Experimental Mechanics

, Volume 58, Issue 4, pp 613–625 | Cite as

Characterization of Stress-Diffusion Coupling in Lithiated Germanium by Nanoindentation

  • M. Papakyriakou
  • X. Wang
  • S. XiaEmail author


There is currently a growing demand for low-cost, high-performance electrochemical energy storage solutions to consumer electronics, vehicle electrification and stationary power management. The successful development and deployment of such solutions necessitate a fundamental understanding of the mechanical properties of electrochemical materials, as well as the intricate coupling between the electro-chemo-mechanical processes in these materials. In this work, we performed a combined experimental and modelling investigation of the stress-diffusion coupling behavior of lithiated germanium (Ge) for its use in high-performance lithium-ion batteries. Thin films of Ge were fabricated using sputtering deposition and then electrochemically lithiated, after which they were subjected to nanoindentation at varying load levels to study indentation-induced creep deformation. Concurrently, a continuum chemo-mechanical model of the nanoindentation test was developed and used to investigate the fundamental mechanisms underlying the stress-gradient-driven creep deformation. The stress-diffusion coupling coefficient and diffusivity of lithium in Ge were obtained by quantitatively comparing the simulated nanoindentation response with the experimental measurements. This integrative experimental and computation work provides important insights into the chemo-mechanical coupling process in high-performance rechargeable battery electrodes.


Rechargeable batteries Electrode materials Stress-diffusion coupling Nanoindentation Chemo-mechanical modelling 



The authors acknowledge the supports of the National Science Foundation (Grants CMMI-1300458 and CMMI-1554393). This work was performed in part at the Georgia Tech Institute for Electronics and Nanotechnology, a member of the National Nanotechnology Coordinated Infrastructure, which is supported by the National Science Foundation (Grant ECCS-1542174).


