# Insight into the Role of Cerium (III) Addition to a MgAl-LDH Coating on AA6082
## 3 Results
The effect of cerium in the LDH coating and its corrosion inhibition potential were better investigated by collecting EIS spectra in 0.05 M NaCl + 0.1 M Na\({}_{2}\)SO\({}_{4}\) solution during 216 h. As explained in a previous section, the electrolyte was selected to reduce the electrochemical noise in the low-frequency range. Figure 10 shows the impedance and phase diagrams of the investigated coatings during immersion time (2, 8, 24, 72, 168, and 216 h) in the electrolyte. Notice that the impedance modulus in the low-frequency range (about 0.01 Hz) shows an initial slight decrease in the very first hours of immersion and then a gradual increase with time elapsed. At the end of the immersion test (216 th h), the C10-1 and C10-4.5 samples show impedance values higher than at the beginning. The observed trend is consistent with a sort of healing effect provided by the dissolution of cerium compounds, release of cerium ions, and precipitation of cerium oxides/hydroxides in correspondence of the cathodic sites on the metal surface, according to the previously discussed mechanism. At an early stage of immersion, two-time constants can be observed in the middle-low frequency range. The relaxation processes tend to partially overlap for prolonged immersion time, as suggested by the merging of the phase angle peaks into a single asymmetrical peak. The time constant in the middle-frequency range is recognized to be related to the response of the LDH coating [69], while the attribution of the relaxation process in the low-frequency range is not straightforward. According to [PERSON] et al. [70] the low-frequency time constant derives from the superimposition of the contribution of the faradic process at the interface and that of the aluminum oxide. According to the previous description of the observed time constants, the experimental EIS datasets were fitted employing the circuit depicted in Figure 11. According to the \(R_{sol}(Q_{LDH}(R_{LDH}(Q_{LF}R_{LF})))\) circuit in Figure 11, the equivalent electric parameters are defined as follows: \(R_{sol}\) stands for the solution resistance; \(R_{LDH}\) and the \(CPE_{LDH}\) are the resistance and the constant phase element associated with the  
Figure 9: Three types of agglomerates found on C10-4.5 surface after 400 h of immersion in 0.1 M NaCl (**a–c**). At the bottom, the respective EDS analysis. LDH coating [41; 48; 71; 72]; the resistance \(R_{LF}\) in parallel with the constant phase element \(CPE_{LF}\) were employed to fit the relaxation process in the low-frequency range. Constant phase elements (CPE), were used instead of pure capacitance to account for surface inhomogeneity, fractal geometry, roughness, electrode porosity, and the current and potential distribution of the system surface [73]. Accordingly, \(Z_{CPE}=1/\left[Q(j\omega)^{\alpha}\right]\), where \(\alpha\) is the frequency dispersion factor \((-1<\alpha<1)\) the terms \(Q,j\), and \(\omega\) are the pre-exponential factor, the imaginary unit \(j=\sqrt{-1}\), and the angular frequency, respectively. The results of the fitting are reported in Tables 2-4 for C10-1, 4.5, and 9, respectively. The values of the \(Q_{LDH}\) (pre-exponential factor of the \(CPE_{LDH}\)) are in the order of \(10^{-6}\) S cm\({}^{-2}\) s\({}^{\alpha}\) regardless of the synthesis parameters. The corresponding \(\alpha_{LDH}\) values are quite far from unity and, thus, a clear physical meaning cannot be attributed to the fitting parameter \(Q_{LDH}\). Although \(Q_{LDH}\) is likely to reflect the dielectric properties of the LDH coating, due to the surface roughness, porosity, and corrosion products [74; 75], the \(\alpha_{LDH}\) values differ from unity. Thus, a comparison among the numerical values of the \(Q_{LDH}\) is not consistent. Similarly, for the values of the \(Q_{LF}\) (pre-exponential factor of the \(CPE_{LF}\)) it is not possible to define a clear physical meaning, as the \(\alpha_{\rm LF}\) values scatter from 0.67 to 1 throughout the immersion time.