On the question of fractal packing structure in metallic glasses

Abstract

This work addresses the long-standing debate over fractal models of packing structure in metallic glasses (MGs). Through detailed fractal and percolation analyses of MG structures, derived from simulations spanning a range of compositions and quenching rates, we conclude that there is no fractal atomic-level structure associated with the packing of all atoms or solute-centered clusters. The results are in contradiction with conclusions derived from previous studies based on analyses of shifts in radial distribution function and structure factor peaks associated with volume changes induced by pressure and compositional variations. The interpretation of such shifts is shown to be challenged by the heterogeneous nature of MG structure and deformation at the atomic scale. Moreover, our analysis in the present work illustrates clearly the percolation theory applied to MGs, for example, the percolation threshold and characteristics of percolation clusters formed by subsets of atoms, which can have important consequences for structure-property relationships in these amorphous materials.etallic glasses (MGs) are of significant current interest because of their unique combination of mechanical properties (1-7). Although it is generally understood that these properties arise from the nature of the MG structure, the understanding of this structure, spanning atomic to medium-range scales, remains incomplete. In recent years, fractal concepts have been introduced (e.g., refs. 8-10) to describe the structure of MGs: that is, based on self-similar patterns of packing structure repeated at different length scales (11). These models have been invoked to explain (8,9,(12)(13)(14) widely observed noncubic power laws (D) correlating positions of the first sharp diffraction peak, q, or the first peak of radial distribution functions (RDFs), r, with the average atomic volume, V (or bulk atomic density, ρ = 1/V), that is:Exponents of D ≈ 2.5 or 2.3 have been measured in MGs, or the metallic melts from which they are derived based on scattering experiments and computer simulations (8,9,(12)(13)(14), in which the changes in atomic volume V have been investigated through applications of hydrostatic pressure or compositional variations. These measurements, which are in contrast to the situation for crystalline metals and alloys, where the scaling in Eq. 1 is characterized by D = 3, have led to the proposal of two distinct fractal models for the structure of MGs, associated with the packing of local clusters or atoms (see illustration of atomic configuration in Fig. 1A). In the first such model (9), it was proposed that MGs are composed of solute (minority atom)-centered clusters that are arranged on mediumrange scales in a fractal manner. This description has been the subject of debate in the literature (7,14,15), and more recently Chen et al. (8,10) proposed a description in which the individual atoms of MGs are packed according to a special class of fractal models, namely, a percolation cluster. This latter description serves to solve ...

A transferable machine-learning framework linking interstice distribution and plastic heterogeneity in metallic glasses

“…We proceed to address how these characteristic atoms pack in space. We first perform fractal dimensionality sampling 58,59 for the hardest and softest atoms using the power-law scaling of the mass distribution M(r) ~ r D , where M(r) denotes the number of atoms of each type within radius r centered by an atom (Figure 3c). Theoretically, the slope D of the M(r) curve in log-log plot is the dimensionality, and D < 3 indicates fractal structure 58,59 (i.e., the number of atoms does not straightforwardly increase with the volume of an enclosing sphere).…”

Melts of CrCoNi-based high-entropy alloys: Atomic diffusion and electronic/atomic structure from ab initio simulation

“…5(a)-5(c), we can conclude that significant icosahedral order exists in the melts of CrCoNibased medium-and high-entropy alloys, akin to the icosahedral order that has been observed in a wide range of metallic liquids, including those liquids for MG systems, and elemental crystals. 41 Finally, we have noted a variety of differences between the liquids of HEAs and MGs, which also correspond to dissimilar behavior in solidificaiton. HEAs and MGs are both formed by mixing multiple metallic elements, but the critical idea underlying the selection of metallic atoms for these two classes of alloys is not the same; the constituents/compositions for HEAs need to favor the formation of single-phase crystalline solid solutions, while the MG systems are prone to destabilize the formation of corresponding crystalline counterparts.…”

Power laws in pressure-induced structural change of glasses

“…The anomalous FPLs have been attributed to atomic-scale fractal packing 8 and mediumrange order 6 , but both explanations are derived from a single state, not from a series of states as the FPL arises. Moreover, further studies of metallic glasses did not reveal a fractal structure 9 . S(q 1 ) contains structural information spanning broad length scales in real space.…”

“…In particular, microscopic structural changes in response to mechanical deformation is poorly understood [3][4][5] . A well-known puzzle is the fractional power law (FPL) in the reciprocal space of many metallic glasses 3,6 , whose mechanism and generality remain controversial 3,[6][7][8][9] .…”

“…with a fractional exponent d ≃ 2.5 < D = 3 under composition change 6,8 or compression 3,7,8 . Recently, power laws with large fluctuation of d were observed in glasses under compression and composition change, which raises questions about the generality of the FPL 9 . Here we summarize five open questions: (1) Does the FPL generally hold in glasses?…”