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Phase Separation and d Electronic Orbitals on Cyclic Degradation in Li-Mn-O Compounds: First-Principles Multiscale Modeling and Experimental Observations Duho Kim, Jin-Myoung Lim, Min-Sik Park, Kyeongjae Cho, and Maenghyo Cho ACS Appl. Mater. Interfaces, Just Accepted Manuscript • DOI: 10.1021/acsami.6b01595 • Publication Date (Web): 13 Jun 2016 Downloaded from http://pubs.acs.org on June 19, 2016

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ACS Applied Materials & Interfaces

Phase Separation and d Electronic Orbitals on Cyclic Degradation in Li-Mn-O Compounds: FirstPrinciples Multiscale Modeling and Experimental Observations Duho Kim,†,#Jin-Myoung Lim,†,# Min-Sik Park,‡ Kyeongjae Cho|| and Maenghyo Cho†,*

†

Department of Mechanical and Aerospace Engineering, Seoul National University, Seoul 151-

742, Republic of Korea ‡

Advanced Batteries Research Center, Korea Electronics Technology Institute, 68 Yatap-dong,

Bundang-gu, Seongnam, 463-816, Republic of Korea ||

Department of Materials Science and Engineering and Department of Physics, University of

Texas at Dallas, Richardson, TX 75080, USA

KEYWORDS: Li-Mn-O compounds, first principles calculation, phase field model, multiscale modeling, Jahn-Teller distortion

ACS Paragon Plus Environment

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D. Kim and J.-M. Lim contributed equally to this work.

ABSTRACT A combined study involving experiments and multiscale computational approaches is conducted to propose a theoretical solution for the suppression of the Jahn-Teller distortion which causes severe cyclic degradation. As-synthesized pristine and Al-doped Mn spinel compounds are focused to understand the mechanism of the cyclic degradation in terms of the Jahn-Teller distortion, and the electrochemical performance of the Al-doped sample shows enhanced cyclic performance than that of the pristine one. Considering the electronic structures of the two systems using first-principles calculations, the pristine spinel suffers entirely from the Jahn-Teller distortion by Mn3+, indicating an anisotropic electronic structure, but, the Al-doped spinel exhibits an isotropic electronic structure, which means the suppressed Jahn-Teller distortion. A multiscale phase field model in nanodomain shows that the phase separation of the pristine spinel occurs to inactive Li0Mn2O4 (i.e. fully delithiated) gradually during cycles. In contrast, the Al-doped spinel does not show phase separation to an inactive phase. This is why the Al-doped spinel maintains the capacity of the first charge during the subsequent cycles. Based on these mechanistic understanding of the origins and mechanism on the suppression of the Jahn-Teller distortion, fundamental insight for making tremendous cuts in the cyclic degradation could be provided for the Li-Mn-O compounds of Li-ion batteries.

Introduction


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Lithium ion batteries (LIBs) have been considered as solutions for various energy demands ranging from portable electronic devices to large-scale energy storage applications (e.g., electric vehicles (EVs) and energy storage systems (ESSs)).1, 2 To meet these requirements, Mn spinel LiMn2O4 has been studied extensively as an alternative cathode material to currently commercialized layered oxides because of its advantages, such as high power, low cost, and ecofriendliness.3-6 However, cubic spinel LiMn2O4 experiences capacity degradation for the following reasons: i) Jahn-Teller distortion derived from Mn3+ in the pristine structure,7, 8 and ii) Mn2+ dissolution in the acidic electrolyte.9 To resolve these problems, several research groups have reported the improved electrochemical performance of LiMn2-xAlxO4 compared to LiMn2O4.10, 11 They claimed that the enhanced performance of LMAO is mainly attributed to the suppression of the Jahn-Teller distortion. Although direct evidence of the Jahn-Teller distortion and the suppressed effect have been obtained through diverse experiments,12,

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the detailed

theoretical origins and mechanism on the suppression of the Jahn-Teller distortion have not been understood yet. Furthermore, it is unclear that this Jahn-Teller distortion generated on the atomic scale affects the particle-level phase transformation and the cyclic degradation. Therefore, multiscale approaches bridging the atomic scale phenomena to mesoscale behaviors are needed to understand the experimental phenomena and overcome the limitations of the atomic scale analyses.14-20 This study examined the origins and mechanism on the suppression of the Jahn-Teller distortion of the pristine Mn spinel (LiMn2O4, denoted hereafter as LMO) by doping with aluminum (LiMn2-xAlxO4 (x = 0.125), denoted hereafter as LMAO), as well as how this suppressed JahnTeller distortion affects the cyclic degradation. With the experimental observations of the cyclic degradation, first-principles electronic structure analysis and multiscale modeling on the phase


