Ferroelastic twin angles at the surface of CaTiO$_\mathrm{3}$ quantified by PhotoEmission Electron Microscopy

We use photoemission electron microscopy to measure the ferroelastic twin wall angles at the surface of CaTiO$_\mathrm{3}$(001) and deduce the strain ordering. We analyze the angular dependence of the photoelectron emission from different domain surfaces, each with their own characteristic tilt angle in the factory roof-like topography. By considering the surface topography as a field perturbation, the offset in the photoemission threshold can be directly related to the tilt angles. With knowledge of the symmetry allowed twin walls we quantify twin topography between 179.1{\deg} to 180.8{\deg}.