Derivation and discussion of crystal structures of compounds ABX 3 and A 2BX 6: Part I. Derivation of the Structures

Abstract

In this series of papers the crystal structures of compounds with composition ABX3 and A2BX6 are derived from a basic lattice, mainly using qualitative ionic bonding rules (Part I) (A represents a large cation that can replace an anion, B is a small interstitial cation, χ is halogen ion). In Part II a method will be outlined for selecting the appropriate structure for a particular compound. This method is tested on the experimental structure data of the ABX3 halides in Part II, and applied to compounds A2BX6, A2BK6−p′Yp′ and A2BX6−p′−p″Yp′Zp″ in Parts III, IV and V, respectively (χ = halogen; Y, Z = halogen OH, H2O, N or an anion vacancy). In the present paper (Part I), we start with the derivation of the ideal structures (i.e., for A and χ ions of equal diameter), for hypothetical compounds AX3. It is shown that, if A-A contacts are not allowed in a stacking of triangular nets (viz., in “close-packed” layers), each layer must have the composition AX3 and the same type of order. This order can be one of two simple types (“T” and “R”) or any combination of these. From these AX3 structures the ABX3 and A2BX6 structures are derived. On the basis of mainly simple electrostatic considerations, structures with anion surroundings that are most unlikely are excluded. Use is made of the representation of anion surroundings by space-filling polyhedra (SFP). Finally, the deviations from the ideal ABX3 and A2BX6 structures, resulting from variations in size of the A, B and χ ions, are considered.