Solids that are also liquids: elastic tensors of superionic materials
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Abstract
Abstract Superionics are fascinating materials displaying both solid- and liquid-like characteristics: as solids, they respond elastically to shear stress; as liquids, they display fast-ion diffusion at normal conditions. In addition to such scientific interest, superionics are technologically relevant for energy, electronics, and sensing applications. Characterizing and understanding their elastic properties is, e.g., urgently needed to address their feasibility as solid-state electrolytes in all-solid-state batteries. However, static approaches to elasticity assume well-defined reference positions around which atoms vibrate, in contrast with the quasi-liquid motion of the mobile ions in fast ionic conductors. Here, we derive the elastic tensors of superionics from ensemble fluctuations in the isobaric-isothermal ensemble, exploiting extensive Car-Parrinello simulations. We apply this approach to paradigmatic Li-ion conductors, and complement with a block analysis to compute statistical errors. Static approaches sampled over the trajectories often overestimate the response, highlighting the importance of a dynamical treatment in determining elastic tensors in superionics.
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OpenAlex topics: Advanced Battery Materials and Technologies · Zeolite Catalysis and Synthesis · Thermal Expansion and Ionic Conductivity
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References (100+)
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1. Li, J., Ma, C., Chi, M., Liang, C. & Dudney, N. J. Solid electrolyte: the key for high-voltage lithium batteries. Adv. Energy Mater. 5, 1401408 (2015).10.1002/aenm.201401408 ↗
2. Hori, S. et al. Synthesis, structure, and ionic conductivity of solid solution, Li10+δM1+δP2−δS12 (M= Si, Sn). Faraday Discuss. 176, 83–94 (2015).10.1039/C4FD00143E ↗
3. Deng, Y. et al. Enhancing the lithium ion conductivity in lithium superionic conductor (LISICON) solid electrolytes through a mixed polyanion effect. ACS Appl. Mater. Interfaces 9, 7050–7058 (2017).10.1021/acsami.6b14402 ↗
4. Kato, Y. et al. Synthesis, structure and lithium ionic conductivity of solid solutions of Li10 (Ge1−xMx) P2S12 (M= Si, Sn). J. Power Sources 271, 60–64 (2014).10.1016/j.jpowsour.2014.07.159 ↗
5. Ohtomo, T., Hayashi, A., Tatsumisago, M. & Kawamoto, K. Glass electrolytes with high ion conductivity and high chemical stability in the system LiI–Li2O–Li2S–P2S5. Electrochemistry 81, 428–431 (2013).10.5796/electrochemistry.81.428 ↗
6. Han, F., Zhu, Y., He, X., Mo, Y. & Wang, C. Electrochemical stability of Li10GeP2S12 and Li7La3Zr2O12 solid electrolytes. Adv. Energy Mater. 6, 1501590 (2016).10.1002/aenm.201501590 ↗
7. Sun, Y. et al. A facile strategy to improve the electrochemical stability of a lithium ion conducting Li10GeP2S12 solid electrolyte. Solid State Ion. 301, 59–63 (2017).10.1016/j.ssi.2017.01.014 ↗
8. Yu, C. et al. Accessing the bottleneck in all-solid state batteries, lithium-ion transport over the solid-electrolyte-electrode interface. Nat. Commun. 8, 1–9 (2017).10.1038/s41467-017-01187-y ↗
9. Sakuma, M., Suzuki, K., Hirayama, M. & Kanno, R. Reactions at the electrode/electrolyte interface of all-solid-state lithium batteries incorporating Li–M (M= Sn, Si) alloy electrodes and sulfide-based solid electrolytes. Solid State Ion. 285, 101–105 (2016).10.1016/j.ssi.2015.07.010 ↗
