and Î²-Li2MnP2O7 for Lithium-Ion Cathode Materials

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Insights into Electrochemistry and Mechanical Stability of #- and #LiMnPO for Lithium-Ion Cathode Materials: First-Principles Comparison 2

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Xiaoying Hou, Jing Liang, Tong Zhang, Yuhan Li, Shuwei Tang, Hao Sun, Jingping Zhang, and Hai-Ming Xie J. Phys. Chem. C, Just Accepted Manuscript • DOI: 10.1021/acs.jpcc.7b06814 • Publication Date (Web): 26 Sep 2017 Downloaded from http://pubs.acs.org on October 1, 2017

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The Journal of Physical Chemistry

Insights into Electrochemistry and Mechanical Stability of αand β-Li2MnP2O7 for Lithium-Ion Cathode Materials: First-Principles Comparison Xiaoying Hou,† Jing Liang,† Tong Zhang,† Yuhan Li,†,§ Shuwei Tang,*,†,‡ Hao Sun,*,† Jingping Zhang‡, Haiming Xie‡ †

Institute of Functional Material Chemistry, Faculty of Chemistry, Northeast Normal

University, Changchun, Jilin 130024, People’s Republic of China ‡

National & Local United Engineering Lab for Power Battery, Northeast Normal University, Changchun, Jilin 130024, People’s Republic of China §

College of Chemistry and Biology, Beihua University, Jilin, Jilin 132013, People’s Republic of China

E-mail: [email protected] [email protected]

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ACS Paragon Plus Environment


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ABSTRACT With the aid of first principle calculations, structural characteristics, mechanical stability, electronic and electrochemical properties of two polymorphs of manganese-based pyrophosphate α- and β-phase of Li2MnP2O7 and their relevant delithiated structures are explored for comparison. Our results indicate that although these two polymorphs of Li2MnP2O7 belong to monoclinic space group, considerable differences are discovered in Mn local environment of crystal structures. The cell voltage vs. Li/Li+ are 4.68 and 4.16 V for α- and β-phase of Li2MnP2O7/LiMnP2O7 platform, respectively, comparable to the experimental values (4.45 & 4.00 V) for first voltage plateaus. All the Lithium are practically full ionized in the α- and β-Li2MnP2O7 and their relative half delithiated states, charge transfer mainly concentrated upon Mn and O, which leads to the oxidization state of Mn from Mn2+ to Mn3+, and then from Mn3+ to Mn4+. The band gaps of delithiated configurations decrease gradually with removing lithium ions, and the conductivity changed from insulator nature to conductor characteristic. By the elastic properties calculations, the Pugh ratios (B/G) are 3.28 and 2.86 for the α- and β-Li2MnP2O7, respectively, indicating their high mechanical stability. However, small B/G values are observed for the relevant delithiated phases. In addition, Young’s Modulus (E), and Poisson’s Ratio (ν) for α- and β-phase of Li2MnP2O7 and their delithiated configurations are also presented to explore the hardness and bond characteristic.

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INTRODUCTION

Lithium ion battery (LIB), as one of the most promising candidates for chemical energy storage and conversion devices, has captured dominant market share of the portable electronics and electric transportation in the past decades.1-5 Because the cathode material is vital for energy storage and cost-effectiveness, tremendous efforts are devoted to design and develop next-generation cathode materials with excellent electrochemical properties. Typical examples comprise the layered LiCoO2,6-8 olivine LiMPO4

(M=Fe,

Mn),9-15

and

spinel

LiMn2O4.16-22

However,

under

the

ever-increasing usage of LIBs expand to large-scale application, the conventional cathode materials could not meet the requirement as a consequence of cost-effectiveness or safety hazards. Therefore, searching novel cathode materials for LIBs is an integral aspect of the ongoing quest for building better batteries.

Among the cathode materials investigation, polyanion cathode materials with PO4 group (such as LiFePO4) in the three dimensional framework have attracted considerable attentions due to their high structural and thermal stabilities, good recycling performance, low cost and high safety. Recently, the pyrophosphate Li2FeP2O723-26 and relevant compounds27-30 with characteristic diphosphate (P2O7, i.e., PO4-PO4) provide a new family for electrode research. Such kind of materials exhibits a redox potential at 3.5 eV vs. Li/Li+ with a reversible capacity of ~120mAh/g. Furthermore, the biggest advantage of such compound is its potential to exchange two Li ions per formula unit upon cycling, which would considerably reduce the drawback

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of low volumetric energy density of other conventional polyanion cathode materials. Motivated by the discovery of Li2FeP2O7, many attempts were made to synthesize the isostructural analogues with different 3d transition metal active redox species.31,32 Adam et al.33 firstly synthesized a new isostructural manganese-based pyrophosphate, (α-Li2MnP2O7 hereafter) by introducing the multiple oxidation state of Mn (MnII, MnIII, MnIV).

