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Possible Polymerization of PS at a LiPS/FePO Interface with Reduction of the FePO Phase 4

Masato Sumita, Yoshinori Tanaka, and Takahisa Ohno J. Phys. Chem. C, Just Accepted Manuscript • Publication Date (Web): 24 Apr 2017 Downloaded from http://pubs.acs.org on April 24, 2017

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The Journal of Physical Chemistry

Possible Polymerization of PS4 at a Li3PS4/FePO4 Interface with Reduction of the FePO4 Phase

Masato Sumita*,†, Yoshinori Tanaka‡, and Takahisa Ohno*,†,‡

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*Corresponding author. E-mail: M.S., [email protected] Tel: +81 29 859 2490; T.O., [email protected] Tel:+81 29 859 2622 †

National Institute for Materials Science (NIMS), 1-1 Namiki, Tsukuba, Ibaraki 305-0044, Japan,

‡

Global Research Center for Environment and Energy based on Nanomaterials Science (GREEN),

NIMS, 1-1 Namiki, Tsukuba, Ibaraki 305-0044, Japan

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Abstract An important issue about developing all solid-state Li-ion batteries is to lower the high ionic interfacial resistance between a cathode and an electrolyte. An origin of the interfacial resistance is hypothesized due to a Li-depleted layer at the interface. Our computation has shown that the Li-depleted layer was the result of redox reaction at the interface in the charging process. In this subsequent theoretical study, we validate this redox reaction between the FePO4 phase and the Li3PS4 phase from the viewpoint of their band alignment through the density functional theory with the hybrid functional (HSE06). In addition, we demonstrate that the Li-depleted layer grows up to a defective layer at a Li3PS4/FePO4 interface by exothermic radical polymerization of PS4 anions in the oxidized Li3PS4 phase with the volume reduction. This decrease of Li-ion sites due to the PS4 polymerization makes Li-depleted region long-lived and has the potential as an origin of the resistance against the Li-ion diffusion near the interface.

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1. Introduction All solid-state Li-ion batteries (LIBs) are expected as one of next-generation electronic batteries.1,2 As for solid electrolytes, sulfide ionic conductors are widely used by virtue of their superior properties such as fast ionic conductivity, good connectivity to electrodes, low grain boundary resistance and so on.3,4 However, sulfide electrolytes are known to show high ionic resistances for Li-ions at the interfaces with cathodes. High ionic resistances for Li-ions result in low power density and hamper the practical use of solid-state LIBs. Although the formation of space-charge layers or defective layers at the interfaces have been proposed as an origin of the high interface resistance, these proposals have not been verified yet by experiments.1 In our previous paper,5 we have made an interface between an amorphous Li3PS4 and the LiFePO4 surface as one of viable interfaces between a cathode and a sulfide electrolyte, considering that the lattice mismatch between LiFePO4 and β-Li3PS4 is large. This theoretical investigation on the Li3PS4/LiFePO4 interface showed the instability of the charged state of the Li3PS4/LiFePO4 (Li3PS4/FePO4) interface, that is, the oxidation and lithium depletion on the Li3PS4 side near the interface at the normal generalized gradient approximation (GGA) level with +U correction to the d orbitals of Fe (at the +U level). It was also suggested that the oxidized Li3PS4 could possibly undergo a structural transformation. Since the oxidized Li3PS4 phase has PS4 radical anion species, structural transformations such as radical polymerization of PS4 are not strange in the Li3PS4 phase, as detected at the interface between a liquid organic electrolyte and an anode.6,7 The above phenomenon largely depends on the theoretical band alignment between LiFePO4 and Li3PS4. Because our previous calculation did not include sufficient electronic correlation in the electrolyte of Li3PS4, the band alignment between LiFePO4 and Li3PS4 might be misleading information. In this study, we validate the instability at the interface with the hybrid functional [Heyd-Scuseria-Emzerhof (HSE)]. From this validation, the Li3PS4/FePO4 interface is found to be unstable without depending on the present functionals. We perform accordingly DF-MD 3



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simulations of the Li3PS4/FePO4 interface at the +U level, focusing on the structural transformation in the Li-depleted layer of the oxidized Li3PS4 phase. We have found that the radical polymerization of PS4 anions (that is, the formation of intermolecular S−S bonds) occurs in the oxidized Li3PS4 phase with volume reduction. It is expected that the decrease of possible Li-ion sites due to the PS4 polymerization leads to the increase of the resistance against the Li-ion diffusion.