10. Janek, J. & Zeier, W. G. A solid future for battery development. Energy 500, 300 (2016).
11. Culver, S. P., Koerver, R., Krauskopf, T. & Zeier, W. G. Designing ionic conductors: the interplay between structural phenomena and interfaces in thiophosphate-based solid-state batteries. Chem. Mater. 30, 4179–4192 (2018).10.1021/acs.chemmater.8b01293 ↗
12. Kerman, K., Luntz, A., Viswanathan, V., Chiang, Y.-M. & Chen, Z. Practical challenges hindering the development of solid state Li ion batteries. J. Electrochem. Soc. 164, A1731–A1744 (2017).10.1149/2.1571707jes ↗
13. Zhang, W. et al. Interfacial processes and influence of composite cathode microstructure controlling the performance of all-solid-state lithium batteries. ACS Appl. Mater. Interfaces 9, 17835–17845 (2017).10.1021/acsami.7b01137 ↗
14. Koerver, R. et al. Chemo-mechanical expansion of lithium electrode materials–on the route to mechanically optimized all-solid-state batteries. Energy Environ. Sci. 11, 2142–2158 (2018).10.1039/C8EE00907D ↗
15. Wu, X. et al. Operando visualization of morphological dynamics in all-solid-state batteries. Adv. Energy Mater. 9, 1901547 (2019).10.1002/aenm.201901547 ↗
16. Koerver, R. et al. Capacity fade in solid-state batteries: interphase formation and chemomechanical processes in nickel-rich layered oxide cathodes and lithium thiophosphate solid electrolytes. Chem. Mater. 29, 5574–5582 (2017).10.1021/acs.chemmater.7b00931 ↗
17. Aguesse, F. et al. Investigating the dendritic growth during full cell cycling of garnet electrolyte in direct contact with Li metal. ACS Appl. Mater. Interfaces 9, 3808–3816 (2017).10.1021/acsami.6b13925 ↗
18. Zehnder, A. T. Griffith theory of fracture. In Wang, Q. J. & Chung, Y.-W. (eds.) Encyclopedia of Tribology, 1570–1573 (Springer US, Boston, MA, 2013).10.1007/978-0-387-92897-5_259 ↗
19. Zehnder, A. T. Linear elastic stress analysis of 2d cracks. In Fracture Mechanics, 7–32 (Springer, 2012).10.1007/978-94-007-2595-9_2 ↗
20. Griffith, A. A. VI. The phenomena of rupture and flow in solids. Philos. Trans. Royal Soc. 221, 163–198 (1921).
21. Irwin, G. R. Analysis of stresses and strains near the end of a crack traversing a plate. J. Appl. Mech. 24, 361–364 (1957).10.1115/1.4011547 ↗
22. Turner, C. Fracture toughness and specific fracture energy: a re-analysis of results. Mater. Sci. Eng. 11, 275–282 (1973).10.1016/0025-5416(73)90092-X ↗
23. McGrogan, F. P. et al. Compliant yet brittle mechanical behavior of Li2S–P2S5 lithium-ion-conducting solid electrolyte. Adv. Energy Mater. 7, 1602011 (2017).10.1002/aenm.201602011 ↗
24. Bucci, G., Swamy, T., Chiang, Y.-M. & Carter, W. C. Modeling of internal mechanical failure of all-solid-state batteries during electrochemical cycling, and implications for battery design. J. Mater. Chem. A 5, 19422–19430 (2017).10.1039/C7TA03199H ↗
25. Monroe, C. & Newman, J. The impact of elastic deformation on deposition kinetics at lithium/polymer interfaces. J. Electrochem. Soc. 152, A396 (2005).10.1149/1.1850854 ↗
26. Porz, L. et al. Mechanism of lithium metal penetration through inorganic solid electrolytes. Adv. Energy Mater. 7, 1701003 (2017).10.1002/aenm.201701003 ↗