In the year of 2012, Tamaru et al. reported that the α-Li2MnP2O7 have

the redox potential centered at 4.45V versus lithium, which is the highest cell voltage from experimental results in all of the reports.34 After that, Nishimura et al. performed a more detailed investigation on the Li-Mn-P-O system, and discovered a new polymorph of lithium manganese(II) pyrophosphate,35 named as β-Li2MnP2O7. Though α- and β-Li2MnP2O7 adopt the same monoclinic structures, slight differences are presented in space group (P21/c and P21/n for α- and β-phases) that root in the prominent difference in Mn local environment of crystal structures. Nevertheless, other information of manganese-based pyrophosphate is very limited compared to cathode materials Li2FeP2O7 and Li2FexMn1-xP2O7 (0≤x≤1),26,33,34-37 due to their Jahn-Teller effect.38-41 Although the second intercalation experimental voltage profile for α-Li2MnP2O7 is not obtained, good consistency with the cyclic voltammetry is found: the second voltage platform is observed at 5.3V. Moreover, compared to α-phase of Li2MnP2O7, β-Li2MnP2O7 has lower operating voltage (4.7 V) but with a higher symmetry. However, despite aforementioned differences, some fundamental issues, such as structural and cell changes in the lithiation or delithiation processes, electronic and mechanical stability about these two manganese-based pyrophosphate 4


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α- and β-Li2MnP2O7 are poorly understood. These key problems have profound influences on the Li storage and cycling stability, which in turn determines the electrochemical performance of LIBs.

In this report, with the aid of first-principle calculations, we have performed a detailed investigation on the electronic and electrochemical properties, such as density of states, charge transfer mechanism, intercalation voltage to understand the electronic nature, and elastic properties for two manganese-based pyrophosphate α- and β-Li2MnP2O7 are also calculated to explore the changes of hardness and bond characteristic during charging-discharging process. Our present study would not only provide deep understanding of structural and electronic properties for two manganese-based pyrophosphate α- and β-Li2MnP2O7, but also shed some light on experimental study in developing pyrophosphate compounds for cathode materials.

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METHODS AND COMCULTATIONAL DETALS

All quantum mechanics calculations are performed within in the framework of density functional theory (DFT),42-44 in combination with the Projector Augmented Wave (PAW) method as implemented in the Vienna Ab Initio Simulation Package (VASP). The exchange-correlations are treated in generalized gradient approximation (GGA) with spin-polarized formalism in Perdew-Bruke-Ernzerhof (PBE) functions.45 We further introduce a Hubbard parameter U for Mn according to Dudarev et al. in order to correct the self-interaction error of the standard DFT and to deal with the strong correlation character of 3d electrons in the transition metal ions.46,47 An effective U value of 5.0 eV is adopted for Mn, because it expresses good performance in previous investigation of Mn-based compound cathode material.48 After performing the convergence test, a kinetic energy cut-off of 520 eV is used for all calculations, and the electronic energy convergence was 10-4 eV. Structures were fully relaxed until the remaining force less than 0.001 eV/Å for each atom. Brillouin zone integrations are approximated by special k-point sampling of Monkhorst-Pack scheme49 with 4×4×4 and 2×2×2 k-point grids for α- and β-Li2MnP2O7 compounds, respectively. Magnetic ordering has also been considered in this research. By comparing the free energy αand β-Li2MnP2O7 configurations with ferromagnetic (FM) and antiferromagnetic (AFM) ordering specifying on Mn ions, it is found that the energy differences between various magnetic configurations are within a few meV for each formula unit (see the Table S1 and S2 in Supporting Information). Therefore, the FM ordering of Mn ion is employed in further electronic and electrochemical property calculations. 6


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Moreover, such strategy for configuration screening is also proved to be reasonable and practicable by previous works.50,51 Charge transfer mechanism is calculated by using the Bader charge analysis. In this method, the total electronic charge of an atom is approximated by the charge enclosed in the Bader volume defined by zero flux surfaces.52-54 In order to calculate the mechanical stability, a pair of normal and shear strains are utilized to fit the energy-strain bights of deformed structures. The polynomial coefficients are used to solve the linear equations to ascertain the elastic constants simultaneously. The elastic moduli, such as bulk modulus (B), shear modulus (G) and Pugh ratio (B/G) are derived on the basis of Voight-Reuss-Hill approximation.55-57 After that, the Young’s modulus (E), and Poisson’s ratio (v) are further deduced.

