Conduction and Surface Effects in Cathode Materials: Li8ZrO6 and

Article pubs.acs.org/JPCC

Conduction and Surface Effects in Cathode Materials: Li8ZrO6 and Doped Li8ZrO6 Shuping Huang,†,§ Yuan Fang,‡ Bo Wang,† Benjamin E. Wilson,‡ Nam Tran,‡ Donald G. Truhlar,*,† and Andreas Stein*,‡ †

Department of Chemistry, Chemical Theory Center, and Minnesota Supercomputing Institute, 207 Pleasant Street SE, University of Minnesota, Minneapolis, Minnesota 55455-0431, United States ‡ Department of Chemistry, 207 Pleasant Street SE, University of Minnesota, Minneapolis, Minnesota 55455-0431, United States § College of Chemistry, Fuzhou University, Fuzhou, Fujian 350108, P. R. China S Supporting Information *

ABSTRACT: Doped Li8ZrO6 (LZO) is a pseudolayered material under consideration for lithium-ion battery cathodes and solid electrolyte coatings. The effects of doping LZO with Ce, Ti, Mg, Nb, and Y on structure, band gaps, conductivity, and activation energy for ion migration are investigated both experimentally and by quantum mechanical calculations. Optical band gaps decrease for all doped materials compared to undoped LZO. While all dopants reduce the electronic conductivity at room temperature slightly, doping with Mg or Nb increases ionic conductivity by an order of magnitude. Introducing a high loading of Nb into LZO decreases the activation energy for Li-ion diffusion in the 22−120 °C range. Calculations on lithium-ion diffusion in LZO show that it occurs by a polaron−vacancy complex mechanism. The energy barrier is lowest for the lithium hopping in a zigzag fashion between tetrahedral voids within adjacent layers. The diffusion barrier is reduced as the number of Li vacancies increases during battery charging. We calculated surface energies for 10 surfaces, and we find that the most stable surface is the (001) surface with the tetrahedral Li layer being exposed. The delithiation energy on the (001) surface was found to be slightly higher than that in the bulk. The Li-ion diffusion barriers from the surface to the bulk were also calculated on the (001) surface, and the diffusion energy barrier across the (001) surface was found to be smaller than the energy barrier along the (001) direction in the bulk, and also lower than the barrier for the lowest-energy path in the bulk (which is a hop between tetrahedral voids in adjacent layers as shown in the related graphic). These characterizations of surface and doping effects will assist future materials design. been investigated for many electrode materials.14−17 To increase the conductivity and specific capacity of Li8ZrO6, the effect on electrochemical delithiation and relithiation of doping with Mn2+, Fe3+, Co2+, Ni2+, Cu2+, and Ce3+ was investigated.18 The effect on the high-temperature conductivity of doping Li8ZrO6 with Ce, Nb, Mg, Sr, and Y was also studied in previous papers.19−23 However, most lithium-ion batteries operate at room temperature, so it is important to study the properties of doped Li8ZrO6 at room temperature and to develop a better understanding of the lithium-ion diffusion processes in these materials. It is important to understand the location and stability or instability of the dopants in the lattice in order to understand the role of the dopant in conduction.24 Quantum mechanical calculations can be used to discover the paths for lithium-ion diffusion and the associated energy barriers, which are the most important parameters affecting the diffusion rates. For example, in the study of Li diffusion in LiTiS2,25 Li ions were found to hop between neighboring octahedral interstitial sites of the TiS2 host by passing through

1. INTRODUCTION The further development of portable electronic devices, electric vehicles, and smart grids requires electrical energy storage devices with higher energy and power densities. One of the state-of-the-art electrical energy storage devices is the lithiumion battery (LIB),1−6 and some major issues in further development of LIBs are the identification of new electrode materials with higher specific capacities and the development of safer electrolyte systems, including solid electrolytes. One potential class of materials under consideration for LIB cathodes and also as a solid electrolyte coating is based on Li8ZrO6 (LZO) and related lithium zirconate phases.7−11 LZO is a pseudolayered material with a high lithium-to-mass ratio and is thermodynamically stable against decomposition in contact with lithium.12 In a previous paper,13 we showed that nanosized yttrium-doped Li8ZrO6 (LZO) in intimate contact with a conductive carbon phase exhibits an initial specific capacity of over 200 mAh/g, higher than that of the currently used cathode materials LiCoO2, LiFePO4, and LiMn2O4. However, because of the low room-temperature conductivity of LZO, a large polarization effect was observed. Doping has long been an important strategy to tune the electronic and ionic conductivity of materials, and doping has © XXXX American Chemical Society

Received: February 28, 2016 Revised: April 12, 2016

A

DOI: 10.1021/acs.jpcc.6b02077 J. Phys. Chem. C XXXX, XXX, XXX−XXX

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The Journal of Physical Chemistry C

temperature is so low that many commercial impedance instruments are unable to perform the measurement. An alternative method is dc polarization, which uses the time response of a dc current passing through the mixed conductor to obtain the ionic and electronic contribution,36 and this method was used in the current study. Doped or undoped LZO materials were ground into fine powders and pressed into pellets using a hydraulic press at a ram pressure of 10 tons for 5 min. Each pellet contained ∼0.20 g of sample and had a diameter of 12.7 mm and a typical thickness of ∼0.8 mm. Both sides of the pellet were coated with Ag paste. Room-temperature measurements were conducted with a metal holder tightened with springs. For activation energy measurements, the pellet was placed between two current collectors, insulated with Kapton film, fastened with clips, and then placed in a temperature-controlled oven. A potential of 0.1 V was applied, and the current was recorded over time with a CHI 600C potentiostat. 2.4. Density Functional Calculations. We have no evidence that delithiation or doping creates a new phase under the conditions employed in our experimental work. Therefore, we model all systems as single-phase solid solutions, not as two-phase mixtures. All calculations were carried out using a combination of software packages, in particular a locally modified version of VASP,37,38 BAND,39 and CM5PAC.40 The VASP calculations used a 650 eV cutoff energy. A 6 × 6 × 6 Monkhorst−Pack k-point mesh was used for the calculations on the primitive cell, and the k-point grid was reduced to 3 × 3 × 2 in calculations of the supercell, which is a 2 × 2 × 1 repetition of the conventional cell. For the primitive cell, Li8ZrO6, the lattice parameters are a = 6.009 Å, b = 6.009 Å, c = 6.009 Å, α = 53.85°, β = 53.85°, and γ = 53.85°, and the volume is 131.37 Å3. For the conventional unit cell, Li24Zr3O18, the lattice parameters are a = 5.455 Å, b = 5.455 Å, c = 15.393 Å, α = 90.00°, β = 90.00°, and γ = 120.00°, and the volume is 396.75 Å3. The projector augmented wave (PAW) potentials41,42 provided in the VASP package were used in all calculations. We used three exchange-correlation functionals: PBE,43 N12,44 HSE06,45 and we also used PBE+U. The PBE+U calculations involve using the PBE exchange-correlation functional with an empirical Hubbard-model correction, designated as U−J, to the Coulomb and exchange integrals.46 We set U−J = 6.0 eV for oxygen p orbitals, as justified in our previous publications.13,18 We do not apply U−J to Zr4+, Ti4+, Y3+, Nb5+, Ce4+, and Mg2+ because formally the valence spaces of these ions do not involve d electrons, and d electrons make negligible contributions to the tops of the valence bands in those cases. This was verified by the small influence of a U−J value applied to Zr 4d orbital on the voltage and the energy gap of LZO at the Γ point (shown in Table S1 in the Supporting Information). The HSE06 functional has screened nonlocal Hartree−Fock (HF) exchange (decreasing from 25% at small interelectronic separation to zero at large interelectronic separation), and it has a small average error (0.3 eV) in predicting the gaps of 31 semiconductors.47,48 The calculated band gap of ZrO2 by HSE06 is in good agreement with the experimental gap,13 but the HSE06 functional overestimates the band gap of LZO, which may be due to the presence of Li. The overestimate implies that 25% HF is too high to reproduce the band gap of LZO. The HSE functional with 17.5% HF exchange at small interelectronic separation gives a gap of 6.1 eV, which may be

