# High-Temperature Thermodynamics of Uranium from Ab Initio Modeling
## 5 Summary and Conclusions  
We computed thermodynamic properties for \(\gamma\)-U using the DFT + OP + SCAILD technique. Aside from a more limited study on the dynamical stability [13], this approach has not previously been employed for \(\gamma\)-U. All quantities were obtained from a very accurate all-electron method, except for the atomic forces needed for the lattice dynamics that were, for expedience, calculated with the more approximate pseudopotential method. Both techniques include relativistic and magnetic interactions in terms of spin-orbit coupling and orbital polarization. The thermal expansion and large volume (relative to \(\alpha\)-U) of \(\gamma\)-U induces significant polarization of the electronic structure, and the model predicts formation of spin and orbital moments. The relativistic and magnetic interactions lower the electronic energy, and the magnetic moments provide an entropy contribution to Gibbs free energy. The temperature dependence of the Gibbs free energy contribution from these interactions is calculated to be relatively small, 0.021 eV, between 750 and 1250 K. Nevertheless, this difference is noticeable on the scale in Figure 2, and neglecting magnetic interactions worsens the agreement with CALPHAD. The good agreement between our ab initio modeling and CALPHAD computations gives credence to both approaches.  
The lack of relativistic and magnetic correlations In the AIMD electronic structure [66], for example, is not the main cause for the poorly estimated \(\gamma\)-U volumes in Figure 1, but rather the limitation of the pseudopotential approximation. This becomes clear in Table 1, where all pseudopotential calculations strongly underestimate the \(\gamma\)-U volume at low temperatures, contrarily to the all-electron results.  
One of the driving motivations for our study is to shed light on uranium's thermal behavior of the heat capacity at high temperatures. The experimental data are rather scattered with weak temperature dependence, but our DFT + OP + SCAILD calculations indicate an increase of the specific heat with temperature. In our view, it is not likely that the high-temperature heat capacity completely lacks thermal dependence for \(\gamma\)-U because of the non-negligible electronic contribution. The thermal behavior matters because a stronger thermal dependence affects thermal transport predictions of fuel fabrication processes such as casting and forming. The modified properties will hopefully lead to more accurate predictions which can improve efficiency and lower cost of production.  
Conceptualization, P.S. and A.L.; methodology, P.S., A.L., A.P. and E.E.M.; software, P.S., A.L., A.P. and E.E.M.; investigation, P.S., A.L., A.P. and E.E.M.; writing--original draft preparation, A.L. and P.S.; writing--review and editing, P.S., A.L., A.P., E.E.M., 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.  
**Acknowledgments:** We acknowledge helpful discussions with [PERSON] and [PERSON]. This work was performed under the auspices of the U.S. DOE by LLNL under Contract DE-AC52-07 NA27344.