A phase-field simulation of bridge formation process in a nanometer-scale switch

Phase-field modeling for electrodeposition process

“…Hence, other parameters are taken from our previous studies [21] with minor modifications. The diffusion coefficients of Cu 2+ in the electrode and electrolyte are set to be 3.0 Â 10 À13 and 7.2 Â 10 À8 m 2 /s, respectively.…”

“…It is a suitable model for analyzing processes including the flow during electrochemical processes. On the other hand, we have developed a phase-field model [21] in which one of the components is charged and driven by an electrostatic potential caused by an external charge. This model is similar to Pongsaksawad's model, but uses an order parameter field with thin-interface limit parameters, which describe the motion of the interface quantitatively.…”

“…Using this model, the process of bridge formation and disappearance in a nanometer-scale switch [22,23] was studied. In our previous study [21], we assumed the components of the electrode and electrolyte as an ideal metal, M, and an ideal sulfide, M 2 A, instead of the real materials, Ag/Ag 2 S or Cu/CuS, for simplicity.…”

A phase-field simulation of uranium dendrite growth on the cathode in the electrorefining process

“…In addition to the above numerical models, a phase-field model (PFM) [9,10], which can treat a free boundary in a biphasic system, has also been adopted to investigate various electrode reactions [11][12][13][14][15][16][17][18][19][20][21] focusing on complex morphologies of the electrode surface. For example, Guyer et al [12,13] solved distributions of components and obtained an electric double layer by solving Poisson's equation in the one-dimensional (1D) system.…”

“…Han et al [15] examined Li diffusion in secondary battery electrodes using a phasefield model and discussed the diffusion coefficient on the basis of Galvanostatic and Potentiostatic Intermittent Titration Technique (GITT and PITT). Moreover, we have studied electrochemical processes such as bridge formation and disappearance in the atomic switch [16][17][18] and electrodeposition of copper from copper sulfate solution [19][20][21], where a morphological diagram of the copper deposits was summarized as functions of the applied voltage and the concentration of metal ion in the electrolyte.…”