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On the mechanisms of stress relaxation and intensification at the lithium/solid-state electrolyte interface

Published online by Cambridge University Press:  15 November 2019

Erik G. Herbert ,
Nancy J. Dudney ,
Maria Rochow ,
Violet Thole  and
Stephen A. Hackney
Erik G. Herbert*
Affiliation:
Department of Materials Science and Engineering, Michigan Technological University, Houghton, Michigan 49931, USA
Nancy J. Dudney
Affiliation:
Chemical Sciences Division, Oak Ridge National Laboratory, Oak Ridge, Tennessee 37830, USA
Maria Rochow
Affiliation:
Department of Materials Science and Engineering, Michigan Technological University, Houghton, Michigan 49931, USA
Violet Thole
Affiliation:
Department of Materials Science and Engineering, Michigan Technological University, Houghton, Michigan 49931, USA
Stephen A. Hackney
Affiliation:
Department of Materials Science and Engineering, Michigan Technological University, Houghton, Michigan 49931, USA
*
a)Address all correspondence to this author. e-mail: eherbert@mtu.edu
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Abstract

Under electrochemical cycling, stress intensification and relaxation within small volumes at the lithium/solid-state electrolyte (SSE) interface are thought to be critical factors contributing to mechanical failure of the SSE and subsequent short-circuiting of the device. Nanoindentation has been used to examine the diffusion-limited pressure lithium can support in the absence of active dislocation sources at high homologous temperatures. Based on the underlying physics of this deformation mechanism, a simple perturbation model coupling local current density, elastic stress, and diffusional creep relaxation is introduced. Combining this analysis with the indentation results, it is possible to describe a defect length scale which is too large for effective diffusional creep relaxation, but too small for efficient dislocation multiplication. In this instance, the properties of the SSE may become critical, and relevant indentation results of the SSE are described. The final outcome of the proposed analysis is a newly developed deformation mechanism map.

Keywords

energy storagenanoindentationdiffusion
Type
Invited Feature Paper
Information
Journal of Materials Research , Volume 34 , Issue 21 , 14 November 2019 , pp. 3593 - 3616
Copyright
Copyright © Materials Research Society 2019 

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Footnotes

b)

This author was an editor of this journal during the review and decision stage. For the JMR policy on review and publication of manuscripts authored by editors, please refer to http://www.mrs.org/editor-manuscripts/.

This paper has been selected as an Invited Feature Paper.

