LiFePO4 (010) Coherent

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Theoretically Designed LiPO (100)/LiFePO (010) Coherent Electrolyte/ Cathode Interface for all Solid-State Li Ion Second Batteries Masato Sumita, Yoshinori Tanaka, Minoru Ikeda, and Takahisa Ohno J. Phys. Chem. C, Just Accepted Manuscript • DOI: 10.1021/jp5060342 • Publication Date (Web): 12 Dec 2014 Downloaded from http://pubs.acs.org on December 14, 2014

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The Journal of Physical Chemistry

Theoretically Designed Li3PO4 (100)/LiFePO4 (010) Coherent Electrolyte/Cathode Interface for All Solid-State Li Ion Second Batteries

Masato Sumita*,†, Yoshinori Tanaka‡, Minoru Ikeda†, Takahisa Ohno*,†, ‡,¶

———————————————————————————————

*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,

¶

Institute of Industrial Science, University of Tokyo, Meguro, Tokyo 153-8505,

Japan

1 ACS Paragon Plus Environment


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Abstract Controlling electrolyte/electrode interface is of great importance to promote new-generation solid-state Li ion second batteries. In this paper, we report a theoretically designed electrolyte/cathode coherent interface at the density functional theory level, where γ-Li3PO4 and LiFePO4 are used as an electrolyte and a cathode respectively. At the stoichiometric Li3PO4 (100)/LiFePO4 (010) coherent interface, there are vacant Li-sites that give the chance for Li ions to migrate. From the density functional molecular dynamics at 1500 K, it is found that this interface is stable and no impurity phase is produced, and also that Li ions in the Li3PO4 phase around the interface can diffuse with large diffusion coefficients. The dynamic behavior of these Li ions is also reflected in the layered phonon spectra of Li ions, the diffusible Li ions around the interface have the same spectrum. Keywords solid/solid interface, density functional theory, molecular dynamics, diffusion coefficient, phonon spectrum


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1. Introduction Lithium ion secondary batteries are one of the ubiquitous components for electronic devices such as mobile phones and personal computers and also for vehicles such as electronic cars and hybrid cars.1-8 These batteries have already been widely used as high voltage and reliable batteries. To expand the range of their application, Lithium ion secondary batteries of larger size with higher cycle-performance are now demanded. Besides, these batteries have to be safe since they are used in close proximity to us. The present practical batteries, however, use flammable liquid electrolytes, which narrows the range of their application. By replacing flammable liquid electrolytes with non-flammable solid-state ones, the safety of lithium ion secondary batteries can be largely improved. All solid-state lithium ion secondary batteries, where solid-state materials are used as electrolyte, are expected as a next-generation secondary battery.8 For all solid-state lithium ion secondary batteries, not only the safety but the reliability can also be largely improved. This is because non-conducting chemical products are rarely produced at the interfaces between electrodes and solid-state electrolytes. Therefore, all solid-state



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lithium ion secondary batteries have received much attention. Although several materials have been already synthesized for anodes, electrolytes, and cathodes of all solid-state lithium secondary batteries,2-5,9 suitable combinations between solid-state electrolytes and electrodes for high performance are still not unveiled. Controlling electrolyte/electrode interfaces is an important issue for all solid-state lithium secondary batteries. The interfacial resistance between solid-state electrolyte and electrode, as well as the grain boundary resistance in electrolyte itself, has to be reduced for better battery performance.8,10 The grain boundary resistance in electrolyte can be reduced to some extent by high-temperature heat treatment, but unfavorable impurity phases are formed at interfaces with electrode materials during the heat treatment and increase the resistance at the electrolyte/electrode interfaces such as the LiTi2(PO4)3/LiCoO2 interface.11 In the case of the combination between an oxide electrode and a sulfide electrolyte, the large difference between their lithium chemical potentials builds up a large space-charge layer, which results in a large interfacial resistance.8 To decrease these interfacial resistances, coating of cathode materials by ion-conducting thin films has been proposed.8,12,13 This coating technique is also applied


