Recent research has shown the possible presence of $\alpha$-based hydride superstructures in the two-phase $\alpha \text{−}\delta$ equilibrium region of H-Zr. This evidences the relevance of investigating the coherent phase diagram at the atomic scale, a task performed in this paper using a combination of cluster expansion (CE) and electronic structure methods. Our work points out the existence of various metastable ordered structures, some of them CE predicted and confirmed by the ab initio calculations, and shows the H-Zr system as conveniently described by CEs not exceeding fourth-neighbor interactions. Apart from second-order long-range interactions parallel to the $c$ axis, these interactions stabilize these hydrides as stackings of “$H$ biplanes” parallel to the basal plane.

• Received 23 March 2009

DOI:https://doi.org/10.1103/PhysRevB.80.094111