High-Throughput Description of Infinite CompositionâStructure

Article Cite This: Chem. Mater. 2018, 30, 2287−2298

pubs.acs.org/cm

High-Throughput Description of Infinite Composition−Structure− Property−Performance Relationships of Lithium−Manganese Oxide Spinel Cathodes Weibin Zhang,*,† Damian M. Cupid,† Petronela Gotcu,† Keke Chang,*,‡ Dajian Li,† Yong Du,§ and Hans J. Seifert† †

Institute for Applied Materials−Applied Materials Physics (IAM-AWP), Karlsruhe Institute of Technology (KIT), Hermann-von-Helmholtz-Platz 1, 76344 Eggenstein-Leopoldshafen, Germany ‡ Engineering Laboratory of Nuclear Energy Materials, Ningbo Institute of Materials Technology and Engineering, Chinese Academy of Sciences, 1219 Zhongguan West Road, 315201 Ningbo, Zhejiang, China § State Key Laboratory of Powder Metallurgy, Central South University, 410083 Changsha, Hunan, China S Supporting Information *

ABSTRACT: Lithium−manganese oxide based spinel is attractive as cathode materials in lithium ion batteries. A wide range of spinel solid solution can be directly sintered and result in different properties of identical compositions during the battery operation, making it extremely difficult to understand the intrinsic properties and evaluate the battery performance. In this work, a high-throughput computational framework combining ab initio calculations and a CALPHAD (Calculation of Phase Diagrams) approach is developed to systematically describe infinite composition− structure−property−performance relationships under sintered and battery states of spinel cathodes. Depending on composition and crystallography, various properties (physical, thermochemical, and electrochemical) relating key factors (cyclability, safety, and energy density) are quantitatively mapped. The overall performance is consequently evaluated and validated by key experiments. Finally, 4 V spinel cathodes with codoping of reasonable Li and vacancies on the octahedral sites have been proposed. The presented strategy provides a general guide to evaluate the performance of cathodes with wide composition ranges.

1. INTRODUCTION Over the past two decades, the lithium-ion battery (LIB) has enabled society-changing technological advances in portable electronic devices, electric transportation, and energy storage for renewable energy sources.1 In order to meet the everincreasing demands for such applications, extensive research has been conducted to develop the LIB cathode materials toward the goal of high voltage, high energy density, low cost, superior safety, long cycle life, and environmental friendliness.2−4 Due to its superior properties, lithium−manganese oxide (LMO) based spinel has attracted extensive attention.5−10 However, the LMO spinel has intrinsic complexity from a combination of a wide composition range11 and infinite variations of the crystallography with the identical composition during the battery operation (see the Supporting Information). This leads to the infinite different properties and battery performances for the same spinel electrode composition. The complexity will be further increased by partial substitution of manganese with other elements12−14 (Al, Co, Cr, Cu, Mg, Fe, Ni, Zn, etc.) for the high voltage applications. Experimental study of such a complex case is extremely time and effort consuming, which makes it difficult to select optimized cell performance for the various applications. © 2018 American Chemical Society

Clearly, a model, which can provide an overall map linking materials composition, crystal structure, physical/thermochemical/electrochemical properties, and cell performance, is essential for providing systematic guidance for the battery design and behavior perspective. Currently, most of the computational works focus on understanding the structure or property of electrode materials at an atomic scale. For instance, density functional theory (DFT) based ab initio calculations were performed to predict the fundamental properties (electronic structure, equilibrium voltage, thermal and electrochemical stability, lithium diffusivity) on thousands of potential electrode materials.14−21 However, the pure ab initio calculations cannot be directly applied to describe the continuous properties of complete composition coverage for the electrode materials. Recently, the CALPHAD (Calculation of Phase Diagrams) approach has been proven to be a powerful tool to efficiently evaluate the phase diagrams and continuous properties in the lithium ion batteries.22−27 The essence of this approach is to optimize the parameters of the sublattice Received: December 5, 2017 Revised: March 9, 2018 Published: March 12, 2018 2287

DOI: 10.1021/acs.chemmater.7b05068 Chem. Mater. 2018, 30, 2287−2298

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Chemistry of Materials model28 based on reliable experimental and theoretical data. Using ab initio calculations, the thermodynamic and structural properties of the end-members of the sublattice model can be computed as inputs for the CALPHAD approach. Therefore, the integration of ab initio calculations and CALPHAD approach29 provides an efficient way to describe the phase diagrams and continuous properties of cathode materials with wide solubility range in lithium ion batteries. In the current work, integrating ab initio calculations and the CALPHAD approach, we develop a high-throughput computational framework which is capable of acquiring the composition−structure−property−performance relationships of LMO spinel electrodes spanning wide composition ranges as well as its infinite states corresponding to an identical composition. The purposes of this work are to (i) construct the theoretical model and identify the composition range and crystallography of spinel phase; (ii) quantitatively map the physical, thermochemical, and electrochemical properties of the LMO spinel solid solution, and validate its accuracy using experimental and theoretical data; and (iii) evaluate the cell performance as an entirety from the aspects of cyclability, safety, and energy density, in order to propose a routine to design new 4 V cathode materials.

thermodynamic model for spinel phase with extensive solid solubility was developed within the framework of the Compound Energy Formalism (CEF).37−40 The Gibbs energy expression in the CEF per formula unit is