an adjacent tetrahedral site. Furthermore, the overall diffusion rate was studied by kinetic Monte Carlo methods and was found to depend on the number of vacancies.25 Lithium diffusion has also been studied in LixCoO2,26 rutile,27 spinel LiMn2O4,28 LixMPO4 (M = Mn, Fe, Co, Ni) olivine structures,29,30 and Li3PO4.31 Size control and morphology control of the particles that make up the cathode offer possibilities to tune battery properties and increase conductivity. Because the surface-tovolume ratio is increased by making smaller particles, it is important to understand to what extent Li-ion mobility and delithiation voltages are increased or decreased near surfaces. For example, the energies of various surfaces were studied in previous work for LiFePO4,32 and it was found that (i) the (201) surface has the lowest surface energy, and (ii) the voltage for some surfaces is significantly lower than that for the bulk. There are also some studies of size effects on the conductivity in TiO2.33 The diffusion mechanisms in LZO and the surface effects on diffusion have not previously been studied in detail. In the current study, we investigate the effects of doping on the lattice structure, band gap, conductivity, and activation energy for ion migration in LZO. We also study Li-ion diffusion in LZO and surface effects on Li diffusion of LZO by electronic-structure calculations employing quantum mechanical density functional theory (DFT).

2. METHODS 2.1. Synthesis of Doped or Undoped LZO. Conductivity is sensitive to defects, and the concentrations and uniformity of different kinds of defects may be sensitive to the experimental conditions during synthesis. This sensitivity can be enhanced when synthesizing doped materials, and one should keep this in mind when interpreting conductivity measurements. Therefore, we describe the synthesis method in detail. Doped and undoped LZO samples were synthesized by a modified solid-state method.34 The precursors of the Li, Zr, Ce, Ti, Mg, Nb, and Y components were LiNO3, ZrO(NO3)2, Ce(NO3)3·6H2O, TiO2, Mg(NO3)2·6H2O, Nb2O5, and Y(NO3)3·6H2O, respectively. An excess of 3 Li per formula unit was used to compensate for Li loss at high temperatures, while stoichiometric amounts were used for other precursors. The precursors were ball-milled for 10 min, and then calcined in air within an alumina crucible covered with a lid in a muffle furnace. The temperature was ramped at 2 °C/min, and held at 600 °C for 3 h, then at 800 °C for 2 h and at 900 °C for 4 h. The samples are labeled as M X, where M refers to the dopant and X to the doping level, which is specified as the number of dopant atoms per formula unit. For example, Nb 0.04 refers to Li7.96Nb0.04Zr0.96O6, prepared with 0.96 mmol ZrO(NO3)2, 0.02 mmol Nb2O5, and 10.96 mmol LiNO3. 2.2. Characterization. X-ray diffraction (XRD) patterns were obtained using an X’Pert Pro diffractometer with a Co anode (λ = 0.1789 nm). UV−vis spectra were collected with a Thermo Evolution 220 spectrometer. Band gaps were determined using the Kubelka−Munk transformation and a Tauc plot, similarly to our previous paper.13 Photoluminescence spectra were collected with a HORIBA SPEX 1680 double spectrometer. 2.3. Conductivity Measurements. The conventional method to determine the conductivity of a mixed ionic− electronic conductor is to measure the impedance spectrum.15,35 However, the conductivity of Li8ZrO6 at room B


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The Journal of Physical Chemistry C compared to a gap of 6.8 eV with 25% HF exchange at small interelectronic separation. However, the HSE06 functional with 25% HF exchange at small interelectronic separation provides good voltage data and a correct polaronic picture. We use 25% HF in the following work. All calculations were spin polarized. Both the coordinates of the ions and the lattice constants were optimized. The energy criterion for self-consistency was set to less than 0.0001 eV/unit cell, and the force criterion in structure relaxation was set to less than 0.001 eV/Å. For surface calculations, we only consider stoichiometric systems (only systems with the formula nLi8ZrO6). The initial unrelaxed surface structures are cut from the fully relaxed bulk crystal. The lattice parameters are fixed at their bulk values in the slab calculations. The surface energy is converged with respect to the thickness of the vacuum; a vacuum layer of 10 Å is found to be sufficient to remove any spurious interaction between the periodically repeated slabs in the surface normal direction. A surface with a given Miller index can terminate anywhere along the direction of the surface normal, and we calculated the various possibilities; for example, for the 001 surface, the termination can be oxygen, Li (tetrahedral layer), or Li + Zr (octahedral layer). The nudged elastic band (NEB)49 method was used to determine the energy barriers for Li-ion diffusion; four images were employed between two end points. In the study of Li-ion diffusion in the bulk, the lattice constants are fixed in calculations using 2 × 2 × 1 supercells, whereas the lattice constants are relaxed in the calculations using primitive cells because the concentrations of Li-ion vacancies are high in the primitive cell, and the vacancies have a larger effect on the lattice constants when they are at a high concentration than when they are at a low concentration.

Figure 1. (a) Conventional unit cell of Li8ZrO6: Zr, blue ball; O, red ball; Li, yellow ball. (b) Unit cell with the lithium and oxygen atoms labeled.

Ti 0.33, Mg 0.33, and Y 0.33 did not show a single solid solution phase. Instead, peaks of Li4ZrO4, MgO, and LiYO2 as impurity phases were observed, as shown in Figure 2b. However, Nb 0.33 and Ce 0.33 formed solid solutions. In all of these samples, a small amount of Li2O or Li6Zr2O7 was present as a result of lithium excess or deficiency, respectively. The lattice parameters along the c axis (the axis perpendicular to the oxide layers) were determined from the XRD (003) peak positions, and they are compared with quantum mechanical results in Table 1. In Ti 0.33, Mg 0.33, and Y 0.33, the changes of lattice parameters were not significant, because the actual doping levels were much lower than 0.33 due to the limited solubilities. For the other two dopants, Nb caused a significant reduction of the c dimension of Li8ZrO6, whereas Ce caused an increase of the c dimension. This trend is consistent with the quantum mechanical results, and it follows the trend of increasing ionic radius in the series Nb5+ (78 pm), Zr4+ (86 pm), and Ce4+ (101 pm). 3.2. Band Structure: Theory and Experiment. The band structure affects the electronic conductivity of a material, and therefore, it is an important design parameter for electrodes and solid electrolytes. The effect of doping on the band structure of Li8ZrO6 was characterized using UV−vis spectroscopy. All dopants characterized here had a low doping level (0.04) to ensure phase purity (see Figure S1 in the Supporting Information). As shown in Figure 3a, undoped Li8ZrO6 has a band gap of 5.76 eV, estimated using the Kubelka−Munk transformation and a Tauc plot (Figure 3b).50,51 Whereas Mg and Y dopings change the band gap by less than 0.6 eV, Nb and Ce dopings cause a red shift of the absorption edge, indicating a decreased band gap by 1.2 and 2.2 eV, respectively. This trend is explained by the quantum mechanical results, which show that these dopants generate empty states between the valence

