Abstract
The lighter group-V element phosphorus forms the As-type (hR2) structure under pressure, above 5 GPa, and at 10 GPa transforms to the simple cubic structure (cP1), similar to arsenic. Despite its low packing density, the simple cubic structure is stable in phosphorus over a very wide pressure range up to 103 GPa. On further pressure increase, the simple cubic structure transforms into a simple hexagonal structure (hP1) via a complex phase that was solved recently as incommensurately modulated. Structural transformations of phosphorus are connected with the changes of physical properties. Above 5 GPa phosphorus shows superconductivity with Tc reaching ~9.5 K at 32 GPa. The crystal structures and properties of high-pressure phases for phosphorus are discussed within the model of the Fermi sphere and Brillouin zone interactions.
Highlights
Recent high-pressure X-ray diffraction studies revealed unusual complex and low symmetry structures in some simple elements [1], including incommensurate modulated (IM) structures
An IM structure was found in a light group V element phosphorous in the phase P-IV stable in the pressure range 107–137 GPa between two simplest phases; simple cubic and simple hexagonal [2,3,4,5]
At pressure ~260 GPa P-hP1 transforms to the body-centered cubic structure that was recently redfound to form a superlattice structure cI16 [6]
Summary
Recent high-pressure X-ray diffraction studies revealed unusual complex and low symmetry structures in some simple elements [1], including incommensurate modulated (IM) structures. All IM structures were observed when elements become metallic under pressure This implies the importance of the two main contributions to the lattice energy: electrostatic (Ewald) and electronic (band structure) energies. The latter can be lowered due to a formation of Brillouin zone planes near the Fermi level and an opening of an energy gap at these planes. For a classical Hume-Rothery phase Cu5Zn8, the Brillouin zone filling by electron states is equal to 93%, and is around this number for many other phases stabilized by the Hume-Rothery mechanism [12,13,14,15]. With the BRIZ program one can obtain a qualitative picture and some quantitative characteristics on how a structure matches the criteria of the Hume-Rothery mechanism
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