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12) for the side and the tip of the protrusion, around which the spherical diffusion layer is formed, respectively. Hence: is ¼ i0 ð f c À f a Þ  À Á s 1 þ i0iLf c δÀh δ ð2:21Þ and if the spherical diffusion layer around the tip of a protrusion can be formed (r < δ), it will be valid as in Eq. 1 Electrodeposition on Native Substrate 31 However, if the spherical diffusion layer around the tip of a protrusion cannot be formed (r > δ), it will be valid: itip ¼ i0 ðf c À f a Þ    δÀhp 1 þ i0iLf c δ ð2:23Þ The effective rate of growth of the side elevation is equal to the rate of motion of the side elevation relative to the rate of motion of the flat surface [11].

1): ispher ¼ i0 ð f c À f a Þ 1 þ iiL0 Á rδel Á f c ð2:4Þ and if a condition of the Eq. 3) is also valid, but 1 The reversible potential of a surface with radius of curvature rcur would depart from that of a planar surface by the quantity ΔEr ¼ 2γ V=ðnFr cur Þ, where γ is the interfacial energy between metal and solution and V molar volume of metal [5]. It is valid at extremely low rcur, being of the order of few millivolts, and it can be neglected except in some special cases, like the stability of the shape of the tips of dendrites [5].

Winand R (1994) Electrodeposition of metals and alloys – new results and perspectives. Electrochim Acta 39:1091–1105 25. Nikolic´ ND, Popov KI, Pavlovic´ LjJ, Pavlovic´ MG (2007) Determination of critical conditions for the formation of electrodeposited copper structures suitable for electrodes in electrochemical devices. Sensors 7:1–15 26. Nikolic´ ND, Brankovic´ G, Pavlovic´ MG, Popov KI (2008) The effect of hydrogen codeposition on the morphology of copper electrodeposits II. Correlation between the properties of electrolytic solutions and the quantity of evolved hydrogen.

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