Medium-range imperfect order determining the slow β-relaxation in metallic glasses

Secondary (slow beta) relaxation and structural heterogeneity are crucial in several critical unresolved issues in metallic glasses (MGs). However, their intrinsic correlations and composition dependence are not established despite extensive work for decades. In this work, we modulated the secondary relaxation and structural heterogeneity of Dy-based bulk MGs by microalloying different metalloids (B, C, N, and Si) and demonstrated the atomic-scale mechanism. We shed light on the effects of enthalpy of mixing, degree of elastic heterogeneity on the micrometer scale, intensity of interaction, and imperfect orders (IPOs) on beta-relaxation dynamics. We revealed that both the obviousness/intensity of the shoulder and the activation energy for beta-relaxation are closely associated with the fraction of medium-range IPO. This shows that the cooperative string-like atomic rearrangements considered as the structural origin in terms of the first-order transition theory probably occur in soft medium-range structures (or defects) with IPO. In addition, the intensity of interaction between Dy and metalloid elements is found to play a crucial role in the formation of medium-range IPO. This work offers new insights into the longstanding mystery regarding the atomic mechanism of beta-relaxation and shows significance for tuning the properties of MGs.