Stacking sequence variations in vaterite resolved by precession electron diffraction tomography using a unified superspace model

As a metastable phase, vaterite is involved in the first step of crystallization of several carbonate-forming systems including the two stable polymorphs calcite and aragonite. Its complete structural determination would consequently shed important light to understand scaling formation and biomineralization processes. While vaterite's hexagonal substructure (a₀ ~ 4.1 Å and c₀ ~ 8.5 Å) and the organization of the carbonate groups within a single layer is known, conflicting interpretations regarding the stacking sequence remain and preclude the complete understanding of the structure. To resolve the ambiguities, we performed precession electron diffraction tomography (PEDT) to collect single crystal data from 100 K to the ambient temperature. The structure was solved ab initio and described over all the temperature range using a unified modulated structure model in the superspace group C12/c1(α0γ)00 with a = a₀ = 4.086(3) Å, b = [Formula: see text]a₀ = 7.089(9) Å, c = c₀ = 8.439(9) Å, α = β = γ = 90° and q = [Formula: see text]a* + γc*. At 100 K the model presents a pure 4-layer stacking sequence with γ = [Formula: see text] whereas at the ambient temperature, ordered stacking faults are introduced leading to γ < [Formula: see text]. The model was refined against PEDT data using the dynamical refinement procedure including modulation and twinning as well as against x-ray powder data by the Rietveld refinement.