First-Principles Study of Spinel MgTiS2 as a Cathode Material

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First Principles Study of spinel-MgTiS as a Cathode Material Sanjeev Krishna Kolli, and Anton Van der Ven Chem. Mater., Just Accepted Manuscript • DOI: 10.1021/acs.chemmater.8b00552 • Publication Date (Web): 20 Mar 2018 Downloaded from http://pubs.acs.org on March 20, 2018

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Chemistry of Materials

First Principles Study of spinel-MgTiS2 as a Cathode Material Sanjeev Krishna Kolli† and Anton Van der Ven∗,†,‡ †Materials Department, University of California Santa Barbara, Santa Barbara ‡Current address: 1361A Engineering II University of California, Santa Barbara,Santa Barbara, CA 93106-5050 E-mail: [email protected] Phone: +1(805)893-7920

Abstract Spinel intercalation hosts are well known to to facilitate high rate capability and high voltage Li-ion batteries. A recent experimental study has shown that Mg can reversibly intercalate in spinel TiS2 , demonstrating the viability of Li intercalation host crystal structures for Mg-ion batteries. 1 We report on a first-principles statistical mechanics study of Mg insertion into spinel TiS2 , accounting for occupancy on both octahedrally and tetrahedrally coordinated interstitial sites. In contrast to Li containing spinels, we predict mixed octahedral and tetrahedral site occupancy at non-dilute Mg concentrations consistent with the recent experimental study of Sun et al. 1 The onset of mixed occupancy is correlated with an increase in the spinel volume upon Mg insertion, which is more pronounced in Mgx TiS2 than in its Li counterpart. The results in this study suggest that the degree of mixed occupancy could be controlled through the volume of the host with addition of electrochemically inactive species.

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Introduction Spinel is a common crystal structure among the multitude of viable insertion chemistries for Li-ion batteries as its three dimensional network of interstitial sites often enables fast cation diffusion. 2–9 One of the very first successful intercalation compounds for Li ion batteries was a Mn containing spinel compound having chemical formula Lix Mn2 O4 . 10–12 The Li excess spinel form of Li4 Ti5 O12 exhibits exceptionally fast insertion kinetics through a two-phase reaction with almost no volume change upon Li insertion to form Li7 Ti5 O12 , making it a superb anode for high rate Li-ion batteries. 13–16 Spinel compounds consisting of mixtures of Mn and Ni over the transition metal sites of Lix Ni2y Mn2−2y O4 are now actively being investigated as high voltage cathodes. 17–22 The spinel crystal structure is complex, especially when compared with the crystal structures of other common insertion compounds such as layered intercalation compounds. 3,4,23,24 It offers intercalating cations two types of interstitial sites within its close-packed anion sublattice: octahedrally coordinated sites and tetrahedrally coordinated sites. There are twice as many octahedral sites as tetrahedral sites, leading to peculiar voltage profiles and phase transformation behavior when the intercalating species prefer tetrahedral sites. 11 Li prefers the tetrahedral sites in transition metal oxides having the spinel crystal structure. Once these are filled, though, the compound undergoes a first order phase transition in which the Li ions in LiM2 O4 (where M is a transition metal) displace from the tetrahedral sites to the more numerous octahedral sites to form Li2 M2 O4 . 3,8,10–12,25,26 In sulfides, such as TiS2 , Li instead prefers the octahedral sites and the compound exhibits simple solid solution behavior. 9 The recent study of Sun et al 1 demonstrated the ability of spinel TiS2 to intercalate Mg. In addition to being a true breakthrough in the search for viable cathode materials for Mg-ion batteries beyond the Chevrel phases, 27,28 this study also presented evidence for mixed octahedral and tetrahedral occupancy, a phenomenon that has so far never been seen in Li containing spinels. Early first-principles work on spinel Mgx TiS2 29 showed that Mg overwhelmingly prefers octahedral sites over tetrahedral sites in the dilute limit, similar to 2


