Paving the way for cristobalite TiO2 and GeO2 attainable under moderate tensile stress: A DFT study of transformation paths and activation barriers in cristobalite-rutile transformations of MO2 (M = Si, Ge, Ti)

摘要

We investigate energetics of interconversions between cristobalite-type and rutile-type structures of SiO2, GeO2, and TiO2 at different pressures within Density Functional Theory. Cristobalite-SiO2 is succeeded by the rutile-type, stishovite-SiO2, at high pressures. The rutile-types of GeO2 and TiO2 are favored at ambient pressure, but small tensile stresses are sufficient to yield cristobalite-GeO2 and TiO2. The transition from one structure-type into the other is modeled using collective movements of cations or anions with different degrees of freedom for the remaining structure parameters. We find that increasing the external pressure decreases activation barriers of the cristobalite-rutile transformation. Activation barriers of the reverse transformation from rutile to critobalite decrease with decreasing pressure. If only a fraction of cations follows the collective movement we find even lower activation barriers. The final states are still tetrahedrally or octahedrally coordinated structures, albeit not the high-symmetry variants of cristobalite or rutile, respectively. The small tensile stresses needed to favor cristobalite-GeO2 and TiO2 over their respective rutile counterparts, and the low activation barriers involved in their interconversion let us propose a simple route to synthesize cristobalite-GeO2 and a new cristobalite-TiO2.