phase stability of post-spinel compound amn 2 o 4 ...

Phase Stability of Post-spinel Compound AMn2O4 (A = Li, Na, or Mg)and Its Application as a Rechargeable Battery CathodeChen Ling* and Fuminori Mizuno

Toyota Research Institute of North America, 1555 Woodridge Avenue, Ann Arbor, Michigan 48105, United States

*S Supporting Information

ABSTRACT: At high pressures, spinel compounds can transform toCaFe2O4, CaMn2O4, or CaTi2O4 phases, which are regarded as post-spinelphases. Here, first-principles calculations are used to systematically study thestability of post-spinel LiMn2O4, NaMn2O4, and MgMn2O4, as well as theirpotential application as rechargeable battery cathodes. Thermodynamically,the stability of the post-spinel phase is highly related to the electronicconfiguration of transition-metal ions. By changing the concentration ofJahn−Teller active Mn3+, the relative stabilities of post-spinel phases can beeasily monitored. It provides a practical way to obtain post-spinel compoundswith desirable structures. Kinetically, post-spinel phases can be stable underambient conditions, because of the high barrier that must be overcome torearrange MnO6 octahedrons. The most spectacular finding in this work isthe high cationic mobility in post-spinel compounds. The activation energybarrier of the migration of Mg2+ in CaFe2O4-type MgMn2O4 is 0.4 eV, suggesting that the mobility of Mg2+ in this compound iscomparable to that of Li+ in typical Li-ion battery cathodes. To explore the potential application of post-spinel compounds asrechargeable battery cathodes, the voltage profile for the electrochemical insertion/removal of Mg in CaFe2O4-type MgMn2O4 ispredicted. Its theoretical energy density is 1.3 times greater than that of typical Li-ion battery cathodes. These outstandingproperties make CaFe2O4-type MgMn2O4 an attractive cathode candidate for rechargeable Mg batteries.

KEYWORDS: post-spinel phases, phase stability, Mg battery, cathode

1. INTRODUCTION

At high pressures, many spinel compounds can transform toone of the three denser structures: CaMn2O4 (CM), CaFe2O4(CF), and CaTi2O4 (CT), which are often regarded as post-spinel phases. For instance, the spinel-to-F phase trans-formation at pressures greater than 25 GPa was reported forMgAl2O4, which is one of the common constituent of low-pressure peridotite xenoliths.1 Replacing Al3+ with larger Mn3+

ions reduces the pressure required for the phase transition. Thespinel-to-CM transformation was observed for MgMn2O4(MMO) at 14.5 GPa.2 Another manganite spinel compound,LiMn2O4 (LMO), transforms to the CF phase at 6 GPa.3 Thesehigh-pressure phase transformations are significant scientificsubjects and provide a potential pathway to obtaining newmaterials with desirable properties.The structures of post-spinel AM2O4 are highly similar, with

distorted MO6 octahedrals forming so-called “double-rutilechains” (see Figure 1), and cation A being 8-fold coordinatedwith oxygen. In CM and CT phases, each double-rutile chain isconnected to two adjacent chains through edge-sharing oxygenand another two chains through corner-sharing oxygen,whereas, in the CF-type structure, the double-rutile chains areinterconnected through vertex sharing oxygen only. In CF andCT phases, all atoms are located in the mirror plane, while allatoms in the CM phase are displaced from the mirror plane.Because of their similar crystal structures, precise phase

identification is challenging, especially with the lack of high-quality X-ray diffraction (XRD) data.4 Therefore, the needremains for a systematic study that helps to eliminate theconfusion in the literature and provides instructive informationfor future studies.4 It is especially beneficial to provide amechanistic study about the phase transformation and thestabilities of post-spinel compounds.One interesting property of the post-spinel compounds is the

potentially high mobility of cations through the lattice. Thestructures of post-spinel phases have one-dimensional channelsalong one of the lattice axis for the migration of cations (seeFigure 1). Although a systematical study has not been reported,several literature reports have hinted at the high cationicmobility in post-spinel phases. The electrochemical insertion ofLi was reported in CF-Li0.92Mn2O4.

3 The measured activationenergy barrier for the ionic conduction in CF-LMO wasapproximately two-thirds of that of the spinel phase,3 indicatingthe enhancement of Li+ mobility after the spinel-to-post-spinelphase transition. In CF-Ca(Fe,Mn)2O4, Ca

2+ cations can beremoved either by chemical oxidation or by the ion exchangewith Li+.5 It suggested high mobility of Ca2+ and Li+ ions in CFphases.5 Very recently, CF-LMO has been reported as a

Received: April 17, 2013Revised: May 24, 2013Published: June 28, 2013

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© 2013 American Chemical Society 3062 dx.doi.org/10.1021/cm401250c | Chem. Mater. 2013, 25, 3062−3071

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rechargeable Li-ion battery cathode.6 Enhancing the diffusion ofcations (Li+, Na+, or Mg2+) is one of the key challenges in thedevelopment of cathode materials for rechargeable batteries.7

The potentially high ionic mobility makes post-spinel phasespromising candidates for cathode research. However, becauseof the challenges to effectively synthesize post-spinelcompounds,3 the possibility of using post-spinel compoundsas rechargeable battery cathodes has been highly overlookedright now. From this point of view, a theoretical study on theionic mobility in the post-spinel phases is necessary to attractthe experimental interest for deeper investigations.In this paper, a first-principles density functional theory

(DFT) study is performed to investigate the spinel-to-post-spinel phase transformation, as well as the potential applicationof post-spinel compound as rechargeable battery cathodes forAMn2O4 with A = Li, Na, or Mg. The thermodynamical and thekinetical stabilities of the post-spinel phases have been analyzedto provide instructive insights for future experimentalinvestigations. The study of the migrations of cations in thepost-spinel phases shows that the ionic mobilities in CF-typeAMn2O4 are high enough to meet the request of rechargeablebattery cathodes. Particularly, the high mobility of Mg2+ in CF-MgMn2O4 suggests its potential as a rechargeable Mg batterycathode. Possible synthesis routes to obtain desirablecompounds are also suggested.

