Soft spots and their structural signature in a metallic glass

Abstract

In a 3D model mimicking realistic Cu 64 Zr 36 metallic glass, we uncovered a direct link between the quasi-localized low-frequency vibrational modes and the local atomic packing structure. We also demonstrate that quasi-localized soft modes correlate strongly with fertile sites for shear transformations: geometrically unfavored motifs constitute the most flexible local environments that encourage soft modes and high propensity for shear transformations, whereas local configurations preferred in this alloy, i.e., the full icosahedra (around Cu) and Z16 Kasper polyhedra (around Zr), contribute the least.liquid-like regions | heterogeneity | structure-property relationship | uncommon motifs | shear transformation zones M etallic glasses (MGs) have an inherently inhomogeneous internal structure, with a wide spectrum of atomic-packing heterogeneities (1-4). As a result, an a priori identification of structural defects that carry atomic rearrangements (strains) under imposed stimuli such as temperature and externally applied stresses has always been a major challenge (3-6). In several quasi-2D or 3D models of amorphous solids (such as jammed packings of soft spheres interacting via repulsive potentials or colloidal particles), low-frequency vibrational normal modes have been characterized, and it has recently been demonstrated that some of these modes are quasilocalized (7)(8)(9)(10)(11)(12)(13)(14). A population of "soft spots" has been identified among them in terms of their low-energy barriers for local rearrangements (13,14), correlating also with properties in supercooled liquids such as dynamic heterogeneity (15-17). However, it is not certain where the soft spots are in realistic MGs (18), in terms of an explicit correlation with local atomic packing and topological arrangements (18)(19)(20). In particular, there is a pressing need to determine whether it is possible to identify shear transformation zones, i.e., the local defects that carry inelastic deformation (21,22). Accomplishing this would permit the characterization of MG microstructure in a way that directly ties atomic configuration with mechanical response beyond the elastic regime. We will show here that there is indeed a correlation between soft modes and atoms that undergo shear transformations, and both have their structural signature in specific atomic packing environments defined in terms of coordination polyhedra (3). Fig. 1 displays the vibrational density of states (V-DOS), D(ω), calculated from the eigen-frequencies obtained by normal mode analysis of the Cu 64 Zr 36 MG prepared with a cooling rate of 10 9 K/s (Methods). The main peak stays around 14 meV and becomes only slightly narrower (or wider) when the cooling rate used to prepare the MG is slower (or faster), as seen in Fig. S1; the glasses cooled at slower rates exhibit fewer low-frequency (or low-energy) vibrational modes. The blue portion in Fig. 1 indicates the 1% lowest-frequency normal modes, which will be summed over in our calculations of the participation fraction, P i , in s...

Intrinsic structural defects on medium range in metallic glasses

“…In the first group, most polyhedra are stable or solid-like clusters with high density of fivefold bonds. Such as <0, 0, 12, 0>, <0 [51,52]. In contrast, most of the minor polyhedra are usually liquid-like clusters fragmented with high disclination density [4].…”

Softening of phonon spectra in metallic glasses

“…Both θ D and ω D may also be regarded as a measure of the stiffness of a material, 12 as they are related to the curvature of the energy landscape at the local minimum of a basin (stiffness). 14 Assuming that the contribution of electrons to the specific heat in an electrical conductor is proportional to T, then it can be shown that C V /T = βT 2 +γ, where β and γ are the gradient and intercept of C V /T as a function of T 2 . Table 1 Softening of phonon spectra R Mahjoub et al casting thickness (Z c ), 15 as depicted in Figure 4b.…”

Effects of cooling rate on particle rearrangement statistics: Rapidly cooled glasses are more ductile and less reversible

“…In many prior studies, somewhat arbitrary thresholds in either energy or nonaffine displacements have been employed to identify particle rearrangement events during athermal, quasistatic shear [1,8,52]. In this study, we developed a novel particle rearrangement detection method that identifies particle rearrangements with accuracies that approach numerical precision.…”