⎞

⎛

Gm =

∑ ∑ yiT yjO °Gij + RT ⎜⎜∑ yiT ln yiT + 2 ∑ yjOln yjO⎟⎟ i

⎝

j

i

j

⎠

E

+ Gm yTi

(2)

yOj

and are the site fractions of constituents i and j on the where tetrahedral and octahedral sublattices; °Gij is the Gibbs energy of an end-member (i)T1 [j]O2 O4 of the solution; and EGm is the excess Gibbs energy of mixing due to interactions of ions in the mixture, which can be described as follows E

Gm =

∑ ∑ ∑ yiT yjT ykOLij :k + ∑ ∑ ∑ ykT yiOyjOLk :ij + ··· i

j

k

i

j

k

(3) where Lij:k and Lk:ij represent the interaction energies between cations i and j on one sublattice when the other sublattice is occupied only by k. From eqs 2 and 3, it can be seen that site occupation must be taken into consideration of the Gibbs energy expression of a phase using CEF model. In the frame of current work, the LMO spinel phase shows not only considerable composition range but also different site occupations even for the same composition, depending on the route by which composition has been reached. In order to keep the clarity of the main manuscript, detailed description of the modeling process has been given in the Figure S2 and related discussions are in Supporting Information. The Gibbs energy of the stoichiometric tetragonal LiMnO2 compounds is expressed by

2. METHODS Ab Initio Calculations. Enthalpies of formation and lattice parameters for spinel oxides in the Li−Mn−O system are obtained using DFT based ab initio calculations. The generalized gradient approximation (GGA) method, as implemented in the Vienna ab initio simulation package (VASP),30 is performed with the Blö chl corrections for the total energy.31 The valence electrons are explicitly treated by projector augmented plane-wave (PAW) potentials.32 A plane-wave cutoff energy of 500 eV and an energy convergence criterion of 0.01 meV for electronic structure self-consistency are used in the calculations. The integration in the Brillouin zone is done on appropriate k-points determined after Monkhorst−Pack.33 All structures are relaxed with respect to atomic positions and volumes. Spin polarization effects are included in all the calculations. A detailed description of this calculation technique can be found elsewhere.34 The enthalpy of formation for the spinel oxides at 0 K is calculated using the following equation (LiMn2O4 taken as an example):

m m °G LiMnO − H SER = A + BT + 0.5°G Lim2O + 0.5°G Mn 2 2O3

(4)

Since there are experimental data on heat capacity of Li2MnO3 in a wide temperature range, the Gibbs energy of Li2MnO3 is expressed as °G Lim2MnO3 − H SER = A + BT + CT ln T + DT 2 + ET −1

(5)

where A and B in eqs 4 and 5 are the parameters to be evaluated; the coefficients C, D, and E are taken from the expression of heat capacity for solid Li2MnO3.41 The parameters in the model are optimized based on the data of heat capacity,41−43 enthalpy of formation,41,44−46 phase diagram,11,47 and open cell voltages.48 The optimized thermodynamic parameters are summarized in Table S1. The enthalpy of formation is an essential property for the stability of the compound. It can be calculated using

ΔHf (LiMn2O4 ) = E(LiMn2O4 ) − [E(Li) + 2E(Mn) + 2E(O2 )] (1) where E(LiMn2O4), E(Li), E(Mn), and E(O2) denote the total energies of LiMn2O4, Li, Mn, and O2, respectively. To calculate E(O2), 10 × 10 × 10 Å3 supercells are used to diminish the long-range interactions due to periodic boundary conditions imposed within the VASP code. For one composition of the spinel oxide with Li or Mn defects, models with various possible vacancy positions are adopted in the calculations. The one with the most negative enthalpy value is considered to be stable. Gibbs Energy. CALPHAD assessments of the Li−O35 and Mn− 36 O systems have been reported satisfactorily, whereas the Li−Mn phase diagram shows neither components nor solid solubility in the entire temperature range. Therefore, the binary compounds sub-binary thermodynamic description has been accepted from literature without modification. Only pure O2 has been taken into consideration for the gas phase. For the description of the ternary Li−Mn−O system at room temperature, three ternary phases, namely, spinel, LiMnO2, and Li2MnO3, have been modeled during current work. The spinel structure of the general formula AB2O4 belongs to the space group Fd3̅m (No. 277). The oxygen ions are located in the 32e sites, where only one-eighth of the 64 tetrahedral sites is occupied by lithium ions (8a) and one-half of the 32 octahedral sites by manganese ions [16d]. The tetrahedral (8a) and octahedral (16c) sites form a three-dimensional network for the transport of lithium ions. The

ΔH = ΔG − T

∂ΔG ∂T

(6)

where T stands for temperature in K. Molar volume and lattice parameter. The 1 molar formula volume of the spinel phase have also been modeled using the CEF model as

Vm =

∑ ∑ yiT yjO°Vij + EV m i

j

(7)

where the first term at the right side stands for a linear combination of the molar volume of the end members, and the second term is the part to be fitted to the experimental results when required. It must be pointed out that the vacancies must be counted to the amount of atoms during the calculation. No thermal expansion of the molar volume has been taken into consideration during current work. The detailed description of the modeling process and optimized parameters have been given in the Supporting Information and Table S2, respectively. The lattice parameter for the spinel phase can be calculated using following equation: 2288


