Lithium Ion Conduction in LiTi2(PO4) - American Chemical Society

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Lithium Ion Conduction in LiTi2(PO4)3 and Related Compounds Based on the NASICON Structure: A First-Principles Study Britta Lang,*,†,‡ Benedikt Ziebarth,‡,§ and Christian Elsas̈ ser†,‡ †

Albert-Ludwigs-Universität Freiburg, Freiburger Materialforschungszentrum (FMF), Stefan-Meier-Straβe 21, 79104 Freiburg, Germany ‡ Fraunhofer Institut für Werkstoffmechanik IWM, Wöhlerstraβe 11, 79108 Freiburg, Germany § Karlsruher Institut für Technologie, Institut für Angewandte Materialien (IAM-CMS), Engelbert-Arnold-Straβe 4, 76131 Karlsruhe, Germany ABSTRACT: LiTi2(PO4)3 (LTP) and related materials based on the structure of NaZr2(PO4)3 (NZP) belong to a family of Li ion conducting compounds for applications in Li ion batteries. Because of their three-dimensional framework of TiO6 octahedra and PO4 tetrahedra, which provide several positions for mobile charge carriers, and the large number of possible compounds crystallizing in this type of structure, they are promising ion conducting materials. In this work, we investigate the migration barriers for an interstitial Li ion and a Li vacancy in the rhombohedral structure of these compounds using density functional theory. Our results show that the substitution of Ti atoms in LTP by a variety of tri-, tetra-, and pentavalent cations X (LXTP) leads to structural changes influencing the Li mobility. The calculated activation energies for migrating vacancies vary between 0.29 and 0.75 eV and are related to the sizes of LiO6 octahedra in the structure. For migrating interstitials in bulk LTP, the calculated activation energy of about 0.19 eV is much lower. However, substitution by trivalent ions like Al introduces interstitial Li ions for charge compensation, but these additional Li ions get trapped near the trivalent ions.

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INTRODUCTION

and three PO4 tetrahedra sharing O atoms. The structure is shown in Figure 1. In the rhombohedral structure, the Li ions are placed at sites surrounded by six O atoms located at the inversion symmetric Wyckoff position 6b (M1). There exists a second structural site for Li atoms (M2, 18e) between two M1 positions with an irregular 10-fold oxygen coordination. Both sites are sketched in Figure 2. They are arranged in an alternating way along the conduction channels and build up a three-dimensional migration network throughout the crystal (Figure 3). Some of the compositions with large tetravalent cations like Zr, Sn, and Hf show also a low-temperature triclinic phase of lower symmetry induced by a displacement of the Li ions. In this triclinic structure, the Li ions are moved to M1/2 positions, which are located midway between M1 and M2 in a 4-fold-oxygen coordination.8−11 Ionic migration in crystals is driven by thermally activated hopping of ions between interstitial or vacant sites. Moreover, macroscopic diffusion depends on the microstructure of the material. Numerous experimental investigations on the Li diffusion for the rhombohedral structure of LiTi2(PO4)3 (LTP)12,13 and related materials14,15 have been done. Yet to our knowledge there are no published atomic-scale simulations

The demand of energy storage devices with large specific energy densities has increased rapidly in recent years. In Li ion batteries, the ionic transport between the electrodes mostly occurs through Li salts dissolved in organic solvents. These liquid electrolytes suffer from problems like toxicity, flammability, and leakage, and so there is a strong demand for alternatives. Solid-state electrolytes based on NZP structures, named by the composition NaZr2(PO4)3 and also called NASICON (Na Super-Ionic Conductor),1−4 are promising candidates because of their three-dimensional diffusion network. As compared to other battery materials such as lithium titanate,5,6 which also provide a three-dimensional diffusion network, their ionic conduction is much faster.7 These materials show desired properties like thermal and chemical stability, low electronic conductivity, and adjustable thermal expansion coefficients, but their low ionic conductivities still impede their successful application. Hundreds of compositions based on the NZP structure are known, which makes it desirable to build up an understanding of the relationship between the concentration of Li ions, the crystal structure of the NZP-type host material, and the ionic conductivity from which predictions for useful Li ion conductors can be made. NZP structures based on Na and Li crystallize in the rhombohedral structure with a space group R3c.̅ They have a framework of X2(PO4)3 units consisting of two XO6 octahedra © XXXX American Chemical Society

