Compressibility of cubic white, orthorhombic black, rhombohedral black, and simple cubic black phosphorus

Abstract

The effect of pressure on the crystal structure of white phosphorus has been studied up to 22.4 GPa. The $\ensuremath{\alpha}$ phase was found to transform into the ${\ensuremath{\alpha}}^{\ensuremath{'}}$ phase at $0.87\ifmmode\pm\else\textpm\fi{}0.04\text{ }\text{GPa}$ with a volume change in $0.1\ifmmode\pm\else\textpm\fi{}0.3\text{ }\text{cc}/\text{mol}$. A fit of a second-order Birch-Murnaghan equation to the data gave ${V}_{\text{o}}=16.94\ifmmode\pm\else\textpm\fi{}0.08\text{ }\text{cc}/\text{mol}$ and ${K}_{\text{o}}=6.7\ifmmode\pm\else\textpm\fi{}0.5\text{ }\text{GPa}$ for the $\ensuremath{\alpha}$ phase and ${V}_{\text{o}}=16.4\ifmmode\pm\else\textpm\fi{}0.1\text{ }\text{cc}/\text{mol}$ and ${K}_{\text{o}}=9.1\ifmmode\pm\else\textpm\fi{}0.3\text{ }\text{GPa}$ for the ${\ensuremath{\alpha}}^{\ensuremath{'}}$ phase. The ${\ensuremath{\alpha}}^{\ensuremath{'}}$ phase was found to transform to the A17 phase of black phosphorus at $2.68\ifmmode\pm\else\textpm\fi{}0.34\text{ }\text{GPa}$ and then with increasing pressure to the A7 and then simple cubic phase of black phosphorus. A fit of a second-order Birch-Murnaghan equation to our data combined with previous measurements gave ${V}_{\text{o}}=11.43\ifmmode\pm\else\textpm\fi{}0.05\text{ }\text{cc}/\text{mol}$ and ${K}_{\text{o}}=34.7\ifmmode\pm\else\textpm\fi{}0.5\text{ }\text{GPa}$ for the A17 phase, ${V}_{\text{o}}=9.62\ifmmode\pm\else\textpm\fi{}0.01\text{ }\text{cc}/\text{mol}$ and ${K}_{\text{o}}=65.0\ifmmode\pm\else\textpm\fi{}0.6\text{ }\text{GPa}$ for the A7 phase and, ${V}_{\text{o}}=9.23\ifmmode\pm\else\textpm\fi{}0.01\text{ }\text{cc}/\text{mol}$ and ${K}_{\text{o}}=72.5\ifmmode\pm\else\textpm\fi{}0.3\text{ }\text{GPa}$ for the simple cubic phase.