Reuse & Permissions

It is not necessary to obtain permission to reuse this article or its components as it is available under the terms of the Creative Commons Attribution 4.0 International license. This license permits unrestricted use, distribution, and reproduction in any medium, provided attribution to the author(s) and the published article's title, journal citation, and DOI are maintained. Please note that some figures may have been included with permission from other third parties. It is your responsibility to obtain the proper permission from the rights holder directly for these figures.

Export citation

Export citation

Choose format for download:

Download Citation
  • Open Access

Non-Arrhenius Lithium Diffusion With Temperature-Independent Haven Ratio in Garnet-Type Li6.5La3Zr1.5Ta0.5O12 Single Crystals

Kaori Sugii1, Gen Hasegawa1, Kunimitsu Kataoka2, Kenjiro Hashi3, Junji Akimoto1, Kazunori Takada1, and Naoaki Kuwata1,4,*

  • *Contact author: KUWATA.Naoaki@nims.go.jp

PRX Energy 5, 043003 – Published 21 October, 2026

DOI: https://doi.org/10.1103/zld4-bjxp

Abstract

Lithium-ion dynamics of garnet-type Li6.5La3Zr1.5Ta0.5O12 single crystals were investigated using pulsed field gradient (PFG) NMR and impedance spectroscopy over a wide temperature range up to 700 K. The diffusion coefficient measured by PFG-NMR exhibits non-Arrhenius behavior at elevated temperatures (>400  K). The conductivity diffusion coefficient is consistently higher than the PFG-NMR diffusion coefficient across the entire temperature range, with a Haven ratio of 0.3–0.4, indicating that the motion of mobile Li+ ions is correlated. Remarkably, the Haven ratio exhibits little temperature dependence despite the non-Arrhenius behavior, representing the first experimental observation in garnet-type electrolytes and consistent with the molecular dynamics simulations. This indicates that ion-ion correlations remain essentially unchanged over a wide temperature range. Combined with the local Li+ ion dynamics obtained from spin-lattice relaxation analysis, these results suggest that long-range diffusion is suppressed at low temperatures due to short-range ordering of Li+ ions.

View figure in article

Physics Subject Headings (PhySH)

Popular Summary

Article Text

Supplemental Material

References (50)