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what is observed in spinel Lix TiS2 . The same study therefore restricted its focus to the octahedral sites when predicting electrochemical properties at non-dilute Mg concentrations. 29 However, the experimental evidence of Sun et al 1 showed that while Mg ions initially only occupy octahedral sites, they begin to distribute among both octahedral and tetrahedral sites at non-dilute concentrations. The recent upsurge in activity seeking to develop viable Mg-ion batteries 5,7,24,26,30–32 motivates fundamental studies of the behavior of Mg in common intercalation compounds. Here we explore mixed occupancy in Mgx TiS2 from first-principles and identify its effect on electrochemical properties. We perform a first-principles statistical mechanics study of the electrochemical and structural properties of Mgx TiS2 as a function of composition and temperature and find, in agreement with the experimental results of Sun et al, 1 that Mg does distribute over both octahedral and tetrahedral sites at non-dilute concentrations. The onset of mixed site occupancy is correlated with the increase in volume accompanying Mg insertion, which in Mgx TiS2 is more pronounced than in Lix TiS2 due to the higher valence of the Mg cations. It is likely that mixed occupancy is beneficial for cation transport due to the interconnected topology of the octahedral and tetrahedral networks within spinel: any hop between neighboring octahedral (tetrahedral) sites must pass through an intermediate tetrahedral (octahedral) site. The results of this study suggest that the site occupancy in spinel intercalation compounds and therefore its electrochemical properties can be modified by varying the volume of the host.

Methods We performed a first-principles statistical mechanics study of the electrochemical properties of Mgx TiS2 using the cluster expansion approach. 33,34 This approach enables a rigorous treatment of the configurational degrees of freedom arising from all the possible ways of distributing Mg cations and vacancies over the tetrahedral and octahedral sites of spinel TiS2 .

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Configurational entropy plays an important role in determining electrochemical properties, especially when the compound behaves as a solid solution with respect to Mg insertion. While vibrational excitations will also affect finite temperature thermodynamic properties such as free energies, 35,36 their contribution to derived quantities such as the Mg chemical potential, which determines the voltage, is less significant. 37,38 Considering the enormous computational cost of calculating contributions from vibrational excitations to the free energy of a disordered solid solution, we only account for configurational degrees of freedom in this study. Density functional theory (DFT) within the generalized gradient approximation (GGA) as formulated by Perdew, Burke, and Ernzerhoff (PBE) 39 was used to predict the energies of many different Mg-vacancy orderings over the interstitial sites of spinel TiS2 . DFT calculations were carried out with the Vienna ab initio software package (VASP). 40,41 We used the projector augmented wave (PAW) 42,43 theory and a plane wave energy cutoff of 450 eV. A fully automatic k-point mesh setting that corresponded to a 7 x 7 x 7 Monkhorst-Pack grid for the primitive spinel unit cell was scaled to maintain an equal or greater k-point density for each supercell. The total energies of a large number of Mg-vacancy configurations in Mgx TiS2 within the composition range of 0 < x < 1.5 were calculated to train a cluster expansion Hamiltonian. Any particular arrangement (configuration) of Mg and vacancies over the interstitial sites of spinel Mgx TiS2 can be represented mathematically with an array of occupation variables. Each tetrahedral and octahedral magnesium site i within the spinel TiS2 host is assigned an occupation variable σi that has a value of 1 if a magnesium is present at that site and 0 otherwise. A cluster expansion parameterizes the configuration dependence of the fully relaxed energy of the crystal as an expansion of polynomials of site occupation variables. To describe the energy of binary Mg-vacancy disorder over the interstitial sites of spinel TiS2 , each polynomial basis function is equal to the product of occupation variables belonging to the sites of a particular cluster, such as a pair cluster, a triplet cluster etc. 33,34 While

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the full cluster expansion is expressed as a sum over basis functions corresponding to all possible clusters of sites, in practice it must be truncated. The expansion coefficients of a cluster expansion Hamiltonian for spinel Mgx TiS2 were fit to a training set of 328 energies of different Mg-vacancy configurations in Mgx TiS2 . The resulting cluster expansion has an RMS error of 15.5 meV/ formula unit for 300 configurations having energies within 50 meV/atom from the convex hull and compositions x < 0.8. The Hamiltonian was used in grand canonical Monte Carlo simulations to predict finite temperature properties and phase stability. The Clusters Approach to Statistical Mechanics (CASM) software package 44–47 was used to construct and parameterize the cluster expansion and to perform the grand canonical Monte Carlo simulations.

