Thermodynamics of the Zr-O system from first-principles calculations

We investigate the electronic and thermodynamic properties of Zr and its oxides from first principles to elucidate phase stability in the Zr-O system. Hexagonally close-packed Zr is unusual in its ability to dissolve very high concentrations of oxygen over its interstitial octahedral sites, forming a variety of ordered suboxides that undergo both first-order and second-order phase transitions upon heating. We perform a first-principles, statistical-mechanical analysis of finite temperature phase stability of ZrOₓ using a cluster expansion Hamiltonian and Monte Carlo calculations. This analysis predicts the existence of 0-K ground-state oxygen orderings at composition ZrO1/6, ZrO2/9, ZrO1/3, ZrO4/9, and ZrO1/2 along with evidence of an infinite sequence of ground-state suboxide orderings at intermediate oxygen concentrations consisting of different stackings of empty, 1/3-filled and 2/3-filled two-dimensional oxygen layers. We also predict the stability of a previously uncharacterized Zr-monoxide phase, which we label δ^'-ZrO due to its crystallographic relation to δ-TiO. The δ^'-ZrO structure is equivalent to the high-pressure ω-Zr phase but has interstitial oxygen ordering. Finally, as part of the technical implementation of our statistical mechanical study, we introduce a new algorithm to parametrize the coefficients of a cluster expansion Hamiltonian and apply a k-space analysis to rigorously track order-disorder phenomena at finite temperature.