Coordination formulation of tetrahedrally close packed structures: An addendum to the observations of Yarmolyuk and Kripyakevich
Abstract
Ya. P. Yarmolyuk and P. I. Kripyakevich ( Kristallographiya19, 539 (1974)) showed that all tetrahedrally close packed (t.c.p.) structures have coordination formulae P _{p}Q _{q}R _{r}X _{x} → (PX _{2}) _{i}(Q _{2}R _{2}X _{3}) _{j} (R _{3}X) _{k}, where P, Q, R, and X represent coordination numbers (CN) 16, 15, 14, and 12 polyhedra respectively: p, q, r, and x indicate the numbers of such polyhedra in the unit cells of t.c.p. structures and i, j, and k are positive integers. We propose and demonstrate a limitation to the above formulation: if i ≥ 1 and k ≥ 1, then j ≥ 1 (or if both p > 0 and r > 0, then q > 0). We give reasons for this and discuss the Aufbauprinzip of t.c.p. structures and the results of C. B. Shoemaker and D. P. Shoemaker ( Acta Crystallogr. B42, 3 (1986)).
 Publication:

Journal of Solid State Chemistry France
 Pub Date:
 October 1987
 DOI:
 10.1016/00224596(87)900636
 Bibcode:
 1987JSSCh..70..241H