2. METHOD2.1. Thermodynamics for the Phase Transformation

at High Pressures. Phase transformation induced by highpressures can be well-studied using DFT calculations.8 Toestimate the transition pressure, one may first calculate the freeenergies as a function of the volume for each phase and thenfind the slope of the tangent line between two G(V) curvescorresponding to different crystal structures. Another methodto estimate the transition pressure is to consider the free-energychange at constant pressure:

Δ = Δ + Δ − ΔG P E P P V P TS( ) ( ) ( ) ( ) (1)

If we neglect the contribution of the entropy, the transitionpressure at 0 K can be obtained at the point where two H(P)(H(P) = E(P) + PV) curves cross each other. In eq 1, theenergy can be fitted with Murnagham equation of states:9

=−

+ −−

+

−

−

⎡⎣⎢

⎤⎦⎥E V B V

VB B V

VB V B

E

( )( 1)

11

B

B0 00

1

1 1 11

1 0 1

0

1

1

(2)

where B0 is the bulk modulus, B1 the first derivative of the bulkmodulus, E0 the energy at zero pressure, and V0 the volume atzero pressure. The effect of the pressure on the volume can beexpressed as

= +⎛⎝⎜

⎞⎠⎟V P V

B PB

( ) 1B

01

0

1/ 1

(3)

2.2. Predict the Electrochemical Voltage Profile. Inorder to investigate the electrochemical performance of post-spinel phases as rechargeable battery cathodes, the convex hullapproach is applied to predict the voltage profiles when cationsare electrochemically removed or inserted into the host. Here,the procedure to obtain the voltage profile is briefly explained;the details of the method can be found elsewhere.10,11 Theconvex hull approach begins with the calculations of a series ofstructurally distinct configurations. The formation energy ofeach configuration is then calculated as a function ofconcentration and the convex hull of the formation energycurve is obtained by connecting all the ground states along theconfigurational path. The voltage (vs A/An+) along the convexhull to electrochemically insert cation An+ is calculated as

= −− − −

−V

E E y x E

ne y x

( )

( )A Mn O A Mn O Ay x2 4 2 4

(3)

Here, EAyMn2O4, EAxMn2O4

, and EA represent the total energy ofAyMn2O4, AxMn2O4, and metallic A, respectively. AyMn2O4 andAxMn2O4 are two adjacent ground states along the convex hullof the formation energies; n is the number of electrons carriedby cation An+.

2.3. Computational Details. DFT calculations wereperformed with the Vienna Ab Initio Simulation Package(VASP) using projector augmented waves (PAW) pseudo-potentials and the exchange-correlation functionals para-metrized by Perdew, Burke, and Ernzerhof for the generalizedgradient approximation (GGA).12−14 Numerical convergenceto less than 2.5 meV per MnO2 unit was ensured by using acutoff energy of 550.0 eV and appropriate gamma-centered k-point mesh with the density of at least 0.03 Å−1. The relaxationis first performed on the ionic positions and the unit cell size,followed by a self-consistent calculation with a fixed unit-cellvolume. To study the migration of ions, the nudged elasticband method is applied in the search of transition states.In order to correctly characterize the localization of

transition-metal d-electrons, the GGA+U method with aHubbard-type potential to describe the d-part of theHamiltonian is applied in all our calculations with U-J = 3.9.Previous reports using similar U values showed goodagreements with experiments for various Mn oxides and Liinserted Mn compounds.11,15,16 Calculations with different U-Jvalues were also tested. In most of following discussions, theenergies were compared between compounds with the samecomposition, in which the effect of U-J values is not as

Figure 1. Schematics of the spinel and post-spinel phases. The view isalong the [010] direction for CaFe2O4 and along the [001] directionfor CaMn2O4 and CaTi2O4, respectively. Mn and O are shown aspurple and red spheres, respectively.

Chemistry of Materials Article

dx.doi.org/10.1021/cm401250c | Chem. Mater. 2013, 25, 3062−30713063

significant as in the comparison between compounds withdifferent compositions.17 As a result, the relative stabilities ofpost-spinel phases and the barrier for the migration of cationsin the post-spinel phases were generally not affected by thechoice of U-J value. On the other hand, the choice of U-J doesaffect the voltages profiles. Higher U-J values predicted highervoltages for the insertion and removal of cations in the post-spinel phases, which is consistent with other reports.18