Received: April 28, 2015 Revised: June 23, 2015

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DOI: 10.1021/acs.chemmater.5b01582 Chem. Mater. XXXX, XXX, XXX−XXX

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Chemistry of Materials

problem with Ti-based systems is their instability toward metallic Li due to the reduction of Ti4+ to Ti3+,18,19 so the substitution of Ti is desired. However, although structures with Ge, Zr, and Hf instead of Ti are indeed stable against metallic Li, they are significantly more expensive to produce, and there is the problem of polymorphism in structures with larger cations.8,10,20−22 Therefore, our DFT study focuses on the effect of cation-element substitution on the crystal structure and energy barriers as compared to the unsubstituted case of LTP. In the following sections, the structural NZP model and computational DFT setup are described, the results are presented and discussed, and finally the conclusion is given.

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MODEL AND METHOD

Figure 3. Migration path for Li ion in LiTi2(PO4)3 consisting of M1 (stable sites in green) and M2 (transition sites in yellow) positions.

Structural Model for NZP. For the calculations, the conventional hexagonal unit cell of the rhombohedral structure containing 108 atoms, which is shown in Figure 1, was used. One Li atom was removed to create a vacancy required for diffusion. As a reference structure, the unsubstituted LTP composition has been selected. Calculations have been performed as well for several other LXP compositions with tetravalent cations (X = Si, Ge, Sn, Zr, Hf, Mo) substituting Ti. The relaxation of the unit cell volume and atom positions has been carried out for every composition. The direct influence of substitutional elements in lower concentrations on the diffusion paths has been described by the replacement of just one of the 12 Ti atoms by 3+-, 4+-, and 5+-cations in the unit cell (LXTP). For these structures, only the atom positions have been relaxed, and the relaxed cell constant of LTP has been used as well for all LXTP because of the rather small volume changes by substituting just one of the 12 Ti atoms in the unit cell. Lithium Vacancy and Interstitial Diffusion. The preferential occupancy of the M1 sites (6b) by Li ions in LiGe2(PO4)3 has been deduced from neutron diffraction (ND) experiments.23 LiTi2(PO4)3 shows a disordering of Li cations away from the M1 sites at room temperature,24 which cannot be described by DFT calculations at T = 0 K. At first a vacancy-mediated Li diffusion is assumed. For the case of a Ti substitution by 3+-cations, the concentration of Li atoms increases, and hence it is also necessary to investigate the possibility of interstitial diffusion. The activation energies ΔE are related to the defect jump rates Γ by an Arrhenius-type equation25 Γ = ν e−ΔE/kBT, where ν is the frequency factor, T is the absolute temperature, and kB is the Boltzmann constant. Computational Methods. The DFT calculations have been performed using the Quantum ESPRESSO PWscf code26 using a plane-wave basis to express the wave function of the valence electrons and ultrasoft pseudopotentials to describe the interactions of ionic cores and valence electrons.27 The exchange-correlation contribution was described by the generalized gradient approximation (GGA) of Perdew, Burke, and Ernzerhof.28 For the k-point sampling of Brillouinzone integrals, a 3 × 3 × 1 Monkhorst−Pack grid29 was used, and energy cutoffs 476 and 5442 eV for the plane-wave basis and electrondensity representation have been chosen. The relaxation of unit cell volume was done by total-energy minimization, and atom positions were relaxed until the remaining force acting on the atoms was less than 10−3 eV/Å. The minimum energy paths (MEPs) of Li jumps between neighboring M1 sites were obtained by means of the nudged elastic band (NEB) method.30 The threshold for the total force that is acting on the NEB images of the interpolated reaction path was set to 0.05 eV/Å.

using density functional theory (DFT), and only one study of ion migration pathways in LiTi2(PO4)3 and Li1.3Al0.3Ti1.7(PO4)3 by molecular statics and dynamics simulations based on empirical potentials.16 Partial substitutions of Ti ions have been done for several elements. Yet relations between the substitutional elements, the crystal structure, and the activation energies have only been investigated for a few compounds.17 A

RESULTS Vacancy Migration. The influence of the elements X instead of Ti in the NZP-type structures LXP on the ionic conductivity has been investigated by the calculation of the MEP in these compounds. Furthermore, the effect of a partial substitution of Ti by tri-, tetra-, and pentavalent cations on the migration of Li ion is addressed.

