Quantitative measurement of displacement and strain fields from HREM micrographs

A method for measuring and mapping displacement fields and strain fields from high-resolution electron microscope (HREM) images has been developed. The method is based upon centring a small aperture around a strong reflection in the Fourier transform of an HREM lattice image and performing an inverse Fourier transform. The phase component of the resulting complex image is shown to give information about local displacements of atomic planes and the two-dimensional displacement field can be derived by applying the method to two non-colinear Fourier components. Local strain components can be found by analysing the derivative of the displacement field. The details of the technique are outlined and applied to an experimental HREM image of a domain wall in ferroelectric–ferroelastic PbTiO3.