3. RESULTS3.1. Phase Stability of Stoichiometric AMn2O4. Table 1

compares the calculated lattice parameters for the fully relaxed

structures of the spinel and post-spinel compounds withstoichiometric composition AMn2O4. The calculated latticeparameters are slightly overestimated, compared to theexperimental values. Such a slight overestimation is usually acommon result in GGA calculations. The ground states forLiMn2O4 (LMO) and MgMn2O4 (MMO) are predicted to be

cubic spinel and distorted spinel phases, respectively. Thedistortion of MMO from the cubic to tetragonal symmetry isclearly due to the Jahn−Teller deformation of Mn3+O6octahedrons. For simplicity, it is still denoted as spinel phasehere and afterward. Compared to post-spinel phases, the spinelNaMn2O4 (NMO) is metastable, mainly because of the largesize of Na+ ion.19 Among the structure considered in this study,the most stable NMO is predicted to be the CF phase.All post-spinel phases are denser than their spinel counter-

parts. The volumetric contraction between the spinel and post-spinel phases is ∼6%−14%, with CT-type phases being thedensest phase, in good agreement with the experimentalobservations.2,3 The denser volume suggests the possibletransformation from the spinel to post-spinel phases at highpressures. To study the phase transformation, several fixed-volume calculations are performed. Figure 2 shows the

calculated total energy as a function of the volume, togetherwith the corresponding fit of the DFT data to the Murnaghamequation of state. The fitted parameters are reported in Table 2.The bulk modulus of spinel phases from DFT calculations liesat ∼90−120 GPa. The experimental bulk modulus for spinel−LMO was reported to be 103−119 GPa,2,20,21 which is in goodagreement with our calculations. These values are far below 200GPa, which is typical for most spinel oxides. The unusual lowbulk modulus was reported for spinel−LMO as a result of thelocal compressibility of LiO4 tetrahedral.

20 For LMO, MMO,and NMO, NaO4 should have the highest local compressibility,because of the larger size of Na+ and longer Na−O bondlength, followed by LiO4, then by MgO4 which has thestrongest Mg2+−O bonding. It explains why the bulk moduli

Table 1. Relative Energies, Lattice Parameters, Unit CellVolume, and Volume Contraction (Relative to the SpinelPhase) for LiMn2O4, NaMn2O4, and MgMn2O4 with theSpinel (Space Group Fdmm for LMO and NMO, I41/amdfor MMO, respectively), CaFe2O4 (Space Group Pnma),CaMn2O4 (Space Group Cmcm), and CaTi2O4 (Space GroupPmab) Phases

spinel CF CM CT

LMO

relative energy(meV per MnO2unit)

0 58.4 240.1 239.9

lattice parameters(Å)

a 8.346 8.645 9.496 9.469

b 2.862 9.647 9.517

c 10.986 2.932 2.947

unit-cell volume, v(Å3)

36.33 33.87 33.57 33.20

volume contraction,Δv (%)

−6.77 −7.6 −10.4

NMO


241.2 meV 0 295.0 meV 280.0 meV


a 8.746 8.975 9.839 9.788

b 2.912 9.769 9.744

c 11.022 2.981 3.000


41.81 36.01 35.82 35.77


−13.9 −14.3 −14.5

MMO


0 436.1 meV 216.1 meV 326.1 meV


a 8.170 9.094 9.533 9.820

b 2.974 9.873 9.497

c 248 0.391 3.023 2.969


38.58 35.13 35.57 34.61


−8.9 −7.8 −10.3

Figure 2. Total energy versus volume curves for (a) LiMn2O4, (c)MgMn2O4, and (e) NaMn2O4; total energy versus pressure curves for(b) LiMn2O4, (d) MgMn2O4, and (f) NaMn2O4. Symbols correspondto the DFT calculated data, and lines show the fitting to theMurnagham equation of state. The pressure for the predicted phasetransition is marked with the red arrows.



follow as MMO > LMO > NMO, with the only exception beingfor CT-LMO and CT-MMO. The bulk modulus of post-spinelphase is higher than the spinel phases as CT > CF > CM >spinel, consistent with the experimental measurements.4 Allpost-spinel phases are harder to compress than the spinelphase.Figure 2 also shows the change of enthalpy as a function of

pressure using the equation of states fit with DFT calculateddata. The spinel-to-post-spinel phase transformation ispredicted for LMO and MMO. Spinel LMO transforms tothe CF phase at 3.4 GPa, while the transformation of MMOhappens at 11.1 GPa from spinel to the CM phase, in goodagreement with the experimental reports (6 GPa for LMO3 and14.5 for MMO2). A couple of sources may contribute to thedeviation between the calculated transition pressure and theexperimental value. Apparently, the first contributor is theentropy effect that is neglected in our calculation. Because thespinel phase is always softer than the post-spinel phases, theentropy part would increase the transition pressure at hightemperatures.8 Another possible contributor is the existence ofLi or Mg vacancies,3 which decreases the transition pressure, aswe will discuss later. Overall, the trends for the spinel-to-post-spinel transition predicted from DFT calculations are inremarkable agreement with experiments; i.e., for spinel LMOand MMO, the phase transition ends in the CF and CM phases,respectively. For NMO, the most stable structure is the CFphase, which is consistent with experiments that directlysynthesized CF-NMO.22

Before further discussing the relative stability of the post-spinel phases, it is necessary to give a detailed description abouttheir crystallographical structures. Because the calculationssuggest that the CT phase is metastable for all three AMOcompounds considered in this study, here, only the CM and CFphases are compared. As shown in Figure 3, in both CF andCM phases, MnO6 first forms so-called “double-rutile chains”

interconnecting through the corner-shared oxygen in the CFphase, or through both corner-shared and edge-shared oxygenin the CM phase. One distinct difference between the CF phaseand the CM phase is the number of independent transition-metal sites. In the CF phase, there are two crystallographicallyindependent transition-metal sites (Mna and Mnc), as shown bydifferent colors in Figure 3a, while only one transient site existsin the CM-type structure.In LMO and NMO, Mn has an average oxidation state of

