Crystal structures and sulphate force constants of barite, celestite, and anglesite

The crystal structures of three isostructural sulphates, barite (BaSO₄), celestite (SrSO₄), and anglesite (PbSO₄), were refined by least-squares methods using three-dimensional X-ray data. All three sulphates belong to the orthorhombic space group Pbnm with Z = 4. The final R values are 0.043, 0.053, and 0.067 for BaSO₄, SrSO₄, and PbSO₄, respectively. The average cation to oxygen bond lengths are 2.952A in barite, 2.831A in celestite and 2.87A in anglesite. The average sulphur to oxygen bond lengths are 1.478A in barite, 1.474A in celestite and 1.49A in anglesite.

The force constants of the Urey-Bradley force field in the SO₄ tetrahedron were calculated from the bond lengths and the infrared absorption frequencies. The stretching force constants for barite, celestite, and anglesite are K = 6.27, 6.34, and 5.98 md/A, respectively; the bending force constants H = 0.46, 0.47, and 0.42 md/A; the repulsive force constants F = 0.73, 0.75, and 0.70 md/A. The increase of the field strength of a metal ion gives rise to the increase of the force constants in the SO₄ tetrahedron.