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to improve the electronic/ionic conductivity of LiFePO4.1,2,5 While carbon is the main material for this conductive coating,1,2,5 hybrid coating by Li3PO4 or TiN with carbon shows the good improvement of the drawback of LiFePO4.14,15 It is expected, therefore, that controlling electrolyte/electrode interfaces will bring a breakthrough in the development of all solid-state lithium secondary batteries. To the end of this, atomistic structure at the interface will give a great help in understanding the character of the interface. Despite their crucial importance, researches on the electrolyte/electrode interfaces at an atomistic level have been rarely reported. Recently, Lepley et al,16 have suggested from computational modeling that Li2S buffer layers will stabilize the interface between Li3PS4 electrolyte and metal Li anode. However, atomistic-level researches on the interfaces between solid-state electrolytes and cathodes have not been reported yet. This situation reflects that the electrolyte/electrode interfaces are difficult to investigate at an atomistic level and even atomistic-level modeling of interfaces is a formidable task.1 Therefore, to start by investigating an ideal electrolyte/electrode interface is important. In this paper, we report the theoretically designed stoichiometric γ-Li3PO4/LiFePO4



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coherent interface that is ideally refined for all-solid-state lithium ion secondary batteries at the density functional theory (DFT) level. LiFePO4,17 which has an ordered olivine structure with Pnma space group as shown in Figure 1(a), is a candidate for cathode materials because this is a compound from elements which are abundant in the earth, that is, inexpensive, and environment friendly. Furthermore, the tetrahedral anion structure of PO4 with a strong P—O covalent bond contributes to the stability of LiFePO4. In spite of the great benefit of the LiFePO4 as the cathode material, its low electronic/ionic conductivity hinders the practical use. To overcome this limitation, LiFePO4 has been intensively investigated computationally and experimentally. Specifically, doping several cation atoms18-23 and coating by Li3PO4 or TiN with carbon14,15 are the representative example. These attempts succeeded to improve conductivities of LiFePO4. On the other hand, γ-Li3PO4,24 which has Pnmb space group symmetry as shown in Figure 1(b), is known as practical electrolyte materials or coating materials for cathode as already mentioned8,12-14 and the precursor of LiPON, which is synthesized by doping nitrogen to Li3PO4.25 As shown in Figure 1, the mismatch of the experimental cell


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parameters between LiFePO426 and γ-Li3PO4 (between the a, b, and c axes of LiFePO4 and the b, c, and a axes of γ-Li3PO4, respectively)24 is small (at most 5%). Furthermore, because Pnmb space symmetry is geometrically same with Pnma space group, it is possible to align the PO4 tetrahedral anion of γ-Li3PO4 and LiFePO4 in the same sequence. The geometrical similarity and the small lattice mismatch between γ-Li3PO4 and LiFePO4 motivates us to make an atomistic model of a stable electrolyte/electrode interface. Indeed, the Li/LiPON/LiFePO4 battery, which is fabricated from the deposited Li3PO4 on the thin FePO4 film, experimentally shows the good cyclic performance probably due to the stable interface.27 Hence, the γ-Li3PO4 (the precursor of LiPON)/LiFePO4 interface is a convenient system to investigate electrolyte/electrode interfaces at an atomistic level as the first step of the interfacial study and suitable model system to understand the stability of the LiPON/LiFePO4 interface.



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Figure 1. Unit cells of LiFePO4 with Pnma symmetry (a) and Li3PO4 with Pnmb symmetry (b). In this paper, Li atoms originated from LiFePO4 are depicted as blue balls and Li atoms originated from Li3PO4 are depicted as green balls.

We focus on the Li3PO4 (100)/LiFePO4 (010) interface in this study and present a goal to reach for all solid-state lithium ion batteries. Because Li ions in bulk LiFePO4 diffuse along the [010] direction one-dimensionally,28-30 the (010) surface of LiFePO4 can be regards as the Li active surface. The (010) surface is computationally confirmed as one of the stable surfaces and makes up the large surface area of the Wulff shape of LiFePO4.31 We therefore choose the (010) surface of LiFePO4 as the important surface for Li ion insertion/desertion. For the reason that the (100) surface of Li3PO4 can engage


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with the (010) surface of LiFePO4, we have made the Li3PO4 (100)/LiFePO4 (010) interface without any un-coordinated Fe, P, and O, which contributes to the stability on this interface.31 According to density functional molecular dynamics (DF-MD) calculations at high temperatures, it is found that this interface is stable and no impurity phase is produced, and also that Li ions around the interface are diffusible.