27. Sakuda, A., Hayashi, A. & Tatsumisago, M. Sulfide solid electrolyte with favorable mechanical property for all-solid-state lithium battery. Sci. Rep. 3, 2261 (2013).10.1038/srep02261 ↗
28. Deng, Z., Wang, Z., Chu, I.-H., Luo, J. & Ong, S. P. Elastic properties of alkali superionic conductor electrolytes from first principles calculations. J. Electrochem. Soc. 163, A67–A74 (2016).10.1149/2.0061602jes ↗
29. Zhang, W. et al. (Electro) chemical expansion during cycling: monitoring the pressure changes in operating solid-state lithium batteries. J. Mater. Chem. A 5, 9929–9936 (2017).10.1039/C7TA02730C ↗
30. Aniya, M. Bonding character and ionic conduction in solid electrolytes. Pure Appl. Chem. 91, 1797–1806 (2019).10.1515/pac-2018-1220 ↗
31. Sen, P. & Huberman, B. Low-frequency response of superionic conductors. Phys. Rev. Lett. 34, 1059 (1975).10.1103/PhysRevLett.34.1059 ↗
32. Zeller, H., Brüesch, P., Pietronero, L. & Strässler, S. Lattice dynamics and ionic motion in superionic conductors. In Superionic Conductors, 201–215 (Springer, 1976).10.1007/978-1-4615-8789-7_22 ↗
33. Lundén, A. & Thomas, J. O. The paddle-wheel model for ion conduction in some solid phases. In High Conductivity Solid Ionic Conductors: Recent Trends and Applications, 45–63 (World Scientific, 1989).10.1142/9789814434294_0003 ↗
34. Jansen, M. Volume effect or paddle-wheel mechanism-fast alkali-metal ionic conduction in solids with rotationally disordered complex anions. Angew. Chem. Int. Ed. 30, 1547–1558 (1991).10.1002/anie.199115471 ↗
35. Li, X. & Benedek, N. A. Enhancement of ionic transport in complex oxides through soft lattice modes and epitaxial strain. Chem. Mater. 27, 2647–2652 (2015).10.1021/acs.chemmater.5b00445 ↗
36. Muy, S. et al. Tuning mobility and stability of lithium ion conductors based on lattice dynamics. Energy Environ. Sci. 11, 850–859 (2018).10.1039/C7EE03364H ↗
37. Muy, S. et al. High-throughput screening of solid-state Li-ion conductors using lattice-dynamics descriptors. iScience 16, 270–282 (2019).10.1016/j.isci.2019.05.036 ↗
38. Famprikis, T. et al. A new superionic plastic polymorph of the Na+ conductor Na3PS4. ACS Mater. Lett. 1, 641–646 (2019).10.1021/acsmaterialslett.9b00322 ↗
39. Kraft, M. A. et al. Influence of lattice polarizability on the ionic conductivity in the lithium superionic argyrodites Li6PS5X (X= Cl, Br, I). J. Am. Chem. Soc. 139, 10909–10918 (2017).10.1021/jacs.7b06327 ↗
40. Muy, S. et al. Lithium conductivity and Meyer-Neldel rule in Li3PO4–Li3VO4–Li4GeO4 lithium superionic conductors. Chem. Mater. 30, 5573–5582 (2018).10.1021/acs.chemmater.8b01504 ↗
41. Ngai, K. Meyer–Neldel rule and anti Meyer–Neldel rule of ionic conductivity: conclusions from the coupling model. Solid State Ion. 105, 231–235 (1998).10.1016/S0167-2738(97)00469-4 ↗
42. Meyer, V. & Neldel, H. Über die Beziehungen zwischen der Energiekonstanten ϵ under der Mengenkonstanten α in der Leitwerts-Temperaturformel bei oxydischen Halbleitern. Z. Phys. Chem. 12, 588–593 (1937).
