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Monovalent vs Divalent Cation Diffusion in Thiospinel Ti2S4 Patrick Bonnick, Xiaoqi Sun, Ka-Cheong Lau, Chen Liao, and Linda F. Nazar J. Phys. Chem. Lett., Just Accepted Manuscript • Publication Date (Web): 20 Apr 2017 Downloaded from http://pubs.acs.org on April 23, 2017

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The Journal of Physical Chemistry Letters

Monovalent vs Divalent Cation Diffusion in Thiospinel Ti2S4 Patrick Bonnicka, Xiaoqi Suna, Ka-Cheong Laub,c, Chen Liaob,c and Linda F. Nazara* a – Department of Chemistry and the Waterloo Institute of Nanotechnology, University of Waterloo, Waterloo, Ontario N2L 3G1, Canada b – Chemical Science and Engineering Division, Argonne National Laboratory, 9700 S. Cass Avenue, Lemont, IL 60439, USA * Corresponding author: Prof. Linda F. Nazar, [email protected]

ACS Paragon Plus Environment

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Abstract: Diffusion coefficients (D) for both Li+ and Mg2+ in Ti2S4 were measured using the Galvanic Intermittent Titration Technique (GITT) as a function of both ion concentration (x) and temperature. During discharge at 60°C, DLi descends gradually from 2×10-8 cm2/s at xLi ≈ 0 to 2×10-9 cm2/s at xLi ≈ 1.9. In contrast, DMg decreases sharply from 2×10-8 cm2/s to 1×10-12 cm2/s by xMg ≈ 0.8. This kinetic factor limits the maximum practical discharge capacity of MgxTi2S4. The difference in behavior vis a vis Li+ implies that either increasing Mg2+ occupation of the tetrahedral site at xMg > 0.6 and/or interactions between diffusing cations play a larger role in mediating the diffusion of divalent compared to monovalent cations. Diffusion activation energies (Ea) extracted from the temperature-dependent data revealed that Ea,Mg (540 ± 80 meV) is about twice that of Ea,Li (260 ± 50 meV), explaining the poorer electrochemical performance of MgxTi2S4 at room temperature. Figure for Table of Contents: 1x10-6

Self-Diff., DM (cm2/s)

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

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1x10

-7

1x10

-8

1x10-9

1x10

-10

1x10

-11

1x10-12 0

0.2

0.4

0.6

0.8

1

x in MxTi2S4 (M = Li2 or Mg)


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The pursuit of batteries with higher energy densities than the ubiquitous Li-ion cell has led to focused research efforts on several ‘beyond Li-ion’ technologies, including magnesium batteries. In their most common form, Mg batteries consist of an intercalation positive electrode and Mg metal negative electrode. The latter is the source of the primary advantages of Mg batteries; in comparison to Li, Mg metal is stable when exposed to air, is more abundant in the Earth’s crust, and has a high volumetric capacity density (3832 mAh/cm3) that is nearly double that of Li (2062 mAh/cm3). Additionally, while Li metal is prone to growing dendrites, leading to short circuits, Mg is more resilient to dendritic growth. Despite these attractive advantages, Mg battery research suffers from a paucity of intercalation materials that function as positive electrodes with good reversibility. The first such material, the Chevrel phase Mo6S8, was reported by Aurbach et al. in 2000 . Although Mg2+ reversible insertion into nano, layered TiS2 was first proposed in 2004,3 reversible insertion into micron-sized, polycrystalline particles of both the spinel and layered structures of Ti2S4 were demonstrated only last year.

Many other intercalation

materials that reversibly intercalate Li+ ions do not appear to behave similarly in the case of Mg2+ ions and the reasons for this are under investigation. For instance, Mg2+ mobility was found to be slow in some oxide materials

and the formation of MgO has been reported in a few cases,

signifying that thermodynamics can favor conversion reactions rather than intercalation.

In the

case of oxide spinel-type framework materials, computational studies have provided practical guidelines to explore materials with low migration energies for diffusion (Em). In the search for new materials, inspiration can also be taken from the original Chevrel phase where a combination of soft sulfur anions, and the metallic electronic structure of the lattice screens the divalent charge of the Mg2+ ions. However, we note that several sulfide spinels still remain that have not yet shown reversible Mg intercalation despite some having predicted Em


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values low enough for facile diffusion.

