Correlation between local elastic heterogeneities and overall elastic properties in metallic glasses

The common notion suggests that metallic glasses (MGs) are a homogeneous solid at the macroscopic scale; however, recent experiments and simulations indicate that MGs contain nano-scale elastic heterogeneities. Despite the fundamental importance of these findings, a quantitative understanding is still lacking for the local elastic heterogeneities intrinsic to MGs. On the basis of Eshelby's theory, here we develop a micromechanical model that correlates the properties of the local elastic heterogeneities, being very difficult to measure experimentally, to the measurable overall elastic properties of MGs, such as shear/bulk modulus and Poisson's ratio. Our theoretical modeling is verified by the experimental data obtained from various MGs annealed to different degrees. Particularly, we revealed that the decrease of Poisson's ratio upon annealing of MGs is associated with a much large shear softening over hydrostatic-pressure softening, and $vice$ $versa$ in local elastic inhomogeneities. The relative extent of the bulk versus shear modulus softens is extracted for different MGs, and is found to closely depend on the specific composition and their ductility. The implication of our results on the Poisson's ratio criterion on the ductility as well as the aging dynamics in MGs is discussed.