Quantifying the correlation between the complex structures of amorphous materials and their physical properties has been a long-standing problem in materials science. In amorphous Si, a representative covalent amorphous solid, the presence of a medium-range order (MRO) has been intensively discussed. However, the specific atomic arrangement corresponding to the MRO and its relationship with physical properties, such as thermal conductivity, remain elusive. Here, we solve this problem by combining topological data analysis, machine learning, and molecular dynamics simulations. By using persistent homology, we constructed a topological descriptor that can predict the thermal conductivity. Moreover, from the inverse analysis of the descriptor, we determined the typical ring features that correlated with both the thermal conductivity and MRO. The results provide an avenue for controlling the material characteristics through the topology of nanostructures.
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