Fig. 2.
Mapping picometer scale, periodic displacements of atomic lattice sites. a High-angle annular dark-field scanning transmission electron microscopy projection image along the b-axis. The heavier (Bi, Sr, Ca) sites (green) appear brighter than the lighter Mn sites (red). b Mapping picometer scale periodic lattice displacements (PLDs) Δ 1(r) at each atomic lattice site in response to a single modulation wavevector q 1. PLD maps indicate a displacive modulation rather than an intensity modulation (cation order, charge disproportionation) with transverse polarization and 3a periodicity. Triangles represent displacements, with the area scaling linearly with displacement amplitude. The color represents the angle of the polarization vector, A 1, relative to the modulation wavevector, q 1, where blue (yellow) correspond to 90° (−90°) as indicated in the colorbar. c Map of Δ 2(r) displacements at each atomic lattice site in response to q 2 in the same region as a, b. The significantly weaker Δ 2(r) response is characteristic of locally striped, rather than checkerboard, ordering. The scale bar corresponds to 1 nm