A = Li, Na, or Mg - American Chemical Society

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Phase Stability of Post-spinel Compound AMn2O4 (A = Li, Na, or Mg) and Its Application as a Rechargeable Battery Cathode Chen 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 to CaFe2O4, CaMn2O4, or CaTi2O4 phases, which are regarded as post-spinel phases. Here, first-principles calculations are used to systematically study the stability of post-spinel LiMn2O4, NaMn2O4, and MgMn2O4, as well as their potential application as rechargeable battery cathodes. Thermodynamically, the stability of the post-spinel phase is highly related to the electronic configuration of transition-metal ions. By changing the concentration of Jahn−Teller active Mn3+, the relative stabilities of post-spinel phases can be easily monitored. It provides a practical way to obtain post-spinel compounds with desirable structures. Kinetically, post-spinel phases can be stable under ambient conditions, because of the high barrier that must be overcome to rearrange MnO6 octahedrons. The most spectacular finding in this work is the high cationic mobility in post-spinel compounds. The activation energy barrier of the migration of Mg2+ in CaFe2O4-type MgMn2O4 is 0.4 eV, suggesting that the mobility of Mg2+ in this compound is comparable to that of Li+ in typical Li-ion battery cathodes. To explore the potential application of post-spinel compounds as rechargeable battery cathodes, the voltage profile for the electrochemical insertion/removal of Mg in CaFe2O4-type MgMn2O4 is predicted. Its theoretical energy density is 1.3 times greater than that of typical Li-ion battery cathodes. These outstanding properties 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 to one of the three denser structures: CaMn2O4 (CM), CaFe2O4 (CF), and CaTi2O4 (CT), which are often regarded as postspinel phases. For instance, the spinel-to-F phase transformation at pressures greater than 25 GPa was reported for MgAl2O4, which is one of the common constituent of lowpressure peridotite xenoliths.1 Replacing Al3+ with larger Mn3+ ions reduces the pressure required for the phase transition. The spinel-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 These high-pressure phase transformations are significant scientific subjects and provide a potential pathway to obtaining new materials with desirable properties. The structures of post-spinel AM2O4 are highly similar, with distorted MO6 octahedrals forming so-called “double-rutile chains” (see Figure 1), and cation A being 8-fold coordinated with oxygen. In CM and CT phases, each double-rutile chain is connected to two adjacent chains through edge-sharing oxygen and another two chains through corner-sharing oxygen, whereas, in the CF-type structure, the double-rutile chains are interconnected through vertex sharing oxygen only. In CF and CT phases, all atoms are located in the mirror plane, while all atoms in the CM phase are displaced from the mirror plane. Because of their similar crystal structures, precise phase © 2013 American Chemical Society

identification is challenging, especially with the lack of highquality X-ray diffraction (XRD) data.4 Therefore, the need remains for a systematic study that helps to eliminate the confusion in the literature and provides instructive information for future studies.4 It is especially beneficial to provide a mechanistic study about the phase transformation and the stabilities of post-spinel compounds. One interesting property of the post-spinel compounds is the potentially high mobility of cations through the lattice. The structures of post-spinel phases have one-dimensional channels along one of the lattice axis for the migration of cations (see Figure 1). Although a systematical study has not been reported, several literature reports have hinted at the high cationic mobility in post-spinel phases. The electrochemical insertion of Li was reported in CF-Li0.92Mn2O4.3 The measured activation energy barrier for the ionic conduction in CF-LMO was approximately two-thirds of that of the spinel phase,3 indicating the enhancement of Li+ mobility after the spinel-to-post-spinel phase transition. In CF-Ca(Fe,Mn)2O4, Ca2+ cations can be removed either by chemical oxidation or by the ion exchange with Li+.5 It suggested high mobility of Ca2+ and Li+ ions in CF phases.5 Very recently, CF-LMO has been reported as a Received: April 17, 2013 Revised: May 24, 2013 Published: June 28, 2013 3062

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

Chemistry of Materials

Article

If we neglect the contribution of the entropy, the transition pressure 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, the energy can be fitted with Murnagham equation of states:9 ⎡ V0 B1 − 1 1 ⎤ V ⎥ E(V ) = B0 V0⎢ + − B1 − 1 B1V0 B1 − 1 ⎦ ⎣ B1(B1 − 1)V1 + E0

(2)

where B0 is the bulk modulus, B1 the first derivative of the bulk modulus, E0 the energy at zero pressure, and V0 the volume at zero pressure. The effect of the pressure on the volume can be expressed as 1/ B1 ⎛ B P⎞ V (P) = V0⎜1 + 1 ⎟ B0 ⎠ ⎝

