Metallic glasses are structurally heterogeneous on the atomic and nano scales. However, few investigations have been conducted on how the structural heterogeneities in these two scales co-evolve during annealing. In this work, the atomic and nanoscale structural heterogeneity evolution accompanying the magnetic softness is systematically discussed based on the literature and our previous synchrotron X-ray diffraction and atomic force microscopy results. We revealed the co-evolution mechanism of structural heterogeneities on the atomic and nano scales during annealing via the insight of percolation theory from the point of view of the local five-fold symmetry of the clusters. The results indicate that the reduction of atomic-scale structural heterogeneity during annealing is accompanied by an increase in the degree of local five-fold symmetry of the clusters and an alteration in their connection patterns. As the local five-fold symmetry of clusters in Fe-based metallic glasses reaches the percolation threshold, the nanoscale liquid-like regions tend to transform into solid-like regions. The great degree of percolation causes the pronounced weakening of the nanoscale structural heterogeneity accompanying changes in the shape and number of the liquid-like regions. The reduction of the number of liquid-like regions causes a reduction in vertical anisotropy and magnetic softening due to a more uniform and less free volume within the sub-circular shaped liquid-like region.

金属玻璃在原子和纳米尺度上具有结构异质性。然而，关于这两个尺度的结构异质性在退火过程中如何共同进化的研究很少。在这项工作中，基于文献和我们之前的同步加速器 X 射线衍射和原子力显微镜结果，系统地讨论了伴随磁软化的原子和纳米级结构异质性演变。我们从团簇的局部五重对称性的角度，通过渗流理论的洞察，揭示了退火过程中原子和纳米尺度上结构异质性的协同演化机制。结果表明，退火过程中原子级结构异质性的减少伴随着团簇局部五重对称度的增加和它们连接模式的改变。当铁基金属玻璃中团簇的局部五重对称性达到渗流阈值时，纳米级的类液体区域往往会转变为类固体区域。大程度的渗滤导致纳米级结构异质性明显减弱，伴随着类液体区域的形状和数量的变化。类液体区域数量的减少导致垂直各向异性和磁软化的减少，这是由于亚圆形类液体区域中的更均匀和更少的自由体积。