Interatomic potentials for mixed oxide and advanced nuclear fuels

We extend our recently developed interatomic potentials for UO${}_2$ to the fuel system (U,Pu,Np)O${}_2$. We do so by fitting against an extensive database of ab initio results as well as to experimental measurements. The applicability of these interactions to a variety of mixed environments beyond the fitting domain is also assessed. The employed formalism makes these potentials applicable across all interatomic distances without the need for any ambiguous splining to the well-established short-range Ziegler-Biersack-Littmark universal pair potential. We therefore expect these to be reliable potentials for carrying out damage simulations (and molecular dynamics simulations in general) in nuclear fuels of varying compositions for all relevant atomic collision energies.

Figure 1

Test of approximation validity of $f_{\mathrm{PuPu}}=(90/88)f_{\mathrm{UU}}$ and $f_{\mathrm{NpNp}}=(89/88)f_{\mathrm{UU}}$ by looking at the applicability of similar relations for cations of members of the previous row of the periodic table with similar shell structure, viz., Pm and Nd. The dashed line denotes the result from this approximation while the solid line is the actual charge density[3] for Nd${}^{+4}$.

Figure 2

Quality of fit from our fitted potential (asterisks) for various ab initio energies (circles) for PuO${}_2$. (a) Equation of state, (b) oxygen atom perturbation, and (c) plutonium atom perturbation. For each of oxygen and plutonium, the first four perturbations are along the $\langle 100\rangle$ direction, while the second four are along the $\langle 110\rangle$ direction. The perturbations are on the order of 1 Å or lower from the equilibrium positions.

Figure 3

Quality of fit from our fitted potential (asterisks) for various ab initio energies (circles) for NpO${}_2$. (a) Equation of state, (b) oxygen atom perturbation, and (c) neptunium atom perturbation. For each of oxygen and neptunium, the first four perturbations are along the $\langle 100\rangle$ direction, while the second four are along the $\langle 110\rangle$ direction. The perturbations are on the order of 1 Å or lower from the equilibrium positions.

Figure 4

(a) Fitted O-Pu interaction, and (b) fitted O-Np interaction.

Figure 5

Equation of state for (a) ${\mathrm{U}}_{31}$PuO${}_{64}$ and (b) ${\mathrm{U}}_{30}$Pu${}_2$O${}_{64}$. Circles denote ab initio data while asterisks are the values predicted (not fitted) with current potential.

Figure 6

Equation of state for (a) ${\mathrm{U}}_{31}$NpO${}_{64}$ and (b) ${\mathrm{U}}_{30}$Np${}_2$O${}_{64}$. Circles denote ab initio data while asterisks are the values predicted (not fitted) with current potential.

Figure 7

Lattice parameter at various temperatures for (a) PuO${}_2$ and (b) NpO${}_2$. Straight lines are the experimental values[28] valid between 400 and 1000 K, while circles denote values obtained from MD simulations using current potentials. Plus signs represent (1/$\eta$) times the experimental values actually used in fitting to account for the observation that ZSISA slightly overestimates the MD lattice parameters. Details of the calculation of this adjustment factor $\eta$ (equaling 1.0006 and 1.0008 for PuO${}_2$ and NpO${}_2$, respectively) can be found in the text.

Figure 8

Enthalpy at various temperatures (relative to room temperature enthalpy) for (a) PuO${}_2$ and (b) NpO${}_2$. The circles denote values from NPT MD (predicted and not fitted values) while the asterisks are the known experimental values.[36]