2. Computational details In this computational study, we employed the same setup with the previous study.5 The density functional theory [Perdew-Burke-Ernzerhof (PBE8) functional] was used with +U strategy for molecular dynamics (MD). The value of the effective U (Ueff) was set to the average value between the probable values of Fe3+ and Fe2+ (4.3 eV).9 The hybrid Gaussian basis set10 were used with the Goedecker, Teter, and Hutter (GTH) pseudopotentials11 constructed for the PBE functional. The Γ point was sampled in a super cell for calculations of total energies. We performed DF-MD simulations with an isothermal-isobaric (NPT) ensemble at the temperature of 400 K under the pressure of 1.0 atm. In the NPT ensemble, the cell parameters in the direction parallel to the interface (the a and c axes) were fixed to those of the LiFePO4 (010) surface slab (a = 10.4361 Å, c = 9.48936 Å) that were optimized at the +U level5, whereas the cell parameter perpendicular to the interface (the b axis) was able to be altered flexibly such that the density of the amorphous Li3PS4 slab is automatically adjusted to a suitable value for the present computational level. In our typical DF-MD simulation, 40,000 MD steps were carried out with the time step of 1.0 fs, and after the first 20,000 steps for equilibration the trajectories over 20,000 steps were used for the NPT analysis. The canonical sampling through velocity rescaling (CSVR) thermostat12 was used to control the temperature and the pressure. To validate the band alignment between Li3PS4 and FePO4, we performed single-point energy calculations with the hybrid functional (HSE0613) through the auxiliary density matrix method.14 4


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We used the single-zeta valence (SZV) MOLOPT basis set for Fe and cFIT3 for other atoms as auxiliary basis sets. The same cell parameters optimized with the +U level are used.5,15,16 For comparison, we also revisited the (100) Li3PO4/(010) LiFePO4 coherent interface system.15,16 The equilibrium structure for the Li3PO4/LiFePO4 system was obtained through geometry optimization and the one for the Li3PS4/LiFePO4 system was a snapshot taken from DF-MD at the +U level. CP2K17 package was used for all the above calculations.

3. Results and Discussion 3.1 Validation of band alignment between LiFePO4 and Li3PS4 In this section, we confirm that the reduction of FePO4 by Li3PS4 is possible from the viewpoint of the band alignment between Li3PS4 and LiFePO4, expanding the +U level5 to the HSE06 level. For comparison, we revisit the Li3PO4/LiFePO4 system15,16 at the HSE06 level. When a cathode material is oxidized (delithiated) in the charging process, band alignment between the cathode and an electrolyte is expected to determine the fate of their interface. The valence band maximum (VBM) of the lithiated cathode material should lie at above that of the electrolyte material for a stable electrolyte/cathode interface. If the VBM of the lithiated cathode material is lower than that of the electrolyte material, the delithiated cathode material oxidizes the electrolyte material by getting Li ions from the electrolyte materials. We predicted that this oxidation results in the Li-depleted layer.5 From this viewpoint, our research suggested that the Li3PO4/LiFePO4 system15 is suitable but the Li3PS4/LiFePO4 (Ref. 5) is not as an electrolyte/cathode system for LIB at the +U level. To validate this hypothesis, we have performed single-point calculations at the HSE06 level on each equilibrium structure of the Li3PO4/LiFePO4 and Li3PS4/LiFePO4 interface systems at the +U level. Figure 1 shows the layered density of states (LDOSs) for beta electrons along the b axis (perpendicular to the interfaces) of each system. Switching the functional from PBE+U to HSE06 does not change the qualitative tendencies of 5



