## 3 Results
\begin{table}
\begin{tabular}{c c c c c c c c} \hline \(C_{\text{11}}\) & \(C_{\text{22}}\) & \(C_{\text{33}}\) & \(C_{\text{44}}\) & \(C_{\text{55}}\) & \(C_{\text{66}}\) & \(C_{\text{12}}\) & \(C_{\text{13}}\) & \(C_{\text{23}}\) \\ \hline
56.5 & 45.6 & 62.2 & 10.3 & 10.5 & 19.5 & 31.2 & 26.8 & 19.2 \\ \hline \end{tabular}
\end{table} 
Table 1: Calculated elastic constants \(C_{ij}\) for UI\({}_{3}\) (GPa). Figure 1: Calculated total unit-cell electronic density of states (states/eV) for UI\({}_{3}\). The energy scale on the x-axis is shifted so that the highest occupied level is located at zero energy. relative to the observed one and we find spin and orbital moments on the uranium atoms that are 2.7, and \(-3.3\)\(\upmu_{\text{B}}\), respectively. The calculated magnitude of the moments is presumably not very sensitive to the actual magnetic configuration (a ferromagnetic treatment results in the same moment magnitudes) and we believe our simplification with anti-ferromagnetic moments along (001) is sensible. There is an experimental uncertainty in the exact magnitudes of the moments, but it does appear that the theory predicts smaller total moments than what is observed. Based on our aforementioned results, which exhibit reasonable accuracy, let us now focus on the thermodynamical properties at elevated temperatures. Because UI\({}_{3}\) has a relatively low melting temperature of about 1039 K [14], we assume that anharmonic effects on the phonons are limited and that a quasi-harmonic scheme for the lattice dynamics may suffice. The most sensitive test for this assumption is to compare our quasi-harmonic Gibbs energy with the CALPHAD database, which results from the assessment of existing experimental data. In Figure 2 we contrast our DFT-quasi-harmonic (QH) free energy with that of the CALPHAD (from room temperature and up). Generally, the free energy contains contributions from the electronic structure (here obtained from the DFT calculations), lattice vibrations (Debye-Gruneisen model), electronic excitations, electron-phonon coupling, and finally magnetic entropy. Because we are limiting the model to not too high temperatures, we make the assumption that the latter three contributions can be ignored, considering the overall level of accuracy dictated by the Debye-Gruneisen model. Certainly, that assumption was true for uranium mononitride that we studied recently [15]. Clearly, Figure 2 suggests that the QH result is consistent with CALPHAD for most temperatures. Noticeable deviation between the two approaches is observed only at relatively high temperatures, approaching 1000 K. Apparently, the quasi-harmonic assumption for the lattice vibrations begins to break down at those temperatures. Next, encouraged by the consistency of the QH theory and CALPHAD for the UI\({}_{3}\) free energy, we show their respective heat capacity at constant pressure, C\({}_{\text{P}}\), in Figure 3. As in the case of the free energy, no electron-thermal contribution to the heat capacity is considered in the QH theory. We find in Figure 3 that at lower temperatures the agreement is good, but we notice, consistent with that of the free energies, that C\({}_{\text{P}}\) begins to deviate between the two methods at temperatures approaching 1000 K. We interpret this discrepancy as a need to address anharmonic phonons at temperatures nearing 1000 K or to perform more dedicated experiments on the U-I system to further validate and/or refine the  
Figure 2: Gibbs free energies (kJ/mol) calculated from density-functional theory (DFT) and Debye–Grüneisen quasi-harmonic (QH) theory together with results from the SSUB6 calculation of phase diagram (CALPHAD) database. CALPHAD data. In the CALPHAD data, there may also be implicit effects related to formation of defects such as vacancies at high temperatures that are not addressed in the first-principles theory.