Figure 1. Crystal structure of LiTi2(PO4)3. Red spheres are oxygen ions (Wyckoff position 36f), green spheres are Li ions (Wyckoff position 6b), blue spheres are Ti ions (Wyckoff position 12c), and violet spheres are phosphorus ions (Wyckoff position 18e).

Figure 2. M1 and M2 sites of Li atoms in the crystal structure of LiTi2(PO4)3.

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B


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Chemistry of Materials LTP and LXP (X = Si, Ge, Sn, Zr, Hf, Mo). For compositions LXP with tetravalent cations X with the rhombohedral structure of NZP, the Li vacancy migration paths have been calculated (Figure 4). Note that the migration of the vacancy is shown.

Figure 5. Crystal structure of LiSi0.2Ti1.8(PO4)3. Blue spheres are Ti ions, the orange sphere is the Si ion, red spheres are O ions, green spheres are Li ions, and violet spheres are P ions. Figure 4. MEPs of the migration path of a Li vacancy in LiX2(PO4)3, X = Si, Ge, Sn, Ti, and Mo.

distinct steps for the migration of a Li vacancy in the structure. For all of these, minimum energy paths have been calculated with the NEB-DFT approach. To take possible effects such as trapping of Li vacancies into account, energies of vacancy formation and migration have been calculated. The formation energies of vacancies Ef,vac depend on the chemical potential of Li, μLi. We assume that μLi is the same for all compounds, and relative energies are calculated with respect to LTP according to the following procedure in which μLi cancels out:

Because the M1−M2−M1 path is mirror-symmetric, only onehalf of it is shown. LiSi2(PO4)3 and LiGe2(PO4)3, the compounds with two smaller cations substituting Ti, show larger activation energies than the compounds with the larger cations Mo and Sn. Table 1 lists the ionic radii according to Shannon,31 the energy barriers, and the volumes of the local LiO6 polyhedra Table 1. Shannon Radii rIon,31 Activation Energies Ea for Li+ Diffusion, and Polyhedra Volumes LiO6 in LiX2(PO4)3 X4+

rIon [Å]

Ea [eV]

VM1 [Å3]

Si Ge Sn Ti Mo

0.40 0.53 0.69 0.61 0.65

0.67 0.53 0.43 0.41 0.48

12.14 13.14 15.41 14.66 15.66

LTP LTP LTP = Etot,vac − Etot + μLi Ef,vac LXTP LXTP LXTP = Etot,vac − Etot + μLi Ef,vac LXTP/LTP LXTP LTP ΔEf,vac = Ef,vac − Ef,vac

For the case of X = Si, three regions of migration can be identified. The first one is a bulk-like migration between the three positions 1, 2, and 6 (green arrows in Figure 5 and green lines in Figure 6) because they are remote from the substituted position and therefore hardly influenced by the Si ion, so all

surrounding the mobile Li ion at the initial M1 position of a migration path. According to the correlation between ionic radii of host cations and structural distortion, there is also a correlation between ionic radii and activation energies. As mentioned before, the structures with larger cations like Sn, Zr, and Hf lead to a structural distortion at room or higher temperature. This can be already seen by a local displacement of Li atoms to more stable positions around the M1 site, which results in a local triclinic distortion. This also happened in the relaxation of structures with a Li vacancy and the larger elements Hf and Zr. Introducing a Li vacancy into the compositions with Sn and Mo only leads to small distortions, while no distortion is observed for compositions with smaller elements such as Si, Ge, and Ti. LXTP (X = Al, Si, Ge, Sn, Bi, Ti, Zr, Hf, Nb, Ta, Mo). In the following, we discuss the influence of Ti substitution by other cations on the diffusion in the partial substituted LXTP. The substitution of one Ti by a tetravalent cation is the most simple scenario, because it does not change the content of Li atoms in the structure. At first one Ti atom per unit cell of LTP was replaced by a Si atom. As Figure 5 illustrates, there are now six