3. RESULTS AND DISCUSSION 3.1. Lattice Parameters: Theory and Experiment. Figure 1 shows a conventional unit cell of LZO and the labeling of the atoms. Li8ZrO6 has a layered structure with two kinds of Li atoms. One kind of lithium atom (labeled as 2, 3, 4, 5, 6, 7, 10, 11, 12, 13, 14, 15, 18, 19, 20, 21, 22, 23) occupies the tetrahedral voids formed by the face-centered-cubic oxygen sublattice, and the other kind (labeled as 1, 8, 9, 16, 17, 24) occupies the octahedral voids formed by the face-centeredcubic oxygen lattice. All zirconium atoms are equivalent. For DFT calculations on Mg, Ce, Ti, and Nb doping, only one dopant was added in the conventional cell. For the Mg2+ dopant, we replaced two Li with one Mg. For the Ce4+ or Ti4+ dopants, we replaced one Zr with Ce or Ti. For the Nb5+ dopant, we replaced one Zr and one Li with one Nb. For the Y3+ dopant, we replaced two Zr and one O with two Y in the supercell as in the previous paper.13 We tested various positions to place the dopant and thereby determined the most stable configurations. We found that Mg prefers to replace the Li atoms in the octahedral voids. In the cases of Mg and Nb, where one more Li is replaced, the removed Li is always from a tetrahedral void that is adjacent to the dopant atom. These results show that, in the doped materials, the system tends to locally balance the charge. Experimentally, the lattice parameters of Li8ZrO6 changed slightly as dopants were introduced, resulting in changes of peak positions in XRD, as shown in Figure 2a. A relatively high doping level (0.33) was used here to make the peak shifts more obvious. At such a high doping level, due to limited solubilities, C


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Figure 2. Experimental XRD patterns of undoped and doped Li8ZrO6. (a) Peak shifts caused by dopants. (b) Impurity phases: caret (∧) for Li4TiO4, dot (•) for Li2O, plus (+) for Li6Zr2O7, asterisk (*) for MgO, and number sign (#) for LiYO2.

Table 1. Lattice Parameter c (in pm) for Undoped and Doped LZOa material

exptl

PBE

HSE06

undoped Ce 0.33 Ti 0.33 Mg 0.33 Nb 0.33 Y 0.33

1545 1562 1542 1545 1537 1545

1555 1577 1539 1558 1545 1564

1537 1558 1521 1540 1528 1550

metal current collectors during the measurements; thus, a double-layer capacitor Ci is in series with Ri. Grain boundaries act as a parallel set of resistor and capacitor, which are labeled Rgb and Cgb, on the ionic conduction pathway. The geometrical capacitance of the whole pellet, Cgeom, is very small and should be fully charged over a very short time period, so its effect on the overall current response over time is negligible, and it is omitted from the equivalent circuit. Thus, the equivalent circuit of the pellet is as shown in Figure 4. The current response of this circuit for a constant applied potential U is derived in the Supporting Information. The result derived there is

a

Note that experimentally Ti 0.33, Mg 0.33, and Y 0.33 were not pure phases and the actual doping levels were much lower than 0.33. The other dopants formed solid solutions. For quantum mechanical results, the doping level was consistently 0.33 for all dopants except for Y, the doping level of which was 0.17. The theoretical data are from PBE and HSE06 calculations.

i = i0 + A1e(−t / t1) + A 2 e(−t / t2)

where i is the current; t is the time; and i0, A1, A2, t1, and t2 are fitting parameters. The electronic and ionic conductivities, σe and σi, and the total conductivity, σt, are related to the fitting parameters by

and conduction bands of Li8ZrO6, thus decreasing the band gap. Ti 0.04 was found to be photoluminescent, and the photoluminescence spectrum provides details about its band structure. The spectrum is shown in Figure 3c; the excitation peak at 267 nm is assigned to the transition from the valence band to the conduction band. The emission spectrum shows two peaks, one at 402 nm and the other in the red part of the spectrum out of the wavelength range of the instrument; these are assigned to transitions from the dopant states to the valence band and from the conduction band to dopant states, respectively. The energy values of these peaks correspond well with the quantum mechanical band diagram of Ti-doped Li8ZrO6, as shown in Figure 3d. Table 2 summarizes the experimental and theoretical band gap values for various dopants. 3.3. Conductivity Measurements. Both lithium ions and electrons have to reach interfaces to facilitate the following electrode reaction: +

Li8ZrO6 → Li6ZrO6 + 2Li + 2e

(1)

σe =

d AR e

σi =

d AR i

(2)

and

σt = σe + σi

(3)

In these equations, d is the thickness of the pellet, A the area of the pellet, and Re =

U i0

(4)

U A1 + A 2

(5)

and

Ri =

A related approach to measuring both ionic and electronic conductivities of a mixed conductor under a constant dc potential was reported previously.16 Compared to that method, the approach taken here has two major advantages. First, rather than using only the starting and ending data points for the total and electronic current, our method makes use of all data points. Second, it saves time because there is no need to wait for the capacitors in the equivalent circuit to be fully charged. This is especially significant when the material has a low conductivity. The typical current responses of undoped and doped Li8ZrO6 samples are shown in Figure 5, and the corresponding ionic, electronic, and total conductivities are listed in Table 3.

−

In a previous report,13 a large overpotential was observed for a Y-doped Li8ZrO6/C nanocomposite, and this may indicate that Li8ZrO6 suffers from poor conductivity at room temperature. In the present study, the ionic and electronic conductivities were measured by applying a constant dc potential on a pellet, and the system was modeled using an equivalent circuit given by Huggins.35 Because Li8ZrO6 is a mixed ionic and electronic conductor, the ionic and electronic resistances, Ri and Re, are in parallel. Ions are blocked at the interface of the Li8ZrO6 and the D


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Figure 3. Optical characterization of undoped and doped LZO: (a) UV−vis spectra, (b) determination of the band gap using the Kubelka−Munk transformation and Tauc plot, (c) photoluminescence spectra of Ti 0.04, and (d) photoluminescence wavelengths from the quantum mechanical band structure of Ti-doped LZO.

Table 2. Band Gaps (in eV) of Undoped and Doped LZOa material

exptl

PBE

HSE06

undoped Ce Ti Mg Nb Y

5.75 3.55 3.06 5.57 4.56 c

4.93 2.54 3.40 4.47 3.40 3.02

6.8 4.72b 5.35b 6.39b 5.15b 4.54d

a

The band gap value of Ti 0.04 was calculated from photoluminescence spectra, and the other experimental values were calculated from the UV−vis spectra using the Kubelka−Munk transformation and a Tauc plot. The experimental doping level was 0.04, while the doping level used for quantum mechanical computations was 0.33 for Ce, Ti, Mg, and Nb and 0.17 for Y. b Conventional cell calculation. The gap is indirect. cThe band gap of Y 0.04 was difficult to estimate because of sample fluorescence. dΓ-point calculation on the supercell.

Figure 4. Equivalent circuit of a pellet of bulk Li8ZrO6.

will see below that there is a significant change in activation energy). Other dopants have no or negative effects on ionic conductivity. Lithium vacancies are not favored in the case of Y doping, and although our previous quantum mechanical calculations predicted that the Li-ion diffusion barrier is smaller in Y-doped LZO than in LZO, the present experiments show that the ionic conductivity is reduced by almost 1 order of magnitude by Y doping. The performance improvement by Y doping in our previous paper was the result of smaller crystallite size rather than conductivity change.13 On the other hand, all dopants listed here had a slightly negative effect on electronic conductivity. Although the band gap of Li8ZrO6 was reduced by Ce, Ti, and Nb doping, as characterized by UV−vis and photoluminescence measure-

A low level (0.04) of Mg or Nb doping improves the roomtemperature ionic conductivity of LZO by an order of magnitude. A similar trend was observed in some hightemperature measurements.19 To balance the charge, the introduction of Mg or Nb results in the formation of lithium vacancies, which increases the total number of charge carriers. However, further increasing the Nb doping level to 0.33 gives only a very slight increase in ionic conductivity (although we E


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Figure 5. Typical current response of undoped and doped LZO: (a) comparison between different dopants at a low doping level of 0.04 and (b) comparison between different doping levels of Nb.

