Searching for Missing Binary Equiatomic Phases: Complex Crystal Chemistry in the Hf-In System

There remain 21 systems (out of over 3500 possible combinations of the elements) in which the existence of the simple binary equiatomic phases AB has not been established experimentally. Among these, the presumed binary phase HfIn is predicted to adopt the tetragonal CuAu-type structure (space group P4/ mmm) by a recently developed machine-learning model and by structure optimization through global energy minimization. To test this prediction, the Hf-In system was investigated experimentally by reacting the elements in a 1:1 stoichiometry at 1070 K. Under the conditions investigated, the bulk and surface of the sample correspond to different crystalline phases but have nearly the same equiatomic composition, as revealed by energy-dispersive X-ray analysis. The structure of the bulk sample, which was solved from powder X-ray diffraction data through simulated annealing, corresponds to the γ-brass (Cu₅Zn₈) type (space group I4̅3 m) with Hf and In atoms disordered over four sites. The structure of crystals selected from the surface, which was solved using single-crystal X-ray diffraction data, corresponds to the CuPt₇ type (space group Fm3̅ m) with Hf and In atoms partially disordered over three sites. The discrepancy between the predicted CuAu-type structure and the two experimentally refined crystal structures is reconciled through close inspection of structural relationships, which reveal that the γ-brass-type structure of the bulk HfIn phase is indeed derived through small distortions and defect formation within the CuAu-type structure.