Pseudopotential crystal-structure stability calculations on black phosphorous as a function of pressure

Abstract

The pseudopotential approach is used to make exploratory calculations of the structure-dependent part of the cohesive energy $U_s$ of black phosphorous in a variety of crystal structures as a function of atomic volume. The calculations assume black phosphorous to be a simple $\mathrm{sp}$ metal, and empirical local pseudopotentials from the literature were used to fit a modified "empty-core" pseudopotential form. The effects of considering covalent contributions are also considered but not calculated here. At the 1-bar atomic volume, the $A-7\mathrm{}$ structure is found to be more stable than the observed black P orthorhombic. However, the difference between $U_s$ (orthorhombic) and $U_s\mathrm{}(A-7\mathrm{})\mathrm{}$ increases as the atomic volume is decreased, in agreement with the observed transition from the orthorhombic structure to the $A-7\mathrm{}$ at 50 kbar. At smaller atomic volumes, the calculations also yield a first-order $A-7\mathrm{}$ to simple cubic transition which corresponds to the one observed experimentally at 110 kbar. Although it is possible to imagine a continuous, second-order deformation of the $A-7\mathrm{}$ to the simple cubic, the calculations predict discontinuous behavior. The simple cubic is predicted to remain more stable than the fcc, bcc, or hcp structure for a wide range of very high pressures.