Atomic‐level elastic strain measurement of amorphous materials by quantification of local selected area electron diffraction patterns

Abstract

Metallic glasses have been promising materials for application as structural materials. Therefore, intense research has been carried out to understand their mechanical properties and the underlying physical phenomena [1]. An important aspect of this research is measuring the response of metallic glasses to external and/or internal stresses and the resulting atomic displacements. These atomic level strains can be measured by quantification of the peak shifts in synchrotron diffraction experiments as demonstrated by Poulsen et. al. [2]. Here, we present a novel TEM method for measuring the atomic level strains on a local scale by means of electron diffraction. A series of selected area electron diffraction (SAD) patterns of amorphous TiAl tensile test samples are recorded in a CM200 electron microscope equipped with a Gatan Orion CCD camera. External stress is applied in‐situ and the evolution of the 2D strain tensor is calculated from the distortion of the characteristic amorphous diffraction halo. The full evaluation is carried out automatically by a plugin written for the Digital Micrograph TM platform: The peak maxima positions are extracted with sub‐pixel accuracy from azimuthal integrated sectors of 1° (cf. Fig.1(a)). This is achieved by a non‐linear least squares fit using a pseudo‐Voigt model function (cf. Fig.1(b)). By fitting an ellipse to the maxima positions also the center is determined with sub‐pixel accuracy. By iteration the data is refined and the polar form of the maxima positions is obtained. Using an unstrained SAD pattern as reference, the 2D strain tensor can be calculated from the difference of the peak maxima positions. By fitting the polar form of the strain tensor finally the principal strain magnitude and direction can be obtained relative to the SAD patterns coordinate system (cf. Fig. 2). Simulated diffraction patterns with known parameters and different levels of noise are used to check the strain accuracy of the method. The relative error is calculated with respect to the known input parameters. The method has an accuracy of about 1x10 ‐4 in determination of the parameters, the relative error in principal stress is below 3% even at principal strain below 0.5% (cf. Fig. 3). In addition to measure the atomic‐level strain response to an applied external stress the method allows also to map the strains on a local scale, limited in principle only by selected aperture size and intensity fluctuations of the diffraction data for small sampling volumes. An example for such mapping capabilities is given in Fig. 4, where the strain distribution over the width of a strained specimen is given. In this case the strain distribution is non‐uniform and varies between 1.3% at center and 1.35% at edge regions.