2.2. Predict the Electrochemical Voltage Profile. In order to investigate the electrochemical performance of postspinel phases as rechargeable battery cathodes, the convex hull approach is applied to predict the voltage profiles when cations are 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 The convex hull approach begins with the calculations of a series of structurally distinct configurations. The formation energy of each configuration is then calculated as a function of concentration and the convex hull of the formation energy curve is obtained by connecting all the ground states along the configurational path. The voltage (vs A/An+) along the convex hull to electrochemically insert cation An+ is calculated as

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

rechargeable Li-ion battery cathode.6 Enhancing the diffusion of cations (Li+, Na+, or Mg2+) is one of the key challenges in the development of cathode materials for rechargeable batteries.7 The potentially high ionic mobility makes post-spinel phases promising candidates for cathode research. However, because of the challenges to effectively synthesize post-spinel compounds,3 the possibility of using post-spinel compounds as rechargeable battery cathodes has been highly overlooked right now. From this point of view, a theoretical study on the ionic mobility in the post-spinel phases is necessary to attract the experimental interest for deeper investigations. In this paper, a first-principles density functional theory (DFT) study is performed to investigate the spinel-to-postspinel phase transformation, as well as the potential application of post-spinel compound as rechargeable battery cathodes for AMn2O4 with A = Li, Na, or Mg. The thermodynamical and the kinetical stabilities of the post-spinel phases have been analyzed to provide instructive insights for future experimental investigations. The study of the migrations of cations in the post-spinel phases shows that the ionic mobilities in CF-type AMn2O4 are high enough to meet the request of rechargeable battery cathodes. Particularly, the high mobility of Mg2+ in CFMgMn2O4 suggests its potential as a rechargeable Mg battery cathode. Possible synthesis routes to obtain desirable compounds are also suggested.

V=−

E A yMn2O4 − E A xMn2O4 − (y − x)EA ne(y − x)

(3)

Here, EAyMn2O4, EAxMn2O4, and EA represent the total energy of AyMn2O4, AxMn2O4, and metallic A, respectively. AyMn2O4 and AxMn2O4 are two adjacent ground states along the convex hull of the formation energies; n is the number of electrons carried by cation An+. 2.3. Computational Details. DFT calculations were performed with the Vienna Ab Initio Simulation Package (VASP) using projector augmented waves (PAW) pseudopotentials and the exchange-correlation functionals parametrized by Perdew, Burke, and Ernzerhof for the generalized gradient approximation (GGA).12−14 Numerical convergence to less than 2.5 meV per MnO2 unit was ensured by using a cutoff energy of 550.0 eV and appropriate gamma-centered kpoint mesh with the density of at least 0.03 Å−1. The relaxation is first performed on the ionic positions and the unit cell size, followed by a self-consistent calculation with a fixed unit-cell volume. To study the migration of ions, the nudged elastic band 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 a Hubbard-type potential to describe the d-part of the Hamiltonian is applied in all our calculations with U-J = 3.9. Previous reports using similar U values showed good agreements with experiments for various Mn oxides and Li inserted Mn compounds.11,15,16 Calculations with different U-J values were also tested. In most of following discussions, the energies were compared between compounds with the same composition, in which the effect of U-J values is not as

2. METHOD 2.1. Thermodynamics for the Phase Transformation at High Pressures. Phase transformation induced by high pressures can be well-studied using DFT calculations.8 To estimate the transition pressure, one may first calculate the free energies as a function of the volume for each phase and then find the slope of the tangent line between two G(V) curves corresponding to different crystal structures. Another method to estimate the transition pressure is to consider the free-energy change at constant pressure: ΔG(P) = ΔE(P) + P ΔV (P) − Δ(TS)

(3)

(1) 3063



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cubic spinel and distorted spinel phases, respectively. The distortion of MMO from the cubic to tetragonal symmetry is clearly due to the Jahn−Teller deformation of Mn3+O6 octahedrons. For simplicity, it is still denoted as spinel phase here and afterward. Compared to post-spinel phases, the spinel NaMn2O4 (NMO) is metastable, mainly because of the large size 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 counterparts. The volumetric contraction between the spinel and postspinel phases is ∼6%−14%, with CT-type phases being the densest phase, in good agreement with the experimental observations.2,3 The denser volume suggests the possible transformation from the spinel to post-spinel phases at high pressures. To study the phase transformation, several fixedvolume calculations are performed. Figure 2 shows the

