Extended Data Fig. 8: X-ray diffraction simulations based on dynamical phase-field modelling.

a, Model geometry of the PTO/STO superlattice film and the DSO substrate. The colour scale denotes the vorticity of the polarization vectors. The boundary conditions (Methods) are marked on the right. b, Schematics for the method used to map the phase-field modelling output to atomistic configurations, based on which kinematic X-ray scattering intensities are calculated (Supplementary Note 2). CoM, center ofmass; V and C denote the vortex and cubic phases of PbTiO3, respectively. c, Measured and simulated H0L-cut (along the qx–qz plane in reciprocal lattice units (r.l.u)) RSMs near the 004 reflection with the intensity shown on a logarithmic colour scale. The fringes in the simulated RSM are due to the finite lateral size of the simulation box.