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6e-7 L (cm) Figure 2-18. 5 VSHE, as a function of the pH at the BOI and the barrier layer thickness. 41 3e-7 3e-7 Lss (cm) 2e-7 2e-7 1e-7 5e-8 0 -5e-8 4 5 6 7 8 9 pH Figure 2-19. 5 VSHE, as a function of pH at the BOI, showing the condition for depassivation (Lss →0). Log-linear plot of the total current density as a function of the pH at the BOI are displayed in Figure 2-20. In this instance, the total current density varies exponentially with the pH. This is because the current density for the generation of oxygen vacancies at the MBI is not a function of the respective defect concentrations at that interface, whereas it is a function of the defect concentrations at the BOI, and an expression of the current density, based on the reactions at the BOI, would require knowledge of these concentrations .
The solution in the pore interior is assumed to be dilute, so that aWBOI is taken to be 1. Substitution of Equations (2-52) and (2-53) into Equation (2-46) yields: [ BOI m I ≈ F ⋅ 4k1 − 2k 2 + 6θ ⋅ k 5 ⋅ ( a OH − ) ] (2-54) Note that the current density is a function of V and Lbl. Accordingly, for any arbitrary changes δV and δLbl, we can derive the following expressions by assuming that θ is constant: 19 BOI m δI = F ⋅ [4δk1 − 2δk 2 + 6θ ⋅ δk 5 ( a OH ) ] − and (2-55) δk1 = a1k1δV + b1k1δLbl − a1k1 Rol δI (2-56) δk 2 = a 2 k 2δV + b2 k 2δLbl − a 2 k 2 Rol δI (2-57) δk 5 = a5 k 5δV − a5 k 5 Rol δI (2-58) Substitution of Equations (2-56) to (2-58) into Equation (2-55) yields: BOI m (4a1k1 − 2a2 k2 + 6θ ⋅ a5 k5 (aOH − ) )δV + ( 4b1k1 − 2b2 k 2 )δLbl BOI m + Rol [−4a1k1 + 2a2 k2 − 6θ ⋅ (aOH − ) a5 k5 ]δI δI = F (2-59) The variations in I, V and Lbl are sinusoidal in an EIS measurement, so that we can write: δ I = ∆ I ⋅ e j ⋅ω ⋅ t δV = ∆ V ⋅ e (2-60) j ⋅ω ⋅t (2-61) δ L bl = ∆ L bl ⋅ e j ⋅ω ⋅t C BOI OH − 10 − pK w ( T ) − 6 = C HBOI+ (2-62) (for the unit cm3) (2-63) where Kw(T) is the water dissociation constant, which is a function of temperature .
The data were checked experimentally by stepping the frequencies from high-to-low and then immediately back from low-to-high, with the impedance being measured at each step, to ascertain that the same values were obtained at equivalent frequencies in the two directions. If the system is in the steady state, which means the thickness and current are independent of time, the impedance data should match in the two frequency step directions. Coincidence is observed in all impedance measurements for passive films formed at different potentials.
Oxidation of Zircaloy Cladding in Water-Cooled Nuclear Reactors