Fluoride ions as charge carriers in electrochemical energy storage
Source abstract
Abstract
Lithium-ion batteries are commonplace. However, the large-scale production of lithium-ion batteries also raises concerns related to material criticality and safety. Anion charge carriers are intriguing alternatives that invert the current paradigm of battery development and hold promise for high theoretical energy densities that surpass those of lithium technologies at a markedly lower cost, while mitigating challenges in light metal electrodeposition. This Review outlines the design principles for conversion- and insertion-type electrodes and examines their use in conjunction with liquid and solid electrolytes to create devices. The path of 'hard' fluoride ions is traced across the varying components of possible energy storage constructs. Scale-bridging materials design concepts, such as atomic diffusion pathways in periodic solids, ion diffusion through solid and liquid electrolytes and (electro)chemical reactivity at interfaces, are emphasized, as well as systems considerations at the full-cell level. In particular, issues such as materials compatibility, electrode crosstalk and degradation mechanisms are examined. Finally, the potential pitfalls and critical research fronts that must be considered to realize fluoride-ion batteries as a next-generation energy storage technology are discussed.
Source: europepmc · Quality: candidate unverified · Source record ↗
Research context
OpenAlex topics: Inorganic Fluorides and Related Compounds · Fiber-reinforced polymer composites · Advancements in Battery Materials
SciVX discovery tags are terminology-based. OpenAlex topics are source-provided classifications.
References (100+)
Show source-provided references
1. Xiao, A. W., Galatolo, G. & Pasta, M. The case for fluoride-ion batteries. Joule 5, 2823–2844 (2021).10.1016/j.joule.2021.09.016 ↗
2. Cano, Z. P. et al. Batteries and fuel cells for emerging electric vehicle markets. Nat. Energy 3, 279–289 (2018).10.1038/s41560-018-0108-1 ↗
3. Whittingham, M. S. Lithium batteries: 50 years of advances to address the next 20 years of climate issues. Nano Lett. 20, 8435–8437 (2020).10.1021/acs.nanolett.0c04347 ↗
4. Xu, C. et al. Future material demand for automotive lithium-based batteries. Commun. Mater. 1, 99 (2020).10.1038/s43246-020-00095-x ↗
5. Hao, H. et al. Impact of transport electrification on critical metal sustainability with a focus on the heavy-duty segment. Nat. Commun. 10, 5398 (2019).10.1038/s41467-019-13400-1 ↗
6. Graedel, T. E., Harper, E. M., Nassar, N. T., Nuss, P. & Reck, B. K. Criticality of metals and metalloids. Proc. Natl Acad. Sci. USA 112, 4257–4262 (2015).10.1073/pnas.1500415112 ↗
7. Freeman, S. & Agar, E. The benefits of long-duration energy storage for New England’s energy system decarbonization goals. Next Energy 5, 100154 (2024).10.1016/j.nxener.2024.100154 ↗
8. Scott, K. et al. Pathways to Commercial Liftoff: Long Duration Energy Storage (US Department of Energy, 2023).
9. Schäfer, A. W. et al. Technological, economic and environmental prospects of all-electric aircraft. Nat. Energy 4, 160–166 (2019).10.1038/s41560-018-0294-x ↗
10. Ayers, P. W., Mohamed, M. & Heidar-Zadeh, F. in Conceptual Density Functional Theory: Towards a New Chemical Reactivity Theory (ed. Liu, S.) 263–279 (Wiley, 2022).10.1002/9783527829941.ch14 ↗
