The importance of proper crystal-chemical and geometrical reasoning demonstrated using layered single and double hydroxides

Abstract

Atomistic modelling techniques and Rietveld refinement of X-ray powder diffraction data are widely used but often result in crystal structures that are not realistic, presumably because the authors neglect to check the crystal-chemical plausibility of their structure. The purpose of this paper is to reinforce the importance and utility of proper crystal-chemical and geometrical reasoning in structural studies. It is achieved by using such reasoning to generate new yet fundamental information about layered double hydroxides (LDH), a large, much-studied family of compounds. LDH phases are derived from layered single hydroxides by the substitution of a fraction (x) of the divalent cations by trivalent. Equations are derived that enable calculation ofxfrom theaparameter of the unit cell andvice versa, which can be expected to be of widespread utility as a sanity test for extant and future structure determinations and computer simulation studies. The phase atx= 0 is shown to be an α form of divalent metal hydroxide rather than the β polymorph. Crystal-chemically sensible model structures are provided for β-Zn(OH)2and Ni- and Mg-based carbonate LDH phases that have any trivalent cation and any value ofx, includingx= 0 [i.e.for α-M(OH)2·mH2O phases].