Direct observation of quadrupolar strain fields surrounding Eshelby inclusions in metallic glasses

The data format is DM4 (Gatan Microscopy Suite Software) and processed by lab-written Matlab code. 4D-STEM measurements were conducted using a Themis Z double-corrected TEM (Thermofisher Scientific) operated at 300 kV in microprobe STEM mode with spot size 6 and a semi-convergence angle of 0.26 mrad giving rise to a diffraction-limited probe size of ~5 nm. 4D-STEM records local 2D diffraction patterns over a 2D array of probe positions by stepwise scanning of the probe. The method is called 4D-STEM referring to its typical 4D dataset (2D diffraction pattern on a 2D array of the sample). We used a OneView camera (Gatan Inc.) with a camera length of 1.15 m to record the diffraction patterns. This camera length was chosen to capture the first diffuse diffraction ring with a sufficient diameter on the camera to enhance the sensitivity for measuring distortions. The 2nd diffuse diffraction ring was also included. This preserves the capability for PDF analysis. 4D-STEM maps were acquired with a step size of 5.8 nm and a frame size of 900×500 pixels for the Fe85.2Si0.5B9.5P4Cu0.8 metallic glass ribbon and a step size of 9.7 nm and a frame size of 350×270 pixels for the Zr46Cu38Al8Ag8 bulk metallic glass with an exposure time of 3.3 ms per frame (frame rate of ~300 f/s).
The diffraction pattern of a typical amorphous material shows a diffuse ring pattern (Figure 1a). As described in previous works [23-24, 27], the local stress in the metallic glass induces a structural anisotropy, which results in an elliptic distortion of the diffraction ring leading to a deviation from the ideal circle as illustrated in Figure 1b (the diffraction pattern was artificially elongated for easy presentation). Therefore, the strain can be mapped by determining the ellipticity of the diffraction ring in each local diffraction pattern of the 4D-STEM dataset. Different from high-resolution (HR)TEM-based strain mapping methods such as geometric phase analysis (GPA), which analyzes real space atomic lattice displacements [49], the strain measurement used here analyzes the diffraction ring in the 4D-STEM data. It thus enables the capability to measure strain for amorphous materials and a large field of view (up to micrometers).