Corresponding author

Lijun Fu
Email:L.Fu@...

Max Planck Institute for Solid State Research

References

1.
Maier, J.
Thermodynamics of Electrochemical Lithium Storage
2.
Jamnik, J.; Maier, J.
Nanocrystallinity effects in lithium battery materials. Aspects of nano-ionics. Part IV) 
3.
Fu, L.J.; Chen, C.-C.; Samuelis, D.; Maier, J.
Thermodynamics of Lithium Storage at Abrupt Junctions: Modeling and Experimental Evidence

Department "Physical Chemistry of Solids"

Thermodynamics of lithium storage at abrupt junctions: Modeling and experimental evidence

Authors

L. J. Fu, C.-C. Chen, D. Samuelis, and J. Maier

Departments

Physical Chemistry of Solids (Joachim Maier)

Lithium storage at abrupt junctions is addressed by thermodynamic modeling, and the results are corroborated by experiments, which describe the transition from an interfacial capacitor to a chemical intercalation capacitor. For both Ru:Li2O and Ni:LiF systems, the analysis based on the dependence of storage capacity on voltage indicates that the functionalities and extracted parameters are in good agreement with the thermodynamic model. We also emphasize that a complete understanding of a conventional storage mechanism requires unifying both space charge and bulk storage, in particular but not exclusively for nanocrystalline electrodes.

Knowledge of possible lithium storage mechanisms is key to understand and further develop Li-based batteries. Besides dissolution, phase change and decomposition storage mechanisms, a novel interfacial lithium storage mode was recently proposed [1,2]: In a composite of two phases, none of which may be able to store lithium themselves, Li can be stored in the space charge zones at interface, i.e., Li+ is accumulated in one and the electron in the other phase. This heterogeneous storage is also referred as "job-sharing" mechanism.

The thermodynamic study in terms of analyzing the dependence of the storage capacity on open-circuit voltage provides clear evidence for the occurrence of such a job-sharing mechanism, and excludes conventional bulk storage or the recombination of Li+ and e[3].

Thermodynamics of lithium bulk storage and neutral deposition

For the conventional dissociative bulk storage (Li → Li+ + e), whereby Li+ is accommodated on interstitial sites and e- as conduction electrons, the mass action constant can be written as KLi = n*i / aLi, where n≡concentration of conduction electrons e', i≡concentration of Li+ interstitials Lii . The term αLi denotes Li activity, which is correlated with the chemical potential of lithium (μLi) or the cell voltage (E) in a battery) [3]. Coupling internal electronic and ionic disorder equilibria (electron-hole equilibrium, KB = n·p with p  hole concentration, and Frenkel-equilibrium, KF = i·ν  , with ν  Li+-vacancy concentration, respectively), the relationship between equilibrium cell voltage and charge (Q) is obtained. In the case of perceptible storage, Li-excess (or -deficiency) is prevailing over the intrinsic disorder, then  follows. In case of neutral Li deposition, i.e., recombination of Li+ and e, one gets  .

Thermodynamics of lithium interfacial storage

For the interfacial storage in the form of interstitial lithium ions and excess electrons involving the phases α and β , a "mass action law" can be formulated as  as long as dilute concentrations can be assumed, where  is composed of the chemical standard potentials of the species involved,  and æ represents the electrical potential (Φ) drop between the two sites, æ . When |QLi| values are small, and the potential drop of the contact (cf. æ) can be ignored, Poisson-Boltzmann equation and global electroneutrality lead to  . When both of phases are non-metallic materials, it turns out that n = 4; while n = 3 is obtained when one phase remains non-metallic but the other is a metal. For large |QLi| values, the term æ0 (referring to the two heterophases in contact) will be of relevance, which can be expressed as , where Σ and s are integral charge density and contact distance, respectively. The complete relationship for the whole Q range can be written as:

                         

For small Q (high voltages), the factor Qn in Eq. (1) will dominate, referring to the diffuse part of the capacitance. For large Q (low voltages), the factor exp(γQ) will dominate, corresponding to the rigid part of the capacitance (usual electrostatic capacitance). The factor γ is calculated to be on the order of ≈1 mAh g–1