2. Computational details All calculations were carried out with DFT implemented in CP2K.32 Total energies were calculated at the Γ point in a super cell approach. We used the PBE functional33 with the local spin density approximation (LSD). The hybrid Gaussian (MOLOPT DZVP) and plane-wave (240 Ry for cutoff energy) basis set34, where valence pseudo-wavefunctions are expanded in Gaussian-type orbitals and the density is represented in a plane wave auxiliary basis, were used with the Goedecker, Teter, and Hutter (GTH) pseudopotentials35 constructed for the PBE functional33. To include the electronic correlation within the d orbital of Fe, we applied +U strategy. The value of the effective U was set to 4.3 eV as suggested in the previous research.31,36-38 Although



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LiFePO4 with olivine structure is anti-ferromagnetic as already confirmed theoretically and experimentally,39-41 ferromagnetic LiFePO4 was assumed in our calculation because there is no large physical difference between anti-ferromagnetic and ferromagnetic LiFePO4 at the DFT level.40 For DF-MD, the Nosé-Hoover thermostat42,43 was used with the temperature of 1500 K for NVT ensemble. The time step is set to 1.0 fs. After equilibration, the equilibrium trajectories with 25.0 ps, which are used to carry out sampling, were obtained. Initial structure is prepared by geometry optimization with fixed lattice constants. The (1×3×2) LiFePO4 (010) surface, corresponding to (LiFePO4)24, and (3×1×2) Li3PO4 (100) surface, corresponding to (Li3PO4)24 composition, were used as shown in Figure 2. The thicknesses of the slabs were checked from the viewpoint of the electronic structure as shown in the Supporting information.


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Figure 2. (1×3×2) LiFePO4 (010), (3×1×2) Li3PO4 (100) surface, and the coherent Li3PO4 (100)/LiFePO4 (010) interface constructed of them with the cell parameters. There are five-coordinated Fe atoms (Fe5C) on the LiFePO4 (010) surface. On the other hand, there are one-coordinated O atoms (O1C) on the Li3PO4 surface (100).

The orthorhombic cell with the length of 10.4361×37.3029×9.48936 Å was used for the Li3PO4 (100)/LiFePO4 (010) interface shown in Figure 2, which are decided as the following: the cell parameters along a and c axis are decided by optimizing the (1×6×2) bulk LiFePO4 supercell as the function of its volume (see the Supporting information).



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The cell parameter along the b direction was set to the summation of the length optimized (1×3×2; half of 1×6×2) LiFePO4 as the function of the volume and the b length optimized along b axis of Li3PO4 whose other cell parameters are constrained to those of (1×3×2) LiFePO4. See the Supporting information about the details. To evaluate Li ion dynamics quantitatively, we have calculated the diffusion coefficients (DC) and phonon spectrum [F(ω)] of Li ions based on a velocity-velocity auto-correlation function:

= ∙ 0 ,

(1)

where v(t) is the velocity of each atom at the time t. The integration of (1) gives the D C,

= ,

(2)

where T is the final time of DF-MD. A phonon spectrum is calculated through the Fourier transformation of Z(t):

=

. √

(3)


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3. Results and discussion In this study, we can define the two interfaces because of periodic boundary condition. Though we focus on the one interface for convenience, we have used the both interfaces for numerical analyses.

3.1 Structure We have made the stoichiometric Li3PO4 (100)/LiFePO4 (010) interface so that un-coordinate O and Fe do not appear at the interface. Fe in the LiFePO4 bulk is six-coordinated and O atom in the Li3PO4 bulk is coordinated by three Li ion. However, there are five-coordinated Fe atoms (Fe5C; one oxygen atom removed from FeO6 octahedron) on the LiFePO4 (010) surface as shown in Figure 2. There are four Fe5C on the LiFePO4 (010) surface. On the other hand, there are four one-coordinate O atoms (O1C) (see Figure 2) on the Li3PO4 (100) surface. We have made the interface so that Fe5C is coordinated by O1C. In Figure 2, the optimized interface with fixed lattice constants we have made is shown. The stabilization energy by the interface formation from the Li3PO4 (100) and LiFePO4 (010) slabs is estimated at 0.08 eV/ Å2 (see the