Results Mg can fill interstitial sites that are tetrahedrally and octahedrally coordinated by sulfur within the spinel TiS2 host. These sites correspond to the the 8a and 16c Wyckoff positions of the F d3m space group respectively. Fig. 1 shows the location of these sites within the conventional cubic unit cell. The 8a tetrahedral sites form a diamond cubic network. Each octahedral site resides between two tetrahedral sites. There are twice as many octahedral 16c sites as 8a tetrahedral sites. The sulfur polyhedra surrounding nearest neighbor 8a and 16c sites share faces such that configurations in which adjacent tetrahedral and octahedral sites are simultaneously occupied by Mg have very high formation energies or are unstable with respect to relaxations to new configurations. The spinel primitive unit cell contains 4 formula units of Mgx TiS2 . Fig. 2 shows the formation energies of 328 Mg-vacancy configurations. The black line, connecting the lowest energy orderings as a function of composition, represents the convex hull, which can be viewed as the envelope of common tangents to the energies of perfectly ordered phases. Since the entropy is zero at 0 K, the convex hull is equivalent to the minimum 5



TiS2 Framework

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Spinel Interstitial Network

(a)

Octahedral

(b)

Tetrahedral

Octahedral Octahedral Tetrahedral

Octahedral

Octahedral Tetrahedral (c)

(d)

Figure 1: (a) The TiS2 framework of the spinel crystal structure. (b) Intercalating species can fill a network of interconnected tetrahedral and octahedral sites within the spinel host. The tetrahedral sites form a diamond network with octahedral sites located between neighboring tetrahedral sites. (c) & (d) The tetrahedral and octahedral sites share faces. free energy of Mgx TiS2 as a function of x, with every point on the hull corresponding to a stable ordering at absolute zero. The convex hull shows that there are many ground state configurations. The various combinations of magnesium occupancy (octahedral, tetrahedral, and mixed) are color coded in Fig. 2. At low compositions (x < 0.25), the lowest energy (most stable) configurations have only octahedrally coordinated magnesium. Fig 2 indicates that the configurations with only tetrahedral magnesium tend to be less stable relative to many other configurations at the same composition. At higher Mg compositions (x > 6


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0.375), configurations with a mix of octahedral and tetrahedral coordination tend to be the most stable. For compositions near x = 0.6 mixed coordination is far more favorable than configurations with pure octahedral coordination. At x = 1 only octahedral sites are filled because any other configuration must have high energy nearest neighbor tetrahedraloctahedral occupancy. There are a large number of configurations that are very close to the convex hull for compositions between x = 0 and x = 0.625. This indicates a high degree of degeneracy among the many possible Mg-vacancy orderings in spinel TiS2 .

⏹ Pure Octahedral ▼ Pure Tetrahedral ⏺ Mixed

Figure 2: The formation energies (eV/Mgx TiS2 formula unit) of 328 Mg-vacancy configurations within spinel TiS2 host as a function of magnesium composition. Configurations that contain only octahedrally coordinated magnesium, only tetrahedrally coordinated magnesium, and mixed coordination correspond to blue squares, red triangles, and purple circles respectfully. The convex hull (black line) connects the ground state configurations.

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Fig. 3 shows the cube root of the unit cell volume for configurations that are within 10 meV/atom from the convex hull. This can be viewed as a proxy for the cubic lattice parameter. The black triangles represent the ground states and the other points are configurations that are within 10 meV/atom from the convex hull. There is a clear upturn in lattice parameter of the ground state orderings near x = 0.375. This corresponds to the composition at which mixed orderings become more favorable in Fig. 2. A similar upswing around x = 0.375 occurs for configurations within 3 meV/atom from the hull (green triangles). Configurations that are further from the convex hull (blue squares and orange circles) tend to follow the trend less strictly, suggesting thermal disorder will make the upturn in lattice parameter less pronounced at elevated temperature. The trends revealed in Fig. 3 indicate that low energy configurations with tetrahedral magnesium is correlated with larger volumes.