References

Sharafi, A., Meyer, H.M., Nanda, J., Wolfenstine, J., and Sakamoto, J.: Characterizing the Li–Li7La3Zr2O12 interface stability and kinetics as a function of temperature and current density. J. Power Sources 302, 135–139 (2016).CrossRefGoogle Scholar
Sharafi, A., Haslam, C.G., Kerns, R.D., Wolfenstine, J., and Sakamoto, J.: Controlling and correlating the effect of grain size with the mechanical and electrochemical properties of Li7La3Zr2O12 solid-state electrolyte. J. Mater. Chem. A 5, 21491–21504 (2017).CrossRefGoogle Scholar
Cheng, E.J., Sharafi, A., and Sakamoto, J.: Intergranular Li metal propagation through polycrystalline Li6.25Al0.25La3Zr2O12 ceramic electrolyte. Electrochim. Acta 223, 85–91 (2017).CrossRefGoogle Scholar
Cheng, L., Chen, W., Kunz, M., Persson, K., Tamura, N., Chen, G., and Doeff, M.: Effect of surface microstructure on electrochemical performance of garnet solid electrolytes. ACS Appl. Mater. Interfaces 7, 2073–2081 (2015).CrossRefGoogle ScholarPubMed
Tsai, C-L., Roddatis, V., Chandran, C.V., Ma, Q., Uhlenbruck, S., Bram, M., Heitjans, P., and Guillon, O.: Li7La3Zr2O12 interface modification for Li dendrite prevention. ACS Appl. Mater. Interfaces 8, 10617–10626 (2016).CrossRefGoogle ScholarPubMed
Yu, S. and Siegel, D.J.: Grain boundary softening: A potential mechanism for lithium metal penetration through stiff solid electrolytes. ACS Appl. Mater. Interfaces 10, 38151–38158 (2018).CrossRefGoogle ScholarPubMed
Yu, S., Schmidt, R.D., Garcia-Mendez, R., Herbert, E.G., Dudney, N.J., Wolfenstine, J.B., Sakamoto, J., and Siegel, D.J.: Elastic properties of the solid electrolyte Li7La3Zr2O12 (LLZO). Chem. Mater. 28, 197–206 (2015).CrossRefGoogle Scholar
Porz, L., Swamy, T., Sheldon, B.W., Rettenwander, D., Frömling, T., Thaman, H.L., Berendts, S., Uecker, R., Carter, W.C., and Chiang, Y-M.: Mechanism of lithium metal penetration through inorganic solid electrolytes. Adv. Energy Mater. 7 (2017).CrossRefGoogle Scholar
Herbert, E.G., Hackney, S.A., Dudney, N.J., Thole, V., and Phani, P.S.: Nanoindentation of high purity vapor deposited lithium films: A mechanistic rationalization of diffusion-mediated flow. J. Mater. Res. 33, 1347–1360 (2018).CrossRefGoogle Scholar
Herbert, E.G., Hackney, S.A., Dudney, N.J., Thole, V., and Phani, P.S.: Nanoindentation of high purity vapor deposited lithium films: A mechanistic rationalization of the transition from diffusion to dislocation-mediated flow. J. Mater. Res. 33, 1361–1368 (2018).CrossRefGoogle Scholar
Swamy, T., Park, R., Sheldon, B.W., Rettenwander, D., Porz, L., Berendts, S., Uecker, R., Carter, W.C., and Chiang, Y-M.: Lithium metal penetration induced by electrodeposition through solid electrolytes: Example in single-crystal Li6La3ZrTaO12 garnet. J. Electrochem. Soc. 165, A3648–A3655 (2018).CrossRefGoogle Scholar
Wang, M., Wolfenstine, J., and Sakamoto, J.: Temperature dependent flux balance of the Li/Li7La3Zr2O12 interface. Electrochim. Acta 296, 842–847 (2019).CrossRefGoogle Scholar
LePage, W.S., Chen, Y., Kazyak, E., Chen, K-H., Sanchez, A.J., Poli, A., Arruda, E.M., Thouless, M.D., and Dasgupta, N.P.: Lithium mechanics: Roles of strain rate and temperature and implications for lithium metal batteries. J. Electrochem. Soc. 166, A89–A97 (2019).CrossRefGoogle Scholar
Masias, A., Felten, N., Garcia-Mendez, R., Wolfenstine, J., and Sakamoto, J.: Elastic, plastic, and creep mechanical properties of lithium metal. J. Mater. Sci. 54, 2585–2600 (2019).CrossRefGoogle Scholar
Schultz, R.: Lithium: Measurement of Young’s Modulus and Yield Strength; Technical Report FERMILAB-TM-2191; Fermi National Accelerator Laboratory, 2002.CrossRefGoogle Scholar
Xu, C., Ahmad, Z., Aryanfar, A., Viswanathan, V., and Greer, J.R.: Enhanced strength and temperature dependence of mechanical properties of Li at small scales and its implications for Li metal anodes. Proc. Natl. Acad. Sci. U. S. A. 114, 57–61 (2017).CrossRefGoogle Scholar
