Mapping the strain distribution within embedded nanoparticles via geometrical phase analysis

Abstract

Strain variation within a nanoparticle plays a crucial role in tuning its properties. Geometrical phase analysis (GPA) is typically a powerful tool to investigate the strain in high-resolution transmission electron microscopy (HRTEM) images. It is known that the traditional GPA method measuring the displacement of lattice fringes directly in an HRTEM image is inapplicable to strain measurements on nanoparticles embedded in a matrix, where lattice fringes of nanoparticles are invisible, instead Moiré fringes are present. Furthermore, considering the small size of embedded nanoparticles, generally a few nanometers, no reference region can be chosen and utilized to calculate the relative displacement by GPA. Hence advanced methods need to be developed to break through the barriers of invisible lattice fringes and lack of a reference region. In this work, using α-Fe nanoparticles embedded in sapphire as a test object, we illustrate a GPA method dedicated to embedded nanoparticles. Both the Fourier filter method and the inverse Moiré fringes method were used to reconstruct the invisible lattice fringes of α-Fe nanoparticles. Then a computer-generated image corresponding to an unstrained α-Fe lattice was used as the reference during GPA. The GPA results indicate that there exists a compressive strain in the range of 1.5˜2% within the α-Fe nanoparticles. Our work presents an effective approach to revealing the strain distributions within embedded nanoparticles.