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Supporting information). This interface system has no charge bias because we distribute Li ions in each slab without the charge bias.31,44 The detailed optimized structure at the Li3PO4 (100)/LiFePO4 (010) interface is shown in Figure 3. The Li3PO4 (100) surface connects with the LiFePO4 (010) surface via the chemical O1C—Fe5C bond. Vacant Li-sites, whose positions are shown as the black balls, exist at the interface. The presence of the vacant Li-sites at the interface is to keep the electronic neutrality because two original Li ions, which should be coordinated to O1C in bulk Li3PO4, are replaced by one Fe2+ (Fe5C). Due to the proximity effect of this vacant Li-site, two type O1C—Fe5C bonds appear. One is the shorter O1C—Fe5C (near to the vacant Li-site), whose length is approximately 2.109 Å at the average. The other is the longer O1C—Fe5C (no vacant Li-site in the neighborhood), which is estimated at 2.192 Å at the average. The bonds with O atoms around Fe in bulk LiFePO4 can be classified depending on the style of the coordination bond with PO4 anion. Two Fe—O bonds are made with one PO4 anion (as a chelate ligand) and the other four Fe—O bonds are made with four PO4 anions (as a single coordination ligand) respectively. The O1C—Fe5C bond corresponds to the later. The average of the O—Fe


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single coordination bonds in the bulk is 2.147 Å. Hence, slightly longer and shorter O—Fe bonds than those in bulk coexist at the interface. Similarly, we expected that there were classable two type O1C—P bonds at the interface. Contrary to our expectation, the O1C—P bonds near to the vacant Li-site is estimated as 1.56 Å. The other is 1.57 Å. The difference between these O1C—P bonds and O—P bond length in the bulk Li3PO4 (1.56 Å) are small (in the order of 0.01 Å). Though the slight difference between Fe5C—O1C bonds is observed, that is not reflected in electronic structure.

Figure 3. Optimized structure around the stoichiometric Li3PO4 (100)/LiFePO4 (010) coherent interface is shown in detail. Black balls depict vacant Li-sites. The values are given in Å.

Figure 4 shows partial density of states (PDOSs) in the optimized Li3PO4/ LiFePO4 interface system. The band gap between the valence band maximum (VBM) and



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conduction band minimum (CBM) is calculated as 3.75 eV. The VBM and CBM are attributed to the d orbital of Fe, which is comparable to the band gap of the bulk LiFePO4 system (3.66 eV). Hence, we can conclude that the band gap of this interface system attributes to the bulk LiFePO4. The band gap of Li3PO4 in the interface system is estimated at approximately 5.5 eV, which is slightly smaller than the value of bulk Li3PO4 (5.93 eV). The PDOSs of LiFePO4 and Li3PO4 phase show the similar PDOSs of the bulk LiFePO4 and Li3PO4 respectively as shown in Figure 4. Hence, this interface system has no impurity state and can be defined as the coherent interface.


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Figure 4. Partial density of states (PDOSs) of the stoichiometric Li3PO4 (100)/ LiFePO4 (010) coherent interface (up) and each bulk system of (1×6×2) LiFePO4 and (6×1×2) Li3PO4 (bottom). Fermi energies are aligned zero in each system.



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3.2 Dynamics In order to investigate the stability of the Li3PO4 (100)/LiFePO4 (010) and the dynamic behavior of Li ions at the coherent interface, we have performed DF-MD simulations at 1500 K. This high-temperature MD simulations presumably correspond to the heat treatment to reduce the interfacial resistance. One of the drawbacks of the high-temperature heat treatment is that the impurity phase tends to be formed, which results in high interfacial resistance. However, our calculations indicate that this Li3PO4/LiFePO4 coherent interface is stable and the impurity phase is not formed at the interface during the simulation time, i.e., there are no chemical bond making/breaking and large deformation of structure except for around Li ions. It is noted that the vacant Li-sites are likely to keep staying around the interface. Normalized Li ion distribution profile during the 25.0 ps DF-MD along the b axis is shown in Figure 5 with the distribution profile of optimized structure. The peaks of Li ions around the interface, which have intermediate intensities, appear at approximately 17 Å and 35 Å. Five low peaks from 0-13 Å is due to the Li ions in the LiFePO4 phase. Five high peaks in the area of 20-33 Å indicate the Li ions in the Li3PO4 phase. Except


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that the small peaks which appear between the high peaks in the Li3PO4 phase of the optimized structure are missing, the peaks of 25.0 ps DF-MD appear at the almost same positions of the optimized structure. And the intensities of the five peaks in the LiFePO4 and Li3PO4 phases show the same heights, respectively. Therefore, we can speculate that vacant Li-sites do not diffuse away along the b direction, that is, the vacant Li-sites keep staying near the interface. On the other hand, the following trajectory analysis shows that each Li ion around the interface can diffuse. This means that the diffusion of vacant Li-sites at the interface induces billiard-type diffusion of Li ions without changing the total number of Li ions of each layer. We have analyzed the dynamic behavior of the Li ions depending on each layer (see Figure 6 about the index of Li layers).