Table 3. Conductivity of Undoped and Doped Li8ZrO6 σe (S/cm)

material undoped Y 0.04 Ce 0.04 Ti 0.04 Mg 0.04 Nb 0.04 Nb 0.33

(8.6 (2.4 (3.0 (6.8 (3.9 (4.4 (4.8

± ± ± ± ± ± ±

2.6) 0.8) 0.4) 3.0) 1.3) 1.3) 1.8)

× × × × × × ×

σi (S/cm)

10−11 10−11 10−11 10−11 10−11 10−11 10−11

(4.7 (8.3 (2.5 (3.5 (2.6 (2.8 (3.7

ments, the conductivity was not improved. This implies that the electronic charge carrier density is determined extrinsically by impurities and/or lithium vacancies rather than by the band gap for Li8ZrO6. In other words, the band gap is still not small enough to bring about a significant contribution from intrinsic electronic conductivity. The slight decrease is attributed to the reduced charge carrier mobility, since charge carriers are scattered by the dopants. As compared with other well-studied electrode materials of lithium-ion batteries, including LiFePO4, LiMn2O4, and Li4Ti5O12,15,16,52 both the ionic and the electronic conductivities of Li8ZrO6 are much lower, even with Mg or Nb doping, as shown in Table 4. This explains the large overpotential observed in our previous paper.13

material

ref

σe (S/cm)

σi (S/cm)

15 52 16 present

3.7 × 10−9 2 × 10−6 8 × 10−10 (8.6 ± 2.6) × 10−11

5.0 × 10−5 10−4 3 × 10−8 (4.7 ± 2.1) × 10−11

2.1) 1.9) 0.6) 1.0) 0.1) 0.3) 0.9)

× × × × × × ×

10−11 10−12 10−11 10−11 10−10 10−10 10−10

σt (S/cm) (1.3 (3.3 (5.4 (1.0 (3.0 (3.3 (4.1

± ± ± ± ± ± ±

0.2) 0.9) 1.0) 0.4) 0.1) 0.4) 1.0)

× × × × × × ×

10−10 10−11 10−11 10−10 10−10 10−10 10−10

As shown in Figure 6 and Table 5, undoped Li8ZrO6 has an activation energy of 0.50 eV, which is in very good agreement with the energy barrier of lithium diffusion calculated using PBE+U. This indicates that, at room temperature, Li8ZrO6 is an extrinsic ionic conductor. The number of ionic charge carriers could be considered as a constant in this temperature range. Doping with Nb lowered the activation energy for lithiumion diffusion and also increased the ionic conductivity. In particular, for Nb 0.33, the activation energy was reduced from 0.50 to 0.36 eV. However, at a low doping level of 0.04, for both Nb and Mg, the activation energy was almost unchanged. The improved ionic conductivity can be attributed to the introduction of lithium vacancies. 3.5. Lithium-Ion Diffusion Calculations. 3.5.1. LithiumIon Diffusion in the Bulk. In bulk Li8ZrO6, the Li-centered tetrahedra in the same layers share vertices, and Li-centered tetrahedra in different layers share edges. The Li octahedral ions occupy sites next to the Zr octahedral ions with shared edges, and the Li octahedra and Li tetrahedra sites are edge sharing or vertex sharing. Figure 7 shows the relative positions of Li and Zr atoms. The Li tetrahedral sites form two layers of a 2D triangular lattice (bottom is T1 and top is T2). The Li octahedral sites and Zr sites (labeled as Oh) are above the T1 and T2 lattices, separated by an O layer. We tested the Li-ion diffusion (or vacancy diffusion) in (i) Li7ZrO6 in which only one lithium atom is removed from a primitive unit cell, (ii) Li95Zr12O72 in which one lithium atom is removed from the supercell, and (iii) Li94Zr12O72 in which two lithium atoms are removed from the supercell. The primitive cell is shown in Figure 8a, and a part of the supercell is shown in Figure 8b. There are four possible Li (vacancy) hopping paths: path 1, T1 to T1 (or T2 to T2); path 2, T1 to T2; path 3, Oh to Oh; and path 4, Oh to T1 (or T2). The barriers on the various

Table 4. Comparison of Electronic and Ionic Conductivities of Li8ZrO6 and Other Electrode Materials LiFePO4 LiMn2O4 Li4Ti5O12 Li8ZrO6

± ± ± ± ± ± ±

3.4. Activation Energy of Ionic Conduction. In order to gain a better understanding of lithium-ion diffusion in LZO, the activation energies of ionic conduction were measured for undoped, Mg-doped, and Nb-doped LZO in the temperature range 22−120 °C. The activation energy, Ea, was calculated by fitting ionic conductivity data using the following equation: σ σ = 0 e(−Ea / kT ) (6) T F


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Figure 6. Measurement of activation energies for lithium-ion diffusion in undoped and doped LZO: (a) typical current responses of undoped LZO at 22, 40, 60, 80, 100, and 120 °C, and (b) fitting of data with eq 6.

basis of our previous work13,18 to be more realistic for this problem, yields a localized hole, i.e., a small-polaron hole, close to the Li vacancy in Li7ZrO6. Polaronic diffusion has also been implicated in other cathode materials, such as LiNiO2, LiMnPO4, LiFePO4, and LiCoO2, and in lithium peroxide, and has been well-studied. 54−61 The present PBE+U calculations indicate that Li hopping is accompanied by an electron hopping between nearby transition metal ions. In other words, when Li moves, the accompanying hole polaron migrates in a concerted fashion. Therefore, the diffusion of Li ions is the diffusion of a polaron−vacancy complex, where the vacancy is a Li vacancy. Strong coupling of lithium-ion transport to electron transport is also known in other cathodic materials,54,56 and in titania anodes.62−64 Among the various possible diffusion paths, there are three possible diffusion processes depending on the relative motion between the vacancy and the bound polaron: single diffusion process, in which the Li ion moves while the polaron remains at the same site; side-by-side process, in which the Li ion moves and the polaron diffuses side by side; and cross process, in which the Li ion moves and the polaron diffuses in a direction that crosses to the trace of the Li ion. Table 6 lists the activation barriers and polaron hopping distances of various Li diffusion pathways for Li7ZrO6 as calculated by PBE+U. Diffusion between different layers (as illustrated in Figure 10) is easier than diffusion in the same layer; the zigzag nature of the optimal diffusion path is one feature of the results that is the same in the PBE, N12, and PBE +U calculations. The diffusion barrier for a polaron−vacancy complex as calculated by PBE+U is higher than that found for Li diffusion as calculated by PBE and N12. This can be rationalized by considering that in the PBE and N12 calculations the hole is delocalized over all the oxygens close to the Li vacancy; therefore, a very small charge migration occurs, and a smaller barrier is found. In other words, the formation of the hole polaron impedes the ionic diffusion process. The polaron−vacancy diffusion processes in which the vacancy moves from VLi3 to VLi5 or from VLi3 to VLi6 are both cross processes in which the ion moves from a T1 site to a T2 site. The diffusion barrier from VLi3 to VLi6 is higher than that from VLi3 to VLi5 because the polaron diffusion distance is larger in the diffusion from VLi3 to VLi6. The energy barrier for the lithium atom hopping between tetrahedral voids within

Table 5. Experimental Activation Energies for Lithium-Ion Diffusion in Undoped and Doped LZO material

Ea (eV)

undoped Mg 0.04 Nb 0.04 Nb 0.33

0.50 0.47 0.52 0.36

Figure 7. Li and Zr atoms viewed along the (001) direction. Zr is in blue, and Li is in yellow (T) and orange (Oh), where T denotes a tetrahedral site and Oh denotes an octahedral one. Arrows labeled 2a and 2b show two different paths for Li hopping between T1 and T2 layers.

