such as "ab initio" molecular dynamics (AIMD). ML-based interatomic potentials, therefore, are beginning to be applied to a range of challenging materials-science research questions, such as the modeling of phase-change memory materials, [12][13][14] catalysts, [15] or battery materials. [16] Recently, a number of "general-purpose" ML potentials have been reported, which can accurately describe a broad range of atomic configurations and materials properties-including silicon, [17] carbon, [18] aluminum, [19,20] and the binary Ga-As system. [21] The hope for such potentials is to enable "off-the-shelf" use without further modification: for example, the aforementioned silicon ML potential has been used to study complex structural transitions under pressure [22] or unusual mechanical properties of amorphous silicon (a-Si). [23] The starting point for the present study is a general-purpose Gaussian approximation potential (GAP) ML model for bulk and nanostructured phosphorus-which was shown to be flexible enough to be applicable to the pressure-induced liquidliquid phase transition from the molecular fluid to the network liquid, whilst also accurately describing the crystalline allotropes and the layered structure of phosphorene. [24] This GAP is now set to facilitate even more challenging studies on more extended length or time scales, and the exploration of other structurally complex phases for which it has not been explicitly "trained", such as amorphous phosphorus (a-P).Research interest in a-P has grown because of emerging applications in batteries. [25][26][27][28] As a commercially available anode material, red phosphorus provides a large cation-storage ability with high theoretical capacities by forming binary X-P compounds (X = Li, Na, K), but it suffers from low conductivity and a large volumetric change during cycling. [29] As discussed in ref. [30], these issues can be ameliorated by creating composites of a-P and carbonaceous materials: on the one hand, increasing electronic conductivity; [31,32] on the other hand, minimizing the mechanical stress induced by volume changes. [30,33] The structure and properties of phosphorus itself are clearly important for battery applications: for example, experimental work showed that the size of a-P particles in phosphoruscarbon composite anodes has an effect on the electrochemical performance, [34] and in situ transmission electron microscopy (TEM) revealed images of red phosphorus segments within a carbon nanofiber. [35] Computationally, structurally ordered phases have been studied with density-functional theory (DFT; 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, it is shown 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...
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