A novel phase-field model for electrochemical processes, in which cations were driven by an electrostatic potential coupled with a thermodynamic potential, was formulated from a variation of the Ginzburg-Landau free-energy functional. Using this model, an electrodeposition process of copper deposits from copper-sulfate solution was studied using a phase-field simulation. The dependence of the growth velocity of the electrode on the applied voltage was examined in a one-dimensional system. Then, the morphological transition of the electrodeposits as functions of the applied voltage and the composition ratio of copper ion in electrolyte was examined using a two-dimensional system. Thin and dense branches were observed at a low applied voltage. The shape of the branches became more complicated as the composition ratio was lowered. r
The switching behavior of a Cu/Cu2S nanometer-scale switch was investigated by numerical simulation based on the phase-field method. The appearance and disappearance of a Cu bridge between Cu and Pt electrodes in the void along the surface of Cu2S were observed upon applying negative and positive voltages, respectively. The appearance of the Cu bridge increased the electrical current by four orders of magnitude, which is regarded as activation of the switch. Moreover, the current–voltage characteristic obtained by sweeping the applied voltage was asymmetric as a function of applied voltage, which agrees well with the current–voltage characteristic observed experimentally.
Effect of the phase boundary potential at the electrode electrolyte interface and the anisotropy of interfacial energy on the morphology of the electrodeposits have been investigated by phase field simulation. In equilibrium system, the change in the phase boundary potential due to the interfacial curvature satisfies the Gibbs Thomson effect. The stability analysis of the elec-trode electrolyte interface reveals that the marginal wavelength is proportional to the inverse of the square root of the growth velocity of the interface. It is found that the linear relationship between the marginal wavelength and tip radius during electrodeposition satisfies the crystal growth theory confirmed by the dendrite growth in solidification process.
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