pathways for Li7ZrO6 were calculated using PBE, PBE+U, and N12. Removal of a Li atom creates a Li-ion vacancy and a hole. The creation of a hole is a partial oxidation resulting in a mixedvalence state. In most lithium metal oxides, the species oxidized are variable-valence transition metals, but in LZO the oxidized species are oxygen ions. (Oxidation of oxygen is also believed to be the case in Li2MnO3.53) The PBE and N12 calculations correspond to the case where the hole is delocalized (over several oxygens). These calculations indicate that the Li vacancy prefers to stay at the tetrahedral site and that Li diffusion in the same layer has a much higher energy barrier than diffusion between different layers. The energy barrier for a lithium atom hopping between tetrahedral voids within adjacent layers is the lowest, with an energy barrier of 0.17 eV calculated using PBE and 0.24 eV using N12. The pathways calculated by PBE and N12 are shown in Figure 9. In contrast to N12 and PBE functionals which yield an itinerant hole, the PBE+U functional, which we believe on the G


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Figure 8. (a) Primitive cell of Li8ZrO6. Li1, Li2, and Li3 are in the T1 layer; Li4, Li5, and Li6 are in the T2 layer. Li7 and Li8 are in the Oh layer. (b) A part cut from the 2 × 2 × 1 supercell.

Figure 9. Energy profiles (eV) of Li7ZrO6 calculated by PBE (red) and N12 (blue) calculations.

Table 6. Barriers and Lithium and Polaron Hopping Distances of Different Li Diffusion Pathways for Li7ZrO6 by PBE+Ua Li vacancy polaron process forward barrier (eV) reverse barrier (eV) polaron hopping distance (Å) Li+ hopping distance (Å) a

VLi3 → VLi5 (T1 → T2)

VLi3 → VLi6 (T1 → T2)

VLi3 → VLi7 (T1 → Oh)

VLi5 → VLi6 (T2 → T2)

VLi5 → VLi7 (T2 → Oh)

O6 → O2 cross 0.46 0.44 3.19

O6 → O3 cross 0.58 0.56 4.50

O6 → O2 side-by-side 0.55 0.08 3.19

O2 → O3 side-by-side 1.62 1.62 3.17

O2 → O2 single 0.54 0.09 0.0

2.28

3.88

2.47

3.14

3.55

The labeling of Li and O is shown in Figure 8a. VLix denotes a vacancy at Lix.

diffusion processes VLi13 → VLi25 and VLi10 → VLi25, the polaron positions are different even though the vacancy of the final state is the same. A comparison of these processes shows that diffusion proceeding by a side-by-side process with a shorter polaron diffusion length is more favorable. Comparing the barrier in the supercell model in Tables 7 and 8, we can see that when the concentration of Li vacancies increases, the barrier decreases. Diffusion in the octahedral layer is disfavored by two factors. First, Li vacancies in this layer are energetically less favorable; second, the Zr may constrain Li-ion diffusion. Consequently,

adjacent layers is 0.46 eV by PBE+U, which is close to the experimental activation energy 0.50 eV. Next, we consider Li diffusion pathways in Li95Zr12O72 and Li94Zr12O72. Tables 7 and 8 give the activation barrier and polaron hopping distances. Table 7 shows that the side-by-side process is energetically more favorable than the cross process, even if its polaron hopping distance is larger. The most favorable process has a barrier of 0.40 eV by PBE+U (see Figure S2 in the Supporting Information). The energy difference of the initial structure and the saddle point based on the HSE06 single-point energy calculations is 0.42 eV. In the H


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I

7 → 13 is shorthand for VLi7 → VLi13. bSBS denotes side-by-side. cForward barrier. dReverse barrier. eThe polaron hopping distance in units of Å. fThe Li hopping distance in units of Å. a

O13 → O67 cross 0.60 0.10 5.45 2.48 O67 → O5 cross 0.99 0.99 5.39 3.17 O28 → O13 cross 0.66 0.66 3.25 2.87 O64 → O16 cross 0.66 0.66 3.25 2.87 O28 → O4 SBS 0.52 0.42 3.23 2.33 O13 → O1 SBS 0.40 0.40 4.48 2.28 O43 → O13 SBS 0.40 0.40 4.41 2.28 polaron processb barrierc reversed distancee distancef

O43 → O16 cross 0.52 0.52 3.29 2.33

22 → 68, (Oh → Oh) 10 → 13, (T2 → T2) 58 → 64, (T2 → T2)

where Eb is the total energy per formula unit of bulk Li8ZrO6. Es is the total energy of the given slab containing n formula units of Li8ZrO6, and S is the surface area of the slab (including both sides of the slab). Figure 11 shows the results for unrelaxed surface energies. Several surface terminations are considered. The surfaces with the two tetrahedral layer exposed are the most stable (i.e., they have the lowest surface energies). The coordination loss of Zr atoms on the surface is energetically more unfavorable than for Li, and generally a low-energy surface has fewer Zr−O bonds affected by the cut that creates the surface. We found that the (001) surface has the lowest surface energy, with an unrelaxed surface energy of 0.03 eV/Å2 calculated using PBE and 0.04 eV/Å2 using N12 functionals. To understand how the relaxation energies change with respect to the relaxation and thickness of the slab, we performed calculations on the two lowest-energy surfaces, (001) and (101). The surface energies are shown in Table 9. We found that, during the relaxation, the relaxation energy of the (001) surface is small, while the relaxation energy of the (101) surface is large. The final result is that the (001) surface has the smallest surface energy, which is 0.027 eV/Å2 for the relaxed surface. Figure 12 shows the geometries of the unrelaxed and relaxed (101) surfaces. It shows that ZrO6 octahedra rotate during the relaxation, and the relaxed structure resembles the (001) surface. Including more layers in the slab will impede this rotation and increase the relaxed surface energy. We then performed CM5 charge analysis on the relaxed (001) surface to learn how the charge distribution differs from the bulk. Table 10 shows that the Li atoms on the surface have slightly larger charges than the ones in the bulk, while the Zr atoms near the surfaces have smaller charges than the ones in the bulk. The oxygen atoms on the surface have a slightly more negative charge. The redistribution of the charge may contribute to the stability of the (001) surface.

10 → 25, (T2 → T1)

Es − nE b 2S

7 → 64, (T1 → T2)

γ=

13 → 25, (T2 → T1)

our calculations suggest that Li-ion diffusion in the bulk occurs by a zigzag route between the tetrahedral layers. 3.5.2. Surface Effects on the Charge Distribution and Delithiation Energy. To ascertain the effects of making smaller nanoparticles with a higher fraction of surface sites, we also studied surface effects. First, we calculated the surface energies of various surfaces of Li8ZrO6. Surface energies are calculated by65

7 → 13, (T1 → T2)

Figure 10. Most favorable polaron-Li-ion diffusion pathway.

