DFT-based thermodynamic stabilities of the ternary compounds and calculation of the system U-B-C

Abstract

Based on experimental data for (a) the isothermal section at 1600°C, (b) the melting points of UBC and UB₂C as well as (c) for the energy of formation of the aforementioned two ternary compounds, which were calculated from density functional theory (DFT), the thermodynamic phase equilibria in the ternary system have been calculated i.e. phase relations have been defined for the isothermal sections at 1600°C, 1800°C, 2000°C, 2200°C, 2400°C and for four isopleths B - UC, U - B₄C, UB₂ - UC₂, and B₄C - UC. The equilibrium solidification path of alloys is outlined in a liquidus surface and a Schultz-Scheil diagram. The thermodynamic modelling perfectly complies with the phase equilibria observed experimentally, with the relevant homogeneity regions of the binary and ternary phases, as well as with the regions of primary crystallization of the ternary solid phases, UB_1-xC_1+x and UB₂C. Due to the two-phase equilibria formed between the ternary compounds and between binary borides and carbides, we neither observe compatibility between uranium metal and B₄C, nor between B₄C and UC. Applying the Vienna Ab initio Simulation Package VASP for density-functional-theory (DFT) based first-principles calculations, the compounds UBC, UB₂C (high and low temperature modifications) as well as the hypothetical compounds "U₂B₂C₃" and "U₃B₂C₃", which both adopt the structure of the Th-homologues, were studied. In all cases the crystal structures were fully relaxed by optimizing total energy and strain. Because of the heavy element U, spin-orbit coupling (SOC) was included in the DFT calculations. The resulting total energies serve as basis for deriving the enthalpy of formation at zero Kelvin. Electron densities of states (eDOS) are presented as well as results for magnetic moments, which are in the range of ∼0.2 to ∼1.7 µ_B.