Figure 6. MEPs of the migration path of Li vacancy in LiSi0.2Ti1.8(PO4)3. Green marks the unsubstituted region, red marks the region influenced by the substitutional Si atom, and blue marks the region with lowered activation barriers. C


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that for LiSi0.2Ti1.8(PO4)3, which is shown in Figure 8. The associated values for activation energies and polyhedra volumes are listened in Table 3. Nearly all activation energies are within an energy interval of ±0.1 eV around a linear regression line of the values; only two belonging to the systems containing Mo and Hf deviate more but still follow the trend: the substitution of smaller or larger ions leads to differently sized LiO6 octahedra. A smaller or larger ion results in a smaller or larger LiO6 octahedra around the Li(3) position, respectively. This is a local effect. In the regions remote from the substitution atoms, Li vacancy migration resembles that of Li vacancy in LTP. The vacancy formation energies have been calculated for all tetravalent cations. All of these have values around 0 eV; only those for Mo deviate a lot with values around −2 and −2.2 eV, which are outside the range of the graph. Most of the other values are within an energy interval of ±0.05 eV around a linear regression line of all values. So far, no significant reduction of the energy barriers in the structure is found by replacing Ti by other elements. Only substitution with smaller ions such as Ge or Si leads to lower energies in some regions of the structure close to the substituted element, but simultaneously there exist regions with higher activation energies, as compared to LTP, which cancels out the possibility for faster Li diffusivity. Calculations have been done with the pentavalent cations Nb, Ta, and Bi replacing Ti ions. Each cation creates a vacant Li position, which is required for charge balance and as well useful for diffusion, so for the MEP calculations no explicit addition of a further vacancy is necessary. As shown in Figure 8 and Table 3, Bi follows the general trend, and only two values of Nb and Ta deviate from this trend. To investigate the influence of the substitution of Ti by trivalent Al atoms, at first vacancy migration paths have been calculated as for all other substitutional cations. Per trivalent ion, there is one additional Li that has to be considered for charge balance. Relaxation calculations yield that vacancies at M1 sites next to the Al ion are not structurally stable. Creating vacancies is always followed by filling up the empty position with the additional Li ion. This reduces the number of possible migration paths, because the Li(3) and Li(4) positions are no longer involved in the diffusion network. Only three of the six migration steps in the structure remain active. The activation energies for these are shown in Table 4. The substitution of an Al atom leads also to differently sized LiO6 octahedra and in one case to a reduction of the energy barrier as compared to

three positions have nearly the same energies. The second part of the migration path connects the positions 2, 3, and 4 (red arrows in Figure 5 and red lines in Figure 6), which are located next to the Si atom. The directly adjacent site 3 is about 0.1 eV higher in energy than the bulk-like sites, and the activation energy for the Li vacancy to reach this site is also higher by about 0.5 eV. The third migration region is located around position 5 (blue arrows in Figure 5 and blue lines in Figure 6), which is by about 0.1 eV lower in energy and has a smaller energy barrier by about 0.3 eV for the migrating Li vacancy. Vacancies at the bulk-like sites 1, 2, and 6 remote from the substitutional Si atom behave in the same way as in the unsubstituted LTP. Sites 3 and 5 are clearly different from the others. The substitution of a Ti ion with the smaller Si ion leads to a distinction of the LiO6 octahedra into larger and smaller ones as compared to the pure LTP, which directly influences the energy barriers of the migration paths. The collection of all of the calculated energy barriers is given in Table 2. As in the LXP compounds, we observe again a Table 2. Activation Energies and Volumes of LiO6 Octahedra in LiSi0.2Ti1.8(PO4)3a path B ↔ A

Ea→ [eV]

Ea← [eV]

VA [Å3]

VB [Å3]

