  The low formation energy of atomic vacancies in black phosphorus allows it to
serve as an ideal prototypical system for exploring the dynamics of interlayer
interstitial-vacancy (I-V) pairs (i.e. Frenkel defects) which account for
Wigner energy release. Based on a few-layer model of black phosphorus, we
conduct discrete geometry analysis and investigate the structural dynamics of
intimate interlayer Frenkel pairs from first-principles calculations. We reveal
a highly metastable I-V pair state driven by anisotropic dipole-like strain
fields which can build strong connections between neighbouring layers. In the
2D limit (monolayer), the intimate I-V pair exhibits a relatively low formation
energy of 1.54 eV and is energetically favoured over its isolated constituents
by up to 1.68 eV. The barrier for annihilation of the Frenkel pair is 1.46 eV
in the bilayer, which is remarkably higher than that of similar defects in
graphite. The findings reported in this work suggest that there exist rich
bridging pathways in black phosphorus, leading to stable dimensional reduction
and structural condensation on exposure to moderate electron excitation or
thermal annealing. This study paves the way for creating novel
dimensional-hybrid polymorphs of phosphorus via the introduction of such
metastable interlayer I-V pair defects.
