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

TL;DR

This study uses first principles calculations and cluster expansion to predict the phase diagram of HfO$_X$ with ordered ground states and complex temperature-dependent ordering phenomena.

Contribution

It introduces a comprehensive phase diagram prediction for HfO$_X$ using first principles and cluster expansion, revealing multiple ordered states and a disproportionation at low temperature.

Findings

Four ordered ground states predicted in the composition range.

Disproportionation at approximately 220K for X=5/12.

Devil's Staircases observed at X≈1/3 and X≈1/2.

Abstract

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.