Phase diagram and oxygen-vacancy ordering in the CeO2-Gd2O3 system: a theoretical study.

We present the phase diagram of Ce1-xGdxO2-x/2 (CGO), calculated by means of a combined Density Functional Theory (DFT), cluster expansion and lattice Monte Carlo approach. We show that this methodology gives reliable results for the whole range of concentrations (x ≡ xGd ≤ 1). In the thermodynamic equilibrium, we observe two transitions: the onset of oxygen-vacancy (O-Va) ordering at ca. 1200-3300 K for concentrations xGd = 0.3-1, and a phase separation into CeO2 and C-type Gd2O3 occurring below ca. 1000 K for all concentrations. We also model 'quenched' systems, with cations immobile below 1500 K, and observe that the presence of random-like cation configurations does not prevent C-type vacancy ordering. The obtained transition temperatures for Va ordering agree rather well with existing experimental data. We analyse the effect of vacancy ordering and composition on the lattice parameters and relaxation pattern of cations.

Ordering and phase separation in Gd-doped ceria: a combined DFT, cluster expansion and Monte Carlo study.

Ordering of dopants and oxygen vacancies is studied for Gd-doped ceria (xGd ≤ 0.25) by means of a combined density functional theory (DFT) and cluster expansion approach, where the cluster interactions derived from DFT calculations are further used in Monte Carlo simulations. The methodology is meticulously tested and the stability of the obtained solutions with respect to the volume change, applied exchange-correlation approximation and other modelling parameters is carefully analysed. We study Gd and vacancy ordering in the case of thermodynamic equilibrium and vacancy ordering for quenched Gd configurations. We find that at the thermodynamic equilibrium there exists a transition temperature (TC) below which phase separation into C-type Gd2O3 and pure CeO2 occurs. The phase separation is observed in the whole studied concentration range and the transition temperature increases with concentration from ca. 600 (xGd = 0.03) to 1000 K (xGd = 0.25). Above TC the distribution of Gd is random, oxygen vacancies tend to cluster in the coordination shells along 〈1, 1/2, 0〉 and 〈1, 1, 1〉, and the nearest neighbour position is preferred for Gd-vacancy. In the quenched Gd case, where Gd atoms are immobilised below 1500 K, the vacancy ordering is significantly frustrated. In fact, we observe an oxygen freezing transition below temperature TF ≈ TC - 350 K, which is close to temperatures at which a change in the conductivity slope is observed experimentally.