  First principles based phase diagram calculations were performed for the
hexagonal closest packed octahedral-interstitial solid solution system $\alpha
HfO_{X} ($\alpha Hf[ ]_{1-X}O_{X}$; [ ]=Vacancy; $0 \leq X \leq 1/2$). 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 $0 \leq X \leq 1/2$, but one of these, at X=5/12, is
predicted 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 predict
Devil's Staircases of closely related ordered structures.
