Home Search Collections Journals About Contact us My IOPscience First principles study of the crystal, electronic structure, and diffusion mechanism of polaronNa vacancy of Na3MnPO4CO3 for Na-ion battery applications This content has been downloaded from IOPscience Please scroll down to see the full text 2017 J Phys D: Appl Phys 50 045502 (http://iopscience.iop.org/0022-3727/50/4/045502) View the table of contents for this issue, or go to the journal homepage for more Download details: IP Address: 194.27.18.18 This content was downloaded on 30/12/2016 at 05:07 Please note that terms and conditions apply Journal of Physics D: Applied Physics J Phys D: Appl Phys 50 (2017) 045502 (6pp) doi:10.1088/1361-6463/aa518d First principles study of the crystal, electronic structure, and diffusion mechanism of polaron-Na vacancy of Na3MnPO4CO3 for Na-ion battery applications M Debbichi1, L Debbichi2, Van An Dinh3,4 and S Lebègue5 Laboratoire de la matière condensée et nanosciences, Département de Physique, Faculté des Sciences de Monastir, 5019 Monastir, Tunisia Graduate School of Energy, Environment, Water, and Sustainability (EEWS), Korea Advanced Institute of Science and Technology (KAIST), Yuseong-gu, Daejeon 305-701, Korea Computational Multiscale Material Modeling and Simulation Group, Nanotechnology Program,Vietnam Japan University, Vietnam National University of Hanoi, Vietnam-Australia Building, Luu Huu Phuoc Street, My Dinh I, Nam Tu Liem, Hanoi, Vietnam Center for Atomic and Molecular Technologies, Graduate School of Engineering, Osaka University, Yamadaoka 2-1, Suita, Osaka 565-0871, Japan Laboratoire de Cristallographie, Résonance Magnétique et Modélisations (CRM2, UMR CNRS 7036) Institut Jean Barriol, Université de Lorraine, BP 239, Boulevard des Aiguillettes 54506 Vandoeuvre-lès-Nancy, France E-mail: mourad_fsm@yahoo.fr and dv.an@vju.ac.vn Received November 2016, revised 30 November 2016 Accepted for publication 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) 1. Introduction energy, safety etc) Owing to their remarkable electrochem ical and thermal properties, and their flexibility to increase the open-circuit voltage, transition metal compounds containing different polyanion units [1, 2] are considered as the most promising cathode materials for the next generation of Li-ion batteries Among this class, carbonophosphate materials with the general formula Li3MCO3PO4(M = Fe, Mn, Co, V) reported for the first time in 2011 by Hautier et al [3] are 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 1361-6463/17/045502+6$33.00 © 2016 IOP Publishing Ltd Printed in the UK M Debbichi et al J Phys D: Appl Phys 50 (2017) 045502 promising cathode materials This class of compounds have Table 1. Fractional coordinates of Mn, P, C and O of high theoretical capacity (>200 mAh g−1) and specific energy Na3MnPO4CO3 in the P21/m structure optimized with the (>700 Wh kg−1) [3] A first-principles study has reported GGA + U approximation that Li ions in Li3FeCO3PO4 can diffuse in three dimensions Element Site x y z with a significantly low activation energy Ea (about 0.33 eV) Mn 2e 0.3629 0.7500 0.7784 [4] Moreover, these materials are able to give two voltage P 2e 0.4112 0.2500 0.7033 steps, due to the multi-step oxidization of the TM cation Na(1) 4f 0.7421 0.9982 0.7526 They also have the potential to maintain the safety charac Na(2) 2e 0.0838 0.2500 0.7572 teristics of olivine [5] In particular, the Mn-based materials C 2e 0.0611 0.7500 0.7389 display a specific energy 45% greater that of LiFePO4, but so O(1) 2e 0.1207 0.7500 0.9649 far only ∼135 mAh g−1 has been obtained experimentally O(2) 2e 0.1464 0.7500 0.5382 In addition, they are able to keep a stable structure upon the O(3) 2e 0.9190 0.7500 0.7127 O(4) 4f 0.3201 0.4334 0.7845 extraction of multiple Li+ ions, accompanied by a very low O(5) 2e 0.5677 0.2500 0.8309 volume change compared to LiCoO2, LiFePO4, LiFe(SO4) O(6) 2e 0.5679 0.7500 0.5922 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 Li-ion batteries, Na-ion generalized gradient approximation (GGA), together with the batteries are gaining attention from the scientific commu Hubbard-type on-site Coulomb potential U (GGA + U) Here, nity due to the low cost and wide availability in nature of Na the formulation of Dudarev et al [17] is used with U = 3.9 eV raw materials [8–11] However, the development of suitable for the transition metal Mn [16] To