↔ ↔ ↔ ↔ ↔ ↔

0.41 0.41 0.29 0.39 0.49 0.39

0.41 0.40 0.38 0.32 0.39 0.48

14.69 15.02 15.41 15.19 14.51 14.84

14.84 15.26 14.73 15.49 14.77 14.22

1 6 4 5 2 3

2 1 5 6 3 4

a A and B mark the M1 positions occupied by the initially migrating Li ion.

correlation between polyhedra volumes and energy barriers as well as the energies of vacant positions. Figure 7 demonstrates this even more clear correlation. To move a Li vacancy to a larger polyhedron is easier than to bring it to a smaller polyhedron, and, hence, Li vacancies prefer to occupy larger polyhedra. Further calculations have been done for several tetravalent cations (Ge, Sn, Zr, Hf, Mo). Only two of the six migration steps, one involving the Li ion next to the substituted ion (Li(3) → Li(4)) and one involving the Li(5) position (Li(5) → Li(6)), have been calculated, because we also expect a LTP bulk-like diffusion in the part of the structure remote from the substituted ion. Most of the results follow the same trend as

Figure 7. Activation (left) and formation energies (right, relative to LTP) against the polyhedra volumes of LiO6 octahedra in LiSi0.2Ti1.8(PO4)3. D


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Figure 8. Activation (left) and formation energies (right, relative to LTP) against the polyhedra volumes of LiO6 octahedra in LiX0.2Ti1.8(PO4)3.

Table 3. Formal Charges qIon and Shannon Radii rIon31 for Cations X, Activation Energies Ea for Vacancy Migration, and Volumes of LiO6 Octahedra in LixX0.2Ti1.8(PO4)3 (LXTP)a qIon

X

rIon [Å]

3+ 4+

Al Si

0.535 0.40

Ge

0.53

Sn

0.69

Ti Zr

0.61 0.72

Hf

0.71

Mo

0.65

Nb

0.68

Ta

0.64

Bi

0.76

5+

path B ↔ A 5 3 5 3 5 3 5

↔ ↔ ↔ ↔ ↔ ↔ ↔

6 4 6 4 6 4 6

3 5 3 5 3 5 3 5 3 5 3 5

↔ ↔ ↔ ↔ ↔ ↔ ↔ ↔ ↔ ↔ ↔ ↔

4 6 4 6 4 6 4 6 4 6 4 6

Ea→ [eV]

Ea← [eV]

VA [Å3]

VB [Å3]

0.43 0.39 0.39 0.40 0.43 0.45 0.48 0.41 0.55 0.47 0.46 0.49 0.71 0.45 0.73 0.44 0.75 0.46 0.50 0.54

0.35 0.48 0.32 0.52 0.37 0.51 0.45 0.41 0.41 0.50 0.40 0.49 0.53 0.41 0.47 0.41 0.49 0.43 0.56 0.39

14.63 14.84 15.19 14.86 14.89 14.76 14.45 14.66 14.57 14.38 15.71 14.21 14.52 14.77 14.44 14.61 14.50 14.44 14.92 14.10

15.28 14.22 15.49 14.15 15.12 14.30 14.61 14.66 14.87 14.35 14.60 14.32 14.87 14.67 15.12 14.64 15.18 14.44 14.43 14.63

considered for charge balance in compositions with trivalent substitutional elements may lead to interstitial migration. At first a most stable interstitial position for this additional Li ion has to be found: calculations with different Li positions reveal that the additional Li is preferably located next to the substitutional Al. This location is found to be by 0.2 eV more stable than other locations in the unit cell. As shown in Figure 9, the additional Li(7) atom occupies the M1/2 site


Figure 9. Crystal structure of Li1.2Al0.2Ti1.8(PO4)3. The dark red sphere is the Al ion.