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

3. RESULTS 3.1. Phase Stability of Stoichiometric AMn2O4. Table 1 compares the calculated lattice parameters for the fully relaxed Table 1. Relative Energies, Lattice Parameters, Unit Cell Volume, and Volume Contraction (Relative to the Spinel Phase) for LiMn2O4, NaMn2O4, and MgMn2O4 with the Spinel (Space Group Fdmm for LMO and NMO, I41/amd for MMO, respectively), CaFe2O4 (Space Group Pnma), CaMn2O4 (Space Group Cmcm), and CaTi2O4 (Space Group Pmab) Phases spinel relative energy (meV per MnO2 unit) lattice parameters (Å) a b c unit-cell volume, v (Å3) volume contraction, Δv (%)

0

relative energy (meV per MnO2 unit) lattice parameters (Å) a b c unit-cell volume, v (Å3) volume contraction, Δv (%)

241.2 meV

relative energy (meV per MnO2 unit) lattice parameters (Å) a b c unit-cell volume, v (Å3) volume contraction, Δv (%)

0

8.346

36.33

8.746

41.81

8.170 248 38.58

CF LMO 58.4

CM

CT

240.1

239.9

8.645 2.862 10.986 33.87

9.496 9.647 2.932 33.57

9.469 9.517 2.947 33.20

−6.77

−7.6

−10.4

295.0 meV

280.0 meV

8.975 2.912 11.022 36.01

9.839 9.769 2.981 35.82

9.788 9.744 3.000 35.77

−13.9

−14.3

−14.5

216.1 meV

326.1 meV

9.094 2.974 0.391 35.13

9.533 9.873 3.023 35.57

9.820 9.497 2.969 34.61

−8.9

−7.8

−10.3

NMO 0

MMO 436.1 meV

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 correspond to the DFT calculated data, and lines show the fitting to the Murnagham equation of state. The pressure for the predicted phase transition is marked with the red arrows.

calculated total energy as a function of the volume, together with the corresponding fit of the DFT data to the Murnagham equation of state. The fitted parameters are reported in Table 2. The bulk modulus of spinel phases from DFT calculations lies at ∼90−120 GPa. The experimental bulk modulus for spinel− LMO was reported to be 103−119 GPa,2,20,21 which is in good agreement with our calculations. These values are far below 200 GPa, which is typical for most spinel oxides. The unusual low bulk modulus was reported for spinel−LMO as a result of the local 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 bond length, followed by LiO4, then by MgO4 which has the strongest Mg2+−O bonding. It explains why the bulk moduli

structures of the spinel and post-spinel compounds with stoichiometric composition AMn2O4. The calculated lattice parameters are slightly overestimated, compared to the experimental values. Such a slight overestimation is usually a common result in GGA calculations. The ground states for LiMn2O4 (LMO) and MgMn2O4 (MMO) are predicted to be 3064



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interconnecting through the corner-shared oxygen in the CF phase, or through both corner-shared and edge-shared oxygen in the CM phase. One distinct difference between the CF phase and the CM phase is the number of independent transitionmetal sites. In the CF phase, there are two crystallographically independent transition-metal sites (Mna and Mnc), as shown by different colors in Figure 3a, while only one transient site exists in 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 whereass in MMO, Mn remains as pure Mn3+ ions. Mn3+ is well-known as Jahn−Teller active ion that can induce significant lattice deformation. The distortion of MnO6 can be quantitatively described by the octahedral distortion parameter κ, as

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

103.0 3.4

B0 (GPa) B1

93.1 7.1

B0 (GPa) B1

118.6 1.3

CF LMO 123.8 4.9 NMO 105.8 6.2 MMO 144.8 4.2

CM

CT

119.0 5.8

164.1 2.3

98.7 7.4

113.1 5.1

135.0 5.0

160.8 4.6

follow as MMO > LMO > NMO, with the only exception being for CT-LMO and CT-MMO. The bulk modulus of post-spinel phase is higher than the spinel phases as CT > CF > CM > spinel, consistent with the experimental measurements.4 All post-spinel phases are harder to compress than the spinel phase. Figure 2 also shows the change of enthalpy as a function of pressure using the equation of states fit with DFT calculated data. The spinel-to-post-spinel phase transformation is predicted for LMO and MMO. Spinel LMO transforms to the CF phase at 3.4 GPa, while the transformation of MMO happens at 11.1 GPa from spinel to the CM phase, in good agreement with the experimental reports (6 GPa for LMO3 and 14.5 for MMO2). A couple of sources may contribute to the deviation between the calculated transition pressure and the experimental value. Apparently, the first contributor is the entropy effect that is neglected in our calculation. Because the spinel phase is always softer than the post-spinel phases, the entropy part would increase the transition pressure at high temperatures.8 Another possible contributor is the existence of Li or Mg vacancies,3 which decreases the transition pressure, as we will discuss later. Overall, the trends for the spinel-to-postspinel transition predicted from DFT calculations are in remarkable agreement with experiments; i.e., for spinel LMO and MMO, the phase transition ends in the CF and CM phases, respectively. For NMO, the most stable structure is the CF phase, which is consistent with experiments that directly synthesized CF-NMO.22 Before further discussing the relative stability of the postspinel phases, it is necessary to give a detailed description about their crystallographical structures. Because the calculations suggest that the CT phase is metastable for all three AMO compounds considered in this study, here, only the CM and CF phases are compared. As shown in Figure 3, in both CF and CM phases, MnO6 first forms so-called “double-rutile chains”