+3.5 and exists as a mixture of Mn3+ and Mn4+ (half/half),because of the localization of electrons on Mn ions,23 whereassin MMO, Mn remains as pure Mn3+ ions. Mn3+ is well-knownas Jahn−Teller active ion that can induce significant latticedeformation. The distortion of MnO6 can be quantitativelydescribed by the octahedral distortion parameter κ, as

∑κ = −

⎛⎝⎜

⎞⎠⎟

R RR

16

2

(4)

where R and R are the distance and average distance of theMn−O bonds, respectively. Higher κ values suggest largerdistortion of MnO6 octahedron from the ideal shape.Table 3 reports the calculated κ value for LMO, NMO, and

MMO in the CF and CM phases. In CF-LMO and CF-NMO,strong distortion is clearly recorded on MncO6 octahedron.There are two elongated Mnc−O bonds: 2.19 Å in CF-LMOand 2.15 Å in CF-NMO. The rest of the Mnc−O bond lengthsvary over a range of 1.94−1.96 Å in CF-LMO and over a rangeof 1.94−1.99 Å in CF-NMO. The elongation of the Mnc−Oaxis is consistent with the Jahn−Teller distortion of theMnc

3+O6 octahedron. The MnaO6 octahedron is quite regular,with weaker distortion varying the Mna−O bond lengths overranges of 1.94−1.98 Å and 1.93−2.02 Å in CF-LMO and CF-NMO, respectively. These results suggest that, in CF-LMO andNMO, Mna ions remain as Jahn−Teller inactive Mna

4+ and Mncions are Jahn−Teller active Mnc

3+. The ordering of Mn4+/Mn3+

on the Mna/Mnc site is further verified through the analysis ofthe Bader charge of Mn ions. For CF-LMO and CF-NMO, theBader charge of the Mnc ion is ∼0.1 e lower than that of theMna ion, suggesting that Mnc existing at lower oxidation state.It is consistent with the statement that the oxidation state ofMnc ions is +3, whereas, for Mna, it is +4. We should note herethat the absolute value of the Bader charge does not provideany information on the formal charge of Mn ions.24 It is thedifference of Bader charges that shows the oxidation orreduction of Mn ions.For MMO, all MnO6 octahedrons show strong distortion in

both CF and CM phases. In CF-MMO, the distance of Mn−Obonds varies from 1.95 Å to 2.13 Å, while in CM-MMO, itvaries from 1.95 Å to 2.38 Å. Bader charge analysis proves thatthe oxidation state of Mn in MMO is lower than +4 in both CFand CM phases, with very slight variation between Mna andMnc site in the CF phases. It is consistent with the picture thatall Mn ions in MMO are Jahn−Teller active Mn3+ with largedistortion effect.In CM-LMO and CM-NMO, we fail to distinguish different

Mn ions after DFT relaxation. All MnO6 octahedrons shownoticeable distortion. Bader charge analysis indicates that allMn have the same oxidation state, instead of separating as Mn3+

and Mn4+ ions. To test whether the choice of U-J values inGGA+U calculations affects the results, we repeat thecalculations with U = 5, 6, and 7. However, no characteristicdifference is observed that could distinguish Mn4+ and Mn3+ in

Table 2. Bulk Modulus (B0) and Its First-Order Derivative(B1) for the Spinel and Post-Spinel Compounds

spinel CF CM CT

LMOB0 (GPa) 103.0 123.8 119.0 164.1B1 3.4 4.9 5.8 2.3

NMOB0 (GPa) 93.1 105.8 98.7 113.1B1 7.1 6.2 7.4 5.1

MMOB0 (GPa) 118.6 144.8 135.0 160.8B1 1.3 4.2 5.0 4.6

Figure 3. Structure view of AMn2O4 in (a) the CaFe2O4 phase and (b)the CaMn2O4 phase. Two distinct Mn sites in CaFe2O4 phases aredenoted with purple (Mna) and yellow (Mnc) colors.



CM-LMO and CM-NMO in all calculations. Thus, it isconcluded that all Mn ions in CM compounds are symmetri-cally equivalent, even after DFT relaxation.By learning the details of the structural changes in the series

of compounds, the thermodynamic stability of post-spinelAMn2O4 can be related to the electronic configuration of Mnions. In CF phases, the two distinct crystallographical sites, Mnaand Mnc, are beneficial to distinguish between Jahn−Telleractive Mn3+ and inactive Mn4. The ordering of Mn4+/Mn3+ inthe CF phase helps to stabilize CF-LMO and CF-NMO. Onthe other hand, in MMO, all Mn ions exist as Jahn−Telleractive Mn3+ species. The homogeneous electronic configurationof Mn ions in the CM phase becomes beneficial toaccommodate the structural deformation caused by thecooperative Jahn−Teller distortions of MnO6. It makes CM-MMO more stable than CF-MMO.3.2. Phase Stabi l i ty of Nonstoichiometric

