Nanoindentation of high-purity vapor deposited lithium films: A mechanistic rationalization of diffusion-mediated flow


Nanoindentation experiments performed in 5 and 18 μm thick vapor deposited polycrystalline lithium films at 31 °C reveal the mean pressure lithium can support is strongly dependent on length scale and strain rate. At the smallest length scales (indentation depths of 40 nm), the mean pressure lithium can support increases from ∼23 to 175 MPa as the indentation strain rate increases from 0.195 to 1.364 s−1. Furthermore, these pressures are ∼46–350 times higher than the nominal yield strength of bulk polycrystalline lithium. The length scale and strain rate dependent hardness is rationalized using slightly modified forms of the Nabarro–Herring and Harper–Dorn creep mechanisms. Load-displacement curves suggest a stress and length-scale dependent transition from diffusion to dislocation-mediated flow. Collectively, these experimental observations shed significant new light on the mechanical behavior of lithium at the length scale of defects existing at the lithium/solid electrolyte interface.

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  1. 1.

    E.J. Cheng, A. Sharafi, and J. Sakamoto: Intergranular Li metal propagation through polycrystalline Li6.25Al0.25La3Zr2O12 ceramic electrolyte. Electrochim. Acta 223, 85 (2017).

    CAS  Article  Google Scholar 

  2. 2.

    C. Xu, Z. Ahmad, A. Aryanfar, V. Viswanathan, and J.R. Greer: 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 (2017).

    CAS  Article  Google Scholar 

  3. 3.

    S. Yu, R.D. Schmidt, R. Garcia-Mendez, E. Herbert, N.J. Dudney, J.B. Wolfenstine, and D.J. Siegel: Elastic properties of the solid electrolyte Li7La3Zr2O12 (LLZO). Chem. Mater. 28, 197 (2015).

    Article  Google Scholar 

  4. 4.

    R. Schultz: Lithium: Measurement of Young’s Modulus and Yield Strength; Technical Report FERMILAB-TM-2191; Fermi National Accelerator Laboratory: Batavia, IL, 2002.

    Google Scholar 

  5. 5.

    E.G. Herbert, S.A. Hackney, N.J. Dudney, and P.S. Phani: Nanoindentation of high purity vapor deposited lithium films: The elastic modulus. J. Mater. Res. 33, 1335–1346 (2018).

    CAS  Article  Google Scholar 

  6. 6.

    W.C. Oliver and G.M. Pharr: An improved technique for determining hardness and elastic modulus using load and displacement sensing indentation experiments. J. Mater. Res. 7, 1564 (1992).

    CAS  Article  Google Scholar 

  7. 7.

    W.C. Oliver and G.M. Pharr: Measurement of hardness and elastic modulus by instrumented indentation: Advances in understanding and refinements to methodology. J. Mater. Res. 19, 3 (2004).

    CAS  Article  Google Scholar 

  8. 8.

    B.N. Lucas: An experimental investigation of creep and viscoelastic properties using depth-sensing indentation techniques. Ph.D. dissertation, University of Tennessee, Knoxville, 1997.

    Google Scholar 

  9. 9.

    J.P. Hirth and J. Lothe: Theory of Dislocations, 2nd ed. (John Wiley and Sons, New York, NY, 1982); ch. 17.

    Google Scholar 

  10. 10.

    G. Feng and A.H.W. Ngan: Creep and strain burst in indium and aluminium during nanoindentation. Scr. Mater. 45, 971 (2001).

    CAS  Article  Google Scholar 

  11. 11.

    J.R. Morris, H. Bei, G.M. Pharr, and E.P. George: Size effects and stochastic behavior of nanoindentation pop in. Phys. Rev. Lett. 106, 165502 (2011).

    CAS  Article  Google Scholar 

  12. 12.

    I.N. Sneddon: The relation between load and penetration in the axisymmetric boussinesq problem for a punch of arbitrary profile. Int. J. Eng. Sci. 3, 47 (1965).

    Article  Google Scholar 

  13. 13.

    E.G. Herbert, S.A. Hackney, N.J. Dudney, V. Thole, and P.S. Phani: 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).

    CAS  Article  Google Scholar 

  14. 14.

    T.O. Mulhearn and D. Tabor: Creep and hardness of metals: A physical study. J. Inst. Met. 89, 7 (1960).

    CAS  Google Scholar 

  15. 15.

    W.H. Poisl, W.C. Oliver, and B.D. Fabes: The relationship between indentation and uniaxial creep in amorphous selenium. J. Mater. Res. 10, 2024 (1995).

    CAS  Article  Google Scholar 

  16. 16.