2

1 κ= 6

⎛ R − R̅ ⎞ ⎟ ∑ ⎜⎝ R̅ ⎠

(4)

where R and R̅ are the distance and average distance of the Mn−O bonds, respectively. Higher κ values suggest larger distortion 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-LMO and 2.15 Å in CF-NMO. The rest of the Mnc−O bond lengths vary over a range of 1.94−1.96 Å in CF-LMO and over a range of 1.94−1.99 Å in CF-NMO. The elongation of the Mnc−O axis is consistent with the Jahn−Teller distortion of the Mnc3+O6 octahedron. The MnaO6 octahedron is quite regular, with weaker distortion varying the Mna−O bond lengths over ranges of 1.94−1.98 Å and 1.93−2.02 Å in CF-LMO and CFNMO, respectively. These results suggest that, in CF-LMO and NMO, Mna ions remain as Jahn−Teller inactive Mna4+ and Mnc ions are Jahn−Teller active Mnc3+. The ordering of Mn4+/Mn3+ on the Mna/Mnc site is further verified through the analysis of the Bader charge of Mn ions. For CF-LMO and CF-NMO, the Bader charge of the Mnc ion is ∼0.1 e lower than that of the Mna ion, suggesting that Mnc existing at lower oxidation state. It is consistent with the statement that the oxidation state of Mnc ions is +3, whereas, for Mna, it is +4. We should note here that the absolute value of the Bader charge does not provide any information on the formal charge of Mn ions.24 It is the difference of Bader charges that shows the oxidation or reduction of Mn ions. For MMO, all MnO6 octahedrons show strong distortion in both CF and CM phases. In CF-MMO, the distance of Mn−O bonds varies from 1.95 Å to 2.13 Å, while in CM-MMO, it varies from 1.95 Å to 2.38 Å. Bader charge analysis proves that the oxidation state of Mn in MMO is lower than +4 in both CF and CM phases, with very slight variation between Mna and Mnc site in the CF phases. It is consistent with the picture that all Mn ions in MMO are Jahn−Teller active Mn3+ with large distortion effect. In CM-LMO and CM-NMO, we fail to distinguish different Mn ions after DFT relaxation. All MnO6 octahedrons show noticeable distortion. Bader charge analysis indicates that all Mn have the same oxidation state, instead of separating as Mn3+ and Mn4+ ions. To test whether the choice of U-J values in GGA+U calculations affects the results, we repeat the calculations with U = 5, 6, and 7. However, no characteristic difference is observed that could distinguish Mn4+ and Mn3+ in

Figure 3. Structure view of AMn2O4 in (a) the CaFe2O4 phase and (b) the CaMn2O4 phase. Two distinct Mn sites in CaFe2O4 phases are denoted with purple (Mna) and yellow (Mnc) colors. 3065



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Table 3. Distortion parameter (κ) of MnO6 Octahedrals and Bader Charges on Mn Ions (q) in AMn2O4 with CaFe2O4 and CaMn2O4 Phases CF-Mna

CF-Mnc

CM

A

κ

q (e)

κ

q (e)

κ

q (e)

Li Na Mg

8.9 × 10−5 3.1 × 10−4 1.4 × 10−4

+2.04 +2.02 +1.88

2.1 × 10−3 2.0 × 10−3 2.6 × 10−3

+1.92 +1.90 +1.86

1.4 × 10−3 2.7 × 10−3 7.5 × 10−3

+1.47 +1.97 +1.87

for this effect is probably that the softer structure of Mgdeficient spinel-MgxMn2O4 is easier to compress, making the phase transition happen at lower pressures. Another effect of Mg vacancy is shown in the relative stability of post-spinel phases. The introduction of Mg deficiency raises the relative stability of the CF phase. For compounds with 25% Mg vacancy,