We further investigated the correlation between low energy tetrahedral configurations and larger lattice parameters by calculating the octahedral and tetrahedral site energy in the dilute limit as a function of volume. We performed fixed lattice DFT calculations at various conventional cell lattice parameters of Mg1/32 TiS2 in which Mg is octahedrally coordinated and tetrahedrally coordinated. Fig. 4 shows the energy of a 2 x 2 x 2 supercell of the primitive spinel unit cell containing a single magnesium in an octahedral or tetrahedral site as a function of the cubic lattice parameter. As the lattice parameter and volume increases, the tetrahedrally coordinated site becomes relatively more stable compared to the octahedrally coordinated site. At lattice parameters greater than 10.5 ˚ A, tetrahedrally coordinated magnesium is more stable in the dilute limit. This shows that the preference for tetrahedral or octahedral coordination of Mg in spinel TiS2 is very sensitive to the volume of the host.

The energies of 328 Mg-vacancy configurations in spinel TiS2 were used to train a cluster expansion Hamiltonian with 30 symmetrically unique cluster basis functions. The expansion coefficients of the Hamiltonian are shown in the Supporting Information (S1). This cluster 8


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⏺ ≤10 meV/atom ⏹ ≤ 5 meV/atom ▼ ≤ 3 meV/atom ▲ 0 meV/atom

Figure 3: Cubic cell lattice parameter (calculated as the cube root of the cell volume)for spinel Mgx TiS2 as a function of magnesium composition at 0 K according to DFT for configurations with formation energies within 10 meV/atom from the convex hull. The black triangles, green triangles, blue square, and orange circles represent the ground states, configurations with energies within 3 meV/atom, 5 meV/atom, and 10 meV/atom from the convex hull respectively. expansion Hamiltonian was used to calculate the average composition of magnesium as a function of the magnesium chemical potential using a Metropolis Monte Carlo algorithm within a grand canonical ensemble. The Metropolis Monte Carlo simulations were performed using a supercell that all ground state configurations could tile and contained 2880 primitive unit cells. The voltage of an electrochemical cell can be related to the Mg chemical potential (µMg ) by means of the Nernst equation: V (x) = −[µMg (x) − µ◦Mg ]/2e 9



⏺ Octahedral ⏹ Tetrahedral

Figure 4: Total energies of octahedrally coordinated magnesium (black circle) and tetrahedrally coordinated magnesium (blue square) as a function of the conventional cubic cell lattice parameter. Calculations were performed in the dilute limit in a cell that corresponds to a 2x2x2 supercell of the spinel primitive cell with a composition of Mg1/32 TiS2 . The energy scale is relative to an arbitrary reference such that the points are easily visible on the plot. where µ◦Mg is the chemical potential of the magnesium metal anode. Fig. 5 shows the calculated voltage vs. magnesium composition at 333 K generated from the data of a grand canonical Monte Carlo simulation. The voltage is given relative to a Mg metal anode at 0 K. The voltage curve has a roughly linear slope indicating solid solution behavior and the disappearance of the ordered ground states at 333 K as a result of order-disorder transitions. The voltage remains positive until approximately x = 0.9 and matches the experimentally measured voltage curve of a Mgx TiS2 /Mg coin cell fairly well. 1

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– 333 K Monte Carlo – 333 K Experiment

Figure 5: A comparison of the calculated voltage of Mgx TiS2 relative to magnesium metal and an experimental voltage curve of Mgx TiS2 / Mg coin cell measured by Sun et al. 1 We also tracked the average magnesium occupancy over the tetrahedral and octahedral sites during the Monte Carlo simulations. Fig. 6 shows the fraction of octahedral magnesium and tetrahedral magnesium as a function of magnesium composition at 333 K. Experimental observations 1 of octahedral and tetrahedral coordination of magnesium obtained by Fourier mapping of Rietveld refined x-ray diffraction are also shown in Fig. 6. The sum of the octahedral and tetrahedral curves should sum to the dotted black line representing the total fraction of available magnesium sites that are occupied. There is an onset of tetrahedrally coordinated magnesium at approximately x = 0.3. The experimental observations and the calculated site fractions match fairly well. The discrepancies between calculated and measured values is likely caused in part to the residual tetrahedrally coordinated copper in

