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First principles study of the crystal, electronic structure, and diffusion mechanism of

polaron-Na vacancy of polaron-Na3MnPO4CO3 for polaron-Na-ion battery applications

View the table of contents for this issue, or go to the journal homepage for more

2017 J Phys D: Appl Phys 50 045502

(http://iopscience.iop.org/0022-3727/50/4/045502)

1 Introduction

Lithium ion batteries are well known as a popular power source with many applications in our daily life Despite this success, the improvement of the energy storage capacity of this technology is a challenge To improve the overall bat­

tery performance, it is necessary to explore new cathode mat­

erials with better characteristics (capacity, voltage, specific

energy, safety etc) Owing to their remarkable electrochem­ ical and thermal properties, and their flexibility to increase the open­circuit voltage, transition metal compounds containing different polyanion units [1 2] are considered as the most promising cathode materials for the next generation of Li­ion batteries Among this class, carbonophosphate mat erials with the general formula Li3MCO3PO4(M = Fe, Mn, Co,

V) reported for the first time in 2011 by Hautier et al [3] are

Journal of Physics D: Applied Physics

First principles study of the crystal, electronic structure, and diffusion mechanism of polaron-Na vacancy

of Na 3 MnPO 4 CO 3 for Na-ion battery applications

M Debbichi1, L Debbichi2, Van An Dinh3,4 and S Leb ègue5

1 Laboratoire de la mati ère condensée et nanosciences, Département de Physique, Faculté des Sciences de Monastir, 5019 Monastir, Tunisia

2 Graduate School of Energy, Environment, Water, and Sustainability (EEWS), Korea Advanced Institute

of Science and Technology (KAIST), Yuseong­gu, Daejeon 305­701, Korea

3 Computational Multiscale Material Modeling and Simulation Group, Nanotechnology Program,Vietnam Japan University, Vietnam National University of Hanoi, Vietnam­Australia Building, Luu Huu Phuoc Street, My Dinh I, Nam Tu Liem, Hanoi, Vietnam

4 Center for Atomic and Molecular Technologies, Graduate School of Engineering, Osaka University, Yamadaoka 2­1, Suita, Osaka 565­0871, Japan

5 Laboratoire de Cristallographie, R ésonance Magnétique et Modélisations (CRM2, UMR CNRS 7036) Institut Jean Barriol, Universit é de Lorraine, BP 239, Boulevard des Aiguillettes 54506

Vandoeuvre­l ès­Nancy, France E­mail: mourad_fsm@yahoo.fr and dv.an@vju.ac.vn Received 2 November 2016, revised 30 November 2016 Accepted for publication 5 December 2016

Published 29 December 2016

Abstract

Based on first principles calculations, we investigate the geometry, electronic structure, and diffusion mechanism of Na ions in Na3MnPO4CO3 using density functional theory with a Hubbard potential correction Our results suggest that the structure of Na3MnPO4CO3 can be deintercalated with more than one Na ion, and that the removal of a Na ion can form a bound polaron We find that our calculations of the intercalation voltages for the redox couples

Mn2+ /Mn3+ and Mn3+ /Mn4+ agree very well with the experimental data In addition, we demonstrate that Na in Na3MnPO4CO3 can diffuse in three directions with low activation energy barriers, allowing a fast charging rate

Keywords: DFT method, battery, neb method, Bader population (Some figures may appear in colour only in the online journal)

M Debbichi et al

First principles study of the crystal, electronic structure, and diffusion mechanism of polaron-Na vacancy of Na 3 MnPO 4 CO 3 for Na-ion battery applications

Printed in the UK

045502

JPAPBE

© 2016 IOP Publishing Ltd

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J Phys D: Appl Phys.

