## 5 Discussion  
The results indicate a good correspondence between the grain size determined via LUS and the MLI from reconstructed maps. However, at grain sizes below 10 \(\upmu\)m, the reconstructed MLI slightly exceeds the grain size predicted with LUS, and at grain sizes exceeding 20 \(\upmu\)m, the measured MLI values slightly undershoot the LUS values. With the limited data at hand, it is not clear if this is due to a systematic error or a random outcome. The relative error for the LUS measurements, on the other hand, is roughly the same over the entire range, and the correlation between the LUS and the EBSD grain size, i.e., R\({}^{2}\), for the stainless-steel calibration curve is just over 0.8. Previous studies have shown that the coherency of a boundary does not affect the attenuation of an LUS signal. The grain size given using LUS, then, always includes the attenuation from annealing twin boundaries as well. Moreover, the grain size was determined from an in situ measurement at the annealing temperature just before quenching, and, for a sufficiently fast quench, should be representative of the prior austenite grain size of the phase transformation products. The reconstructed grain map gives the twin boundaries as well. However, as discussed, there are some uncertainties regarding the correct twin orientation in the vicinity of the original annealing twin boundary. Figure 3 shows the issue clearly: some twin boundaries follow the expected morphology, while others appear irregular and incomplete where they would be expected to linearly follow the twinning plane boundary. Figure 6 shows the twinning densities calculated with Equation (1) plotted with respect to the grain size \(D\), given as MLI. Figure 5(a) shows the full range of grain sizes measured for 304, as well as a line plotted using Equation (1) with the parameters \(B\) = 0.2 and \(D_{0}\) = 0.1 \(\upmu\)m. The figure clearly shows the twinning density of 304 has an excellent fit with Equation (1). Figure 5(b) shows the twinning densities for the reconstructed data, along with the 304 densities, and the relationship is given in Equation (1). Figure 5: The grain sizes given via LUS and MLI for the austenitic 304 and the reconstructed low-alloy steels. The twinning densities for the reconstructed data do not follow the relationship given in Equation (1) fitted for the stainless steel results, but instead, exhibit an approximate density of 0.02 for a wide range of grain sizes. The difference is significant enough that it merits consideration on the basis of the quality of the reconstructions as well as the possible physical reasons for the differences in predictions. One measure of reconstruction quality is the fit between each individual reconstructed orientation pixel and the orientation of each domain in the variant graph, measured as the misorientation angle between the pixel and the domain orientations. A low fit indicates that there is very little variability in the orientation relationship between martensite and austenite. Another way to put this is that the orientation map can be described very well in terms of an austenite to martensite transformation, meaning that all structural units in the map indeed correspond to martensite. Furthermore, the low values of fit increase confidence in the correct twin indexation, since the mis-indexation of twins using representative orientation relationships results in a misfit in the reconstructed map [10]. Table 1 shows the mean fit values for each reconstructed orientation map in this study. The tool steel and the quenching and partitioning (Q and P) steel in this study had notably better fit values compared with the rest of the alloys, for all the studied grain sizes. Figure 5b shows there is almost no change in the twinning density for grain sizes above 5 \(\upmu\)m for either material. This is consistent with the rest of the data on the low-alloy steels. The similarities in twinning densities above a grain size of 5 \(\upmu\)m indicate the materials do not exhibit major differences in twin formation.