Diffusion in electrodeposition

Johans et al. derived a model for diffusion-controlled electrodeposition at liquid-liquid interface taking into account the development of diffusion fields in both phases [91]. The current transients exhibited rising portions followed by planar diffusion-controlled decay. These features are very similar to those commonly observed in three-dimensional nucleation of metals onto solid electrodes [173-175]. The authors reduced aqueous ammonium tetrachloropalladate by butylferrocene in DCE. The experimental transients were in good agreement with the theoretical ones. The nucleation rate was considered to depend exponentially on the applied potential and a one-electron step was found to be rate determining. The results were taken to confirm the absence of preferential nucleation sites at the liquid-liquid interface. Other nucleation work at the liquid-liquid interface has described the formation of two-dimensional metallic films with rather interesting fractal shapes [176]. 

In this section we treat the bulk and surface properties of metals relevant to the problems of electrochemical deposition. First, we discuss briefly the bulk and electronic structure of metals and then analyze the surface properties. Surface properties of the greatest interest in electrodeposition are atomic and electronic structure, surface diffusion, and interaction with the metal surface (adsorption) of atoms and molecules in solution. 

When the charge-transfer step in an electrodeposition reaction is fast, the rate of growth of nuclei (crystallites) is determined by either of two steps (I) the lattice incorporation step or (2) the diffusion of electrodepositing ions into the nucleus (diffusion in the solution). We start with the first case. Four simple models of nuclei are usually considered (a) a two-dimensional (2D) cylinder, (b) a three-dimensional (3D) hemisphere, (c) a right-circular cone, and (d) a truncated four-sided pyramid (Fig. 7.2). 

In the discussion of atomistic aspects of electrodepKJsition of metals in Section 6.8 it was shown that in electrodeposition the transfer of a metal ion M"+ from the solution into the ionic metal lattice in the electrodeposition process may proceed via one of two mechanisms (1) a direct mechanism in which ion transfer takes place on a kink site of a step edge or on any site on the step edge (any growth site) or (2) the terrace-site ion mechanism. In the terrace-site transfer mechanism a metal ion is transferred from the solution (OHP) to the flat face of the terrace region. At this position the metal ion is in an adion state and is weakly bound to the crystal lattice. From this position it diffuses onto the surface, seeking a position with lower potential energy. The final position is a kink site. 

In the last section, a description was given of the amplification of a micropeak on a surface due to faster diffusion to the promontory. However, such concepts only offer a peep at the great proliferation of shapes and sizes possible in electrodeposition (Fig. 7.168). 

In a similar spirit, Alkire, Braatz and co-workers developed coupled hybrid continuum-KMC simulations to study the electrodeposition of Cu on flat surfaces and in trenches (Drews et al., 2003b, 2004 Pricer et al., 2002a, b). A 3D KMC simulation accounted for the surface processes as well as diffusion in the boundary layer next to the surface, whereas a ID or 2D continuum model (with adaptive mesh) was applied to simulate the boundary layer farther away. In... 

The properties of the surface layers have a strong effect on the deposition process. The driving force of the electrochemical reaction is the potential difference over the electrochemical double layer. Adsorption of species can change this potential. For example, the additives used in electrodeposition adsorb in the Helmholtz layer. They can change the local potential difference, block active deposition sites, and so on. The thickness of the diffusion layer affects the mass-transfer rate to the electrode. The diffusion layer becomes thinner with increasing flow rate. When the diffusion layer is thicker than the electrode surface profile, local mass-transfer rates are not equal along the electrode surface. This means that under mass-transfer control, metal deposition on electrode surface peaks is faster than in the valleys and a rough deposit will result. 

This concept can be also applied for the case of the electrodeposition of copper. As mentioned earlier, the morphology of the copper deposit obtained at cathodic potential of -500 mV/SCE under the parallel field was of cauliflower-like structure (Fig. 12b), while the morphology of the copper deposit obtained without the applied magnetic field had very dendritic structure (Fig. 12a). It is known that dendritic structures are main characteristic of electrodeposition in conditions of full diffusion control, while cauliflower-like structures are a characteristic of a dominant diffusion in mixed control of electrodeposition process.13... 

Mechanisms describing the formation of holes of this type are based on the amplification of electrode surface coarseness52,53 in diffusion-controlled electrodeposition and to the tip54 and edge55 effects of current density distribution at electrode surface. More about these mechanisms can be found in Ref.13... 

EEA has also been used to follow type conversion in electrodeposited CdTe layers [147]. The change from n-type to p-type is evident in Eigure 1.44 as an inversion in the peaks located at the bandgap energy, and a more detailed analysis has shown that the bandgap of the CdTe decreases slightly as a consequence of diffusion of sulfur into the CdTe from the CdS layer to form CdTe], (S, where X = 0.05-0.07. 

Bozzini, B., Lacitignola, D., Sgura, I. A reaction-diffusion model of spatial pattern formation in electrodeposition. J. Phys. Conf. Ser. 96, 012051 (2008)... 

The polarization curves consist of two parts in the mixed ohmic-diffusion-controlled electrodeposition [12]. The first part corresponds to the ohmic control... 

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