3.1. The Surface Condition of Magnesium during Corrosion
The micrographs of the magnesium electrode surface in the first half-hour of corrosion in an electrolyte of 0.5 mol/L magnesium sulfate are presented at
Figure 1. Before immersion into the electrolyte, the magnesium surface had already been covered with a film formed by surface preparation in the atmosphere, and at washing after grinding, the film possessed a marked thickness (
Figure 1a). After one minute of corrosion, the surface equalize became noticeable due to the growth of the film, and its cracking starting herewith became noticeable too (
Figure 1b).
After 5 min of immersion, cracking increased and, on the surface, a new layer, also subjected to cracking, began to form; the film thickness in the cracks after 5 min may be estimated as units of micron (
Figure 1c). Further, after 20 min, the cracks were gradually tightened and the second more incoherent layer was built up from above, as it had been reported in many works [
3,
4,
5,
12,
16]. The observed cracking of the corrosion films demonstrated above for magnesium sulfate solutions in some investigations was associated with impact of hydrogen evolution [
5].
In magnesium sulfate solutions of higher concentrations, corrosion was rapidly accelerated and in a minute the film appeared thicker and more incoherent than half an hour in a solution of 0.5 mol/L MgSO
4 (
Figure 2). In 2 mol/L MgSO
4 solution, after a minute, the surface of the film became fretted as though it was subjected to dissolving.
In sodium sulfate solutions, the film growth was less expressed and its slight cracking occurred after 30 min of immersion in the electrolyte (
Figure 3). However, formation of the upper crystalline layer occurred as well as in magnesium sulfate after 20 min of exposure of the sample in solution.
During corrosion, the pH of the solution changes in accordance with the main reaction as magnesium hydroxide accumulates in the solution, resulting in it equilibrating to 7.76 and 8.33 for 0.5 mol/L of sodium and magnesium sulfate, respectively, after half an hour of exposure.
This difference corresponds to an almost tenfold increase in the content of magnesium hydroxide in magnesium sulfate solutions over sodium sulfate solutions. With the same area of the electrodes and the volume of the solution, taking into account the type of surface on the micrographs, we can talk about a much higher rate of corrosion in magnesium sulfate.
3.3. 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:
where
Ei is the current value of potential,
Ecor is the corrosion potential,
η is the charge transfer overvoltage,
Rel 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:
where
r0 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,
where
η is the overvoltage process and
L is the film thickness. In this case, the equation takes the form
After logarithming this equation and grouping all the constants, we get
where the constant
and the coefficient
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.
The dependences (1/
b) on the immersion time for anode and cathode polarization curves in different solutions are presented in
Figure 6a.
In most cases, the Tafel’s coefficient was higher than 200 mV, except for the initial stage of corrosion in 0.5 mol/L magnesium sulfate solution at anode polarization. In the anode process in magnesium sulfate at early terms, the Tafel’s coefficient has a value close to 60 mV, formally corresponding to one-electron transfer. However, its completely smooth change to 0.3V in 200 min indicates that this is a characteristic of a growing corrosion film. Accordingly, the Tafel’s coefficient being determined here is 1/b value for transport in high electric fields, and it reflects the thickness of the corrosion film according to Equation (5).
In sodium sulfate solutions, the Tafel’s coefficient was higher from the very outset of the corrosion process for both the anode and cathode processes. The change in the value of 1/
b for almost all the curves except anode ones in sodium sulfate solutions in the first half hour of corrosion presented itself the curve of a parabolic dependence, due to this we presented these curves in 1/
b to
t1/2 coordinates (
Figure 6b)
Such parabolic dependences were often observed when measuring the amount of released hydrogen, as it was reported in [
12]. In [
22], a quantitative implementation of the parabolic law was established for the dependence of the magnesium hydroxide content on time. The parabolic law itself reflects the corrosion process, which is limited by diffusion of the reagent through the thickness
L of the growing product layer according to equation
[
18]. Here,
L0 is the initial film thickness and
τ is the corrosion time.
In these curves, the Tafel’s coefficient change (1/b) was linear in time at the initial regions of ~30 min, except of the dependence for the cathode coefficient in magnesium sulfate having a linear site till 4 h of corrosion. Simultaneously, at all linear sites in these coordinates the periodic deviations in both sites of the straight line were observed. Comparison of emerging deviations with film behavior by microscopic studies showed that they most likely corresponded to cracking and growth of cracks in the film, as well as hydrogen evolution, when parameters of charge transfer through it could change dramatically due to such effects. The rectification of the dependence in coordinates 1/b − τ1/2 indicated that the corrosion process was limited by diffusion of the reagent through the thickness of the growing product layer. The diffusion model underlying the parabolic law of the film growth was the diffusion of metal magnesium in ion-electron form through a layer of corrosion products to the electrolyte. This motion first happened in the primary magnesium oxide film, on the surface of which the electron reacted with water to hydrogen evolution. In the solid phase of magnesium oxide, monovalent magnesium was most likely formed, which was also a reducing agent providing hole conductivity and reacting with water to hydrogen evolution. The existence of monovalent magnesium as a reducing agent in the hydroxide layer was impossible, as well as electron conductivity.