Table 4. Activation Energies and Volumes of LiO6 Octahedra in Li1.2Al0.2Ti1.8(PO4)3a path B ↔ A

Ea→ [eV]

Ea← [eV]

VA [Å ]

VB [Å ]

1↔2 6↔1 5↔6

0.47 0.45 0.43

0.46 0.44 0.35

14.40 14.56 14.63

14.57 14.63 15.28

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(Wyckoff position 36f),which was already mentioned above for the triclinic distortion for larger cations, and it induces the neighboring Li(4) atom to displace from the M1 site to another neighboring M1/2 position. Every M1 site is surrounded by six M1/2 sites, as illustrated in Figure 10. The Li(5) ion is also affected by the additional ion and displaced from its M1 position. To investigate only the influence of the additional Li atom not affected by the substitution by Al on the migration path, a LTP structure containing one additional interstitial Li atom has been constructed, and a MEP of an interstitial M1/2−M1/2 jump has been calculated with the NEB-DFT approach. As shown in Figure 10, every M1 site is surrounded by six M1/2 sites, which are arranged in a buckled hexagonal ring. The relaxation of this structure leads to the occupation of opposite M1/2 ring positions by two Li ions so there is one up and one down interstitial M1/2 site occupied by a Li ion. The shortest

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LTP, but all of the other energy barriers turn out to be higher than in LTP. All activation-energy and polyhedra-volume results for the tri-, tetra-, and pentavalent substitution elements are compiled in Table 3 for comparison. Interstitial Migration. Li1+xAlxTi2−x(PO4)3 (LATP) is known as the best ionic conductor among the NZP-based structures at present.32,33 The additional Li that has to be E


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Figure 10. M1/2 sites (yellow) around one M1 site (green). The up and down sites of the buckled hexagonal ring are denoted by u and d.

Figure 12. MEP for the migration step up (down/up) → down (down/ down) in LTP.

migration path between two distinct hexagonal rings is from a down site (initial down/up configuration) to an up site (final up/ down configuration). This is illustrated in Figure 11. The energy

Figure 13. MEP for the migration step down (down/down) → up (up/ down) in LTP.

the 12 Ti atoms in the supercell to study the local influence of the substitutional element on the Li migration path. All of the investigated Li migration paths for vacancy migration indicate a correlation between the polyhedra volumes surrounding the considered Li ion and the activation energy for its migration (Figures 4, 7, and 8). The energy barrier for moving a Li vacancy to a large polyhedron is lower because a Li ion moves to a smaller polyhedron simultaneously. Furthermore, in all of the compounds, the structures with a vacant Li position inside a larger polyhedron are more stable (Figure 8). This is because O atoms bind the Li+ ion stronger in smaller than in larger polyhedra cages due to the 1/r dependence of the electrostatic Coloumb interaction. The rather strong deviation of the relative formation-energy values for the compound containing Mo (−2 and −2.2 eV) relative to LTP in contrast to all others having values within ±0.05 eV around 0 eV (Figure 8) comes from the fact that it is a transition-metal element, and in contrast to all of the other considered X elements it can exist in even higher oxidation states than 4+, which allows it to compensate the missing charge. As Martinez et al. already showed by X-ray diffraction (XRD) and electrical impedance spectroscopy (EIS),17 there exists a relationship between the activation energy and the bottleneck in the migration path in NZP structures. In the rhombohedral structure, this bottleneck is formed by three oxygen ions, which form a lateral face of a LiO6-octahedron, and therefore it depends directly on the size of the octahedron. Their activation energy results for the pure and mixed compounds with Ge, Ti, Sn, and Hf as tetravalent ions are close to our results and therefore show the same correlation between crystal structures

Figure 11. MEP for the migration step down (up/down) → up (up/ down) in LTP. The light green spheres are the positions of the mobile Li ion during the migration, while the dark green ones are the positions of the neighboring Li ions, which relax from M1/2 to M1 or displace from M1 to M1/2, respectively.

barrier of 0.19 eV for this migration step is significantly lower than that for vacancy migration in LTP (Figure 5). This interstitial migration mechanism is limited to a one-dimensional path. For a three-dimensional diffusion, an exchange between the six M1/2 is necessary to change the migration direction. The change of an up/down to a down/down configuration as indicated in Figure 12 has an energy barrier of 0.20 eV, which is still lower than that for a vacancy migration in LTP (Figure 5). Figure 13 shows the migration path starting from the transition state down/down configuration shown in Figure 12 to a stable up/down configuration with an energy barrier of 0.08 eV. As described above, the interstitial Li ion in LATP is by about 0.2 eV favored to occupy a M1/2 position next to an Al substitutional; hence for Li interstitials next to Al substitutionals this energy barrier has also to be taken into account and leads to a slight trapping of Li next to Al.

