###### Abstract
The increasing distance between the ions should lead to a lower surface tension, as the literature assumes. However, thermal expansion appears due to the asymmetric curvature of the potential energy trough [27] and the Fermi band broadening might induce counteracting force [28; 29], since the ions show a higher probability of having more conduction electrons at increasing temperature. This effect can increase the ion charge and, thereby, the Coulomb forces [30]. In total, these effects can lead to an increased surface tension. The additional effect of extensive vaporization on boiling surfaces, where atoms are ejected from the surface [31], is scarcely explored but can be expected to create 'holes' in the surface layer. The effect of such a lack of atoms in surface on surface tension is still unclear but can probably affect the surface tension, due to missing bonding forces. Surface tension measurements are necessary to evaluate and validate models. There are several surface tension measurement methods categorized as: (1) direct measurement using microbalance, (2) measurement of capillary pressure, (3) capillary-gravity force analysis, (4) gravity-distorted drops and (5) reinforced drop distortion [32]. The measurement of liquid metals is limited to, e.g., the maximum bubble pressure method, measuring the pressure peak while a gas bubble inside the liquid material is formed. Another possibility is the observation of liquid droplets (e.g., the sessile drop method [33]) wetting a surface of another material. However, this method contains potential measurement errors related to the interfacial tension, which is often not known, and surface roughness. Due to the practical measuring challenges at high temperatures, non-contact methods are often preferred for measuring surface tension of liquid metals. Levitated drops [34; 35] or falling drops can be used. The frequency of the oscillations of falling drops can give surface tension values (e.g., [36]). Measuring the surface tension at even higher temperatures than recorded up to \(\sim\)2500 K (e.g., [25; 37; 38]) is challenging. Another method to derive surface tension values is the relation of surface wave propagation characteristics on liquid metals to surface tension [39]. These methods are contactless and are, therefore, in general also suitable to be used at high temperatures. Usable surface waves for such methods must propagate based on restoration by surface tension. This is given at Bond numbers \(\text{Bo}\ll 1\). In this regime, the Kelvin relation [40] can be used to derive the surface tension. For the relation to surface tension, the wave frequency, wavelength, and material density need to be measured or known [41]. Fortunately, the Kelvin equation can be used for a wide temperature range [42]. The impact of several sources of uncertainty were evaluated, e.g., the vapor recoil pressure was shown to have neither a stabilizing nor destabilizing effect on the melt pool surface waves and does not impact the measurement [43]. The Marangoni flow can slightly decrease the surface wave frequencies [44]. However, it can be difficult to create environments at high temperatures that enable identification of relevant features for surface tension measurements. It is a challenge to create a calm and homogeneous material surface at temperatures around the boiling point of metals without inducing additional effects that can disturb the measurements, such as evaporation of the surface [27]. Besides experimental methods, surface tension can be simulated using atom interaction calculations or molecular dynamic simulations. However, these calculations can also show high uncertainties and fluctuations due to the complexity of the induced physical processes and interactions [45]. In general, detailed molecular dynamic simulations require high calculation times, e.g., embedded atom calculations require many steps, since the embedded atom changes its embedding energy and the interaction distances to all other atoms ([45]).