## 2 Materials and Methods
Coating of 1.4542 (X5 CrNiCuNb16-4) fatigue specimens was done via dip-coating into ethanol-based alumina sols according to the procedure demonstrated above and schematically shown in [34]. The sol was applied before exposure to the corrosive environment on fine machined fatigue specimen that had reached endurance limits in previous experiments (run-outs) surfaces by pulling substrates (corrosion fatigue specimen: 15 mm/s and 30 mm/s)). Because of the length of the specimen the coating procedure was undertaken in two consecutive steps resulting a visual barrier on the surface. 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 and loaded into the corrosion chamber. Corrosion fatigue test were conducted using hourglass specimens (critical cross-section is 12.5 mm in diameter) according to the standard DIN EN ISO 11782 1 and to the recommendations of the FKM Research Issue [54; 55]. The resonant testing machine (sinusoidal dynamic test loads, R = \(-\)1; resonant frequency \(\sim\)30 Hz) and corrosion fatigue testing have been explained has been in detail by [PERSON] and [PERSON] [13; 49]. The set up (Figure 1) was used to test 9 specimens between 280 MPa and 390 MPa. \begin{table}
\begin{tabular}{c c c c c c c c} \hline \hline
**Sample Nr.** & **Sol** & **Pulling Velocity** & **Coating Thickness** & **Remarks** \\ \hline  & & & **1.4542** (X5 CrNiCuNb16-4, AISI 630) corrosion fatigue specimen & \\ \hline
6 TOT & water based & 30 mm/s & not applicable \textless{} 0.5 \(\upmu\)m & uneven, layered, lateral detachments at center \\
7 TOT & water based & 15 mm/s & not applicable \textless{} 0.2 \(\upmu\)m & uneven, layered, lateral detachments \\
12 TOT & water based & 15 mm/s & not applicable \textless{} 0.5 \(\upmu\)m & uneven \\
21 TOT & water based & 30 mm/s & not applicable \textless{} 0.6 \(\upmu\)m & uneven \\ \hline  & & & **1.4021** (X20 Cr13, AISI 420) coupons & \\ \hline
20, 21, 22 & water based & 170 mm/min & ca. 1.4 \(\upmu\)m & \\
23, 24 & ethanol based & 40 mm/min & ca. 0.8 \(\upmu\)m & \\
25, 26 & ethanol based & 170 mm/min & ca. 1.9 \(\upmu\)m & \\ \hline \hline \end{tabular}
\end{table} 
Table 2: Chemical composition of 1.4542 (X5 CrNiCuNb16-4, AISI 630) and 1.4021 (X20 Cr13, AISI 420) (in mass percent). \begin{table}
\begin{tabular}{c c c c c c c c} \hline \hline  & \multicolumn{6}{c}{**According to Stuttgart Formation**} \\ \hline  & NaCl & KCl & CaCl2 \(\times\) 2H2O & MgCl2 \(\times\) 6H2O & Na2 SO4 \(\times\) 10H2O & KOH & NaHCO3 & pH value \\ \hline g/L & 224.6 & 0.3902 & 6.452 & 10.62 & 12.074 & 0.3206 & 0.0475 & 8.2–9 \\ \hline  & & & & & & & \\ \hline  & Ca\({}^{+}\) & K2\({}^{+}\) & Mg2\({}^{+}\) & Na2\({}^{+}\) & Cl\({}^{-}\) & SO4\({}^{2-}\) & HCO3\({}^{-}\) & pH value \\ \hline g/L & 1.76 & 0.43 & 1.27 & 90.1 & 14.33 & 3.6 & 0.04 & 8.2–9 \\ \hline \hline \end{tabular}
\end{table} 
Table 3: Chemical composition of the synthetic aquifer electrolyte according to the Stuttgart Formation. X-ray diffraction analysis was performed using a URD-6 (Seifert-FPM) equipped with CoK\(\alpha\)-radiation, featuring automatic slit adjustment, a step size of 0.03, and a 5-s count. Phase analysis was carried out using AUTQUAN(r) by Seifert FPM. For gravimetric measurement, samples were descaled by exposure to 37% HCl for 24 h, and the mass gain was analyzed according to DIN 50 905 part 1-4. Surface corrosion characterization utilized SEM/EDX with a Leo Gemini 1530 VP at an acceleration voltage of 15 kV. Fitting corrosion analysis involved 3D imaging with the Microprof TTV double optical system by FRT. Sections of non-descaled samples were embedded in cold resin (Epoxicure, Buehler), cut, and polished with SiC-Paper ranging from 180 um to 1200 um under water. The final polishing stages included diamond paste with grit sizes of 6 um, 3 um, and 1 um.