Atomistic modeling of thermodynamic properties of Pu-Ga alloys based on the Invar mechanism

We present an atomistic model that accounts for a range of anomalous thermodynamic properties of the fcc $\delta$ phase of Pu-Ga alloys in terms of the Invar mechanism. Two modified embedded atom method potentials are employed to represent competing electronic states in $\delta$-Pu, each of which has an individual configuration dependence as well as distinct interactions with gallium. Using classical Monte Carlo simulations, we compute the temperature dependence of various thermodynamic properties for different dilute gallium concentrations. The model reproduces the observed effects of excessive volume reduction along with a rapid shift in thermal expansion from negative to positive values with increasing gallium concentration. It also predicts progressive stiffening upon dilute-gallium alloying, while the calculated thermal softening is nearly independent of the gallium concentration in agreement with resonant ultrasound spectroscopy measurements in the literature. Analysis of the local structure predicted by the model indicates that the distribution of the gallium atoms is not completely random in the $\delta$ phase due to the presence of short-range order associated with the Invar mechanism. This effect is consistent with the nanoscale heterogeneity in local gallium concentration which is observed in recent extended x-ray absorption fine structure spectroscopy experiments. Implications of the Invar effect for phase stability and physical interpretations of the two states are also discussed.

Figure 1

Calculated temperature dependence of the relative occupation of Pu2 atoms for varying gallium concentration.

Figure 2

Calculated temperature dependence of the heat capacity per atom, scaled with the Boltzmann constant, for varying gallium concentration. The experimental data from Refs. [53, 54] for unalloyed $\delta$-Pu and 3.3 at.%–gallium alloys, respectively, are also included for reference.

Figure 3

Calculated temperature dependence of the atomic volume for varying gallium concentration. The experimental data from Ref. [19] are also included for comparison.

Figure 4

Calculated temperature dependence of the linear coefficient of thermal expansion for varying gallium concentration. The curves obtained by differentiating the fit to the experimental volume data using the Weiss model are also included for reference. Note that these reference curves are subject to relatively high uncertainty due to the sparse data points for the experimental volume.

Figure 5

Calculated temperature dependence of the adiabatic bulk modulus for varying gallium concentration. The experimental data for monocrystalline [42] and for polycrystalline [63] 3.3 at.%–gallium alloys are also included for reference.

Figure 6

Binding energies of the Pu1-Ga and Pu2-Ga systems plotted as a function of atomic volume for varying gallium concentration.

Figure 7

Calculated partial radial-distribution functions for 4 at.% gallium. (a) Like-pair distributions at 300 K. (b) Unlike-pair distributions at 300 K. (c) Like-pair distributions at 700 K. (d) Unlike-pair distributions at 700 K.