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transformation were performed to understand fundamentally the suppressed Jahn-Teller distortion in the atomic scale and reduce the level of cyclic degradation in the mesoscale. First, LMO and LMAO samples were prepared by conventional solid-state method and their electrochemical performance were carefully examined to elucidate the different electrochemical behaviors of LMO and LMAO. Second, first-principles studies were performed to identify the key factors affecting the suppression of the Jahn-Teller distortion. To systematically understand the electronic behavior of Mn ions in these two structures, two perspectives were assessed: i) qualitative calculations of the partial density of states (PDOS) and ii) quantitative calculations of the band-filling (d-band of Mn and p-band of O). These electronic structure analyses show that the anisotropic d- and p-orbitals of LMO cause the Jahn-Teller distortion, whereas the isotropic d- and p-orbitals of LMAO suppress it. Finally, a multiscale modeling for the phase transformation was conducted to bridge the atomic scale calculation to the mesoscale phase transformation behaviors. The multiscale phase separation kinetics indicates that the phase separation to the inactive Li0Mn2O4 phase of LMO degrades the cyclic performance at Li0.828Mn2O4 (composition at the first charge) and the phase of LMAO does not separate at Li0.644Mn2O4 (composition at the first charge). Based on these experimental observations and first-principles multiscale modeling, not only the detail mechanism for the suppression of the Jahn-Teller distortion could be understood in the cubic spinel phase, but also the cycle degradation could be elucidated by the multiscale phase separation kinetics in nanodomain. These findings will be helpful for the design of new cathode materials for LIBs, particularly those that suffer from the cyclic degradation because of the Jahn-Teller distortion.

Materials characterization and electrochemical measurement


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The phase purity of LMO and LMAO were investigated using various structural analysis techniques. Figure 1a shows XRD patterns of the experimentally as-prepared LMO and LMAO with theoretically calculated XRD patterns from the crystal structures of LMO and LMAO (see Figure 2). All XRD patterns were indexed to the cubic spinel structure belonging to the space group, Fd3m , which is in good agreement with the reference (ICSD 16-5872). Figure 1b and 1c in left column presents FESEM images of the samples. The two spherically-shaped powders have a particle size of 1 – 2 µm. As shown in Figure 1b and 1c in right column, STEM analysis was conducted to further identify the microstructure of LMO and LMAO, and energy dispersive X-ray spectroscopy (EDS) mapping was also performed to confirm the uniformly distributed Mn, Al, and O in LMO and LMAO (Figure S1). Right figures in Figure 1b and 1c shows fine atomic arrangements of cubic spinel and the corresponding fast Fourier transformation figures with a zone axis of [110] of LMO(1b) and LMAO (1c), which describes the d-spacing of LMAO (4.8 Å) and LMO (4.8 Å) for (1-11) and (1-1-1). Figure 1d shows galvanostatic charge-discharge profiles of LMO and LMAO with a constant current of 0.1 C (14.83 mA g-1 for LMO and 15.11 mA g-1 for LMAO) over the voltage range, 3.0 – 4.3 V vs. Li/Li+, at the first cycle. The first charge profile of LMO (blue line) shows 122.69 mAh g-1, which is the state of charge (SOC) of 82.8% with respect to theoretical capacity (148.23 mAh g-1). By contrast, the first charge profile of LMAO (gray line) exhibits 97.37 mAh g-1 with slight increase in voltage than LMO and it means SOC of 64.4% with respect to theoretical capacity (151.15 mAh g-1). As for the cycle performances until 50 cycles with a constant current of 0.1 C as shown in Figure 1e, LMO sample showed the remarkable capacity degradation during cycles (blue circles), whereas the LMAO sample exhibited good cyclic retentions (gray circles). Specifically, LMO exhibited a charge capacity of 122.69 mAh g-1 at the


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first cycle, which decreased to 42.03 mAh g-1 after 50 cycles with a remarkable cyclic degradation. In contrast, LMAO barely showed cyclic degradation that the charge capacity at the first cycle represented 97.37 mAh g-1 and it decreased to 89.27 mAh g-1 at the 50th cycle. The critical factors of these phenomena, leading to a decrease in reversible capacity in the pristine LiMn2O4 and good capacity retention by Al-doping, have been reported.10 Despite these efforts, the fundamental origins and mechanism of the redox behaviors of Mn3+ in LMAO in terms of the electronic configurations could not be found, therefore, we performed first-principles electronic structure analysis to elucidate fundamental redox mechanism.

