Classification of structures built up of centred trigonal prisms and ordering principles in ternary rare-earth–transition-metal silicide, germanide and gallide structures

The great majority of the known crystal structures built up only of centred trigonal prisms can be classified according to (a) the number of different prism-axis directions, (b) the dimensionality of the A1B2-type fragments, (c) the value of the prism-linkage coefficient, (d) the ratio of the number of centred prisms to the number of W-type segments and (e) the numbers of prism-centre sites with different waist-contact type. Many ternary rare-earth-transition-metal silicide, germanide and gallide structures are characterized by transition-metal and Si-, Ge- or Ga-centred trigonal rare-earth prisms. Atom ordering on the prism-centre sites is to be expected whenever the transition element and the main-group element tend to induce different rare-earth prism shapes. The atom ordering is characterized by the absence of transition-metal-rare-earth and transition-metal-transition-metal waist contacts. This ordering principle not only explains the structures and compositions of the known ordered compounds, but also allows a prediction of the compositions for full order of compounds where a random distribution of prism sites has been reported previously. The application of this ordering principle is demonstrated on earlier-reported Ce14NisSi9, for which at the predicted, slightly different, composition CelaNi6Sill a fully ordered structure is verified.