Quantifying Mechanical Strength of Metal Using Four-Dimensional Electron Microscopy

The distribution of charge in metals governs their atomic bonding characteristics, which are intimately linked to their mechanical properties. However, experimental studies directly connecting charge distribution to mechanical strength remain limited, due to the lack of methods capable of mapping interatomic charge with high spatial resolution and quantifying bond strength. Here, we employ four-dimensional scanning transmission electron microscopy (4D-STEM) to directly probe and map the electric fields and charge distribution between atoms in pure magnesium (Mg). The strength of interatomic bonding is quantified by calculating and integrating the Coulombic forces between the positive nuclear cores and the spatially resolved negative charge. By comparing the directional Coulombic forces with the known anisotropic elastic moduli of Mg, we establish a direct correlation between atomic-scale charge distribution and macroscopic mechanical strength. This work demonstrates the feasibility of studying metallic bonding and mechanical properties through real space electric field and charge imaging at atomic resolution.