Length-scale dependence of elastic strain from scattering measurements in metallic glasses

Several recent studies have reported that the elastic strain in metallic glasses, as measured from peak shifts in the pair-correlation functions of samples under load, increases with distance from an average atom, approaching the macroscopic strain at large distances. We have verified this behavior using high-energy x-ray scattering on metallic glasses loaded under uniaxial compression, uniaxial tension, and pure shear, and show that the apparent length-scale dependence of elastic strain is not an artifact of the assumption of structural isotropy in the data analysis. Molecular dynamics simulations of a binary Lennard-Jones glass loaded in uniaxial tension reproduce, qualitatively, the behavior observed in the experiments when the elastic strain is calculated from the shifts in the peaks of the pair-correlation function. Under hydrostatic loading, however, the length-scale dependence of elastic strain observed in the simulations is greatly reduced. This suggests that nonaffine atomic displacements, which are smaller under hydrostatic loading than under uniaxial loading, may play a key role in the length-scale dependence of elastic strain. Furthermore, no length-scale dependence is observed in simulations, for either uniaxial or hydrostatic loading, when the elastic strain is calculated from the average local deformation gradient tensor. We explain this apparent contradiction and show that the atomic displacements resulting from elastic loading are largest in the low-density regions between atomic shells around an average atom. Finally, we present an analysis of length-scale dependence of elastic strain calculated from the pair-correlation function for the case of homogeneous deformation, which is in good agreement with the simulations conducted under hydrostatic loading. For uniaxial loading, however, the analysis diverges from both the experimental and simulated results in the first two near-neighbor atomic shells. This suggests, in agreement with our observations from the molecular dynamics simulations, that the observed length-scale dependence of elastic strain from scattering measurements reflects the nature of the nonaffine atomic displacements in the glass.