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Hence, it is important to quantify and analyze the

diffusion processes in the few intercalation positive electrode materials that show reversible activity to better understand the limiting factors at play in otherwise promising materials and potentially improve their electrochemical activity. Here we report an experimental analysis of Mg2+ and Li+ diffusion in spinel Ti2S4 that probes the effect of divalent vs monovalent cation charge on mobility using similarly sized ions (rMg2+ = 72 pm vs rLi+ = 76 pm). The diffusion of Li+ in cubic Ti2S4 has been measured previously and modelled13 to account for the effects of tri-vacancy and di-vacancy hops in the spinel lattice. Scheme 1a illustrates a tri- and di-vacancy hop, which are octahedral-tetrahedral-octahedral hops where either none or one of the two non-participating octahedral sites, connected to the intermediate tetrahedral site, are occupied.14 Van der Ven and Bhattacharya have proposed that such occupation raises the tetrahedral site energy due to cation-cation repulsion, thereby

a Tri-vacancy hop

Di-vacancy hop

b

Octahedral occupancy

Tetrahedral occupancy

Sulfur

Vacancy

Mg2+ or Li+

Blocked

Tet Oct

Scheme 1. Pictoral representations of the two mechanisms discussed herein that might affect the diffusion of ions within thiospinel Ti2S4. Blue squares and red triangles are octahedral and tetrahedral interstitial sites, respectively. a) Tri-vacancy and di-vacancy hops.13,14 b) Occupation of an octahedral interstitial site prevents the occupation of only two nearest neighbour sites; whereas, tetrahedral site occupation prevents four nearest neighbour sites from being occupied.


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retarding diffusion.13,14 Here, a direct, experimental comparison of cation mobility is rendered possible by using precisely the same intercalation host material and cell design, thereby eliminating artifacts due to active surface area of the sample, and/or cell design and fabrication. CuTi2S4 was prepared from the elements at 700°C under vacuum and oxidized with Br2 to remove Cu+, yielding the Cu0.1Ti2S4 active material as described previously.

For simplicity, we omit the residual copper

in the lattice from the formula and refer to this material as simply Ti2S4. To determine the equilibrium potential curves and diffusion coefficients of Mg2+ and Li+ as a function of ion concentration (x), we performed Galvanic Intermittent Titration Technique (GITT) experiments,

using 3-electrode Conflat cells at 60°C. Figure 1 shows the quasi-equilibrium

potential vs x curves for LixTi2S4 (a) and MgxTi2S4 (b). The first discharge profile of LixTi2S4 shown in Figure 1a agrees with the results of Bruce and Saidi.

The similar potential of the

discharge and charge curves signifies that there is virtually no hysteresis; whereas for Mg2+ 2.7

b

Charge Discharge Calculated

2.5

Potential vs Mg (V)

a Potential vs Li (V)

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60


2.3

2.1

1.9

1.7

1.7 Charge Discharge Calculated

1.5

1.3

1.1

0.9

0.7 0

0.4

0.8

1.2

1.6

2

0

0.2

x in LixTi2S4

0.4

0.6

0.8

1

x in MgxTi2S4 +

2+

Figure 1. Quasi-equilibrium profiles for Li (a) and Mg (b) insertion into thiospinel Cu0.1Ti2S4, measured using GITT experiments on 3-electrode Conflat cells at 60°C. The dashed green curves are theoretically calculated and have been reproduced from references 13 in panel (a) and 23 in (b).