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RESULTS AND DISCUSSION

Crystal structure characteristics. Reproduction of experimentally observed crystal structures provides the starting point for the current study. The crystal structures of two polymorphs of manganese-based pyrophosphate α- and β-Li2MnP2O7 are built on the basis of the experimental data,23,35 and the optimized structures are shown in Figure 1(a). All the crystal structures of these two polymorphs are monoclinic, but with the slight difference in space group (P21/c for α-Li2MnP2O7 and P21/n for β-Li2MnP2O7, respectively). There are four and two formula units in each unit cell of α- and β-Li2MnP2O7 crystal. In α-Li2MnP2O7, four the Li ions occupy four different sites, and in every site, four Li ions are located symmetrically. The overall arrangement of all Li ions form [Li2O4]∞ and [Li2O5]∞ layers. In contrast, β-Li2MnP2O7 only has two different Li sites and each position also comprised four symmetrical Li ions. Table 1 presents the theoretical lattice parameters and unitcell volume of α- and β-Li2MnP2O7, together with the corresponding experimental data for comparison. Our calculation results fit well with those in the available experimental literatures in general, and the theoretical lattice parameters are slight larger than the experimental data with reasonable deviation. In terms of cell volume expansion, the discrepancy with experimental values is about 6% (the volume differences between experimental structure and DFT optimized structure is 68.34 Å3 and 20.17 Å3 for αand β-Li2MnP2O7, respectively). Despite the wonderful similarity in formula unit of these two polymorphs of Li2MnP2O7 cathode materials, completely disparate structures are discovered, as reported by Nishimura et al.35 Of great interest in Figure 8


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1(b) are the Mn local arrangements in these two polymorphs. In α-Li2MnP2O7, an edge-sharing Mn2O9 unit is appeared by combining the MnO6 octahedron (Mn1) and MnO5 (Mn2) trigonal-bipyramids. The distance is 3.353 Å between Mn1 and Mn2 for α-Li2MnP2O7. Whereas in β-Li2MnP2O7, a single MnO6 octahedron group with distorted structure is observed, and the distance between two adjacent Mn cations are much longer (the shortest distance is 4.791 Å) than the case in α-Li2MnP2O7. As a consequence, the weaker Mn...Mn electrostatic interaction in β-Li2MnP2O7 leads to a higher symmetry. Moreover, a slight discrepancy in Mn-O bonds for these two phases is also observed simultaneously. Seeing from Figure 1(b), the Mn1-O distances in MnO6 octahedra are quite symmetric, which range from 2.151 Å to 2.322 Å, while for the MnO5 trigonal-bipyramids, the Mn2-O bond lengths vary from 2.142 Å to 2.262 Å, and the average Mn-O bond length for optimized α-Li2MnP2O7 is 2.211 Å. For β-Li2MnP2O7, the average Mn-O distances is 2.239 Å, which is about 0.028 Å longer compared with that of α-phase, in good agreement with experiments.35 The calculated results also show that β-phase has a higher energy than α-phase (0.122 eV higher for per formula unit), indicating the irreversibility of β-Li2MnP2O7. This finding accords well with the experimental report that the β-phase could transform to α-phase structure above 773K.35

For the Li ion occupations in α-phase configuration, there are four different positions, considering the different magnetic alignments of Mn (ferromagnetic and antiferromagnetic), twelve isomeric structures of α-LiMnP2O7 are generated if half of the lithium ions were removed; similarly, four different configurations are discovered 9



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Figure 1. (a) Optimized crystal structures of two manganese-based pyrophosphate αLi2MnP2O7 (P21/c) and β-Li2MnP2O7 (P21/n). (b) Close-up presentation of the local environment of Mn-O coordination in α- and β-Li2MnP2O7 showing the polymorphic differences.

for the β-phase. The detailed structures and energies are presented in the Table S1 and Table S2 in Supporting Information. Starting from the LiMnP2O7, the delithiation occurs once more for the residual Li ions to generate the fully dethiated state of α- and β-MnP2O7. The calculated lattice parameters and unit cell volumes for the most stable delithiated phases are also summarized in Table 1. In the Li ions extraction processes, the Mn valence changes from Mn2+ to Mn3+, which always accompany the occurrence of Jahn-Teller effect, consequently, distorted structures can be expected for half delithiated intermediate phases of α- and β-LiMnP2O7. Interestingly, despite the 10


