Barium titanate nanoparticles: Short-range lattice distortions with long-range cubic order

Barium titanate (BTO) nanoparticles (sizes 10--500 nm) exhibit a displacement of the Ti atom from the center of the perovskite unit cell as inferred from synchrotron x-ray diffraction patterns (XRD) analyzed using atomic pair distribution functions (PDFs). Fits to PDFs acquired at temperatures of 20 \ifmmode^\circ\else\textdegree\fi{}C--220 \ifmmode^\circ\else\textdegree\fi{}C indicate that these Ti displacements (\ensuremath{\sim}0.1 \AA{}) are comparable to or even greater than those in the bulk material. Moreover, these displacements persist at temperatures well above 120 \ifmmode^\circ\else\textdegree\fi{}C, where the tetragonal-to-pseudocubic phase transition occurs in the bulk. Tetragonal Raman spectral lines were observed for all sizes of these BTO nanoparticles and confirm a distorted unit cell up to 120 \ifmmode^\circ\else\textdegree\fi{}C. Above 120 \ifmmode^\circ\else\textdegree\fi{}C, the small BTO nanoparticles (10, 50, 100 nm) continue to display tetragonal Raman lines, though with slowly decreasing amplitudes as the temperature rises. In contrast, the tetragonal Raman lines of large BTO nanoparticles (300, 400, 500 nm) disappear abruptly above 120 \ifmmode^\circ\else\textdegree\fi{}C, suggestive of bulk material. Indeed, fits to large-particle x-ray PDFs over the range 20--60 \AA{} reveal a sharp, long-range structural change toward a cubic lattice at 120 \ifmmode^\circ\else\textdegree\fi{}C, again consistent with bulk material. This sharp, long-range structural change is absent in the small particles. In fact, laboratory XRD Bragg peak profiles for the small BTO particles appear to be singlets at 20 \ifmmode^\circ\else\textdegree\fi{}C, indicating that significant long-range cubic order already exists at room temperature. As temperature rises, this long-range cubic order is gradually reinforced, as inferred from long-range fits of the small particle PDFs. By combining information from x-ray PDFs, Raman spectra, and Bragg peak profiles, we conclude that small BTO nanoparticles exhibit both short-range (unit-cell) distortion and long-range (mesoscale) cubic order from 20 \ifmmode^\circ\else\textdegree\fi{}C to 220 \ifmmode^\circ\else\textdegree\fi{}C, while the large nanoparticles behave as bulk material, differing from small particles only by exhibiting long-range tetragonal order below 120 \ifmmode^\circ\else\textdegree\fi{}C and a mesoscale structural phase change at 120 \ifmmode^\circ\else\textdegree\fi{}C.