11. Ayers, P. W. The physical basis of the hard/soft acid/base principle. Faraday Discuss. 135, 161–190 (2007).10.1039/B606877D ↗
12. Kubota, K., Dahbi, M., Hosaka, T., Kumakura, S. & Komaba, S. Towards K-ion and Na-ion batteries as “beyond Li-ion”. Chem. Rec. 18, 459–479 (2018).10.1002/tcr.201700057 ↗
13. Gschwind, F. et al. Fluoride ion batteries: theoretical performance, safety, toxicity, and a combinatorial screening of new electrodes. J. Fluor. Chem. 182, 76–90 (2016).10.1016/j.jfluchem.2015.12.002 ↗
14. Vishnugopi, B. S., Hasan, M. T., Zhou, H. & Mukherjee, P. P. Interphases and electrode crosstalk dictate the thermal stability of solid-state batteries. ACS Energy Lett. 8, 398–407 (2023).10.1021/acsenergylett.2c02443 ↗
15. Santos, D. A. et al. Chemistry–mechanics–geometry coupling in positive electrode materials: a scale-bridging perspective for mitigating degradation in lithium-ion batteries through materials design. Chem. Sci. 14, 458–484 (2023).10.1039/D2SC04157J ↗
16. Janek, J. & Zeier, W. G. A solid future for battery development. Nat. Energy 1, 16141 (2016).10.1038/nenergy.2016.141 ↗
17. Nakano, H. et al. Fluoride-ion shuttle battery with high volumetric energy density. Chem. Mater. 33, 459–466 (2021).10.1021/acs.chemmater.0c04570 ↗
18. Murphy, B. L. & Gabbaï, F. P. Binding, sensing, and transporting anions with pnictogen bonds: the case of organoantimony Lewis acids. J. Am. Chem. Soc. 145, 19458–19477 (2023).10.1021/jacs.3c06991 ↗
19. Bauzá, A., Mooibroek, T. J. & Frontera, A. Tetrel-bonding interaction: rediscovered supramolecular force? Angew. Chem. Int. Ed. 52, 12317–12321 (2013).10.1002/anie.201306501 ↗
20. Sasano, S., Ishikawa, R., Kawahara, K., Shibata, N. & Ikuhara, Y. Highly reversible conversion-type CoSn2 cathode for fluoride-ion batteries. Small 21, 2408023 (2025).10.1002/smll.202408023 ↗
21. Zhang, L., Reddy, M. A. & Fichtner, M. Electrochemical performance of all solid-state fluoride-ion batteries based on thin-film electrolyte using alternative conductive additives and anodes. J. Solid State Electrochem. 22, 997–1006 (2018).10.1007/s10008-017-3838-2 ↗
22. Nakayama, K. et al. Fluoride-ion conversion alloy for fluoride-ion batteries. J. Mater. Chem. A 10, 3743–3749 (2022).10.1039/D1TA09324J ↗
23. Shannon, R. D. Revised effective ionic radii and systematic studies of interatomic distances in halides and chalcogenides. Acta Crystallogr. A 32, 751–767 (1976).10.1107/S0567739476001551 ↗
24. Re´au, J.-M., Matar, S., Villeneuve, G. & Soubeyroux, J.-L. Conduction mechanisms in fluorides and oxide fluorides with the fluorite structure: ionic conductivity, N.M.R. and neutron diffraction. Solid State Ionics 9–10, 563–570 (1983).10.1016/0167-2738(83)90296-5 ↗
25. Rongeat, C., Reddy, M. A., Witter, R. & Fichtner, M. Solid electrolytes for fluoride ion batteries: ionic conductivity in polycrystalline tysonite-type fluorides. ACS Appl. Mater. Interfaces 6, 2103–2110 (2014).10.1021/am4052188 ↗
26. Zhang, D. et al. Understanding the reaction mechanism and performances of 3d transition metal cathodes for all-solid-state fluoride ion batteries. J. Mater. Chem. A 9, 406–412 (2021).10.1039/D0TA08824B ↗
27. Inoishi, A. et al. FeF3 as reversible cathode for all-solid-state fluoride batteries. Adv. Energy Sustain. Res. 3, 2200131 (2022).10.1002/aesr.202200131 ↗
28. Xia, J. et al. Super-reversible CuF2 cathodes enabled by Cu2+-coordinated alginate. Adv. Mater. 34, 2205229 (2022).10.1002/adma.202205229 ↗