    A.F. Bower, N.A. Fleck, A. Needleman, and N. Ogbonna: Indentation of a power law creeping solid. Proc. R. Entomol. Soc. Lond. Ser. A Gen. Entomol. 441, 97 (1993).

    Google Scholar 

  17. 17.

    C. Su, E.G. Herbert, S. Sohn, J.A. LaManna, W.C. Oliver, and G.M. Pharr: Measurement of power-law creep parameters by instrumented indentation methods. J. Mech. Phys. Solid. 61, 517 (2013).

    Article  Google Scholar 

  18. 18.

    T.P. Weihs and J.B. Pethica: Monitoring time-dependent deformation in small volumes. Mater. Res. Soc. Symp. Proc. 239, 235 (1991).

    Google Scholar 

  19. 19.

    W.B. Li and R. Warren: A model for nano-indentation creep. Acta Metall. Mater. 41, 3065 (1993).

    CAS  Article  Google Scholar 

  20. 20.

    S.A. Asif and J.B. Pethica: Nanoindentation creep of single-crystal tungsten and gallium arsenide. Philos. Mag. A 76, 1105 (1997).

    CAS  Article  Google Scholar 

  21. 21.

    H. Li and A.H.W. Ngan: Size effects of nanoindentation creep. J. Mater. Res. 19, 513 (2004).

    CAS  Article  Google Scholar 

  22. 22.

    W.D. Nix and H. Gao: Indentation size effects in crystalline materials: A law for strain gradient plasticity. J. Mech. Phys. Solid. 46, 411 (1998).

    CAS  Article  Google Scholar 

  23. 23.

    T.G. Langdon: An analysis of flow mechanisms in high temperature creep and superplasticity. Mater. Trans. 46, 1951 (2005).

    CAS  Article  Google Scholar 

  24. 24.

    F.R.N. Nabarro: Report of a Conference on Strength of Solids, Vol. 75 (The Physical Society, London, U.K., 1948).

  25. 25.

    C. Herring: Diffusional viscosity of a polycrystalline solid. J. Appl. Phys., 21, 437 (1950).

    Article  Google Scholar 

  26. 26.

    J. Harper and J.E. Dorn: Viscous creep of aluminum near its melting temperature. Acta Metall. 5, 654 (1957).

    CAS  Article  Google Scholar 

  27. 27.

    R.J.D. Tilley: Defects in Solids, Vol. 244 (John Wiley & Sons, Hoboken, New Jersey, 2008).

  28. 28.

    E.H. Lee and J.R.M. Radok: The contact problem for viscoelastic bodies. J. Appl. Mech. 27, 438 (1960).

    Article  Google Scholar 

  29. 29.

    T.C.T. Ting: The contact stresses between a rigid indenter and a viscoelastic half-space. J. Appl. Mech. 33, 845 (1966).

    Article  Google Scholar 

  30. 30.

    D. Tabor: Hardness of Metals (Clarendon Press, Oxford, 1951).

    Google Scholar 

  31. 31.

    A. Lodding, J.N. Mundy, and A. Ott: Isotope inter-diffusion and self-diffusion in solid lithium metal. Phys. Status Solidi B 38, 559 (1970).

    CAS  Article  Google Scholar 

  32. 32.

    D.A. Porter, K.E. Easterling, and M.Y. Sherif: Phase Transformations in Metals and Alloys, 3rd ed. (CRC Press, London, 2009).

    Google Scholar 

  33. 33.

    S.G. Corcoran, R.J. Colton, E.T. Lilleodden, and W.W. Gerberich: Anomalous plastic deformation at surfaces: Nanoindentation of gold single crystals. Phys. Rev. B 55, 57 (1997).

    Article  Google Scholar 

  34. 34.

    G.M. Pharr, E.G. Herbert, and Y. Gao: The indentation size effect: A critical examination of experimental observations and mechanistic interpretations. Annu. Rev. Mater. Res. 40, 271 (2010).

    CAS  Article  Google Scholar 

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This research was sponsored jointly by the U.S. Department of Energy, Office of Energy Efficiency and Renewable Energy’s Advanced Battery Materials Research program (managed by Tien Duong) and by TARDEC, the U.S. Army Tank Automotive Research Development and Engineering Center. E.G.H. is grateful for start-up funding from the Department of Materials Science and Engineering at Michigan Technological University. V.T.’s contributions were financially supported through the MSE Department’s McArthur Internship program. The authors are also grateful for the guidance and input provided by Professor George M. Pharr during the writing of this manuscript.

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Correspondence to Erik G. Herbert.

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Herbert, E.G., Hackney, S.A., Thole, V. et al. Nanoindentation of high-purity vapor deposited lithium films: A mechanistic rationalization of diffusion-mediated flow. Journal of Materials Research 33, 1347–1360 (2018).

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