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Chemistry of Materials

Figure 1. Flowchart of the high-throughput computational framework to systematically evaluate the performance of the spinel compounds in Li-ion batteries.

a0 =

3

8Vm NA

cathode materials include cyclability, safety, and energy density. To evaluate the battery performance of the LMO spinel electrodes within the wide composition range, we consider several properties depending on the composition and crystallography as listed below: (i) the lattice parameter (electrochemical stability) and Jahn−Teller distortion of the spinel electrodes (relating to the cyclability), (ii) the enthalpy of formation (thermochemical stability) and the oxygen gas release of the spinel electrodes (relating to the safety), and (iii) the cell voltage and capacity of the spinel electrodes (relating to the energy density). The evaluation incorporates systematically mapping the above-mentioned properties under the different states of the LMO spinel. A flowchart for the high-throughput computational framework is shown in Figure 1. Phase Diagrams of the Li−Mn−O System. As discussed in the Supporting Information, a spinel phase with the identical composition obtained by delithiating from different sintered compositions shows different crystallography. This means a proper study must start from a specified sintered composition, which makes the study for the complete region extremely time and effort consuming. Even using computational modeling, it is nearly impossible to visualize the complete combinations. In the following calculation section, only the starting compositions located at the edge from LiMn2O4 to Li4Mn5O12 have been selected as an example to demonstrate the changes during the battery operation. They can provide the highest amount of extractable Li followed by covering the complete composition range of the spinel compound. For convenience, the materials just sintered and during the battery operation will be named as “sintered state” and “battery state”, respectively. Once the thermodynamic modeling has been established, the phase diagrams of the Li−Mn−O system can be constructed to identify the phase relationship. Figure 2a,b presents the calculated room temperature phase diagrams of the Li−Mn− O system for “sintered” and “battery” states, respectively. The phase diagram of the “sintered state” is considered as a stable state, while the “battery state” is a metastable phase diagram calculated with MnO2 suspended. The calculated spinel solid solubilities in both diagrams agree satisfactorily with that given

(8)

where NA is Avogadro constant. Eight times of the molar formula volume (Vm) is due to the structure cell of the spinel containing 8 formula units of AB2O4. Cell Voltage, Capacity, and Energy Density. The cell voltage E0 is directly linked to the chemical potential of Li at a given state by the Nernst equation:

E0 =

α Cathode RT ln LiAnode zF αLi

(9)

where R is the gas constant, z is the number of moles of electrons transferred during the cell reaction (1 for Li), F is the Faraday and αAnode are the activity of Li in the electrodes, constant, and αCathode Li Li = 1 for half-cell setup with pure Li as the anode material. where αAnode Li The capacity of the spinel cathode is equal to the amount of Li cations which can be extracted during the battery operation. The theoretical capacity CM (in mAh/g) is determined by the amount of active materials and is calculated as follows: CM =

nF 3.6M

(10)

where M is the molecular mass of the spinel material and n is the number of moles of electrons, which originates from the Mn3+/Mn4+ redox reactions during lithium insertion and extraction from the spinel framework. Because the amount of removable Li in the spinel structure is always higher than that of Mn3+, n should be equal to the Mn3+ content on the octahedral sites. Energy density, an important factor in determining battery performance, is the amount of energy stored per unit mass or volume (in mWh/g or mWh/L). The theoretical energy that can be obtained from 1 mol of reactant is given as follows:

EM = CME 0

(11)

0

where E is the operating potential in volt (V) obtained from the energy change for the cell reaction and CM is the theoretical capacity.

3. RESULTS Framework To Evaluate the Battery Performance of LMO Spinel. General requirements for advanced LMO spinel 2289


