Ab initio energetic study of oxide ceramics with rare-earth elements

Ab initio energetic calculations based on the density functional theory (DFT) and the projector augmented wave method (PAW) for determining the polymorphisms of lanthanide sesquioxides Ln(2)O(3) (where Ln = rare-earth element, Y, and Sc), LnMO(3) perovskites (where M = Al and Ga), and Ln(2)B(2)O(7) pyrochlores (where B = Ti, Zr, and Hf) were reported. The relative lattice stabilities agreed well with the critically assessed results or the experimental results except the C-type Ln(2)O(3) with a cubic structure, for which the calculated total energies were considerably more negative. With the increase of the Ln(3+)-cation radius, the polymorphic structures showed a degenerative tendency. The tendencies and quantities of the enthalpies of formation of the ternary oxide ceramics synthesized from their constituent binary oxides reasonably agreed with the available experimental results, and valuable thermodynamic properties were afforded to the compound, for which no experimental data is available. The enthalpies of formation of both perovskites and pyrochlores tend to become more negative with the increase of the Ln(3+)-cation radius.