ensure convergence, a Na cathode materials still represents a challenge [12–14] plane wave basis set with an energy cutoff of 500 eV was used Among the most used compounds, Mn-based carbonophos in our calculations and all the structures were relaxed until the phate materials represent the most stable chemical class [15] energy and the forces were converged to less than 10−6 eV and ˚ −1 respectively The Brillouin zones were sampled and demonstrate a good reversibility of Na intercalation and 10−3 eV A deintercalation [7, 16] Recently, Chang et al [16] have dem with a × × Monkhorst–Pack [22] grid to ensure geo onstrated that a compound with the sidorenkite structure metrical and energetic convergence The average intercalation (Na3MnPO4CO3) could play an important role in Na-ion bat voltage Vavg was calculated by using the already developed teries due to its good cyclability, high average voltage (∼ 4V ) methods [23, 24] with Vavg = −∆E /F , where F is the Faraday and its high capacity (∼125 mAh g−1: 66% of the theoretical constant and ∆E is the internal energy calculated as: value), which is superior to most oxide cathode materials [10, 18] In addition to that, it is able to deliver two-electron ∆E = E tot (Na3MnPO4CO3) − E tot (Na2MnPO4CO3) − E tot (Na), (1) transfer reactions per formula via electrochemically active Mn2+ /Mn3+ and Mn3+ /Mn4+ redox reactions These results and were recently confirmed by experimental studies [16, 19], ∆E = E tot (Na2MnPO4CO3) − E tot (NaMnPO4CO3) − E tot (Na), which demonstrate for the first time that this material exhibits (2) a high specific capacity of 176.7 mAh g−1, reaching 92.5% where Etot(Na) is the total energy for metallic sodium in a of its theoretical value (191 mAh g−1) These findings dem body-centered-cubic (bcc) crystal structure The activation onstrate the potential of this material as a very good cathode barriers were calculated using the nudged elastic band (NEB) material for the future In spite of this, the electronic structure method [25] and a × × supercell Finally, Bader popula and the electrochemical properties of this compound have not tion analysis was used to determine the atomic charges with a been sufficiently investigated 300 × 200 × 200 grid for the electron density 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 3. Results and discussion polaron is formed when the defect has been created, and then Three structures were studied: Na3MnPO4CO3, determine the elementary diffusion processes that might occur Na2MnPO4CO3 and NaMnPO4CO3 The starting coordinates during the Na ion diffusion process in Na3MPO4CO3 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 2. Computational details and methods relaxing the geometry The original structure Na3MnPO4CO3 Our calculations were performed using density functional has a monoclinic structure with the group symmetry P21/m theory (DFT) as implemented in the Vienna ab initio simula (11) made of distorted MnO6 octahedra, PO4 tetrahedra and tion package (VASP) [20] The electron–ion interaction was CO3 plane triangles These groups are connected with each described by using the projector-augmented wave (PAW) other, forming a two dimensional chain in the (0 1 0) plane method The exchange-correlation functional was treated [16] Our optimized Wyckoff positions of the Na3MnPO4CO3 by the Perdew–Burke–Ernzerhof (PBE) [21] form of the are presented in the table 1 M Debbichi et al J Phys D: Appl Phys 50 (2017) 045502 Table 2. Lattice parameters a,b,c in (Å), α, β, γ in (deg) and magnetic moment of Mn in (µ B) of Na3MnPO4CO3, Na2MnPO4CO3 and NaMnPO4CO3 together with the available experimental data Compound Na3MnPO4CO3 Na2MnPO4CO3 NaMnPO4CO3 Exp [16] Exp [16] Exp [7] Exp [26] AFM AFM FM a b c α β γ V Sym m(Mn) 8.986 9.014 8.988 8.997 9.066 8.782 9.485 6.74 6.64 6.74 6.74 6.847 6.964 6.155 5.160 5.189 5.162 5.163 5.23 5.095 5.123 90 90 90 90 90 90 91.78 90.12 89.70 90.13 90.10 89.9 88.013 88.59 90 90 90 90 90 90 87.82 312.32 310.74 312.78 313.13 315.1 311.4 298.7 P21/m P21/m P21/m P21/m P21/m P21/m P1¯ — — — — 4.227 3.494 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 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 M Debbichi et al J Phys D: Appl Phys 50 (2017) 045502 Table 3. Calculated Bader atomic charges (in units of e) for Table 4. The calculated intercalation voltages of Na3MnPO4CO3 battery with GGA + U approximation Na3MnCO3PO4, Na2MnCO3PO4 and