43. Krauskopf, T., Culver, S. P. & Zeier, W. G. Bottleneck of diffusion and inductive effects in Li10Ge1−x Snx P2S12. Chem. Mater. 30, 1791–1798 (2018).10.1021/acs.chemmater.8b00266 ↗
44. Wang, Z. et al. Elastic properties of new solid state electrolyte material Li10GeP2S12: a study from first-principles calculations. Int. J. Electrochem. Sci. 9, 562–568 (2014).10.1016/S1452-3981(23)07739-8 ↗
45. Ahmad, Z. & Viswanathan, V. Quantification of uncertainty in first-principles predicted mechanical properties of solids: application to solid ion conductors. Phys. Rev. B 94, 064105 (2016).10.1103/PhysRevB.94.064105 ↗
46. Yang, Y. et al. Elastic properties, defect thermodynamics, electrochemical window, phase stability, and Li+ mobility of Li3PS4: insights from first-principles calculations. ACS Appl. Mater. Interfaces 8, 25229–25242 (2016).10.1021/acsami.6b06754 ↗
47. Yu, S. et al. Elastic properties of the solid electrolyte Li7La3Zr2O12 (LLZO). Chem. Mater. 28, 197–206 (2016).10.1021/acs.chemmater.5b03854 ↗
48. Wu, M., Xu, B., Lei, X., Huang, K. & Ouyang, C. Bulk properties and transport mechanisms of a solid state antiperovskite Li-ion conductor Li3OCl: insights from first principles calculations. J. Mater. Chem. A 6, 1150–1160 (2018).10.1039/C7TA08780B ↗
49. Mehl, M. J., Osburn, J. E., Papaconstantopoulos, D. A. & Klein, B. M. Structural properties of ordered high-melting-temperature intermetallic alloys from first-principles total-energy calculations. Phys. Rev. B 41, 10311–10323 (1990).10.1103/PhysRevB.41.10311 ↗
50. Mehl, M. J., Klein, B. M. & Papaconstantopoulos, D. A. First-principles calculation of elastic properties. Intermetallic Compd. 1, 195–210 (1994).
51. Le Page, Y. & Saxe, P. Symmetry-general least-squares extraction of elastic data for strained materials from ab initio calculations of stress. Phys. Rev. B 65, 104104 (2002).10.1103/PhysRevB.65.104104 ↗
52. Zhao, J., Winey, J. M. & Gupta, Y. M. First-principles calculations of second- and third-order elastic constants for single crystals of arbitrary symmetry. Phys. Rev. B 75, 094105 (2007).10.1103/PhysRevB.75.094105 ↗
53. Le Page, Y. & Saxe, P. Symmetry-general least-squares extraction of elastic coefficients from ab initio total energy calculations. Phys. Rev. B 63, 174103 (2001).10.1103/PhysRevB.63.174103 ↗
54. Nielsen, O. H. & Martin, R. M. First-principles calculation of stress. Phys. Rev. Lett. 50, 697–700 (1983).10.1103/PhysRevLett.50.697 ↗
55. Uesugi, T., Takigawa, Y. & Higashi, K. Elastic constants of AlLi from first principles. Mater. Trans. 46, 1117–1121 (2005).10.2320/matertrans.46.1117 ↗
56. Klarbring, J. & Simak, S. I. Phase stability of dynamically disordered solids from first principles. Phys. Rev. Lett. 121, 225702 (2018).10.1103/PhysRevLett.121.225702 ↗
57. Pavone, P. et al. Ab initio lattice dynamics of diamond. Phys. Rev. B 48, 3156 (1993).10.1103/PhysRevB.48.3156 ↗
58. Mounet, N. & Marzari, N. First-principles determination of the structural, vibrational and thermodynamic properties of diamond, graphite, and derivatives. Phys. Rev. B 71, 205214 (2005).10.1103/PhysRevB.71.205214 ↗
59. Dragoni, D., Ceresoli, D. & Marzari, N. Thermoelastic properties of α-iron from first-principles. Phys. Rev. B 91, 104105 (2015).10.1103/PhysRevB.91.104105 ↗
60. Parrinello, M. & Rahman, A. Strain fluctuations and elastic constants. J. Chem. Phys. 76, 2662–2666 (1982).10.1063/1.443248 ↗
61. Parrinello, M. & Rahman, A. Crystal structure and pair potentials: a molecular-dynamics study. Phys. Rev. Lett. 45, 1196 (1980).10.1103/PhysRevLett.45.1196 ↗
62. Parrinello, M. & Rahman, A. Polymorphic transitions in single crystals: a new molecular dynamics method. J. Appl. Phys 52, 7182–7190 (1981).10.1063/1.328693 ↗