  1. 1.
    Dunn B, Kamath H, Tarascon J-M (2011) Electrical energy storage for the grid: a battery of choices. Science 334:928–935CrossRefGoogle Scholar
  2. 2.
    Liu XH, Huang S, Picraux ST, Li J, Zhu T, Huang JY (2011) Reversible nanopore formation in Ge nanowires during lithiation–delithiation cycling: an in situ transmission electron microscopy study. Nano Lett 11:3991–3997CrossRefGoogle Scholar
  3. 3.
    Liu XH, Liu Y, Kushima A, Zhang S, Zhu T, Li J, Huang JY (2012) In situ TEM experiments of electrochemical lithiation and delithiation of individual nanostructures. Adv Energy Mater 2:722–741CrossRefGoogle Scholar
  4. 4.
    Liu XH, Wang JW, Huang S, Fan F, Huang X, Liu Y, Krylyuk S, Yoo J, Dayeh SA, Davydov AV (2012) In situ atomic-scale imaging of electrochemical lithiation in silicon. Nat Nanotechnol 7:749–756CrossRefGoogle Scholar
  5. 5.
    McDowell MT, Lee SW, Harris JT, Korgel BA, Wang C, Nix WD, Cui Y (2013) In situ TEM of two-phase Lithiation of amorphous silicon Nanospheres. Nano Lett 13:758–764CrossRefGoogle Scholar
  6. 6.
    Wang JW, He Y, Fan F, Liu XH, Xia S, Liu Y, Harris CT, Li H, Huang JY, Mao SX (2013) Two-phase electrochemical lithiation in amorphous silicon. Nano Lett 13:709–715CrossRefGoogle Scholar
  7. 7.
    Wang J, Fan F, Liu Y, Jungjohann KL, Lee SW, Mao SX, Liu X, Zhu T (2014) Structural evolution and pulverization of tin nanoparticles during lithiation-delithiation cycling. J Electrochem Soc 161:F3019–F3024CrossRefGoogle Scholar
  8. 8.
    Nadimpalli SP, Sethuraman VA, Bucci G, Srinivasan V, Bower AF, Guduru PR (2013) On plastic deformation and fracture in Si films during electrochemical lithiation/delithiation cycling. J Electrochem Soc 160:A1885–A1893CrossRefGoogle Scholar
  9. 9.
    Gonzalez J, Sun K, Huang M, Lambros J, Dillon S, Chasiotis I (2014) Three dimensional studies of particle failure in silicon based composite electrodes for lithium ion batteries. J Power Sources 269:334–343CrossRefGoogle Scholar
  10. 10.
    Gonzalez J, Sun K, Huang M, Dillon S, Chasiotis I, Lambros J (2015) X-ray microtomography characterization of Sn particle evolution during lithiation/delithiation in lithium ion batteries. J Power Sources 285:205–209CrossRefGoogle Scholar
  11. 11.
    Sethuraman VA, Srinivasan V, Bower AF, Guduru PR (2010) In situ measurements of stress-potential coupling in lithiated silicon. J Electrochem Soc 157:A1253–A1261CrossRefGoogle Scholar
  12. 12.
    Sethuraman VA, Chon MJ, Shimshak M, Srinivasan V, Guduru PR (2010) In situ measurements of stress evolution in silicon thin films during electrochemical lithiation and delithiation. J Power Sources 195:5062–5066CrossRefGoogle Scholar
  13. 13.
    Chon MJ, Sethuraman VA, McCormick A, Srinivasan V, Guduru PR (2011) Real-time measurement of stress and damage evolution during initial lithiation of crystalline silicon. Phys Rev Lett 107:045503CrossRefGoogle Scholar
  14. 14.
    Sethuraman VA, Nguyen A, Chon MJ, Nadimpalli SP, Wang H, Abraham DP, Bower AF, Shenoy VB, Guduru PR (2013) Stress evolution in composite silicon electrodes during lithiation/delithiation. J Electrochem Soc 160:A739–A746CrossRefGoogle Scholar
  15. 15.
    Bucci G, Nadimpalli SP, Sethuraman VA, Bower AF, Guduru PR (2014) Measurement and modeling of the mechanical and electrochemical response of amorphous Si thin film electrodes during cyclic lithiation. J Mech Phys Solids 62:276–294CrossRefGoogle Scholar
  16. 16.
    Nadimpalli SP, Tripuraneni R, Sethuraman VA (2015) Real-time stress measurements in germanium thin film electrodes during electrochemical lithiation/delithiation cycling. J Electrochem Soc 162:A2840–A2846CrossRefGoogle Scholar
  17. 17.
    Pharr M, Choi YS, Lee D, Oh KH, Vlassak JJ (2016) Measurements of stress and fracture in germanium electrodes of lithium-ion batteries during electrochemical lithiation and delithiation. J Power Sources 304:164–169CrossRefGoogle Scholar
  18. 18.
    Chen C-H, Chason E, Guduru PR (2017) Measurements of the phase and stress evolution during initial Lithiation of Sn electrodes. J Electrochem Soc 164:A574–A579CrossRefGoogle Scholar
  19. 19.
    Sethuraman VA, Chon MJ, Shimshak M, Van Winkle N, Guduru PR (2010) In situ measurement of biaxial modulus of Si anode for li-ion batteries. Electrochem Commun 12:1614–1617CrossRefGoogle Scholar