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intercalation in Ti2S4, the voltage separation between discharge and charge,

shown in Figure

1b, suggests that hysteresis exists. MgxTi2S4 was discharged to a maximum x value of 0.9, while Li2yTi2S4 achieved y = 0.95 (x = 1.9 in Figure 1a). MgxTi2S4 did not reach x = 0.95 because the overpotential during discharge pulses at x > 0.8 became so large that the discharge potential neared 0 V vs Mg, which eventually terminated the discharge half-cycle. Figure 1 also demonstrates that both the LixTi2S4 and MgxTi2S4 experimental potential curves have a shallower general slope and lie above the theoretical curves calculated previously, although the difference is smaller for MgxTi2S4. In the case of MgxTi2S4 (Figure 1b), the experimental and theoretical curves have different profiles between x = 0 and 0.4 signifying that there may be some additional factors unaccounted for in the model, but the curves match quite well from 0.4 upward if we attribute the shorter experimental curve to the residual copper in the

Lithium

b

1x10-7

Mg2+ Self-Diff., DMg (cm2/s)

a Li+ Self-Diff., DLi (cm2/s)

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

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1x10-8 1x10-9 1x10-10 1x10-11

Discharge Charge

1x10-12

Magnesium 1x10-7 1x10-8 1x10-9 1x10-10 1x10-11

Discharge Charge

1x10-12 0

0.4

0.8

1.2

1.6

2

0

+

2+

x in LixTi2S4

0.2

0.4

0.6

0.8

1

x in MgxTi2S4

Figure 2. Self-diffusion coefficients of Li (a) and Mg (b) in Ti2S4 as a function of ion concentration in the lattice (x), determined via GITT experiments on 3-electrode Conflat cells at 60°C. The working electrode was a 50 mg, binderless pellet with a single-sided geometric surface area of 1.13 cm2.


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spinel. According to Emly et al., the small change in slope in the theoretical potential curve at x = 0.5 is due to Mg2+ ordering on octahedral sites. This dip in potential is also present in the experimental data, albeit at a slightly lower x value, due to the residual copper in the lattice. The GITT experiments also generated self-diffusion coefficients (DLi and DMg, see SI for details), which are shown in Figure 2. The diffusion experiments performed in this work are more refined than, and thus supersede, those performed for our previous paper.4 Surprisingly, a comparison of the first discharge in panels (a) and (b) reveals that just above x = 0, Mg2+ diffusion coefficients are equal to those of Li+, suggesting that in the dilute lattice, ionic charge does not play a large role. However, up to x ≈ 0.55, DMg values descend to values ~10 – 20 times lower than DLi. While this is a surprisingly small factor, it still contributes to the larger overpotentials exhibited on cycling MgxTi2S4 in comparison to LixTi2S4. Nonetheless, beyond x = 0.55, DMg decreases precipitously, which is likely due to two possible factors. 1) The first factor is the onset of di-vacancy hops at x ≈ 0.55 (or equivalently, the decrease in the availability of tri-vacancy hops) in the spinel lattice (Scheme 1a), as predicted by Bhattacharya et al. by kinetic Monte Carlo simulations.

Interestingly, DLi does not decrease precipitously until x >

1.8, which is well past the predicted onset of di-vacancy hops.13 It is possible that di-vacancy hops are a higher energy process for Mg2+ than Li+ owning to stronger cation-cation repulsion in the former. It is also possible that the screening effect of a metallic, sulfide lattice11 fully masks Li+ but cannot do the same for the divalent Mg2+ion. 2) The second factor is the overall decrease in available interstitial sites due to tetrahedral site occupation by Mg2+ ions at x ≈ 0.6 that we demonstrated previously.4 Tetrahedral site occupation within a spinel would reduce the available number of destination sites for a diffusing ion by a factor of two (Scheme 1b). Since Li+ does not occupy tetrahedral sites at any composition,24 DLi is unaffected by this factor. With regard to


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the effect of the desolvation energy of intercalating ions, such an energy barrier only exists at the surface and should thus contribute a constant value to the overpotential (i.e. IR drop) during each current pulse. Since the shape, and not the offset, of the potential during each pulse generates the diffusion coefficient, the desolvation energy should not affect the diffusion coefficient. During charge, the MgxTi2S4 cell shorted due to Mg dendrites (see SI Figure S2) around x =