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the experimental study. 1

– 333 K ★ Experiment Total Octahedral

Tetrahedral

Figure 6: Mg concentration in the octahedral and tetrahedral sites of spinel (blue line) at 333 K as calculated with Monte Carlo simulations. The black stars are experimentally measured concentrations from Sun et al. 1

The zero Kelvin formation energy calculations suggest that the lattice parameter of the spinel host is correlated with the amount of tetrahedrally coordinated magnesium due to the amount of mixed orderings at high magnesium concentration. We parametrized a cluster expansion of the volume of the unit cell as a function of Mg-vacancy configurational disorder. This volume cluster expansion was evaluated in the Monte Carlo simulations to predict the thermally averaged volume of the unit cell as a result of configurational disorder among Mg and vacancies at elevated temperature. Fig. 7 shows the cube root of the calculated average volume of the Mgx TiS2 conventional cell as a function of x at 60 ◦ C. Experimental 12


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measurements of the lattice parameter at various states of charge as determined from x-ray diffraction by Sun et al. 1 are also shown in Fig. 7. The Monte Carlo calculated lattice parameters match fairly well with experimental observations. While there is a slight upturn in the calculated lattice parameter at 60 ◦ C at the composition corresponding to the onset of tetrahedral Mg in Fig. 6, it is not as pronounced as the upturn predicted at zero Kelvin (Fig. 3).

Figure 7: Predicted conventional cell lattice parameter for spinel Mgx TiS2 as a function of magnesium composition at 333 K as calculated with Monte Carlo simulations (blue circles). Experimental observations of the lattice parameter at various charge states are shown by the black stars. 1

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Discussion The spinel crystal structure is common among electrode materials used in Li-ion batteries. Lithium excess Li7 Ti5 O12 (LTO), having a spinel crystal structure, is often used as an anode, while Mn containing spinels such as Lix Mn2 O4 and Lix Ni2y Mn2−2y O4 are actively investigated as cathodes. The recent study of Sun et al 1 was the first to demonstrate reversible Mg insertion in and removal from spinel TiS2 and showed that Mg behaves very differently within a spinel host when compared to Li. A particularly surprising result of the experimental study of Sun et al 1 was the observation of a mixed distribution of Mg over both octahedral and tetrahedral sites.

Our first-principles statistical mechanics study of spinel Mgx TiS2 supports these observations, predicting that Mg, while still in large part occupying octahedral sites at intermediate concentrations, can also reside in tetrahedral sites. In fact, a large number of ground state Mg-vacancy orderings within spinel Mgx TiS2 contain both octahedrally and tetrahedrally coordinated Mg. The Monte Carlo simulations applied to a cluster expansion parameterized with DFT formation energies predicts that mixed tetrahedral and octahedral occupancy persists above room temperature. This is in stark contrast to the intercalation behavior within lithium spinel analogs. For example, lithium in spinel Lix Ti2 O4 exclusively favors tetrahedrally coordinated sites between 0 < x < 1 and octahedrally coordinated sites at x = 2. 8,25 The voltage curve of Lix Ti2 O4 exhibits a plateau in the composition range of 1 < x < 2 due to a two-phase reaction between Li2 Ti2 O4 having only octahedral occupancy and LiTi2 O4 having only tetrahedral occupancy. The two phase region emerges due to the strong Li preference for tetrahedral sites in spinel oxides and their limited supply when x > 1. Similar behavior is observed in other transition metal oxides having the spinel structure such as Lix Mn2 O4 . 3,12 While spinel Lix TiS2 behaves differently from its oxide counterpart, lithium, nevertheless, exclusively favors octahedrally coordinated sites. 9