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16d sites, where the Va concentration decreases from the Li4Mn7O16−Li2Mn4O9 edge to the LiMn2O4 composition. In this case, no Mn ions exist on the 8a sites. The amounts of Mn3+ and Mn4+ are determined by the global composition as well as the electroneutrality condition. The concentrations of Mn3+ and Mn4+ on the 16d sites are shown in Figure S3e,f, respectively. As can be seen, the maximum amount of Mn3+ is equal to the minimum amount of Mn4+, both locating at the composition of LiMn2O4. Figure S4 shows the calculated cations and vacancy distribution on the 8a and 16d sites of spinel phase under the condition of “battery state”, covering the composition range of the λ-MnO2−LiMn2O4−Li4Mn5O12 triangle. As shown in Figure S4a, the delithiation process must start from the LiMn2O4−Li4Mn5O12 edge and goes through a path parallel to the connection of LiMn2O4−λ-MnO2. The lengths of possible paths in the λ-MnO2−LiMn2O4−Li4Mn5O12 triangle present the amount of Li which can be extracted from the spinel. Clearly, the maximum Li capacity comes from the LiMn2O4 composition, which can be delithiated up to λ-MnO2, whereas the Li4Mn5O12 has no usable Li capacity in the triangle of possible composition range. The amount of vacancies on the 8a sites is equal to the removed Li cations and can be considered as the theoretical charge capacity (Figure S4b). The Li contents during the battery operation process on the 16d sites are constant in the direction of delithiation (Figure S4c). This indicates that the Li cations on the 16d sites are not extractable following the current model, in agreement with the experimental results.50,51 Figure S4d,e show the amount of Mn3+ and Mn4+ on the 16d sites, respectively. Following the electroneutrality condition, the extraction of one Li+ must be accompanied by the oxidation of one Mn3+ to Mn4+. Therefore, the remaining amount of Mn3+ in spinel also presents the capacity of the cathode materials, corresponding to the removable Li capacity shown in Figure S4a. Compared with Figure S3, it is clear that the same composition has different site occupation under the “sintered state” and “battery state”. Physical Property: Lattice Parameter. Calculated lattice parameters for spinel based on the “sintered state” within the LiMn2O4−Li4Mn5O12−Li2Mn4O9 triangle are illustrated in Figure 3a. A ridge of lattice parameters can be observed along the LiMn2O4−Li4Mn7O16 (LiMn7/4O4) line. The reason can be explained using the change of the site occupations (see Figure S3). For clarity, Figure 3b shows the calculated lattice parameter together with site occupations from Li4Mn5O12 to Li2Mn4O9 (LixMn2−0.25xO4, 0.89 ≤ x ≤ 1.33, x indicates the amount of Li) spinel compound as an example. The lattice parameter has a maximum value at x = 1 (LiMn7/4O4 composition), where all the site occupation profiles have the kinks excepted for Mn4+ on 16d. Ab initio calculation has been performed on the composition of LiMn7/4O4 (Li4Mn7O16) following the calculated results. Excellent agreement between the ab initio calculation and the prediction has been achieved. Figure 3c shows the calculated lattice parameters of Li1+yMn2−yO4 (0 ≤ y ≤ 0.33, y indicates the excess amount of Li on 16d sites) and Li1−zMn2−2zO4 (0 ≤ z ≤ 0.11, z indicates the amount of vacancies on 8a sites) spinel in the “sintered state” for the Li-excess and Li-defect spinel, respectively, along with the experimental data.44,50−54 Three LMO samples with different compositions are prepared in this work. The synthesis process and experimental measurements can be found in the Supporting Information. The Li/Mn ratio and XRD patterns of samples are shown in Table S3 and Figure

Figure 2. Calculated room temperature phase diagrams of the Li− Mn−O system for (a) “sintered state” (stable) and (b) “battery state” (metastable with MnO2 suspended). The shaded regions of the phase diagram represent the spinel single phase. 1, 2, and 3 represent the stoichiometric spinel compounds LiMn 2 O 4 , Li 4 Mn 5 O 12 , and Li2Mn4O9, respectively.

by Thackeray et al.,11 as shown in Figure S1. We have found that the “sintered” and “battery” states can be used to predict the intrinsic properties for the fresh made batteries and electrochemical behaviors during the battery operation, respectively. Composition and Crystallography of the Spinel Phase. The site occupation of the different components in the crystallography of LMO spinel is the essential character affecting physical, thermochemical, and electrochemical properties. In order to calculate the properties accurately, site occupation in spinel solid solution must be correctly described using proper models for different conditions. Figure S3 shows the calculated cations and vacancy (Va) distributions on tetrahedral (8a) or octahedral (16d) sites of spinel phase under the condition of “sintered state”, covering the composition range of the LiMn2O4−Li4Mn5O12−Li2Mn4O9 triangle. As can be seen from the Li ions and Va occupation on 8a and 16d sites, this triangle can be divided into two parts, Li-excess spinel (LiMn2O4−Li4Mn5O12−Li4Mn7O16) and Li-defect spinel (LiMn2O4−Li4Mn7O16−Li2Mn4O9).49 In the Li-excess spinel, the 8a sites are fully occupied by the Li ions and excess Li ions go into the 16d sites, replacing Mn ions. Meanwhile, the concentration of Va on the 16d sites shows a different trend from the Li cations, decreasing from Li4Mn7O16 to the connection of LiMn2O4−Li4Mn5O12. For the Li-defect spinel, all the Li cations occupy the 8a sites together with vacancies, whose concentration decreases from the Li2Mn4O9 composition to LiMn2O4−Li4Mn7O16 edge. No Li cations exist on the 2290


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area of Figure 3c, the experimental lattice parameter shows higher values than the calculated results which are extrapolated from the oxygen-defect-free Li1+yMn2−yO4 region (0 < y < 0.2). For the Li-defect spinel, as z in Li1−zMn2−2zO4 increases, the lattice parameter decreases due to higher vacancy concentration on the tetrahedral and octahedral sites. Figure 4 shows the calculated lattice parameter of spinel phase under the condition of “battery state”, covering the

Figure 4. Calculated lattice parameter of spinel phase under the condition of “battery state”, covering the composition range of the λMnO2−LiMn2O4−Li4Mn5O12 triangle.

