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

First principles based phase diagram calculations were performed for the hexagonal closest packed octahedral-interstitial solid solution system $αHfO_{X} ($αHf[ ]_{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.

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