Experiment results and discussion

<strong>Fig. 1: </strong>(a) Dependence of lithium interfacial storage on lithium activity in the first and second cycle in Ni:LiF nano-composites. the 1/n value varies by not more than 0.05. It has to be noted that the results for the second cycle are more reliable, as the first discharge lacks of reversibility. (b) Dependence of lithium interfacial storage on lithium activity. (c) The fit derived from data in Fig. 1(b) displays the validity of Eq. (1) over the whole Q range for Ni:LiF. The <em>y</em> axis refers to <em>F(Q,E)&equiv;</em>E+(4<em>k<sub>B</sub>T</em>/e)ln<em>Q</em>, here with n = 4. All dashed lines are shown for comparison. Bold red line is fitted; black curve refers to experiment data [3]. Zoom Image
Fig. 1: (a) Dependence of lithium interfacial storage on lithium activity in the first and second cycle in Ni:LiF nano-composites. the 1/n value varies by not more than 0.05. It has to be noted that the results for the second cycle are more reliable, as the first discharge lacks of reversibility. (b) Dependence of lithium interfacial storage on lithium activity. (c) The fit derived from data in Fig. 1(b) displays the validity of Eq. (1) over the whole Q range for Ni:LiF. The y axis refers to F(Q,E)≡E+(4kBT/e)lnQ, here with n = 4. All dashed lines are shown for comparison. Bold red line is fitted; black curve refers to experiment data [3]. [less]

The experimental results fit our model very well in both Ru:Li2O and Ni:LiF systems.  In Ni:LiF system, the interfacial storage occurs at higher E values, where the interference of typical passivation layers can be neglected. Figure 1(a) shows that when the voltage is above 1.6 V vs. Li/Li+, a power law with a slope of the predicted magnitude can be observed. Figure 1(b) shows that the experimental results follow a power law in the range of small Q (V > 1.60 V) but deviates at lower voltage (large Q) as expected. When the whole voltage range is considered and described by the complete Eq. (1), the curve indeed linearizes with a γ- value of the expected order of magnitude, as shown in Fig. 1(c).

<strong><strong>Fig. 2:&nbsp;</strong></strong>(a) Dependence of lithium interfacial storage on lithium activity in Ru:Li<sub>2</sub>O nanocomposites (10<sup>th</sup> cycle); (b) Dependence of <em style="font-size: 0.8em;">F (Q, E) </em>on interfacial storage <em style="font-size: 0.8em;">Q</em>, taking account of both diffusive and electrostatic storage. These plots are derived from galvanostatic discharge/charge measurements of Ru:Li<sub>2</sub>O nanocomposites (prepared by lithiation method from RuO<sub>2</sub>) in voltage range of 1.2&nbsp;&ndash; 0.005V vs. Li<sup>+</sup>/Li, with a current density of 600 mA g<sup>&ndash;1</sup>; (c) Sketch of Li storage in a nanocrystalline electroactive material which can store Li in bulk and subsurface at both (a) small and (b) high Li activity. Higher storage increases both bulk and space charge storage, but the latter to a lesser degree. In addition, the profiles narrow owing to increased screening [3]. Zoom Image
Fig. 2: (a) Dependence of lithium interfacial storage on lithium activity in Ru:Li2O nanocomposites (10th cycle); (b) Dependence of F (Q, E) on interfacial storage Q, taking account of both diffusive and electrostatic storage. These plots are derived from galvanostatic discharge/charge measurements of Ru:Li2O nanocomposites (prepared by lithiation method from RuO2) in voltage range of 1.2 – 0.005V vs. Li+/Li, with a current density of 600 mA g–1; (c) Sketch of Li storage in a nanocrystalline electroactive material which can store Li in bulk and subsurface at both (a) small and (b) high Li activity. Higher storage increases both bulk and space charge storage, but the latter to a lesser degree. In addition, the profiles narrow owing to increased screening [3]. [less]

For Ru:Li2O, the cells have been cycled several times to get a stable passivation layer, and a high current of 600 mA g–1 is applied to filter out the fast interfacial storage and reduce the side reaction (electrolyte decomposition). The voltage hysteresis does not influence strongly the applicability of Eq. (1). As expected only at high voltages the exponents develop toward the right magnitude as Fig. 2(a) shows. When however the complete description is used as in Fig. 2(b), the whole curve linearizes very nicely with slopes (γ) of the correct magnitude when plotting F (Q, E) vs. Q.

It is to be addressed that even for a conventional electroactive electrode, the storage effects in the space charge zones are important as they are decisive for the charge carrier concentrations at the boundaries. These values are relevant for the charge transfer process, a fact that is usually overlooked in the battery community, see [3] for details. Only with a comprehensive consideration of both bulk and space charge storage, a unified understanding of conventional storage can be achieved (cf. Fig. 2(c)).

Conclusion

In short, the novel lithium heterogeneous interfacial storage has been investigated theoretically and experimentally. The parameters extracted from results are in good agreement with the derived thermodynamic model, which excludes bulk dissociative storage and neutral Li deposition. Moreover, the point is stressed that only a unified treatment of space charge and bulk storage enables a comprehensive understanding of conventional storage mechanism.

 
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