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[Tomoaki Kaneko](https://orcid.org/0000-0002-5296-7403), [Yui Fujihara](https://orcid.org/0000-0002-4842-5740), [Hiroaki Kobayashi](https://orcid.org/0000-0001-6705-9515), [Keitaro Sodeyama](https://orcid.org/0000-0002-9228-0729)

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[First-principles study of the reconstruction of MgM2O4 (M = Mn, Fe, Co) spinel surface](https://mdr.nims.go.jp/datasets/e6311a1d-f6a2-4c61-9ffa-7125ace8dced)

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First-principles study of the reconstruction of Mg[formula omitted]O4 ([formula omitted] = Mn, Fe, Co) spinel surfaceApplied Surface Science 613 (2023) 156065A0Contents lists available at ScienceDirectApplied Surface Sciencejournal homepage: www.elsevier.com/locate/apsuscFull length articleFirst-principles study of the reconstruction of Mg𝑀2O4 (𝑀 = Mn, Fe, Co)spinel surfaceTomoaki Kaneko a,∗, Yui Fujihara a,b,c,1, Hiroaki Kobayashi b,∗, Keitaro Sodeyama a,d,∗a Research and Services Division of Materials Data and Integrated System (MaDIS), National Institute for Materials Science (NIMS), Namiki1-1, Tsukuba, 305-0044, Japanb Institute of Multidisciplinary Research for Advanced Materials, Tohoku University, 2-1-1 Katahira, Sendai, 980-8577, Japanc Department of Chemistry, Graduate School of Science, 6-3 Aramaki-Aza-Aoba, Sendai, 980-8578, Japand Element Strategy Initiative for Catalysts & Batteries (ESICB), Kyoto University, Nishikyo-ku, Kyoto, 615-8245, JapanA R T I C L E I N F OKeywords:Mg-batteryCathodeSpinel surfaceSurface reconstructionFirst-principles calculationsA B S T R A C TMg𝑀2O4 (𝑀 = Mn, Fe, Co) spinels, which transform into rock-salt phases on Mg incorporation, are attractivecathode materials for future Mg battery applications. In this study, we investigated the energetics andreconstruction of Mg𝑀2O4 (𝑀 = Mn, Fe, Co) spinel surfaces using first-principles calculations. We foundthat the Mg𝑀2O4 spinels stabilized when the Mg atoms in the topmost layer occupied the rock-salt-like sites.With an increase in the number of Mg atoms, the rock salt phase preferentially grew on the spinel surfacerather than in the bulk. These features agree well with the core–shell growth of the rock-salt phase observedby recent aberration-corrected scanning transmission electron microscopy measurements.1. IntroductionThe development of high-energy-density rechargeable batteries is ingreat demand. Mg batteries, in particular, have attracted much interestowing to their high specific capacity (2200 mAh g−1) compared toconventional lithium-ion batteries (370 mAh g−1) [1,2]. Thus, the highrechargeability of Mg batteries makes them a potential option for ourfuture energy storage needs. In Mg batteries, Mg𝑀2O4 (𝑀 = Mn, Fe,Co)-based spinels (SPs) are considered promising cathode materials.During battery discharge, the SP transforms into the Mg𝑀O2 rock-salt(RS) phase, that is,Mg𝑀2O4 +Mg2+ + 2𝑒− ⇌ 2Mg𝑀O2. (1)Although Mg batteries with an SP cathode exhibit high potential (2–3 V vs. Mg2+/Mg) and high capacities (260–270 mAh g−1), theirpoor reversibility and slow kinetics are critical problems impedingtheir application [1]. For the reversibility problem, the amount of Mgextracted is less than that of the Mg inserted, that is, the RS phasesurvives after charging. The purpose of this study was to investigate thestability of the RS phase at the Mg𝑀2O4 SP surface using first-principlescalculations.