CM-LMO and CM-NMO in all calculations. Thus, it is concluded that all Mn ions in CM compounds are symmetrically equivalent, even after DFT relaxation. By learning the details of the structural changes in the series of compounds, the thermodynamic stability of post-spinel AMn2O4 can be related to the electronic configuration of Mn ions. In CF phases, the two distinct crystallographical sites, Mna and Mnc, are beneficial to distinguish between Jahn−Teller active Mn3+ and inactive Mn4. The ordering of Mn4+/Mn3+ in the CF phase helps to stabilize CF-LMO and CF-NMO. On the other hand, in MMO, all Mn ions exist as Jahn−Teller active Mn3+ species. The homogeneous electronic configuration of Mn ions in the CM phase becomes beneficial to accommodate the structural deformation caused by the cooperative Jahn−Teller distortions of MnO6. It makes CMMMO more stable than CF-MMO. 3.2. Ph ase S tabi li ty of Non sto ic hi ome tri c Mgx(Fe,Mn)2O4. In this section, our study is extended from stoichiometric AMn2O4 to nonstoichiometric compounds. Specifically, we consider nonstoichiometric Mgx(Fe,Mn)2O4 containing cation deficiency and/or substitutional Fe at Mn sites. 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-, and spinel-MMO. It is possible that more-complex ordering may appear within multiple unit cells. However, quantitative information can still be obtained by only considering the ordering in a single unit cell with moderate computational cost. DFT calculations are then used to obtain the H(P) curves for different polymorphs of MgxMn2O4, and the phase transitions are identified by checking how the H(P) curves cross each other. For all of the x values that we have considered, spinelMgxMn2O4 is always the most stable at ambient pressures. Table 4 lists the phase transition from spinel-MgxMn2O4 to

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

the CF phase becomes more stable than the CM phase. For Mg0.75Mn2O4, 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 from spinel to CF phase at 8.8 GPa. All these effects can be explained by the replacement of Mn3+ with Mn4+ when a Mg vacancy is introduced. It raises the relative stability of the CF phases, in which the two crystallographical sites are beneficial to distinguish between Mn4+ and Mn3+. The replacement of Jahn−Teller active Mn3+ with inactive species can also be achieved by substituting Mn for other transition-metal ions. For example, Fe3+, with d5 (t2g3eg2) electronic configuration, is Jahn−Teller inactive. To examine the effect of Fe doping, the relative stability for CF- and CMMg1−x(FeyMn1−y)2O4 is investigated. In order to avoid the appearance of Fe4+ ions, the composition space is limited by the boundary condition y ≤ x. The relative phase stability at ambient pressure is characterized by the difference between the ground-state energies. As shown in Figure 4, the relative stability of the CF phase is improved by Mg vacancies and substitional Fe doping, both of which decreases the concentration of Jahn−Teller active Mn3+ ions. It further confirms that the relative stability of the post-spinel phases is

Table 4. Possible Phase Transition of MgxMn2O4 and the Corresponding Transition Pressure x

phase transition

pressure (GPa)

0.25 0.5 0.75 0.75 1

spinel to CF spinel to CF spinel to CF CM to CF spinel to CM

5.4 7.7 8.8 4.7 11.1

post-spinel phases. The presence of a Mg vacancy has two noticeable effects on the relative stabilities of spinel and postspinel phases. First, the Mg vacancy decreases the pressure required for the phase transition. For example, 25% of Mg vacancy decreases the pressure required for spinel-to-postspinel phase transition from 11.1 GPa to 8.8 GPa. The reason 3066



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migration of cation A as well as the rearrangement of Mn ions in order to form the double-rutile chain as the building block in the post-spinel frameworks.25 In order to investigate the kinetics quantitatively, we adapt the mechanism proposed by Arévalo-López et al., in which the phase transition begins with the migration of half transition-metal ions to the edgeneighbored unoccupied octahedral sites (Figure 5a), followed

highly related to the electronic configuration of the transitionmetal ions. Summarizing the results presented in the previous and this section, a general mechanism can be provided to explain the relative thermodynamical stability of post-spinel phases. In general, if ion B is Jahn−Teller active species in compound AB2O4, the most stable post-spinel structure should be the CM phase. Replacing ion B with Jahn−Teller inactive species raises the relative stability of the CF phases. Eventually, for compounds containing a certain level of Jahn−Teller inactive ions, the CF phase becomes more stable than the CM phase. The natural CF and CM phases are named after CaFe2O4 and CaMn2O4, in which all transition-metal ions are Jahn−Teller inactive Fe3+ and active Mn3+, respectively. As listed in Table 5, Table 5. Structure of AB2O4 Compound Reported in PostSpinel Phases and the Electronic Configuration of B Ions composition

