## 3 Experimental Results
### Microstructure Analyses  
The results of the EBSD analyses are shown as orientation maps in Figure 5, where the inverse pole figure (IPF) color scheme is used for the illustration of the martensite orientations. Note that the raw data have been smoothed and filtered using the half-quadratic minimization of manifold-valued data [44]. Within the measuring accuracy, no retained austenite could be detected for all heat treatments. In accordance with [30], the present measured orientations confirm the Kurdjumov-Sachs [45] orientation relationship. Based on this, PAG boundaries are automatically reconstructed and depicted as black lines in Figure 5. White lines indicate recrystallization twin boundaries of PAGs, which are identified via their special orientation to each other. Contrary to expectations, in several cases, the (twin) boundaries follow somewhat jagged lines, which is a sign that some orientations have been misindexed. This can be attributed to the fact that austenite grains and their twins share equal martensite variants. A detailed discussion about this can be found, for example, in [46]. In the context of the statistical analyses in the present study, twins are considered as single PAGs. Figure 4: Correlation between measured hardness and cooling time; numbers above data points indicate cooling rates. Figure 3: Variation of the hardness measurements by indicating the deviation from the mean value of the individual samples (**a**) A1, (**b**) A2, (**c**) A3, (**d**) A4. Moreover, the CPP packets (in the following, these are referred to as packets) are calculated, which are shown in Appendix A. For the grain reconstruction, the threshold misorientation angle indicating a grain boundary is defined with \(\theta_{\text{crit}}=5^{\circ}\). Since the laths cannot be clearly identified in this purely orientation-based reconstruction, the reconstructed \"martensite grain\" is called a \"block\". As a reminder, in the martensite hierarchy, blocks are the superordinate structure of the laths and a block consists of several laths of the same or a very similar orientation. The cross-section areas of the structure recorded with the EBSD system are referred to as areas \(A^{\text{2D}}\). According to the heat treatment, no significant differences in the grain sizes of the PAGs are expected. In Figure 6, this is checked by means of the median and mean equivalent grain diameter  
\[\bar{d}=2\sqrt{\frac{A^{\text{2D}}}{\pi}}. \tag{2}\]  
Reconstructed austenite grains which are intersected by the measurement boundary are excluded from the evaluation. Furthermore, here and in the following, grains and martensite blocks with a size smaller than \(0.32\,\mathrm{\SIUnitSymbolMicro m}^{2}\) are not evaluated. The resulting number of evaluable grains is indicated above the corresponding bars. Experiments with a higher amount of evaluable grains tend to have a smaller mean; however, a systematic influence from the heat treatment cannot be identified. Differences are therefore due to the size of the measurement section. Figure 5: EBSD map in an inverse pole figure color scheme with superimposed prior austenite grain boundaries (black) and recrystallization twin boundaries (white): (**a**) A1, (**b**) A2, (**c**) A3, (**d**) A4. In Figure 7 the empirical cumulative distribution function (ECDF) of the packet and martensite block areas--respectively, \(A^{\text{2D}}_{\text{CPP}}\) and \(A^{\text{2D}}_{\text{B}}\)--are shown. Note the different scale of the abscissa in Figure 7b. No systematic correlation between the quenching rate and the packet areas as well as the martensite block areas can be derived. The diagrams in Figure 7 only represent a one-dimensional representation of the data, which is why the analyses are supplemented by a two-dimensional representation. Thus, Figure 8 shows the packet areas \(A^{\text{2D}}_{\text{CPP}}\) over the PAG areas \(A^{\text{2D}}_{\text{PAG}}\). In Figure 8a, the complete data of the highest and lowest tested quenching rates are documented as an example.