A two-dimensional structure map for prediction of the transition-metal Laves phases

Abstract

Although it is well accepted that atomic size and electronic factors control the formation of transition-metal (TM) Laves phases, a geometrical description of the occurrence of the TM-TM Laves phases is lacking. In this paper, a two-dimensional structure map is proposed to predict the Laves phases using atomic radius ratio (R) and d-electron total count (DET) as coordinates, where DET is empirically developed to describe the bonding features in the TM-TM Laves phases. Within the structure map, the criterion R>1.116 is found for the formation of 16-coordinated Frank-Kasper polyhedra in TM-TM Laves phases through liquid alloys; while the narrowed range of 5<DET<10 may offer an empirical measurement on the formation tendency of unsaturated covalent bonds in the TM-TM systems. The existence of TM-TM Laves phases forming through liquid alloys defined in the present work satisfies both R>1.116and5<DET<10 simultaneously. The proposed two-dimensional structure map method provides a possible new strategy to predict the Laves phases in the TM-TM systems.