B ion

structure

ref

Li0.92Mn2O4 NaMn2O4 MgMn2O4 CdCr2O4 CaCo2O4 Mn3O4 MgAl2O4 Ca(Fe,Mn)2O4

Mn4+ t2g3, Mn3+ t2g3eg1 Mn4+ t2g3, Mn3+ t2g3eg1 Mn3+ t2g3eg1 Cr3+ t2g3 Co3+ t2g6 Mn3+ t2g3eg1 Al3+ Fe3+ t2g3eg2, Mn3+ t2g3eg1

CF CF CM CF CF CM CF CF

3 23 2 26 27 28 1 5, 29

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

our conclusion holds for a variety of AB 2 O 4 compounds.1−3,5,22,25−28 Apparently, this mechanism not only provides instructive information for future experimental studies, but also suggests an effective and practical way to obtain postspinel compounds with desirable structures. Because the thermodynamical stability of post-spinel phases is controlled by the electronic configuration of the transition-metal ions, it is possible to monitor the stabilities of post-spinel phases by varying the concentration of Jahn−Teller active ions. For example, the crystal structure of CaMn2 O 4 has been successfully switched from the CM structure to the CF structure with the introduction of Ca deficiency and/or Fe doping.5 Our study suggests it can also be used to monitor the relative stability of CF- and CM-Mg1−x(FeyMn1−y)2O4 (see Figure 5). We believe that this approach can be helpful to synthesize 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 to the kinetic phase stability. The kinetic limitation of the phase transformation was indicated by the experimental observation that the phase transformation usually required temperatures of >1000 K, and the release of the pressure at ambient temperatures did not inversely transform crystalline CF-LMO and CM-MMO to their spinel forms.2,3 It suggested that the phase transformation is controlled not only by the thermodynamic stability, but also by the kinetics of the transition. Under ambient conditions, especially at low temperatures, the slow kinetics prevents the reverse transition from post-spinel to spinel phases. It is easy to qualitatively understand the kinetic limitation from the large structural difference between the spinel and post-spinel phases (for illustration, see Figure 1).25 However, quantitative study about the kinetical phase transition is very challenging, because the transformation of spinel AMn2O4 to post-spinel phases is a complicated solid process. It involves the

by the rotation of the chain in order to obtain appropriate connection of octahedrons.25 More specifically, we analyze the migration of Mn ions between edge-shared MnO6 octahedrons in MgMn2O4 as an example to study the kinetics of spinel-topost-spinel phase transition. We evaluate two possible hopping paths for the migration of Mn ions. The direct hopping of Mn ions between neighbored octahedral sites is considered first, as shown in Figure 5b. The displacement of Mn into the unoccupied octahedral sites causes a great amount of repulsion between Mn and neighbored Mg ions, because of their short distances (1.85 Å). It results in high instability of the final configuration. To avoid this strong repulsion, two Mg ions that are too close to Mn are manually removed along the hopping path. This operation is reasonable and explains why cation vacancies were always observed in post-spinel compounds.3 The energy of final state is 456 meV higher than the initial state, in the similar level as the energy difference between spinel MMO and CF-MMO (Table 1). However, the barrier for the direct hop is 1.67 eV, which suggests 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 tetrahedral site, then to the final octahedral sites (Figure 6b). It is distinguished as the indirect hopping path. To locate Mn ions at tetrahedral sites, one neighbored Mn and two Mg ions must be manually removed in order to avoid the strong repulsion between these ions and the hopping Mn ion. The energy profile along the indirect hopping path is plotted in Figure 6d. Surprisingly, the configuration with Mn located at O2 site in Figure 6b is identified as a saddle point between two tetrahedral 3067



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

interchannel migration. The activation energy barriers for the migration of Li+, Mg2+, and Na+ in three post-spinel phases are plotted in Figure 6. Curiously, although the crystal structures of the three post-spinel phases are similar, the ionic mobility through the channel is quite different. The migration in the CF structure is noticeably faster than in the CM and CT structures. The migration barrier for Li+ is 0.12 eV, which is smaller than the typical migration barrier in Li-ion battery cathodes, such as layered LiMO2,30,31 olivine LiMPO4,17,32 and spinel LiMn2O4.23 Even for large cations (Na+) or divalent cations (Mg2+), the migration barrier is still comparable to that of Li migration in spinel-LiMn2O4.23 To our knowledge, a barrier as low as 0.4 eV for the migration of Mg2+ ions has never been reported previously in the literature. To explain this unusual low migration barrier in the CF phases, the migration path is analyzed in Figure 7. The creation