Kraft, O., Gruber, P.A., Mönig, R., and Weygand, D.: Plasticity in confined dimensions. Annu. Rev. Mater. Res. 40 (2010).CrossRefGoogle Scholar
Nix, W.D. and Gao, H.: Indentation size effects in crystalline materials: A law for strain gradient plasticity. J. Mech. Phys. Solids 46, 411–425 (1998).CrossRefGoogle Scholar
Pharr, G.M., Herbert, E.G., and Gao, Y.F.: The indentation size effect: A critical examination of experimental observations and mechanistic interpretations. Annu. Rev. Mater. Res. 40, 271–292 (2010).CrossRefGoogle Scholar
Phani, P.S., Johanns, K.E., George, E.P., and Pharr, G.M.: A simple stochastic model for yielding in specimens with limited number of dislocations. Acta Mater. 61, 2489–2499 (2013).CrossRefGoogle Scholar
Mullins, W.W. and Sekerka, R.F.: Morphological stability of a particle growing by diffusion or heat flow. J. Appl. Phys. 34, 323–329 (1963).CrossRefGoogle Scholar
Mullins, W.W. and Sekerka, R.F.: Stability of a planar interface during solidification of a dilute binary alloy. J. Appl. Phys. 35, 444–451 (1964).CrossRefGoogle Scholar
McCarty, E.D. and Hackney, S.A.: The morphological stability of lateral growth in solid–solid phase transformation during thin-film interdiffusion in Al/Cu bimetal films. Metall. Mater. Trans. A 25, 1613–1625 (1994).CrossRefGoogle Scholar
Herbert, E.G., Hackney, S.A., Dudney, N.J., and Phani, P.S.: Nanoindentation of high purity vapor deposited lithium films: The elastic modulus. J. Mater. Res. 33, 1335–1346 (2018).CrossRefGoogle Scholar
Dudney, N.J.: Approaches toward lithium metal stabilization. MRS Bull. 43, 752–758 (2018).CrossRefGoogle Scholar
Zener, C.: Theory of growth of spherical precipitates from solid solutions. J. Appl. Phys. 20, 950–953 (1949).CrossRefGoogle Scholar
Stefan, J.: Über einige Probleme der Theorie der Wärmeleitung. Sitzungsber. Akad. Wiss. Berlin Math. Kl. 98, 473–484 (1889).Google Scholar
Bower, A.F.: Applied Mechanics of Solids. Available at: http://solidmechanics.org/contents.php (accessed 1 January 2018).CrossRefGoogle Scholar
Johnson, K.L.: The correlation of indentation experiments. J. Mech. Phys. Solids 18, 115–126 (1970).CrossRefGoogle Scholar
Monavari, M. and Zaiser, M.: Annihilation and sources in continuum dislocation dynamics. Mater. Theory 2, 1–30 (2018).CrossRefGoogle Scholar
Basappa, R.H., Ito, T., and Yamada, H.: Contact between garnet-type solid electrolyte and lithium metal anode: Influence on charge transfer resistance and short circuit prevention. J. Electrochem. Soc. 164, A666–A671 (2017).CrossRefGoogle Scholar
Narayan, S. and Anand, L.: A large deformation elastic–viscoplastic model for lithium. Extreme Mech. Lett. 24, 21–29 (2018).CrossRefGoogle Scholar
Wang, Y. and Cheng, Y-T.: A nanoindentation study of the viscoplastic behavior of pure lithium. Scr. Mater. 130, 191–195 (2017).CrossRefGoogle Scholar
Mesarovic, S.D.: Lattice continuum and diffusional creep. Proc. R. Soc. A 472, 1–22 (2016).CrossRefGoogle ScholarPubMed
Bates, J.B., Dudney, N.J., Neudecker, A.U., and Evans, C.D.: Thin-film lithium and lithium-ion batteries. Solid State Ionics 135, 33–45 (2000).CrossRefGoogle Scholar
Dudney, N.J.: Solid-state thin-film rechargeable batteries. Mater. Sci. Eng., B 116, 245–249 (2005).CrossRefGoogle Scholar
Dieter, G.E.: Mechanical Metallurgy (McGraw-Hill Book Company, Inc., New York, Toronto, London, 1961).CrossRefGoogle Scholar
Larche, F.C. and Cahn, J.W.: The interactions of composition and stress in crystalline solids. J. Res. Natl. Bur. Stand. 89, 467–500 (1984).CrossRefGoogle Scholar
Suezawa, M., Saitoh, K., Kojima, K., and Kasuya, A.: Vacancy formation energy at metal-silicon interface region. Jpn. J. Appl. Phys. 44, 593–595 (2005).CrossRefGoogle Scholar
