Ab initio calculations for void swelling bias in α - and δ -plutonium

Void swelling can develop in materials under persistent irradiation when nonequilibrium vacancy and self-interstitial populations migrate under sufficiently asymmetric interaction biases. In conventional metals, the propensity is determined to the first approximation by comparing point-defect relaxation strains. We thus present DFT-based calculations of structures and formation energies and volumes of point defects in the $\ensuremath{\alpha}$ and the $\ensuremath{\delta}$ phases of plutonium. We discuss the pros and cons of various levels of electronic structure theory: spin polarization, spin-orbit coupling, and orbital polarization. Our results show that lattice defects in $\ensuremath{\delta}$-Pu, in contrast to most fcc metals, have surprisingly small formation volumes. Equally unexpected are the large defect formation volumes found in the low-symmetry $\ensuremath{\alpha}$-Pu phase. Both these unusual properties can be satisfactorily explained from defect-induced spin/orbital moment formation and destruction in the Pu phases. Surprisingly, the point defects in $\ensuremath{\alpha}$-Pu are found to induce far larger transformation of the local electronic structure than in $\ensuremath{\delta}$-Pu. When we use the calculated defect properties to estimate the classic void swelling bias in each of the phases, we find it to be unusually small in $\ensuremath{\delta}$-Pu but likely much larger in $\ensuremath{\alpha}$-Pu. Hence, swelling rates and mechanisms can diverge dramatically between the different phases of Pu. Especially in the transient regime before the formation of large defect clusters, the swelling rate of $\ensuremath{\alpha}$-Pu can reliably be expected to be much larger than $\ensuremath{\delta}$-Pu. However, accurate forecasts over longer times will require the conventional void-swelling theory to be modified to handle the complexities presented by the different Pu phases. As a case in point, we show the possible anomalous temperature dependence of vacancy properties in $\ensuremath{\delta}$-Pu, caused by entropic contributions from defect-induced spin-lattice fluctuations. Such complications may affect defect-defect interactions and thus alter the void swelling bias.