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10.1088/1361-6463/aa518d

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Journal of Physics D: Applied Physics

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doi:10.1088/1361-6463/aa518d

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2

promising cathode materials This class of compounds have

high theor etical capacity (>200 mAh g−1) and specific energy

(>700 Wh kg−1) [3] A first­principles study has reported

that Li ions in Li3FeCO3PO4 can diffuse in three dimensions

with a significantly low activation energy Ea (about 0.33 eV)

[4] Moreover, these materials are able to give two voltage

steps, due to the multi­step oxidization of the TM cation

They also have the potential to maintain the safety charac­

teristics of olivine [5] In particular, the Mn­based materials

display a specific energy 45% greater that of LiFePO4, but so

far only ∼135 mAh g−1 has been obtained experimentally

In addition, they are able to keep a stable structure upon the

extraction of multiple Li+ ions, accompanied by a very low

volume change compared to LiCoO2, LiFePO4, LiFe(SO4)

F, or Li2FePO4F [3 6] Theoretical and experimental [3 7]

works have also suggested that the Li3MnCO3PO4 structure

can admit deintercalation by more than one Li

As an attractive alternative to Li­ion batteries, Na­ion

batteries are gaining attention from the scientific commu­

nity due to the low cost and wide availability in nature of Na

raw mat erials [8–11] However, the development of suitable

Na cathode materials still represents a challenge [12–14]

Among the most used compounds, Mn­based carbonophos­

phate materials represent the most stable chemical class [15]

and demonstrate a good reversibility of Na intercalation and

deintercalation [7 16] Recently, Chang et al [16] have dem­

onstrated that a compound with the sidorenkite structure

(Na3MnPO4CO3) could play an important role in Na­ion bat­

teries due to its good cyclability, high average voltage (∼ V4 )

and its high capacity (∼125 mAh g−1: 66% of the theoretical

value), which is super ior to most oxide cathode materials

[10, 18] In addition to that, it is able to deliver two­electron

transfer reactions per formula via electrochemically active

Mn2+ /Mn3+ and Mn3+ /Mn4+ redox reactions These results

were recently confirmed by experimental studies [16, 19],

which demonstrate for the first time that this material exhibits

a high specific capacity of 176.7 mAh g−1, reaching 92.5%

of its theoretical value (191 mAh g−1) These findings dem­

onstrate the potential of this material as a very good cathode

material for the future In spite of this, the electronic structure

and the electrochemical properties of this compound have not

been sufficiently investigated

Here, using DFT calculations, we report the electronic

structure and magnetic properties of Na3MnPO4CO3 before

and after the removal of Na ions Also, we show how a bound

polaron is formed when the defect has been created, and then

determine the elementary diffusion processes that might occur

during the Na ion diffusion process in Na3MPO4CO3

2 Computational details and methods

Our calculations were performed using density functional

theory (DFT) as implemented in the Vienna ab initio simula­

tion package (VASP) [20] The electron–ion interaction was

described by using the projector­augmented wave (PAW)

method The exchange­correlation functional was treated

by the Perdew–Burke–Ernzerhof (PBE) [21] form of the

generalized gradient approximation (GGA), together with the Hubbard­type on­site Coulomb potential U (GGA + U) Here,

the formulation of Dudarev et al [17] is used with U = 3.9 eV

for the transition metal Mn [16] To ensure convergence, a plane wave basis set with an energy cutoff of 500 eV was used

in our calculations and all the structures were relaxed until the energy and the forces were converged to less than 10−6 eV and

10−3 eV A˚−1 respectively The Brillouin zones were sampled with a 8× ×6 6 Monkhorst–Pack [22] grid to ensure geo­ metrical and energetic convergence The average intercalation

voltage Vavg was calculated by using the already developed methods [23, 24] with Vavg= −∆E F/ , where F is the Faraday

constant and ∆E is the internal energy calculated as:

∆ =E EtotNa MnPO CO3 4 3 −EtotNa MnPO CO2 4 3 −EtotNa ,

(1) and

∆ =E Etot(Na MnPO CO2 4 3)−Etot(NaMnPO CO4 3)−Etot( )Na ,

(2)

where Etot(Na) is the total energy for metallic sodium in a body­centered­cubic (bcc) crystal structure The activation barriers were calculated using the nudged elastic band (NEB) method [25] and a 1× ×2 2 supercell Finally, Bader popula­ tion analysis was used to determine the atomic charges with a

× ×

300 200 200 grid for the electron density

3 Results and discussion

Three structures were studied: Na3MnPO4CO3,

Na2MnPO4CO3 and NaMnPO4CO3 The starting coordinates

of the structure Na3MnPO4CO3 were taken from the exper­ imental data [16], while the structure of the other compounds was determined by removing the Na atoms and subsequently relaxing the geometry The original structure Na3MnPO4CO3 has a monoclinic structure with the group symmetry P21/m (11) made of distorted MnO6 octahedra, PO4 tetrahedra and

CO3 plane triangles These groups are connected with each other, forming a two dimensional chain in the (0 1 0) plane [16] Our optimized Wyckoff positions of the Na3MnPO4CO3 are presented in the table 1

Table 1. Fractional coordinates of Mn, P, C and O of

Na3MnPO4CO3 in the P21/m structure optimized with the GGA + U approximation.

J Phys D: Appl Phys 50 (2017) 045502

M Debbichi et al

All of the structures mentioned were relaxed (atomic posi­

tions and cell dimensions) in nonmagnetic (NM) as well as

ferromagnetic (FM) and antiferromagnetic (AFM) spin

polarized configurations By comparing the total energies,

we found that Na3MnPO4CO3 and Na2MnPO4CO3 are more

stable in the AFM order However, when two Na ions are

removed, NaMnPO4CO3 becomes FM Also we found that

Na2MnPO4CO3 and NaMnPO4CO3 are obtained preferentially

when the Na ions are removed, respectively, from the second

site (Na(2)) and from both the first (Na(1)) and second sites,

which is in accordance with the experimental observation [16]

The full set of structural parameters and magnetic moments

of the Mn atoms obtained after relaxation is given in table 2

together with the available experimental data Here, only

the magnetic ground state of each compound is shown For

Na3MnPO4CO3, the calculated lattice parameters a and c are

slightly overestimated compared to the parameters of natural

sidorenkite, by about ∼1.3%, but basically in agreement with

those of synthetic sidorenkite as reported by Chen et al [16]

After removing the alkali atoms, we found that the resulting volume change is about −1% and −4% for Na2MnPO4CO3 and NaMnPO4CO3 respectively For the latter, the angles between the lattice vectors are changed after removing two

Na ions, inducing a symmetry change from monoclinic to tri­ clinic In addition to the geometrical optimization, we have also calculated the total energy difference between the FM and AFM configurations of Na3MnPO4CO3 We found that the difference is very small, with ΔEFM –AFM = 3.49 meV, which means that the FM and AFM ordering are in competition When the alkali cation are removed, we found that the magn­ etic moment of Mn is decreased by ∼17% and ∼18% for the

Na3MnPO4CO3 and Na2MnPO4CO3 compounds respectively The decrease of the magnetic moment indicates that the trans­ ition metal exists in two spin states This is confirmed by the experimental finding, which shows that Mn exists in two dif­ ferent states at each step

Table 2. Lattice parameters a,b,c in ( Å), α, β, γ in (deg) and magnetic moment of Mn in (µB ) of Na3MnPO4CO3, Na2MnPO4CO3 and NaMnPO4CO3 together with the available experimental data.

Na3MnPO4CO3 Exp [ 16 ] 8.986 6.74 5.160 90 90.12 90 312.32 P21/m —

Exp [ 16 ] 9.014 6.64 5.189 90 89.70 90 310.74 P2 1 /m —

Exp [ 26 ] 8.997 6.74 5.163 90 90.10 90 313.13 P2 1 /m —

Na 2 MnPO 4 CO 3 AFM 8.782 6.964 5.095 90 88.013 90 311.4 P2 1 /m 3.494 NaMnPO 4 CO 3 FM 9.485 6.155 5.123 91.78 88.59 87.82 298.7 P¯1 2.872

Figure 1. Density of states (DOS) of Na3MnPO4CO3, Na2MnPO4CO3 and NaMnPO4CO3 computed with the GGA + U approximation The Fermi levels are set to zero.