  20. 20.
    Wang X, Fan F, Wang J, Wang H, Tao S, Yang A, Liu Y, Beng Chew H, Mao SX, Zhu T, Xia S (2015) High damage tolerance of electrochemically lithiated silicon. Nat Commun 6:8417CrossRefGoogle Scholar
  21. 21.
    Wang X, Yang A, Xia S (2016) Fracture toughness characterization of Lithiated germanium as an anode material for lithium-ion batteries. J Electrochem Soc 163:A90–A95CrossRefGoogle Scholar
  22. 22.
    Pharr M, Suo Z, Vlassak JJ (2013) Measurements of the fracture energy of lithiated silicon electrodes of li-ion batteries. Nano Lett 13:5570–5577CrossRefGoogle Scholar
  23. 23.
    Liu XH, Fan F, Yang H, Zhang S, Huang JY, Zhu T (2013) Self-limiting lithiation in silicon nanowires. ACS Nano 7:1495–1503CrossRefGoogle Scholar
  24. 24.
    Haftbaradaran H, Gao H, Curtin W (2010) A surface locking instability for atomic intercalation into a solid electrode. Appl Phys Lett 96:091909CrossRefGoogle Scholar
  25. 25.
    Gu M, Yang H, Perea DE, Zhang J-G, Zhang S, Wang C-M (2014) Bending-induced symmetry breaking of Lithiation in germanium nanowires. Nano Lett 14:4622–4627CrossRefGoogle Scholar
  26. 26.
    Bhandakkar TK, Johnson HT (2012) Diffusion induced stresses in buckling battery electrodes. J Mech Phys Solids 60:1103–1121MathSciNetCrossRefGoogle Scholar
  27. 27.
    Zhang J, Lu B, Song Y, Ji X (2012) Diffusion induced stress in layered li-ion battery electrode plates. J Power Sources 209:220–227CrossRefGoogle Scholar
  28. 28.
    Cannarella J, Leng CZ, Arnold CB (2014) On the coupling between stress and voltage in lithium-ion pouch cells. In: Proc. of SPIE, pp 91150KGoogle Scholar
  29. 29.
    Jacques E, Lindbergh GR, Zenkert D, Leijonmarck S, Kjell MH (2015) Piezo-electrochemical energy harvesting with lithium-intercalating carbon fibers. ACS Appl Mater Interfaces 7:13898–13904CrossRefGoogle Scholar
  30. 30.
    Cannarella J, Arnold CB (2015) Toward low-frequency mechanical energy harvesting using energy-dense Piezoelectrochemical materials. Adv Mater 27:7440–7444CrossRefGoogle Scholar
  31. 31.
    Kim S, Choi SJ, Zhao K, Yang H, Gobbi G, Zhang S, Li J (2016) Electrochemically driven mechanical energy harvesting. Nat Commun 7:10146CrossRefGoogle Scholar
  32. 32.
    Schiffer Z, Arnold C (2017) Characterization and model of Piezoelectrochemical energy harvesting using Lithium ion batteries. Exp Mech.
  33. 33.
    Gueshi T, Tokuda K, Matsuda H (1978) Voltammetry at partially covered electrodes: part I. Chronopotentiometry and chronoamperometry at model electrodes. J Electroanal Chem Interfacial Electrochem 89:247–260CrossRefGoogle Scholar
  34. 34.
    Fung Y, Chad S (1993) Investigation of the 1-methyl-3-ethylimidazolium chloride-AlCl3/LiAlCl4 system for lithium battery application part I: physical properties and preliminary chronopotentiometric study. J Appl Electrochem 23:346–351CrossRefGoogle Scholar
  35. 35.
    Gueshi T, Tokuda K, Matsuda H (1979) Voltammetry at partially covered electrodes: part II. Linear potential sweep and cyclic voltammetry. J Electroanal Chem Interfacial Electrochem 101:29–38CrossRefGoogle Scholar
  36. 36.
    Itagaki M, Kobari N, Yotsuda S, Watanabe K, Kinoshita S, Ue M (2004) In situ electrochemical impedance spectroscopy to investigate negative electrode of lithium-ion rechargeable batteries. J Power Sources 135:255–261CrossRefGoogle Scholar
  37. 37.
    Kuriyama N, Sakai T, Miyamura H, Uehara I, Ishikawa H, Iwasaki T (1992) Electrochemical impedance spectra and deterioration mechanism of metal hydride electrodes. J Electrochem Soc 139:L72–L73CrossRefGoogle Scholar
  38. 38.
    Hertzberg B, Benson J, Yushin G (2011) Ex-situ depth-sensing indentation measurements of electrochemically produced Si–li alloy films. Electrochem Commun 13:818–821CrossRefGoogle Scholar
  39. 39.
    Ratchford JB, Crawford BA, Wolfenstine J, Allen JL, Lundgren CA (2012) Young's modulus of polycrystalline Li12Si7 using nanoindentation testing. J Power Sources 211:1–3CrossRefGoogle Scholar
  40. 40.
    Ratchford JB, Schuster BE, Crawford BA, Lundgren CA, Allen JL, Wolfenstine J (2011) Young's modulus of polycrystalline Li22Si5. J Power Sources 196:7747–7749CrossRefGoogle Scholar
