Fractal arrangement of atomic structures in metallic glasses

Abstract

Understanding and properly describing at.-level structure in metallic glasses and other amorphous materials represents a long-standing and significant scientific problem. Metallic glasses have been shown to exhibit anomalous non-cubic scaling in vol. with respect to their first diffraction peak position, , with a power law exponent in the range of ∼2.3-2.5. This range of exponent values is characteristic of fractals, and, in contrast to crystals, where the exponent is always 3, suggests that the at. structure in metallic glasses may be fractal. However, the nature of this underlying fractal structure is ambiguous. Our in-situ x-ray tomog. measurements of the sample vol. along with corresponding x-ray diffraction data shows a shift in this power law exponent with measurements of the second diffraction peak, . We also show a crossover in the scaling behavior from exponent ∼2.5 (fractal) to ∼3 (homogeneous) that occurs at the second and third nearest neighbor positions, , in the real space radial distribution functions as a function of hydrostatic pressure for three distinct simulated metallic glasses. These results are explained using continuum percolation theory where the at. structure has a correlation length, . Expts., simulations, and theory on multiple glass compns. all corroborate that the at. structure is well described by a specific class of fractal, the percolation cluster, demonstrating a unifying picture of how long-range structure may organize without order in metallic glasses. The long-range structural detail afforded by this model may have significant implications on the phys. properties of glasses as well as the origin of the glass transition phenomenon.