Figure 1. Quantitative measurements of polarization in PZT thin film on SrTiO₃ substrate.

This region is 24-unit cells thick. (a) A high angle annular field image of a substrate–film interface. The arrow shows the position of interface, TiO₂ plane, between the first SrO and PbO planes. Inset: the interface is determined by the intensity profile. Scale bar, 1 nm. (b) The simultaneous recorded ABF image of the interface. Inset: enlarged view of PZT. The contrast is inverted for clarity. The polarization is upward, that is, pointing to the surface as denoted by the big arrow. Scale bar, 1 nm. (c) Schematic shows the projection of tetragonal PZT seen along [010] direction. d₁ and d₂ denote the long and short distances between Pb atoms (cyan) and O atoms (yellow) along the c direction; d₃ and d₄ denote the short and long distances between Zr/Ti atoms (green) and O atoms (yellow) along the c direction. Both SrTiO₃ (STO) and PZT are expressed as ABO₃ structure, where A represents for Sr and Pb, and B represents for Ti or Zr/Ti. The lattice constants c is calculated from the (d) A sublattice, and (e) B sublattice. (f) The calculated bond lengths d₁ and d₂ in the AO plane. (g) The calculated bond lengths d₃ and d₄ in the BO₂ plane. (h) Mean of lattice c. The error bar is the s.d. (i) Mean of bond lengths of d₁, d₂, d₃ and d₄. The error bar is the s.d. (j) Averaged displacements of |d₁–d₂|/2 and |d₃–d₄|/2. The error bar is the s.d. (k) Mean of polarization calculated from the displacements in PbO plane, TiO₂ plane and the total. The error bar is the s.d.