Thermodynamics of Plutonium Monocarbide from Anharmonic and Relativistic Theory

Abstract

Thermodynamics of plutonium monocarbide is studied from first-principles theory that includes relativistic electronic structure and anharmonic lattice vibrations. Density-functional theory (DFT) is expanded to include orbital-orbital coupling in addition to the relativistic spin-orbit interaction for the electronic structure and it is combined with anharmonic, temperature dependent, lattice dynamics derived from the self-consistent ab initio lattice dynamics (SCAILD) method. The obtained thermodynamics are compared to results from simpler quasi-harmonic theory and experimental data. Formation enthalpy, specific heat, and Gibbs energy calculated from the anharmonic model are validated by direct comparison with a calculation of phase diagram (CALPHAD) assessment of PuC and sub-stochiometric PuC0.896. Overall, the theory reproduces CALPHAD results and measured data for PuC rather well, but the comparison is hampered by the sub-stoichiometric nature of plutonium monocarbide. It was found that a bare theoretical approach that ignores spin-orbit and orbital-orbital coupling (orbital polarization) of the plutonium 5f electrons promotes too soft phonons and Gibbs energies that are incompatible with that of the CALPHAD assessment of the experimental data. The investigation of PuC suggests that the electronic structure is accurately described by plutonium 5f electrons as “band like” and delocalized, but correlate through spin polarization, orbital polarization, and spin-orbit coupling, in analogy to previous findings for plutonium metal.

High-Temperature Thermodynamics of Uranium from Ab Initio Modeling

“…In this case, we set up a 3 3 (27 atoms) supercell of bcc (γ) uranium and perform 400 SCAILD iterations to ensure very good convergency of the free energy and heat capacity. The supercell size is consistent with our previous SCAILD works [13,53,60,65] and is assumed to be sufficient. Three strategic volumes and six temperatures are simulated with this approach.…”

“…The stability of uranium and its alloys has been explored using different methods founded on density-functional theory (DFT) . These methods include the all-electron fullpotential linear muffin-tin orbitals (FPLMTO) method [9][10][11][12][13][14][15][16]27,53,60,64,65] and the planewave-based projector augmented wave (PAW) method that utilizes the pseudopotential approximation [17][18][19][20][21][22][23][24][25][26]32,37,39,45,46,52,55,56,58,61,62,66]. The temperature effects on uranium or actinide systems have been studied by means of the self-consistent ab initio lattice dynamics (SCAILD) 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][33]…”

“…As was mentioned in Refs. [36,53,60,64,65], anharmonic effects and conduction electrons play significant roles determining the heat capacity of uranium metal and its alloys and compounds. Ren et al [39], using the quasi-harmonic Debye-Grüneisen model, calculated the constant-pressure heat capacity (C p ) of α-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 Flotow and Lohr [67] and Jones et al [68].…”

“…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 γ-U with this technique, but calculations of thermodynamic properties were not included in that limited study [13].…”