3.8 d. Size effects on the structure and phase transition behaviour of baddeleyite TiO₂ (V. Swamy/Victoria, N.A. Dubrovinskaia, L.S. Dubrovinsky and F. Langenhorst)

Several high-pressure studies on nanocrystalline semiconductor systems such as CdSe and CdS have shown that these nanocrystals behave as nearly defect-free single structural domains that cycle through the transitions between four-coordinated (wurtzite and sphalerite) and six-coordinated (rock salt) structures reproducibly, with attendant simple phase transition kinetics. While considerable understanding of the microscopic mechanisms and kinetics of the pressure-induced first-order solid-solid phase transition has been achieved by investigating CdSe type nanocrystal systems, the size effects on the detailed atomic arrangements in the crystal structures and on other physical properties of the resulting high-pressure phases have not been investigated in detail. As the crystallites’ size shrinks to the nanoscale dimensions (up to a few hundred nanometers and less), a fraction of the constituent atoms placed at or near the surface in coordination environments (substantially different from the coordination environments in the bulk material) becomes significant. Such changes in the atomic arrangements may not be clearly noticed in high symmetry systems such as nanocrystalline Cd chalcogenides. We, therefore, chose to study nanocrystalline TiO₂ to understand the size-effects on the crystal structure, bulk modulus, and crystallite size evolution across the pressure-induced orthorhombic α-PbO₂ – monoclinic baddeleyite structural phase transition. TiO₂ is a particularly important model system in the study of phase transition behaviours of oxides. First, bulk (microparticle) TiO₂ has long served mineral physicists as a model system in the study of the pressure-induced phase transitions of rutile-structured stishovite SiO₂ in the depths of Earth’s mantle. Second, nanocrystalline TiO₂ has been used as a prototype to investigate the size-dependent phase transition behaviour of nanoscale oxides in terrestrial environments. Furthermore, in our view, the low-symmetry structure of baddeleyite TiO₂ is an ideal case for examining size-induced changes in the crystal structure because of the extra degrees of freedom in the fractional atomic coordinates.

We investigated pressure-induced changes in nanocrystalline TiO₂ in compression-decompression cycles spanning 0-46 GPa. A comparison of the in situ high-pressure XRD spectra of the nanocrystalline and bulk baddeleyite structures at 34(1) GPa shown in Fig. 3.8-6 reveals distinct differences at medium to high 2θ ranges. Additional diffraction peaks are seen in the case of nanocrystalline baddeleyite. Rietveld refinement of the data in the space group P2₁/c yielded comparable good quality solutions (Fig. 3.8-6). Significantly, the a and b unit cell parameters of the nanocrystalline baddeleyite are 1.4 % and 1.7 % larger than those of the bulk phase. Similarly, the unit cell constant c is marginally bigger (0.4 %), whereas the cell angle β is essentially the same in comparison with the bulk structure parameters. The calculated unit cell volume for the nanocrystalline baddeleyite at 34(1) GPa, 104.20 ų, is about 3.6 % larger than that of the bulk structure, 100.60 ų, clearly demonstrating size-induced lattice expansion.

The crystallite size and shape changes accompanying the pressure-induced structural transformations in nanocrystalline TiO₂ were examined by comparative TEM observations of the starting anatase and the samples quenched to room pressure in the DAC after 50 compression-decompression cycles in the 0-40 GPa pressure range. The baddeleyite structure is not quenchable even as nanocrystals and, therefore, could not be examined under TEM. As seen in Fig. 3.8-7, the starting anatase has fairly equant crystallites with an average size of 34 nm (30-40 nm range). A recovered α-PbO₂ sample (Fig. 3.8-7) shows crystallites that are elongated with sizes in the 26-35 nm range and an average value of about 30 nm. The crystallite size reduction in the α-PbO₂ is approximately consistent with the density difference between the two phases. Crystallite coarsening as a result of sintering could not be observed in the transformed material, despite laser- and electrical-heating. This indicates that the majority of the crystallites are preserved as coherent units across multiple transitions involving 6 to 7 Ti-O coordination change amongst anatase, α-PbO₂, and baddeleyite. This is suggestive of the “single structural domain” behaviour of the nanocrystalline system.

Fig. 3.8-6: Powder XRD spectra of baddeleyite structured TiO2 recorded at room temperature and 34(1) GPa along with calculated and difference (experimental-calculated) XRD profiles obtained from Rietveld analyses. The short vertical bars indicate XRD peak positions obtained in the Rietveld refinement. (A) The baddeleyite synthesized from nanocrystalline anatase has the following crystal structural data: a = 4.589(1) Å, b = 4.849(1) Å, c = 4.736(1) Å, and β = 98.6(1)°. Space group P21/c. The x, y, and z fractional atomic coordinates for the titanium and two oxygen atoms in the asymmetric unit are: Ti = 0.309(1), 0.045(2), 0.218(1); O(1) = 0.056(1), 0.347(1), 0.282(1); and O(2) = 0.425(1), 0.727(1), 0.463(1). Rp = 4.6 % and Rwp = 5.4 %. (B) The baddeleyite synthesized from microcrystalline anatase has the following crystal structural data: a = 4.525(1) Å, b = 4.767(1) Å, c = 4.718(1) Å, and β = 98.7(1)°. The fractional atomic coordinates for titanium and oxygen atoms are: Ti = 0.276(2), 0.037(1), 0.212(2); O(1) = 0.109(1), 0.382(1), 0.261(1); and O(2) = 0.435(1), 0.768(1), 0.488(1). Rp = 3.0 % and Rwp = 3.5 %.

Fig. 3.8-7: (A) TEM image of the starting nanocrystalline anatase. The crystallites are equiaxial with an average diameter of 34 nm (size range 30-40 nm). (B) Electron diffraction of the α-PbO2 structured TiO2 recovered from the DAC after 50 compression-decompression cycles in the pressure range, where bulk α-PbO2 and baddeleyite structures are stable (up to 40 GPa). (C) TEM image of the recovered a-PbO2 sample shown in (B). The crystallites are elongated and have sizes in the range of 26-35 nm with an average diameter of about 30 nm.