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.

Advances in modelling and simulation of halide perovskites for solar cell applications

“…It is important to understand the anharmonic effects in the phase transition of halide perovskites. When the potential energy of a crystalline solid is expanded as a Taylor series of ionic displacements, only the second term (d U dr 2 2 ) is considered in the harmonic approximation with the temperature-independent frequencies and infinite lifetime, while the effects of temperature and first-order anharmonicity can be considered in the QHA [150]. It is associated with the imaginary (or negative) frequency, i.e.…”

Reply to “Comment on ‘High-pressure phases of group-II difluorides: Polymorphism and superionicity’ ”

“…The softening of a phonon mode at the harmonic level results in an increase in amplitude of the softening mode and the corresponding creation of a double-well energy potential [29], which can favour defect creation and increase the probability of interstitial site occupation, as discussed for superionic ThO 2 [25]. However, the details require analysis of the soft mode's eigenvectors [1,17,24,25] to understand their effect on ionic motion. We consider this to be an important point.…”

Superioniclike Diffusion in an Elemental Crystal: bcc Titanium

“…We can make yet another analogy between the behavior of bcc Ti and type-II superionics. A particular phonon mode of B1u symmetry appears to be connected to the superionic behavior in type-II superionic transitions [54][55][56][57][58]. The atomic displacements in this mode are closely connected to diffusion processes in fluorite crystal structures, analogous to the case of w-mode displacements/concerted-migration in bcc Ti.…”