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First principles based phase diagram calculations were performed for thehexagonal closest packed octahedral-interstitial solid solution system $\alphaHfO_{X} ($\alpha Hf[ ]_{1-X}O_{X}$; [ ]=Vacancy; $0 \leq X \leq 1/2$). Thecluster expansion method was used to do a ground state analysis, and tocalculate the phase diagram. The predicted diagram has four orderedground-states in the range $0 \leq X \leq 1/2$, but one of these, at X=5/12, ispredicted to disproportionate at T$\approx 220K$. At X$\approx 1/3 ($Hf_{3}O$)and X$\approx 1/2 ($Hf_{2}O$), order-parameter vs temperature plots predictDevil's Staircases of closely related ordered structures.

First Principles Phase Diagram Calculations for the Octahedral-Interstitial System $HfO_{X}$, $0 \leq X \leq 1/2$