Crystal-chemical model of atomic interactions. 3. Convex polyhedra with regular faces

Abstract

Convex polyhedra with regular faces were used for developing the crystal-chemical model of atomic interactions. Some examples of inorganic crystal structures with coordination polyhedra belonging to convex polyhedra with regular faces are considered. Only four polyhedra -tetrahedron, octahedron, trigonal bipyramid and cube (without due regard for displacement of some atomic groups as a whole) -are shown to be stable at any value of the atomic interaction potential.

Crystal-chemical model of atomic interactions. 4. Prognostic ability: crystals and quasicrystals

“…The concept summarizes previous ideas (Aslanov, 1988a, b;Aslanov & Markov, 1989). A structural ensemble is a minimal set of atoms (i) consisting of the central atom (cluster) and its coordination spheres, (ii) having a minimum of potential energy of atomic interactions (iii) at the peripheral coordination sphere possessing the atoms (clusters) of the same sort as in the center, (iv) crossing similar ensembles in such a way that the common part of the pair of crossing ensembles consists of at least three atoms; these atoms do not lie in a straight line.…”

“…The ensemble coincides with one multisphere complex in many structures, for example perovskite or K2PtCI6 (Aslanov, 1988a). But in many crystals such as Pb304, Nil2P5 or Ni3P (Aslanov & Markov, 1989) the ensembles are formed by two or three complexes.…”

“…Of course the distance from the center of the structural ensemble O 1989 International Union of Crystallography to the vertices of the polyhedra is a very important value, but it should be considered as an average, because some atoms of the inner coordination sphere in intermetallic compounds could lie farther from the center of the structural ensemble than certain atoms in the outer coordination sphere. This situation was met, for example, in the Cu3As structure (Aslanov & Markov, 1989). Such an approach will be used throughout this paper.…”

“…In the previous papers in this series (Aslanov, 1988a, b;Aslanov & Markov, 1989) the crystal structures were considered as sets of coordination polyhedra. The atoms were assumed to be attracted to each other by different sorts of chemical bondings and mutually repelled by atomic electron shells.…”

Crystal Structure and Magnetic Properties of the Compounds Yb(Zn,Al)~6 and YbZn~6

“…The Zn6/Al polyhedron (CN10) is similar to that present in several intermetallic compounds, for instance around Mn in MnAl 6 and around one of two Si atoms in W 5 Si 3 [21]. It is formed by two quadrangular and twelve triangular faces and is called a bicapped dodecahedron [22], a decatetrahedron [23] or a sphenocorona [24]. The curvature in the field-dependent magnetization at 1.8 K arises due to the contribution from the trace impurity phases.…”