29. Shimoda, K. et al. Practical Reversibility of CuF2 in a bulk-type all-solid-state fluoride-ion battery. ACS Energy Lett. 8, 2570–2575 (2023).10.1021/acsenergylett.3c00459 ↗
30. Badway, F. et al. Structure and electrochemistry of copper fluoride nanocomposites utilizing mixed conducting matrices. Chem. Mater. 19, 4129–4141 (2007).10.1021/cm070421g ↗
31. Yu, Y., Lei, M., Li, D. & Li, C. Near-room-temperature quasi-solid-state F-ion batteries with high conversion reversibility based on layered structured electrolyte. Adv. Energy Mater. 13, 2203168 (2023).10.1002/aenm.202203168 ↗
32. Wang, J. & Ma, C. Superior room-temperature cycling stability of fluoride-ion batteries enabled by solid electrolytes synthesized by the solid-state reaction. Sci. China Mater. 65, 3025–3032 (2022).10.1007/s40843-022-2146-2 ↗
33. Ladd, M. F. C. & Lee, W. H. The solubilities of some inorganic halides. Trans. Faraday Soc. 54, 34–39 (1958).10.1039/tf9585400034 ↗
34. Stenger, V. A. Solubilities of various alkali metal and alkaline earth metal compounds in methanol. J. Chem. Eng. Data 41, 1111–1113 (1996).10.1021/je960124k ↗
35. Gschwind, F. & Bastien, J. Parametric investigation of room-temperature fluoride-ion batteries: assessment of electrolytes, Mg-based anodes, and BiF3-cathodes. J. Mater. Chem. A 3, 5628–5634 (2015).10.1039/C4TA06625A ↗
36. Yamamoto, T., Matsumoto, K., Hagiwara, R. & Nohira, T. Room-temperature fluoride shuttle batteries based on a fluorohydrogenate ionic liquid electrolyte. ACS Appl. Energy Mater. 2, 6153–6157 (2019).10.1021/acsaem.9b01260 ↗
37. Thieu, D. T. et al. CuF2 as reversible cathode for fluoride ion batteries. Adv. Funct. Mater. 27, 1701051 (2017).10.1002/adfm.201701051 ↗
38. Hou, P. et al. Alleviating the Jahn–Teller distortion of P3-type manganese-based cathodes by compositionally graded structure for sodium-ion batteries. ACS Sustain. Chem. Eng. 11, 10785–10794 (2023).10.1021/acssuschemeng.3c01854 ↗
39. Zheng, Y. et al. Insights into the Jahn–Teller effect in layered oxide cathode materials for potassium-ion batteries. Adv. Energy Mater. 14, 2400461 (2024).10.1002/aenm.202400461 ↗
40. Nowroozi, M. A., Wissel, K., Rohrer, J., Munnangi, A. R. & Clemens, O. LaSrMnO4: reversible electrochemical intercalation of fluoride ions in the context of fluoride ion batteries. Chem. Mater. 29, 3441–3453 (2017).10.1021/acs.chemmater.6b05075 ↗
41. Jacobs, J. et al. Structural and electronic tunability of Ruddlesden–Popper oxyfluorides through nickel–copper substitution in La2Ni1−xCuxO2.5F3 (0 ≤ x ≤ 1). J. Mater. Chem. A 13, 32539–32550 (2025).10.1039/D5TA05605E ↗
42. Jacobs, J. et al. Ruddlesden–Popper oxyfluorides La2Ni1−xCuxO3F2 (0 ≤ x ≤ 1): impact of the Ni/Cu ratio on the structure. Inorg. Chem. 63, 6075–6081 (2024).10.1021/acs.inorgchem.4c00399 ↗
43. Chatterji, T. & Hansen, T. C. Magnetoelastic effects in Jahn–Teller distorted CrF2 and CuF2 studied by neutron powder diffraction. J. Phys. Condens. Matter 23, 276007 (2011).10.1088/0953-8984/23/27/276007 ↗
44. Omenya, F. et al. Intrinsic challenges to the electrochemical reversibility of the high energy density copper(II) fluoride cathode material. ACS Appl. Energy Mater. 2, 5243–5253 (2019).10.1021/acsaem.9b00938 ↗
45. Luo, Y.-R. & Kerr, J. A. in CRC Handbook of Chemistry and Physics 89th edn (ed. Lide, D. R.) 65–98 (CRC Press, 2012).
46. Liu, A. et al. Reviewing metal fluorides as the cathode materials for high performance Li batteries. Inf. Funct. Mater. 1, 26–67 (2024).
