Power-Law Feature of Structure in Metallic Glasses

The atomic packing in metallic glasses (MGs) is a long-standing issue. We investigate the atomic packing on different length scales for various MGs by X-ray diffraction and small-angle X-ray scattering techniques. Our findings are that (1) a noncubic power-law relationship exists between both normalized average basic volume (V_a = M / (ρ × N), where N is the Avogadro constant and M and ρ are the molar mass and density of the sample, respectively) and the center of mass of the first four peaks (q_i) of structural factors in reciprocal space, having an exponent of about 2.52 ± 0.15 on the length scale of about 2.2-3.1 Å for 25 studied MGs, (2) a power-law relationship of the normalized scattering intensity vs q vector has an exponent of about 2.62 ± 0.12 on the length scale of about 250-785 Å for 5 studied MGs, and (3) in contrast, normalization of V_a and r _i (the center of mass of the first four peaks of pair correlation functions) in real space for 25 studied MGs reveals an exponent close to 3, similar to crystals. This discrepancy is elucidated by the fact that the pair correlation functions link with the atomic distribution along the radial direction but neglect how they are spatially packed on each shell. The perspective of the power-law relations on both length scales for the studied MGs deepens the understanding of the atomic packing structures in MGs.