First Principles Phase Diagram Calculations for the   Octahedral-Interstitial System ZrO$_{X}$, $0 \leq X \leq 1/2$
  First principles based phase diagram calculations were performed for the octahedral-interstitial solid solution system \alpha ZrOX (\alpha Zr[ ]_(1-X)OX; [ ]=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 20K, well below the experimentally investigated range T \approx 420K. Thus, at T \succeq 420K, the first-principles based calculation predicts three ordered phases rather than the four that have been reported by experimentalists. 
Benjamin P. Burton, Axel van de Walle, Harold T. Stokes
cond-mat.mtrl-sci