  41. 41.
    Zinn A-H, Borhani-Haghighi S, Ventosa E, Pfetzing-Micklich J, Wieczorek N, Schuhmann W, Ludwig A (2014) Mechanical properties of SiLix thin films at different stages of electrochemical li insertion. Phys Status Solidi A 211:2650–2656CrossRefGoogle Scholar
  42. 42.
    Berla LA, Lee SW, Cui Y, Nix WD (2015) Mechanical behavior of electrochemically lithiated silicon. J Power Sources 273:41–51CrossRefGoogle Scholar
  43. 43.
    Fuller C, Severiens J (1954) Mobility of impurity ions in germanium and silicon. Phys Rev 96:21CrossRefGoogle Scholar
  44. 44.
    Jung SC, Choi JW, Han Y-K (2012) Anisotropic volume expansion of crystalline silicon during electrochemical lithium insertion: an atomic level rationale. Nano Lett 12:5342–5347CrossRefGoogle Scholar
  45. 45.
    Lee SW, McDowell MT, Berla LA, Nix WD, Cui Y (2012) Fracture of crystalline silicon nanopillars during electrochemical lithium insertion. Proc Natl Acad Sci 109:4080–4085CrossRefGoogle Scholar
  46. 46.
    Lee SW, Ryu I, Nix WD, Cui Y (2015) Fracture of crystalline germanium during electrochemical lithium insertion. Extreme Mechanics Letters 2:15–19CrossRefGoogle Scholar
  47. 47.
    Liang W, Yang H, Fan F, Liu Y, Liu XH, Huang JY, Zhu T, Zhang S (2013) Tough germanium nanoparticles under electrochemical cycling. ACS Nano 7:3427–3433CrossRefGoogle Scholar
  48. 48.
    Graetz J, Ahn CC, Yazami R, Fultz B (2004) Nanocrystalline and thin film germanium electrodes with high lithium capacity and high rate capabilities. J Electrochem Soc 151:A698–A702CrossRefGoogle Scholar
  49. 49.
    Pinson MB, Bazant MZ (2013) Theory of SEI formation in rechargeable batteries: capacity fade, accelerated aging and lifetime prediction. J Electrochem Soc 160:A243–A250CrossRefGoogle Scholar
  50. 50.
    Fischer-Cripps AC (2004) Nanoindentation, 2nd edn. Springer-Verlag, New York CityGoogle Scholar
  51. 51.
    Neale MJ (1995) The tribology handbook. Butterworth-Heinemann, OxfordGoogle Scholar
  52. 52.
    Larcht'e F, Cahn J (1982) The effect of self-stress on diffusion in solids. Acta Metall 30:1835–1845CrossRefGoogle Scholar
  53. 53.
    Bower AF, Guduru PR, Sethuraman VA (2011) A finite strain model of stress, diffusion, plastic flow, and electrochemical reactions in a lithium-ion half-cell. J Mech Phys Solids 59:804–828MathSciNetCrossRefzbMATHGoogle Scholar
  54. 54.
    Oliver WC, Pharr GM (1992) An improved technique for determining hardness and elastic modulus using load and displacement sensing indentation experiments. J Mater Res 7:1564–1583CrossRefGoogle Scholar
  55. 55.
    Shenoy VB, Johari P, Qi Y (2010) Elastic softening of amorphous and crystalline li–Si phases with increasing li concentration: a first-principles study. J Power Sources 195:6825–6830CrossRefGoogle Scholar
  56. 56.
    Qi Y, Hector LG, James C, Kim KJ (2014) Lithium concentration dependent elastic properties of battery electrode materials from first principles calculations. J Electrochem Soc 161:F3010–F3018CrossRefGoogle Scholar
  57. 57.
    Zeng Z, Liu N, Zeng Q, Ding Y, Qu S, Cui Y, Mao WL (2013) Elastic moduli of polycrystalline Li15Si4 produced in lithium ion batteries. J Power Sources 242:732–735CrossRefGoogle Scholar
  58. 58.
    Schuh CA, Hufnagel TC, Ramamurty U (2007) Mechanical behavior of amorphous alloys. Acta Mater 55:4067–4109CrossRefGoogle Scholar
  59. 59.
    Ding N, Xu J, Yao Y, Wegner G, Fang X, Chen C, Lieberwirth I (2009) Determination of the diffusion coefficient of lithium ions in nano-Si. Solid State Ionics 180:222–225CrossRefGoogle Scholar
  60. 60.
    Tritsaris GA, Zhao K, Okeke OU, Kaxiras E (2012) Diffusion of lithium in bulk amorphous silicon: a theoretical study. J Phys Chem C 116:22212–22216CrossRefGoogle Scholar
  61. 61.
    Gao Y, Zhou M (2011) Strong stress-enhanced diffusion in amorphous lithium alloy nanowire electrodes. J Appl Phys 109:014310CrossRefGoogle Scholar

Copyright information

© Society for Experimental Mechanics 2018

Authors and Affiliations

  1. 1.Woodruff School of Mechanical EngineeringGeorgia Institute of TechnologyAtlantaUSA
  2. 2.Department of Materials Science and EngineeringNorthwestern UniversityEvanstonUSA

Personalised recommendations