Crystal structures and calculated voltages The cubic spinel structures of LMO and LMAO with eight formula units were modeled and calculated to study the structural parameters and the electrochemical behaviors upon the removal of Li ions. Figure 2 shows the atomic structure of LMO and LMAO, in which Li, Mn, and O ions occupy the 8a, 16d, and 32e sites with respect to the Wyckoff positions, respectively. As indicated in Figure 2, the Li ions occupy the tetrahedral sites with 4 coordinated O ions and the Mn ions are positioned in the octahedral sites with 6 coordinated O ions. Based on Eqn. (1) (see First-principles calculations), the theoretical average voltages were calculated and compared with the experimental voltages of LMO and LMAO during the initial delithiation process in Figure 3. The calculated delithiation potentials of the two systems are in good agreement with the experimental charge profile, as shown in Figure 3. In LMO, the redox behaviors, originated from Mn3+ oxidation, calculated by first-principles are similar to the experimentally measured charge curve until approximately the extraction of Li+ 0.875 mol. However, when the Li+ content is more than 0.875 mol, it is difficult to extract more Li+ from the LMAO structure because the


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fully oxidized Al3+ has a stable electronic structure with a completely occupied L shell (the primary quantum number, n = 2). Table 1 lists the calculated and experimental lattice parameters of LMO and LMAO. To obtain the lattice parameters of the two samples, the refinement of the XRD patterns by the Rietveld method was conducted based on the cubic phase with a space group Fd3m as described in Figure S2. Through the refinement parameters (Rp and Rwp) related to the quality and good identification between the experimental and calculated data in Table 1, the as-prepared powders showed a pristine cubic spinel phase. In LMO and LMAO, the lattice parameter, a, from the refinement was 8.244 Å and 8.232 Å, respectively, which is in good agreement with the previous report10 and the calculated parameters of 8.289 Å and 8.256 Å from the first-principles calculations, respectively. The lattice parameter of the Al-doped structure was slightly smaller than the pristine LMO structure. This change appears to be related to the electronic configuration of Mn3+ in those structures, which will be discussed in the following section.

Electronic structures To examine the role of aluminum in suppressing the Jahn-Teller distortion, the detailed electronic structures of LMO and LMAO were calculated. Figure 4a shows the d orbitals in a TM ion surrounded by six oxygen ions in an octahedral site and illustrates the schematic energy state divided into two distinct sets of orbitals, which are denoted conventionally as the eg and t2g bands by crystal field splitting (CFS). Based on CFS, Figure 4b indicates schematically that Mn ions in LiMn2O4 have three (Mn4+: t2g3) and four (Mn3+: t2g3, eg1) spin-up electrons at high-spin states, respectively. As reported previously, the structural instability of LiMn2O4 is derived from the Jahn-Teller distortion of Mn3+, as shown in Figure 4b. The presence of a charge order of


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Mn3+ and Mn4+ is due to charge disproportionation in Figure 4b, even though theoretically, stoichiometric LiMn2O4 spinel has Mn3.5+. These schematic energy states can be understood directly by calculating the partial density of states (PDOS) in terms of Mn and O ions in the structures. As shown in the PDOS in Figure 5a, the charge order of Mn3+ in LMO is determined by the eg band (dz2) bound to the pz orbital of O ions ( σ bonding). In particular, the PDOS indicate that three spin-up states in the t2g band are fully occupied below the Fermi level and one spin-up state in the eg band (dz2) is fully occupied under the Fermi level. Therefore, an electron of the highest occupied band (dz2) in LMO would be extracted by withdrawing Li+. Considering the CFS and electronic configuration of Mn in LMO, the electronic structure of LMAO was calculated to examine the redox behavior of Mn ions. As described in Figure 4b, LMAO has the same Mn3+ and Mn4+ charge order as LMO. However, the electronic structure of Mn3+ in LMAO has a different configuration compared to that in LMO. From the schematic energy splitting of Mn ions in Figure 4b, three spin-up electrons occupy the t2g band, while one spin-up electron is split into the eg band (dz2 and dx2-y2) in LMAO, which is consistent with the calculated PDOS in Figure 5b. The PDOS show that three spin-up electrons in the t2g band are fully occupied below the Fermi level, whereas one spin-up electron in the eg band (dz2 and dx2-y2) is occupied under the Fermi level with each orbital divided. Therefore, the distributed electron within the dz2 and dx2-y2 orbital at the highest occupied band would be extracted with the removal of Li+. For a further quantitative examination of the behavior of the abovementioned electronic structures, the band filling of Mn (d-band) and O (p-band) ions in the crystal structures of LMO and LMAO were calculated. Table 2 lists integration of the whole energy states (Total) and the occupied states (Valence) from the PDOS of LMO and LMAO in Figure 5, and the band filling ( f ) derived from the integrations as expressed in Eqn. (2) (see First-principles calculations). The