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considerably change of lattice parameters in delithiated structures of α-Li2MnP2O7, the volume decrease in reasonable. On the contrary, β-phase configuration experiences a complete contrast process, because the volume decreases gradually with Li ion extraction. Table 1. Optimized lattice parameters of α- and β-Li2MnP2O7 and their most stable delithiated intermediate configurations. The corresponding experimental data are shown in boldface for comparison. compound

β(°)

V (Å3)

a (Å)

b (Å)

c (Å)

∆V(%)

11.0170

9.7542

9.8046

11.3211

9.9511

10.0090 102.55 1100.64

6.62

11.1061

9.7997

9.8685

100.00 1057.73

2.46

11.0235 10.2449

9.7488

103.54 1070.40

3.69

8.2522

12.9533

4.9819

92.83

531.80

8.3609

13.1345

5.0329

92.93

551.97

3.79

β-LiMnP2O7

8.0785

12.9785

5.1158

92.76

535.75

0.74

β-MnP2O7

8.0109

12.5576

4.8620

90.75

489.06

8.04

101.54 1032.30

α-Li2MnP2O7

α-LiMnP2O7 α-MnP2O7

β-Li2MnP2O7

Electronic and electrochemical properties. The cell voltage is one of the most important electrochemical parameters to evaluate the performance of cathode materials for LIBs. The calculation of cell voltage in performed through the already 11



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developed DFT theoretical frameworks, in which cell voltage can be directly estimated from total energies of relevant systems. Such computational method has been well-established,58,59 which has been successfully used in inspecting cell voltage for fluorosulfate, phosphate, and silicate cathode materials.50,60 Here, it can be computed directly from the energy change during the cycling process using the following equation:

V=-

E (Lix2 MnP2 O 7 ) - E (Lix1MnP2 O7 ) - ( x2 - x1 ) E (Li) ( x2 - x1 )e

(1)

where (x2-x1) is the number of lithium atoms participating in the process of delithiation or lithiation, and x2>x1. In present work, x2 is assumed as 2 or 1, and x1 is set accordingly to 1 or 0, respectively. The E(LixMnP2O7) represents the total energy of relevant systems in both α- and β-phase of LixMnP2O7. E(Li) is the total energy of primitive cell of lithium metal.

Figure 2 shows the calculated voltage curve for the α- and β-phase of Li2MnP2O7 vs. Li/Li+. Seeing from Figure 2, we find that the intercalation voltage for the first Li ion extraction process of α-Li2MnP2O7 occurs at 4.68 V, comparable to the value of experiment (4.45V).34 The second intercalation voltage plateaus for α-phase Li2MnP2O7 compound is 5.33 V, in a good agreement with 5.30 V that report by Ceder et al.36 Nevertheless, this value is considerably high for stable operation of typical electrolyte, which could provide one of reasonable explanations for the phenomenon that in α-Li2MnP2O7, only one Li ion exchange is discovered 12


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successfully upon cycling. Compared with the α-phase, β-Li2MnP2O7 displays more excellent

voltage

characteristics:

the

intercalation

voltage

of

β-Li2MnP2O7/β-LiMnP2O7 is 4.16 V, which is 0.52 V lower in comparison with the corresponding voltage plateaus of α-phase, but in a good agreement with the experiments (~ 4.0 V).35 The second intercalation

voltage plateaus for

β-Li2MnP2O7/β-MnP2O7 is 4.73 V, relatively lower than that of α-phase, and it is still in the safe operational window of current generation organic electrolytes. Consequently, it is possible to extract the residual one Li ions to obtain higher energy density.