  1. T. Famprikis, P. Canepa, J. A. Dawson, M. S. Islam, and C. Masquelier, Fundamentals of inorganic solid-state electrolytes for batteries, Nat. Mater. 18, 1278 (2019).
  2. J. C. Bachman, S. Muy, A. Grimaud, H. H. Chang, N. Pour, S. F. Lux, O. Paschos, F. Maglia, S. Lupart, P. Lamp, L. Giordano, and Y. Shao-Horn, Inorganic solid-state electrolytes for lithium batteries: Mechanisms and properties governing ion conduction, Chem. Rev. 116, 140 (2016).
  3. C. Wang, K. Fu, S. P. Kammampata, D. W. McOwen, A. J. Samson, L. Zhang, G. T. Hitz, A. M. Nolan, E. D. Wachsman, Y. Mo, V. Thangadurai, and L. Hu, Garnet-type solid-state electrolytes: Materials, interfaces, and batteries, Chem. Rev. 120, 4257 (2020).
  4. V. Thangadurai, S. Narayanan, and D. Pinzaru, Garnet-type solid-state fast Li ion conductors for Li batteries: Critical review, Chem. Soc. Rev. 43, 4714 (2014).
  5. K. Kataoka, Oxide single crystals with high lithium-ion conductivity as solid electrolytes for all-solid-state lithium secondary battery applications, J. Ceram. Soc. Jpn. 128, 7 (2020).
  6. K. Kataoka and J. Akimoto, High ionic conductor member of garnet-type oxide Li6.5La3Zr1.5Ta0.5O12, ChemElectroChem 5, 2551 (2018).
  7. K. Kataoka and J. Akimoto, Lithium-containing garnet crystal body, method for producing same, and all-solid-state lithium ion secondary battery, WO2016017769A1 (2015).
  8. K. Kataoka and J. Akimoto, Lithium composite oxide single crystal, lithium composite oxide polycrystal, lithium composite oxide material, solid electrolyte material, all-solid-state lithium ion secondary battery, and method for producing solid electrolyte material, WO2022107687A1 (2021).
  9. K. Kataoka and J. Akimoto, Lithium-ion conductivity and crystal structure of garnet-type solid electrolyte Li7−xLa3Zr2−xTaxO12 using single-crystal, J. Ceram. Soc. Jpn. 127, 521 (2019).
  10. S. Adams and R. P. Rao, Ion transport and phase transition in Li7−xLa3(Zr2−xMx)O12(M=Ta5+,Nb5+,x=0,0.25), J. Mater. Chem. 22, 1426 (2012).
  11. R. P. Rao, W. Gu, N. Sharma, V. K. Peterson, M. Avdeev, and S. Adams, In situ neutron diffraction monitoring of Li7La3Zr2O12 formation: Toward a rational synthesis of garnet solid electrolytes, Chem. Mater. 27, 2903 (2015).
  12. N. Kuwata, G. Hasegawa, S. Xing, K. Hashi, Y. Matsushita, R. Jalem, K. Takada, H. Onodera, and S. Yoshida, Fast lithium-ion diffusion in pyrochlore-type oxyfluoride Li1.25La0.58Nb2O6F, Solid State Ion. 428, 116924 (2025).
  13. Y. Okada, M. Ikeda, and M. Aniya, Non-Arrhenius ionic conductivity in solid electrolytes: A theoretical model and its relation with the bonding nature, Solid State Ion. 281, 43 (2015).
  14. G. Hasegawa, N. Kuwata, K. Hashi, Y. Tanaka, and K. Takada, Lithium-ion diffusion in perovskite-type solid electrolyte lithium lanthanum titanate revealed by pulsed-field gradient nuclear magnetic resonance, Chem. Mater. 35, 3815 (2023).
  15. Y. V. Pogorenko, R. M. Pshenychnyi, A. O. Omelchuk, and V. V. Trachevskyi, Conductivity of aliovalent substitution solid solutions Pb1−xRxSnF4+x(R=Y,La,Ce,Nd,Sm,Gd) with β−PbSnF4 structure, Solid State Ion. 338, 80 (2019).
  16. M. Ikeda and M. Aniya, An extended theory of vacancy formation and its application to ionic conduction in the intrinsic and extrinsic regions, Philos. Mag. 103, 101 (2023).
  17. H. Mehrer, Diffusion in Solids (Springer Science & Business Media, Berlin, 2007).
  18. A. B. Lidiard, Correlation effects in difiusion in solids, Nuovo Cim 7, 620 (1958).
  19. J. Dai, Y. Jiang, and W. Lai, Study of diffusion and conduction in lithium garnet oxides LixLa3Zrx−5Ta7−xO12 by machine learning interatomic potentials, Phys. Chem. Chem. Phys. 24, 15025 (2022).
  20. B. J. Morgan, Lattice-geometry effects in garnet solid electrolytes: A lattice-gas Monte Carlo simulation study, R. Soc. Open Sci. 4, 170824 (2017).
  21. J. E. Tanner, Use of the stimulated echo in NMR diffusion studies, J. Chem. Phys. 52, 2523 (1970).
  22. E. O. Stejskal and J. E. Tanner, Spin diffusion measurements: Spin echoes in the presence of a time-dependent field gradient, J. Chem. Phys. 42, 288 (1965).
  23. K. K. Kim, J. N. Mundy, and W. K. Chen, Diffusion and ionic conductivity in sodium beta alumina, J. Phys. Chem. Solids 40, 743 (1979).
  24. T. J. Willis, D. G. Porter, D. J. Voneshen, S. Uthayakumar, F. Demmel, M. J. Gutmann, M. Roger, K. Refson, and J. P. Goff, Diffusion mechanism in the sodium-ion battery material sodium cobaltate, Sci. Rep. 8, 3210 (2018).
  25. P. Heitjans and S. Indris, Diffusion and ionic conduction in nanocrystalline ceramics, J. Phys. Condens. Matter 15, R1257 (2003).
  26. G. J. Redhammer, M. Meven, S. Ganschow, G. Tippelt, and D. Rettenwander, Single-crystal neutron and X-ray diffraction study of garnet-type solid-state electrolyte Li6La3ZrTaO12: An in situ temperature-dependence investigation (2.5≤T≤873  K), Acta Crystallogr. Sect. B 77, 123 (2021).
  27. A. Dorai, N. Kuwata, R. Takekawa, J. Kawamura, K. Kataoka, and J. Akimoto, Diffusion coefficient of lithium ions in garnet-type Li6.5La3Zr1.5Ta0.5O12 single crystal probed by Li7 pulsed field gradient-NMR spectroscopy, Solid State Ion. 327, 18 (2018).