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f in Table 2 is divided into the d-band filling ( fd ) of Mn ions and the p-band filling ( f p ) of O

ions, and the calculations of fd and f p are split into the five sets of d-band filling ( fd xy , fd yz ,

f d xz , fd z2 , f d x2 − y2 ) and the three sets of p-band filling ( f p x , f py , f pz ), respectively. The calculated band filling of fd xy , fd yz and f d xz in LMO and LMAO are similar, corresponding to the PDOS observations in Figure 5. On the other hand, the distinct changes in the calculated dband filling ( fd z2 , f d x2 − y2 ) are observed together with the calculated p-band filling ( f p x , f py , f pz ). As described in Figures 4 and 5, the majority of electrons in the eg band occupy the dz2 orbital under the Fermi level instead of the dx2-y2 orbital in LMO, which is related directly to the larger

fd z2 than the smaller f d x2 − y2 . These tendencies from band filling are comparable to the calculated PDOS in Figures 4 and 5. With quantitative analysis of the band filling in LMO, the variations of the d and p-band filling with respect to the eg band in Al-doped LMAO were examined. The larger fd z2 in LMO was decreased, whereas the smaller f d x2 − y2 in LMO was increased in LMAO. These indicate that the major reason for the Jahn-Teller distortion (Mn3+:

fd z2 ) was suppressed in LMAO, as shown in the PDOS (See Figure 5). Considering the quantitatively electronic configurations of Mn ions, the p-band filling of O ions could be analyzed using the correlations of the Mn ions because both the electrons of a TM ion and the electrons of O ions occupied in the eg band are bound directly, σ bonding (e.g., bonding state), compared to the π bonding (e.g., non-bonding state) of the electrons in the t2g band. The comparatively larger f pz in LMO is 0.880, forming mainly σ bonding with the Mn dz2 orbital, which decreases to 0.870 in LMAO. In contrast, the relatively smaller f py and f pz for mostly binding with the Mn dx2-y2 orbital and σ bonding are 0.859 and 0.859 in LMO, which increase to


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0.872 and 0.873 in LMAO, respectively, as described in PDOS (See Figure 5). Therefore, through the qualitative behaviors of the electronic structures and the quantitative values of the electronic configurations, the LMO structure could be elucidated as an anisotropically electronic structure affected by the Jahn-Teller distortion (Mn3+: dz2). In contrast, the LMAO structure was demonstrated to be an isotropically electronic configuration determined by the suppressed JahnTeller distortion (Mn3+: dz2, dx2-y2).

Multiscale phase separation kinetics The multiscale modeling on the phase transformation, which is a bridged methodology from first-principles calculation to the multiscale phase separation kinetics, was adopted to understand the enhanced cyclic performance of LMAO in terms of a mesoscale phase transformation.21 The qualitative phase behaviors of LMO and LMAO can be predicted based on zero-temperature mixing enthalpy shown in Figure 6. Figure 6a describes the 4 ground states of LMO at x = 0.0, 0.125, 0.375, and 1.0. From x = 0.375 to 1.0, a two-phase reaction would occur in LMO, and LMO could be transformed to an irreversible Li0Mn2O4 phase (e.g., L0MO), which causes cyclic degradation. On the other hand, LMAO has two additional ground states at x = 0.625, and 0.875, which could prevent the transformation to L0MAO. For detailed analysis of the phase behaviors, Figure 7 shows the homogeneous bulk free energy, fh , and chemical potential, −µh e , of LMO and LMAO at room temperature, and the spinodal points are represented as black dotted lines for LMO (x = 0.18, 0.32, 0.51, and 0.85) and blue dotted lines for LMAO (x = 0.33, 0.54, 0.68, and 0.82). Figure 7a and 7c shows that phase separation is likely to occur in LMO because the SOC of the first charge of LMO (82.8%) is between the spinodal points (light gray area in Figure 7a and 7c), which is in the stable two-phase reaction region. In contrast, the SOC of the first charge


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of LMAO (64.4%) is outside of the spinodal regions in Figure 7b and 7d, which is an unstable nucleation region, meaning that the two-phase reactions could not be generated. From the phenomenological descriptions of the phase separation kinetics presented in Figure 8, the better cyclic performance of LMAO could be understood by a phase separation phenomenon. Both phase separation simulations were performed with 256 × 256 computational cell using a solid solution at SOC of the first charge (LMO: 82.8% and LMAO: 64.4%), and phase separation was triggered by random noise. We took a nearest-neighbor distance for the characteristic lengths (LMO: 0.3591 nm, LMAO: 0.3601 nm), and utilized the square-shaped nanodomains with the side of 91.93 nm for LMO and 92.19 nm for LMAO, as described in Figure 8. After the first charge process, the phase of LMO was separated to L0.625MO and L0MO, which caused irreversible MnO2 phase generation, as shown in Figure 8a. In contrast, Figure 8b shows that phase separation did not occur in LMAO after the first charge process. This is because of the existence of a ground state at approximately x = 0.625, shown in Figure 6b. Because LMAO reacts until an SOC of 64.4% is achieved at 4.3 V vs. Li/Li+ in the electrochemical experiment shown in Figure 1e, L0.356MAO would remain at around x = 0.625 rather than separate to L0.375MAO and L0.125MAO, which prevents an change of inactive Li0Mn2O4 phase. From the different phase separation kinetics of LMO and LMAO, better cyclic performance of LMAO could be understood in terms of the mesoscale phase behaviors.