∗ Corresponding authors.E-mail addresses: KANEKO.Tomoaki@nims.go.jp (T. Kaneko), hiroaki.kobayashi.c7@tohoku.ac.jp (H. Kobayashi), SODEYAMA.Keitaro@nims.go.jp(K. Sodeyama).1 Current affiliation: Energy Transformation Research Laboratory, Central Research Institute of Electric Power Industry, Nagasaka 2-6-1, Yokosuka, Kanagawa,240-0196, Japan.Structural analysis of Mg𝑀2O4 SPs has been performed by sev-eral authors [3,4]. Recently, Truong et al. performed an aberration-corrected scanning transmission electron microscopy (STEM) analysisof MgMn2O4 (MMO) [3]. The observed STEM images showed a differ-ent atomic ordering at the MMO SP surface from that of the bulk region.They concluded that an RS phase layer was formed on the MMO SPsurface. A similar structural transformation was observed for MgCo2O4(MCO) SP induced by electron irradiation without Mg incorporation[4]. In this case, the formation of a defective RS structure with cationsite disorder was indicated. These findings help to identify ways ofimproving the performance of Mg batteries.As an alternative to experiments, computational simulations basedon density functional theory (DFT) is a powerful tool to investigateseveral properties of materials, such as atomic structure, electronicstructure, energetics, and magnetic properties. However, computationalstudies concerning the surface of cathode materials in Mg batter-ies are limited. Jin et al. investigated the stabilities of MMO andMgNi0.5Mn1.5O4 SP surface [5]. Guo et al. systematically studied thestability of normal, mixed, and inverted MgFe2O4 (MFO) SP surfaces[6,7]. Han et al. investigated the electronic properties of Mg𝑀2O4 (𝑀= Mn, Fe, Co) surface to understand the reductive decomposition at thevailable online 17 December 2022169-4332/© 2022 The Author(s). Published by Elsevier B.V. This is an open access ahttps://doi.org/10.1016/j.apsusc.2022.156065Received 27 July 2022; Received in revised form 2 December 2022; Accepted 10 Drticle under the CC BY license (http://creativecommons.org/licenses/by/4.0/).ecember 2022https://www.elsevier.com/locate/apsuschttp://www.elsevier.com/locate/apsuscmailto:KANEKO.Tomoaki@nims.go.jpmailto:hiroaki.kobayashi.c7@tohoku.ac.jpmailto:SODEYAMA.Keitaro@nims.go.jphttps://doi.org/10.1016/j.apsusc.2022.156065https://doi.org/10.1016/j.apsusc.2022.156065http://crossmark.crossref.org/dialog/?doi=10.1016/j.apsusc.2022.156065&domain=pdfhttp://creativecommons.org/licenses/by/4.0/Applied Surface Science 613 (2023) 156065T. Kaneko et al.Fig. 1. (a) Lattice structure of (i) SP and (ii) RS. The orange, blue, and red ballsrepresent Mg, 𝑀 (𝑀 = Mn, Fe, Co), and O atoms, respectively. In the side view, the8𝑎 sites of Mg can be seen at the interstitial sites, whereas the 16𝑏 sites of Mg areoverlapped by O and 𝑀 atoms. (b) Local atomic configuration of (i) SP and (ii) RS.cathode surface [8]. In their study, the lattice plane dependence wascarefully investigated, whereas the possibility of reconstruction, whichwas observed experimentally [3,4], was not considered. Therefore, theRS phase growth in the SP phase is still unexplored. To understand theexperimental results and accelerate future research, a computationalstudy of the Mg𝑀2O4 (𝑀 = Mn, Fe, Co) SP surfaces can provide keyinsights. In this study, we investigated the energetics and reconstructionof Mg𝑀2O4 SP surface by using first-principles calculations.2. Methods2.1. Computational detailsIn this study, we performed first-principles calculations based onDFT with a plane wave basis set within the spin polarized generalizedgradient approximation (GGA) [9] using the quantum espresso code[10]. Ultrasoft pseudopotentials were used [11,12]. The semi-corestates of 2s and 2p orbitals of Mg and 3s and 3p orbitals of Mn, Fe,and Co were also treated as valence electrons. For 𝑑 orbitals of Mn, Fe,and Co, the isotropic type of DFT+𝑈 was adopted [13]. Mn, Fe, and Cohave 𝑈eff of 5.0, 5.0, and 6.0 eV, respectively, which are typical valuesfor these elements, as summarized in the Supplemental Materials. Thecutoff energy of the plane-wave basis set and the charge density were35 and 315 Ry, respectively.The lattice structures of the Mg𝑀2O4 SP and Mg𝑀O2 RS are