Figure 6. Role of biaxial strain-induced tetragonal distortion.

(a) Schematic of the unit cell of ceria in the absence of strain (green), under compression (blue) and tension (red). Only the front half is shown for clarity. (b) Change in Ce-O, O₀-O_IP and O₀-O_CP distances (denoted ‘d') and Ce₀-O₀-Ce_IP and Ce₀-O₀-Ce_CP bond angles (denoted ‘A') as a function of biaxial strain. While the change in Ce-O distance is monotonic with biaxial strain and does not split, the other quantities split into doublets whose values are distributed on either side of the unstrained values. Lines are for guiding the eye. (c) Vacancy formation energy (E_vac) per oxygen released in bulk ceria as a function of relative volume (with respect to the unstrained bulk) under biaxial and isostatic strain for CeO_1.97 (1 oxygen vacancy in a 2 × 2 × 2 supercell) and CeO_1.50 (2 oxygen vacancies in a unit cell). (d) Vibrational free energy and entropy change per oxygen released in bulk ceria calculated under the harmonic approximation at 550 °C for three different strain states. In all figures, lines are for guiding the eye.