Figure 2. The trends in cell voltage as a function of decreasing Li concentrations in αand β-Li2MnP2O7. The dash lines represent the experimental values. It is of considerable interests to elucidate the charge transfer mechanism during lithiation or delithiation process in α- and β-phase of Li2MnP2O7, because charge distribution is closely involved for manganese and oxygen upon Li removal. To 13



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describe the charge transfer between Mn cations and the host structures, we have carried out Bader analysis to quantitatively identify charge transfer machanisms of Mn, P, O and Li atoms. Here, the average net charge per atom has been computed, as shown in Table 2. All the lithium atoms are practically full ionized in the α- and β-Li2MnP2O7 and relative half delithiated intermediate configurations. The average Bader charges for the two types of Mn atoms (Mn1 and Mn2) in α-Li2MnP2O7 are 1.56 and 1.54|e|, respectively; while in the β-phase, the corresponding charge distribution for Mn is 1.57|e|, slight higher than that of α-phase. The average Bader charge of the O atoms in α-Li2MnP2O7 produces result essentially in agreement with β-phase configuration, leading to the oxidation state of O2-. Upon the gradual deinsertion of Li ions from α- and β-phase of Li2MnP2O7, the charge distributions of Mn and O vary significantly, while the effective charges of P and Li undergo negligible changes during this process. From α-Li2MnP2O7 to α-LiMnP2O7, the Mn1 (Mn2) charge increases from 1.56 (1.54|e|) to 1.86 (1.81|e|), while in fully delithiated phase structures, they have charges of 1.89 and 1.79|e|, respectively. Such noticeable change is caused by the oxidization state of Mn from Mn2+ to Mn3+, and from Mn3+ to Mn4+ in a formal sense. For the β-phase of Li2MnP2O7 system, a similar charge transfer process is observed with much stronger tendency, which is suggestive of a more covalent character of Mn-O bonds or weak Mn…Mn interaction. Such results could be easily explained by the Mn local environments in the crystal structures. In α-Li2MnP2O7, two types of Mn cations in edge-share Mn2O9 unit would take part in the delithiation process, so charge sharing occurs during transfer process; while in 14


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β-case, the charge transfers just take place from one type of Mn cations to adjacent O anions.

Simultaneously, the removal of lithium ions is also accompanied by a decrement of charges in the oxygen atoms from -1.53 to -1.44|e| in α-Li2MnP2O7. For the cases in β-Li2MnP2O7, a similar charge transfer mechanism is observed for O, which ranges from -1.53 to -1.45|e|. Therefore, a noticeable electron migration from Mn to O is concluded. It means that the Mn and O ions are mainly responsible for the charge redistribution during the delithiation reaction, which is also give a confirmation of the active role of Mn2+/Mn3+, and Mn3+/Mn4+ in the redox couple.

Table 2. The distributions of average Bader charges in α- and β-Li2-xMnP2O7 (x=0, 1, 2). compound

Mn1/Mn2

P

O

Li

α-Li2MnP2O7

1.56/1.54

3.68

-1.53

0.90

α-LiMnP2O7

1.86/1.81

3.68

-1.44

0.90

α-MnP2O7

1.89/1.79

3.67

-1.31

―

β-Li2MnP2O7

1.57

3.66

-1.53

0.90

β-LiMnP2O7

1.88

3.69

-1.45

0.90

β-MnP2O7

2.01

3.69

-1.34

―

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This charge transfer mechanism can be graphically displayed by the contour plots of charge-density difference61 for the delithiation processes of α- and β-phase of Li2MnP2O7, as presented in Figure 3. The positive (in yellow) or negative (in blue) region indicates where the electron density is enriched or depleted, respectively. For α-case, because the first extraction process of Li ions, namely from Li2MnP2O7 to LiMnP2O7 prefers to occur around Mn1 cations, so the electron density around this region considerably decreases, while the corresponding electron density close to Mn2 cations undergoes smaller variation. Similar tendency is also observed for the fully delithiated process, which is as evidenced by a small reduction of 0.02|e| for Mn2 cations. On the contrary, the electron density adjacent to oxygen anions significantly increases simultaneously. This represents a charge transfer mainly from Mn1 to the

Figure 3. Contour plots of charge-density difference for the delithiation processes of Li2MnP2O7: (a) α-phase and (b) β-phase. The yellow and blue isosurfaces represent electron accumulation and depletion.

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adjacent oxygen anions. In the case of the β-phase of Li2MnP2O7, a similarity is observed for charge transfer process, which also accords well with the Bader charge analysis.

