Crystal structure of cobalt hydroxide carbonate Co$_2$CO$_3$(OH)$_2$: density functional theory and X-ray diffraction investigation

We have investigated the structure of Co$_2$CO$_3$(OH)$_2$ using Density Functional Theory (DFT) simulations as well as Powder X-Ray Diffraction (PXRD) measurements on samples synthesized via deposition from aqueous solution. We consider two possible monoclinic phases, with closely related but symmetrically different crystal structures, based on those of the minerals malachite and rosasite, as well as an orthorhombic phase that can be seen as a common parent structure for the two monoclinic phases, and a triclinic phase with the structure of the mineral kolwezite. Our DFT simulations predict that the rosasite-like and the malachite-like phases are two different local minima of the potential energy landscape for Co$_2$CO$_3$(OH)$_2$, and are practically degenerate in energy, while the orthorhombic and triclinic structures are unstable and experience barrierless transformations to the malachite phase upon relaxation. The best fit to the PXRD data is obtained using a rosasite model (monoclinic with space group P1121/n and cell parameters a = 3.1408(4) {\AA}, b = 12.2914(17) {\AA}, c = 9.3311(16) {\AA}, $\gamma$ = 82.299(16)$^{\circ}$). However, some features of the PXRD pattern are still not well accounted for by this refinement and the residual parameters are relatively poor. We discuss the relationship between the rosasite and malachite phases of Co$_2$CO$_3$(OH)$_2$ and show that they can be seen as polytypes. Based on the similar calculated stability of these two polytypes, we speculate that some level of stacking disorder could account for the poor fit of our PXRD data. The possibility that Co$_2$CO$_3$(OH)$_2$ could crystallize, under different growth conditions, as either rosasite or malachite, or even as a stacking-disordered phase intermediate between the two, requires further investigation.