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LDOSs, i.e., the VBM of Li3PO4 is sufficiently lower than that of LiFePO4 but the VBM of Li3PS4 lies at slightly higher than that of LiFePO4 in spite of a large difference on the band gap of each material. The band gaps of the LiFePO4, Li3PO4, and Li3PS4 phases at the HSE06 level are estimated at 3.9, 7.7, and 4.2 eV, respectively. In comparison with the +U level, the band gaps at the HSE06 level are increased by 5% for LiFePO4, 31% for Li3PO4, and 56% for Li3PS4. Concerning the band alignment, the VBM of Li3PO4 is lower than that of LiFePO4 by 2.6 eV at the HSE06 level. The difference between the +U and the HSE06 level are over 1.0 eV, that is comparable to the water system.18 Hence, the Li3PO4/FePO4 interface would be stable from the viewpoint of the band alignment. On the other hand, the VBM of Li3PS4 lies at only 0.1 eV above that of LiFePO4 at the HSE06 level. The difference between VBMs of Li3PS4 and LiFePO4 at the HSE06 level is smaller than that at the +U level by 0.6 eV. Although this fact indicates that the diffusion property of electrons does not change, we can deduce that the noticeable reduction of FePO4 by Li3PS4 at the +U level might not occur at the HSE06 level. Moreover, this small gap of VBMs between LiFePO4 and Li3PS4 is not decisive for us to conclude that the Li3PS4 phase reduces the FePO4 phase (delithinated LiFePO4). To deal with this, we have performed preliminary DF-MD calculations of the Li3PS4/FePO4 system at the HSE06 level during 1.0 ps. According to these preliminary calculations, FePO4 is certainly reduced by Li3PS4 (See the Supporting Information). Therefore, we believe that the following discussion about phenomena after the redox reaction between FePO4 and Li3PS4 would be rational and meaningful for practical LIBs.

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Figure 1. Contour maps of layered density of states (LDOSs) for beta electrons in the system of Li3PO4/LiFePO4 (left column) and Li3PS4/LiFePO4 (right column) systems along the b axis. Fermi level of each system is set to zero. Upper LDOSs are calculated on the structures at the +U level. Bottom ones are calculated at the HSE06 hybrid functional level on the same equilibrium structures obtained at the +U level. Green and blue balls indicate the Li atoms originated from the electrolyte (Li3PO4, Li3PS4) and LiFePO4 phase respectively. Oxygen and sulfur atoms are represented as red and yellow bolls respectively. One FeO6 is depicted as an octahedron. PO4 and PS4 are depicted as tetrahedra.

3.2 Polymerization of PS4 anions As mentioned above, the redox reaction is a probable phenomenon at the Li3PS4/FePO4 (the fully charged state of LiFePO4) interface. In this section, we focus on the structural transformation processes in the oxidized Li3PS4. This transformation is energetically favorable and results in the 7



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decrease of the volume of the Li3PS4/FePO4 system. In the reduction process of the FePO4 phase, selectivity of electronic spin appears in the electrons involved in the redox reaction because we have assumed that FePO4 is a ferromagnetic material. Although this magnetic phase is not the ground state,19 we do not expect large differences in the diffusion properties of electrons and Li-ions at the temperature of our simulation. In our model system of Li3PS4/FePO4 interfaces, however, the magnetic structure of FePO4 has effects on the atomic reactions such as S−S bond formation. When Fe3+ is reduced to Fe2+ by PS4, only a beta-spin electron is allowed to occupy the acceptor level of Fe3+ and an alpha-spin electron remains in the S-3p orbital of the oxidized PS4 anion. This means that all of the oxidized PS4 anions have one radical alpha-spin electron. When two of the PS4 radical anions meet together, both the bonding and anti-bonding states of the S-3p orbitals are occupied by alpha-spin electrons, and the bond formation between the two S atoms never occur. All of the oxidized PS4 anions have one radical alpha-spin electron in the DF-MD simulations with an NPT ensemble for the ferromagnetic FePO4. In order to make bonds between the PS4 radical anions, it is necessary to change the spin state of some radical electrons from alpha-spin to beta-spin. The spin flip process can be successfully undergone by decreasing the number of the alpha-spin (increasing the same number of beta-spin), i.e., decreasing total spin multiplicity of the system with the interval of "2". By this spin flip process, there appear several PS4 radical anions with different spin-state electrons, which will form S−S bonds between them. We can deduce that the spin flip process is energetically favorable through DF-MD simulations in the Li3PS4/FePO4 interface system. Figure 2 shows the normalized histograms of the enthalpies (= E+PV, here E is total energy, P and V are the constant pressure and volume respectively) of the systems where the flipped alpha-spin electrons of zero, two, three, four, and five PS4 radical anions exist. At the glance, the system energies are gradually stabilized with increasing the number of the flipped alpha-spin electrons. The system with two-spin flipped electrons is more stable than that 8