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Differences between Mgx TiS2 and Lix TiS2 likely arise from valence differences between Mg and Li since the two cations have nearly identical ionic radii. 48 As revealed by the Li containing spinels, the more ionic the compound, the stronger the Li preference for tetrahedral sites. Indeed, the more ionic oxide spinels favor tetrahedral occupancy while the more covalent sulfides favor octahedral Li. The octahedral 16c sites in spinel share edges with transition metal containing octahedra, while the tetrahedral 8a sites only share corners with the same transition metal sites. Hence, the tetrahedral sites are better able to shield the guest cation (i.e. Li or Mg) from the electrostatic repulsion originating with the transition metal cations. The higher positive valence of Mg is, therefore, likely a factor leading to some tetrahedral site occupancy in TiS2 . The calculations presented in Figs. 2, 3, 4 and 6 also show an important correlation between mixed octahedral and tetrahedral occupancy and the volume of the spinel host. Our DFT calculations show a steady increase in the spinel volume upon insertion of Mg. Similar calculations show that the volume of spinel TiS2 also increases with the insertion of Li, but by substantially less (See S2 in Supporting Information). Since Li and Mg have similar ionic radii, the more rapid increase in volume of Mgx TiS2 compared to Lix TiS2 with x must have an electronic origin. Both Li and Mg donate their valence electrons to the host crystal structure upon insertion, thereby affecting bonding between the transition metals (i.e. Ti) and the anions (i.e. S). The rehybridization between Ti and S and the reduction in the formal oxidation state of Ti that occurs as the guest cation donates its valence electrons to the host will result in a change in the lattice parameter of the crystal. While each Li donates one electron to the host, a Mg donates two electrons. The degree of rehybridization between Ti and S accompanying the insertion of Mg to TiS2 will therefore be more extreme compared to that due to Li insertion. As the volume of the spinel host increases by a sufficient amount, the tetrahedral sites become energetically competitive with the octahedral site, making new orderings with mixed octahedral and tetrahedral occupancy favorable. While the calculations of this work clearly show that volume plays an important role in affecting the relative site

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energies between tetrahedral and octahedral occupancy, it should be noted that a recent study of candidate chalcogenide spinel hosts for solid electrolyte applications showed that the chemistry of the transition metal cation can also alter the relative site energies. 49

Mixed tetrahedral and octahedral occupancy is likely beneficial for fast ion transport. Long-range diffusion within the spinel host requires cation hops through both tetrahedral and octahedral sites. 6,8,9 The migration barrier separating a pair of adjacent tetrahedral and octahedral sites is related to the difference in energy between the two sites. 9,29 As was shown by Emly, 29 the barrier decreases, as the energies of the octahedral and tetrahedral sites come closer together. This suggests that strategies to increase the volume of the spinel host will increase Mg mobility. Volumetric control of the spinel cathode could be realized by addition of electrochemically inactive and kinetically immobile species. In fact, the study by Sun et al. 1 showed an expansion of the lattice parameter of cubic TiS2 due to the presence of residual Cu ions in the host from synthesis procedures. This phenomenon could be extended to other immobile and electrochemically inactive guest cations to design for optimal Mg diffusion. Careful consideration should be given to percolation theory, 50,51 however, to ensure that dopants do not plug diffusion pathways.

Conclusions We performed a first-principles statistical mechanics study of Mg insertion into spinel TiS2 accounting for both octahedral and tetrahedral occupancy. The predicted electrochemical properties of Mgx TiS2 , including the voltage profile and the concentration dependence of the volume, are in very good agreement with experimental observations. In agreement with the experimental work of Sun et al, 1 and in stark contrast to Li containing spinels, we predict mixed octahedral and tetrahedral site occupancy at non-dilute Mg concentrations. The onset of mixed occupancy is correlated with an increase in the spinel volume upon Mg insertion, which is more pronounced in Mgx TiS2 than in its Li counterpart due to the high valence of 16


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Mg.

Supporting Information: Expansion coefficients of the Mg-vacancy cluster expansion of spinel Mgx TiS2 and calculated volumes of spinel Lix TiS2 as a function of Li concentration.

Acknowledgement S. K. Kolli is grateful for helpful discussions with Dr. Maxwell D. Radin, Julija Vinckeviciute, and John G. Goiri. This material is based upon work supported by the National Science Foundation, Grant DMR- 1410242. We acknowledge support from the Center for Scientific Computing from the CNSI, MRL: an NSF MRSEC (DMR-1121053). This research used resources of 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-AC02-05CH11231.

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Table of Contents Figure

23


First-Principles Study of Spinel MgTiS2 as a Cathode Material

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