First principles phase diagram calculations for the octahedral-interstitial system ,

First principles based phase diagram calculations were performed for the hexagonal closest packed octahedral-interstitial solid solution system α HfO X  ( α Hf [ ] 1 − X O X ; [  ] =  vacancy; 0 ≤ X ≤ 1 / 2 ). The cluster expansion method was used to do a ground state analysis, and to calculate the phase diagram. The predicted diagram has four ordered ground-states in the range 0 ≤ X ≤ 1 / 2 , but one of these, at X = 5 / 12 , is predicted to disproportionate at T ≈ 220 K . At X ≈ 1 / 3  ( Hf 3 O ) and X ≈ 1 / 2  ( H f 2 O ), order-parameter vs. temperature plots evince cascades of closely related ordered structures that are suggestive of Devil’s Staircases.