composition range of the λ-MnO2−LiMn2O4−Li4Mn5O12 triangle. Figure 4 shows a similar trend to the Li cation on the 8a sites (Figure S4a). This is because the delithiation process is reducing Li+ cations from the 8a sites combined with oxidation of Mn3+ to Mn4+ on the 16d sites, and both effects decrease the lattice parameter. Physical Property: Jahn−Teller Distortion. Jahn−Teller distortion is one of the most important reasons for capacity fading for spinel cathode materials for lithium ion batteries. The onset of Jahn−Teller distortion in spinel electrodes occurs when the amount of Mn3+ reaches approximately 50% (average Mn oxidation state is 3.5).56 The excess Li therefore has been introduced in order to prohibit the Jahn−Teller and increase cyclability.52 This has been attributed to the decrease of the Mn3+ amount. However, this does not explain the fact that rapid charge/discharge leads to faster capacity fading. It is clear that the kinetic issue has to be taken into consideration. As discussed before, with high current operation, the nonequilibrium state can cause the local Jahn−Teller distortion. Therefore, the tolerance, i.e., how much diversion from the equilibrium state is allowed, before capacity fading occurs, needs to be studied. The voltage−composition profiles of Li/LixMn2O4 (0 ≤ x ≤ 2) and Li/LixMn1.85O4 (0 ≤ x ≤ 2) at room temperature have been calculated as illustrated in Figure 5a,b, respectively, with a good agreement with the literature data.48,57 LiMn2O4 as electrode material offers the possibility of both Li extraction and insertion. For 0 ≤ x ≤ 1 in LixMn2O4, Li ions on the 8a sites undergo intercalation/deintercalation around 4 V in the spinel single phase region. The voltage drops suddenly to 2.95 V at x = 1 and remains at this value for 1 ≤ x ≤ 2. From the structural point of view, this step is related to the phase transition from the spinel LiMn2O4 to tetragonal Li2Mn2O4 (tLiMnO2) because of the Jahn−Teller distortion of Mn3+ ion. Even though the cutoff voltage is controlled between 3.0 and

Figure 3. (a) Calculated lattice parameters for spinel based on the “sintered state” within the LiMn2O4−Li4Mn5O12−Li2Mn4O9 triangle. (b) Calculated lattice parameters and site occupations for LixMn2−0.25xO4 (0.89 ≤ x ≤ 1.33) spinel compound. (c) Calculated lattice parameters of Li1+yMn2−yO4 (0 ≤ y ≤ 0.33) and Li1−zMn2−2zO4 (0 ≤ z ≤ 0.11) spinel in the “sintered state” for the Li-excess and Lidefect spinel, respectively, along with the experimental data.44,50−54

S5, respectively. The measured lattice parameters of samples in this work are also listed on Figure 3c. Note that the experimental data are fluctuated because of different synthesis conditions. Nevertheless, the difference between the calculated and the experimental values is within an acceptable range of −0.55−1.33%. As reported in refs 44 and 55, in the Li-rich Li1+yMn2−yO4, with y < 0.2, the lattice parameter decreases linearly with the increase of excess lithium y in Li1+yMn2−yO4 resulting from a substitution of Li+ ions for Mn3+ ions combined with oxidation of Mn3+ to Mn4+ (ionic radius: Mn4+ < Mn3+ < Li+). For y > 0.2, oxygen-defect free Li1+yMn2−yO4 is difficult to sinter.44 Therefore, more Mn3+ and less Mn4+ must exist to balance the electroneutrality, and this consequently leads to increased lattice parameter. Therefore, in the shaded 2291


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Figure 5. Calculated phase transition and cell voltages of (a) Li/LixMn2O4 (0 ≤ x ≤ 2) and (b) Li/LixMn1.85O4 (0 ≤ x ≤ 2) at room temperature compared to the literature data48,56 and (c) calculated half cell voltage related to the composition within the t-LiMnO2−Li2MnO3−λ-MnO2 triangle. The dashed line presents the starting composition of Jahn−Teller distortion.

during the battery operation, the composition range within the spinel + Li2MnO3 two-phase region can act as a buffer region, prohibiting the formation of t-LiMnO 2 phase. According to the calculation shown in Figure 5b, the spinel Li1.15Mn1.85O4 should show better cycle performance than the pure spinel LiMn2O4 because of the more extended buffer region. This calculation is in agreement with the literature data.47,50,52 Meanwhile, when overcharged to 0 ≤ x ≤ 0.60 in LixMn1.85O4, the spinel materials tend to be thermally unstable and release O2 gas during overcharge. Figure 5c shows the calculated cell voltage related to the composition within the t-LiMnO2−Li2MnO3−λ-MnO2 triangle. During the cycling process, especially at high C rates, the state of the batteries is under a nonequilibrium condition. In the vicinity of the electrode surface, the local composition may exceed the spinel phase region and lead to formation of other phases. The local equilibrium will affect the cell voltage following the actual phase components. Obviously, the voltage in the different phase region leads to different voltage plateaus. The spinel single phase is corresponding to the upper 4 V voltage plateau. The voltage plateau around 3.1 V is due to the coexistence of the spinel + Li2MnO3 phases. The voltage within the three phases spinel + Li2MnO3 + t-LiMnO2 region is the 2.95 V flat plateau.

