The Moiré phenomenon is well known in conventional optics as well as in transmission electron microscopy but since the recent evolutions towards high spatial resolution, the use of the Moiré patterns has lost its importance. We propose here a new insight into this phenomenon and we show how it can be used to obtain the thickness of two superimposed crystals.

  We worked with (111) reflections of copper and silver to study the pseudo-lattice fringes appearing inside the Moiré patterns (fig.1a). The high resolution images are simulated using the dynamical mutislice technique on a crystal of two superimposed thin films of copper and silver. Some of the simulations were carried out in kinematic conditions of electron diffraction in order to model the (111) fringes analytically. These pseudo-lattice fringes appear in both cases in the simulations.

  In the first place we studied the variation of the periodicity of the pseudo-lattice fringes with the relative thicknesses of the two superimposed films. We can see that when the value of s, the deviation parameter from Bragg reflections, is small (dynamical condition) the variation of this periodicity with the thickness fraction of copper is independent of the total thickness and has a linear form. This result allows us to find the thickness fraction from a single high resolution image.

 On the contrary, for the large values of s (kinematics conditions) it has been found that this variation is not linear and depends on the total thickness. This result is confirmed using an analytic equation representing the intensity of the transmitted and diffracted waves superimposed.

  In the last part we have used this equation to fit the intensity profile of the simulated images(in the kinematics conditions) and we have used the thickness fraction obtained above as a fixed parameter and the total thickness as a fit variable. In many cases we can find the right total thickness with this fitting method (fig.1b).

 We conclude this study with a discussion on the possible application of this technique.                                                       

• Legal notice:
  

  Copyright (c) Pielaszek Research, all rights reserved.
  The above materials, including auxiliary resources, are subject to Publisher's copyright and the Author(s) intellectual rights. Without limiting Author(s) rights under respective Copyright Transfer Agreement, no part of the above documents may be reproduced without the express written permission of Pielaszek Research, the Publisher. Express permission from the Author(s) is required to use the above materials for academic purposes, such as lectures or scientific presentations.
  In every case, proper references including Author(s) name(s) and URL of this webpage: https://science24.com/paper/18062 must be provided.

1. Cu/Ag interfaces TEM characterization for core-shell nanoparticles
2. Growth of CuAg core-shell nanoparticles: silver-enhanced cluster diffusion on amorphous carbon