0.45. Therefore, the Mg0.45Ti2S4 pellet was transferred to a fresh cell and the experiment continued, beginning with comparatively low DMg values at x = 0.4. Although a local minimum in DMg was predicted to accompany Mg2+ ordering on the lattice,

the absence of this feature

in the discharge half-cycle suggests that the dip during charge was caused by re-fabrication of the cell and is thus an artifact. Upon charging, Figure 2b illustrates that above x = 0.55, DMg is significantly higher than during discharge. Although this same phenomenon occurs at x > 1.8 for LixTi2S4 (Figure 2a), its effect is less pronounced. Since these x ranges correspond to the regions with a suspected paucity of available tri-vacancy hops during intercalation, it is likely that tri-vacancies are more prevalent during deintercalation in these x ranges. Considering that the potential response of the MgxTi2S4 working electrode (WE) (and thus the signal that generates the DMg values in Figure 2b) is dictated by the Mg2+ concentration within the WE at the WE/electrolyte interface, we propose the mechanism illustrated in Scheme 2. During deintercalation, the Mg occupying the sites at the surface of the particle (Scheme 2a) can hop into the electrolyte without being limited by the higher activation energy associated with di-vacancies (Scheme 2b). The next layer of Mg2+ ions can then hop towards the surface via a tri-vacancy mediated pathway since the previously interfering Mg2+ ions have been extracted (Scheme 2c). Conversely, during intercalation cation-cation interactions (i.e. di-vacancy hops and/or tetrahedral site occupancy)


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that slow down diffusion are compounded as ions that enter the surface first move slower than the next set of ions that enter the surface behind them.

Scheme 2. Proposed mechanism to account for the difference in DMg between Mg2+ intercalation and deintercalation: a) full lattice; b) extraction of the first layer of Mg2+ from the surface; c) diffusion of Mg2+ ions from the underlying layer into the sites emptied in (b).

To compare the theoretically calculated migration energy of Mg2+ from our previous study (Em = 610 meV) to experimentally determined activation energies (Ea), we carried out experiments similar to GITT that we will refer to as Galvanostatic Alternating Pulse (GAP) experiments, which we have described previously. GAP experiments are more expeditious than performing full GITT cycles and bypass some systematic errors by using a current vs dE/d√t relation, instead of a single dE/d√t value, to generate the diffusion coefficient. Note that Em is a minimum value, since experimental Ea values can contain contributions not modelled in the calculation of theoretical Em values.


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Figure 3 shows representative Arrhenius plot data for two MgxTi2S4 cells with x set to 0.35 (theoretical capacity based on mass) that demonstrates the reproducibility of the GAP experiment. The measured diffusion activation energies (Ea) during discharge were 730 ± 40 meV and 750 ± 50 meV, and during charge they were 600 ± 100 meV and 610 ± 70 meV for cells A and B, respectively.25 Extrapolating to 25°C, Figure 3 indicates that at room temperature DMg is about 1×10-11 cm2/s during charge or 1×10-12 cm2/s during discharge, which is a factor of 100 or 1000 times lower than DLi (2×10-9 cm2/s) in the same material (see Figure S3). This difference explains the larger overpotential and reduced capacity (xmax) of MgxTi2S4 in comparison with LixTi2S4 at 25°C. We note that the electrochemically active surface area of the pressed pellets examined here was assumed to be the geometric (i.e. minimum) surface area (i.e. face of the pellet); thus, the absolute value of the self-diffusion coefficients might be lower than

80

Temperature (°C) 70 60 50

40

-21

-23

ln(DMg)

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

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A Discharge

-25

A Charge B Discharge B Charge -27 2.8

2.9

3

3.1

3.2

1000 / T (1000 / K) Figure 3. Representative Arrhenius plot demonstrating the reproducibility of the GAP experiment, for both discharge and charge pulses. Cells A and B were a 3-electrode, Conflat design, with a 50 mg Ti2S4 pellet working electrode discharged to x = 0.35, 0.5 M Mg(CB11H12)2 in tetraglyme electrolyte and Mg foil reference and counter electrodes.


