Exact inversion of partially coherent dynamical electron scattering for picometric structure retrieval

Exact inversion of partially coherent phaseless scattering data

The frozen phonon (FP) approach translates time-dependent potentials V(r, t) arising from the thermal motion of atoms, to an incoherent superposition of different stationary states V_i(r). Figure 1a exemplifies this concept via the projected potentials of two slices \({V}_{{{{{{{{\rm{FP}}}}}}}}}^{(1,2)}({{{{{{{\bf{r}}}}}}}})\) in a ferroelectric PbZr_0.2Ti_0.8O₃ (PZT) crystal. The potentials contain thermal disorder via statistically perturbing the ideal atomic positions of the crystal by thermal displacements u, and thereby…