The observed difference of the Tafel’s characteristics for the anode and cathode process was apparently determined by the nature of the particle transferred through the film, which, in accordance with Equation (6), determined the b value. In the cathode process, it was an electron being carried from the metal through the film to the solution and a magnesium cation moving in the reverse direction, whereas in the anode process, only the cation was being carried. Based on the data of the NDE study, it may be assumed that it was a single-charged magnesium cation. Higher values of the Tafel’s coefficient (1/b) for cathode sites in 0.5 mol/L magnesium sulfate solutions characterized particle transfer with a smaller value of the activated jump distance. In sodium sulfate solutions, this difference was not significant compared to the experimental spreading.
The sharp change in the shape of the curves after half an hour of corrosion after the linear site on the dependences of 1/b to time is also drawn the attention. In this area, the Tafel’s coefficient values for cathode and anode polarization began to converge dramatically and their practical matching after the one-hour corrosion became noticeable. Such behavior indicates the transformations in the film resulting in the identity of charge transfer therein in the cathode and anode processes, while there was a marked difference in the initial sites. According to SEM images for half an hour of corrosion, the surface was almost completely covered with the crystalline layer of the second product, but this did not allow to explain the change transfer parameters in cathode and anode polarization.
As the Tafel’s coefficient (1/
b) determined in this experiment was a value proportional to the film thickness, it was noticed that the effective film thickness in sodium sulfate solutions decreased while for magnesium sulfate increased. The dependences of the polarization resistance of the magnesium electrode with the film in sodium sulfate solution presented in
Figure 6c also confirmed the film resistance reduction. The polarization resistance, which in this case was the film resistance, was calculated from the initial site of the polarization curve (10–20 mV).
The same as on the dependence curves of the Tafel’s coefficient on time the fact of convergence and stabilization of the film resistance on magnesium in magnesium and sodium sulfate solutions after 100 min of corrosion attracts itself the attention, when the rates of their change are markedly slowed down and the values themselves are converged, demonstrating a movement towards independence from the nature of the electrolyte. This is also perfectly confirmed by the dependence of the magnesium electrode potential on time, which also passes through the acute maximum during the first half hour, and after 100 min, it does not depend on the composition of the solution, demonstrating the identity of the state in different solutions. The positive displacement of the potential of the magnesium electrode during corrosion characterizes the passivation of the surface by the corrosion film. The negative shift in the first 15 min of the magnesium potential of 0.5 mol/L MgSO
4 coincides with the trend of increasing film cracking in this time interval (
Figure 1). The same interpretation of the potential shift in the negative direction, due to the introduction of an additive into the electrolyte that dissolves the oxide part of the film, is presented in [
27].
A negligible period of the film growth under parabolic law ended with its transformation into another state, where parameters of cathode and anode process transfer were equalized. The most likely variant of such a conversion was the hydration of the primary film’s magnesium oxide and its conversion to hydroxide. The general perception is that the characteristics of charge transfer through the film were solely determined by its dense part, which included only the part adjacent to the metal, initially consisting of magnesium oxide and possibly a dense part of the amorphous hydroxide layer. The layers lying above had an incoherent morphology and little determine polarization. That is why there was observed a strong change of electrical characteristics during the initial period of time and the formation of the similar final product over time.
Similar regularities of behavior were demonstrated by the concentration dependence of corrosion parameters in magnesium sulfate solutions (
Figure 7). When the salt concentration was increased to 1 mol/L, the coefficient of 1/
b as opposed to 0.5 mol/L was no longer practically increased over time, maintaining a roughly constant value. In the electrolytes with 2 mol/L salt concentration, the value of 1/
b decreased sharply from very high values at the beginning of the process to values comparable referred low concentrations in 30 min (
Figure 7). Such a reduction in 1/
b in the initial corrosion time period should also characterize the film thickness decrease. It also, as in the previous case, confirmed the dependence of polarization resistance on time (
Figure 7b), which demonstrated the growth of film resistance in 0.5 mol/L magnesium sulfate solutions, almost constant value in 1 mol/L solutions and its decrease in 2 mol/L solution. At the same time, according to SEM, the film thickness increased distinctly with increasing the magnesium sulfate concentration from 0.5 mol/L to 2 mol/L (
Figure 2). Formally, this contradicted the observed change of the Tafel’s coefficient and polarization resistance in electrolytes with a high concentration of magnesium sulfate and in sodium sulfate solutions. However, it was clear that the formed film was a rather incoherent formation, which was particularly well seen in the example of magnesium sulfate solutions of increased concentration. The state of the surface in the 2 mol/L magnesium sulfate solution was quite consistent with the dissolving film. In this case, it was logical to consider the reduction of film resistance as a consequence of the replacement of the dense primary film by the incoherent secondary film, and it was more expressed for sodium sulfate solutions and high concentrations of magnesium sulfate, in which the solubility of magnesium hydroxide [
29] was higher, which allowed the primary film to dissolve.
