**6. Discussion**

The present contribution presents an overview of experimental measurements and theoretical treatment to obtain physical and thermophysical properties of liquid metals and liquid binary alloys in the context of phase diagrams. We have carried out high-precision sound velocity, electrical resistivity and density measurements on several column III to V elements and their binary alloys.

Measurements were carried out as a function of temperature in the liquid state. We found that, where relevant, the present measurements stand in a good agreemen<sup>t</sup> with previously published data. These measurements were used to map phase transformations by direct measurements, i.e., electrical resistivity, or by incorporating sound velocity and density measurements into a thermodynamic model to calculate phase diagrams of binary alloys under pressure.

The measurements of the physical properties were also analyzed with respect to composition. Regarding sound velocity measurements, we observed that as the concentration of the element having a larger sound velocity is increased, the alloy sound velocity increases, respectively. Moreover, there is a connection between the elements' temperature coefficient and that of the alloys. For example, if the two elements have normal behavior, then the alloys of both the elements present normal behavior as well. In the Pb-Sn system, both the elements and the different compositions of the alloy display normal temperature coefficients. In the Bi-Sb binary system, the Sb rich alloy displays anomalous behavior similar to Sb. As the Bi concentration increases, the behavior becomes semi-normal similar to in Bi. With regard to electrical resistivity, we observe that the Bi-Ga system shows a parabolic correlation with composition, as expected from mixed valence alloys. The Ga-In system, in which the elements have the same valences, presents a complex dependence on composition and not a linear ratio as expected [42].

Electrical resistivity is sensitive to structural changes, for example, as manifested upon a transition from a solid to liquid phase where the resistivity in metals usually increases. Furthermore, the thermal coefficient of the resistivity is also strongly connected to the structural properties, and thus a change in the slope can indicate a change in the liquid's short-range order [32]. Such a change in the thermal coefficient is seen in the Bi-Ga system and is related to the region of the phase diagram presenting a phase separation in the liquid. The electrical resistivity measurements indicate, with high accuracy, these phase transformations from a homogenous liquid to the two liquids region and, then, to the zone of mixed phases of liquid and solid.

The use of CALPHAD allows us to exploit data measured at ambient pressure to calculate phase diagrams of binary alloys under pressure. The sound velocity and the density are used to calculate the pressure dependence of the interaction parameters on pressure to the second order. We apply this formalism for two examples, the isomorphic system Bi-Sb and the eutectic system Pb-Sn.

We demonstrated the use of experimental measurements to obtain nontraditional thermal analysis. These are thermophysical measurements that can shed some light on the dependence of the structure on temperature, and provide evidence on the presence or absence of a local change in the liquid state. From sound velocity and density measurements at ambient conditions, we are able to calculate the pressure dependence of the interaction parameters in the liquid state, which is required to calculate the phase diagram under pressure of binary systems. This provides an innovative path to predict properties of the material under pressure and the dependence of eutectic point and liquidus temperature as a function of composition.

**Supplementary Materials:** The following are available online at http://www.mdpi.com/1996-1944/12/23/3999/s1.

**Author Contributions:** Conceptualization, J.L., E.Y., and G.M.; methodology, E.Y., G.M., and Y.G.; investigation, Y.K., S.B.S., M.E., and Y.G.; writing—original draft preparation, all authors; writing—review and editing, S.B.S., E.Y., and G.M.

**Funding:** This research was partially funded by the Pazy Research Foundation and by the Korea–Israel Joint Research Program, Nano & Pressure Phase Diagram of Alloys (NADIA), by the National Research Foundation of Korea (NRF) gran<sup>t</sup> funded by the Ministry of Science and ICT (MSIT) (NRF-2016K1A3A1A31913031) and by a gran<sup>t</sup> from the Ministry of Science, Technology & Space, Israel.

**Acknowledgments:** The authors acknowledge the technical assistance of Aviram Berko.

**Conflicts of Interest:** The authors declare no conflict of interest. The funders had no role in the design of the study; in the collection, analyses, or interpretation of data; in the writing of the manuscript, or in the decision to publish the results.