  28. B. Stanje, D. Rettenwander, S. Breuer, M. Uitz, S. Berendts, M. Lerch, R. Uecker, G. Redhammer, I. Hanzu, and M. Wilkening, Solid electrolytes: Extremely fast charge carriers in garnet-type Li6La3ZrTaO12 single crystals, Ann. Phys. 529, 1700140 (2017).
  29. See Supplemental Material at http://link.aps.org/supplemental/10.1103/zld4-bjxp for brief explanations of the EMA method, the BSCNF model, and the correlation factors associated with HR.
  30. K. Hashi, S. Ohki, Y. Mogami, A. Goto, and T. Shimizu, High-temperature pulsed-field-gradient Li7-NMR measurements of Li2CO3 over 700 K, Anal. Sci. 37, 1477 (2021).
  31. A. Kuhn, S. Narayanan, L. Spencer, G. Goward, V. Thangadurai, and M. Wilkening, Li self-diffusion in garnet-type Li7La3Zr2O12 as probed directly by diffusion-induced Li7 spin-lattice relaxation NMR spectroscopy, Phys. Rev. B 83, 094302 (2011).
  32. L. van Wüllen, T. Echelmeyer, H.-W. Meyer, and D. Wilmer, The mechanism of Li-ion transport in the garnet Li5La3Nb2O12, Phys. Chem. Chem. Phys. 9, 3298 (2007).
  33. J. Fan, T. Wang, C. A. Bridges, A. Y. Borisevich, C. A. Steren, P. Li, B. P. Thapaliya, C.-L. Do-Thanh, Z. Yang, Y. Yuan, and S. Dai, Entropy stabilized cubic Li7La3Zr2O12 with reduced lithium diffusion activation energy: Studied using solid-state NMR spectroscopy, RSC Adv. 13, 19856 (2023).
  34. G. Larraz, A. Orera, J. Sanz, I. Sobrados, V. Diez-Gómez, and M. L. Sanjuán, NMR study of Li distribution in Li7−xHxLa3Zr2O12 garnets, J. Mater. Chem. A Mater. 3, 5683 (2015).
  35. Y. Wang, Y. Su, J. Carrete, H. Zhang, N. Wu, Y. Li, H. Li, J. He, Y. Xu, S. Guo, Q. Cai, D. L. Abernathy, T. Williams, K. V. Kravchyk, M. V. Kovalenko, G. K. H. Madsen, C. Li, and X. Chen, Origin of intrinsically low thermal conductivity in a garnet-type solid electrolyte: Linking lattice and ionic dynamics with thermal transport, Phys. Rev. X Energy 4, 033004 (2025).
  36. N. Bloembergen, E. M. Purcell, and R. V. Pound, Relaxation effects in nuclear magnetic resonance absorption, Phys. Rev. 73, 679 (1948).
  37. M. Wilkening and P. Heitjans, From micro to macro: Access to long-range Li+ diffusion parameters in solids via microscopic Li6,7 spin-alignment echo NMR spectroscopy, ChemPhysChem 13, 53 (2012).
  38. K. Hayamizu, Y. Terada, K. Kataoka, and J. Akimoto, Toward understanding the anomalous Li diffusion in inorganic solid electrolytes by studying a single-crystal garnet of LLZO-Ta by pulsed-gradient spin-echo nuclear magnetic resonance spectroscopy, J. Chem. Phys. 150, 194502 (2019).
  39. R. Landauer, The electrical resistance of binary metallic mixtures, J. Appl. Phys. 23, 779 (1952).
  40. D. Marion Fischer, P. Duwe, S. Indris, and P. Heitjans, Tracer diffusion measurements in solid lithium: A test case for the comparison between NMR in static and pulsed magnetic field gradients after upgrading a standard solid state NMR spectrometer, Solid State Nucl. Magn. Reson. 26, 74 (2004).
  41. P. Posch, S. Lunghammer, S. Berendts, S. Ganschow, G. C.;nther J. Redhammer, A. Wilkening, M. Lerch, B. Gadermaier, D. Rettenwander, and H. M. R. Wilkening, Ion dynamics in Al-Stabilized Li7La3Zr2O12 single crystals–macroscopic transport and the elementary steps of ion hopping, Energy Storage Mater. 24, 220 (2020).
  42. G. E. Murch, The Haven ratio in fast ionic conductors, Solid State Ion. 7, 177 (1982).
  43. J. C. Dyre, P. Maass, B. Roling, and D. L. Sidebottom, Fundamental questions relating to ion conduction in disordered solids, Rep. Prog. Phys. 72, 046501 (2009).
  44. X. He, Y. Zhu, and Y. Mo, Origin of fast ion diffusion in super-ionic conductors, Nat. Commun. 8, 15893 (2017).
  45. R. Sasaki, B. Gao, T. Hitosugi, and Y. Tateyama, Nonequilibrium molecular dynamics for accelerated computation of ion–ion correlated conductivity beyond Nernst–Einstein limitation, npj Comput. Mater. 9, 48 (2023).
  46. R. Sato, Y. Ando, K. Sau, and Y. Shibuta, Visualizing concerted ion migration of superionic conductors via directed graphs, Chem. Mater. 38, 287 (2026).
  47. M. J. Klenk, S. E. Boeberitz, J. Dai, N. H. Jalarvo, V. K. Peterson, and W. Lai, Lithium self-diffusion in a model lithium garnet oxide Li5La3Ta2O12: A combined quasi-elastic neutron scattering and molecular dynamics study, Solid State Ion. 312, 1 (2017).
  48. M. Amores, T. E. Ashton, P. J. Baker, E. J. Cussen, and S. A. Corr, Fast microwave-assisted synthesis of Li-stuffed garnets and insights into Li diffusion from muon spin spectroscopy, J. Mater. Chem. A Mater. 4, 1729 (2016).
  49. R. Jalem, Y. Yamamoto, H. Shiiba, M. Nakayama, H. Munakata, T. Kasuga, and K. Kanamura, Concerted migration mechanism in the Li ion dynamics of garnet-type Li7La3Zr2O12, Chem. Mater. 25, 425 (2013).
  50. C. Chen, Z. Lu, and F. Ciucci, Data mining of molecular dynamics data reveals Li diffusion characteristics in garnet Li7La3Zr2O12, Sci. Rep. 7, 40769 (2017).

Outline

Information

Sign In to Your Journals Account

Filter

Filter

Article Lookup

Enter a citation