Atomistic mechanisms of nonstoichiometry-induced twin boundary structural transformation in titanium dioxide

Grain boundary (GB) phase transformations often occur in polycrystalline materials while exposed to external stimuli and are universally implicated in substantially affecting their properties, yet atomic-scale knowledge on the transformation process is far from developed. In particular, whether GBs loaded with defects due to treatments can still be conventionally considered as disordered areas with kinetically trapped structure or turn ordered is debated. Here we combine advanced electron microscopy, spectroscopy and first-principles calculations to probe individual TiO2 GB subject to different atmosphere, and to demonstrate that stimulated structural defects can self-assemble at GB, forming an ordered structure, which results in GB nonstoichiometry and structural transformations at the atomic scale. Such structural transformation is accompanied with electronic transition at GB. The three-dimensional transformations afford new perspectives on the structural defects at GBs and on the development of strategies to manipulate practically significant GB transformations.


Fabrication of pre-designated GBs by bicrystal technique
In general, polycrystalline materials contain various interfaces between grains which can be influenced by numerous factors, such as thermal processing and growth condition.
To restrain the degree of freedom associated with grain boundaries (GBs) so as to provide a realistic opportunity to probe every individual GBs, we took advantage of the bicrystal technique to fabricate a model Σ3 (112) Fig. 1a. Size of each single-crystal block was set to be 9 × 12 × 5 mm 3 , and a bicrystal block of 9 × 12 × 10 mm 3 was eventually acquired. To fabricate bicrystals with the designated orientation relations, the two single crystals were first cut precisely along (112) plane of TiO2 lattices, followed by one-side grinding and polishing to mirror finish for each crystals with diamond slurry of 0.25 μm. Subsequently, the shiny surfaces of the two single crystals were placed together at 1773 K for 10 h in air. Both heating and cooling rates were set to 300 K/h. Supplementary Fig. 1b shows a real photograph of the final bicrystal where the boundary is indicated by arrows. Several slices with dimensions of 9(12) × 10 × 1.5 mm 3 were cut from the final bicrystal blocks to prepare specimens for the transmission electron microscopy (TEM) and scanning TEM (STEM) observations, which were further thermally treated at different atmosphere.

Atomistic models of grain boundaries
To determine GB atomic models, we construct two starting models within GB mirror symmetry: one has a cation monolayer (Supplementary Fig. 6a) and the other has a cation bilayer on the GB mirror plane (Supplementary Fig. 6e). These two starting models are O over-stoichiometric at GB from the consideration of space filling (i.e. containing enough oxygen atoms at GB), on which one can introduce systematically charge-compensating oxygen vacancies (denoted   O V in Kröger-Vink notation). Specifically, for the starting model with a cation monolayer, we first consider a total of ten most likely oxygen sites to introduce a vacancy (labeled in Supplementary Fig. 6a)  For the starting model with a cation monolayer ( Supplementary Fig. 6a), we identify that the site 7 is favorable for oxygen vacancy because it shows the lowest Eseg (see "a" in Supplementary Table 1). Supplementary Fig. 6b shows the corresponding relaxed model, based on which a total of ten possible sites are considered further to introduce an oxygen vacancy once at a time. The GB atomic model with an O vacancy at the site 1 (labeled in Supplementary Fig. 6b) shows the lowest Eseg ("b" in Supplementary Table 1). Its relaxed model is given in Supplementary Fig. 6c. We further introduce an oxygen vacancy to this 13 model and find that it favors the site 6 ( Supplementary Fig. 6c), that is, the relaxed model ( Supplementary Fig. 6d) has the lowest Eseg ("c" in Supplementary Table 1). We also conduct a similar searching process for the starting model with a cation bilayer. Supplementary Fig. 6e-h illustrates the evolution of models as an O vacancy is gradually introduced. The corresponding segregation energies are listed in Supplementary Table 1.
The eventual atomic structure (Fig. 3d) is obtained via a relaxation of the GB model with an oxygen vacancy at the site 9 in Supplementary Fig. 6h ("h" in Supplementary Table 1).
Of all the examined models, we identify three models which match correspondingly the observed images (Fig. 2) of o-GB (Fig. 3a), r-GB (Fig. 3d) and v-GB (Fig. 3g). The relative stability of the three models is shown in Fig. 5a. To provide further support, we simulated HAADF and ABF STEM images using the determined GB atomic models and compared them (Fig. 3, Supplementary Fig. 7) with their experimental counterparts (Fig.   2, Supplementary Fig. 5). A good agreement is found for the two orthogonal projections, thereby validating the application of these models to describe the three GBs.
Since the stoichiometry of every GB configuration can be described in terms of the To gain insights into the conditions at which the models are stable, we calculated Gibbs free energy () of the three GBs as a function of the atomic chemical potentials of constituents (μα) using the following expression 5 , where E(defective,q) is the energy of a GB supercell with an oxygen vacancy in a charge state q; nα is the number of α atom; EF is the electron Fermi energy; A is the interface area.

Electronic structure of the GBs
To resolve orbital contribution, we calculate partial density of states (PDOS) of the three GBs using their determined atomic geometries, as shown in Supplementary Fig. 8.
All the five Ti 3d orbitals almost contribute equally to the valence-band (VB) minima, irrespective of the GB species. The conduction-band (CB) minima for the three species of GBs, however, differ remarkably with one another: the dxy orbital is suppressed heavily in spin-majority channel in the o-GB case ( Supplementary Fig. 8a), while all five 3d orbitals contribute to CB in the v-GB case ( Supplementary Fig. 8c). The contribution to CB at EF in the r-GB case originates predominantly from dyz, dx 2 -y 2 , and dz 2 orbital in spin-majority channel as revealed in the charge-density isosurface (Fig. 5e). However, there is no state at EF at all in spin-minority channel, confirming a ferromagnetic alignment of spins for the r-GB. The differences offer unequivocal evidence that local structural transformation can give rise to an orbital modification at the GB, highlighting the relevance in probing GB transformations at the atomic scale.
To shed more light on the electronic nature of the lowest-lying CB for the r-GB, we calculated band structure, as shown in Supplementary Fig. 9. Like what was seen in the PDOS plot ( Supplementary Fig. 8b), a ferromagnetic alignment of spins is preferred: the Ti 3d orbitals are filled around EF in spin-majority channel as there appear states cross EF ( Supplementary Fig. 9a), while they are empty in spin-minority channel, opening a band gap ( Supplementary Fig. 9b). The band structure along the Γ-Z high-symmetry line in the spin-majority channel shows little dispersion. Importantly, the two lowest-lying bands display no discernible dispersion along the Γ-X, while a strong dispersion along the Γ-Y, indicative of a spin-polarized quasi-1D dispersion behavior for the lowest-lying bands of r-GB 6 . A total of eight bands cross EF and contribute to Fermi surface.