The Use of the Geometrical Phase Analysis to Measure Strain in Nearly Periodic Images

Abstract

The geometrical phase analysis (GPA) is a simple and efficient method to measure strain in nearly periodic images and especially high resolution transmission electron microscopy (HRTEM) images. In a few steps, GPA averages and fits the best lattice parameter in a given region. The accuracy of GPA is determined by analyzing Si perfect crystal HRTEM images. This precision varies with the mask size employed, that is to say with the size of the region over which the measure is averaged. When averaging on large areas (9x9nm 2) variations of 0.1 pm on lattice fringe periods d of about 0.2nm, that is to say ∆d/d ~ 5 10-4 , can be detected. The correction of the distortions introduced by the imaging system (lenses or CCD camera) is presented. It is shown that, for a given JEOL4000FX microscope and a given magnification, the correction images did not change significantly during a 3 year period and were similar at 400kV and 300kV. On the contrary, the absolute measure of the (111) Si lattice parameter (in pixels) varies significantly during time (it is certainly a function of the fine tuning of the objective lens). The method is applied to Moiré images where large strains (more than 100%) are accurately measured by GPA.