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with zero-spin flipped electron by 480.8 kJ/mol at the average enthalpy. From the two-spin flipped to four-spin flipped system, the enthalpy decreases with the interval of 238.4-284.9 kJ/mol. Although the five-spin flipped system has no great advantage relative to the four-spin flipped system, the five-spin flipped system is more stable than the four-spin flipped system by 71.6 kJ/mol.

Figure 2. Normalized histograms of relative enthalpies (kJ mol-1) of the systems where zero, two, three, four, and five alpha-spin electrons are flipped in the Li3PS4 phase (the average enthalpy of the zero alpha-spin flipped system set to zero). The values in parentheses are the averaged enthalpies during 20.0 ps DF-MD at the +U level.

Radial distribution functions for S-S (gS-S) of the systems (Figure 3) indicate that a new S-S interaction appears with the spin-flip. gS-S of the systems exhibit the growth of the sharp peak at around 2.0 Å (inset of Figure 3) with the number of flipped alpha spin electrons increasing, albeit not monotonically (There is the exception at the three-spin flipped system). First, let us see the gS-S of the no flipped alpha-spin system. The sharp peak at around 3.4 Å is due to the intra-molecular S-S length of PS4 anions. The broad peak at around 4.0 Å indicates the inter-molecular S-S length between PS4 anions. At this stage, no peak at around 2.0 Å appears during 60.0-ps DF-MD after reaching energetic equilibrium condition. From the two-spin flipped system, the sharp peak appears 9



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at around 2.0 Å and grows with the number of flipped alpha spin electrons increasing. The sharpness of the peak indicates that this S-S interaction is steady. In contrast to the growth of this peak, the peak at around 3.4 Å is gradually reduced. Furthermore, the flip of alpha-spin electrons also influences the peak at around 4.0 Å (the inter-molecular S-S distance between PS4 anions), although we cannot find clear correlation between the intensity of this peak and the number of flipped alpha-spin electrons. The analyses based on gS-S indicate that chemically different species appear (interaction between PS4 anions change to another S-S interaction). Considering the histograms of enthalpies in Figure 2, therefore, we conclude that the formation of this new S-S interaction is energetically favorable in this system.

Figure 3. Radial distribution functions for S-S during 20.0 ps DF-MD of the systems where zero, two, three, four, and five alpha-spin electrons are flipped in the Li3PS4 phase, and the intensity of the peak at around 2.0 Å as a function of the number of flipped alpha-spin (inset). As the number of flipped alpha spin electrons increasing from zero to five, the peak at around 2.0 Å, which indicates the S−S bond formation between PS4 radical anions, grows up.

