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

Abstract

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.

The Neodymium Nickel Silicides Nd42Ni22−xSi31and Nd6Ni2−xSi3

“…The Ni9 atoms on the Wyckoff position 2a are again situated in trigonal prisms of neodymium atoms, however, the rectangular faces of these prisms are not capped by silicon, but by neodymium atoms. In this case this is not in violation of the waist-contact-restriction rule, since these trigonal prisms are compressed along the threefold axes and not elongated, as was discussed earlier (13,25). In addition, the trigonal faces of the prisms around the Ni9 atoms are capped by nickel atoms, thereby increasing the CN of these atoms to 11.…”

“…The three rectangular faces of these prisms are capped by silicon atoms. All of these trigonal prisms are elongated (i.e., stretched along the threefold axes of the prisms), and the fact that these prisms are capped by silicon atoms is in agreement with the waist-contact-restriction rule (13,25). According to this rule, a central transition metal atom within an elongated trigonal prism of rare earth atoms should not have any rare earth or transition metal neighbors outside the rectangular faces of the trigonal prism.…”

“…The Nd-Nd distances cover the range between 350 and 418 pm with a weighted average distance of 393.2 pm. This distance is somewhat greater than twice the (metallic) radius of neodymium for CN 12 of 364.2 pm (25). The Nd-Ni distances vary between 281 and 321 pm (not counting the Nd-Ni distances of 350 and 394 pm involving the disordered nickel atoms Ni8 and Ni9 on the sixfold axis) with an average of 304.0 pm, which is slightly smaller than the sum of the radii for CN 12 of 306.7 pm.…”

Ternary BaAl4-type derivative structures

“…The absence of T-T contacts is also characteristic of intergrowth structures where slabs occur with atom arrangements as in BaAln-type derivative structures. It can be mentioned that the absence of T-T contacts has also been a guide-line for the interpretation of the atom ordering in ternary rare-earth structures built up of centred trigonal prisms (Parth& Chabot & Hovestreydt, 1983). …”

A classification scheme for ternary structures with infinite antiprism and octahedron columns used to predict the structure of Sc3Re2Si4

“…In the case of ternary structures with centered trigonal prisms it was, for example, possible to formulate the so-called waistcontact-restriction rule. This rule permits the calculation of the correct composition for complete atom ordering at the prism centers for structures which were previously reported as partially ordered (Parth6, Chabot & Hovestreydt, 1983;Parth6 & Hovestreydt, 1985).…”