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Figure 5. Normalized Li ion distribution profiles along b axis of the 25.0 ps DF-MD (PMD(b)) and optimized structure (POpt(b)), which is obtained by geometry optimization. The area from 0.0 to 13.0 Å is due to LiFePO4 phase. The area from 20 to 33 Å is due to Li3PO4 phase. The peaks at approximately 17 Å and 35 Å are attributed to the Li ions at the interfaces.

Figure 6. Numbering Li ion layers up to the medium of each Li3PO4 and LiFePO4


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phase based on the initial structure (optimized structure). The position of Li layers are correspond to the peak of Li ion distribution profile of geometry optimized structure which shown in Figure 5. Blue characters and lines depict Li layers of the LiFePO4 phase. Green characters and lines depict Li layers of the Li3PO4 phase.

3.2.1 LiFePO4 phase Trajectories of the Li ions that are originated from LiFePO4 are shown in Figure 7. The Li ions in the second and up layers of the LiFePO4 phase vibrate around the initial positions and never diffuse during 25.0 ps DF-MD calculation. On the other hand, the Li ions in the first layer of the LiFePO4 phase diffuse up to the third layer in the side of the Li3PO4 phase and mix with their Li ions. This trajectory analyses is consistent with the mean square displacements (MSD) of Li ions in each layer as a function of time (see the Supporting information). The Li ions in the first layer show remarkable diffusion behavior. On the other hand, the Li ions in the second and up layers of the LiFePO4 phase show only small fluctuation.



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Figure 7. Trajectories (depicted as small blue balls) of Li ions in each layer of the LiFePO4 phase from c axis (up) and b axis (bottom) during the 25.0 ps DF-MD. The positions of elements except for Li are their averages during 25.0 ps. Li ions in the first layer of the LiFePO4 phase diffuse to the third layer of the Li3PO4 phase and the direction along the c axis. Li ions in the second and up of LiFePO4 do not diffuse during the 25.0 ps DF-MD.

Therefore, in the LiFePO4 phase the diffusive Li ions are only on the LiFePO4 (010) surface. The Li ion that diffuses along the direction of the c axis also exists. Diffusion


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pathway of Li ions can be identified as three-dimensional as in bulk Li3PO4.45 To estimate the mobility of Li ions quantitatively we have calculated the diffusion coefficient (DC) by integrating the velocity-velocity auto-correlation function. In Table 1, the values of DC of the diffusible Li ions in Li3PO4 and LiFePO4 phase are tabulated. The DC of Li ions in the first layer of the LiFePO4 phase (interfacial Li ions) are 2.62×10−8 m2/s.

Table 1. Diffusion coefficient (DC) of diffusible Li ions in each layer, which is calculated by the integration of velocity-velocity auto-correlation function. See Figure 6 about the index of Li layers in LiFePO4 and Li3PO4 phase. DC (×10−8 m2/s)

Layer LiFePO4 First

2.62 Li3PO4

First

1.94

Second

0.12

Third

0.60

Fourth

0.91

Fifth

0.95



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3.2.2 Li3PO4 phase The Li ions originated from the Li3PO4 phase are diffusible only in the limited region within 6.0 Å from the interface (up to the fourth layer of Li3PO4). Trajectories of the Li ions in the Li3PO4 phase are shown in Figure 8. Three-dimensional diffusion of Li ions similar to in bulk Li3PO444 are observed up to the fourth layer. The Li ions up to the fifth layer can diffuse to the interface. The MSD of the Li ions in the Li3PO4 phase as a function of time supports this trajectory analyses (Supporting information). The Li ions up to fourth layer of the Li3PO4 phase show the remarkable diffusion behavior. On the other hand, the Li ions in the fifth and up layers exhibit small fluctuation, though the Li ions in the fifth layer begin to diffuse fairly after 15 ps is observed. This suggests that the vacant Li-site diffusion at the interface affects the Li diffusion in the Li3PO4 phase. The Li ions in the first layer diffuse up to the fourth Li3PO4 layer. The DC of Li ions in the first Li3PO4 layer is calculated to be 1.94×10−8 m2/s, which is comparable to the DC of Li ions in the first LiFePO4 layer.


