## 3 Results and Discussion
### Analysis of the Laws of Charge Transfer during Polarization  
In the view of classical electrochemistry, such polarization relationships should describe the charge transfer across the interface according to Butler-Volmer, when the cathode process is hydrogen evolution and the anode process is the electrochemical dissolution of the metal. However, these exponents are characterized by high value of Tafel's coefficient (\(>\)200 mv). The high value of Tafel's coefficient in the cathode process is usually associated with the formation of gas bubbles at the surface resulting in an overvoltage increase [15]. However, such an explanation cannot be satisfactory, as gas bubble shielding should result in the addition of an ohmic component to the polarization while increasing the resistance of the electrolyte. At the same time, the total overvoltage will be the sum of the overvoltage of the electrochemical reaction and the voltage drop in the electrolyte:  
\[E_{i}\ =\ E_{cor}+\eta_{f}+iR_{el}\ =\ E_{cor}+a+blni+iR_{el} \tag{1}\]  
\[\frac{\partial E_{i}}{d(lni)}\ =\ b+R_{el}\frac{\partial i}{\partial(lni)}\ =\ b+iR_{el} \tag{2}\]  
where \(E_{i}\) is the current value of potential, \(E_{cor}\) is the corrosion potential, \(\eta\) is the charge transfer overvoltage, \(R_{el}\) is the electrolyte resistance, and \(a\) and \(b\) are the Tafel's equation coefficients. Equation (2) means that the appearance of additional resistance in surface shielding does not result in an increase in the Tafel's coefficient, but leads to a nonlinear dependence in the Tafel's coordinates. The same conclusion was made regarding the inclusion of a voltage drop in the corrosion film into the total polarization overvoltage, and as the corrosion film resistance was quite significant, linear dependencies in the Tafel's coordinates would not have to be observed. As the presence of the film on the metal surface is quite obvious, it is most likely that we register an exponential dependence characterizing the charge transfer not through a double layer according to Butler-Folmer, but through a corrosion film in the high electric fields, as it had been already reported in [18]. To analyze the charge transport through the solid electrolyte film in high electric fields, consider the equation proposed to describe this process:  
\[i\ =\ zFr_{0}vn_{+}\exp(-\frac{W}{RT})\exp\frac{r_{0}zFE}{2 RT} \tag{3}\]  
where \(r_{0}\) is the distance between adjacent defects in a solid, \(v\) is the ion oscillation frequency in equilibrium position, \(n_{+}\) is the concentration of defects in the solid phase, \(W\) is the activation energy of charge movement, \(z\) is the charge of the transferred particle, and \(E\) is the electric field voltage. With considerable thickness and resistance of the film, the overvoltage of the process is almost equal to the voltage drop in the film. Then, for the high electric field, the following expression may be written,  
\[E\ =\ \frac{\eta}{L} \tag{4}\]  
where \(\eta\) is the overvoltage process and \(L\) is the film thickness. In this case, the equation takes the form  
\[i\ =\ zFr_{0}vn_{+}\exp(-\frac{W}{RT})\exp\frac{r_{0}zF\eta}{2 RTL} \tag{5}\]  
After logarithming this equation and grouping all the constants, we get  
\[lni\ =\ lna+b\eta \tag{6}\]  
where the constant \(a\ =\ zFr_{0}vn_{+}\exp(-\frac{W}{RT})\) and the coefficient \(b\ =\ \frac{r_{0}zF}{2 RTL}\) are inversely proportional values to the film thickness. In this case, the value \(1/b\) may be a parameter to estimate the thickness change of the corrosion film \(L\) in time. If we reduce Equation (5) to the form of the Tafel's equation, we shall see that the Tafel's coefficient conforms to 1/_b_ and is proportional to the film thickness. \[\eta\ =\ -\frac{1}{b}hua\ +\frac{1}{b}lni \tag{7}\]  
The dependences (1/_b_) on the immersion time for anode and cathode polarization curves in different solutions are presented in Figure 6a.