To identify the specific atomic contributions involved in the charge transfer occurring during delithiation process, the density of states (DOS) of α- and β-Li2MnP2O7 and their delithiated structures are explored, as shown in Figure 4. By comparison of the total DOS in α- and β-phase of Li2MnP2O7, large band gaps are found (4.32 and 3.67 eV for α- and β-phases, respectively), indicating the insulator nature of these materials. With the extraction of Li ions, the peaks of occupied states in both α- and β-phases significantly shift to higher energy range, which is accompanied with negligible variation for the virtual states. As a consequence, the band gaps gradually decrease from the lithiated state to delithiated intermediate configurations, and the corresponding band gaps range from 4.32eV to 0.64eV in α-case, and 3.67 eV to 0.29 eV in β-case, respectively. Such decreasing tendency of band gaps is similar to the situation of olivine LiFeSiO4 cathode materials62 and NaV3(PO4)3.63 As the half Li ions remove from the original structure, the band gaps decrease significantly, 2.86 and 1.04eV are found for the α- and β-LiMnP2O7, respectively. As a consequence, the semiconductor nature of LiMnP2O7 materials is observed. Therefore, it can be speculated that the electrical conductivity of raw materials would be considerably improved through delithiation process. Due to the electron states closed to the Fermi level play an essential role upon cycling, so we check the corresponding partial density of states (PDOS) of Mn and O around the 17



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Fermi level and found that the results is consistent with Shi’s work64 (those peaks of Mn, and O are shown because of their greater contributions), as also presented in Figure 4. It is clear that in all configurations of α- and β-LiMnP2O7, the valance bands of Mn-3d states below Fermi level are hybridized with O-2p states, which devotes prominent contributors to the strong interaction between Mn and O. Therefore, an enhancement of Mn-O bond could be expected, which would be beneficial for the stability of crystal structures. Careful exploration on α-LiMnP2O7 indicates that the Mn1 present slightly stronger hybridization of Mn-O bonds than Mn2. Similarly, the phenomenon in β-LiMnP2O7 arises that the total intensity of peaks for valence states is also contributed by 3d state and 2p states of Mn and O. As more Li is extracted, the

Figure 4. The total density of states (TDOS) and projected density of states (PDOS) of (a) α-Li2MnP2O7, (b) β-Li2MnP2O7 and delithiated intermediate configurations. The Fermi level is set at zero energy. The gray, violet, blue, and red lines represent TDOS, Mn1-3d, Mn2-3d, and O-2p states, respectively.

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increase in O intensity with decrease of Mn in α- and β-LiMnP2O7, and new valence bands contributed by Mn-3d and O-2p states are separated below the Fermi level. For the fully delithiated structures, the intensity of new valence bonds further increase sharply, in consistent with the above Bader charge analysis.

Elastic property. The mechanical response of cathode materials has main effect to the

cycling

performance

during

charge-discharge

process,

because

phase

transformation would take place if the deformed cell structure is mechanically unstable, which leads to degradation of LIBs. In order to investigate the mechanical stability of the energetically favorable delithiated intermediate structures, the stiffness matrixes of relevant α- and β-Li2MnP2O7 configurations are explored. For the monoclinic α- and β-phase of Li2MnP2O7, thirteen independent elastic constants Cij are deduced. The Cij, which regards as a ligament between the mechanical and dynamical performance of crystals, would be respond to the external force change of crystals by way of bulk modulus (B), shear modulus (G), Young’s modulus (E), and Poisson’s ratio (ν). These moduli are critical in determining stability and ductility of materials. Here, Voigt-Reuss-Hill (VRH) method is used to calculate the polycrystalline modulus which has been proved that Voigt and Reuss equations represent the upper and lower limits of the genuine polycrystalline constants. Young’s modulus and Poisson’s ratio can be further determined by using the below relations:13,65-67

E=

9 BG 3B + G

(2) 19



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v=

3B − 2G 6 B + 2G

Page 20 of 34

(3)

The mechanical stability criterion is determined by the eigenvalues of elastic stiffness matrixes, and the more positive values for all the materials give an indication of high stability against elastic deformations. Pugh ratio (B/G) is also introduced, in which the high and low B/G values are associated with ductility and brittleness characteristic, respectively, and the critical value is 1.75.13,68-70 Table S3 and Table S4 in Supporting Information list the calculated elastic constants for α- and β-Li2MnP2O7 and their delithiated configurations. According to the criteria proposed by Meng et al.,55 the mechanical stability of monoclinic structures can be described using following equations:

Cij > 0 (i=j)

(4)

[C11 + C22 + C33 + 2(C12 + C13 + C23)] > 0

(5)

(C33C55 - C352) > 0

(6)

(C44C66 - C462) > 0

(7)

(C22 + C33 - 2C23) > 0

(8)

[C22(C33C55 - C352) + 2C23C25C35 - C232C35 - C252C35] > 0

(9)

