Ab initio construction of interatomic potentials for uranium dioxide across all interatomic distances

We provide a methodology for generating interatomic potentials for use in classical molecular-dynamics simulations of atomistic phenomena occurring at energy scales ranging from lattice vibrations to crystal defects to high-energy collisions. A rigorous method to objectively determine the shape of an interatomic potential over all length scales is introduced by building upon a charged-ion generalization of the well-known Ziegler-Biersack-Littmark universal potential that provides the short- and long-range limiting behavior of the potential. At intermediate ranges the potential is smoothly adjusted by fitting to ab initio data. Our formalism provides a complete description of the interatomic potentials that can be used at any energy scale, and thus, eliminates the inherent ambiguity of splining different potentials generated to study different kinds of atomic-materials behavior. We exemplify the method by developing rigid-ion potentials for uranium dioxide interactions under conditions ranging from thermodynamic equilibrium to very high atomic-energy collisions relevant for fission events.

Figure 1

(Color online) (a) ZBL screened potential (solid line) and Morelon et al. potential (dashes), joined together by a fifth-order polynomial (plus signs), for the case of two oxygen atoms. (b) First derivative of the net potential resulting from the same. (c) Second derivative of the potential. Since the spline was not fit to any data, one cannot decide whether the resulting behavior in (b) and (c) is correct or spurious.

Figure 2

(Color online) Charge-density times $4\pi r^2$ fitted to sum of Slater functions for (a) oxygen and (b) uranium. Open circles denote values used by Ziegler et al. (Ref. 2) while the solid lines indicate our fit using sum of Slater functions. The resultant error in the short-range interatomic potential as compared to ZBL’s original potential was well within the latter’s standard deviation for both (a) and (b). Thus trying to capture more peaks for uranium, by introducing more Slater functions, was not necessary. The coefficients used here are provided in Table .

Figure 3

(Color online) Comparison of our analytical potential form (dashed line) with (a) the currently used neutral atom ZBL interaction (solid line) for small distances and (b) the ionic coulombic interaction (solid line) between two $\left(-2e\right)$ point charges for large distances for the case of two oxygen atoms.

Figure 4

(Color online) (a) The interatomic potential for oxygen-oxygen as per current work [Eq. (10)]. (b) First derivative of the net potential resulting from the same. (c) Second derivative of the potential. These are to be compared with Fig. 1.

Figure 5

(Color online) Quality of fit from our fitted potential for various ab initio energies: (a) expansion/contraction (open circles), (b) oxygen-atom perturbation (plus signs), and (c) uranium-atom perturbation (cross signs). Asterisks denote ab initio data. For each of oxygen and uranium, the first four perturbations are along $⟨100⟩$ direction while the second four are along $⟨110⟩$ direction.

Figure 6

(Color online) (a) Relative lattice-parameter variation using potential from current work (open circles) compared with corresponding experimental values (dashed line) (Ref. 27). The scatter in the experimental values is also shown (solid lines). (b) Enthalpy variation using potential from current work (open circles) compared with corresponding experimental values (solid line) (Ref. 27). The scatter in the experimental values was less than 1% and is thus not shown.