Instability in electrodeposition: the critical wavelength

Krishnan, R.; Johns, L. E.; Narayanan, R.

doi:10.1016/s0013-4686(02)00445-0

Cited by 2 publications

(2 citation statements)

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Section: A Approximationssupporting

confidence: 91%

“…We observe that k c scales as Ca − 1 2 = γ − 1 2 , which is expected because the surface energy stabilizing effect appears in the form of γk 2 in Ĝ1 in Equation 42, and this scaling agrees with that obtained in previous work done on linear stability analysis of electrodeposition. 149,150,158,164,203 Convergence analysis.-Before analyzing the physical significance of the linear stability analysis results, we would want to first establish the accuracy and convergence of the full numerical solution of the dispersion relation ω(k). To this end, we perform a numerical convergence analysis in which we examine the convergence of the numerical solution as the number of grid points N increases.…”

Section: A2288mentioning

confidence: 99%

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Linear Stability Analysis of Transient Electrodeposition in Charged Porous Media: Suppression of Dendritic Growth by Surface Conduction

Khoo

Zhao

Bazant

2019

J. Electrochem. Soc.

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We study the linear stability of transient electrodeposition in a charged random porous medium, whose pore surface charges can be of any sign, flanked by a pair of planar metal electrodes. Discretization of the linear stability problem results in a generalized eigenvalue problem for the dispersion relation that is solved numerically, which agrees well with the analytical approximation obtained from a boundary layer analysis valid at high wavenumbers. Under galvanostatic conditions in which an overlimiting current is applied, in the classical case of zero surface charges, the electric field at the cathode diverges at Sand's time due to electrolyte depletion. The same phenomenon happens for positive charges but earlier than Sand's time. However, negative charges allow the system to sustain an overlimiting current via surface conduction past Sand's time, keeping the electric field bounded. Therefore, at Sand's time, negative charges greatly reduce surface instabilities and suppress dendritic growth, while zero and positive charges magnify them. We compare theoretical predictions for overall surface stabilization with published experimental data for copper electrodeposition in cellulose nitrate membranes and demonstrate good agreement between theory and experiment. We also apply the stability analysis to how crystal grain size varies with duty cycle during pulse electroplating.

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