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Figure 8. Trajectories (depicted as small green balls) of Li ions in each layer of the Li3PO4 phase from c axis (up) and b axis (bottom) during 25.0 ps DF-MD. The positions of elements except for Li are their averages during 25.0 ps. Li ions from the first to fifth layer of the Li3PO4 phase diffuse from the interface to the fourth layer.

Similar to the first layer, Li ions in the second layer of the Li3PO4 phase also diffuse in the region between the interface and the fourth Li3PO4 layer three-dimensionally. Their DC is calculated to be 0.12×10−8 m2/s, which is smaller than that of the first layer. This means that the Li ions in the second Li3PO4 layer dominantly vibrate rather than diffuse. The Li ions in the third Li3PO4 layer can diffuse in a larger region than the Li ions in



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the second layer. The trajectories of Li ions in the third layer spread from the interface to the fourth Li3PO4 layer as shown in Figure 8. Additionally, though the staying time is less than 1.0 ps, Li ions in the third layer intrude the second layer of LiFePO4. This suggests that a barrier for Li ion intercalation to LiFePO4 phase from Li3PO4 phase might be small. The large diffusion area of the Li ions in the third layer is reflected in DC, which is calculated to be 0.60×10−8 m2/s larger than the Dc of Li ions in the second Li3PO4 layer. The diffusion area of the Li ions in the fourth Li3PO4 layer spreads from the interface to the fifth layer. One of the Li ions migrates to the fifth layer and occupies the vacant Li-site which is produced as the result of the Li diffusion in the fifth layer to the interface, and then vibrates at that position. On the other hand, the Li ions that migrate to the interface diffuse in the a-c plane, similar to the Li ions in the third and down layers. Though the Li ions in the fourth Li3PO4 layer seem to be less diffusible than the Li ions in the third layer, the DC of Li ions in the fourth Li3PO4 layer is calculated to be 0.91×10−8 m2/s larger than that of Li ions in the third layer, which is probably due to the Li ions diffusing to the interface.


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Most of the Li ions in the fifth Li3PO4 layer remain in their initial layer, except for one Li ion diffusing to the interface. As a result of this Li diffusion to the interface, one Li ion in the fourth layer migrates to this fifth layer as mentioned above. Slight migration from the fifth layer to fourth layer is also observed. We conclude that the Li ions in the fifth layer are not diffusible, together with consideration of the phonon spectra that will be shown later. Due to the Li ion that migrates from the fifth layer to the interface, the DC of Li ions in the fifth layer is calculated to be 0.95×10−8 m2/s slightly larger than fourth layer. Li ions in the sixth and seventh layers never migrate to other layers. According to the trajectories of the Li ions in the sixth layer in Figure 8, there is no Li ion that shows inter and intra layer diffusion. In the seventh layer, there are Li ions that undergo intra layer diffusion since slight disorder of Li ions is observed. This indicates that there is some difference in the dynamic behavior of Li ions between the sixth and seventh layers, which is expected to be detected in the photon spectra.



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3.2.3 Phonon spectra Phonon spectra provide the information about the constraint force, which influence the mobility of atoms. The phonon spectra of Li ions of each layer are shown in Figure 9 (see the Supporting information about the phonon spectra of the whole system). In all spectra, peaks from 200 cm−1 to 600 cm−1 due to Li ions are present. The spectrum of the Li ions in the second and up layers of the LiFePO4 phase shows clear difference from those in other layers, having mainly two peaks at 250 cm−1 and 550 cm−1 due to two vibration modes. To analyze the anisotropy of these vibration modes, we have split the calculated the phonon spectra into the a, b, and c components (see the Supporting information). The soft mode at 250 cm−1 mainly assigns to the vibration along the a direction. On the other hand, the hard mode at 550 cm−1 mainly assigns to the vibration along the b and c directions. Interestingly, the vibration along the b direction, which is the Li ion diffusion direction, is not the principle component of the soft mode. This suggests that the vibration of the Li ion along the a direction is primarily involved in the diffusion events in bulk LiFePO4.


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Figure 9. Phonon spectra of Li ions in each layer (see Figure 6 about the index of Li layer). Upper seven spectra are due to Li ions of the Li3PO4 phase. Down two spectra are due to Li ions of the LiFePO4 phase.