Mgx(Fe,Mn)2O4. In this section, our study is extended fromstoichiometric AMn2O4 to nonstoichiometric compounds.Specifically, we consider nonstoichiometric Mgx(Fe,Mn)2O4containing cation deficiency and/or substitutional Fe at Mnsites. By creating Mg vacancies or by replacing Mn with Fe,Jahn−Teller active Mn3+ ions are replaced with Mn4+ or Fe3+

ions, both of which are Jahn−Teller inactive.We first look at how Mg deficiency affects the phase stability

of Mg-deficient MgxMn2O4. To model Mg/vacancy ordering,Mg atoms are removed from the unit cells of CF-, CM-, andspinel-MMO. It is possible that more-complex ordering mayappear within multiple unit cells. However, quantitativeinformation can still be obtained by only considering theordering in a single unit cell with moderate computational cost.DFT calculations are then used to obtain the H(P) curves fordifferent polymorphs of MgxMn2O4, and the phase transitionsare identified by checking how the H(P) curves cross eachother. For all of the x values that we have considered, spinel-MgxMn2O4 is always the most stable at ambient pressures.Table 4 lists the phase transition from spinel-MgxMn2O4 to

post-spinel phases. The presence of a Mg vacancy has twonoticeable effects on the relative stabilities of spinel and post-spinel phases. First, the Mg vacancy decreases the pressurerequired for the phase transition. For example, 25% of Mgvacancy decreases the pressure required for spinel-to-post-spinel phase transition from 11.1 GPa to 8.8 GPa. The reason

for this effect is probably that the softer structure of Mg-deficient spinel-MgxMn2O4 is easier to compress, making thephase transition happen at lower pressures. Another effect ofMg vacancy is shown in the relative stability of post-spinelphases. The introduction of Mg deficiency raises the relativestability of the CF phase. For compounds with <25% Mgvacancy, the CM phase is the most stable post-spinel phase(also see Figure 4). For compounds with >25% Mg vacancy,

the CF phase becomes more stable than the CM phase. ForMg0.75Mn2O4, at ambient pressure, CM-MMO is more stable.However, CF-MMO becomes more stable at 4.7 GPa. Thus,the only observable phase transition for Mg0.75Mn2O4 is fromspinel to CF phase at 8.8 GPa. All these effects can be explainedby the replacement of Mn3+ with Mn4+ when a Mg vacancy isintroduced. It raises the relative stability of the CF phases, inwhich the two crystallographical sites are beneficial todistinguish between Mn4+ and Mn3+.The replacement of Jahn−Teller active Mn3+ with inactive

species can also be achieved by substituting Mn for othertransition-metal ions. For example, Fe3+, with d5 (t2g

3eg2)

electronic configuration, is Jahn−Teller inactive. To examinethe effect of Fe doping, the relative stability for CF- and CM-Mg1−x(FeyMn1−y)2O4 is investigated. In order to avoid theappearance of Fe4+ ions, the composition space is limited by theboundary condition y ≤ x. The relative phase stability atambient pressure is characterized by the difference between theground-state energies. As shown in Figure 4, the relativestability of the CF phase is improved by Mg vacancies andsubstitional Fe doping, both of which decreases theconcentration of Jahn−Teller active Mn3+ ions. It furtherconfirms that the relative stability of the post-spinel phases is

Table 3. Distortion parameter (κ) of MnO6 Octahedrals and Bader Charges on Mn Ions (q) in AMn2O4 with CaFe2O4 andCaMn2O4 Phases

CF-Mna CF-Mnc CM

A κ q (e) κ q (e) κ q (e)

Li 8.9 × 10−5 +2.04 2.1 × 10−3 +1.92 1.4 × 10−3 +1.47Na 3.1 × 10−4 +2.02 2.0 × 10−3 +1.90 2.7 × 10−3 +1.97Mg 1.4 × 10−4 +1.88 2.6 × 10−3 +1.86 7.5 × 10−3 +1.87

Table 4. Possible Phase Transition of MgxMn2O4 and theCorresponding Transition Pressure

x phase transition pressure (GPa)

0.25 spinel to CF 5.40.5 spinel to CF 7.70.75 spinel to CF 8.80.75 CM to CF 4.71 spinel to CM 11.1

Figure 4. Energy difference between Mg1−x(FeyMn1−y)2O4 with theCaFe2O4 structure and the CaMn2O4 structure. Negative valuesindicate that the CaFe2O4 phase is more stable than the CaMn2O4phase and vice versa. The solid black line shows where the energies oftwo structures are the same.



highly related to the electronic configuration of the transition-metal ions.Summarizing the results presented in the previous and this

section, a general mechanism can be provided to explain therelative thermodynamical stability of post-spinel phases. Ingeneral, if ion B is Jahn−Teller active species in compoundAB2O4, the most stable post-spinel structure should be the CMphase. Replacing ion B with Jahn−Teller inactive species raisesthe relative stability of the CF phases. Eventually, forcompounds containing a certain level of Jahn−Teller inactiveions, the CF phase becomes more stable than the CM phase.The natural CF and CM phases are named after CaFe2O4 andCaMn2O4, in which all transition-metal ions are Jahn−Tellerinactive Fe3+ and active Mn3+, respectively. As listed in Table 5,

our conclusion holds for a variety of AB2O4 com-pounds.1−3,5,22,25−28 Apparently, this mechanism not onlyprovides instructive information for future experimental studies,but also suggests an effective and practical way to obtain post-spinel compounds with desirable structures. Because thethermodynamical stability of post-spinel phases is controlledby the electronic configuration of the transition-metal ions, it ispossible to monitor the stabilities of post-spinel phases byvarying the concentration of Jahn−Teller active ions. Forexample, the crystal structure of CaMn2O4 has beensuccessfully switched from the CM structure to the CFstructure with the introduction of Ca deficiency and/or Fedoping.5 Our study suggests it can also be used to monitor therelative stability of CF- and CM-Mg1−x(FeyMn1−y)2O4 (seeFigure 5). We believe that this approach can be helpful tosynthesize other materials with desirable post-spinel structures.3.3. Kinetics for the Spinel to Post-spinel Transition.

