First principles free energy model with dynamic magnetism for δ -plutonium
We present an ab initio free energy model derived from a fully relativistic density functional theory (DFT) electronic structure with dynamic magnetism for δ -plutonium (face-centered cubic, fcc). The DFT model is extended with orbital-orbital interaction in a parameter free orbital polarization (OP) mechanism consistent with previous modeling of plutonium. Gibbs free energy is built from components associated with the temperature dependence of the electronic structure and the corresponding electronic entropy, lattice vibrations within an anharmonic lattice dynamics model, and dynamical fluctuations of the magnetization density, i.e. magnetic fluctuations. The fluctuation model consists of transverse and longitudinal modes driven by temperature induced excitations of the DFT + OP electronic structure. The ab initio model thus incorporates fluctuating states beyond the electronic ground state. Thanks to the dynamic magnetism, the theory predicts excellent thermodynamic properties and a Gibbs free energy in accord with CALPHAD and semi-empirical modeling developed from the thermodynamic observables. The magnetic fluctuations further explain anomalous behaviors of the thermal expansion in plutonium. Specifically, a thermal expansion for the δ -plutonium system turning from positive to negative at temperatures above room temperature, a tendency for gallium to reduce and remove the negative thermal expansion depending on composition, and a positive thermal expansion for the high temperature ϵ phase.