Li vacancya

Table 7. Barriers (eV) and Lithium and Polaron Hopping Distances (Å) of Different Li Diffusion Pathways in Li95Zr12O72 by PBE+Ua

13 → 22, (T2 → Oh)



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Table 8. Barriers (eV) and Lithium and Polaron Hopping Distances (Å) of Different Li Diffusion Pathways for Li94Zr12O72 by PBE+Ua

a

Li vacancy

VLi7Li10 → VLi7Li25 (T2 → T1)




polaron process barrier distanceb distancec

O28O43 → O4O43 side-by-side 0.34 (0.39) 3.20 2.33

O28O43 → O16O43 side-by-side 0.77 (0.59) 3.18 2.87

O16O43 → O4O43 side-by-side 0.17 (0.40) 3.20 2.28

O4O43 → O37O61 side-by-side 0.83 (0.78) 3.18, 3.33 3.15

The barrier in parentheses is for the reverse diffusion. bThe polaron hopping distance in units of Å. cThe Li hopping distance in units of Å.

particles to increase the utilization of active material, the voltage of the Li8ZrO6 material corresponding to the tetrahedral layer can still be maintained at the level of the bulk material. 3.5.3. Energy Barriers for the Diffusion from Bulk to the Surface. Figure 13 shows the energy profile for Li-ion diffusion from the (001) surface to the bulk by PBE. When there are multiple paths, the path with the lower energy barrier is shown. It is found that the diffusion energy barrier across the (001) surface (0.30 eV) is smaller than the energy barrier along the (001) direction in the bulk (∼0.40 eV), but is larger than the barrier for the lowest-energy path in the bulk (which is hopping between tetrahedral voids within adjacent layers with a barrier of 0.17 eV). We may compare this to the findings of Dathar et al.66 in lithium iron phosphates; they found that surface diffusion has higher barriers than bulk diffusion and suggested that this could limit performance as particle size is reduced. Table 12 gives the barriers and polaron hopping distances of three Li diffusion pathways across the (001) surface as calculated by PBE+U. The energy difference between tetrahedral layers and octahedral layers is smaller than the difference in the bulk. The diffusion barrier from the surface tetrahedral layer to the subsurface octahedral layer is lower than the corresponding diffusion barrier in the bulk, and also lower than the most favorable path in the bulk (see also Figures S2 and S3 in the Supporting Information).

Figure 11. Ten nonpolar low-index surfaces and the positions of the (001) and (101) planes. In some surfaces, O atoms are added or deleted to form the complete ZrO6 octahedra. The numbers are the PBE (red) and N12 (blue) unrelaxed surface energies (eV/Å2). The M06-L optimized bulk geometry is used to create the surfaces.

Table 9. Surface Energy (eV/Å2) with Respect to the Thickness of Slabs for (001) and (101) Surfaces as Calculated Using PBEa surface

thickness (Å)

not relaxed

relaxed

(001) (001) (001) (101) (101) (101)

5.2 10.3 15.5 4.5 9.0 13.6

0.030 0.030 0.030 0.110 0.108 0.108

0.028 0.027 0.027 0.043 0.063 0.064

4. CONCLUSION We studied the effects of various dopants on the crystal structure, band gap, and electronic and ionic conductivity of Li8ZrO6. Mg and Nb doping increases the ionic conductivity by 1 order of magnitude, while electronic conductivity is reduced for all dopants, even though the band gap is also reduced, most significantly with Ce, Nb, and Ti doping. The activation energy for lithium-ion diffusion is 0.50 eV for undoped LZO. Small amounts of doping with Mg or Nb do not significantly influence the activation energy, but it is reduced by a high doping level of Nb. The lithium diffusion and surface effects of LZO were studied by PBE+U density functional calculations with the nudged elastic band method. We found that the most favorable path for Li diffusion in the Li8‑xZrO6 crystal is a zigzag path between the Li-tetrahedral layers. The (001) surface is found to be the most stable surface. On the (001) surface, the partial atomic charges on surface Li atoms are larger than on Li atoms in the bulk, and the voltage afforded by reaction on the (001) surface is slightly higher than that afforded by reaction in the bulk. The diffusion barrier from the surface tetrahedral layer to the subsurface octahedral layer on the (001) surface is lower than for the most favorable path in the bulk material.

The lattice constants are fixed at the M06-L optimized bulk parameters. a

Figure 12. Geometries of unrelaxed and relaxed (101) surfaces.

The delithiation energies of Li atoms on the (001) surface are shown in Table 11. The voltage afforded by a reaction at the surface is about 0.1 eV higher than that in the bulk on the basis of PBE results (see Table S2 in Supporting Information). The delithiation energy for the surface tetrahedral layer by PBE+U is higher than that in the bulk while the delithiation energy for the subsurface octahedral layer by PBE+U is lower than that in bulk. This shows that even when one prepares nanosized J


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The Journal of Physical Chemistry C Table 10. CM5 Charges for Atoms in the Bulk and in (001) Slabs with Various Thicknesses in Åa thickness (Å)

Li1 (T)

Li2 (Oh)

Li3 (T)

Li4 (T)

Li5 (Oh)

Zr1

Zr2

O1

O2

O3

bulk 5.2 slab 10.3 slab 15.5 slab

0.50 0.54 0.55 0.57

0.43 0.41 0.42 0.42

0.50

0.50

0.43

1.54

−0.89

0.49

0.43

−0.89 −0.91 −0.92 −0.91

−0.89

0.50 0.49

1.54 1.42 1.48 1.47

−0.90 −0.91

−0.90

1.51

a

Charges are derived using M06-L/DZ in BAND with PBE optimized structures. Atoms are labeled according to their distances to the surface. Li1, Zr1, and O1 are the atoms that are closest to the surface.

Notes

Table 11. Delithiation Energy (eV) in the Bulk and in (001) Slabs by PBE+Ua thickness (Å) bulk (supercell, Li96Zr12O72) (001) slab

Li1 (T)

Li2 (Oh)

3.28

3.83

Li3 (T) Li4 (T) 3.28

3.28

3.83

3.53

3.61

3.35

3.37

3.89

The authors declare no competing financial interest.

■

Li5 (Oh)

ACKNOWLEDGMENTS This work was supported in part by the U.S. Department of Energy, Office of Basic Energy Sciences, under Award Number DE-SC0008662. Computations were performed using resources of (1) the Molecular Science Computing Facility in the W R. Wiley Environmental Molecular Sciences Laboratory of Pacific Northwest National Laboratory sponsored by the U.S. Department of Energy, (2) the National Energy Research Scientific Computing Center, a DOE Office of Science User Facility supported by the Office of Science of the U.S. Department of Energy under Contract No. DE-AC0205CH11231, and (3) Minnesota Supercomputing Institute.

a

Atoms are labeled according to their distances to the surface. Li1 is the atom that is closest to the surface.

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(1) Ellis, B. L.; Lee, K. T.; Nazar, L. F. Positive Electrode Materials for Li-Ion and Li-Batteries. Chem. Mater. 2010, 22, 691−714. (2) Jeong, G.; Kim, Y.-U.; Kim, H.; Kim, Y.-J.; Sohn, H.-J. Prospective Materials and Applications for Li Secondary Batteries. Energy Environ. Sci. 2011, 4, 1986−2002. (3) Lithium-Ion Batteries; Yuan, X., Liu, H., Zhang, J., Eds.; CRC Press: New York, 2012. (4) He, P.; Yu, H.; Li, D.; Zhou, H. Layered Lithium Transition Metal Oxide Cathodes Towards High Energy Lithium-Ion Batteries. J. Mater. Chem. 2012, 22, 3680−3695. (5) Goodenough, J. B.; Park, K.-S. The Li-Ion Rechargeable Battery: A Perspective. J. Am. Chem. Soc. 2013, 135, 1167−1176. (6) Yoo, H. D.; Markevich, E.; Salitra, G.; Sharon, D.; Aurbach, D. On the Challenge of Developing Advanced Technologies for Electrochemical Energy Storage and Conversion. Mater. Today 2014, 17, 110−121. (7) Duan, Y. Structural and Electronic Properties of Li8ZrO6 and its CO2 Capture Capabilities: an Ab Initio Thermodynamic Approach. Phys. Chem. Chem. Phys. 2013, 15, 9752−9760. (8) Duan, Y. Electronic Structural and Electrochemical Properties of Lithium Zirconates and Their Capabilities of CO2 Capture: A FirstPrinciples Density-Functional Theory and Phonon Dynamics Approach. J. Renewable Sustainable Energy 2011, 3, 013102. (9) Neudecker, B. J.; Dudney, N. J.; Bates, J. B. Battery with an InSitu Activation Plated Lithium Anode. Patent WO2000060689 A1, October 20, 2000. (10) Agostini, M.; Ulissi, U.; Lecee, D. D.; Ahiara, Y.; Ito, S.; Hassoun, J. A Lithium-Ion Battery Based on an Ionic Liquid Electrolyte, Tin-Carbon Nanostructured Anode, and Li2O-ZrO2Coated Li(Ni0.8Co0.15Al0.05)O2 Cathode. Energy Technol. 2015, 3, 632−637. (11) Ito, S.; Fujiki, S.; Yamada, T.; Aihara, Y.; Park, Y.; Kim, T. Y.; Baek, S.-W.; Lee, J.-M.; Doo, S.; Machida, N. A Rocking Chair Type All-Solid-State Lithium Ion Battery Adopting Li2O-ZrO2 coated LiNi0.8Co0.15Al0.05O2 and a Sulfide Based Electrolyte. J. Power Sources 2014, 248, 943−950. (12) Zou, Y.; Petric, A. Thermodynamic Stability of the Lithium Zirconates and Lithium Yttrate. J. Phys. Chem. Solids 1994, 55, 493− 499.

