## Hf-Ox First principles phase diagram calculations for the octahedral-interstitial system

##### Abstract

The group IV hexagonal closest packed (hcp) suboxides MOX (M = Ti, Zr or Hf) all exhibit octahedral interstitial ordering of oxygen, O, and vacancies, in solid solutions of the form View the MathML source, 0≤X≤1/2. By far, the most studied of these systems is ZrOX, because of issues related to the oxidation of Zircaloy cladding on UO2 fuel rods in
light-water reactors. The hcp-based HfOX system has attracted less attention, and but Hafnium alloys are also potential cladding materials; e.g. for long-lived nuclear waste transmutation applications in Boiling Water Reactors. Also, investigating the chemical systematics of all three group IV suboxides enhances understanding of each binary system. In the ZrOX system, long-period superstructure (LPSS) phases were reported
in samples with X≈1/3, but not predicted in a recent first principles phase diagram (FPPD) calculation; however, in the HfOX FPPD calculations described below, a cascade of closely related ordered structures is predicted at X≈1/3 and X≈1/2; this cascade strongly suggests a Devil’s Staircase; i.e. an infinite array of closely related structures with first-order transitions (singularities) between them.