## 3 Results and Discussion
### Electrochemical Impedance Spectroscopy  
EIS results at 0 V (SCE) showed that diffusion controls oxide or passive layer growth in conventional rebar and DP rebar. Figure 6 shows the equivalent circuit, where \(Q\) is the constant phase element CPE, \(R_{\text{S}}\) the solution resistance, \(W\) the Warburg impedance, and \(R_{\text{t}}\) the layer transition resistance. According to diffusion boundary conditions, there are three types of diffusion impedances for plane electrodes [39; 40].  
Warburg impedance, one of the common diffusion impedances, assumes the infinity diffusion layer thickness. This equivalent circuit impedance can be expressed as follows:  
\[\text{ZF}=R_{\text{s}}+Z_{\text{F}}^{0}+Z_{\text{w}}, \tag{1}\]  
where \(Z_{\text{F}}^{0}\) the Faraday impedance and \(Z_{\text{W}}\) the Warburg impedance. \(Z_{\text{F}}^{0}\) and \(Z_{\text{W}}\) are expressed as follows:  
\[Z_{\text{F}}^{0}=R_{\text{t}}, \tag{2}\]  
\[Z_{\text{w}}=\frac{\gamma\ R_{\text{t}}\ |I_{\text{F}}|}{nF_{\text{Cs}}\sqrt{2 \omega D}}\ (1-j), \tag{3}\]  
where \(I_{\text{F}}\) the Faraday current, \(\gamma\) the series of the reactant in the electrode reaction, \(\omega\) the sine potential frequency, \(n\) the chemical coefficient of electrode, \(F\) the Faraday constant, and \(D\) the diffusion coefficient.  
When the Warburg impedance controls the electrode reaction, impedance is expressed as follows:  
\[Z_{\text{F}}=R_{\text{s}}+R_{\text{t}}+\frac{\gamma\ R_{\text{t}}\ |I_{\text{F}}|}{nF_{\text{Cs}}\sqrt{2 \omega D}}\ (1-j) \tag{4}\]  
Figure 6: Equivalent circuit impedance for (**a**) conventional rebar, and (**b**) DP rebar. Rebar, reinforced steel bars; DP, dual phase.  
The second impedance is represented by cotangent hyperbolic (O) diffusion, and the impedance (\(Z_{\text{F}}\)) is expressed as follows:  
\[Z_{\text{F}}=R_{\text{s}}+Z_{F}^{0}+Z_{\text{d}}=R_{\text{s}}+R_{\text{t}}\left(1 +\frac{\gamma\left|I_{\text{F}}\middle|I\right.}{nFC_{\text{s}}\text{D}}\right) \tag{5}\]  
where Q is the magnitude of admittance of the constant phase element CPE and n is the CPE exponent. The n value refers to the phase shift and can characterize different surface phenomena such as surface heterogeneity (inhomogeneity) resulting from surface roughness, dissolution of the metal, impurities, distribution of the active sites, or porous layer formation. The value of the coefficient (n) gives the frequency dependence.  
Limiting values of the coefficient (n) are zero for a pure resistor and one for an ideal capacitor. Intermediate values of (n) indicate imperfect capacitive behavior and a CPE with (\(n=0.5\)) usually referred to a Warburg Element, where \(\chi 2\) gives the overall regression coefficient for the fit.  
The interfacial charge transfer resistance Rt and the double layer capacitance C\({}_{\text{d}}\) are the key parameters characterizing the passive behavior of ductile iron, while higher Rt and lower C\({}_{\text{d}}\) on the surface of ductile iron results is meaning better corrosion resistance.  
Figures 7-9 show Nyquist planes for the above two diffusion elements. Experimental EIS spectra of conventional rebar and DP rebar are shown in Figure 7. For DP rebar, the Nyquist plot indicates hyperbolic diffusion, which existed only in the passive process. In contrast, conventional rebar diffusion changed from the Warburg impedance (\(W\)) to a high-frequency capacitive loop.  
All parameters of potentiodynamic polarization and EIS results in an alkaline solution with and without different Cl\({}^{-}\) ion concentrations are listed in Table 2. The polarization resistance (\(R_{\text{t}}\)) for the DP rebar oxide or passive layer was larger compared to conventional rebar. This result also verified that the passive current density of DP rebar is lower compared to conventional rebar as concluded from Figures 8 and 9.  
Figure 7: Electrochemical impedance spectroscopy (EIS) Nyquist curve in an alkaline solution (without Cl\({}^{-}\) ions). EIS, electrochemical impedance spectroscopy.