Conclusions Experimental observations and multiscale modeling were performed to obtain a fundamental understanding of the suppression of the Jahn-Teller distortion (e.g., Mn3+) by Al doping. The electrochemical properties of as-synthesized LMO showed a decreasing capacity after cycling,


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while the cycle performance of LMAO was retained during cycling. To examine the origins and mechanism of electrochemically improved properties, the electronic structures of Mn and O ions were calculated using first-principles. The electronic structure of LMO revealed an anisotropic behavior induced by the Jahn-Teller distortion from Mn3+. In contrast, the electronic structure of LMAO exhibited an isotropic shape, suggesting that the stable electronic structure would positively affect the electrochemical performances during cycling. Based on this mechanistic understanding, the multiscale phase separation kinetics showed that the phase separation of L0.828MO to L0.625MO and L0MO causes an irreversible phase transformation to the inactive Li0Mn2O4 phase. In contrast, LMAO has a stable ground state at x = 0.625 (L0.375MAO), which would prevent the transformation to the inactive phase. Finally, these findings provide an essential understanding of the cyclic performance closely related to the Jahn-Teller distortion of both the LMO and LMAO. In addition to the isotropic electronic structures are expected to provide a solution to overcome the drawbacks of the Jahn-Teller distortion in the atomic scale, mesoscale phase separation behaviors could help to predict and improve the cyclic performances in newly designed cathode materials for LIBs.

Experimental details The pristine LMO and LMAO powder samples were prepared using a typical solid state reaction. First, stoichiometric amounts of Li2CO3, Mn3O4, and Al(OH)3 were dissolved in deionized water with stirring for 3 h at room temperature. To evaporate the water, the solutions were heated to 80°C and maintained at that temperature for 12 h. Additional drying was conducted overnight to remove the little water that remained after heating to 80 °C. The collected powder was ground, heated to 750 °C for 18 h in air, and quenched to room temperature. The


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two samples were characterized by X-ray diffraction (XRD) with a three-dimensional (3D) pixel semiconductor detector using Cu-K α radiation (λ = 1.54056 Å) over the range, 10° to 80° 2θ. The particle size and morphology of LMO and LMAO were confirmed by a field-emission scanning electron microscopy (FESEM, JEOL JSM-7000F). The microstructures of LMO and LMAO were investigated by high-resolution transmission electron microscopy (HRTEM, JEOL ARM-200F). To examine the electrochemical properties of LMO and LMAO, CR2032 coin-type half cells were assembled as follows. The electrode was prepared from a cathode slurry, including the active material (80 wt. %), carbon black (Super-P, 10 wt. %), and a polyvinylidene fluoride (PVDF, 10 wt. %) binder dissolved in an N-methyl pyrrolidinone (NMP) solution. After the slurry was coated on an Al foil as a current collector, the electrode was dried at 80 °C for 3h to evaporate the NMP. The as-prepared electrode was pressed uniformly and punched, and then dried again at 120 °C overnight in a vacuum oven. In a dry room, the coin cells were assembled with Li metal as the counter and reference electrode. A porous polyethylene (PE) membrane was used as a separator and 1.15 M LiPF6 in ethylene carbonate (EC) / ethylmethyl carbonate (EMC) at a 3 : 7 volume ratio was used as the electrolyte (PANAX Etec Co. Ltd.). The loading of the active materials and the electrode density were fixed to 3.9 mg cm-2 and 1.0 g cm-3, respectively.

First-principles calculations To conduct the first-principles calculations, the density functional theory (DFT) method was performed using the spin-polarized generalized gradient approximation (GGA). The pseudopotential plane-wave method, as implemented in the Vienna Ab Initio Simulation Package (VASP), was used to calculate the total energies of the thermodynamic quantities and the density


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of states in the LMO and LMAO. The GGA with a Hubbard-type U correction (GGA+U) was performed to take the strong correlations of the 3d electrons of the manganese ions into account. The value of the effective parameter, Ueff, of 4.84 eV was obtained from the literature.22 The typical computational parameters contained a plane-wave cutoff energy of 400 eV, and reciprocal-space k-point meshes of 4 × 4 × 4 for Brillouin zone sampling. The atomic coordinates and cell parameters were fully relaxed to obtain the optimized crystal structures, thermodynamic quantities, and electronic structures. The theoretical calculation for the average de-lithiation potential based on the Gibbs free energy has been organized. The average intercalation voltage is given by Eqn. (1). V =−