van Loo, F.J.J., Pieraggi, B., and Rapp, R.A.: Interface migration and the kirkendall effect in diffusion-driven phase transformations. Acta Metall. Mater. 38, 1769–1779 (1990).CrossRefGoogle Scholar
Krauskopf, T., Hartmann, H., Zeier, W.G., and Janek, J.: Toward a fundamental understanding of the lithium metal anode in solid-state batteries-an electrochemo-mechanical study on the garnet-type solid electrolyte Li6.25Al0.25La3Zr2O12. ACS Appl. Mater. Interfaces 11, 14463–14477 (2019).CrossRefGoogle Scholar
Blech, I.: Electromigration in thin aluminum films on titanium nitride. J. Appl. Phys. 47, 1203–1208 (1976).CrossRefGoogle Scholar
Blech, I. and Herring, C.: Stress generation by electromigration. Appl. Phys. Lett. 29, 131–133 (1976).CrossRefGoogle Scholar
Shatzkes, M. and Lloyd, J.: A model for conductor failure considering diffusion concurrently with electromigration resulting in a current exponent of 2. J. Appl. Phys. 59 (1986).CrossRefGoogle Scholar
Kirchheim, R. and Kaeber, U.: Atomistic and computer modeling of metallization failure of integrated circuit by electromigration. J. Appl. Phys. 70, 172–181 (1991).CrossRefGoogle Scholar
Clement, J.J. and Lloyd, J.R.: Numerical investigations of the electromigration boundary value problem. J. Appl. Phys. 71 (1991).Google Scholar
Tu, K.: Electromigration in stressed thin films. Phys. Rev. B 45, 1409–1413 (1992).CrossRefGoogle ScholarPubMed
Ross, C.: Stress and electromigration in thin film metallization. Mater. Res. Soc. Proc. 225, 35–46 (1991).CrossRefGoogle Scholar
Kirchheim, R.: Stress and electromigration in Al-lines of the integrated circuits. Acta Metall. Mater. 40, 309–323 (1992).CrossRefGoogle Scholar
Korhonen, M.A., Borgesen, P., Tu, K.N., and Li, C-Y.: Stress evolution due to electromigration in confined metal lines. J. Appl. Phys. 73, 3790–3799 (1993).CrossRefGoogle Scholar
Zarudi, I., Zhang, L.C., Cheong, W.C.D., and Yu, T.X.: The difference of phase distributions in silicon after indentation with Berkovich and spherical indenters. Acta Mater. 53, 4795–4800 (2005).CrossRefGoogle Scholar
Sneddon, I.N.: The relation between load and penetration in the axisymmetric boussinesq problem for a punch of arbitrary profile. Int. J. Eng. Sci. 3, 47–57 (1965).CrossRefGoogle Scholar
Soman, P.S., Herbert, E.G., Aifantis, K.E., and Hackney, S.A.: Analysis of local grain boundary strengthening utilizing the extrinsic indentation size effect. J. Mater. Res. 34, 2347–2369.CrossRefGoogle Scholar
El-Awady, J.A.: Unravelling the physics of size-dependent dislocation-mediated plasticity. Nat. Commun. 6, 1–9 (2015).CrossRefGoogle ScholarPubMed
Gleiter, H.: Interaction of lattice defects and grain boundaries. J. Less-Common Met. 28, 297–323 (1972).CrossRefGoogle Scholar
Swinburne, T.D., Arakawa, K., Mori, H., Yasuda, H., Isshiki, M., Mimura, K., Uchikoshi, M., and Dudarev, S.L.: Fast, vacancy-free climb of prismatic dislocation loops in bcc metals. Sci. Rep. 6, 30596 (2016).CrossRefGoogle ScholarPubMed
Liu, Y., Li, N., Shao, S., Gong, M., Wang, J., McCabe, R.J., Jiang, Y., and Tomé, C.N.: Characterizing the boundary lateral to the shear direction of deformation twins in magnesium. Nat. Commun. 7, 1–6 (2016).Google ScholarPubMed
Barai, P., Higa, K., and Srinivasan, V.: Lithium dendrite growth mechanisms in polymer electrolytes and prevention strategies. Phys. Chem. Chem. Phys. 19, 20493–20505 (2017).CrossRefGoogle ScholarPubMed
Herbert, E.G., Tenhaeff, W.E., Dudney, N.J., and Pharr, G.M.: Mechanical characterization of LiPON films using nanoindentation. Thin Solid Films 250, 413–418 (2011).CrossRefGoogle Scholar
Berla, L.A., Lee, S.W., Cui, Y., and Nix, W.D.: Mechanical behavior of electrochemically lithiated silicon. J. Power Sources 273, 41–51 (2015).CrossRefGoogle Scholar
Lacivita, V., Westover, A.S., Kercher, A., Phillip, N.D., Yang, G., Veith, G., Ceder, G., and Dudney, N.J.: Resolving the amorphous structure of lithium phosphorus oxynitride (lipon). J. Am. Chem. Soc. 140, 11029–11038 (2018).CrossRefGoogle Scholar
