Fully anharmonic calculations of the free energy of migration of point defects in UO2 and PuO2

Abstract

Calculating diffusion rates of point defects in materials typically relies on the harmonic approximation to estimate migration free energies. However, anharmonic effects can have a large impact on diffusion properties, and explicitly accounting for them is usually computationally demanding and difficult to achieve in practice. In this work, we investigate the role of anharmonic effects on defect migration in UO2 and PuO2 using the potential of average force integration (PAFI) method. Fully anharmonic migration free energies are computed for several cation and anion defect types, using the Cooper-Rushton-Grimes (CRG) potential and a recently developed machine learning spectral neighbour analysis potential (SNAP) for UO2. Results are systematically compared to harmonic estimates based on attempt frequencies and the Debye approximation. Our results reveal that the validity of the harmonic approximation strongly depends on the defect type and the underlying potential, with significant deviations observed in several cases. In particular, defect migration barriers are found to decrease strongly with increasing temperature (up to 1 eV between 0 and 1200 K), and anharmonic contributions can substantially modify migration entropies and, consequently, diffusion coefficients. Comparing defect migration in UO2 and PuO2 using the CRG potential reveals that PuO2 has lower migration enthalpies at 0~K for all considered defects, but this is compensated by higher attempt frequencies, resulting in similar overall jump frequencies in UO2 and PuO2. These findings provide insight into the limitations of commonly used approximations and highlight the importance of anharmonic effects for predictive modeling of diffusion in nuclear fuels as well as in other classes of materials.

Figures (7)

• Figure 1: Defect configurations and migration pathways investigated in this work. (a) Migration mechanisms for vacancy and interstitial defects in the fluorite lattice. Diffusing atoms are highlighted in green for oxygen and purple for cations. From left to right: (top) bound Schottky defect (BSD), oxygen vacancy (V$_\mathrm{O}$), cation vacancy (V$_C$); (bottom) oxygen interstitial (I$_\mathrm{O}$), cation interstitial with collinear (I$_C$) and noncollinear (I$_C^\mathrm{nc}$) migration. (b) Bound Schottky defect configurations, with cations shown in grey and oxygen atoms in red, with vacancy positions marked by square symbols.
• Figure 2: Minimum energy migration pathways obtained using nudged elastic band (NEB) calculations for the CRG-PuO$_2$, CRG-UO$_2$, and SNAP-UO$_2$ interatomic potentials. Migration enthalpy barriers for UO$_2$ reported from DFT calculations (GGA+$U$ and LDA+$U$) dorado_first-principles_2011dorado_first-principles_2012 and experiments matzke_atomic_1990 are included for comparison.
• Figure 3: Temperature-dependent migration free energy profiles for interstitial defects (cation interstitial I$_C$, cation interstitial with noncollinear mechanism I$_C^\mathrm{nc}$, and oxygen interstitial I$_\mathrm{O}$) computed using the projected average force integrator (PAFI) method between 0 and 1 200 K with the three interatomic potentials.
• Figure 4: Temperature-dependent migration free energy profiles for vacancy defects (bound Schottky defect BSD, cation vacancy V$_C$, and oxygen vacancy V$_\mathrm{O}$) computed using the projected average force integrator (PAFI) method between 0 and 1 200 K with the three interatomic potentials.
• Figure 5: Phonon density of states calculated using the CRG-UO$_2$ and the SNAP-UO$_2$ interatomic potentials. Spectra are shown for the perfect lattice, the initial defect configuration, and the defect transition state (saddle point).