sites, instead of being a local minimum. Although the barrier is lower than the direct hopping, the indirect hopping is unlikely to happen in real cases, because it is easier to be blocked by the repulsion between Mn and other cations neighbored to the hopping path. The instability of the final configurations also suggests the double-rutile chain may not be formed through the indirect hopping path. After the migration of Mn ions, MnO6 octahedrons must been further rotated in order to achieve appropriate connections between the double-rutile chains.25 The rotation is very likely to be even more difficult than the migration of Mn ions.25 Thus, the migration barrier calculated in this study gives a lower boundary for the kinetic phase transition. The high barrier for the migration of Mn indicates the phase transformation is kinetically limited by the rearrangement of transition-metal ions under ambient conditions.19 Therefore, it is necessary to promote the kinetics by increasing the temperatures for the phase transition. It explains why typical spinel-to-post-spinel phase transformation only happens at temperatures higher than 1000 K. The high kinetic barrier also explains why the inverse transition from post-spinel to spinel phase is hindered at room temperature. Therefore, although post-spinel phases are usually thermodynamically metastable species, they can still be kinetically stable under ambient conditions, as has already been demonstrated in the study of CF-LMO and CM-MMO.2,3 3.4. Cationic Mobility in Post-spinel Phases. In spinel LiMn2O4, the migration of Li+ is of great interest, because of its importance as rechargeable Li-ion battery cathodes. The structure of spinel AMn2O4 has only half of the octahedral sites occupied by Mn, and a quarter of the tetrahedral sites are occupied by cation A, respectively, with the other octahedral and tetrahedral sites being unoccupied. It indicates ion A in the spinel compounds is confined in a relatively small space with a large portion of empty space in the structure. On the other hand, in post-spinel compounds, cations are located in a relative larger space. This characteristic could be favorable to enhance the cationic mobility.29 Although a comprehensive study is still missing, several experiments have already provided a hint for high ionic mobility in post-spinel phases.3,5,6 It motivates us to study the migration of Li+, Mg2+, and Na+ in post-spinel phases. In the post-spinel phases, the framework of MnO 6 octahedrons has a one-dimensional (1D) channel along one of 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 ionic migration only happens through the channel and ignore the

Figure 7. Schematic diagram describing the cooperative onedimensional (1D) migration of A(1) ions (blue arrows) and adjacent A(2) and A(3) (green arrows) in the post-spinel phases. We use the distance between Mg2+ ions in MgMn2O4 (in units of Å) for illustration.

of a vacancy displaces two adjacent cations (A(1) and A(2) in Figure 8) toward the vacancy. If A(1) hops from the equilibrium position to the vacancy, large Columbic repulsion is generated, because of the short distance between A(1) and A(2). It pushes A(2) along the hopping direction of A(1). Meanwhile, A(3) is also attracted by the vacancy toward the direction of the migration of A(1). Unlike the migration of individual Li+ in spinel-LiMn2O4,23 this migrating behavior in CaFe2O4-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 3068



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MgxMn2O4. Compared to a recent report that examined the voltage profile of Li0.81Mn2O4,6 the difference between the firstprinciples-calculated voltage and the experimental values is on the order of 0.1−0.2 V. This level of agreement is typical in the DFT prediction of voltage profile for Li-ion battery cathodes.39 The voltage for Li insertion/removal is lower than the lithiation of spinel MnO2,40 mainly because the longer distances between Li and O in CF-LixMn2O4 weaken the bonding strength. On the other hand, the voltages predicted for Mg insertion/ removal lie between 2.84 V and 1.68 V (vs Mg/Mg2+), higher than most of the reported Mg battery cathodes.34,41 It makes CF-MMO an attractive candidate as a high-voltage Mg battery cathode. The voltages presented in Figure 8 are calculated based on the assumption that the electrochemical reaction follows the intercalation/retraction of Li+ or Mg2+ without phase transition from the CF phase to the more-stable spinel structures. We have already shown in the previous sections that this assumption is reasonable because of the kinetic stability of the CF phase under ambient conditions. In principle, if Li or Mg reacts with CF-MnO2, it may also follow the conversion reaction path as

