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

Abstract

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 non-affine 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 non-affine atomic displacements in the glass.

Mechanical Properties of Metallic Glasses

“…In particular they found that the strains at short distances are smaller than those at large distances. Similar results were obtained by several groups [30][31][32][33][34][35][36][37][38][39], and it is clear that such inhomogeneous response is a common feature of elasticity in metallic glasses, distinct from those of crystalline solids. There is, however, a minor problem before we discuss the implications of these results.…”

“…A majority of researchers interpret these results in terms of distance-dependent strain [28][29][30][31][32][33][35][36][37][38][39] or chemical inhomogeneity [34]. The strain is small at short distances, and increases as r is increased.…”

“…This results in small but significant differences in the anisotropic PDF particularly at short distances [23,38]. [21].…”

“…There is, however, a minor problem before we discuss the implications of these results. In all of these measurements, with the exception of [34,38], g(r) was obtained by the standard Fourier-transformation, Equation (9). But this equation applies only to an isotropic body [40].…”

Deformation in Metallic Glasses Studied by Synchrotron X-Ray Diffraction

“…They are clearly different due to extensive non-affine deformation and atomic rearrangement as discussed below. The isotropic and anisotropic PDFs, obtained by Equations (19) and (20), are shown in Figures 4 and 5. Again, the anisotropic PDF is compared to the affine anisotropic PDF in Figure 5.…”