In this section, our focus changes from the thermodynamics tothe kinetic phase stability. The kinetic limitation of the phasetransformation was indicated by the experimental observationthat the phase transformation usually required temperatures of>1000 K, and the release of the pressure at ambienttemperatures did not inversely transform crystalline CF-LMOand CM-MMO to their spinel forms.2,3 It suggested that thephase transformation is controlled not only by the thermody-namic stability, but also by the kinetics of the transition. Underambient conditions, especially at low temperatures, the slowkinetics prevents the reverse transition from post-spinel tospinel phases.It is easy to qualitatively understand the kinetic limitation

from the large structural difference between the spinel andpost-spinel phases (for illustration, see Figure 1).25 However,quantitative study about the kinetical phase transition is verychallenging, because the transformation of spinel AMn2O4 topost-spinel phases is a complicated solid process. It involves the

migration of cation A as well as the rearrangement of Mn ionsin order to form the double-rutile chain as the building block inthe post-spinel frameworks.25 In order to investigate thekinetics quantitatively, we adapt the mechanism proposed byArevalo-Lopez et al., in which the phase transition begins withthe migration of half transition-metal ions to the edge-neighbored unoccupied octahedral sites (Figure 5a), followed

by the rotation of the chain in order to obtain appropriateconnection of octahedrons.25 More specifically, we analyze themigration of Mn ions between edge-shared MnO6 octahedronsin MgMn2O4 as an example to study the kinetics of spinel-to-post-spinel phase transition.We evaluate two possible hopping paths for the migration of

Mn ions. The direct hopping of Mn ions between neighboredoctahedral sites is considered first, as shown in Figure 5b. Thedisplacement of Mn into the unoccupied octahedral sites causesa great amount of repulsion between Mn and neighbored Mgions, because of their short distances (1.85 Å). It results in highinstability of the final configuration. To avoid this strongrepulsion, two Mg ions that are too close to Mn are manuallyremoved along the hopping path. This operation is reasonableand explains why cation vacancies were always observed inpost-spinel compounds.3 The energy of final state is 456 meVhigher than the initial state, in the similar level as the energydifference between spinel MMO and CF-MMO (Table 1).However, the barrier for the direct hop is 1.67 eV, whichsuggests the kinetic difficulty for the migration of Mn ions.We have also considered another migration path starting

from the initial octahedral site, to the intermediate tetrahedralsite, then to the final octahedral sites (Figure 6b). It isdistinguished as the indirect hopping path. To locate Mn ionsat tetrahedral sites, one neighbored Mn and two Mg ions mustbe manually removed in order to avoid the strong repulsionbetween these ions and the hopping Mn ion. The energy profilealong the indirect hopping path is plotted in Figure 6d.Surprisingly, the configuration with Mn located at O2 site inFigure 6b is identified as a saddle point between two tetrahedral

Table 5. Structure of AB2O4 Compound Reported in Post-Spinel Phases and the Electronic Configuration of B Ions

composition B ion structure ref

Li0.92Mn2O4 Mn4+ t2g3, Mn3+ t2g

3eg1 CF 3

NaMn2O4 Mn4+ t2g3, Mn3+ t2g

3eg1 CF 23

MgMn2O4 Mn3+ t2g3eg

1 CM 2CdCr2O4 Cr3+ t2g

3 CF 26CaCo2O4 Co3+ t2g

6 CF 27Mn3O4 Mn3+ t2g

3eg1 CM 28

MgAl2O4 Al3+ CF 1Ca(Fe,Mn)2O4 Fe3+ t2g

3eg2, Mn3+ t2g

3eg1 CF 5, 29

Figure 5. Migration of Mn ions in the spinel MgMn2O4 to form thedouble rutile chains: (a) side view from the [001] direction (themigration is indicated by the arrows; green octahedrons illustrate theposition of Mn ions after the migration); (b) direct hopping path (O1to O2) and indirect hopping path (O1 to T to O2) for the migration ofsingle Mn (Mg ions are not shown for the sake of simplicity); (c)migration barrier for the direct hopping path; and (d) migrationbarrier for the indirect hopping path.



sites, instead of being a local minimum. Although the barrier islower than the direct hopping, the indirect hopping is unlikelyto happen in real cases, because it is easier to be blocked by therepulsion between Mn and other cations neighbored to thehopping path. The instability of the final configurations alsosuggests the double-rutile chain may not be formed through theindirect hopping path.After the migration of Mn ions, MnO6 octahedrons must

been further rotated in order to achieve appropriateconnections between the double-rutile chains.25 The rotationis very likely to be even more difficult than the migration of Mnions.25 Thus, the migration barrier calculated in this study givesa lower boundary for the kinetic phase transition. The highbarrier for the migration of Mn indicates the phase trans-formation is kinetically limited by the rearrangement oftransition-metal ions under ambient conditions.19 Therefore,it is necessary to promote the kinetics by increasing thetemperatures for the phase transition. It explains why typicalspinel-to-post-spinel phase transformation only happens attemperatures higher than 1000 K. The high kinetic barrier alsoexplains why the inverse transition from post-spinel to spinelphase is hindered at room temperature. Therefore, althoughpost-spinel phases are usually thermodynamically metastablespecies, they can still be kinetically stable under ambientconditions, as has already been demonstrated in the study ofCF-LMO and CM-MMO.2,3