Figure 4 shows the snapshots taken from DF-MD simulations of each system described above. Without spin flip process, five Fe3+ are reduced to Fe2+, that is, five residual alpha-spin radical 10


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electrons should exist in the Li3PS4 phase. As expected, we cannot find any reaction products as shown in Figure 4(a) and gS-S of zero-spin flipped system in Figure 3 also shows no peak around 2.0 Å, since there are no pair of PS4 radicals with different spin-state electrons. Next, we have flipped two alpha-spins among the five alpha-spin radical electrons. Then, we have found that two S−S bonds, that result in the peak around 2.0 Å in the gS-S (Figure 3) of two-spin flipped system, are certainly formed between two PS4 radical electrons as shown in Figure 4(b). The S−S bond formation induces further reduction of the FePO4 phase, that is, the Li3PS4 phase is further oxidized to generate more alpha-spin radical electrons of the PS4 anions. Thus, further spin flip processes are possible, which makes it possible to form new bonds of PS4 radical electrons. This spin flip process can be done iteratively until five S−S bonds are formed with stabilizing the system energetically, as already shown in Figure 2. In the DF-MD simulations, the S−S bonds of the same number as the flipped spin electrons are formed, resulting in the polymerization of PS4 radical anions. However, more than five alpha-spin flip induced the artificial spin-contamination in the target system (the delta from the ideal value of S2 is more than 1.0) at the +U level because the reduction of the FePO4 phase was stopped. At the present computational condition, the redox reaction stopped when 41% Fe3+ was reduced. The degree of the reduction of the FePO4 phase probably depends on the slab thickness and the area of the interface. If we employed a larger system, more reduction of the FePO4 phase would progress with the polymerization of PS4 radical anions in the Li3PS4 phase. The S−S bond length in each system is estimated to be approximately 2.0 Å at the average (Table 1), that agrees with the position of the progressive peak at around 2.0 Å of gS-S (Figure 3) and the S−S bond length in typical organic molecules.20 Therefore, we can conclude that structural transformation is definitely attributed to the S−S bond formation.

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Table 1. Average S−S bond lengths during the DF-MD simulations of each system.

S−S / Å

Two

Three

Four

Five

2.028±0.01

2.033±0.01

2.017±0.02

2.049±0.01

Figure 4. Snapshots taken from the DF-MD calculations at the +U level of the systems where (a) zero, (b) two, (c) three, (d) four, and (e) five alpha-electrons are flipped in the Li3PS4 phase. Polymers of PS4 in each system around the interfaces are highlighted. Li (lithium), O (oxygen), and S (sulfur) atoms are denoted as green, red, and yellow bolls respectively. FeO6 is depicted as an octahedron. PO4 and PS4 are depicted as tetrahedra

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Figure 5 shows that the contour maps of DOSs at the HSE06 level for beta-spin electrons along the b axis at the snapshots that are shown in Figure 4. In the Li3PS4 phase for the spin states in Figure 5(a)-(d), there are several beta-spin hole states (that are attributed to the S-3p orbitals) near the Fermi level not only around the interface region but also bulk region of the Li3PS4 phase. The analysis at the +U level also indicates the same result as shown in Figure S3 of the Supporting Information. Although these widely scatted states might be attributed to the self-interaction error of the DFT,21 they implicitly indicate that the further redox reaction is possible while the hole states exist in the Li3PS4 phase. At the +U level, the Li3PS4 phase of the five alpha-spin electron flipped system does not have any localized beta-spin hole state near the Fermi level as shown in Figure S3(e). Hence, further growth of PS4 polymer is not expected at the +U level. LDOSs at the HSE06 level also exhibit that the hole states gradually disappear with the growth of PS4 polymers (increasing the number of the flipped alpha-spin electrons) as shown in Figure 5. The final five alpha-spin electron flipped system [Figure 5(e)] shows no hole state in the Li3PS4 phase. Hence, we conclude that this polymer is semiconductive and hinder the further redox reaction at the interface, suppressing electronic flow in the similar way to the solid electrolyte interphase (SEI).22 The PS4 polymerization would have the Li-depleted region fasten at the interface and be long-lived at the interface.

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Figure 5. Contour maps of density of states (DOSs) at the HSE06 level for beta-spin electrons at the snapshots of each system shown in Figure 4 as the function of the b axis. Fermi energy of each system is set to zero.

