Mass transfer and electrocrystallization analyses of nanocrystalline nickel production by pulse plating

A comparison between the experimental process parameters employed for the pulse plating of nanocrystalline nickel and the solution-side mass transfer and electrokinetic characteristics has been carried out. It was found that the experimental process parameters (on-time, off time and cathodic pulse current density) for cathodic rectangular pulses are consistent and within the physical constraints (limiting pulse current density, transition time, capacitance effects and integrity of the waveform) predicted from theory with the adopted postulates. This theoretical analysis also provides a means of predicting the behaviour of the process subject to a change in the system, kinetic and process parameters. The product constraints (current distribution, nucleation rate and grain size), defined as the experimental conditions under which nanocrystalline grains are produced, were inferred from electrocrystallization theory. High negative overpotential, high adion population and low adion surface mobility are prerequisites for massive nucleation rates and reduced grain growth; conditions ideal for nanograin production. Pulse plating can satisfy the former two requirements but published calculations show that surface mobility is not rate-limiting under high negative overpotentials for nickel. Inhibitors are required to reduce surface mobility and this is consistent with experimental findings. Sensitivity analysis on the conditions which reduce the total overpotential (thereby providing more energy for the formation of new nucleation sites) are also carried out. The following lists the effect on the overpotential in decreasing order: cathodic duty cycle, charge transfer coefficient, Nernst diffusion thickness, diffusion coefficient, kinetic parameter () and exchange current density.Nomenclature A constant employed in Fig. 8, (nFi₀)/(RT_eC_a)(s^–1) - B constant in Equation 38 (V²) - C cation concentration (molcm^–3) - C_a capacitance of double layer (µFcm^–2) - C_s cation surface concentration (molcm^–3) - C_s^* dimensionless cation surface concentration, C_s/C(–) - C cation bulk concentration (molcm^–3) - D diffusion coefficient of cation (cm²s^–1) - E total applied potential (V) - E⁰ standard cell potential (V) - F Faraday constant (Cmol^–1) - function defined in Appendix C(–) - Fr frequency of waveform (Hz) - f_i,p function defined in Appendix C for pth period (–) - f_i, function defined in Appendix C for p period (–) - G_j function defined in Appendix B (–) - gi function defined in Appendix B (–) - i current density (Acm^¨) - i_ac unsteady fluctuating a.c. current density (Acm^–2) - i_c capacitance current density (Acm^–2) - i_dc steady time-averaged d.c. current density (Acm^–2) - i_F Faradaic current density (Acm^–2) - i_lim limiting d.c. current density (Acm^–2) - i₀ exchange current density (Acm^–2) - i_PL limiting pulse current density, i₁{Cs = 0 at t = (p – 1) T + t₁(Acm^–2) - i₁ cathodic pulse current density (Acm^–2) - i₂ relaxed or low current pulse current density (Acm^–2) - iin anodic pulse current density (Acm^–2) - i^* dimensionless current density, i/|i_lim| (–) - i₀^* dimensionless exchange current density, i_dc/|i_lim| (–) - i_dc^* dimensionless steady time-averaged d.c. current density, i_dc/|i_lim| (–) - i_PL^* dimensionless limiting cathodic pulse current density, i_PL/|i_lim| (–) - i_PL,p^* dimensionless limiting pulse current density at pth period, i₁(C_s = 0)/|i_lim| (–) - i_PL,^* dimensionless limiting pulse current density for p , i₁(C_s = 0)/|i_lim| (–) - i₁^* dimensionless cathodic pulse current density, i₁/|i_lim| (–)