∆Gr , ( Lix2 − Lix1 ) F

(1)

where ( Lix2 − Lix1 ) is the two Li ions intercalation limits, ∆Gr is the change in Gibbs free energy, and F is the Faraday constant. The calculation of the voltage can be simplified by approximating

∆Gr ≡ ∆Er + P∆Vr − T ∆Sr as the change in internal energy, ∆Er , at 0 K. This approximation is reasonable because the terms, P∆Vr and T ∆Sr , are negligible considering the small changes in volume and entropy. The fractional band filling ( f ) of the LMO and LMAO was calculated by integrating the density of states (DOS) using Eqn. (2).18

f =

Noccupiedstates N states

=

∫ ∫

Ef

−∞ ∞ −∞

g ( E )dE ,

(2)

g ( E )dE


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where Noccupiedstates is the total number of states in the occupied bands and Nstates is the total number of states in the occupied and unoccupied bands. g ( E ) refers to the DOS projected onto the atomic orbitals in the two systems.

Multiscale modeling on the phase transformation To describe the mesoscale phase separation phenomena, the Cahn-Hilliard equation23 was solved by adopting the Cahn-Hilliard free energy functional, GCH , and introducing the mixing enthalpy coefficient, ε i f , from the initial inverse Li content, xi , to the final inverse Li content, x f , using a double-well potential to represent the homogeneous bulk free energy, f h , as follows:21  κf 2 GCH = ∫ ρ n  f h + i ∇x  dV , V 2  

(3)

where x is the inverse Li content in L1-xMO and L1-xMAO, ρn is the number of Li sites per volume, V , and κ i f is the gradient energy coefficient. f h = ∑ H i f + k BT ( x ln x + (1 − x ) ln (1 − x ) ) H if = ε if ( x − xi )

2

(x

− x ) , xi ≤ x ≤ x f , 2

f

(4)

(5)

where H i f is the mixing enthalpy at the reaction region from xi to x f , kB is Boltzmann’s constant, and T is the absolute temperature. In this numerical simulation, ε i f and κ i f , which are listed in Table S1, were determined using the multiscale-based phase transformation model from the scheme reported elsewhere Lim et −10 2 −1 al.21 For the diffusion coefficient, D , experimental values of 5 ×10 cm ⋅ s for LMO and


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5×10−9 cm2 ⋅ s−1 for LMAO were obtained from the literature, respectively.24, 25 Finally, a semiimplicit Fourier Spectral Method was used to solve the Cahn-Hilliard equation.26

ASSOCIATED CONTENT Supporting Information The Supporting Information is available free of charge on the ACS Publications website.

Rietveld refinement data of LMO and LMAO, table summarizing first-principles bulk free energy coefficient, and the corresponding gradient energy coefficient in LMO and LMAO

AUTHOR INFORMATION Corresponding Author *E-mail: [email protected] (M. Cho) ACKNOWLEDGMENT This study was supported by a National Research Foundation of Korea (NRF) grant funded by the Korean government (MEST) (2012R1A3A2048841) and the IT R&D program (Grant No. 10046306) funded by the Ministry of Trade, Industry & Energy (MOTIE), Republic of Korea. This work was also supported by the New & Renewable Energy Core Technology Program of the Korea Institute of Energy Technology Evaluation and Planning (KETEP) granted financial


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resource from the Ministry of Trade, Industry & Energy, Republic of Korea (No. 20152020105420).

