Cluster Fragments in Amorphous Phosphorus and their Evolution under Pressure

Amorphous phosphorus (a-P) has long attracted interest because of its complex atomic structure, and more recently as an anode material for batteries. However, accurately describing and understanding a-P at the atomistic level remains a challenge. Here we show that large-scale molecular-dynamics simulations, enabled by a machine learning (ML)-based interatomic potential for phosphorus, can give new insights into the atomic structure of a-P and how this structure changes under pressure. The structural model so obtained contains abundant five-membered rings, as well as more complex seven- and eight-atom clusters. Changes in the simulated first sharp diffraction peak during compression and decompression indicate a hysteresis in the recovery of medium-range order. An analysis of cluster fragments, large rings, and voids suggests that moderate pressure (up to about 5 GPa) does not break the connectivity of clusters, but higher pressure does. Our work provides a starting point for further computational studies of the structure and properties of a-P, and more generally it exemplifies how ML-driven modeling can accelerate the understanding of disordered functional materials.