The more the FePO4 phase is reduced, the more Li-ions diffuse into the FePO4 phase and simultaneously the more S−S bonds are formed in the Li3PS4 phase. The Li-ions that have migrated 14


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to the FePO4 phase once never diffuse back to the Li3PS4 phase. The charge separation due to the reduction of the FePO4 phase and the annihilation of possible Li-ion sites due to the PS4 polymerization may act as the driving force for Li-ions to diffuse into the FePO4 phase. The Li distribution profiles along the b axis during the sequential spin flip processes are shown in Figure 6, which certainly exhibits that Li-ions in Li3PS4 diffuse to the FePO4 phase as the number of S−S bonds increases in the Li3PS4 phase except for the five-spin flipped system. Since the DF-MD calculation is stopped at the five-time spin-flip process, we could not find further Li-ion diffusion into the FePO4 phase.

Figure 6. Normalized Li and the FePO4 phase distribution profiles in the unit cell along the b axis during 20-ps DF-MD in the system where (a) zero, (b) two, (c) three, (d) four, and (e) five alpha-electrons are flipped and as the result the same number S-S bonds are formed. Black broken lines of each system indicate the atomic distributions in the FePO4 phase during 20-ps DF-MD.

The decrease of the number of Li-ions and the PS4 polymerization due to the S−S bond formation in the Li3PS4 phase causes the decrease of the volume of the oxidized Li3PS4 phase. The histograms of the volume of the total system during 20-ps DF-MD shown in Figure 7 definitely indicate a considerable volume decrease. When two radical alpha-spins are flipped, the system volume is 15



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reduced by 5.0%. Then, the lost of the volume is approximately 1.0% when one more radical alpha-spin is flipped. But, when the five bonds are made, the system volume is increased by 0.2%. This slight volume increase is possibly attributed to the formation of a large PS4 polymer as shown Figure 4. The system volume is finally about 6.7% reduced by the five-bond formation. The loss of the system volume mainly comes from the volume loss of the Li3PS4 region of about 10.1%.

Figure 7. Normalized histograms of volume of the systems where zero, two, three, four, and five alpha-electrons are flipped in the Li3PS4 phase. The values in parentheses are the averaged volumes during 20.0-ps DF-MD.

4. Conclusions In this study, we have revisited the LiFePO4/Li3PS4 systems to validate its band alignment at the HSE06 level. The LDOS at the HSE06 level shows that VBM of the Li3PS4 phase is higher than that of the LiFePO4 phase by only 0.1 eV, which is too small to expect the drastic reduction of FePO4 by Li3PS4 phase. Hence, we have confirmed the probable redox reaction between the FePO4 (the state of charged LiFePO4) and the Li3PS4 phase by the short DF-MD calculation at the HSE06 level. After the oxidation of the Li3PS4 phase by the FePO4 phase, we have found the S−S bond formation is energetically favorable. Consecutive bond formation in the Li-depleted layer of the 16


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Li3PS4/FePO4 interface produces the polymer of PS4 that results in volume reduction of the oxidized Li3PS4 phase. Moderate growth of the PS4 polymer may be helpful to prevent the redox reaction between cathode and electrolyte materials because of its electronic semiconductivity. However, the excess growth may not be beneficial for the Li-ion conductivity because the decrease of possible Li-ion sites due to the PS4 polymerization, results in the long-lived Li-depleted layer, increases the resistance against the Li-ion diffusion. In this study, we assumed that the FePO4 phase is ferromagnetic. When an anti-ferromagnetic FePO4 is reduced by Li3PS4, it is likely that almost the same number of alpha-spin and beta-spin radical electrons are generated in the Li3PS4 phase, and the S−S bond formation and the PS4 polymerization proceed like the present simulations without spin flip processes.

Acknowledgment. This work was supported by JST ALCA project. The computations in this work were carried out on the supercomputer centers of NIMS.

Supporting Information Available: The results of DF-MD calculations of the Li3PS4/FePO4 interface systems at the HSE06 level and the LDOSs at the +U level are shown. This information is available free of charge via the Internet at http://pubs.acs.org.

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FePO4 Interface with

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