Atomic structure of nanometer-sized amorphous ${\text{TiO}}_2$

Amorphous titania $\left({\text{TiO}}_2\right)$ is an important precursor for synthesis of single-phase nanocrystalline anatase. We synthesized amorphous titania by hydrolysis of titanium ethoxide at the ice point. Transmission electron microscopy examination and nitrogen gas adsorption indicated that the particle size of the synthesized titania is $\sim 2\text{nm}$. Synchrotron wide-angle x-ray scattering (WAXS) was used to probe the atomic correlations in this amorphous sample. Atomic pair-distribution function (PDF) derived from Fourier transform of the WAXS data was used for reverse Monte Carlo (RMC) simulations of the atomic structure of the amorphous ${\text{TiO}}_2$ nanoparticles. Molecular-dynamics simulations were used to generate input structures for the RMC. X-ray-absorption spectroscopy (XAS) simulations were used to screen candidate structures obtained from the RMC by comparing with experimental XAS data. The structure model that best describes both the WAXS and XAS data shows that amorphous ${\text{TiO}}_2$ particles consist of a highly distorted shell and a small strained anataselike crystalline core. The average coordination number of Ti is 5.3 and most Ti-O bonds are populated around $1.940\text{Å}$. Relative to bulk ${\text{TiO}}_2$, the reduction in the coordination number is primarily due to the truncation of the Ti-O octahedra at the amorphous nanoparticle surface and the shortening of the Ti-O bond length to the bond contraction in the distorted shell. The pre-existence of the anataselike core may be critical to the formation of single-phase nanocrystalline anatase in crystallization of amorphous ${\text{TiO}}_2$ upon heating.

Figure 1

(Color online) XRD pattern of nanometer-sized amorphous ${\text{TiO}}_2$. Diffraction data (in relative intensities) from the ICDD database for three ambient ${\text{TiO}}_2$ phases, anatase (Ref. 31), brookite (Ref. 32), and rutile (Ref. 33) are also shown for comparison.

Figure 2

TEM images of nanometer-sized ${\text{TiO}}_2$. (a) Low-resolution image showing aggregate sizes is $\sim 0.2\mu \text{m}$ in diameter. Inset: selected area electron-diffraction pattern. (b) High-resolution image showing primary particles is $\sim 2–3\text{nm}$ in diameter. Bottom: integration of contrast from ${\text{TiO}}_2$ nanoparticles.

Figure 3

(Color online) Comparison between experimental PDF of amorphous nano-${\text{TiO}}_2$ and those calculated for anatase particles: (a) as-constructed (unrelaxed), 2 nm in diameter, after charge balancing; (b) from MD, 2 nm; (c) from RMC, 2 nm; and (d) from RMC, 2.5 nm. Input structures for the RMC were from MD using the MA interatomic potentials (Ref. 18). Insets show structure models used for the PDF calculations.

Figure 4

(Color online) Comparison between experimental PDF of amorphous nano-${\text{TiO}}_2$ and those calculated from RMC structures. Input structures for the RMC were from MD of [(a) and (c)] 2 nm and [(b) and (d)] 3 nm ${\text{TiO}}_2$ particles using [(a) and (b)] the MA interatomic potentials (Ref. 18) and [(c) and (d)] the KIM potentials (Ref. 20).

Figure 5

(Color online) Experimental XANES spectra of bulk anatase, bulk rutile, and amorphous nano-${\text{TiO}}_2$.

Figure 6

(Color online) Comparison of calculated XANES spectra of (a) bulk anatase and (b) bulk rutile with the experimental spectra. Finite difference method and multiple-scattering method were used in the calculations with atomic cluster radii $\left(R\right)$ of 5.6 and $7.0\text{Å}$. Characteristic peaks are shown on the experimental spectra.

Figure 7

(Color online) Comparison of calculated XANES spectra of nano-${\text{TiO}}_2$ with the experimental spectra of amorphous nano-${\text{TiO}}_2$. MS method (cluster radius, $7.0\text{Å}$) and FDM method (cluster radius, $4.0\text{Å}$) were used in the calculations. Structure models for the spectra calculations were from RMC with input structures from MD of (a) 2 and 3 nm anatase particles, and (b) 2 nm anatase, brookite, and rutile particles (all with MS method). The MA (Ref. 18) and KIM (Ref. 20) interatomic potentials were used in the MD.

Figure 8

(Color online) Structure of a ${\text{TiO}}_2$ nanoparticle generated by RMC of [(a) and (b)] an $\sim 2\text{nm}$ anatase particle (model 1), and [(c) and (d)] an $\sim 3\text{nm}$ anatase particle (model 2). (b) and (d) are cross-section views. Input structures for the RMC were from MD using [(a) and (b)] the MA interatomic potentials (Ref. 18) and [(c) and (d)] the KIM potentials (Ref. 20). Ti: smaller balls; O: bigger balls.

Figure 9

(Color online) Structural characteristics of amorphous nano-${\text{TiO}}_2$. (a) RDF $\left(g\right)$ and CN of model 1. $g$—total RDF; $g\left(AB\right)$—partial RDF of $B$ around $A$; $\text{CN}\left(AB\right)$—CN of $B$ around $A$. (b) RDF and CN of model 2. (c) Bond length distribution. (d) Coordination number distribution of Ti. (e) Coordination number distribution of O. (f) Ti-O-Ti bond-angle distribution. (g) O-Ti-O bond-angle distribution. Vertical lines represent the corresponding values in bulk anatase (shown in relative magnitudes).

Figure 10

(Color online) Structural characteristics of the surface, core, and whole amorphous nano-${\text{TiO}}_2$ particle (model 1). (a) RDF of O around Ti. (b) Coordination number distribution of Ti. (c) Coordination number distribution of O. (d) Ti-O-Ti bond-angle distribution. (e) O-Ti-O bond-angle distribution. Vertical lines represent the corresponding values in bulk anatase (shown in relative magnitudes).