First-Principles Study for Fluorination/Defluorination Reaction Mechanism in Fluoride-Shuttle Batteries
Authors: Haruyama Jun , Okazaki Ken–ichi , Morita Yoshiyuki , Nakamoto Hirofumi , Matsubara Eiichiro , Ikeshoji Tamio , Otani Minoru 
Published: May 2020

INTRODUCTION
Rechargeable batteries with energy densities higher than those of the present Li-ion batteries (LIBs) are required for electric vehicles. We focus on fluoride-ion (F−) transfer batteries whose electrodes are composed of metal/metal fluoride (M|MF
n
) combinations. Electrochemical charge-transfer reactions occur during the discharge/charge processes at the two electrodes. Defluorination of the metal fluoride MF
n
and fluorination of another metal M’ occurs at the positive and negative electrodes, respectively, during the discharging process as
M1/n
F + e− → M1/n
+ F− (1),
M’1/m
+ F− → M’1/m
F + e− (2).
This type of battery is called a fluoride-shuttle battery (FSB), which is expected to produce high voltage and have large capacity.1 In 2017, Okazaki et al. fabricated a Bi|BiF3 electrode with a liquid electrolyte prepared by dissolving an organic fluoride in an ionic liquids (ILs) at room temperature. 2 In 2018, Davis et al. reported another type of liquid electrolyte composed of a simple organic solvents (OSs) with F−conductivity greater than 1 mS/cm.3 From the development of these liquid electrolytes, the F− conductivity has been dramatically increased in recent years. After improvement of the electrolyte conductivity, the fluorination and defluorination reactions at the electrodes are considered to be the rate-determining steps in FSBs. However, the mechanism of the fluorination and defluorination reactions in FSBs has not been clarified in contrast to the well-investigated Li-intercalation reaction in LIBs.
METHODS
In this study, we classify the fluorination and defluorination reactions into two possible reaction pathways from a thermodynamic point of view: reaction through the solid-solution state and reaction through the two-phase state. It is possible to find which reaction pathway is realized from the free energy difference. Selection of these reaction pathways can be determined from the enthalpies of all of the intermediate states, since the entropy term in the free energy is fairly cancelled when we consider the difference of free energies. Selection rule for the fluorination and defluorination reactions in FSBs is schematically illustrated in Figure 1. The solid-solution states of M1/n
F
x
for x ≈ 0 and for x ≈ 1 are assumed to be formed by introducing an interstitial and a vacancy defect, respectively. In this case, the free energy relation for the selection can be described as

G
ss(x) < G
tp(x) → H
I(M1/n
) < H(M1/n
F) or H(M1/n
F) < −H
V(M1/n
F) (3),
where G
ss(x), G
tp(x), H (M1/n
F), H
I(M1/n
F) , H
V(M1/n
F) are the free energy of the solid-solution state of M1/n
F
x
, that of two-phase state, the formation enthalpy of M1/n
F, that of interstitial defect in M1/n
, and that of vacancy defect in M1/n
F, respectively. We use the energies from first-principles calculations for the enthalpy differences, whose accuracy is validated by comparing them with experimentally obtained thermodynamic enthalpy data.4 The first-principles calculations were performed with the configurations of the bulk crystal systems using Quantum Espresso package.5 The crystal data were taken from the AtomWork database.6

RESULTS
The relative formation enthalpies of typical, transition, and relativistic metal fluorides are well reproduced by first-principles calculations within 0.1, 0.2, and 0.4 eV, respectively. By comparing the formation enthalpies of H, H
V, and H
I, the relation H
I > H > −H
V is always satisfied in all of the calculated metal and metal-fluoride combinations (M = Li, Mg, Ca, Al, Co, Ni, Cu, Pb, Bi). Thus, the selection rule of eq. (3) strongly suggests that fluorination and defluorination in FSB electrodes occur by two-phase reaction.7 This fluorination and defluorination mechanism will be useful to clarify the rate-determining step in FSBs.
Acknowledgments
This work was supported by the Research and Development Initiative for Scientific Innovation of New Generation Batteries 2 Project (RISING2) administrated by the New Energy and Industrial Technology Development Organization (NEDO).
REFERENCES
1) F. Gschwind, G. Rodriguez-Garcia, D. Sandbeck, A. Gross, M. Weil, M. Fichtner, N. Hörmann, J. Fluorine Chem.
182, 76 (2016).
2) K.-I. Okazaki, Y. Uchimoto, T. Abe, Z. Ogumi, ACS Energy Lett.
2, 1460 (2017).
3) V. K. Davis et al., Science
362, 1144 (2018).
4) Handbook of Chemistry: Pure Chemistry, 5th ed.
5) P. Giannozzi et al., J. Phys.: Condens. Matter.
29, 465901 (2017).
6) National Institute for Materials Science (NIMS) AtomWork <http://crystdb.nims.go.jp/>
7) J. Haruyama, K.-I. Okazaki, Y. Morita, H. Nakamoto, E. Matsubara, T. Ikeshoji, M. Otani, “Two-Phase Reaction Mechanism for Fluorination and Defluorination in Fluoride-Shuttle Batteries: A First-Principles Study” in revision.

Figure 1. Two reaction pathways considered in this study. In the fluorination and defluorination reactions, the solid-solution (M1/n
F
x
, 0 < x< 1) and two-phase (M1/n
and M1/n
F) states are considered to be possible intermediate states.

Figure 1