TiO_X

Abstract

First principles based phase diagram calculations were performed for the hexagonal closest packed octahedral-interstitial solid solution system aTiOX, or aTi½ 1 XOX ([ ]¼Vacancy; 0rXr1=2), by the cluster expansion (CE) method. The predicted diagram has ordered ground-state (GS) phases at: X¼0 (hcp aTi, P63mmc); X¼1/6 (Ti6O: P31c, R3, R3); X 1=3 (Ti3O: R3, P31c, R3 0 ); and X¼1/2 (Ti2O: Pbcn; contrary to previous reports that it is anti-CdI2). Both at X¼ 1/6 and X¼ 1/3 density functional theory (DFT) calculations predict at least triply degenerate GS (three structure energies at each composition that are within 0.001 eV; i.e. within DFT error). In the CE, this leads to exactly triply degenerate GS at both compositions. The calculated phase diagram includes a broad field between Ti6O and Ti3O in which the stable phases have layer-structures that are related to the anti-CdI2-structure. It appears that disordering of the Ti6O- and Ti3O-GS involves cascades of first-order transitions that are suggestive of Devil’s staircases.