shownin Fig. 1(a). In the SP phase, the Mg atoms occupy 8𝑎 sites of spacegroup 227, that is, Mg is tetrahedrally coordinated. Conversely, in theRS phase, the Mg atoms occupy 16𝑐 sites. We assumed antiferromag-netic ordering which is explained in detail in supplemental materials,whereas Co3+ ions in MCO do not have a magnetic moment. While MFOand MCO belong to the cubic lattice, MMO belongs to the tetragonallattice because of the strong Jahn–Teller effect in MMO. The latticeconstants of MMO were optimized using the stress tensor methodwithin the cutoff energy of the plane wave basis set and charge densityof 55 and 495 Ry, respectively, while cell parameters of MFO and MCOSP are determined by the total energy minimization. The threshold ofstress is 0.1 kbar. To perform the calculations for a primitive cell, weused a special k-sampling of 2 × 2 × 2.As summarized in Table 1, the optimized lattice constants agreewell with the experimental values, except for small deviations. We also2Table 1Results for bulk materials.MgMn2O4 MgFe2O4 MgCo2O4𝑎SP, 𝑐SP (Å) 8.246, 9.637 8.602 8.203Exp. 8.099, 9.284a 8.397b 8.138cDiff. +1.8%, +3.8% +2.4% +0.8%𝑎RS (Å) 8.848 8.706 8.619Exp. 8.672d 8.503cDiff. + 2.0% +1.4%𝑉Mg∕Mg2+ (V) 2.20 1.86 2.75Exp. 2.3c 2.2c 2.9caRef. [16].bRef. [17].cRef. [14].dRef. [3].analyzed the RS phase of the Mg𝑀O2. For simplicity, we assumed thatthe transition metal atoms remain at the same sites in the SP phase andthat the Mg atoms occupy the 16𝑐 sites in the RS phase. The voltage atthe Mg metal anode is defined as:𝑉Mg∕Mg2+ = − 12𝑒[2𝐸Mg𝑀O2− 𝐸Mg𝑀2O4− 𝐸Mg], (2)where 𝐸Mg𝑀O2, 𝐸Mg𝑀2O4, and 𝐸Mg denote the total energies of RS,SP, and hcp-Mg per formula unit, respectively. The 𝑉Mg∕Mg2+ valuesobtained for Mn, Fe, and Co were 2.20, 1.86, and 2.75, respectively.These results agree well with the experimental results reported in Ref.Okamoto et al. [14], namely, 2.3 for Mn, 2.2 for Fe, and 2.9 for Co.The effect of 𝑈eff on 𝑉Mg∕Mg2+ is summarized in the SupplementaryInformation. Note that the obtained 𝑉Mg∕Mg2+ depends on 𝑈eff . Thus,a quantitative comparison between different SPs might be difficult.However, the electronic and structural properties of Mg𝑀2O4 shouldbe insensitive to variations in 𝑈 by approximately 1 eV [15].We considered the (001) cleaved slab models of SP, which consistof two periods of the primitive cell. As MMO exhibits lattice distortioncaused by the Jahn–Teller effect, we considered the (001) and (100)surfaces of this material. For the calculations concerning the surfaces,we used a special k-sampling of 2 × 2 × 1. An effective screeningmedium (ESM) was employed to remove spurious interactions betweenperiodic images [18]. We introduced a vacuum layer of thicknessgreater than 10 Å on both sides of the slab. For comparison, we alsoconsidered the RS phase formation in the bulk SP. In these calculations,we used a 1 × 1 × 2 supercell.2.2. Surface terminationFirst, we discuss the surface models of Mg𝑀2O4. In the (001)direction, the atoms in the bulk SP were arranged as follows:−𝑀4O8 −Mg2 −𝑀4O8 −Mg2 −𝑀4O8 −Mg2 − . (3)In this study, we considered two slab models, as shown in Fig. 2(a),one with an asymmetric cut and the other with a symmetric cut. In theasymmetrically cut model, the slab was cleaved between the 4𝑀8O and2Mg layers, that is,𝑀4O8 −Mg2 −𝑀4O8 −Mg2 −𝑀4O8 −Mg2. (4)By contrast, in the symmetrically cut model, the slab was cleaved acrossthe Mg layers, and the Mg atoms were equally arranged at the top andbottom sides of the slab model, that is,Mg −𝑀4O8 −Mg2 −𝑀4O8 −Mg2 −𝑀4O8 −Mg. (5)In the following, we investigated the stability of these slab models byconsidering the effect of surface reconstruction.Fig. 2(b) shows the reconstructions of the SP surfaces. At the SPsurface, there are four 16𝑐 sites on each side of the surface unit cell,Applied Surface Science 