3.4. Cationic Mobility in Post-spinel Phases. In spinelLiMn2O4, the migration of Li+ is of great interest, because of itsimportance as rechargeable Li-ion battery cathodes. Thestructure of spinel AMn2O4 has only half of the octahedralsites occupied by Mn, and a quarter of the tetrahedral sites areoccupied by cation A, respectively, with the other octahedraland tetrahedral sites being unoccupied. It indicates ion A in thespinel compounds is confined in a relatively small space with alarge portion of empty space in the structure. On the otherhand, in post-spinel compounds, cations are located in a relativelarger space. This characteristic could be favorable to enhancethe cationic mobility.29 Although a comprehensive study is stillmissing, several experiments have already provided a hint forhigh ionic mobility in post-spinel phases.3,5,6 It motivates us tostudy the migration of Li+, Mg2+, and Na+ in post-spinel phases.In the post-spinel phases, the framework of MnO6

octahedrons has a one-dimensional (1D) channel along oneof the crystal axes (the b-axis for CF, the c-axis for CM and CT;see Figure 1). It is reasonable to assume that the ionicmigration only happens through the channel and ignore the

interchannel migration. The activation energy barriers for themigration of Li+, Mg2+, and Na+ in three post-spinel phases areplotted in Figure 6. Curiously, although the crystal structures ofthe three post-spinel phases are similar, the ionic mobilitythrough the channel is quite different. The migration in the CFstructure is noticeably faster than in the CM and CT structures.The migration barrier for Li+ is 0.12 eV, which is smaller thanthe typical migration barrier in Li-ion battery cathodes, such aslayered LiMO2,

30,31 olivine LiMPO4,17,32 and spinel LiMn2O4.

23

Even for large cations (Na+) or divalent cations (Mg2+), themigration barrier is still comparable to that of Li migration inspinel-LiMn2O4.

23 To our knowledge, a barrier as low as 0.4 eVfor the migration of Mg2+ ions has never been reportedpreviously in the literature.To explain this unusual low migration barrier in the CF

phases, the migration path is analyzed in Figure 7. The creation

of a vacancy displaces two adjacent cations (A(1) and A(2) inFigure 8) toward the vacancy. If A(1) hops from theequilibrium position to the vacancy, large Columbic repulsionis generated, because of the short distance between A(1) andA(2). It pushes A(2) along the hopping direction of A(1).Meanwhile, A(3) is also attracted by the vacancy toward thedirection of the migration of A(1). Unlike the migration ofindividual Li+ in spinel-LiMn2O4,

23 this migrating behavior inCaFe2O4-type compounds is a cooperative motion of A(1),A(2), and A(3) together, along the same direction. Apparently,such a collective and collaborative hopping is energetically

Figure 6. Energy barriers for the migration of Li+, Mg2+, and Na+ ions in post-spinel phases.

Figure 7. Schematic diagram describing the cooperative one-dimensional (1D) migration of A(1) ions (blue arrows) and adjacentA(2) and A(3) (green arrows) in the post-spinel phases. We use thedistance between Mg2+ ions in MgMn2O4 (in units of Å) forillustration.



advantageous, because it shortens the migration distance foreach ion.33

It is possible that the distinct two Mn sites in the CF phasesare also beneficial to high ionic mobilities. In fact, the creationof cation vacancies oxidizes Mn3+ to Mn4+. On the basis of theanalysis in the previous sections, this process is easier to beachieved in the CF structure, with two distinct sites for Mn3+

and Mn4+. Although the detailed mechanism is still underinvestigation, it may explain the different diffusion barriers inthe CF, CM, and CT phases.3.5. Potential Application of Post-spinel Phases as

Rechargeable Battery Cathodes. Materials with highcationic mobilities have good potential as rechargeable batteryelectrodes. For electrode materials, high ionic conductivity isalways required in order to provide good rate capability.7 Slowdiffusion limits the rate capability of the electrodes or evenprevents the practical insertion and removal of cations. Thediffusion of cations is especially important in the study of Mgbatteries, where the search of appropriate cathode materials isgreatly challenged by the sluggish mobility of the Mg2+ ion inthe host lattice.34−38 The barrier for the migration of Li+ in CF-LMO is lower than that of typical Li-ion battery cathodes. Itsuggests that CF-LMO may work as high rate cathode materialsfor Li-ion batteries. The low barrier for the migration of Mg2+

in CF-MMO also suggests it has the potential for the fastinsertion/removal of Mg2+ into/from the host lattice.To provide information for the experimental investigations of

post-spinel phases as rechargeable battery cathodes, the voltageprofiles are plotted in Figure 8 for the electrochemicalinsertion/removal of Li and Mg in CF-LixMn2O4 and

MgxMn2O4. Compared to a recent report that examined thevoltage profile of Li0.81Mn2O4,

6 the difference between the first-principles-calculated voltage and the experimental values is onthe order of 0.1−0.2 V. This level of agreement is typical in theDFT prediction of voltage profile for Li-ion battery cathodes.39

The voltage for Li insertion/removal is lower than the lithiationof spinel MnO2,

40 mainly because the longer distances betweenLi and O in CF-LixMn2O4 weaken the bonding strength. Onthe other hand, the voltages predicted for Mg insertion/removal lie between 2.84 V and 1.68 V (vs Mg/Mg2+), higherthan most of the reported Mg battery cathodes.34,41 It makesCF-MMO an attractive candidate as a high-voltage Mg batterycathode.The voltages presented in Figure 8 are calculated based on

the assumption that the electrochemical reaction follows theintercalation/retraction of Li+ or Mg2+ without phase transitionfrom the CF phase to the more-stable spinel structures. Wehave already shown in the previous sections that thisassumption is reasonable because of the kinetic stability ofthe CF phase under ambient conditions. In principle, if Li orMg reacts with CF-MnO2, it may also follow the conversionreaction path as

