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Abstract The Equation of Nucleation first worked out by Erdey-Gruz and Volmer, which has been widely accepted as a fundamental equation to describe the ki- netics of eleetroplated crystal grain formation,is N=a·exp[-b·η_k~(-2)] where N is the number of nuclei formed per unit time and η_k the total overpoten- tial. As a result of more general consideration,it is shown in this paper that the electrode overpotential can also be related to the free energy of the elec- trode/solution interface by the electrocapillary equation of Lippman.Then a more generalized equation of electro-crystallization can be proposed. When the exchange current density is large and surface diffusion is the rate determining step,i.e.,when η_k=η_(crystal),this generalized equation can be simplified to the E-G-V equation;and when the cathode has a very large activation overpotential,i.e.,η_kη_(crystal),this equation will be N=a·exp{-b'{σ_0-[(_(eq)-η_k)~3-_0~2]}~3} where _0 is the zero potential and σ_0 the free energy of the interface at zero potential;_(eq) is the equilibrium potential and b' is a constant. The authors tend to feel that generalized equation in this paper can des- ceibe the kinetics of nucleation in electrocrystallization more exactly,and can provide means of detecting any effects caused by addition agents etc.of the plating solution and so it can be used to develop means for laboratory research and plating shop controlling and monitoring.
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Received: 25 February 1984
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