4.5 V, the Li contents in some particles may also be across the onset of the Jahn−Teller effect (dashed line) and deteriorate the cycle performance. This may be caused by the nonequilibrium condition depending, e.g., on the C rates. Consequently, the poor reversibility with a rapid capacity fade cannot be avoided with standard spinel LiMn2O4. With an excess of Li ions inserted on the 16d sites, Li1.15Mn1.85O4 displays more complicated electrochemical behavior during charge and discharge, as shown in Figure 5b. The voltage plateau around 4 V appears in the range of 0.60 ≤ x ≤ 1.15 in LixMn1.85O4, corresponding to a spinel single phase region. Further discharge to 1.15 ≤ x ≤ 1.375 in LixMn1.85O4 leads to a 3.1 V plateau when the composition enters the spinel + Li2MnO3 two-phase region. During the battery operation, extremely small particle sizes and uniform distribution of the formed Li2MnO3 can be expected. As reported by Thackeray et al.,58 these Li2MnO3 particles can facilitate Li-ion transport in the cathode material and benefit from the cyclability of the Liion battery. Moreover, when the LixMn1.85O4 cathode is over lithiated to 1.375 ≤ x ≤ 2, a flat 2.95 V plateau can be observed as it enters a three-phase (spinel, Li2MnO3, and t-LiMnO2) region. In this region, the formation of the t-LiMnO2 via the Jahn−Teller distortion causes the capacity loss. Therefore, the entry to the spinel, Li2MnO3, and t-LiMnO2 three-phase region should be avoided. Considering the nonequilibrium state 2292


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the rate performance of the electrode materials has an obvious improvement with the increasing Li concentration, and Li1.052Mn1.948O4 and Li1.062Mn1.938O4 can still respectively retain 87% and 89% of their initial discharge capacity from C/2 to 1C, which are much higher than that of LiMn2O4. As a final cycling step, the C-rate is set back to C/10 to determine whether any cell degradation occurred during these galvanostatic measurements. The discharge capacity of samples does not show much difference, and a small capacity loss (approximately 5−7%) is observed at the end of the measurements. Therefore, these measurements show that increased excess lithium in cells with Li1.062Mn1.938O4 and Li1.052Mn1.948O4 improve the high rate capability for such 4 V spinel cathode materials due to the smaller lattice parameters (Figure 3) and wider buffer region (Figure 5), which validate the accuracy of this framework. Thermochemical Property: Enthalpy of Formation. The enthalpy of formation is essential for the safety of the lithium ion battery because it directly indicates the thermodynamic stability of the electrode materials. The calculated enthalpies of formation for the phases based on the presently thermodynamic descriptions or ab initio calculation of the Li− Mn−O system together with the experimental data41,44−46 are summarized in Table S4, where an overall good agreement can be observed. The calculated enthalpies of formation per mole atom of Li1+yMn2−yO4 (0 ≤ y ≤ 0.33) and Li1−wMn2O4 (0 ≤ w ≤ 1, w indicates the removed amount of Li) spinel in the “battery state” are compared to the experimental data41,44,59 in Figure 7a. As can be seen, an increase in the enthalpies of formation of Li1−wMn2O4 (0 ≤ w ≤ 1) spinel results in the decreasing phase stability with the Li extraction from LiMn2O4. The measured enthalpies of formation are perfectly reproduced by this work. The values from ab initio calculations show the same trend with the experimental results for the delithiated Li1−wMn2O4 within good error range (3.52−5.79%). The less negative enthalpies of formation of Li1−wMn2O4 with the decreasing of Li content is due to the feature that Li has higher oxygen affinity than Mn. According to our calculations, the enthalpy of formation of the λ-MnO2 spinel is −487.50 kJ/mol, which is less negative than that of the stable β-MnO2 (−521.449 kJ/mol).60 The calculated enthalpies of formation of the Li1+yMn2−yO4 (0 ≤ y ≤ 0.33) spinel increase slightly with increasing Li content, indicating a slightly increased thermodynamic stability. Calculated enthalpies of formation per mole atom for spinel based on the “battery state” within the λMnO2−LiMn2O4−Li4Mn5O12 triangle and “sintered state” within the LiMn2O4−Li4Mn5O12−Li2Mn4O9 triangle are illustrated in Figures 7b and 8, respectively. As shown in Figure 8, the enthalpy of formation becomes less negative from the LiMn2O4−Li4Mn5O12 edge to the Li2Mn4O9 compound. Li2Mn4O9 is thus less stable than the Li1+yMn2−yO4 (0 ≤ y ≤ 0.33) stoichiometric compounds. Similar to the lattice parameters shown in Figure 3a, a kink (dashed line) appears along the LiMn2O4−Li4Mn7O16 connection, dividing the Lirich and Li-defect spinel. This energetic trend is the overall effect of the different site occupations of Mn3, Mn4+, and Va in the spinel materials. The site occupations along the Li4Mn5O12−Li2Mn4O9 have been illustrated in Figure 3b as an example. Thermochemical Property: Oxygen Gas Release. As discussed in Figure 5b, the LMO spinel releases oxygen gas when the cell voltage exceeds the stability window of the electrodes during overcharge. Oxygen release inside the cells may lead to thermal runaway and combustion of the electrolyte.

In order to verify the aforementioned prediction, the electrochemical tests were carried out using three LMO halfcells with different compositions (see the Supporting Information). Galvanostatic testing measurements were performed using galvanostatic cycling with potential limitation technique in a voltage range between 3.0 and 4.2 V vs Li/Li+. Figure 6a shows the charge−discharge curves under C/10

Figure 6. (a) Charge−discharge curves under C/10 between 3.0 and 4.2 V vs Li/Li+ together with the calculated cell voltage profiles. A constant, M, is added in order to separate the curves for different samples in the figure. (b) Discharged capacity determined by galvanostatic cycling with potential limitation using different C-rates, applied on cells containing different LMO cathodes.

together with the calculated cell voltage profiles. Although the two plateaus are not distinguished in the current modeling, good agreement between the calculations and the experimental results is obtained. After initial capacity determination, the rate capability of cells was determined by applying successively increased C-rates from C/10 up to 1C, as shown in Figure 6b. It is observed that there is no significant discharge capacity differences among the samples at C/10 and C/5. However, under higher discharge rates, the capacity of the cell containing LiMn2O4 decreases significantly, i.e., at C/2, its retained capacity is only around 90%, and furthermore, at 1C such a cell shows lower than 80% capacity. It is interesting to note that 2293


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Figure 7. Calculated enthalpies of formation per mole atom for (a) Li1−wMn2O4 (0 ≤ w ≤ 1) and Li1+yMn2−yO4 (0 ≤ y ≤ 0.33) spinel in the “battery state” are compared to the experimental data41,44,59 and (b) spinel based on the “battery state” within the λ-MnO2−LiMn2O4−Li4Mn5O12 triangle.