47. Zaheer, W. et al. Lessons learned from FeSb2O4 on stereoactive lone pairs as a design principle for anion insertion. Cell Rep. Phys. Sci. 2, 100592 (2021).10.1016/j.xcrp.2021.100592 ↗
48. Zaheer, W. et al. Reversible room-temperature fluoride-ion insertion in a tunnel-structured transition metal oxide host. ACS Energy Lett. 5, 2520–2526 (2020).10.1021/acsenergylett.0c01328 ↗
49. Takeiri, F., Yajima, T., Hosokawa, S., Matsushita, Y. & Kageyama, H. Topochemical anion insertion into one-dimensional Bi channels in Bi2PdO4. J. Solid State Chem. 286, 121273 (2020).10.1016/j.jssc.2020.121273 ↗
50. Nowroozi, M. A. et al. High cycle life all-solid-state fluoride ion battery with La2NiO4+d high voltage cathode. Commun. Mater. 1, 27 (2020).10.1038/s43246-020-0030-5 ↗
51. Fraggedakis, D. et al. A scaling law to determine phase morphologies during ion intercalation. Energy Environ. Sci. 13, 2142–2152 (2020).10.1039/D0EE00653J ↗
52. Nitta, N., Wu, F., Lee, J. T. & Yushin, G. Li-ion battery materials: present and future. Mater. Today 18, 252–264 (2015).10.1016/j.mattod.2014.10.040 ↗
53. Agbeworvi, G. et al. Stereochemical expression of Bi 6s2 lone pairs mediates fluoride-ion (de)insertion in tunnel-structured Bi2PdO4 and Bi1.6Pb0.4PtO4. Chem. Sci. 16, 5129–5141 (2025).10.1039/D4SC08111K ↗
54. Laurita, G. & Seshadri, R. Chemistry, structure, and function of lone pairs in extended solids. Acc. Chem. Res. 55, 1004–1014 (2022).10.1021/acs.accounts.1c00741 ↗
55. Kolář, M. H. & Hobza, P. Computer modeling of halogen bonds and other σ-hole interactions. Chem. Rev. 116, 5155–5187 (2016).10.1021/acs.chemrev.5b00560 ↗
56. Bauzá, A., Seth, S. K. & Frontera, A. Tetrel bonding interactions at work: impact on tin and lead coordination compounds. Coord. Chem. Rev. 384, 107–125 (2019).10.1016/j.ccr.2019.01.003 ↗
57. Pakhira, A. et al. Interplay between stereochemically active lone pair repulsions, sigma hole interactions, and delocalized redox processes in topochemical fluoride-ion insertion. Angew. Chem. Int. Ed. 64, e202507650 (2025).10.1002/anie.202507650 ↗
58. Andrews, J. L. et al. Room-temperature electrochemical fluoride (de)insertion into CsMnFeF6. ACS Energy Lett. 7, 2340–2348 (2022).10.1021/acsenergylett.2c01324 ↗
59. Bashian, N. H. et al. Electrochemical oxidative fluorination of an oxide perovskite. Chem. Mater. 33, 5757–5768 (2021).10.1021/acs.chemmater.1c01594 ↗
60. Zhang, D. et al. Cathode design based on nitrogen redox and linear coordination of Cu center for all-solid-state fluoride-ion batteries. J. Am. Chem. Soc. 147, 5649–5657 (2025).10.1021/jacs.4c12391 ↗
61. Radomsky, R. C. Electrides as Solid-State Ionic Conductors for Fluoride-Ion Batteries. PhD thesis, Univ. North Carolina at Chapel Hill (2024).
