## 4 Discussion
### Oxygen Concentration Control in LBE  
An YSZ oxygen sensor was used to control the oxygen concentration in LBE, mainly utilizing redox reactions described as a (Bi/Bi2O3)! YSZ! (LBE/LBE-O) galvanic cell [41]. The YSZ membrane acted as a solid electrolyte and an oxygen ion conductor, while Bi/Bi2O3 functioned as a reference couple located inside the YSZ tube. The electromotive force (EMF) signal was generated by the metal/oxide reference determined by the oxygen concentration in LBE and was transmitted via a Mo wire inserted into the YSZ tube. The above oxygen sensor was calibrated using electrochemical impedance spectroscopy (EIS) to overcome its disadvantage of signal hysteresis upon heating and cooling and to achieve reproducibility between measurements, as described in Ref. [41]. Based on EMF measurements during corrosion tests, each signal could be converted to oxygen concentration with a measured LBE bulk temperature. The activity of oxygen dissolved in LBE, \(a_{O}\), can be expressed as  
\[a_{O}=\frac{C_{O}}{C_{s,O}}, \tag{1}\]where \(C_{O}\) is the concentration of oxygen, and \(C_{s,O}\) is the solubility of oxygen in LBE, both in wt.%. The following simple relation has been reported [50]:  
\[\log C_{s,O}=1.2-\frac{3400}{T}\ (673-973\ \text{K}). \tag{2}\]  
According to the [PERSON] equation, the EMF across the YSZ membrane acting as a solid electrolyte is directly related to oxygen potential [51]:  
\[\log a_{O}=-\frac{10079}{T}(E-0.1381)-0.7173, \tag{3}\]  
where \(T\) is the bulk LBE temperature in K and \(E\) the measured EMF in V, respectively. By combining Equation (1) with Equations (2) and (3), the expression for oxygen concentration is obtained as  
\[\log C_{O}=\log a_{O}+\log C_{s,O}=0.4872-\frac{10079}{T}(E+0.1992). \tag{4}\]  
The concentration of oxygen determined using Equation (4) is shown in Figure 4.  
PbO precipitation occurs at oxygen concentrations above \(\sim\)1 \(\times\) 10\({}^{-3}\) wt.%, and iron oxides start to decompose at oxygen levels below 2 \(\times\) 10\({}^{-8}\) wt.% at 600 \({}^{\circ}\)C, as shown in Figure 14 which illustrates the upper and lower boundaries of dissolved oxygen control as the oxygen solubility and magnetite formation limit, respectively, even though the reported solubility of oxygen in LBE is subject to variation [50,52]. Therefore, corrosion tests had to be carried out at an oxygen level of \(\sim\)1 \(\times\) 10\({}^{-6}\) wt.%, at which magnetite and Fe-Cr spinel are stable. In other words, specimens were exposed to oxide-forming and oxide-growing environments, while the oxide layer growth rates differed among the three alloys. Notably, the oxygen concentration remained stable during testing, except for several transients attributed to external causes as mentioned in Section 3.1. In the stable region, the oxygen concentration varied from 1 \(\times\) 10\({}^{-6}\) to 3 \(\times\) 10\({}^{-6}\) wt.%, as intended. However, several events due to external causes were observed, with oxygen levels being outside the controlled range. After the start of corrosion tests, the concentration of oxygen in LBE seemed to be lower than that required for the onset of magnetite formation, as described by No. 1 in Figure 4, which was attributed to excess hydrogen gas. Even though the oxygen concentration decreased at an early stage, magnetite and Fe-Cr spinel were in a stable region, considering that the oxide layer thickness showed similarity to previously reported trends. Subsequently, aeration occurred, as indicated by No. 2 in Figure 4. As the oxide layer growth was hindered, passivation was accelerated by the increased oxygen partial pressure, leading to a steep rise in oxygen concentration. The maximum oxygen concentration (1 \(\times\) 10\({}^{-4}\) wt.%) was lower than that required for PbO formation and declined in a few hours. Several hours after this peak, the duplex layer growth could be sustained. This process still holds for event No.