## 4 Discussion  
Both experimental and simulation results show similar global trends. Although simplifications were introduced for the modeling, the global, macroscopic trends in measured surface tension values seem to be possible to reproduce. The presented calculation results are able to show the trends in temperature dependence on surface tension, which was seen also in [45]. The measured and calculated surface tension values in this work deviate from the typically assumed linear decreasing extrapolations in the literature (e.g., Equation (1)) (Figure 5). Below boiling temperature, a tendency, typical for most pure materials, was  
Figure 4: Average forces along the evaluation lines in x- and y-directions in the 1 st and 2 nd layers. Figure 5: Surface tension measurements and calculations around the boiling temperature of steel, including surface wave analysis, simulation results and extrapolation from Equation (1) [24]. seen, showing a decrease in surface tension values with increasing temperature (e.g., [22]). This tendency was also seen in the simulation and surface wave analyses (Figure 5). An exponential decrease was suggested from previous experiments when analyzing surface tension data below boiling temperature [51]. The negative surface tension gradient is typically explained by the reduced bonding forces between the metal ions at elevated temperatures and the increasing distance between them [31]. However, the negative slope of the decrease is larger than expected. Such a steeper decrease was also seen during recent measurements using electromagnetic levitation of pure iron drops [24] and stainless steel drops with acoustic levitation [25]. Niobium also showed a much steeper trend in recent studies compared to earlier literature values [55]. However, the temperature range was around the melting temperature, which leads to the conclusion of a linear trend. The decrease can be assumed to derive from the significantly increased reduction in bonding strength between the ions and the interaction of at least two surface atomic layers, as calculated in the ion interaction model. Above boiling temperature, the experiments show a tendency to an increase in surface tension values at high temperatures, although uncertainties are still high. The same trend was seen when evaluating model calculations (Figure 5). The suggested method in this work enabled escaping from some restrictions and limitations of typically used surface tension measurement methods and a first insight into surface tension above boiling temperature. However, up to now, no related literature data have been found to compare with the data. Possible explanations for the increasing trend in surface tension values above boiling temperature can be suspected as: (1) the altered surface topology induced by atom losses due to vaporization of the surface layers and (2) the strength and kind of bonding forces between the surface ions. Since the calculation results show the experimentally observed trend and do not consider alterations in the vaporization effects, it can be assumed that the underlying effect is implemented in the current model, which is based on the calculation of forces between the ions in the bulk and surface. Attractive and repulsive forces act between the ions in the liquid bulk. It is known that, at melting temperature, few bonds are broken, and lattice ions can rearrange [56] until they find an energetically comfortable position. This means that this reordering is mainly driven by repulsive forces between the ions [56]. At increasing temperature, the distances between the ions increase (thermal expansion) and the attracting forces are reduced [27], which enables an even easier ion separation and, in turn, reduced forces in the material surface plane, which should result in reduced surface tension. Increasing the temperature to boiling leads to smaller attraction at higher ion separation according to the pair potential theory (Figure 6). Figure 6: Pair potentials used in the ion calculation below and above boiling temperature.