− + → − +x y x x y(4 2 )Li MnO (2 )Li O Mn Ox y2 2

− + → − +x y x x y(4 2 )Li 2 MnO (2 )Li O 2Mn Ox y2 2 2

− + → − +x y x x y(2 )Mg MnO (2 )MgO Mn Ox y2

(here, MnxOy represents possible Mn oxides including Mn2O3,Mn3O4, and MnO).To further assess the thermodynamical stability of the

intercalation path, we construct the convex hull of the energychange along the conversion reaction path, and plot theenergies of the intercalated compounds (CF-LixMn2O4 or CF-MgxMn2O4) in the same figure. If the energy of theintercalation compound lies below the convex hull of theconversion reaction, the intercalation path is then morethermodynamically preferable than the conversion reaction.Otherwise, it is more preferable to have the conversionreaction. As shown in Figure 9, for all of the ground states ofCF-LixMn2O4 and CF-MgxMn2O4, only CF-MgMn2O4 liesabove the convex hull. It indicates that the intercalation of Mg2+

into CF-MnO2 is at least achievable to Mg0.875Mn2O4. In fact,the energy of CF-MgMn2O4 is only 33.5 meV per atom higherthan that of a mixture of MgO and Mn2O3. Considering theconversion reaction also requires overcoming the kinetic barrierto destruct the crystal structure, we postulate that evenMgMn2O4 is still achievable through the intercalation reaction.If the full capacity can be achieved in CF-MMO (270.1 mAh/g,half Mg per Mn), its theoretical energy density will be ∼1.3times greater than the typical energy density of Li ion batterycathodes (3.5 V vs Li/Li+, 150 mAh/g). Therefore, it is of greatinterest to obtain CF-MMO experimentally and test itsperformance as a rechargeable Mg battery cathode.In order to obtain the desirable MMO with the CF structure,

special attention must be paid to the synthesis, because thestoichiometric CF-MMO is metastable, compared to the spinelphase or even the CM phase. Nonetheless, it is possible to firstsynthesize a precursor with the kinetically stable CF phase as atemplate for the desirable CF-MMO. On the basis of the resultspresented in this study, three possible ways are suggested toobtain CF-MMO, as illustrated in Figure 10. Obviously, route 3is the most cost-friendly, because it does not require any high-

Figure 8. Voltages for the electrochemical insertion of (a) Li intoCaFe2O4-phase LixMn2O4 and (b) Mg into CaFe2O4-phaseMgxMn2O4.



pressure step. Experimentally, the ionic exchange between Ca2+

and Li+ in CF-phase compounds has already been suggested.25

It will be interesting to see if similar approaches could give CF-Mgx(Fe,Mn)2O4 and how the targeted compound works as arechargeable Mg battery cathode.

5. CONCLUSIONSTo conclude, in this work, the thermodynamics and kinetics ofthe spinel-to-post-spinel phase transition have been systemati-cally studied for LiMn2O4, MgMn2O4, and NaMn2O4. Ourstudy correctly predicts the stability of these compounds indifferent polymorphs, as well as the phase transition induced byhigh pressures. The thermodynamic stability of post-spinelphases is controlled by the electronic configuration oftransition-metal ions. The relative stability of the CaFe2O4phase is higher for compounds with less Jahn−Teller activeions. Kinetically, because of the large barrier to rearrange Mn

ions, the post-spinel phase can be stable under ambientconditions. Our results not only help the experimentalinvestigation of high-pressure spinel to post-spinel phasetransition, but also provide an easy way to obtain materialswith desirable post-spinel structures.Perhaps the most interesting finding in this work is the high

mobilities of Li+, Na+, and Mg2+ in post-spinel phases, especiallyin the CaFe2O4 phase. The mobility of Li+ in CaFe2O4−LiMn2O4 is higher than in typical Li-ion battery cathodes,suggesting its potential as a high rate cathode. The barrier forthe migration of Mg2+ in CaFe2O4−MgMn2O4 is calculated tobe 0.4 eV, suggesting that the mobility of Mg2+ in thiscompound is fast enough to satisfy the requirements for use asa rechargeable Mg battery cathode. The theoretical energydensity of CaFe2O4-MgMn2O4 is ∼1.3 times greater than thatof the typical Li-ion battery cathode, making it an attractivecandidate for the study of high-energy-density Mg batteries. Tothe best of our knowledge, this is the first report about Mgbattery cathode candidate with both high Mg mobility and hightheoretical energy density. Possible methods to obtainCaFe2O4−MgMn2O4 are also suggested in this study. It isthus of great interest to experimentally test the performance ofCaFe2O4−MgMn2O4 in rechargeable Mg batteries.

■ ASSOCIATED CONTENT*S Supporting InformationThe effect of U-J values in the calculations. This material isavailable free of charge via the Internet at http://pubs.acs.org.

■ AUTHOR INFORMATIONCorresponding Author*E-mail: [email protected] authors declare no competing financial interests.

■ ACKNOWLEDGMENTSWe appreciate the fruitful discussions with Dr. R. Asahi atToyota Center Research and Development Laboratory. Imagesof crystal structures were generated with the VESTAprogram.42

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