613 (2023) 156065T. Kaneko et al.Fig. 2. Surface model of MCO: (a) Effect of cutting position. (b) Schematics of surface reconstructions. The surface Mg atoms are highlighted in yellow. (c) Optimized structuresfor MCO. Panels (i) and (ii) show the slab model with an asymmetric cut, and panels (iii) and (iv) show the slab model with a symmetric cut. The upper side of (ii) and bothsides of (iv) are reconstruction models.which are referred to as RS-like sites. In the asymmetrically cut model,as schematically shown in Fig. 2(b)–(i), two surface Mg atoms and twosubsurface Mg atoms occupy four surface RS-like sites, that is,Mg4𝑀4O8 −𝑀4O8 −Mg2 −𝑀4O8 −Mg2 −⋯ . (6)Conversely, in the symmetrically cut model, one surface Mg atomoccupies the surface RS-like site, which pulls a subsurface Mg atom toanother surface RS-like site, as shown in Fig. 2(b)–(ii), that is,Mg2𝑀4O8 −Mg −𝑀4O8 −Mg2 −𝑀4O8 −Mg2 −⋯ . (7)It should be noted that the Mg atoms located at the RS-like sites arefive-fold coordinated, whereas the surface and subsurface Mg atoms inthe SP surface are two- and four-fold coordinated, respectively.3. Results and discussion3.1. Surface reconstructionThe optimized structure of MCO is shown in Fig. 2(c). The opti-mized structures of the other two Mg𝑀2O4 SPs are summarized in theSupplemental Materials. We considered the pristine surface and the RS-reconstructed surface for both the asymmetrically and symmetricallycut slabs. For the pristine surface structures, the Mg atoms closest tothe surface shrink and tend to reach the RS-like sites.Next, we discussed the energetics of the surface models. The surfaceenergy is defined as follows:𝛾 =𝐸surf − 𝐸bulk , (8)32𝑆where 𝑆 denotes the area of the surface model, 𝐸surf denotes the totalenergy of the surface, and 𝐸bulk denotes the total energy of the bulkwith the number of atoms being the same as the surface model. Theobtained surface energies are summarized in Table 2. Although thesurface energy is defined for the symmetric slab mode, that for theasymmetric slab model can be understood as the average of surfaceenergy over the top and bottom surfaces of the slab [19].We found that the surface with the RS-like reconstruction wasmore stable than the pristine surface, except for MMO(100) with anasymmetric cut. In the MMO(100) model, the surface unit cell wasdeformed from the square shape owing to the Jahn–Teller effect, whichmight destabilize the Mg atoms at the RS-like sites on the surface. TheRS reconstruction with a symmetric cut was found to be the most stable,irrespective of the transition metal element type. For these stabilization,the increase of coordination number of Mg ions presumably plays animportant role.An RS-like reconstruction can be realized without the addition ofextra Mg atoms. Therefore, the experimentally observed RS phase atthe surface of SP should be off-stoichiometric, that is, the number ofMg atoms should be higher than that of Mg𝑀2O4. Next, we examinedthe growth of the RS phase by increasing the number of Mg atoms.3.2. Mg incorporation and RS phase growthFor this purpose, we defined the Mg incorporation energy as follows:𝐸 =𝐸SP+𝑛Mg − 𝐸SP − 𝑛𝐸Mg , (9)inc 𝑛Applied Surface Science 613 (2023) 156065T. Kaneko et al.Fig. 3. Model of Mg incorporation: (a) Mg incorporation on the MCO surface. The light-green shades represent the RS-like phase. (b) Mg incorporation into the bulk MCO. Theunit cells are indicated by cyan dotted lines.Table 2Calculated results of surface energies, 𝛾 (eV/Å2).MMO(001) MMO(100) MFO(001) MCO(001)Asymmetric, pristine 0.0538 0.0669 0.0750 0.1035Asymmetric, RS reconstructed 0.0485 0.0699 0.0700 0.0973Symmetric, pristine 0.0521 0.0689 0.0703 0.1097Symmetric, RS reconstructed 0.0338 0.0628 0.0578 0.0823Table 3Calculated results of Mg incorporation energies, 𝐸inc (eV/Mg).MMO(001) MMO(100) MFO(001) MCO(001)Surface +1Mg −3.733 −3.826 −3.246 −4.263Mg incorporation +2Mg −3.753 −4.418 −3.820 −4.653(eV/Mg) +3Mg −3.789 −4.191 −3.655 −4.032Bulk +1Mg −1.728 −1.733 −1.319 −0.953Mg incorporation +2Mg −2.689 −2.672 −2.314 −2.342(eV/Mg) +4Mg −3.259 −3.241 −2.995 −2.631Fully magnesiated RS −4.402 −4.402 −3.724 −5.510where 𝑛 denotes the number of additional Mg atoms, 𝐸SP+𝑛Mg denotesthe total energy with 𝑛 extra Mg atoms, 𝐸SP denotes the total energy ofSP. For a fully magnesiated SP, that is, for the RS phase, 𝐸inc is givenby −2 eVMg∕Mg2+ .In this study, we used the symmetrically cut slab model for simplic-ity. We added Mg atoms near both sides of the surface RS-like sites. Thestructures obtained for MCO are shown in Fig. 3(a), where the grownRS phases are highlighted in light green.The calculated Mg incorporation energies are summarized inTable 3. The obtained 𝐸inc values are negative, indicating that the Mginsertion was exothermic. However, the absolute values of the reactionenergies of Mg insertion are slightly smaller than or comparable tothose for the bulk case, that is, the fully magnesiated RS case.Next, we considered the RS phase growth in the bulk SP. The Mgincorporation model is schematically illustrated in Fig. 3(b). With themovement of four adjacent Mg atoms from 8𝑎 sites to 16𝑐 sites, a single-layer RS phase can be generated in the bulk SP without introducing4Mg atoms, as shown in Fig. 3(b)–(ii). This process was endother-mic by 3.813, 2.311, 2.822, and 2.343 eV/unit cell for MMO(001),MMO(100), MFO(001), and MCO(001), respectively. As we explainedin Section 2.2, the distance between nearest 16c and 8a sites is too shortto occupy the two Mg ions. Then, strong repulsive forces make the Mgion at 16c to empty 8a site. Therefore, the formation of a single-layerRS phase is necessary to model the RS phase growth in the bulk SP.The calculated 𝐸inc values for the bulk case are summarized inTable 3. With the introduction of one Mg atom, the 𝐸inc values obtainedwere −1.7, −1.3, and −1.0 for MMO, MFO, and MCO, respectively,indicating that magnesiation preferentially occurs at the surface ofSP. The effect of lattice distortion on the magnesiation energy wasestimated for MCO SP with four Mg incorporation by changing theperpendicular cell parameter. As the result was shown in SupplementalMaterials, the cell parameter change is 0.1 Angstrom, and the changein magnesiation energy should be of order of 0.1 eV at most. Although𝐸inc decreases monotonically with an increase in the number of Mgatoms, the absolute value of the reaction energy is much smallerthan that for the surface. As the initial growth of the RS phase isenergetically unfavorable, the RS phase cannot overcome the surfacereaction energy. In other words, the RS-like reconstruction effectivelylowered the energy barrier of the RS phase nucleation. Therefore, wecan conclude that the RS phase grew on the surface of SP.Recent STEM measurements showed the formation of RS phase onSP [3,4]. Our results agreed well with the experimental results reportedby Truong et al. for the MMO surface [3]. The MCO SP transformedinto defective RS with cation disorder, as observed by Okamoto et al.and electron beam irradiation was realized without Mg incorporation[4]. However, it seems difficult to draw firm conclusions from thecalculations. More recently, RS phase formation on the SP surface wasreported for MgCrMnO4 SP [20,21]. Although we did not performcalculations for MgCrMnO4 SP surface, we can speculate that a similartrend in energetic stability will be valid for MgCrMnO4 SP.As we mentioned in the introduction, the reversibility of Mg-batterywith SP cathode is not acceptable for practical application. Our resultsand experimentally observed RS-phase on SP surfaces imply that Mgions are fixed at the surface region due to high