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DISCUSSION The influence of substitution of Ti by various isovalent and aliovalent cations on the migration of Li ions in LiTi2(PO4)3 has been investigated in detail. This has been done in two distinct ways: by complete substitution of all 12 Ti atoms in the supercell by tetravalent atoms, and by substituting just one of F


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of M1/2 sites at higher temperatures that reduces the correlation effects of Li ion migration.14,38−40 Although we find that bulk diffusion is only slightly changed by substitution, it may still alter the diffusion behavior of Li ions at finite temperature due to, for example, a different thermal expansion or a different anharmonic behavior of oxygen atoms. However, for LATP, Arbi et al. showed that the thermal expansion of LATP is very similar to that of pure LTP.37 We therefore conclude that the microstructure should have a more important influence on diffusion processes in the investigated compounds. One reason for the enhanced conductivity in LATP was pointed out by Duluard et al., who suggested a large influence of sintering parameters on the composition, microstructure, and conductivity of ceramic pellets.34 Further investigations on influences of grain boundary (GB) resistance on the diffusion have been done by Kosova et al.41 and Mariappan et al.42,43 Adachi et al. have reported values of 0.29 eV for activation energy for bulk diffusion and 0.46 eV for GB diffusion in LTP.12 Their experimental value for the bulk conductivity is significantly lower than ours obtained by DFT calculations (Table 3), but also lower than the experimental values by Martinez et al.17 Furthermore, Gellert et al. pointed out that also amorphous intergranular films can cause higher activation energies.44 This was also mentioned by Arbi et al.45 In LATP a secondary amorphous phase surrounding the grains is formed during the ceramic processing, and it increases the conductivity in the grain interior, but only up to that of a composition Li1.2Al0.2Ti1.8(PO4)3. If the content of Al is higher than 0.2, the conductivity in the grain interior does not change further, but the formation of secondary phases Li4P2O7 and AlPO4 is observed.14,46

and energy barriers. Duluard et al. mentioned as well the bottleneck between the M1 and M2 sites as a limiting factor of diffusion.34 They argued that the substitution by trivalent atoms like Al contributes to an opening of the bottleneck in LATP by the increase of the Li concentration. This can result in a higher diffusion than in LTP. Opening the bottleneck by bringing in larger cations just works up to a certain degree, and then local distortions begin to influence the ion conductivity. These distortions can lead to a local trapping of Li ions,35 but also to a trapping of vacancies in large octahedra, as our results show for LiSi0.2Ti1.8(PO4)3 as indicated (Figures 6 and 7) where the vacancy at position Li(5) is around 0.2 eV more stable than that at Li(3). There are two strategies for enhancing conductivity: increasing the mobility of charge carriers or increasing their concentration. Substitution by trivalent cations leads to an increase of the Li concentration for charge neutrality. At first the position of these interstitial Li atoms has to be identified. Contrary to the assumption of Duluard et al.34 and Martinez et al.17 that the additional Li ion (Li(7)) occupies an M2 position (Wyckoff position 18e), from our results we propose that the additional Li atom is placed at a midway M1/2 position (Wyckoff position 36f) between M1 and M2 sites (Figure 9). This possibility is further supported by high-resolution neutron diffraction (ND) experiments.36 To reduce electrostatic repulsion, the neighboring Li ion at the M1 site (Li(4)) is also displaced to an M1/2 site.37 Moreover, Francisco et al. argue that the room-temperature ion conduction of LiGe2(PO4)3 (LGP) can be increased by 3 orders of magnitude by substitution of Ge by Al.35 Because Ge4+ (0.53 Å) and Al3+ (0.535 Å) have nearly the same ionic radii, there must be an influence of the additional Li+, which is required for charge neutrality. In contrast, our results show that vacancy migration is apparently not influenced by additional Li atoms. As given in Table 3, the activation energy in LATP and LGTP for the migration path 5 → 6 of the vacancy is 0.43 eV for both; for the reverse direction 6 → 5 it is 0.35 eV for LATP and 0.37 eV for LGTP. The involved LiO6 octahedra have slightly different sizes, 14.63 and 15.28 Å3 (14.89 and 15.12 Å3) for LATP (LGTP). So the additional Li ion influences the mobility only slightly by opening the bottleneck, which results in a decrease of the activation energy by 0.02 eV. However, this does not explain the increase of conductivity by 3 orders of magnitude if we assume migration of vacancies. Another result of Arbi et al. is the temperature dependence of the activation energy for the bulk conductivity in LTP and LATP.36 They argue that the Li mobility is triggered by a distortion due to local vibrational motion of O ions, and the thermal displacement parameters for O ions obtained from Rietveld analysis increase considerably above 250 K. The observed activation energies decrease from 0.27 eV in LATP to 0.18 eV at 250 K and higher temperatures. In LTP the same behavior is observed, but the activation energies drop from 0.31 to 0.21 eV. These lower values at higher temperatures fit very well to the 0.19 eV that we obtained for the interstitial diffusion in LTP (Figure 11) for the migration of Li between two M1/2 sites. If the increase of temperature leads to the occupation of M1/2 sites by Li atoms, as discussed in Arbi et al.36,37 and as described above, the dominant diffusion mechanism is Li migration beween M1/2 sites, which essentially resembles the interstitial Li migration mechanism. Another possible explanation for the improvement of conductivity is the creation of M1 vacancies and occupation

