Modeling of grain size and hardness for pulse current electroplating

A mathematical model was developed to describe the effect of the current shape waveform on the grain size, formation, growth rate, and deposits hardness for progressive nucleation (simultaneous nucleation and growth) when four pulse current waveforms are applied: rectangular, ramp up, ramp down, and triangular waveforms. In the model, it is considered that species diffusion across the limit layer is the rate determinant step. The Hall-Petch expression was used to relate the grain size in the metal to its hardness. The model results are compared with the experimental data for nickel electrodeposit hardness, which were presented by Wong et al. (K.P. Wong, K.C. Chan, T.M. Yue, J. Appl. Electrochem. 31 (2001) 25). The model predictions are consistent with the experimental results for the four current waveforms, with an average hardness deviation of about 10% for currents between 1 and 6 kA/m2.