# High-Temperature Thermodynamics of Uranium from Ab Initio Modeling
###### Abstract
These methods include the all-electron full-potential linear muffin-tin orbitals (FPLMTO) method [9, 10, 11, 12, 13, 14, 15, 16, 27, 53, 60, 64, 65] and the plane-wave-based projector augmented wave (PAW) method that utilizes the pseudopotential approximation [17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29, 30, 31, 32, 33, 34, 35, 36, 37, 39, 40, 41, 42, 43, 44, 45, 46, 47, 48, 49, 50, 51, 52, 55, 56, 58, 59, 60, 61, 62, 66]. The temperature effects on uranium or actinide systems have been studied by means of the self-consistent ab initio lattice dynamics (SCALID) method [13, 53, 60, 64, 65], and classical molecular dynamics with either the embedded atom method (EAM) or with the modified embedded atom method (MEAM) [28, 29, 30, 31, 32, 33, 34, 35, 36, 37, 38, 39, 40, 41, 42, 43, 44, 45, 46, 47, 48, 49, 51, 54, 57, 59, 63]. Quantum molecular or ab initio molecular dynamics (AIMD) [18, 19, 21, 22, 23, 24, 25, 26, 27, 39, 40, 41, 42, 43, 44, 46, 52, 55, 56, 58, 61, 62, 66] have also been applied to study thermal effects in uranium, but only in conjunction with pseudopotential electronic-structure methods. As was mentioned in Refs. [36, 60, 64, 65], anharmonic effects and conduction electrons play significant roles determining the heat capacity of uranium metal and its alloys and compounds. [PERSON] et al. [39], using the quasi-harmonic Debye-Gruneisen model, calculated the constant-pressure heat capacity (\(C_{p}\)) of \(\alpha\)-U in the temperature range up to 900 K. At low temperatures, up to 300 K, the calculated heat capacity has a reasonable agreement with the experimental data of [PERSON] and [PERSON] [67] and [PERSON] et al. [68]. However, as temperature increases, there is a substantial underestimation of the quasi-harmonic heat capacity relative to the experimental data [69] with errors of the order of 50%. Generally, the heat capacity consists of electronic and lattice vibration contributions. In magnetic systems there is a contribution from magnetism as well. We shall define these contributions below in Section 2 and note here that at high temperatures the electronic contribution is proportional to the electronic density of states and the temperature according to the Sommerfeld assumption [70]. This contribution is particularly important for \(\gamma\)-U as we shall show in this article. According to Ref. [36], \(\gamma_{\text{e}}\) (see definition in Section 2) for \(\alpha\)-U have been shown to be microstructurally dependent, with an average value of the experimental results to be about 10.12 mJ/(molK\({}^{2}\)). To our knowledge, no measurements have been published for \(\gamma\)-U. Recent AIMD calculations [66] significantly underestimate the heat capacity for \(\gamma\)-U when compared to experimental data [71], especially in the high-temperature region (1300-1400 K). The early measurements by [PERSON] and [PERSON] [72] suggested very weak temperature dependence of \(C_{p}\) for \(\gamma\)-U, while [PERSON] [73] proposed a completely temperature-independent \(C_{p}\) for the liquid. The results of the measurements by [PERSON] and [PERSON] [72] and [PERSON] [73] were questioned by [PERSON] et al. [74], who emphasized the importance of the electronic excitations for the heat capacity. This electronic contribution has a substantial temperature dependence, thus contradicting the conclusion of the experiments [72; 73]. In this study, we use DFT electronic structure combined with the SCAILD method [75] to determine the Gibbs free energy and heat capacity for high-temperature uranium in the \(\gamma\) phase. This approach is computationally efficient, very robust (insignificant noise), and it accounts for strong anharmonic phonon-phonon interactions. We employed this scheme with good results recently for actinide monocarbides and mononitrides [53; 60; 65], and graphite [76]. Approximately a decade ago, we predicted dynamical stability of \(\gamma\)-U with this technique, but calculations of thermodynamic properties were not included in that limited study [13].