Morphological Instability of Lithium Electrodeposition Due to Stress-Driven Interface Diffusion
Authors: Hebert Kurt 
Published: July 2022

Morphological instability of the lithium-electrolyte interface is a critical problem limiting the development of lithium-metal negative electrodes for batteries. At high current densities approaching the diffusion-limited current density, dendrites form due to depletion of Li+ ions near the electrode surface (1). At lower current densities, unstable deposition produces whiskers (2). Whiskers are separated by typically several micrometers, and in contrast to dendrites grow by addition of Li atoms to their base or "root" (3). Experimental evidence indicates that whisker growth is fed by large-scale interface or grain boundary diffusion, and that whiskers relieve compressive stress in the metal generated by electrodeposition (4-7).
The present study proposes that Li electrodeposition is destabilized by interface diffusion driven by compressive stress due to incorporation of Li atoms at grain boundaries. The competition between stress and stabilizing surface energy effects generates a surface pattern which determines (in part) whisker sites. A morphological instability model is formulated based on the Asaro-Tiller-Grinfel'd (ATG) surface instability on elastically stress solids (8). The model applies to deposits less than 1 micron thick for which elastic deformation is expected to dominate (9,10). The Li electrode is depicted by a three-layer elastic model consisting of a stress-free substrate (current collector) layer, a Li layer with uniform diffusion-induced in-plane stress, and top layer. The top layer can simulate submicron thickness solid-electrolyte interface (SEI) layers, or macroscopically thick polymer separators and solid electrolytes. The Li-top layer interface deforms by diffusion. Out-of-plane normal stress is included to simulate the effect of applied stress on the instability (11,12).
For model calculations, the interface stress was estimated from neutron-depth-profiling measurements of Li diffusion into Cu current collectors (13). The measured Li incorporation was found to be consistent with a whisker spacing of several microns, in agreement with experimental results (3,6,14). Calculations showed that the instability is inhibited significantly by the use of substrates with elastic modulus much greater than that of Li. This substrate stiffness effect is consistent with experimental observations of Sn whiskers (15). The effect of a stress-free SEI layer on the instability was found to be negligible, due to its small thickness. Whisker growth was suppressed by macroscopically thick top layers with elastic modulus at least 10 times that of Li. No significant whisker inhibition was found at applied stress levels of ~ 1 MPa, which are found experimentally to stabilize deposition in Li films significantly exceeding 1 micron thickness (11,12). This effect may be due to an instability associated with viscoplastic rather than elastic deformation (16).
REFERENCES

P. Bai et al., Energy Environ. Sci., 9, 3221(2016).

L Frenck et al., Front. Energy Res., 7, 115 (2016)

A. Kushima et al., Nano Energy, 32, 271 (2017).

J. H. Cho et al., Energy Storage Mater., 24, 281 (2020).

X. Wang et al., Nat. Energy, 3, 227 (2018).

A. A. Rulev et al., J. Phys. Chem. Lett., 11, 10511 (2020).

E. Chason et al., Prog. Surf. Sci., 88, 103 (2013).

B. J. Spencer et al., J. Appl. Phys., 73, 4956 (1993).

C. Xu et al., Proc. Nat. Acad. Sci., 114, 57 (2017).

L. Q. Zhang et al., Nat. Nanotechnol., 15, 94 (2020).

A. J. Louli et al., J. Electrochem. Soc., 166, A1291 (2019).

K. L. Harrison et al., ACS Appl. Mater. Interfaces, 13, 31668 (2021).

S. Lv et al., Nat. Commun., 9, 2152 (2018).

J. Steiger et al., J. Power Sources, 261, 112 (2014).

B. Hutchinson et al., Mater. Sci. Forum, 467-470, 465 (2004).

S. Narayan and L. Anand, J. Electrochem. Soc., 167, 040525 (2020).