Dynamical response and instability in ceria under lattice expansion

Abstract

We present results of density functional theory calculations on the phonon dispersion and elastic constants of bulk ceria (CeO${}_{2}$) as a function of positive and negative isotropic strain, which could be induced thermally or by cationic doping. We find that, as the lattice is expanded, there is a significant softening of the ${B}_{1u}$ mode at the $X$ point. This mode consists of motions of oxygens in the $[001]$ direction. At a strain of $1.6$$%$, corresponding to a temperature of 1600 K, the ${B}_{1u}$ and ${E}_{u}$ modes at the $X$ point cross, with an associated high, narrow peak in the phonon density of states appearing. We infer that this crossing indicates a coupling of the modes, leading to a transition to a superionic phase, where conductivity occurs in the $[001]$ direction, mediated by anion interstitial site occupation. As the lattice is expanded further, the ${B}_{1u}$ mode continues to soften, becoming imaginary at a strain of $3.4$$%$, corresponding to a temperature of 2500 K. Following the imaginary mode would result in a cubic to tetragonal phase transition, similar to those known to occur with reducing temperature in zirconia (ZrO${}_{2}$) and hafnia (HfO${}_{2}$). Our calculated elastic constants, however, indicate that the structure remains mechanically stable, even at this level of expansion. As confirmed by our semiclassical free energy calculations, the cubic phase of ceria remains the most stable, while the imaginary mode indicates a change to a thermally disordered cubic phase, with the majority of disorder occurring on the anion sublattice. Our results explain the high temperature ionic conductivity in ceria and other fluorite-structured materials in terms of the intrinsic lattice dynamics, and give insight to the stability and anionic disorder at elevated temperatures.