3.4. Determination of Charge Transfer Parameters Using EIS
The electrochemical impedance technique was also used to addition analysis of charge transfer through corrosion films. The Nyquist plots for the magnesium electrode in the investigated solutions are shown in
Figure 8 and
Figure 9. The presence of two semicircles in the hodographs of electrochemical impedance most often refers to RC circuits describing the double electric layer and dense part of the film [
5,
30,
31].
Figure 8 shows the EIS data of electrochemical impedance of the surface film on the magnesium electrode in 0.5 mol/L magnesium and sodium sulfate solutions obtained at open-circuit potentials at different immersion times. Nyquist plots have one form type for a single solution. It can be seen that with the increase of the electrode holding time in the solution, the radius of the semi-circle increases, which indicates an increase in the resistance of the RC circuit.
The difference between the Nyquist plots in sodium sulfate solutions was proved by the presence of an inductive loop appearing after the indication of transition to the second half-circle. The EIS Nyquist plots of magnesium electrode in higher concentration magnesium sulfate solutions are shown in
Figure 9.
The proposed versions of electrical equivalents of electrochemical processes for magnesium electrodes contain a serial connection of RC-circuits, where the capacity is represented by an element with distributed parameters of Constant Phase Element (CPE) for describing a complex nature of charge transfer through a film and double layer [
30]. When considering the case of partial coating of the surface with a dense corrosion film, their parallel connection is used [
5,
31]. Application of addition elements responsible for the inductance loop in the circuits is more as an adjustable element to obtain a better approximation of the experimental data and does not have sufficient justification [
5,
27].
In our process of designing the equivalent scheme, we assume that the above-mentioned RC-circuits characterize two parts of the film: dense oxide part and more incoherent hydroxide part. This understanding is based on the defining role of the film in the charge transfer process shown in this work and the undetectable effect of the double interface layer on it. In addition, the Warburg element is introduced in the equivalent scheme describing the loose part of the film to reflect the diffusion transfer in it. An equivalent electrical circuit of charge transfer in corrosion films formed in magnesium and sodium sulfate solutions is shown in
Figure 10. In view of the fact that the inductive loop was expressed in sodium sulfate solutions, an inductive element for the entire volume of the film was introduced into the circuit.
The equivalent circuits presented in
Figure 11 satisfactorily approximate the experimental EIS data for solutions of magnesium sulfate and slightly worse in the low-frequency region for sodium sulfate.
The resistance of oxide and hydroxide parts of the film at corrosion in magnesium and sodium sulfate solutions calculated from the Nyquist plots is shown in
Figure 12. The resistance of the magnesium oxide film [
32] was almost always less than the resistance of the hydroxide film and possessed a small maximum on its dependence on the corrosion time. The resistance of the hydroxide oxide layer was growing relatively stable except for the 2 mol/L magnesium sulfate solution due to its dissolution as can be seen from the images (
Figure 2). This result, at first glance, contradicts the generally accepted idea of the determining role of the oxide film in the corrosion process as a barrier layer. However, the protective properties of the film are determined not by its general conductivity, but by the absence of electronic conductivity.
The polarization resistance of the film-coated electrode
RpSEI under direct current (DC) polarization conditions will be combined from the resistance of the electrolyte
Rel, the resistance of the magnesium oxide film
RSEI(II), and the resistance of the hydroxide layer
RSEI(I), provided that the charge transfer is limited by the corrosion film. The resistance of the electrolyte due to the high conductivity of the solutions (
Table 1) was very small and had no effect on the total value of the resistance.
The total resistance of the film parts, together with the polarization resistance
Rp (LV) determined experimentally, are demonstrated at
Figure 12. A fairly good match of the polarization resistance values of the magnesium electrode calculated from the EIS data and polarization curves can be also observed. The calculations for sodium sulfate solutions, where the absence of coincidence was obvious, acted as exceptions. The reason for the latter is most likely the inadequacy of the equivalent circuits for sodium sulfate solutions with a satisfactory approximation of the Nyquist plots. Based on the analysis of impedance measurements, it can be concluded that the hydroxide layer made the main contribution to polarization, whereas the oxide layer was very thin and its resistance were significant only at the initial corrosion time.