advantageous, because it shortens the migration distance for each ion.33 It is possible that the distinct two Mn sites in the CF phases are also beneficial to high ionic mobilities. In fact, the creation of cation vacancies oxidizes Mn3+ to Mn4+. On the basis of the analysis in the previous sections, this process is easier to be achieved in the CF structure, with two distinct sites for Mn3+ and Mn4+. Although the detailed mechanism is still under investigation, it may explain the different diffusion barriers in the CF, CM, and CT phases. 3.5. Potential Application of Post-spinel Phases as Rechargeable Battery Cathodes. Materials with high cationic mobilities have good potential as rechargeable battery electrodes. For electrode materials, high ionic conductivity is always required in order to provide good rate capability.7 Slow diffusion limits the rate capability of the electrodes or even prevents the practical insertion and removal of cations. The diffusion of cations is especially important in the study of Mg batteries, where the search of appropriate cathode materials is greatly challenged by the sluggish mobility of the Mg2+ ion in the host lattice.34−38 The barrier for the migration of Li+ in CFLMO is lower than that of typical Li-ion battery cathodes. It suggests that CF-LMO may work as high rate cathode materials for Li-ion batteries. The low barrier for the migration of Mg2+ in CF-MMO also suggests it has the potential for the fast insertion/removal of Mg2+ into/from the host lattice. To provide information for the experimental investigations of post-spinel phases as rechargeable battery cathodes, the voltage profiles are plotted in Figure 8 for the electrochemical insertion/removal of Li and Mg in CF-LixMn2O4 and

(4x − 2y)Li + x MnO2 → (2x − y)Li 2O + MnxOy

(4x − 2y)Li + 2x MnO2 → (2x − y)Li 2O2 + 2MnxOy (2x − y)Mg + x MnO2 → (2x − y)MgO + MnxOy

(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 energy change along the conversion reaction path, and plot the energies of the intercalated compounds (CF-LixMn2O4 or CFMgxMn2O4) in the same figure. If the energy of the intercalation compound lies below the convex hull of the conversion reaction, the intercalation path is then more thermodynamically preferable than the conversion reaction. Otherwise, it is more preferable to have the conversion reaction. As shown in Figure 9, for all of the ground states of CF-LixMn2O4 and CF-MgxMn2O4, only CF-MgMn2O4 lies above 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 higher than that of a mixture of MgO and Mn2O3. Considering the conversion reaction also requires overcoming the kinetic barrier to destruct the crystal structure, we postulate that even MgMn2O4 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 ∼1.3 times greater than the typical energy density of Li ion battery cathodes (3.5 V vs Li/Li+, 150 mAh/g). Therefore, it is of great interest to obtain CF-MMO experimentally and test its performance 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 the stoichiometric CF-MMO is metastable, compared to the spinel phase or even the CM phase. Nonetheless, it is possible to first synthesize a precursor with the kinetically stable CF phase as a template for the desirable CF-MMO. On the basis of the results presented in this study, three possible ways are suggested to obtain CF-MMO, as illustrated in Figure 10. Obviously, route 3 is the most cost-friendly, because it does not require any high-

Figure 8. Voltages for the electrochemical insertion of (a) Li into CaFe 2 O 4 -phase Li x Mn 2 O 4 and (b) Mg into CaFe 2 O 4 -phase MgxMn2O4. 3069



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ions, the post-spinel phase can be stable under ambient conditions. Our results not only help the experimental investigation of high-pressure spinel to post-spinel phase transition, but also provide an easy way to obtain materials with 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, especially in 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 for the migration of Mg2+ in CaFe2O4−MgMn2O4 is calculated to be 0.4 eV, suggesting that the mobility of Mg2+ in this compound is fast enough to satisfy the requirements for use as a rechargeable Mg battery cathode. The theoretical energy density of CaFe2O4-MgMn2O4 is ∼1.3 times greater than that of the typical Li-ion battery cathode, making it an attractive candidate for the study of high-energy-density Mg batteries. To the best of our knowledge, this is the first report about Mg battery cathode candidate with both high Mg mobility and high theoretical energy density. Possible methods to obtain CaFe2O4−MgMn2O4 are also suggested in this study. It is thus of great interest to experimentally test the performance of CaFe2O4−MgMn2O4 in rechargeable Mg batteries.

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ASSOCIATED CONTENT

S Supporting Information *

The effect of U-J values in the calculations. This material is available free of charge via the Internet at http://pubs.acs.org.

■

AUTHOR INFORMATION

Corresponding Author

*E-mail: [email protected].

Figure 9. Convex hull of the conversion reaction between CaFe2O4type MnO2 and cation A, and the formation energy of the intercalated compounds CaFe2O4-type Ax(MnO2)1−x: (a) A = Li and (b) A = Mg.

Notes

The authors declare no competing financial interests.

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ACKNOWLEDGMENTS We appreciate the fruitful discussions with Dr. R. Asahi at Toyota Center Research and Development Laboratory. Images of crystal structures were generated with the VESTA program.42

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Figure 10. Possible synthetic routes to obtain MgMn2O4 with the CaFe2O4 structure.

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A = Li, Na, or Mg - American Chemical Society

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