63. Landau, L. S. & Lifshitz, E. M. Statistical Physics (Addison-Wesley, Reading, Mass., 1958).
64. Sprik, M., Impey, R. W. & Klein, M. L. Second-order elastic constants for the lennard-jones solid. Phys. Rev. B 29, 4368 (1984).10.1103/PhysRevB.29.4368 ↗
65. Kamaya, N. et al. A lithium superionic conductor. Nat. Mater. 10, 682 (2011).10.1038/nmat3066 ↗
66. Kuhn, A., Duppel, V. & Lotsch, B. V. Tetragonal Li10GeP2S12 and Li7GePS8–exploring the Li ion dynamics in LGPS Li electrolytes. Energy Environ. Sci. 6, 3548–3552 (2013).10.1039/c3ee41728j ↗
67. Rabadanov, M. K., Pietraszko, A., Kireev, V., Ivanov-Schitz, A. & Simonov, V. Atomic structure and mechanism of ionic conductivity of Li 3.31 Ge 0.31 P 0.69 O 4 single crystals. Crystallogr. Rep. 48, 744–749 (2003).10.1134/1.1612594 ↗
68. Gilardi, E. et al. Li4−x Ge1−x Px O4, a potential solid-state electrolyte for all-oxide microbatteries. ACS Appl. Energy Mater. 3, 9910 (2020).10.1021/acsaem.0c01601 ↗
69. Materzanini, G., Kahle, L., Marcolongo, A. & Marzari, N. High Li-ion conductivity in tetragonal LGPO: a comparative first-principles study against known LISICON and LGPS phases. Phys. Rev. Mater. 5, 035408 (2021).10.1103/PhysRevMaterials.5.035408 ↗
70. Martyna, G. J., Klein, M. L. & Tuckerman, M. Nosé–Hoover chains: the canonical ensemble via continuous dynamics. J. Chem. Phys. 97, 2635–2643 (1992).10.1063/1.463940 ↗
71. Bernasconi, M. et al. First-principle-constant pressure molecular dynamics. J. Phys. Chem. Solids 56, 501–505 (1995).10.1016/0022-3697(94)00228-2 ↗
72. Car, R. & Parrinello, M. Unified approach for molecular dynamics and density-functional theory. Phys. Rev. Lett. 55, 2471 (1985).10.1103/PhysRevLett.55.2471 ↗
73. Frenkel, D. & Smit, B. Understanding molecular simulation: from algorithms to applications, vol. 1 (Elsevier, 2001).
74. Wachtman Jr, J., Tefft, W., Lam Jr, D. & Apstein, C. Exponential temperature dependence of Young’s modulus for several oxides. Phys. Rev. 122, 1754 (1961).10.1103/PhysRev.122.1754 ↗
75. Anderson, O. L. Derivation of Wachtman’s equation for the temperature dependence of elastic moduli of oxide compounds. Phys. Rev. 144, 553 (1966).10.1103/PhysRev.144.553 ↗
76. Rajagopalan, S. On the validity of modified Wachtman’s equation for nonoxide solids. Phys. Status Solidi B 40, 513–516 (1970).10.1002/pssb.19700400208 ↗
77. Kanno, R. & Murayama, M. Lithium ionic conductor thio-LISICON: the Li2S GeS2 P2S5 system. J. Electrochem. Soc. 148, A742–A746 (2001).10.1149/1.1379028 ↗
78. Ong, S. P. et al. Phase stability, electrochemical stability and ionic conductivity of the Li10±1MP2X12 (M = Ge, Si, Sn, Al or P, and X = O, S or Se) family of superionic conductors. Energy Environ. Sci. 6, 148–156 (2013).10.1039/C2EE23355J ↗
