A Physically-Intuitive Method for Calculation of the Local Lattice Constant from a High-Resolution Transmission Electron Microscopy Image by Fourier Analysis

We have developed a physically-intuitive method to calculate the local lattice constant as a function of position in a high-resolution transmission electron microscopy image by performing a two-dimensional fast Fourier transform. We apply a Gaussian filter with appropriate spatial full-width-half-max (FWHM) bandwidth to the image centered at the desired location to calculate the local lattice constant (as opposed to the average lattice constant). Fourier analysis of the filtered image yields the vertical and horizontal lattice constants at this location. The process is repeated by stepping the Gaussian filter across the image to produce a set of local lattice constants in the vertical and horizontal direction as a function of position in the image. The method has been implemented in a freely available tool on nanoHUB [1].