Abstract
Bottom-up and top-down derived nanoparticle structures refined by accurate ab initio calculations are used to investigate the size dependent emergence of crystallinity in titania from the monomer upwards. Global optimisation and data mining are used to provide a series of (TiO2)N global minima candidates in the range N = 1-38, where our approach provides many new low energy structures for N > 10. A range of nanocrystal cuts from the anatase crystal structure are also considered up to a size of over 250 atoms. All nanocrystals considered are predicted to be metastable with respect to non-crystalline nanoclusters, which has implications with respect to the limitations of the cluster approach to modelling large titania nanosystems. Extrapolating both data sets using a generalised expansion of a top-down derived energy expression for nanoparticles, we obtain an estimate of the non-crystalline to crystalline crossover size for titania. Our results compare well with the available experimental results and imply that anatase-like crystallinity emerges in titania nanoparticles of approximately 2-3 nm diameter.
Highlights
Size reduction from the macroscopic to length scales of only a few nanometres can lead to dramatic changes in a material’s properties
Our finding for N = 1–8 coincide with those reported in both ref. 40 and 41 where global optimisation was performed and, as in the present study, the final structures were optimised with density functional theory (DFT) using a hybrid functional
For (TiO2)N nanocluster sizes with N = 11–14, 16–24, 28, 35 and 38, we report new candidate global minima from our bottom-up global optimisation and datamining approach
Summary
Size reduction from the macroscopic to length scales of only a few nanometres can lead to dramatic changes in a material’s properties. Further to the effects directly arising from high surface-to-bulk ratios, nano-sized particles often possess distinct atomic and electronic structures with respect to stable bulk crystals. Titania (TiO2) is a prototypical example of a material displaying an extreme size-dependence of both structure and properties.[1] Under ambient conditions bulk titania is most thermodynamically stable with atomic ordering following the rutile crystal structure. Upon reduction in size, titania nanoparticles with average diameters less than ∼14 nm begin to exhibit the anatase crystal structure.[2] This structural transition has been thermodynamically rationalised by topdown calculations of the size-dependent enthalpies of titania
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