79. Materials cloud archive. https://archive.materialscloud.org/record/2021.15.
80. Sun, Y. et al. Oxygen substitution effects in Li10GeP2S12 solid electrolyte. J. Power Sources 324, 798–803 (2016).10.1016/j.jpowsour.2016.05.100 ↗
81. Hohenberg, P. & Kohn, W. Inhomogeneous electron gas. Phys. Rev. 136, B864 (1964).10.1103/PhysRev.136.B864 ↗
82. Kohn, W. & Sham, L. J. Self-consistent equations including exchange and correlation effects. Phys. Rev. 140, A1133 (1965).10.1103/PhysRev.140.A1133 ↗
83. Payne, M. C., Teter, M. P., Allan, D. C., Arias, T. & Joannopoulos, aJ. Iterative minimization techniques for ab initio total-energy calculations: molecular dynamics and conjugate gradients. Rev. Mod. Phys. 64, 1045 (1992).10.1103/RevModPhys.64.1045 ↗
84. Galli, G. & Pasquarello, A. First-principles molecular dynamics. In Computer simulation in chemical physics, 261–313 (Springer, 1993).10.1007/978-94-011-1679-4_8 ↗
85. Giannozzi, P. et al. Quantum espresso: a modular and open-source software project for quantum simulations of materials. J. Phys. Condens. Matter 21, 395502 (2009).10.1088/0953-8984/21/39/395502 ↗
86. Nosé, S. A unified formulation of the constant temperature molecular dynamics methods. J. Chem. Phys. 81, 511–519 (1984).10.1063/1.447334 ↗
87. Perdew, J. P., Burke, K. & Ernzerhof, M. Generalized gradient approximation made simple. Phys. Rev. Lett. 77, 3865 (1996).10.1103/PhysRevLett.77.3865 ↗
88. Isaacs, E. B. & Wolverton, C. Performance of the strongly constrained and appropriately normed density functional for solid-state materials. Phys. Rev. Mater. 2, 063801 (2018).10.1103/PhysRevMaterials.2.063801 ↗
89. Monkhorst, H. J. & Pack, J. D. Special points for brillouin-zone integrations. Phys. Rev. B 13, 5188 (1976).10.1103/PhysRevB.13.5188 ↗
90. Grasselli, F. Investigating finite-size effects in molecular dynamics simulations of ion diffusion, heat transport, and thermal motion in superionic materials. J. Chem. Phys. 156, 134705 (2022).10.1063/5.0087382 ↗
91. Kahle, L., Marcolongo, A. & Marzari, N. High-throughput computational screening for solid-state Li-ion conductors. Energy Environ. Sci. 13, 928–948 (2020).10.1039/C9EE02457C ↗
92. Nye, J. F. et al. Physical properties of crystals: their representation by tensors and matrices (Oxford university press, 1985).
93. Sakuda, A., Hayashi, A., Takigawa, Y., Higashi, K. & Tatsumisago, M. Evaluation of elastic modulus of Li2S–P2S5 glassy solid electrolyte by ultrasonic sound velocity measurement and compression test. J. Ceram. Soc. Jpn. 121, 946–949 (2013).10.2109/jcersj2.121.946 ↗
94. Kato, A. et al. Mechanical properties of sulfide glasses in all-solid-state batteries. J. Ceram. Soc. Jpn. 126, 719–727 (2018).10.2109/jcersj2.18022 ↗
95. Mangani, L. R. & Villevieille, C. Mechanical vs. chemical stability of sulphide-based solid-state batteries. Which one is the biggest challenge to tackle? Overview of solid-state batteries and hybrid solid state batteries. J. Mater. Chem. A 8, 10150–10167 (2020).10.1039/D0TA02984J ↗
96. Garcia-Mendez, R., Smith, J. G., Neuefeind, J. C., Siegel, D. J. & Sakamoto, J. Correlating macro and atomic structure with elastic properties and ionic transport of glassy Li2S–P2S5 (LPS) solid electrolyte for solid-state Li metal batteries. Adv. Energy Mater. 10, 2000335 (2020).10.1002/aenm.202000335 ↗
97. Keane, A. The gravitational compression of an elastic sphere. Aust. J. Phys. 8, 167–175 (1955).10.1071/PH550167 ↗
98. Anderson, O. L. On the use of ultrasonic and shock-wave data to estimate compressions at extremely high pressures. Phys. Earth Planet. Inter. 1, 169–176 (1968).10.1016/0031-9201(68)90006-X ↗
99. Kuhn, A., Köhler, J. & Lotsch, B. V. Single-crystal X-ray structure analysis of the superionic conductor Li10GeP2S12. Phys. Chem. Chem. Phys. 15, 11620–11622 (2013).10.1039/c3cp51985f ↗
100. Song, S., Dong, Z., Deng, F. & Hu, N. Lithium superionic conductors Li10MP2O12 (m= Ge, Si). Funct. Mater. Lett. 11, 1850039 (2018).10.1142/S179360471850039X ↗