Hume-Rothery controlled formation of structurally complex alloy phases in the ternary Ga–Mg–Pd system

Abstract The Hume-Rothery rule has been used as a guide to search for new approximants of the Mackay icosahedron and Bergman cluster type in the Ga–Mg–Pd system. Ternary alloys with target compositions close to the e / a ratios 1.67 and 2.09 were synthesized by melting the elements and subsequent annealing in sealed tantalum ampoules. Six new intermetallic phases have been characterized: a cubic face-centered Mackay icosahedron approximant Ga 15− x − y Mg 38+ y Pd 13+ x , a rhombohedral Mackay icosahedron approximant Ga 30− x Mg 32+ x Pd 21 , a cubic Bergman cluster approximant Ga 12+ x + y Mg 11− y Pd 6− x , a cubic phase with interpenetrating I3 and Frank–Kasper networks Ga 32.6 Mg 43.4 Pd 29 , an ordered ternary variant of the NiTi 2 structure type GaMg 3 Pd 2 and a ternary Laves phase. The e / a ratios for the approximants with Mackay icosahedra or Bergman clusters show a strong experimental correlation indicating that the valence electron concentration is an important factor concerning the stability of the phases. The approximant phases exist over a wide range of composition. The structure of the rhombohedral phase is based on the geometry of the canonical cell tiling CB 2 C. The results support the proposal by Henley and Mihalkovic on the geometrical structures of Mackay icosahedron-type quasicrystals in ternary systems with one transition and two main group metals.