Figure 9. Calculated mole fraction of the oxygen gas release during the delithiation from the sintered Li1+yMn2−yO4 (0 ≤ y ≤ 0.33) spinel.

Figure 8. Calculated enthalpies of formation per mole atom for spinel based on the “sintered state” within the LiMn2O4−Li4Mn5O12− Li2Mn4O9 triangle.

additional Li+ ions and electrons can only be removed via the concomitant reduction of O2− to 0.5 O2, leading to oxygen gas formation. With the increasing of the excess Li, larger amounts of oxygen gas are released from the spinel electrodes, especially at a high state of charge. Electrochemical Property. When considering the composition of electrode materials in various applications, one must be aware of the key electrochemical properties, such as voltage, capacity, and energy density. Figure 10 shows the calculated

Figure 9 shows the calculated mole percent of the oxygen gas release during the delithiation from the sintered Li1+yMn2−yO4 (0 ≤ y ≤ 0.33) spinel. Similarly, it can be seen from the phase diagram (Figure 2b) that all of the Li1+yMn2−yO4 (0 < y ≤ 0.33) spinel phase line may release oxygen gas when being overcharged except for LiMn2O4. The path for delithiation of Li1+yMn2−yO4 (0 ≤ y < 0.33) compositions crosses the line λMn2O4−Li4/3Mn5/3O4. As soon as this line is crossed, 2294


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Figure 10. Calculated theoretical capacity of Li1+yMn2−yO4 (0 ≤ y ≤ 0.33) and Li1−zMn2−2zO4 (0 ≤ z ≤ 0.11) solid solutions in the “sintered state” are compared to the experimental data.50 The corresponding site occupation of Mn3+ in 16d sites is also marked.

“stable state”. However, the identical composition delithiated from the sintered Li-excess LimMn1.94O4 (1 < m ≤ 1.06) spinel has infinite variations of the site occupations and properties. The Gibbs energy of the composition delithiated from the sintered Li-excess spinel has a less negative value and represents the “metastable state”. The shaded regions represent the possible site occupations and properties for the identical compositions under the different states. The detailed discussion of the infinite states for the identical composition (with the example of Li0.97Mn1.94O4) is referenced in Figure S8 and related Supporting Information.

theoretical capacity of Li1+yMn2−yO4 (0 ≤ y ≤ 0.33) and Li1−zMn2−2zO4 (0 ≤ z ≤ 0.11) solid solutions under the “sintered state” in comparison with the experimental data.50 As discussed before, the theoretical capacity is equal to the amount of Mn3+, which is given on the right Y axis. The capacity decreases with an increase of excess lithium y in Li-rich spinel Li1+yMn2−yO4 or vacancy content z in Li-defect spinel Li1−zMn2−2zO4. All the calculated values are slightly higher than the experimental results because the practical capacity cannot achieve the maximum theoretical values. Meanwhile, well matching indicates good electrochemical efficiency from the spinel cathodes. Figure 11a−c presents the calculated voltage, capacity, and energy density of spinel based on the “sintered state” within the LiMn2O4−Li4Mn5O12−Li2Mn4O9 triangle. As can be seen in Figure 11a, the LiMn2O4 and Li2Mn4O9 compounds show the lowest and highest voltage in this triangle, respectively. Contradictory, the theoretical capacity increases from the Li4Mn5O12−Li2Mn4O9 edge to LiMn2O4 compound, as shown in Figure 11b. Although the trends of voltage and capacity of the spinel electrode are almost opposite, the calculated energy densities show nearly identical trend with the capacities (see Figure 11c). This is because the difference of voltages for spinel is only about 0.2 V, which is quite small compared to the voltage plateau around 4 V against pure Li. Infinite States at the Identical Compositions. As mentioned previously, one spinel compound with the fixed composition has infinite variations of the site occupation during the battery operation, which leads to the infinite states/ properties related to the battery performance for an identical composition under the “battery state”. It is impossible to visualize the infinite variations of the “battery state” for all the compositions. Therefore, the Li mMn1.94 O4 composition (dashed line in Figure S1b) is selected as an example to demonstrate the changes of the site occupations and properties under the “battery state”, compared to their “sintered state”, as shown in Figures S6 and S7. It is obvious that the site occupations and properties for LimMn1.94O4 (0.97 ≤ m ≤ 1.06) can be divided into two parts, Li-defect and Li-excess spinel. As can be seen in Figures S6 and S7, the identical composition delithiated from the sintered Li-defect LimMn1.94O4 (0.97 ≤ m ≤ 1) spinel has the same site occupations and properties as the sintered state. The lowest Gibbs energy represents the relatively

