The crystal structure of γ-P₄, a low temperature modification of white phosphorus

Abstract

The crystal structure of γ-P₄, one of three modifications hitherto reported on white phosphorus, was determined from X-ray powder diffraction data collected at T = 123 K on a Guinier-Simon camera equipped with a cold gas blower and an image plate detector. Crystallographic data at T = 123 K are: space group C2/m, a = 9.1709(5) Å, b = 8.3385(5) Å, c = 5.4336(2) Å, and β = 90.311(3)°, V = 415.51(6) ų, Z = 4. The crystal structure of γ-P₄ was solved by the method of simulated annealing. The subsequent Rietveld refinement in the range 12° < 2θ < 92° employing rigid-body constraints on the P₄ molecule converged at R_p = 3.8, wR_p = 5.0, and R_F² = 14.0%. The asymmetric unit of γ-P₄ contains three P atoms; two P atoms in a molecule are related by a mirror plane which bisects the molecule. The centers of gravity of these P₄ molecules show a distorted body-centered cubic arrangement. The four apices of the P₄ tetrahedron point to the largest possible voids formed by neighbor molecules. The difference to the crystal structures of SiF₄ and GeF₄ with an exact bcc arrangement of tetrahedral molecules is discussed as well as, in terms of layer stackings, the similarity of the structures of γ- and β-P₄.