stability. Then, we canApplied Surface Science 613 (2023) 156065T. Kaneko et al.cststeelruCnPcDciDANopsGAaRpresume that RS-phase formation on SP surfaces might prohibit Mgdiffusion and demagnetization from SP. However, the simulations ondiffusion of Mg ions in SP and RS would be necessary to conclude it,which is beyond the scope of the present paper.In our calculations, we calculated the final structures of each mag-nesiation reaction. Each reaction path contains Mg ion adsorptionand migration processes, which have not negligible energy barriers.However, the calculations of energy barriers beyond the scope of thepaper, since these processes are not uniquely determined.4. SummaryIn this study, we investigated the energetics and reconstruction ofMg𝑀2O4 (𝑀 = Mn, Fe, Co) spinel surfaces using first-principles cal-ulations. We found that the rock-salt-like reconstruction of the spinelurfaces in the (001) direction stabilized the system, irrespective of theransition metal element. We also found that the growth of the rock-alt phase preferentially occurred at the surface of the spinel comparedo the bulk. As the formation of a single-layer rock-salt phase wasndothermic, the growth of the rock salt phase in the bulk spinel wasnergetically unfavorable. The rock-salt-like reconstruction effectivelyowered the energy barrier of the rock-salt phase nucleation. Theseesults are in good agreement with a recent experiment performedsing aberration-corrected scanning transmission electron microscopy.RediT authorship contribution statementTomoaki Kaneko: Investigation, Methodology, Writing – origi-al draft. Yui Fujihara: Resources, Investigation. Hiroaki Kobayashi:roject administration, Funding acquisition. Keitaro Sodeyama: Con-eptualization, Supervision, Funding acquisition.eclaration of competing interestThe authors declare that they have no known competing finan-ial interests or personal relationships that could have appeared tonfluence the work reported in this paper.ata availabilityData will be made available on request.cknowledgmentsThe authors would like to thank Yoshitaka Tateyama and Masanobuakayama for the fruitful discussions. The calculations were carried outn the Numerical Materials Simulator at NIMS and the ITO supercom-uter at Research Institute for Information Technology, Kyushu Univer-ity. This research was partially supported by JST, Japan ALCA-SPRINGrant Nos. JPMJAL1301, Japan.ppendix A. Supplementary dataSupplementary material related to this article can be found onlinet https://doi.org/10.1016/j.apsusc.2022.156065.5eferences[1] K. Shimokawa, T. 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Mater. 32 (2020) 10456–10462, http://dx.doi.org/10.1021/acs.chemmater.0c03121, arXiv:https://doi.org/10.1021/acs.chemmater.0c03121.http://dx.doi.org/10.1103/PhysRevB.92.115411http://dx.doi.org/10.1103/PhysRevB.92.115411http://dx.doi.org/10.1103/PhysRevB.92.115411https://link.aps.org/doi/10.1103/PhysRevB.92.115411https://link.aps.org/doi/10.1103/PhysRevB.92.115411https://link.aps.org/doi/10.1103/PhysRevB.92.115411http://dx.doi.org/10.1021/acs.chemmater.0c01988http://dx.doi.org/10.1021/acs.chemmater.0c01988http://dx.doi.org/10.1021/acs.chemmater.0c01988https://doi.org/10.1021/acs.chemmater.0c01988http://dx.doi.org/10.1021/acs.chemmater.0c03121http://dx.doi.org/10.1021/acs.chemmater.0c03121http://dx.doi.org/10.1021/acs.chemmater.0c03121https://doi.org/10.1021/acs.chemmater.0c03121 First-principles study of the reconstruction of MgM2O4 (M = Mn, Fe, Co) spinel surface Introduction Methods Computational details Surface termination Results and discussion Surface reconstruction Mg incorporation and RS phase growth Summary CRediT authorship contribution statement Declaration of Competing Interest Data availability Acknowledgments Appendix A. Supplementary data References