The spectra of Li ions except for the second and up layers of the LiFePO4 phase are relatively broad with one peak. Vibration mode is isotropic with respect to the a, b, and c components. The first layer of LiFePO4 and up to the fourth layer of Li3PO4 show similar spectra. This is consistent with the trajectories shown in Figure 7 and 8, that is, the Li ions up to the fourth Li3PO4 layer diffuse three-dimensionally in the area from the interface to the fourth layer. From the fifth layer, the peak at 400 cm−1 gradually grows. Though the fifth layer of Li3PO4 has the Li ion that diffuses to the interface, its phonon spectrum is similar to the seventh layer rather than the fourth and down layer of the



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Li3PO4 phase. Therefore, we rule out the fifth layer from the diffusion area of Li ions. Indeed, most of the Li ions in the fifth layer remain at their original positions. Although most Li ions in both the sixth and seventh layers vibrate at their original positions, the phonon spectrum of the sixth Li3PO4 layer shows the similar spectrum to the fourth and down layers of the Li3PO4 phase rather than the seventh layer. This suggests that the Li ions in the sixth layer have the similar dynamic property to the diffusible region (the fourth and down layer of the Li3PO4 phase). However, the fifth Li3PO4 layer prevents the sixth layer from diffusing. On the other hand, the spectrum of the seventh Li3PO4 layer shows the peak shifts to higher wave number than those of the fourth and down layers of the Li3PO4 phase. Consequently, layered phonon spectrum suggests that the first layer of the LiFePO4 phase and up to fourth layer of the Li3PO4 phase have the same dynamic property and diffusible.

4. Conclusion We have theoretically designed the stoichiometric Li3PO4 (100)/LiFePO4 (010) coherent interface as an ideal electrolyte/cathode interface of all-solid-state lithium ion


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batteries at the DFT level and investigated the dynamic behavior of Li ions by using DF-MD. The PDOSs of the Li3PO4 and LiFePO4 phases of the Li3PO4 (100)/LiFePO4 (010) interface system show the same electronic structures with their bulk systems. This indicates that the designed interface is a coherent interface. The stoichiometric Li3PO4 (100)/LiFePO4 (010) coherent interface contains the vacant Li-sites that give the chance for Li ions to migrate. Indeed, DF-MD calculation at 1500 K suggests that the Li ions within about 6.0 Å from the interface (up to the fourth layer in the Li3PO4 phase) are diffusible. Around the interface, it is difficult to discriminate between the Li ions originated from the LiFePO4 (010) phase and the Li ions from the Li3PO4 (100) phase since both of the Li ions actively diffuse in the same region. The dynamic behavior of Li ions is also reflected in the phonon spectrum. The Li ions in the first layer of the LiFePO4 phase show the same spectra with the Li ions of the Li3PO4 phase within 6.0 Å (the fourth layer) from the interface. It is found that no impurity phase is formed in the theoretically designed Li3PO4 (100)/LiFePO4

(010)

interface

during

the

25.0

ps

DF-MD

simulations.

High-temperature heat treatment employed to reduce the grain boundary resistance in



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solid electrolytes tend to form impurity phases at the interface with electrode materials, which increase the resistance at the electrolyte/electrode interface.8 The present DF-MD simulation shows that no impurity phase is formed at the Li3PO4/LiFePO4 interface, i.e., the coherent interface would suppress the growth of the impurity products at the interface. This result implies that the coherent interface contributes the good cyclic performance of the Li/LiPON/LiFePO4 battery experimentally shown27. Recently, Zhao et al, have reported that the electrochemical performance of LiFePO4 cathode materials can be improved by Li3PO4 coating such that the rate capability is markedly improved.22 The three-dimensional diffusion of Li ions around the Li3PO4/LiFePO4 interface shown by this study may imply that the improvement by Li3PO4 coating is attributed to the formation of stable Li3PO4/LiFePO4 coherent interfaces.

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


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Supporting Information Available: Cell parameters optimization, the validity of the slab thickness of Li3PO4 (100) and LiFePO4 (010) surfaces we used in this study are discussed. The stabilization energy by the interface formation from the surfaces is estimated. Mean square displacements (MSD) of Li ions in the LiFePO4 and Li3PO4 phase as a function of time is shown. Phonon spectra of the whole system, and second and up layer of LiFePO4 split into a, b, and c components are also included. This information is available free of charge via the Internet at http://pubs.acs.org.



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TOC


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LiFePO4 (010) Coherent

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