NaMnCO3PO4 compounds Atom Na3MnCO3PO4 Na2MnCO3PO4 NaMnCO3PO4 Na(1)/Na(2) Mn P C O(1) O(2) O(3) O(4) O(5) O(6) +0.93/+ 0.91 +1.47 +4.86 +3.93 −1.88 −1.86 −1.90 −1.81 −1.82 −1.81 +0.89/+ 0.89 +2.14 +4.85 +3.93 −1.64 −1.81 −1.89 1.73 −1.81 −1.71 Redox couple +0.90/+ 90 +3.03 +4.86 +3.94 −1.70 −1.61 −1.89 −1.70 −1.71 −1.64 2+ 3+ Mn /Mn Mn3+ /Mn4+ Method Voltage (V) GGA + U GGA + U [16] Exp [16] GGA + U GGA + U [16] Exp [16] 3.23 3.10 3.40 3.79 4.00 4.00 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 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: Na2-Na14, Na2-Na16 and Na2-Na22 However for the interblock diffusion we only considered the most preferable EDP called N2-N12 The couple of Na vacancies with its accompanying polaron are shown in figure 2(a) and are indexed as Na2-Mn8, Na12-Mn2, Na14-Mn6 and Na22-Mn8 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 Na2Mn8 complex to occupy Na14-Mn6 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 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 Mn-PDOS 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 two-stage 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 M Debbichi et al J Phys D: Appl Phys 50 (2017) 045502 Figure 2. Schematic view of the Na elementary diffusion pathway for the intrablock (a) and interblock (b) processes of Na3MnPO4CO3 battery 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 References Figure 3. Calculated activation energy of polaron-Na vacancy diffusion in Sidorenkite (Na3MnPO4CO3) [1] Jain A, Hautier G, Moore C, Kang B, Lee J, Chen H, Twu N and Ceder G 2012 J Electrochem Soc 159 A622 [2] Kim H, Park I, Seo D-H A, Lee S, Kim S-W, Kwon W J, Park Y-U, Kim C S, Jeon S and Kang K 2012 J Am Chem Soc 134 10369 [3] Hautier G, Jain A, Chen H, Moore C, Onga S H P and Ceder G 2011 J Mater Chem 21 17147 [4] Duong D M, Dinh V A and Ohno T 2013 Appl Phys Express 6 115801 [5] Delacourt C, Poizot P, Tarascon J M and Masquelier C 2005 Nat Mater 4 254 [6] Ellis B L, Makahnouk W R M, Weetaluktuk W N R, Ryan D H and Nazar L 2010 Chem Mater 22 1059 [7] Chen H, Hautier G, Jain A, Moore C, Kang B, Doe R, Wu L, Zhu Y, Tang Y and Ceder G 2012 Chem Mater 24 2009 [8] Yabuuchi N, Kubota K, Dahbi M and Komaba S 2014 Chem Rev 114 11636 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 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 M Debbichi et al J Phys D: Appl Phys 50 (2017) 045502 [19] Wang C, Sawicki M, Kaduk J A and Shawa L L 2015 J. Electrochem Soc 162 A1601 [20] Kresse G and Hafner J 1993 Phys Rev B 47 558 [21] Perdew J P, Burke K and Ernzerhof M 1996 Phys Rev Lett 77 3865 [22] Monkhorst H J and Pack J D 1976 Phys Rev B 13 5188 [23] Ceder G, Adynol M K and Kohn A F 1997 Comput Mater Sci 8 161 [24] Debbichi M and Lebègue S 2015 Phys Rev B 92 085127 [25] Sheppard D, Terrell R and Henkelman G 2008 J Chem Phys 128 134106 [26] Khomyakov A P 1983 Int Geol Rev 25 368 [27] Huang W, Zhou J, Li B, Ma J, Tao S, Xia D, Chu W and Wu Z 2014 Sci Rep 4 4188 [28] Yabuuchi N, Kajiyama M, Iwatate J, Nishikawa H, Hitomi S, Okuyama R, Usui R, Yamada Y and Komaba S 2012 Nat. Mater 11 512 [29] Dinh V A, Nara J and Ohno T 2012 Appl Phys Express 5 045801 [30] Bui K M, Dinh V A and Ohno T 2012 Appl Phys Express 5 125802 [31] Okubo M, Tanaka Y, Zhou H, Kudo T and Honma I 2009 J Phys Chem B 113 2840 [9] Palomares V, Serras P, Villaluenga I, Hueso K B, Gonzalez J C and Rojo T 2012 Energy Environ Sci 5 5884 [10] Ellis B L and Nazar L F 2012 Curr Opin Solid State Mater Sci 16 168 [11] Slater M D, Kim D, Lee E and Johnson C S 2013 Adv Funct Mater 23 947 [12] Kabbour H, Coillot D, Colmont M, Masquelier C and Mentre O 2011 J Am Chem Soc 133 11900 [13] Song W, Cao X, Wu Z, Chen J, Zhu Y, Hou H, Lan Q and Ji X 2014 Langmuir 30 12438 [14] Bui K M, Dinh V A, Okada S and Ohno T 2015 Phys Chem Chem Phys 17 30433 [15] Chen H, Hautier G and Ceder G 2012 J Am Chem Soc 134 19619 [16] Chen H, Hao Q, Zivkovic O, Hautier G, Du L S, Tang Y, Hu Y Y, Ma X, Grey C P and Ceder G 2013 Chem Mater 25 2777 [17] Dudarev S L, Botton G A, Savrasov S Y, Humphreys C J and Sutton A P 1998 Phys Rev B 57 1505 [18] Zhang Z and Zhang S S 2015 Rechargeable Batteries: Materials, Technologies and New Trends (New York: Springer) ... 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... presence of polaron migration, show 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... 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