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CONCLUSION Li-based NZP-type compounds are promising materials for electrolytes in all-solid-state Li ion batteries. Ionic conductivity is governed by the microstructure of a material, but also by local crystal-chemical factors such as the coordination as well as the concentration of mobile Li ions. The influence of the local structure of substitution variants of LiTi2(PO4)3 on the mobility of Li ions has been analyzed by means of MEP calculations based on DFT. In particular, we investigated the direct influence of tri-, tetra-, and pentavalent cations substituting Ti ions in the crystal structure of LTP on the migration of Li vacancies. There exists a direct correlation between the size of the LiO6 octahedra of the mobile Li ions and the energy barrier for jumps of the Li ions. Larger polyhedra volumes lead to lower activation energies because of two effects: the size of the bottleneck in the diffusion path depends directly on the polyhedron volume, so larger octahedra lower the energy barrier for Li ions leaving such positions. Also, vacant positions are more stable than occupied ones in large octahedra; thus the occupation with a vacancy is also favored. The replacement of Ti by ions of different sizes leads to a splitting of LiO6 octahedra, which results in different regions in the structure with activation barriers for the ionic migration between 0.29 and 0.75 eV instead of 0.41 eV in LTP. Yet altogether this does not lead to an enhancement of the Li mobility. The sizes of LiO6 octahedra size vary between 14.10 and 15.49 Å3; in the unsubstituted structure of LTP they have a size of 14.66 Å3. Substitution by trivalent atoms such as Al or lithiation influences the mobility by increasing the density of Li ions in the material, but also by causing additional interstitial migration with lower activation energies. Besides bulk G


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conductivity, there is grain-boundary conductivity, which is the rate-determining step for diffusion. Hence, for understanding the conductivity of ceramic ion-conducting materials further, atomic-scale investigtions of migration paths and barriers for Li vacancies and interstitials along and across grain boundaries are desirable.

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AUTHOR INFORMATION

Corresponding Author

*E-mail: [email protected]. Notes

The authors declare no competing financial interest.

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ACKNOWLEDGMENTS This work was funded by the German Research Foundation (DFG Grant no. El 155/26-1). B.Z. receives financial support by the Hans L. Merkle foundation of Robert Bosch GmbH. Structure figures were prepared with VESTA.47 This work was performed on the computational resource ForHLR Phase I funded by the Ministry of Science, Research and the Arts Baden-Württemberg and DFG ("Deutsche Forschungsgemeinschaft").

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Lithium Ion Conduction in LiTi2(PO4) - American Chemical Society

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