Overpotential crystallization

The first connection between the surface processes in electrocrystallization and the overpotential were discussed in papers of Lorenz and Vermilyea. In these papers an overpotential was defined by the difference between the ad-atom concentration in the 

Gerischer made an experimental attempt to measure the crystallization overvoltage of Ag deposition in a chronopotentiometric experiment. In this experiment two results were obtained. From the slope at t - 0 the capacitance was determined. This capacitance was much larger than the double-layer capacitance and was interpreted as adsorption capacitance Qd- The ad-atom concentration was calculated from the adsorption capacitance 

This is a confirmation of Eq. (4.55) derived in Chapter 4 for the ad-atom adsorption isotherm with fl = X(l - = 0.2. The position of the ad-atom in the potential gradient 

Finally, the crystallization exchange current density was calculated and interpreted as the rate of deposition and separation of ad-atoms into kink site positions. 

In the following section, a statistical description of the surface processes will be presented. This is based on the definition of a residence time of an atom in a kink site position. 

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Reaction overpotential. Both overpotentials mentioned above are normally of higher importance than the reaction overpotential. It may happen sometimes, however, that other phenomena, which occur in the electrolyte or during electrode processes, such as adsorption and desorption, are the speed-limiting factors. Crystallization overpotential. This exists as a result of the inhibited intercalation of metal ions into their lattice. This process is of fundamental importance when secondary batteries are charged, especially during metal deposition on the negative side. 

Processes at metal/metal-ion electrodes include crystallization partial reactions. These are processes by which atoms are either incorporated into or removed from the crystal lattice. Hindrance of these processes results in crystallization overpotential The slowest partial reaction is rate determining for the total overall reaction. However, several partial reactions can have low reaction rates and can be rate determining. 

Surfaces of cadmium with various morphological properties were electro-formed on the Cd electrode from sulfate solutions by varying current densities, temperature, and pulse electrolysis conditions [218]. The surface properties were defined by the values of slopes of quasi-steady state E versus logarithm current density dependencies and exchange current densities in 0.5 M CdS04 + 0.15 M H2SO4 solution. The dependence of the slope values on surface properties was explained in terms of the influence of crystallization overpotential. 

Although the kinetic variable in electrode reactions in the current density, extensive use of the overpotential concept has been made in the electrochemical literature to indicate the departure from equilibrium [7]. Depending on the particular rate-determining process, in the overall electrode kinetics ohmic, charge transfer, reaction, concentration or mass transport, and crystallization overpotentials are described in the literature. Vetter [7] distinguished the concept of overpotential from that of polarization in the case of mixed potentials when the zero current condition does not correspond to an equilibrium potential as will be discussed in Sect. 8. 

See also crystallization overpotential (polarization), - nucleation and growth kinetics, - equilibrium forms of crystals and droplets, - half-crystal position, - Kaischew, - metal deposition, - supersaturation, - Stranski, - Zeldovich. 

Crystallization overpotential (polarization) — Figure. Schematic representation of the mechanism of a metal deposition... 

Electrocrystallization — A term first coined by Fischer [i] to describe a crystallization process in which the electrode potential provides the driving force, either directly in the form of a crystallization overpotential, or indirectly in the form of a supersaturation. (A solution is said to be supersaturated if it contains a concentration of a dissolved substance that is greater than the equilibrium concentration.)... 

Overpotential — is the deviation of the - electrode potential from its equilibrium value required to cause a given -> current density to flow through the electrode. This notion is widely applied to the qualitative characteristic of electrode activity in various reactions, namely low overpotential means high activity, and high overpotential means low activity (it is assumed that the values of overpotential are compared for some fixed current density and solution composition). See also - activation overpotential, -> crystallization overpotential, - diffusion overpotential, -> reaction overpotential. 

Resistance overpotential p and activation overpotential p are characteristic of irreversible reactions and are, therefore, termed irreversible overpotentials . Since deviations from the equilibrium potential due to changes in the concentrations of the reactants are largely reversible, concentration overpotential p is known as a reversible polarization . Crystallization overpotential p is more complicated. It can be caused either by reversible polarization or irreversible polarization . The details will be discussed later. 

Crystallization overpotential is treated as a special type of overpotential. In the PEVD system, any barrier to the process by which atoms are incorporated into or removed from the crystal lattice of the PEVD product (D) leads to crystallization overpotential r. ... 

According to Stranski s theory of crystal growth, each component of the deposited product (D) must first find its way to a suitable site at the edge of a lattice plane before it can be accepted into the lattice. The additional overpotential observed when this reaction is inhibited is known as crystallization overpotential. 

The characteristics of the observed crystallization overpotential are again determined by the stages which proceed at the lowest rate. Usually, step (c), inclusion into the lattice, is not a rate limiting step. 

If this step is the rate-limiting step, the working electrode overpotential is dominated by a crystallization overpotential p. This crystallization overpotential behavior is similar to a concentration overpotential. 

At lower temperatures, e.g. 500°C, the /-r curve is almost linear from the origin up to a cathodic overpotential of 450 mV. This kind of linear /-r behavior occurs since resistance or crystallization overpotential dominates the total working electrode overpotential. According to the previous discussion, the PEVD reaction rate-hmiting step at the working electrode is either Step 2b (electron diffusion) or Step 5 (surface transport of charged reactants). 

The asymmetry of the reduction peak may also be attributed to crystallization overpotential. At the peak the rate of production of Pt, and hence the crystallization overpotential (7/cry) is at a... 

The difference in overpotential between the curves for a given supersaturation (nucleation on an inert substrate) and the curve for a supersaturation equal to unity (deposition on a native substrate) gives the value of the crystallization overpotential, ijcr [48]. It is equal to the difference in the overpotential at point c and at point e in Fig. 2.16. If the current is switched off at point e, the electrode potential will approach to the reversible potential of the deposited metal (point g) after switching on the current again at point g, the overpotential returns to the same value as at point e, i.e., the deposition overpotential, r/, meaning that a new phase is formed. On the contrary, if current is switched off before point c, the electrode potential will approach the initial stationary potential of the inert electrode, meaning that new phase has not been formed [47]. 

Fig. 2.17 (a) Dependence of the ///q ratio on the overall overpotential for different Ccr,a/Co,a ratios, indicated on the curves upper scale for = 1, lower scale for n = 2) and (b) dependence of the crystallization overpotential, rjcr (in mV), for the cathodic reaction on i/io for different Ccr,a/Co,a ratios, indicated on the curves left-hand scale for 1, right-hand scale for n = 2) (Reprinted from Ref. [48] with permission from the Collection of Czechoslovak Chemical Communications and Ref. [13] with kind permission from Springer)... 

The crystallization overpotential strongly decreases with increasing ///q ratio. As a result of this, it can be measured only in the case of a metal deposition which is characterized by very high values of the exchange current density [48]. 

The radius of a nucleation exclusion zone can be calculated on the basis of the following discussion, taking into account the charge transfer overpotential also. If there is a half-spherical nucleus on a flat electrode, the extent of the deviation in the shape of the equipotential surfaces which occurs around it depends on the crystallization overpotential, current density, a resistivity of the solution and on the radius of the nucleus, r. If the distance from the flat part of the substrate surface to the equipotential surface which corresponds to the critical nucleation overpotential, rj, is /n, then this changes around defect to the extent where A is a number, as is presented in Fig. 2.18. 

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