# Thermodynamics Modeling for Actinide Monocarbides and Mononitrides from First Principles
## 1 Introduction  
Actinide carbides and nitrides are of practical importance as possible nuclear fuels for Generation-IV (fast neutron fission) reactors [1; 2]. Currently, nuclear fuels are often ceramic fuel pellets of actinide dioxides or actinide mixes of dioxides. More advanced fuels may consist of actinide, primarily uranium and plutonium, carbides and nitrides, due to their greater density and thermal conductivity. Furthermore, they release more neutrons than consumed in the reactor which is beneficial for energy production. However, the suitability of the nuclear carbide and nitride fuels is still being evaluated and fundamental research, experimental and modeling, has increased significantly in recent years [3; 4; 5; 6; 7; 8; 9; 10; 11; 12; 13; 14; 15; 16; 17; 18]. These radioactive and toxic compounds are not trivial to work with and their material properties at higher temperatures, central for nuclear fuels, are difficult to measure accurately. From a modeling point of view, the electronic structure is complex, and the high temperatures of interest for fuels cause the atoms to behave in a challenging anharmonic fashion. The physics models presented to date for the actinide monocarbides and mononitrides have been, with few exceptions, either semi-empirical in nature or restricted to a quasi-harmonic (QH) treatment of the lattice dynamics. The QH approach, however, is known to be less predictive at higher temperatures [8; 15]. In this report, we address these shortcomings in modeling by combining advanced first-principles electronic structure with a lattice-dynamics method that can treat strong lattice anharmonicity at high temperatures. For comparison and validation of the modeling, we apply the CALPHAD method to compare the assessments of experimental data in addition to directly contrasting the theory with measurements, where available. Actinide-bearing materials, including the present potential fuels, are complicated to handle, both theoretically and experimentally. Consequently, some basic properties,including details of the magnetism, are not yet well categorized for the actinide carbides and nitrides. For fundamental theory, the challenges often focus on the electronic and crystal structure. In regard to the latter, the 5f electrons play important roles for all actinides up to plutonium. Even for thorium, that has the least amount of 5f electrons, their presence dictates the crystal structure [19]. The dominance in the chemical bonding of the 5f electrons is reflected in the gradual increase in complexity of the crystal structures with atomic number up to plutonium that has an extraordinary monoclinic phase [20]. The actinide monocarbides and mononitrides, however, solidify in the sodium chloride (NaCl) or rock salt structure, i.e., a cubic phase with the two atoms in the (000) and (1/2 1/2 1/2) positions, respectively. This simple phase, also referred to as B1, makes the theoretical treatment considerably easier than that of more complex structures. While the crystal structure is basic for these rock salt compounds, the electronic structures are very intricate and require careful consideration. For uranium and plutonium compounds, particularly oxides, the 5f electrons are often treated in a physics model with density-functional theory (DFT) and a Hubbard U parameter designed to address a large intra-atomic Coulomb repulsion in the DFT + U method. A broad study [21] of actinide oxides, carbides, and nitrides, in the rock salt structure, considered both the DFT + U (U-4 eV) and the screened-hybrid-DFT approaches. In the latter, a chosen arbitrary amount of Hartree-Fock electron exchange interaction is explicitly included in the model. The conclusion from this investigation [21] was that for actinide dioxides these models are appropriate but for the metallic carbides and nitrides, the screened-hybrid-DFT is problematic. Namely, the photoemission for UN is not correctly reproduced, contrary to the conventional DFT model that compares well with experiment.