62. Wang, G., Huang, P., Qian, Z., Zhang, P. & Wei, S.-H. High-temperature superconductivity in a two-dimensional electride. Phys. Rev. B 109, 014504 (2024).10.1103/PhysRevB.109.014504 ↗
63. Lee, S. Y. et al. Ferromagnetic quasi-atomic electrons in two-dimensional electride. Nat. Commun. 11, 1526 (2020).10.1038/s41467-020-15253-5 ↗
64. Hartman, S. T. & Mishra, R. Layered electrides as fluoride intercalation anodes. J. Mater. Chem. A 8, 24469–24476 (2020).10.1039/D0TA06162J ↗
65. Tojigamori, T. et al. Fluorination/defluorination behavior of Y2C in fluoride-ion battery anodes. ACS Appl. Energy Mater. 7, 1100–1108 (2024).10.1021/acsaem.3c02613 ↗
66. Pattanathummasid, C. et al. Topochemical fluoride exchange reaction with anionic electrons toward fluoride-ion conduction in layered Ba2−xAxNF1−x (A = Na, K). Chem. Mater. 36, 5671–5677 (2024).10.1021/acs.chemmater.4c00716 ↗
67. Giem, A. R. et al. Interphase formation versus fluoride-ion insertion in tunnel-structured transition metal antimonites. Chem. Commun. 60, 14589–14592 (2024).10.1039/D4CC04331F ↗
68. de Laune, B. P. et al. Topotactic fluorine insertion into the channels of FeSb2O4-related materials. Inorg. Chem. 56, 10078–10089 (2017).10.1021/acs.inorgchem.7b01613 ↗
69. Nowroozi, M. A., Ivlev, S., Rohrer, J. & Clemens, O. La2CoO4: a new intercalation based cathode material for fluoride ion batteries with improved cycling stability. J. Mater. Chem. A 6, 4658–4669 (2018).10.1039/C7TA09427B ↗
70. Slater, P. R. Poly(vinylidene fluoride) as a reagent for the synthesis of K2NiF4-related inorganic oxide fluorides. J. Fluor. Chem. 117, 43–45 (2002).10.1016/S0022-1139(02)00166-5 ↗
71. Sheng, J. et al. Solvothermal fluorination: a new chemical fluorination method to insert fluorine into Sr2CuO3 and NdSr2Cu2O6−δ. Mater. Chem. Phys. 115, 483–487 (2009).10.1016/j.matchemphys.2009.01.019 ↗
72. Blakely, C. K., Bruno, S. R., Kraemer, S. K., Abakumov, A. M. & Poltavets, V. V. Low-temperature solvothermal fluorination method and synthesis of La4Ni3O8Fx oxyfluorides via the La4Ni3O8 infinite-layer intermediate. J. Solid State Chem. 289, 121490 (2020).10.1016/j.jssc.2020.121490 ↗
73. Pigłowska, M. et al. Challenges for safe electrolytes applied in lithium-ion cells—a review. Materials 14, 6783 (2021).10.3390/ma14226783 ↗
74. Xu, K. Electrolytes and interphases in Li-ion batteries and beyond. Chem. Rev. 114, 11503–11618 (2014).10.1021/cr500003w ↗
75. Huggins, R. Advanced Batteries: Materials Science Aspects 315–316 (Springer, 2009).
76. Lee, H. S., Yang, X. Q., Xiang, C. L., McBreen, J. & Choi, L. S. The synthesis of a new family of boron-based anion receptors and the study of their effect on ion pair dissociation and conductivity of lithium salts in nonaqueous solutions. J. Electrochem. Soc. 145, 2813 (1998).10.1149/1.1838719 ↗
77. Konishi, H., Minato, T., Abe, T. & Ogumi, Z. Electrochemical performance of a bismuth fluoride electrode in a reserve-type fluoride shuttle battery. J. Electrochem. Soc. 164, A3702 (2017).10.1149/2.0931714jes ↗
78. Davis, V. K. et al. Room-temperature cycling of metal fluoride electrodes: liquid electrolytes for high-energy fluoride ion cells. Science 362, 1144–1148 (2018).10.1126/science.aat7070 ↗
79. Alshangiti, O. et al. Solvent-in-salt electrolytes for fluoride ion batteries. ACS Energy Lett. 8, 2668–2673 (2023).10.1021/acsenergylett.3c00493 ↗
80. Lewis, J. A. et al. Linking void and interphase evolution to electrochemistry in solid-state batteries using operando X-ray tomography. Nat. Mater. 20, 503–510 (2021).10.1038/s41563-020-00903-2 ↗
81. Lotsch, B. V. & Maier, J. Relevance of solid electrolytes for lithium-based batteries: a realistic view. J. Electroceram. 38, 128–141 (2017).10.1007/s10832-017-0091-0 ↗
82. Nowroozi, M. A. et al. Fluoride ion batteries—past, present, and future. J. Mater. Chem. A 9, 5980–6012 (2021).10.1039/D0TA11656D ↗
