## 2 Materials and Methods  
Immersive tests were conducted under ambient pressure using coupons measuring 50 mm \(\times\) 20 mm \(\times\) 4 mm, fabricated from high-alloyed martensitic stainless steel 1.4021 (X20 Cr13, AISI 420). Corrosion fatigue tests were carried out using high-alloyed martensitic corrosion resistant stainless steel 1.4542 (X5 CrNiCuNb16-4, AISI 630, PRE number 15.0-18.9 (PREN = %Cr + 3.3% Mo + 16% N) [49; 50]). The chemical composition was analyzed using spark emission spectrometry (SPEKTROLAB M) and the Electron Probe Microanalyzer JXA8900-RLn (Table 1). The microstructure of alloy 1.4542, revealed through etching before exposure and fatigue testing, displays martensite with varying needle-shaped sizes and a minor percentage of delta phase precipitation. For the preparation of water and ethanol-based sols and coatings, the procedures outlined in [34; 35; 43; 44; 51; 52; 53], and illustrated in [34] were followed. Initially, an aluminum nitrate (V) solution was heated to 87 \({}^{\circ}\)C, and aluminum tri-sec-butylate dissolved in secbutane was added under vigorous stirring for up to 1 h. After cooling to room temperature, the sol was directly used for the dip-coating process. The preparation of aqueous modified Yoldas sols followed the method described in [51; 52], resulting in sols with a solid content of 10 wt.% Al\({}_{2}\)O\({}_{3}\) and a NO\({}_{3}\)\({}^{-}\)/Al ratio of 0.6, yielding an acidity of pH = 3.5. Additional information on this type of sol is provided in [51; 53]. The sol was applied before exposure to the corrosive environment on polished (coupons) or fine machined (fatigue specimen) surfaces by pulling substrates ((coupons: water based sol: 170 mm/min, ethanol based sol: 40 mm/min and 170 mm/min) and (corrosion fatigue specimen: 15 mm/s and 30 mm/s)). Then the samples were dried at 120 \({}^{\circ}\)C for 2:30 min and heat treated in inert atmosphere at 500 \({}^{\circ}\)C for 30 min h to form a well adhesive alumina coating. The coating thickness on the flat coupons was measured via TEM and varied according to the pulling velocity (Table 2). Measurements of the coating thickness on round fatigue specimen were not successful due to unevenness and lateral detachment at the specimen center: \begin{table}
\begin{tabular}{c c c c c c c c c c} \hline \hline
**Elements** & **C** & **Si** & **Mn** & **P** & **S** & **Cr** & **Mo** & **Ni** & **Cu** & **Nb** \\ \hline \multicolumn{10}{c}{**1.4542 (X5 CrNiCuNb16-4, AISI 630)**} \\ \hline acc standarda analysedb & \textless{}0.07 & \textless{}0.70 & \textless{}1.50 & \textless{}0.04 & \textless{}0.015 & 15.0–17.0 & \textless{}0.60 & 3.00–5.00 & 3.00–5.00 & 0.20–0.45 \\ \hline \multicolumn{10}{c}{**1.4021 (X20 Cr13, AISI 420)**} \\ \hline acc standarda analysedb & \textless{}0.22 & \textless{}0.39 & \textless{}0.32 & \textless{}0.007 & \textless{}0.006 & 13.3 & 0.123 & \\ \hline \end{tabular}  
* \({}^{\text{a}}\) elements as specified according to DIN EN 10088-3 in \({}^{\circ}\)% b spark emission spectrometry \(\pm\)1%.  
\end{table} 
Table 1: Chemical composition of 1.4542 (X5 CrNiCuNb16-4, AISI 630) and 1.4021 (X20 Cr13, AISI 420) (in mass percent). For ambient pressure (X20 Cr13) and fatigue experiments (X5 CrNiCuNb16-4) technically clean CO2 (99.999%) was used to saturated the aquifer water. The laboratory brine similar to the Stuttgart Aquifer [7] (Table 3) was synthesized in a strictly orderly way to avoid precipitation of salts and carbonates. Exposure of the coupons (a set of two or three per parameter) was disposed according to [PERSON] [13] in a chamber kil at 60 \({}^{\circ}\)C and ambient pressure. Flow control of CO2 (3 NL/h) was done by a capillary meter GDX600_man by QCAL Messtechnik GmbH, Munchen [13]. Corrosion fatigue specimens were manufactured by means of precision turning without an additional surface finish in order to replicate the prefabricated technological conditions (Rz = 4, surface roughness 2.6 \(\upmu\)m to 4.7 \(\upmu\)m with mean arithmetic value of 3.65 (1.4542).