Oliver, W.C. and Pharr, G.M.: An improved technique for determining hardness and elastic modulus using load and displacement sensing indentation experiments. J. Mater. Res. 7, 1564–1583 (1992).CrossRefGoogle Scholar
Su, C., Herbert, E.G., Sohn, S., LaManna, J.A., Oliver, W.C., and Pharr, G.M.: Measurement of power-law creep parameters by instrumented indentation methods. J. Mech. Phys. Solids 61, 517–536 (2013).CrossRefGoogle Scholar
Bower, A., Fleck, N.A., Needleman, A., and Ogbonna, N.: Indentation of a power law creeping solid. Proc. R. Soc. London, Ser. A 441, 97–124 (1993).CrossRefGoogle Scholar
Oliver, W.C. and Pharr, G.M.: Measurement of hardness and elastic modulus by instrumented indentation: Advances in understanding and refinements to methodology. J. Mater. Res. 19, 3–20 (2004).CrossRefGoogle Scholar
Callister, W.D. and Rethwisch, D.G.: Fundamentals of Materials Science and Engineering—An Integrated Approach, 5th ed. (J.W. Wiley & Sons, New York, 2015).Google Scholar
Oyen, M.L. and Cook, R.F.: Load–displacement behavior during sharp indentation of viscous–elastic–plastic materials. J. Mater. Res. 18, 139–150 (2003).CrossRefGoogle Scholar
Urazgil’dyaev, K.U., Cheberyak, A.G., Chubok, V.A., and Shishkin, P.G.: Stressed state of a two-layer plate with undulating surface. Int. Appl. Mech. 11, 1283–1287 (1975).Google Scholar
Christensen, J. and Newman, J.: Stress generation and fracture in lithium insertion materials. J. Solid State Electrochem. 10, 293–319 (2006).CrossRefGoogle Scholar
Christensen, J. and Newman, J.: A mathematical model of stress generation and fracture in lithium manganese oxide. J. Electrochem. Soc. 153, A1019–A1030 (2006).CrossRefGoogle Scholar
Zhang, X., Shyy, W., and Sastry, A.M.: Numerical simulation of intercalation-induced stress in Li-ion battery electrode particles. J. Electrochem. Soc. 154, A910–A916 (2007).CrossRefGoogle Scholar
Zhang, X., Sastry, A.M., and Shyy, W.: Intercalation-induced stress and heat generation within single lithium-ion battery cathode particles. J. Electrochem. Soc. 155, A542–A552 (2008).CrossRefGoogle Scholar
Verbrugge, M.W. and Cheng, Y-T.: Stress and strain-energy distributions within diffusion-controlled insertion-electrode particles subjected to periodic potential excitations. J. Electrochem. Soc. 156, A927–A937 (2009).CrossRefGoogle Scholar
Golmon, S., Maute, K., Lee, S-H., and Dunn, M.L.: Stress generation in silicon particles during lithium insertion. Appl. Phys. Lett. 97, 1–3 (2010).CrossRefGoogle Scholar
Lim, C., Yan, B., Yin, L., and Zhu, L.: Simulation of diffusion-induced stress using reconstructed electrodes particle structures generated by micro/nano-CT. Electrochim. Acta 75, 279–287 (2012).CrossRefGoogle Scholar
Malave, V., Berger, J., Zhu, H., and Kee, R.J.: A computational model of the mechanical behavior within reconstructed LixCoO2 Li-ion battery cathode particles. Electrochim. Acta 130, 707–717 (2014).CrossRefGoogle Scholar
Song, Y., Lu, B., Ji, X., and Zhang, J.: Diffusion induced stresses in cylindrical lithium-ion batteries: Analytical solutions and design insights. J. Electrochem. Soc. 159, A2060–A2068 (2012).CrossRefGoogle Scholar
Song, Y., Shao, X., Guo, Z., and Zhang, J.: Role of material properties and mechanical constraint on stress-assisted diffusion in plate electrodes of lithium ion batteries. J. Phys. D: Appl. Phys. 46, 1–10 (2013).CrossRefGoogle Scholar
Purkayastha, R. and McMeeking, R.: A parameter study of intercalation of lithium into storage particles in a lithium-ion battery. Comput. Mater. Sci. 80, 2–14 (2013).CrossRefGoogle Scholar
Deshpande, R., Qi, Y., and Cheng, Y-T.: Effects of concentration-dependent elastic modulus on diffusion-induced stresses for battery applications. J. Electrochem. Soc. 157, A967–A971 (2010).CrossRefGoogle Scholar