentsdidnot contain otherphases. Ithas beenpostulatedthat thespin transi-tioninMg1-xFexCO3couldinduceironenrichment(Cerantolaetal.,

2015;Liuetal.,2015),inasimilarmannertothatobservedduring thespintransitioninferropericlase(MuirandBrodholt,2016). Ac-cordingtoourcalculationsthedegreeofiron enrichmentneeded for Fe4C3O12 to formin the lower mantle,is Fe/(Mg

+

Fe)

>

0.7,

whichismuch greaterthan themaximumofFe/(Mg

+

Fe)

=

0.35 calculatedforMg1-xFexO(MuirandBrodholt,2016). Furtherwork

isrequired toinvestigateiron partitioningto determineifsuch a degreeofironenrichmentispossible,andexplorethereasonwhy the Fe4C4O13 phase reported by Cerantola etal. (2017) was not

observedinotherstudies(Boulardetal.,2012;Liuetal.,2015). Our study has only considered the MgCO3-FeCO3 system and

neglectedtheroleofCaCO3.Therehavebeenseveralstudiesofthe

structureandstabilityofCaCO3atlowermantlepressures(Oganov

etal., 2008; PickardandNeeds,2015;Santos etal., 2019; Zhang et al., 2018). The most recent investigation (Zhang et al., 2018) indicates that CaCO3 readily reacts with SiO2 and so is unlikely

tobea majorhostofcarboninthelowermantle.However, more workisneededtoinvestigatetheMgCO3-CaCO3-FeCO3 system.

4. Conclusions

To summarise, we have performed ab initio calculations to determine the thermodynamic and elastic properties of various phases of MgCO3 and FeCO3, Fe4C3O12 and C (diamond), in

or-der to establish thestable phasesin the lower mantleand their possibleseismicdetectability.

Based on ourcalculations, we predict that Mg1-xFexCO3 (with

x

<

0.7) undergoes a transition from R3c to C 2/m structure at conditions corresponding to a depth of about 1800 km in the lower mantle. Inclusion of iron at these concentrations leads to a narrowbinary phaseloop ofonlya fewgigapascals. Forhigher iron concentrations, Mg1-xFexCO3 (with x

>

0.7), we predict an

additional intermediate layer comprising (1-x) MgCO3 (C 2/m)

+

(x/4)(Fe4C3O12

+

C(diamond)),thethicknessofwhichincreases

with iron content. In agreement with recent experimental work (Cerantola et al., 2017), we show that FeCO3 (R3c) undergoes

self-oxidation-reductionatconditionscorresponding toadepthof about1300kminthelower mantle,toformFe4C3O12

+

C

(dia-mond).Theunusualshapeofthephaseboundaryforthereaction is governed by the oxidation and spin state of iron in the two phases, which leads todifferentmagnetic entropiesat high tem-perature.

Similartoanumberofpreviousstudies(Marcondesetal.,2016; Sanchez-Valle et al., 2011; Stekiel et al., 2017; Yao et al., 2018), our calculations indicate that the seismic anisotropy of MgCO3

(R3c) and FeCO3 (R3c) is extremely high, meaning it might be

possible to use it as a diagnostic tool in regions of subduction of lithosphere. In contrast,we findthe seismic anisotropy ofthe correspondinghigh-pressurephases,MgCO3 (C 2/m)andFe4C3O12

(R3c), to be considerably weaker, meaning that if carbonates do persistinto thelowermostmantle,they are likelynot seismically detectable.

Ourworkhighlightstheimportanceofaccountingformagnetic entropy in calculations of iron-rich phases in planetary interiors andcomplexchemistryofiron-bearingminerals,arisingfromtheir unpaired d-electrons. Magnetic entropy can also influence phase transitionsatlowertemperatures(Zhou etal., 2014). Ouroriginal investigation began usingcrystalstructure prediction softwareto predictthe high-pressurephase ofFeCO3.Thisdidnottake

lowerenthalpythanFeCO3 (R3c).Itmaybepossibletoincludean

expression,similartoEq.(3),incrystalstructureprediction calcu-lations,toactasafirst-orderapproximationformagneticentropy, when comparing the stability of phases with different magnetic states.

Declarationofcompetinginterest

Theauthorsdeclarethattheyhavenoknowncompeting finan-cialinterestsorpersonalrelationshipsthatcouldhaveappearedto influencetheworkreportedinthispaper.

Acknowledgements

Theauthors thankthe anonymousreviewer,whosecomments greatly improved the manuscript. This work was supported by NERCgrantnumberNE/K006290/1.Thiswork was undertakenon ARC2andARC3,partoftheHighPerformanceComputingfacilities attheUniversityofLeeds,UK.ZLthanksAndrewWalkerandJohn BrodholtforhelpfulcommentsonhisMaster’sDissertation,which formedthe basisofthismanuscript. ZLalsothanks ElenaBykova forprovidingthecrystallographicstructurefileofFe4C3O12.

Appendix A. Supplementarymaterial

Supplementarymaterialrelatedtothisarticlecanbefound on-lineathttps://doi.org/10.1016/j.epsl.2019.115959.

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