J Phys D: Appl Phys 50 (2017) 045502

M Debbichi et al

4

For more analysis of the effect of defects in the electronic

structure of Na3MnPO4CO3, the density of states (DOS) of all

compounds have been calculated and are shown in figure 1

All the results are presented in the magnetic order (FM or

AFM) corresponding to the ground state of each material We

found that Na3MnPO4CO3 is an insulator with a band gap of

3.32 eV—this value is slightly smaller than the gap obtained

when Fe is used rather Mn (3.4 eV) [27] However, when the

Na ions are removed, the systems retain insulating character­

istics, except for the smaller band gaps, which are 0.78 and

1.37 eV for Na2MnPO4CO3 and NaMnPO4CO3 respectively

As shown in figure 1, when one Na ion is removed, the total

DOS is slightly changed compared to the starting structure

The difference between the two structures is observed near

the Fermi level with the presence of some new states below

the Fermi level for Na2MnPO4CO3 These states are due to

hybridization between Mn and O atoms after the removal of

the Na ion However, in the case of NaMnPO4CO3, the shape

of the total DOS is totally changed due the reconstruction of

the structure after the removal of two Na ions For the trans­

ition from Na3MnPO4CO3 to Na2MnPO4CO3, the unoccupied

states located at about 5 eV are split into two different groups

Consequently, the peak at 1 eV in the partial density (PDOS)

of Mn in Na2MnPO4CO3 has totally disappeared in the corre­

sponding Mn­PDOS of Na3MnPO4CO3, which indicates an

important charge reorganization From Na2MnPO4CO3 to

NaMnPO4CO3, we found the presence of some new spin states

in the vicinity of 1 eV, due to the strong hybridization between

O and Mn atoms This is related to the presence of vacancies

leading to the oxidization of manganese from Mn3+ to Mn4+

These results confirm the two­stage redox reaction mech­

anism as proposed in [16] The charge reorganization also

affects the PDOS of the other elements for Na2MnPO4CO3

and NaMnPO4CO3 by shifting toward higher energies This is

due to a modified hybridization with the Mn ion

To gain more information about the charge distribution in

the different systems, the Bader charges were calculated and

are shown in table 3 Upon the desintercalation of the Na ions,

we found that the charge of the Mn atom is changed signifi­

cantly compared to the others elements From Na3MnPO4CO3

to Na2MnPO4CO3 the Mn charge increases from +1.47

to +2.14, while in NaMnPO4CO3 it has a charge of +3.03

This change is related the change of the oxidization state of

Mn from Mn2+ to Mn3+ and from Mn3+ to Mn4+

In addition, the intercalation voltage of both Mn2+ /Mn3+ and Mn3+ /Mn4+ redox couples were also calculated and are shown in table 4 with the available experimental data The values obtained reproduce the available experimental results very well, with a small error of ∼0.17 V for Mn2+ /Mn3+ and ∼0.21 V for Mn3+ /Mn4+ Due to the inductive effect (the increase in voltage from the oxide voltage) [16], the obtained voltage of the redox couples are slightly higher with respect to most known oxide cathode materials [10, 28]

Since the mobility of the alkali atoms in the electrode compound is a key aspect of the rate capability of recharge­ able batteries, the determination of the activation barriers for the migration of the Na ion in the material is essential As shown in the previous paragraph, the removal of a Na ion from

