# High-Temperature Thermodynamics of Uranium from Ab Initio Modeling
###### Abstract  
We present high-temperature thermodynamic properties for uranium in its \(\gamma\) phase (\(\gamma\)-U) from first-principles, relativistic, and anharmonic theory. The results are compared to CALPHAD modeling. The ab initio electronic structure is obtained from density-functional theory (DFT) that includes spin-orbit coupling and an added self-consistent orbital-polarization (OP) mechanism for more accurate treatment of magnetism. The first-principles method is coupled to a lattice dynamics scheme that is used to model anharmonic lattice vibrations, namely, Self-Consistent Ab Initio Lattice Dynamics (SCAILD). The methodology can be summarized in the acronym DFT + OP + SCAILD. Upon thermal expansion, \(\gamma\)-U develops non-negligible magnetic moments that are included for the first time in thermodynamic theory. The all-electron DFT approach is shown to model \(\gamma\)-U better than the commonly used pseudopotential method. In addition to CALPHAD, DFT + OP + SCAILD thermodynamic properties are compared with other ab initio and semiempirical modeling and experiments. Our first-principles approach produces Gibbs free energy that is essentially identical to CALPHAD. The DFT + OP + SCAILD heat capacity is close to CALPHAD and most experimental data and is predicted to have a significant thermal dependence due to the electronic contribution. uranium; specific heat; anharmonic; first principles; CALPHAD; DFT +
Footnote †: journal: Applied Sciences  
anisotropic growth during irradiation, and along with susceptibility of \(\alpha\)-U to corrosion by water, prompted the choice of the MOX rather than metal form of uranium as a fuel for commercial light water reactors [6,7]. Most of the experimental work has been performed on the \(\alpha\) phase and not on the \(\gamma\) phase because of the mechanical and dynamical instability of the latter at room temperature [9]. Performing high-temperature experiments on nuclear materials poses significant challenges that ultimately limit experimental investigations of the \(\gamma\) phase [6, 7, 8]. Uranium is also a fascinating metal from a fundamental and academic standpoint. The electronic structure dominates by narrow 5f bands that tend to break crystal symmetry and bond the atoms in a complex and distorted fashion [9, 10, 11, 12, 13, 14, 15]. The mechanism that stabilizes the open and complex structures in systems with narrow bands can be described in terms of a Peierls or Jahn-Teller distortion [9, 12]: a system with narrow bands close to the Fermi level can gain energy by lowering the crystal-structure symmetry. This phenomenon explains the low-symmetry orthorhombic structure of \(\alpha\)-uranium as well as the complex structures of the light actinides Pa-Pu. Higher symmetry allotropes, such as \(\gamma\)-U, are dynamically unstable at low temperatures due to the Peierls crystal symmetry-breaking mechanism. At higher temperatures, however, \(\gamma\)-U is dynamically stabilized and favored over \(\alpha\)-U due to entropy of thermal atomic vibrations [13], analogous to the temperature-driven formation of the body-centered cubic phase in the hexagonal elements Ti, Zr, and Hf, for example. Numerous first-principles calculations have been performed to evaluate uranium's structural, mechanical, and thermal properties, as well as radiation damage (defects). The stability of uranium and its alloys has been explored using different methods founded on density-functional theory (DFT) [9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29, 30, 31, 32, 33, 34, 35, 36, 37, 38, 39, 40, 41, 42, 43, 44, 45, 46, 47, 48, 49, 50, 51, 52, 53, 54, 55, 56, 57, 58, 59, 60, 61, 62, 63, 64, 65].