Anisotropic Thermal Expansion and Compressibility of Black Phosphorus

Abstract

The anisotropic thermal expansion and compressibility coefficients of black phosphorus have been determined by high temperature single‐crystal x‐ray diffraction, by high pressure x‐ray diffraction and by neutron (time‐of‐flight) diffraction and are ${\mathrm{K}}_{\mathrm{a}}\text{\hspace{0.17em}=\hspace{0.17em}1.5(2)}$ , ${\mathrm{K}}_{\mathrm{b}}\text{\hspace{0.17em}=\hspace{0.17em}15.1(4)}$ , ${\mathrm{K}}_{\mathrm{c}}\text{\hspace{0.17em}=\hspace{0.17em}12.1(4)}$ , ${\mathrm{K}}_{\mathrm{v}}{\text{\hspace{0.17em}=\hspace{0.17em}30.2(1.0)\hspace{0.17em}×\hspace{0.17em}10}}^{\text{−4}}\hspace{0.17em}{\mathrm{kbar}}^{\text{−1}}$ . The volume changes agree well with that reported by Bridgman. The Burch‐Murnaghan coefficient B_T is 325 kbar and B′_T is 6.114. The a‐axis parameter undergoes irreversible and inconsistent changes not yet understood so that the data on the thermal expansion coefficients is unreliable. Single crystals have been grown from a bismuth‐red phosphorus solution at 400°C and have been examined by x‐ray diffractometer techniques in a miniature high temperature single crystal furnace to 200°C. The zig‐zag phosphorus bond lengths and angles along the a‐axis increase from 2.209A.U. and 96.2° at room temperature to 2.224A.U. and 96.5° at 200°C whilst the other bond lengths show little change. These anisotropic properties of black phosphorus appear to be determined to a large extent by the structural feature of the zig‐zag chain of atoms along the a‐axis.