Hummer, Daniel R., Kubicki, James D., Kent, Paul R. C., Post, Jeffrey E., and Heaney, Peter J. 2009. "Origin of Nanoscale Phase Stability Reversals in Titanium Oxide Polymorphs." Journal of Physical Chemistry C, 113, (11) 4240–4245. https://doi.org/10.1021/jp811332w.
We have monitored the hydrothermal crystallization of titania nanoparticles by in situ X-ray diffraction (XRD). Using the refined average structures from the XRD measurements, we calculated potential energy variations with particle size on periodic bulk structures using density functional theory (DFT). These variations cannot account for the enthalpy required to stabilize anatase relative to rutile. Thus, the hypothesis that the strain of the surface structure of nanoparticles accounts for the stabilization of anatase is not applicable to the growth of titania in water. DFT calculations on model nanoparticles do generate lower surface energies for anatase than for rutile that are large enough to explain the stability reversal in nanoparticles relative to the bulk phase. Rather than arising from two-dimensional surface structure alone, as previously thought, the total surface energies are critically dependent upon defects associated with edges and corners of nanocrystals at particle sizes <= 3 nm (i.e., during the nucleation process). As the particles grow, the bulk free energy becomes relatively more important, causing rutile to become stable at larger particle sizes. This study quantifies for the first time the critical role of edge and vertex energies in determining the relative phase stabilities of TiO2 nanoparticles.
