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

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 of x from the a parameter of the unit cell and vice 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 at x = 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)2 and Ni- and Mg-based carbonate LDH phases that have any trivalent cation and any value of x, including x = 0 [i.e. for α-M(OH)2·mH2O phases].