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reported here. Nonetheless, the comparison between DMg and DLi should be valid. For comparison, Honders et al.28 measured the room temperature chemical diffusion coefficient of Li in pressed pellets to be about 2×10-8 cm2/s in Li0.5CoO2, and 1×10-8 cm2/s in layered Li0.5Ti2S4, which are similar to what we measured in thiospinel Li0.5Ti2S4: 1.5×10-8 cm2/s (see Figure S3). Thus, our use of the geometric surface area yields results consistent with the literature. The Ea values for other x values, and for Li, are shown in

Table 1. The Ea values for Mg2+ follow the same trends as shown in Figure 2 and described by the mechanisms explained in Scheme 1; the discharge Ea values increase with x likely because tri-vacancy hops become more scarce and/or because tetrahedral site occupation reduces the number of destination sites. Upon charge, Ea values remain close to constant between x = 0.25 and 0.55, suggesting that the mechanisms of Scheme 1 no longer affect diffusion, perhaps because of the mechanism proposed in Scheme 2. Previously, we reported computationally derived values for the migration barrier (Em) of 607 meV at x = 0.125 and 511 meV at x = 0.875. The 607 meV value at low x agrees with experiment during both charge and discharge, but the 511 meV value at high x does not agree with the experimental value on discharge because those calculations did not include the loss of tri-vacancy hops as x increases. More recent computations show that di-vacancies increase the barrier to 800 meV, while the mono-vacancy barrier is > 1 eV (private communication, G. Ceder group). That is in accord with the precipitous drop in DMg at x > 0.6, illustrating the value of computation in searching for (and evaluating) new intercalation materials.

In the case of Li+,

the Ea values agree reasonably well with the experimental results of Bruce et al., who reported


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Ea values around 410 meV at x = 0.5 (in LixTi2S4) and 240 meV at x = 0.8, and the calculated Em results of Bhattacharya et al.

Table 1. Diffusion activation energy barriers of MxTi2S4 (M = Li or Mg) at various x values. Ea values were acquired using GAP experiments at 60°C. x

Ea (meV) from Discharge Pulses

Ea (mev) from Charge Pulses

Mg2+ in MgxTi2S4 0.25

570 ± 50

510 ± 50

0.35

740 ± 50

610 ± 90

0.55

850 ± 60

590 ± 50

Li+ in LixTi2S4 0.54

270 ± 40

240 ± 30

In summary, at 60°C, Mg2+ self-diffusion coefficients (DMg) in MgxTi2S4 lie between 10-8 and 10-10 cm2/s up to around x = 2/3, which is sufficient for practical cell operation and are only 10 to 20 times lower than those of Li+ in LixTi2S4 in this range of x. Experimental diffusion activation energies (Ea) at low x values for both Mg2+ (540 ± 80 meV) and Li+ (260 ± 50 meV) agree with theoretical calculations, and provide an explanation for the poor electrochemical behaviour of MgxTi2S4 at room temperature. The fact that Ea for Mg2+ diffusion is approximately twice higher than that for Li+ means that DMg is about two orders of magnitude lower than DLi at room temperature in the same active material. Furthermore, on discharge, DMg decreases precipitously above x = 0.55, likely due to either a growing paucity of available tri-vacancy hops or tetrahedral site occupation, which explains why MgxTi2S4 cannot be discharged beyond x = 0.8. Upon


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charging, the immediately sharp increase in DMg leads us to propose that crowding of the ions during insertion leads to vacancy mediated diffusion but that deinsertion of the near-surface ions into the electrolyte removes the blocking ions from the diffusion path. In general, the confirmation of theoretically calculated Em values using the GAP technique demonstrates the value of this approach and shows that it is useful to compute the theoretical migration energy barriers for ion diffusion of new positive electrode materials before embarking on the (often) laborious synthetic routes to prepare them. This research also demonstrates new phenomena, namely the differing DMg during charge vs discharge at x > 0.55 and the lack of trivacancy dependence in DLi, which leads to a better understanding of interstitial ion diffusion. ASSOCIATED CONTENT Supporting Information Experimental methods, electrolyte synthesis procedure, pictures of Mg dendrites, and the extrapolation of D to room temperature are provided in the SI. AUTHOR INFORMATION Corresponding Author E-mail: [email protected] Notes The authors declare no competing financial interest. ACKNOWLEDGMENTS This work was supported by the Joint Center for Energy Storage Research (JCESR), an Energy Innovation Hub funded by the US Department of Energy (DOE), OSce of Science, Basic Energy Sciences. We thank Prof. Gerd Ceder and his team (UC Berkeley) for helpful discussions.


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NSERC is acknowledged by LFN for a Canada Research Chair, and support through the NSERC Discovery Grant program.

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