83. Bollmann, W., Görlich, P., Hauk, W. & Mothes, H. Ionic conduction of pure and doped CaF2 and SrF2 crystals. Phys. Status Solidi A 2, 157–170 (1970).10.1002/pssa.19700020120 ↗
84. Figueroa, D. R., Chadwick, A. V. & Strange, J. H. NMR relaxation, ionic conductivity and the self-diffusion process in barium fluoride. J. Phys. C 11, 55–73 (1978).10.1088/0022-3719/11/1/017 ↗
85. Barsis, E. & Taylor, A. F− vacancy conductivity in BaF2 crystals. J. Chem. Phys. 48, 4357–4361 (1968).10.1063/1.1667999 ↗
86. Dieudonné, B. et al. Exploring the Sm1−xCaxF3−x tysonite solid solution as a solid-state electrolyte: relationships between structural features and F− ionic conductivity. J. Phys. Chem. C 119, 25170–25179 (2015).10.1021/acs.jpcc.5b05016 ↗
87. Kavun, V. Y., Uvarov, N. F., Slobodyuk, A. B., Merkulov, E. B. & Polyantsev, M. M. Ion mobility and transport properties of bismuth fluoride-containing solid solutions with tysonite-type structure. J. Solid State Chem. 263, 203–207 (2018).10.1016/j.jssc.2018.04.029 ↗
88. Buchinskaya, I. I. & Sorokin, N. I. Tysonite type nanocrystalline solid solutions R1−xScxF3 (R = La, Pr): synthesis and electrical conductivity. Russ. J. Inorg. Chem. 68, 804–811 (2023).10.1134/S0036023623600806 ↗
89. Zhang, M. et al. Recent progress, challenges and prospects of electrolytes for fluoride-ion batteries. Energy Rev. 3, 100083 (2024).10.1016/j.enrev.2024.100083 ↗
90. Hanif, M. B. et al. Recent progress of perovskite-based electrolyte materials for solid oxide fuel cells and performance optimizing strategies for energy storage applications. Mater. Res. Bull. 146, 111612 (2022).10.1016/j.materresbull.2021.111612 ↗
91. Ishihara, T., Matsuda, H. & Takita, Y. Doped LaGaO3 perovskite type oxide as a new oxide ionic conductor. J. Am. Chem. Soc. 116, 3801–3803 (1994).10.1021/ja00088a016 ↗
92. Rupp, G. M., Glowacki, M. & Fleig, J. Electronic and ionic conductivity of La0. 95Sr0. 05Ga0. 95Mg0. 05O3−δ (LSGM) single crystals. J. Electrochem. Soc. 163, F1189–F1197 (2016).10.1149/2.0591610jes ↗
93. Momai, M., Tamura, S., Saeki, S. & Imanaka, N. Crystal phase control and ionic conductivity of magnesium ion-doped lanthanum oxyfluoride. J. Ceram. Soc. Jpn 128, 863–865 (2020).10.2109/jcersj2.20091 ↗
94. Momai, M., Tamura, S. & Imanaka, N. Fluoride ion conducting behavior in nonstoichiometric lanthanum oxyfluoride. Ceram. Int. 49, 1502–1506 (2023).10.1016/j.ceramint.2022.10.079 ↗
95. Cheng, J. et al. Synthesis, chloride-ion diffusion mechanisms, and anisotropic sintering of 2D layered erbium oxychloride nanoplatelets. CrystEngComm 26, 5165–5176 (2024).10.1039/D4CE00585F ↗
96. Sinitsyn, V. V., Lips, O., Privalov, A. F., Fujara, F. & Murin, I. V. Transport properties of LaF3 fast ionic conductor studied by field gradient NMR and impedance spectroscopy. J. Phys. Chem. Solids 64, 1201–1205 (2003).10.1016/S0022-3697(03)00050-7 ↗
97. El Omari, M., Sénégas, J. & Réau, J.-M. Ionic conductivity properties and 19F NMR investigation in Ln1− yCdyF3−y (Ln = Ce, Nd) solid solutions with tysonite-type structure: part I: ionic conductivity properties. Solid State Ionics 107, 281–291 (1998).10.1016/S0167-2738(97)00535-3 ↗
98. Udayakantha, M. et al. Halide replacement with complete preservation of crystal lattice in mixed-anion lanthanide oxyhalides. Angew. Chem. Int. Ed. 60, 15582–15589 (2021).10.1002/anie.202104231 ↗
99. Udayakantha, M., Schofield, P., Waetzig, G. R. & Banerjee, S. A full palette: crystal chemistry, polymorphism, synthetic strategies, and functional applications of lanthanide oxyhalides. J. Solid State Chem. 270, 569–592 (2019).10.1016/j.jssc.2018.12.017 ↗
100. Kizilyalli, M., Corish, J. & Metselaar, R. Definitions of terms for diffusion in the solid state. Pure Appl. Chem. 71, 1307–1325 (1999).