Order and disorder among the layered double hydroxides: combined Rietveld and DIFFaX approach

A combined approach using the Rietveld technique of structure refinement and DIFFaX simulations of the powder patterns enables us to not only arrive at the complete structure of the layered double hydroxides (LDHs), but also classify and quantify the nature of structural disorder. Hydrolysis of urea dissolved in mixed-metal salt solutions containing a divalent metal $(Mg^{2+}, Co^{2+})$ with $Al^{3+}$ results in the homogeneous precipitation of the corresponding LDH. The products obtained are highly crystalline enabling a complete structure determination including subsequent refinement by the Rietveld method. In contrast, the LDH of $Ni^{2+}$ with $Al^{3+}$ crystallizes with the incorporation of stacking faults. A combined Rietveld–DIFFaX approach shows that even 'crystalline' samples of this LDH incorporate up to 9% of stacking faults, which are not eliminated even at elevated temperatures (473 K). These studies have implications for the order, disorder and 'crystallinity' of layered phases in general and metal hydroxides in particular