First principles phase diagram calculations for the octahedral-interstitial system αTiOX, 0≤X≤1/2

First principles based phase diagram calculations were performed for the hexagonal closest packed octahedral-interstitial solid solution system α TiO X , or α Ti [ ]   1 − X O X ([ ]=Vacancy; 0 ≤ X ≤ 1 / 2 ), by the cluster expansion (CE) method. The predicted diagram has ordered ground-state (GS) phases at: X=0 (hcp α Ti , P63mmc); X=1/6 ( Ti 6 O : P 3 ¯ 1 c , R3, R 3 ¯ ); X ≈ 1 / 3 ( Ti 3 O : R 3 ¯ , P 3 ¯ 1 c , R 3 ¯ ′ ); and X=1/2 ( Ti 2 O : Pbcn; contrary to previous reports that it is anti-CdI2). Both at X= 1/6 and X= 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 Ti 6 O and Ti 3 O in which the stable phases have layer-structures that are related to the anti-CdI2-structure. It appears that disordering of the Ti 6 O - and Ti 3 O -GS involves cascades of first-order transitions that are suggestive of Devilʹs staircases.