Assessing the Structural Diversity of Form II Red Phosphorus via Stepwise Crystal Structure Search

Recently, the long less-known Form II red phosphorus
(RP) (viz.
Type II RP) was ascertained by the state-of-the-art 3-dimensional
electron diffraction technique with a triclinic lattice, completely
distinct from other known elemental phosphorus and leaving atomic
coordinates not determined. The cell composed of ∼250 atoms
might exceed the capacity of current readily available crystal structure
search packages, which have been widely applied to systems with several
tens of atoms. Besides, mistaking Form II RP for violet phosphorus
is still surprisingly common in the studies on allotropic phosphorus
due to misinterpretations on JCPDS card #00-044-0906. Herein, by reproducing
annealing synthesis and cell relaxation of structures obtained in
the literature, we verified two former crystal structures for Form
II RP to be wrong and explained how the misinterpretations have occurred.
Then, on the basis of experimental lattice data, we provided possible
Form II RP models containing atomic positions by a nearly exhaustive
high-throughput stepwise crystal structure search approach optimized
by molecular mechanics, machine-learned force field, and density functional
theory in succession. The energetic stability of Form II RP was found
to rank between white phosphorus and black phosphorus, similar to
the nanorod modifications.