Figure 13. Energy profile (eV) for moving a void in Li7.67ZrO6 from the (001) surface as calculated by using PBE.

Table 12. Barriers and Polaron Hopping Distances of Different Li Diffusion Pathways across the (001) Surface by PBE+U Li vacancy

T1 → Oh1

Oh1 → T2

T2 → T3

process barrier (eV) polaron hopping distance (Å)

side-by-side 0.28 (0.0) 2.97

side-by-side 0.18 (0.43) 3.06

cross 0.4 (0.41) 3.21

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ASSOCIATED CONTENT

S Supporting Information *

The Supporting Information is available free of charge on the ACS Publications website at DOI: 10.1021/acs.jpcc.6b02077. Derivation of eqs 1−5, XRD patterns of samples with low doping levels, energy profiles, and delithiation energies (PDF)

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REFERENCES

AUTHOR INFORMATION

Corresponding Authors

*E-mail: [email protected]. Phone: 1-612-624-7555. *E-mail: [email protected]. Author Contributions

S.H. and Y.F. contributed equally. K


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(35) Huggins, R. Simple Method to Determine Electronic and Ionic Components of the Conductivity in Mixed Conductors: a Review. Ionics 2002, 8, 300−313. (36) Liu, J.; Chang, D.; Whitfield, P.; Janssen, Y.; Yu, X.; Zhou, Y.; Bai, J.; Ko, J.; Nam, K.-W.; Wu, L.; Zhu, Y.; Feygenson, M.; Amatucci, G.; Van der Ven, A.; Yang, X.-Q.; Khalifah, P. Ionic Conduction in Cubic Na3TiP3O9N, a Secondary Na-Ion Battery Cathode with Extremely Low Volume Change. Chem. Mater. 2014, 26, 3295−3305. (37) Kresse, G.; Furthmuller, J. Efficiency of Ab-Initio Total Energy Calculations for Metals and Semiconductors using a Plane-Wave Basis Set. Comput. Mater. Sci. 1996, 6, 15−50. (38) Kresse, G.; Furthmuller, J. Efficient Iterative Schemes for Ab Initio Total-Energy Calculations using a Plane-Wave Basis Set. Phys. Rev. B: Condens. Matter Mater. Phys. 1996, 54, 11169−11186. (39) Philipsen, P. H. T.; Velde, G. t.; Baerends, E. J.; Berger, J. A.; Boeij, P. L. d.; Groeneveld, J. A.; Kadantsev, E. S.; Klooster, R.; Kootstra, F.; Romaniello, P.; Skachkov, D. G.; Snijders, J. G.; Wiesenekker, G.; Ziegler, T. BAND2013; SCM, Theoretical Chemistry, Vrije Universiteit: Amsterdam, The Netherlands, 2013. (40) Marenich, A. V.; Cramer, C. J.; Truhlar, D. G. CM5PAC; University of Minnesota: Minneapolis, 2013. http://comp.chem.umn. edu/cm5pac/. (41) Blochl, P. E. Projector Augmented-Wave Method. Phys. Rev. B: Condens. Matter Mater. Phys. 1994, 50, 17953−17978. (42) Kresse, G.; Joubert, D. From Ultrasoft Pseudopotentials to the Projector Augmented-Wave Method. Phys. Rev. B: Condens. Matter Mater. Phys. 1999, 59, 1758−1775. (43) Perdew, J. P.; Burke, K.; Ernzerhof, M. Generalized Gradient Approximation Made Simple. Phys. Rev. Lett. 1996, 77, 3865−3868. (44) Peverati, R.; Truhlar, D. G. Exchange−Correlation Functional with Good Accuracy for Both Structural and Energetic Properties While Depending Only on the Density and its Gradient. J. Chem. Theory Comput. 2012, 8, 2310−2319. (45) Krukau, A. V.; Vydrov, O. A.; Izmaylov, A. F.; Scuseria, G. E. Influence of the exchange screening parameter on the performance of screened hybrid functionals. J. Chem. Phys. 2006, 125, 224106. (46) Dudarev, S. L.; Botton, G. A.; Savrasov, S. Y.; Humphreys, C. J.; Sutton, A. P. Electron-Energy-Loss Spectra and the Structural Stability of Nickel Oxide: An LSDA+U Study. Phys. Rev. B: Condens. Matter Mater. Phys. 1998, 57, 1505−1509. (47) Peverati, R.; Truhlar, D. G. Performance of the M11-L density functional for bandgaps and lattice constants of unary and binary semiconductors. J. Chem. Phys. 2012, 136, 134704. (48) Peverati, R.; Truhlar, D. G. Quest for a universal density functional: the accuracy of density functionals across a broad spectrum of databases in chemistry and physics. Philos. Trans. R. Soc., A 2014, 372, 20120476. (49) Jónsson, H.; Mills, G.; Jacobsen, K. W. Nudged Elastic Band Method for Finding Minimum Energy Paths of Transitions. In Classical and Quantum Dynamics in Condensed Phase Simulations; Berne, B. J., Ciccotti, G., Coker, D. F., Eds.; World Scientific: Singapore, 1998; pp 385−404. (50) López, R.; Gómez, R. Band-Gap Energy Estimation from Diffuse Reflectance Measurements on Sol−Gel and Commercial TiO2: a Comparative Study. J. Sol-Gel Sci. Technol. 2012, 61, 1−7. (51) Tauc, J.; Grigorovici, R.; Vancu, A. Optical Properties and Electronic Structure of Amorphous Germanium. Phys. Status Solidi B 1966, 15, 627−637. (52) Guan, J.; Liu, M. Transport Properties of LiMn2O4 Electrode Materials for Lithium-Ion Batteries. Solid State Ionics 1998, 110, 21− 28. (53) Koyama, Y.; Tanaka, I.; Nagao, M.; Kanno, R. First-Principles Study on Lithium Removal from Li2MnO3. J. Power Sources 2009, 189, 798−801. (54) Zhou, F.; Kang, K.; Maxisch, T.; Ceder, G.; Morgan, D. The Electronic Structure and Band Gap of LiFePO4 and LiMnPO4. Solid State Commun. 2004, 132, 181−186. (55) Maxisch, T.; Zhou, F.; Ceder, G. Ab Initio Study of the Migration of Small Polarons in Olivine LixFePO4 and their Association