REFERENCES 1. Tarascon, J. M.; Armand, M. Issues and Challenges Facing Rechargeable Lithium Batteries. Nature 2001, 414, 359-367. 2. Dunn, B.; Kamath, H.; Tarascon, J. M. Electrical Energy Storage for the Grid: A Battery of Choices. Science 2011, 334, 928-935. 3. Thackeray, M. M.; Johnson, P. J.; Depicciotto, L. A.; Bruce, P. G.; Goodenough, J. B. Electrochemical Extraction of Lithium from LiMn2O4. Mater Res Bull 1984, 19, 179-187. 4. Okubo, M.; Mizuno, Y.; Yamada, H.; Kim, J.; Hosono, E.; Zhou, H. S.; Kudo, T.; Honma, I. Fast Li-Ion Insertion into Nanosized LiMn2O4 without Domain Boundaries. Acs Nano 2010, 4, 741-752. 5. Put, B.; Vereecken, P. M.; Labyedh, N.; Sepulveda, A.; Huyghebaert, C.; Radu, I. P.; Stesmans, A. High Cycling Stability and Extreme Rate Performance in Nanoscaled LiMn2O4 Thin Films. ACS Appl Mater Interfaces 2015, 7, 22413-22420. 6. Kim, D. K.; Muralidharan, P.; Lee, H. W.; Ruffo, R.; Yang, Y.; Chan, C. K.; Peng, H.; Huggins, R. A.; Cui, Y. Spinel LiMn2O4 Nanorods as Lithium Ion Battery Cathodes. Nano Lett 2008, 8, 3948-3952. 7. Chung, K. Y.; Yoon, W. S.; Kim, K. B.; Yang, X. Q.; Oh, S. M. Suppression of Structural Fatigue by Doping in Spinel Electrode Probed by in situ Bending Beam Method. J Electrochem Soc 2004, 151, A484-A492. 8. Lee, H. W.; Muralidharan, P.; Ruffo, R.; Mari, C. M.; Cui, Y.; Kim, D. K. Ultrathin Spinel LiMn2O4 Nanowires as High Power Cathode Materials for Li-Ion Batteries. Nano Lett 2010, 10, 3852-3856. 9. Lu, J.; Zhan, C.; Wu, T. P.; Wen, J. G.; Lei, Y.; Kropf, A. J.; Wu, H. M.; Miller, D. J.; Elam, J. W.; Sun, Y. K.; Qiu, X. P.; Amine, K. Effectively Suppressing Dissolution of Manganese from Spinel Lithium Manganate via a Nanoscale Surface-doping Approach. Nat Commun 2014, 5. 6693-6701. 10. Myung, S. T.; Komaba, S.; Kumagai, N. Enhanced Structural Stability and Cyclability of Al-doped LiMn2O4 Spinel Synthesized by the Emulsion Drying Method. J Electrochem Soc 2001, 148, A482-A489. 11. Xiao, L. F.; Zhao, Y. Q.; Yang, Y. Y.; Cao, Y. L.; Ai, X. P.; Yang, H. X. Enhanced Electrochemical Stability of Al-doped LiMn2O4 Synthesized by a Polymer-pyrolysis Method. Electrochim Acta 2008, 54, 545-550. 12. Li, X.; Ma, X. H.; Su, D.; Liu, L.; Chisnell, R.; Ong, S. P.; Chen, H. L.; Toumar, A.; Idrobo, J. C.; Lei, Y. C.; Bai, J. M.; Wang, F.; Lynn, J. W.; Lee, Y. S.; Ceder, G. Direct Visualization of the Jahn-Teller Effect Coupled to Na Ordering in Na5/8MnO2. Nat Mater 2014, 13, 586-592.


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13. Kim, H.; Yoon, G.; Park, I.; Park, K. Y.; Lee, B.; Kim, J.; Park, Y. U.; Jung, S. K.; Lim, H. D.; Ahn, D.; Lee, S.; Kang, K. Anomalous Jahn-Teller Behavior in a Manganese-based Mixed-phosphate Cathode for Sodium Ion Batteries. Energy Environ Sci 2015, 8, 3325-3335. 14. Bai, P.; Cogswell, D. A.; Bazant, M. Z. Suppression of Phase Separation in LiFePO4 Nanoparticles During Battery Discharge. Nano Lett 2011, 11, 4890-4896. 15. Cubuk, E. D.; Wang, W. L.; Zhao, K. J.; Vlassak, J. J.; Suo, Z. G.; Kaxiras, E. Morphological Evolution of Si Nanowires upon Lithiation: A First-Principles Multiscale Model. Nano Lett 2013, 13, 2011-2015. 16. Stournara, M. E.; Qi, Y.; Shenoy, V. B. From Ab Initio Calculations to Multiscale Design of Si/C Core-Shell Particles for Li-Ion Anodes. Nano Lett 2014, 14, 2140-2149. 17. Cogswell, D. A.; Bazant, M. Z. Coherency Strain and the Kinetics of Phase Separation in LiFePO4 Nanoparticles. Acs Nano 2012, 6, 2215-2225. 18. Kim, D.; Lim, J. M.; Lim, Y. G.; Yu, J. S.; Park, M. S.; Cho, M.; Cho, K. Design of Nickel-rich Layered Oxides Using d Electronic Donor for Redox Reactions. Chem Mater 2015, 27, 6450-6456. 19. Kim, D.; Lim, J. M.; Lim, Y. G.; Park, M. S.; Kim, Y. J.; Cho, M.; Cho, K. Understanding of Surface Redox Behaviors of Li2MnO3 in Li-Ion Batteries: First-Principles Prediction and Experimental Validation. Chemsuschem 2015, 8, 3255-3262. 20. Lim, J. M.; Kim, D.; Lim, Y. G.; Park, M. S.; Kim, Y. J.; Cho, M.; Cho, K. The Origins and Mechanism of Phase Transformation in Bulk Li2MnO3: First-principles Calculations and Experimental Studies. J Mater Chem A 2015, 3, 7066-7076. 21. Lim, J. M.; Kim, D.; Cho, K.; Cho, M. Under review, Phys Rev Lett 2016. 22. Xu, B.; Meng, S. Factors Affecting Li Mobility in Spinel LiMn2O4-A First-principles Study by GGA and GGA+U Methods. J Power Sources 2010, 195, 4971-4976. 23. Cahn, J. W.; Hilliard, J. E. Free Energy of a Nonuniform System .1. Interfacial Free Energy. J Chem Phys 1958, 28, 258-267. 24. Tang, X. C.; Song, X. W.; Shen, P. Z.; Jia, D. Z. Capacity Intermittent Titration Technique (CITT): A Novel Technique for Determination of Li+ Solid Diffusion Coefficient of LiMn2O4. Electrochim Acta 2005, 50, 5581-5587. 25. Song, D.; Ikuta, H.; Uchida, T.; Wakihara, M. The Spinel Phases LiAlyMn2-yO4 (y = 0, 1/12, 1/9, 1/6, 1/3) and Li(Al,M)(1/6)Mn11/6O4 (M = Cr, Co) as the Cathode for Rechargeable Lithium Batteries. Solid State Ionics 1999, 117, 151-156. 26. Chen, L. Q.; Shen, J. Applications of Semi-implicit Fourier-spectral Method to Phase Field Equations. Comput Phys Commun 1998, 108, 147-158.


