  Phase diagram of Np-U-Zr, a key ternary alloy system of relevance for
metallic nuclear fuels, is still largely undetermined. Here a thermodynamic
model for the Np-U-Zr system is developed based on Muggianu extrapolation of
our models for the U-Zr, Np-Zr, and Np-U binary systems, all employing the
CALculation of PHAse Diagrams (CALPHAD) method. This model reproduces available
experimental data for the high temperature phases reasonably well, but is
uncertain for the lower temperature phases for which experimental data are
scarce. Ab initio calculations are performed on the BCC phase of the Np-U-Zr
system at 28 compositions employing density functional theory (DFT) both in its
standard form and the so-called DFT plus Hubbard U (DFT + U) modification. When
referencing to our CALPHAD model, standard DFT on average overestimates the
enthalpy of mixing of the BCC phase by 0.093 eV/atom, while DFT + U reduces the
error to 0.009-0.036 eV/atom when the effective Hubbard U parameters are in the
ranges of single-structure optimized Ueff's determined in our previous studies
of the Np-Zr and U-Zr systems (0.65-0.90 for Ueff(Np) and 0.99-1.49 eV for
Ueff(U), respectively). Our combined CALPHAD and ab initio modeling provides an
initial attempt to determine the phase diagram of the Np-U-Zr system but
further work is needed for a reliable determination.