{2[C15C25(C33C12–C13C23)+C15C35(C22C13–C12C23)+C25C35(C11C23–C12C13)]– [C152(C22C33–C232) + C252(C11C33–C132) + C352(C11C22–C122)] + C55g} > 0

(10)

g = C11C22C33 - C11C232 - C22C132 - C33C122 + 2C12C13C23

(11)

20


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Clearly, all the eigenvalues meet the mechanical stability criterion. In general, C11, C22, and C33 measure the values corresponding to a, b, and c directional resistance to the linear compressions, while C44, C55, and C66 are the elastic constants associated with angle strain between respective axes.71 Seeing from Table S3, the C11, C22, and C33 are considerably larger than C44, C55, and C66 in six matrixes, which gives an indication that the resistance of materials against uniaxial tensions is very strong, so that the shear deformations are more likely to occur. This finding is quite similar to the situations of LiMPO4 (M=Fe, Mn) compounds reported by Xie and Yi et al.13 When Li ions extract from α-Li2MnP2O7 material, all the elastic constants Cij decrease simultaneously; however, in β-Li2MnP2O7 configuration, an anomaly occurs during this process, i.e., no uniform trend for Cij is observed. Such phenomenon is caused by the entirely different Mn local environment in β-Li2MnP2O7 and stronger changes in Mn-O bond features.

Table 3 presents the bulk Modulus (B), Shear Modulus (G) for α- and β-Li2MnP2O7 configurations. It is obvious that the all B values in α- and β-Li2MnP2O7 are considerably larger in comparison with the corresponding G values, and the Pugh ratio are 3.28 and 2.86, respectively, so these two phases of Li2MnP2O7 show excellent ductility. In particular, the smaller B/G value for β-phase of Li2MnP2O7 would provide a reasonable explanation for the experimentally observed phenomenon that β-phase of Li2MnP2O7 could transform to α-phase at higher temperature. In the cases of deintercalated configurations, the B and G values decrease simultaneously, and as a consequence, small B/G values for delithiated phases are generated. The 21



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Page 22 of 34

Pugh ratios are 2.27 and 2.24 for the α-LiMnP2O7 and α-MnP2O7, respectively, while the values of B/G are 2.72 and 1.75 for delithiated β-phase of LiMnP2O7 and MnP2O7. Fortunately, all the B/G parameters are larger than that of criterion72 for discriminating ductile and brittle nature of cathode materials, which indicates that these materials are ductile. This finding consists well with the small crystal cell expansion with the extraction and insertion of Li ions. Table 3 also gives the Young’s Modulus (E), and Poisson’s Ratio (ν) for α- and β-Li2MnP2O7 compounds.

Table 3. Bulk Modulus (B, in GPa), Shear Modulus (G, in GPa), Young’s Modulus (E, in GPa), and Poisson’s Ratio (ν) for α- and β-Li2-xMnP2O7 (x=0, 1, 2) configurations. Compound

B

G

B/G

E

ν

α-Li2MnP2O7

92.70

28.30

3.28

65.20

0.30

α-LiMnP2O7

58.70

25.88

2.27

55.97

0.21

α-MnP2O7

15.84

7.08

2.24

12.44

0.20

β-Li2MnP2O7

110.73

38.70

2.86

88.12

0.27

β-LiMnP2O7

127.10

46.76

2.72

107.17

0.25

β-MnP2O7

103.15

58.95

1.75

115.56

0.12

The Young’s Modulus E that represents the ratio of stress and strain can reflect the hardness of materials is calculated to be 65.20 for α-Li2MnP2O7 and 88.12 for 22


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β-Li2MnP2O7, respectively. Therefore, the β-Li2MnP2O7 is harder than α-Li2MnP2O7, which indicates good covalent character in β-Li2MnP2O7, according well with the Mn-O and P-O bonds calculations. Nevertheless, the E values in α- and β-phase intermediate configurations go to the different trend along with lithium deinsertion processes, namely E values in α-case range from 55.97 for half delithiated α-LiMnP2O7 to the 12.44 of fully delithiated α-MnP2O7; while the corresponding E values for β-LiMnP2O7 and β-MnP2O7 compounds are 107.17 and 115.56, respectively. The Poisson’s Ratio (ν), as an indicator of the covalent bonds, usually is about 0.1 for covalent materials, and about 0.25 for the ionic materials.73 Seeing from Table 3, we found that the ν values for α- and β-Li2MnP2O7 materials are 0.30 and 0.27, respectively, comparable to those of LiFePO4 (0.289) and LiMnPO4 (0.296),13 therefore, both α- and β-Li2MnP2O7 are ionic materials. Nevertheless, with the removing process of Li ions, all the α- and β-Li2MnP2O7 of relative materials change from ionic nature to covalent characteristic, as evidenced by the ν values for the fully delithiated structures. Previous study shows that larger (smaller) value of ν (E) usually coupled with better elastic property. Based on our calculations, we found that the elastic properties go worse along with lithium extraction process for β-phase Li2MnP2O7, however, a significant discrepancy is observed in the α-phase structures, in which both the B/G parameters and ν values decrease along with a decline of E values. Therefore, a short conclusion could be drawn here that the α-phase structures of Li2MnP2O7 is a good candidate for ideally elastic materials.

