Kinetics of Electrochemical Nanonucleation during Induced Codeposition of Iron-Group Metals with Refractory Metals (W, Mo, Re)

Abstract

It is shown that the earlier discovered features of the composition and properties of electrochemical coatings obtained by induced codeposition of alloys of iron-group metals (W, Mo, Re)—such as nanocrystallinity (X-ray amorphous phase), macroscopic size effects of microhardness and corrosion resistance, the effect of the volume current density on the properties and composition—are a consequence of the fractality of the solutions of relevant metal complexes (e.g., citrate and gluconate) in combination with the intensive interfacial exchange. In this case, the kinetics of nano-nucleation limits the size of growing nuclei of the alloy and, as a result, water molecules participate in the formation of coatings, leading to the incorporation of oxide-hydroxide inclusions into the solid phase and hydrogenation.

APPENDIX

The problems associated with the introduction of the concept of Tolman parameter δ for the case of electrochemical nucleation were considered in detail in [31]. Because the Tolman parameter is a theoretical quantity (even though there is a thermodynamic definition of it that cannot be directly measured in experiment), this parameter can characterize different physical processes in the case of specific physical processes of nucleation. This parameter was introduced by Tolman to obtain the size dependence of the surface tension. In nanotechnologies, the Tolman parameter now determines the surface layer thickness of a nanoparticle (during its nucleation and growth).

Fig. A1.

Scheme of overvoltage at cathode in the case of electrochemical nucleation.

Let us consider a case of electrochemical deposition. Let us provide for clarity a known qualitative scheme of the distribution of the surface potential in the near-surface layer of the cathode [39, 40]:

In considering the growth of a cylindrical nanoparticle, we can associate the Tolman parameter with the diffuse part of the double layer, for which the diffusion equation for the concentration of fragments forming a cylindrical nanoparticle, denoted as c, is valid. In the case of cylindrical symmetry, the equation is as follows [39, 40; Eqs. (2.391) and (1.45), respectively]:

$$c{\kern 1pt} {''}\,\, + \frac{1}{r}c{\kern 1pt} '\,\, - \frac{1}{{{{\lambda }^{2}}}}\left( {c - 1} \right) = 0.$$

(A.1)

(Concentration at the infinity is taken to be unity.) Eq. (A.1) is analogous to Eq. (2). Consequently, one can compare the λ value from Eq. (A.1) with the δ value from Eq. (2).

It should be noted that it is interesting to consider diffusion current based on the equation analogous to Eq. (6). However, this is beyond the scope of this work.