# Thermodynamics of Liquid Uranium from Atomistic and Ab Initio Modeling
## 6 Summary and Conclusions  
The key to metallic fuel development is the fabrication of uranium metal and alloys into fuel forms. Casting (the process in which a liquid metal is poured into a mold) has been a key component of the metallic fuel cycle, and process models require thermophysical parameters at elevated temperatures, particularly above the melting temperatures regarding which experimental data are scarce, for accurate simulations and process development. Specific heat and thermal diffusivity are the critical parameters of casting because the former parameter defines how much energy is necessary to raise the temperature necessary to melt and superheat the metallic alloy, and the former parameter defines the rate of heat transfer inside a material. Additional challenges to the measurement of the needed values are contamination and the rapid oxidation of the melt. These complications introduce uncertainty into the measurements and often have unforeseen influences on the measured values. It is therefore very useful to have thermophysical data without these influences. Present calculations address the need to develop these trusted thermophysical property data.  
The atomistic properties of liquid uranium in the temperature range of 1400 K \(\leq\) T 2000 K are calculated using the EAM potential [4] and the LAMMPS classical MD package. The melting temperature of uranium metal, defined from the simulation of coexisting phases, is found to be \(T_{2}\approx 1445\) K which is about 37 degrees above the experimental melting point, \(T_{m}=1408\) K. The calculated melting temperature is confirmed independently from the classical nucleation theory.  
For the first time, the electronic contribution to the specific heat of liquid uranium is calculated by ab initio full-potential formalism, which is applied to the atomic con figurations generated by the classical MD. We strongly believe that the specific heat of liquid uranium increases linearly with temperature and that this behavior is solely due to the characteristics of the electronic contribution to the heat capacity imposed by the Sommerfelt model. At the same time, we realize the practical difficulties in measuring the thermodynamic properties of liquid uranium that could explain the disagreement of the experiments with the theoretical results (see Ref [1] for details).  
We found that the low border of the supercooling of liquid uranium, \(T_{sc}\approx 800\) K, is approximately 645 K below the calculated melting temperature, \(T_{2}\approx 1445\) K. We also found that uranium metal can be supercooled about 1.5 times more than it can be overheated.  
The success of the atomistic modeling of U-Zr [6; 58; 59] and U-Mo [60; 61; 62] alloys encourages further modeling of U-Nb alloys, which are considered to be promising metallic fuel candidates for Gen-IV fast breeder reactors [63] due to their high melting point, good corrosion resistance, good thermos-conductivity, continuous BCC region ad high temperatures (there are UZr\({}_{2}\) and U\({}_{2}\)Mo compounds in U-Zr and U-Mo alloys, respectively), and excellent mechanical properties.  
Conceptualization, A.L. and P.S.; methodology, A.L. and P.S.; software, A.L. and P.S.; investigation, A.L. and P.S.; writing--original draft preparation, A.L. and P.S.; writing--review and editing, P.S., A.L., J.R., and J.T.M. All authors have read and agreed to the published version of the manuscript.  
This research received no external funding.  
Not applicable.  
Data is contained within the article.  
We acknowledge helpful discussions with [PERSON], [PERSON], [PERSON], and [PERSON]. This work was performed under the auspices of the U.S. DOE by LLNL under Contract DE-AC52-07 NA27344.  
The authors declare no conflicts of interest.