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 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].
Highlights
Gibbs et al (2009) stated recently that ‘ . . . if mineralogists and geochemists persist in their study of minerals, their properties and relationships within the framework of empirical parameters like ionic radii, bond strength and electrostatic potential and forces and do not include first-principles quantum mechanical calculations and the study of ED distributions, it questionable whether our understanding of the crystal chemistry and the properties of minerals in their natural environments will advance much beyond that of last century’ (ED = electron density)
Much has been written about layered double hydroxides (LDH) phases – including some highly cited review articles (e.g. Cavani et al, 1991; Braterman et al, 2004; Evans & Slade, 2006; Forano et al, 2006; Mills, Christy, Genin et al, 2012) – and so it is perhaps surprising to find that such a large and important family of compounds could be studied so extensively for over half a century without crystal-chemical and geometrical arguments being pursued more effectively. This paper provides such a treatment, which necessitates a consideration of aspects of the crystal chemistry of layered divalent metal hydroxides because LDH phases are derived from them by the substitution of a fraction (x) of the divalent cations by trivalent cations
The crystal-chemical treatment described in this paper and the extent of the data collated in Figs. 4 and 6 mean that model structures that are crystal-chemically sensible can be provided for Ni- and Mg-based LDH phases that have any value of x, seemingly any trivalent cation, and that have carbonate as the charge-balancing interlayer ion; i.e. phases that have the general formula (24), where M2+ is Ni2+ or Mg2+
Summary
If the ions are considered to be packed as hard spheres, the cation in the CdI2-type structure must be ‘in contact’ (West, 1984) with the anions and so for -M(OH) phases the distance between the divalent metal cation and the O atoms of the hydroxyl ions, d(M—O), is equal to the sum of the effective ionic radii dðMÀOÞ 1⁄4 rÀM2þÁ þ rðOHÀÞ: ð3Þ. Comparison with Baneyeva and Popova’s structure show that it gives an improved match with the X-ray diffraction data and that the Zn—O distance is the same as that calculated using the effective ionic radii instead of being much longer, so the proposed structure is crystal-chemically more sensible.
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