4. DISCUSSION Based on the previous calculations, it is clear that both “sintered state” and “battery state” must be taken into consideration to select the suitable 4 V spinel cathode material for specific applications. The key factors (cyclability, safety, and energy density) for the battery performance are summarized in Figure 12. The same trend of these factors as experimentally reported by Yonemura et al.47 has been observed. The shaded area in Figure 12 represents the spinel compounds with the theoretical energy density in the range of 400−500 mWh/g. For clarity, the energy densities are given in the red trapezoid in which brighter color indicates preferred area (dashed ellipse). The safety is evaluated by considering the thermochemical properties to select the compounds with higher thermodynamic stability (less negative enthalpies of formation) and less oxygen gas release. The possibly preferred safety performance is marked in the region of the dashed ellipse in Figure 12. The cyclability is evaluated based on the physical properties to find the compounds with higher electrochemical stability and suppression of the Jahn−Teller distortion. The lattice parameter is a key factor for the electrochemical stability because the spinel electrodes with smaller lattice parameter can increase the structural stability due to homogeneous reaction during intercalation/deintercalation and show the improved cycling efficiencies.50,52 Besides the effect of the lattice parameter, a wider buffer region for suppression of the Jahn− Teller distortion can obviously improve the cyclability. This could be the root for the well-known fact that Li-rich spinel shows cyclability superior to that of the standard LMO spinel.50,52 When small amount excess Li is substituted by 2295


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Figure 12. Schematic diagram to visualize the key factors (energy density, cyclability, and safety) related to the battery performance, compared with Yonemura et al.47 The spinel compounds with the theoretical energy density in the range of 400−500 mWh/g are located in the shaded area (a−b−c−d). An expanded view of key properties in the shaded area is also shown in the figure. The favorable compositions for each property are represented with the dashed ellipses.

5. CONCLUSIONS In summary, we have developed a high-throughput computational framework based on ab initio calculations and the CALPHAD approach to systematically describe the infinite composition−structure−property−performance relationships and evaluate the performance of the spinel compounds for battery applications. The framework includes a physically based model combining the composition and site occupation to quantitatively map the physical, thermochemical, and electrochemical properties of the spinel solid solution under the infinite states. The cyclability is evaluated based on the physical properties to find the compounds with higher electrochemical stability and suppression of the Jahn−Teller distortion. The safety is evaluated by considering the thermochemical properties to select the compounds with higher thermodynamic stability and less oxygen gas release. The energy density is evaluated according to the electrochemical properties (cell voltage and capacity). Based on the framework, we acquire the infinite composition−structure−property−performance relationships of LMO spinel electrodes spanning wide composition ranges under both sintered and battery states, which is applied to screen the whole composition range of LMO spinel electrodes to find the overall best performance for 4 V cathode materials. This novel high-throughput computational framework employs combinatorial approaches to reveal complex phenomena and highly efficiently screens the ideal cathode materials according to the practical application.

Figure 11. Calculated (a) voltage, (b) capacity, and (c) energy density of spinel based on the “sintered state” within the LiMn2O4− Li4Mn5O12−Li2Mn4O9 triangle.

vacancies on the 16d sites, the global Li content of the LMO spinel cannot exceed the original composition when cycled against the commonly used graphite based anode materials. Therefore, the composition with codoping of Li and vacancies on the 16d sites can further extend the buffer region to prevent the Jahn−Teller distortion (especially at high rates) while keeping the good energy density and safety. This can also be applied to other anode materials which cannot provide extra Li. The assessed cyclabilities are given in the purple trapezoid in which the bright area has been selected based on the combination of smaller lattice parameter and wider buffer region for the Jahn−Teller distortion.

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ASSOCIATED CONTENT

S Supporting Information *

The Supporting Information is available free of charge on the ACS Publications website at DOI: 10.1021/acs.chemmater.7b05068. Introduction and illustration of the infinite variations of the crystallography of LMO spinel, thermodynamic and molar volume modeling, synthesis process and exper2296


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imental measurements, calculated enthalpies of formation, calculated infinite site occupations, and properties at the identical composition (PDF)

AUTHOR INFORMATION

Corresponding Authors

*E-mail: [email protected] (W.Z.). *E-mail: [email protected] (K.C.). ORCID

Weibin Zhang: 0000-0001-6584-5053 Notes

The authors declare no competing financial interest.

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ACKNOWLEDGMENTS W.Z. appreciates financial support from the Institute for Applied Materials−Applied Materials Physics (IAM-AWP) at Karlsruhe Institute of Technology (KIT). D.M.C. and P.G. acknowledge financial support from the Helmholtz Association of German Research Centres through the Helmholtz Young Investigator Group (VH-NG 1057). K.C. acknowledges financial support from the National Natural Science Foundation of China (51701232), CAS Pioneer Hundred Talents Program and the German Research Foundation DFG project (CH 1688/1-1), within the Nachwuchsakademie program. D.L. acknowledges financial support from the German Research Foundation DFG project (LI 2389/1-1). Y.D. acknowledges financial support from the National Natural Science Foundation of China (51531009). We would like to thank Dr. Thomas Bergfeldt (Institute for Applied Materials-Applied Materials Physics, Karlsruhe Institute of Technology) for the ICP-OES measurements.

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