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Figure 1. (a) XRD patterns of the synthesized and calculated LMO and LMAO. FESEM and STEM images of (b) LMO and (c) LMAO particles with d-spacings based on the corresponding fast Fourier transformation (FFT) images with a zone axis of [110]. (d) Galvanostatic charge profiles at the first cycle and (e) cyclic performances of LMO (blue line and circles) and LMAO (gray line and circles) in the voltage range, 3.0 V to 4.3 V vs. Li/Li+, with a constant current of 0.1 C.


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Figure 2. (a) Tetrahedron of LiO4 and (b) octahedron of MnO6 in the atomic model of LMO. (c) LiO4 and (d) the MnO6 and AlO6 in the atomic model of LMAO.


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Figure 3. Experimentally evaluated profiles at the first charge and the calculated delithiation potentials of LMO and LMAO with the removal of Li+.


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Compounds

a-cal. (Å)

a-exp. (Å)

Rp (%)

Rwp (%)

LMO

8.289

8.244

2.537

4.087

LMAO

8.256

8.232

2.422

4.514

Table 1. Calculated lattice parameters and Rietveld refinement results of the lattice parameters in LMO and LMAO.


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Figure 4. (a) Regular octahedral 6 coordination geometries of a transition metal (TM) with oxygen atoms (TMO6) and d orbitals of a TM positioned in an octahedral site and the corresponding schematic energy levels known as the eg band and t2g band within the 3d bands. (b) Schematic energy levels and occupied electron configurations of the 3d bands from the Mn ions in LMO and LMAO.


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Figure 5. 3d-electron PDOS of Mn and 2p-electron PDOS of O. Corresponding PDOS of the 3 degeneracies of dxy, dyz, dxz in the t2g band and 2 degeneracies of the dz2, dx2-y2 in the eg band with respect to Mn ions, and similarly, 3 degeneracies of px, py and pz with respect to O ions in (a) LMO and (b) LMAO.


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Mn d orbitals

O p orbitals

Compounds

LMO

LMAO

dxy

dyz

dxz

dz2

dx2-y2

px

py

pz

Total

1.909

1.897

1.897

1.973

1.995

1.360

1.360

1.360

Valence

1.044

1.031

1.031

0.955

0.746

1.169

1.169

1.198

Fractional band filling

0.547

0.543

0.543

0.484

0.374

0.859

0.859

0.880

Total

1.863

1.864

1.864

1.945

1.946

1.328

1.328

1.328

Valence

1.014

1.016

1.015

0.814

0.851

1.159

1.159

1.155

Fractional band filling

0.545

0.545

0.545

0.419

0.438

0.872

0.873

0.870

Table 2. Integration of the entire energy states (Total) and the occupied states (Valence) from the indicated PDOS in Figure 5. The fractional band fillings from each band were calculated through the total and valence.


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Figure 6. Zero-temperature mixing enthalpy calculated from first-principles calculations in (a) L1-xMO (black circles) and (b) L1-xMAO (gray circles) from x =0 to 1.


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Figure 7. Homogeneous bulk free energy, fh , of (a) LMO and (b) LMAO, and the chemical potential, −µh e , of (c) LMO and (d) LMAO at room temperature with respect to the inverse Li content x. The black dashed lines in (a) and (c) are the spinodal points of LMO and the blue dashed lines in (b) and (d) are the spinodal points of LMAO.


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Figure 8. Phase separation kinetics in (a) LMO (SOC = 82.8%) and (b) LMAO (SOC=64.4%) during relaxation from a solid solution at various dimensionless time tˆ .


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First-Principles Multiscale Modeling and ... - ACS Publications

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