Na3MnPO4CO3 results in the oxidization of Mn2+ to Mn3+

In addition, we found that the average Mn3+–O bond is short­ ened by ∼0.13 Å compared with that of the Mn2+–O bond, which caused the lattice distortion of the Na23(MnPO4CO3)8 This effect is in fact a sign of the presence of a small polaron

at the Mn3+ site As pointed out by Dinh et al [14, 29], when

the Na vacancy moves, the bound polaron at the transition metal site consequently migrates To describe the migration pathway of the polaron, the Na diffusion path was calculated and is presented in figure 2 with a green color We found that the diffusion can occur inside a double layer (intrablock) and between two adjacent double layers (interblock) as shown in figures 2(a) and (b) (demonstrated by the highlighted Na ions and their connected lines) For the intrablock diffusion, three possible elementary diffusion processes (EDP) have been considered and called: Na2­Na14, Na2­Na16 and Na2­Na22 However for the interblock diffusion we only considered the most preferable EDP called N2­N12

The couple of Na vacancies with its accompanying polaron are shown in figure 2(a) and are indexed as Na2­Mn8, Na12­Mn2, Na14­Mn6 and Na22­Mn8 The activation energy profile of the preferable processes are shown in figure 3, and their behavior can be described as follows: the first intrablock process, which we called P1, consist of the movement of Na2­ Mn8 complex to occupy Na14­Mn6 with an activation energy

Ea of 0.56 eV The second process (called P2) corresponds to

a single Na diffusion, in this case the Na2 vacancy moves through the C layer to occupy the Na22 site and the polaron remains at the Mn8 site The activation energy Ea of this pro­ cess was found to be 0.64 eV These intrablock diffusions, with and without the presence of polaron migration, show

Table 3. Calculated Bader atomic charges (in units of e) for

Na3MnCO3PO4, Na2MnCO3PO4 and NaMnCO3PO4 compounds.

Atom Na 3 MnCO 3 PO 4 Na 2 MnCO 3 PO 4 NaMnCO 3 PO 4

Na(1)/Na(2) +0.93/+ 0.91 +0.89/+ 0.89 +0.90/+ 90

Table 4. The calculated intercalation voltages of Na3MnPO4CO3 battery with GGA + U approximation.

Redox couple Method Voltage (V)

Mn 2+ /Mn 3+ GGA + U [ 16 ] 3.10

Exp [ 16 ] 3.40

Mn 3+ /Mn 4+ GGA + U [ 16 ] 4.00

Exp [ 16 ] 4.00

J Phys D: Appl Phys 50 (2017) 045502

M Debbichi et al

comparable activation barriers—meaning that the change of

the magnetic element does not significantly alter the diffusion

of the Na ions

For the interblock diffusion (called P3), as shown in

figure 2(b), the Na2 vacancy intends to move to the left side

to occupy Na12, while the polaron jumps from the Ma8 to

the Mn2 site and the activation energy of this path is 0.85 eV

By combining these preferential elementary processes, we

conclude that the diffusion of Na can occur in 3 dimen­

sions: along the [1 0 0] direction with an Ea=0.85 eV, in the

[0 1 0] direction with Ea=0.56 eV and in the [0 0 1] direc­

tion through the double carbon layer with Ea=0.64 eV These

activation barriers are considerably low compared with that

of Li2FeSiO4 [30], but higher than those of LiFePO4 [29] and LiCoO2 [31]

4 Conclusion

In summary, density functional theory with the +U correc­ tion was employed to study the structural, electronic structure, the intercalation voltages and the Na diffusion mechanism in

Na3MnPO4CO3 The calculated lattice parameters and average voltages were found to be in good agreement with the avail­ able experimental data We have also shown that sidorenkite possesses three preferable diffusion pathways: two intrablock diffusion pathways with activation energies of 0.56 and of 0.64 eV, and one interblock pathway with Ea=0.85 eV These compounds show a low diffusion barrier for the transport of ions, which is needed to achieve a fast charging rate, making them very promising in view of future applications

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J Phys D: Appl Phys 50 (2017) 045502

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