Symmetry and Stability of $\delta$ Plutonium: The Influence of Electronic Structure

Using first-principles density-functional theory, we calculate the bond strengths between the 12 nearest neighbors in $\delta$ plutonium for both pure Pu and a Pu-3.7 at. % Ga alloy. Our results for pure Pu reveal a structure with the monoclinic space group $Cm$ rather than face-centered cubic $Fm\overline{3}m$, showing that the anomalously large anisotropy of $\delta$ plutonium is a consequence of greatly varying bond strengths between the 12 nearest neighbors. Further results for a Pu-3.7 at. % Ga alloy show that the nearest-neighbor bond strengths around a Ga atom are more uniform. Hence, our calculations address (i) why the ground state of Pu is monoclinic, (ii) why distortions of the $\delta$ phase are viable, with considerable implications for the behavior of the material as it ages due to anisotropic response to self-irradiation, and (iii) why Ga stabilizes face-centered cubic $\delta$-Pu.

Figure 1

Two periodic arrays illustrating repetition of a lattice (points) and a motif (blocks). (a) A pattern showing a plane group symmetry of $4mm$ and (b) a pattern showing a plane group symmetry of $2mm$, reduced only by a change in the motif, not the lattice.

Figure 2

The structure of $\alpha$-iron. The crystal has a body-centered cubic space group of $Im\overline{3}m$ when paramagnetic but is reduced to $I4/m{m}^{\prime }{m}^{\prime }$ when the crystal becomes ferromagnetic with aligned moments in the $[001]$ direction.

Figure 3

Two stacked fcc unit cells with the central atom showing the 12 nearest neighbors. In the case of pure plutonium, the 12 bonds with the nearest neighbors vary widely with strength and can be separated into six pairs. When the fcc lattice is combined with the motif of these bond strengths, the resultant structure is monoclinic $Cm$.