A computational study on the superionic behaviour of ThO₂

This study reports the density functional theory (DFT) and classical molecular dynamics (MD) study of the lattice dynamical, mechanical and anionic transport behaviours of ThO₂ in the superionic state. DFT calculations of phonon frequencies were performed at different levels of approximation as a function of isotropic dilation (ε) in the lattice parameter. With the expansion of the lattice parameter, there is a softening of B_1u and E_u phonon modes at the X symmetry point of the Brillouin zone. As a result of the nonlinear decrease at the X point, the B_1u and E_u phonon modes cross each other at ε = 0.03, which is associated with a sharp increase in the narrow peak of the phonon density of states, signifying a higher occupation and hence a higher coupling of these modes at high temperatures. The mode crossing also indicates anionic conductivity in the 〈001〉 direction leading to occupation of interstitial sites. Moreover, MD and nudged elastic band calculated diffusion barriers indicate that 〈001〉 is the easy direction for anion migration in the normal and superionic states. With a further increase in the lattice parameter, the B_1u mode continues to soften and becomes imaginary at a strain (ε) of 0.036 corresponding to a temperature of 3430 K. The calculated temperature variation of single crystal elastic constants shows that the fluorite phase of ThO₂ remains elastically stable up to the superionic regime, though the B_1u phonon mode is imaginary in that state. This leads to anionic disorder at elevated temperatures. Tracking of anion positions in the superionic state as a function of time in MD simulations suggests a hopping model in which the oxygen ions migrate from one tetrahedral site to another via octahedral interstitial sites.