23



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Page 24 of 34

4. CONCLUSION

Relying on first principle calculations, the structural characteristics, electronic and electrochemical properties of two polymorphs of manganese-based pyrophosphate αand β-Li2MnP2O7 and their delithiated intermediate configurations are explored in detail for comparison. In particular, considerable interests are concentrated on quantifying the dependency of elastic property during the delithiation process. Our computational results show that although all the crystal structures of these two polymorphs of Li2MnP2O7 compounds are monoclinic, significant differences are still observed for the utterly different Mn local environment in crystal structures. By investigating the total energy of a fully lithiated and corresponding delithiated configurations, the cell voltage vs. Li/Li+ are 4.68 and 4.16 V for α- and β-phase of Li2MnP2O7/LiMnP2O7, respectively, comparable to the values of experiment (4.45&4.00 V) for first intercalation voltage plateaus. The second intercalation voltage plateaus for α-Li2MnP2O7 compound is 5.33 V, considerably high for stable operation of typical electrolyte; while the corresponding value for β-Li2MnP2O7 is 4.73 V, 0.60 V lower than that in α-MnP2O7, providing a possibility for extract the residual one Li ions to obtain higher energy density. A quantitative analysis of Bader charge provide an accurate picture on the detail of rearrangement of charge upon cycling, and the results show that all the lithium are practically full ionized in the αand β-Li2MnP2O7 and relative half delithiated configurations, and charge transfer in α-Li2MnP2O7 system mainly concentrated upon Mn and O, which leads to the

24


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oxidization state of Mn from Mn2+ to Mn3+, and then from Mn3+ to Mn4+. For the β-phase of Li2MnP2O7 system, a similar charge transfer process is observed with much stronger tendency, which is suggestive of a more covalent character of Mn-O bond or weak Mn-Mn interactions. Further DOS analysis presents that with removing lithium ions from α- and β-phases of Li2MnP2O7, the band gaps of delithiated configurations decrease gradually, and the conductivity changed from insulator nature to conductor character. The mechanical stability is determined by the eigenvalues of elastic stiffness matrixes, and the Pugh ratio B/G are 3.28 and 2.86 for the α- and β-Li2MnP2O7, respectively, which indicates excellent ductility. Moreover, the small B/G value for β-Li2MnP2O7 provides a reasonable explaination for the experimentally observed phenomenon that β-phase of Li2MnP2O7 could transform to α-phase at higher temperature > 773K. With the deintercalation of Li ions, smaller Pugh ratios for delithiated phases are observed. In addition, Young’s Modulus (E), and Poisson’s Ratio (ν) for α- and β-phase of Li2MnP2O7 and relevant delithiated configurations are also presented to explore the hardness and bond characteristic upon cycling process. Our calculation shows α-Li2MnP2O7 is a good candidate for ideally elastic materials.

ASSOCIATED CONTENT

Supporting Information

25



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Page 26 of 34

The half delithiated configurations of α- and β-LiMnP2O7 with different magnetic alignments (ferromagnetic and antiferromagnetic), and the relevant elastic stiffness matrices. This material is available free of charge via the Internet at http://pubs.acs.org.

AUTHOR INFORMATION Corresponding Author E-mail: [email protected]; [email protected]

Notes The authors declare no competing financial interests.

ACKNOWLEDGMENTS

Financial supports from the National Natural Science Foundation of China (Grant No. 21503039), the Specialized Research Fund for the Doctoral Program of Higher Education (Grant No. 20130043120008), the Science and Technology Research Program of Education Department of Jilin Province (Grant No. 2014B036) are greatly acknowledged.

26


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Table of Contents Graphic

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and Î²-Li2MnP2O7 for Lithium-Ion Cathode Materials

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