(13) Huang, S.; Wilson, B. E.; Wang, B.; Fang, Y.; Buffington, K.; Stein, A.; Truhlar, D. G. Y-doped Li8ZrO6: A Li-Ion Battery Cathode Material with High Capacity. J. Am. Chem. Soc. 2015, 137, 10992− 11003. (14) Tukamoto, H.; West, A. Electronic Conductivity of LiCoO2 and its Enhancement by Magnesium Doping. J. Electrochem. Soc. 1997, 144, 3164−3168. (15) Wang, C.; Hong, J. Ionic/Electronic Conducting Characteristics of LiFePO4 Cathode Materials The Determining Factors for High Rate Performance. Electrochem. Solid-State Lett. 2007, 10, A65−A69. (16) Wolfenstine, J.; Allen, J. Electrical Conductivity and Charge Compensation in Ta-Doped Li4Ti5O12. J. Power Sources 2008, 180, 582−585. (17) Luo, W. B.; Dahn, J. R. Comparative Study of Li[Co1‑zAlz]O2 Prepared by Solid-State and Co-Precipitation Methods. Electrochim. Acta 2009, 54, 4655−4661. (18) Huang, S.; Wilson, B. E.; Smyrl, W. H.; Truhlar, D. G.; Stein, A. Transition-Metal-Doped M-Li8ZrO6 (M = Mn, Fe, Co, Ni, Cu, Ce) as High-Specific-Capacity Li-Ion Battery Cathode Materials: Synthesis, Electrochemistry, and Quantum Mechanical Characterization. Chem. Mater. 2016, 28, 746−755. (19) Pantyukhina, M. I.; Andreev, O. L.; Martem’Yanova, Z. S.; Batalov, N. N. Cation Conductivity of Li8ZrO6 − LiYO2 Solid Solutions. Inorg. Mater. 2004, 40, 404−406. (20) Pantyukhina, M. I.; Shchelkanova, M. S.; Plaksin, S. V. Ionic Conductivity of Li8−2xSrxZrO6. Inorg. Mater. 2012, 48, 382−385. (21) Pantyukhina, M.; Shchelkanova, M.; Plaksin, S. Synthesis and Electrochemical Properties of Li8−xZr1−xNbxO6 Solid Solutions. Phys. Solid State 2013, 55, 707−709. (22) Pantyukhina, M.; Shchelkanova, M.; Plaksin, S. Electrochemical Properties of Solid Solutions in the Li8Zr1−xCexO6 System. Russ. J. Electrochem. 2013, 49, 144−148. (23) Pantyukhina, M.; Shchelkanova, M.; Plaksin, S. Ionic Conduction of Li8−2xMgxZrO6 Solid Solutions. Russ. J. Electrochem. 2010, 46, 780−783. (24) Wagemaker, M.; Ellis, B. L.; Lutzenkirchen-Hecht, D.; Mulder, F. M.; Nazar, L. F. Proof of Supervalent Doping in Olivine LiFePO4. Chem. Mater. 2008, 20, 6313−6315. (25) Van der Ven, A.; Thomas, J. C.; Xu, Q. C.; Swoboda, B.; Morgan, D. Nondilute Diffusion from First Principles: Li Diffusion in LixTiS2. Phys. Rev. B: Condens. Matter Mater. Phys. 2008, 78, 104306. (26) Van der Ven, A.; Ceder, G. Lithium Diffusion Mechanisms in Layered Intercalation Compounds. J. Power Sources 2001, 97−8, 529− 531. (27) Koudraichova, M. V.; Harrison, N. M.; de Leeuw, S. W. Diffusion of Li-ions in Rutile. An Ab Initio Study. Solid State Ionics 2003, 157, 35−38. (28) Xu, B.; Meng, S. Factors Affecting Li Mobility in Spinel LiMn2O4-A First-Principles Study by GGA and GGA Plus U Methods. J. Power Sources 2010, 195, 4971−4976. (29) Morgan, D.; Van der Ven, A.; Ceder, G. Li Conductivity in LixMPO4 (M = Mn, Fe, Co, Ni) Olivine Materials. Electrochem. SolidState Lett. 2004, 7, A30−A32. (30) Ouyang, C. Y.; Shi, S. Q.; Wang, Z. X.; Huang, X. J.; Chen, L. Q. First-Principles Study of Li Ion Diffusion in LiFePO4. Phys. Rev. B: Condens. Matter Mater. Phys. 2004, 69, 104303. (31) Du, Y. J. A.; Holzwarth, N. A. W. Li Ion Diffusion Mechanisms in the Crystalline Electrolyte Gamma-Li3PO4. J. Electrochem. Soc. 2007, 154, A999−A1004. (32) Wang, L.; Zhou, F.; Meng, Y. S.; Ceder, G. First-Principles Study of Surface Properties of LiFePO4: Surface Energy, Structure, Wulff Shape, and Surface Redox Potential. Phys. Rev. B: Condens. Matter Mater. Phys. 2007, 76, 165435. (33) Sushko, M. L.; Rosso, K. M.; Liu, J. Size Effects on Li+/Electron Conductivity in TiO2 Nanoparticles. J. Phys. Chem. Lett. 2010, 1, 1967−1972. (34) Yin, X. S.; Zhang, Q. H.; Yu, J. G. Three-Step Calcination Synthesis of High-Purity Li8ZrO6 with CO2 Absorption Properties. Inorg. Chem. 2011, 50, 2844−2850. L


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The Journal of Physical Chemistry C with Lithium Ions and Vacancies. Phys. Rev. B: Condens. Matter Mater. Phys. 2006, 73, 104301. (56) Ellis, B.; Perry, L. K.; Ryan, D. H.; Nazar, L. F. Small Polaron Hopping in LixFePO4 Solid Solutions: Coupled Lithium-Ion and Electron Mobility. J. Am. Chem. Soc. 2006, 128, 11416−11422. (57) Ong, S. P.; Chevrier, V. L.; Hautier, G.; Jain, A.; Moore, C.; Kim, S.; Ma, X.; Ceder, G. Voltage, Stability and Diffusion Barrier Differences between Sodium-Ion and Lithium-Ion Intercalation Materials. Energy Environ. Sci. 2011, 4, 3680−3688. (58) Ong, S. P.; Mo, Y.; Ceder, G. Low Hole Polaron Migration Barrier in Lithium Peroxide. Phys. Rev. B: Condens. Matter Mater. Phys. 2012, 85, 081105. (59) Moradabadi, A.; Kaghazchi, P. Mechanism of Li Intercalation/ Deintercalation into/from the Surface of LiCoO2. Phys. Chem. Chem. Phys. 2015, 17, 22917−22922. (60) Hoang, K.; Johannes, M. D. First-Principles Studies of the Effects of Impurities on the Ionic and Electronic Conduction in LiFePO4. J. Power Sources 2012, 206, 274−281. (61) Fisher, C. A.; Kuganathan, N.; Islam, M. S. Defect Chemistry and Lithium-Ion Migration in Polymorphs of the Cathode Material Li2MnSiO4. J. Mater. Chem. A 2013, 1, 4207−4214. (62) Kerisit, S.; Rosso, K.; Yang, Z.; Liu, J. Dynamics of Coupled Lithium/Electron Diffusion in TiO2 Polymorphs. J. Phys. Chem. C 2009, 113, 20998−21007. (63) Sushko, M. L.; Rosso, K.; Liu, J. Size Effects on Li+/Electron Conductivity in TiO2 Nanoparticles. J. Phys. Chem. Lett. 2010, 1, 1967−1972. (64) Sushko, M. L.; Rosso, K.; Liu, J. Mechanism of of Li+/Electron Conductivity in Rutile and Anatase TiO2 Nanoparticles. J. Phys. Chem. C 2010, 114, 20277−20283. (65) Wang, L.; Zhou, F.; Meng, Y. S.; Ceder, G. First-Principles Study of Surface Properties of LiFePO4: Surface Energy, Structure, Wulff Shape, and Surface Redox Potential. Phys. Rev. B: Condens. Matter Mater. Phys. 2007, 76, 165435. (66) Dathar, G. K. P.; Sheppard, D.; Stevenson, K. J.; Henkelman, G. Calculations of Li-Ion Diffusion in Olivine Phosphates. Chem. Mater. 2011, 23, 4032−4037.

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