Structural Principles of Polyhedral Allotropes of Phosphorus

Abstract

We derive the structural principles of polyhedral allotropes of phosphorus, introducing three distinct families of black phosphorus nanostructures. The predicted tetrahedral, octahedral, and icosahedral phosphorus cages can also be considered as phosphorus fullerenes. Phosphorus cages up to P888 are systematically investigated by quantum chemical methods, and their thermodynamic stabilities are compared with the experimentally known allotropic forms of phosphorus. The tetrahedral cages are thermodynamically favored over the octahedral and icosahedral structures, although large octahedral structures become nearly as stable as the tetrahedral ones. The stability trends of the studied polyhedral families can be rationalized on the basis of their structural characteristics. The phosphorus polyhedra can be further stabilized by fitting smaller structures inside larger ones, resulting in multilayered, bulk‐like cages. The synthesis of the predicted black phosphorus nanostructures is suggested to be viable from the thermodynamic point of view, and several approaches for their experimental preparation can be envisaged.

Laser desorption ionization of red phosphorus clusters and their use for mass calibration in time‐of‐flight mass spectrometry

“…Phosphorus can be obtained in a great variety of structures in its solid state: white, red and black phosphorus 11–14. Black phosphorus is the most stable and it has been suggested to possess various cage structures up to P 888 15. Red phosphorus is non‐toxic, is usually amorphous15 and by laser vaporization a large number of homoatomic clusters are generated 14, 16–19.…”

“…Black phosphorus is the most stable and it has been suggested to possess various cage structures up to P 888 15. Red phosphorus is non‐toxic, is usually amorphous15 and by laser vaporization a large number of homoatomic clusters are generated 14, 16–19. The stabilities of these clusters differ.…”

Simulated scanning tunneling microscopy images of few-layer phosphorus capped by graphene and hexagonal boron nitride monolayers

“…Few-layer phosphorene bears promise for intriguing optoelectronics applications [17] since the fundamental band gap can be tuned by the number of layers and by inlayer stretching or compression [12,[18][19][20][21][22][23]. But what truly sets phosphorene apart from other 2D systems is its polymorphism: Besides the well-studied black phosphorus allotrope, energetically near-degenerate alternate structures have been postulated including blue phosphorus, γ-P, δ-P and their combination in one layer [24][25][26][27][28][29][30][31][32]. Identifying and discriminating between these structures requires a tool capable of probing structures in real space with sub-nanometer resolution.…”

A G3(MP2B3) investigation on the structures and properties of silaprismanes

“…Their related derivatives and nanostructures have also been extensively studied [24,26,[28][29][30][31]. Kumar and Kawazoe have reported the small caged silicon fullerenes with n = 8-28 [24].…”