The crystal structures of the isostructural orthorhombic sulfates celestite (SrSO4), anglesite (PbSO4), and barite (BaSO4) were refined by Rietveld methods using synchrotron high-resolution powder X-ray diffraction (HRPXRD) data. Their structural model was refined in space group Pbnm . The unit-cell parameters are a = 6.87032(3), b = 8.36030(5), c = 5.34732(1) Å, and V = 307.139(3) Å3 for SrSO4; a = 6.95802(1), b = 8.48024(3), c = 5.39754(1) Å, and V = 318.486(1) Å3 for PbSO4; and a = 7.15505(1), b = 8.88101(3), c = 5.45447(1) Å, and V = 346.599(1) Å3 for BaSO4. The average [12] distances are 2.827(1), 2.865(1), and 2.953(1) Å for SrSO4, PbSO4, and BaSO4, respectively, and their corresponding average [4] distances are 1.480(1), 1.477(3), and 1.471(1) Å. The geometrical features of the SO4 and MO12 polyhedra become more symmetrical from SrSO4 to BaSO4. Across the series, the a , b , and c parameters vary non-linearly with increasing V . The radii of the M2+ cations, rM, [12], and [4] distances vary linearly with V . These structural trends arise from the effective size of the M2+ cation (rM: Sr < Pb < Ba) that is coordinated to 12 O atoms.

The cause of birefringence in several garnet-group minerals with general chemical formula, ^[8] X ₃ ^[6] Y ₂ ^[4] Z ₃ ^[4] O ₁₂ , which was observed over 100 years ago, is unknown, although many different reasons were proposed, including symmetry lower than cubic. In this study, electron microprobe analyses (EMPA) were obtained for a Ti-rich andradite, ideally Ca ₃ (Fe ₂ ³⁺ )Si ₃ O ₁₂ , from Magnet Cove, Arkansas, USA, and the results show that the sample is inhomogeneous with two distinct compositions. The crystal structure was refined by the Rietveld method, cubic space group $Ia\overline 3 d$ , and monochromatic synchrotron high-resolution powder X-ray diffraction (HRPXRD) data, which shows a mixture of three distinct cubic phases that are intergrown together and cause birefringence because of strain arising from small structural mismatch. This mixture of three cubic phases was not observed by any other experimental technique. These results have many implications, including garnet phase transitions from cubic to lower symmetry in the mantle, which has important geophysical consequences.

The crystal structures of four samples of anhydrite, CaSO ₄ , were obtained by Rietveld refinements using synchrotron high-resolution powder X-ray diffraction (HRPXRD) data and space group Amma . As an example, for one sample of anhydrite from Hants County, Nova Scotia, the unit-cell parameters are a = 7.00032(2), b = 6.99234(1), c = 6.24097(1) Å, and V = 305.487(1) Å ³ with a > b . The eight-coordinated Ca atom has an average distance of 2.4667(4) Å. The tetrahedral SO ₄ group has two independent S-O distances of 1.484(1) to O1 and 1.478(1) Å to O2 and an average distance of 1.4810(5) Å. The three independent O-S-O angles [108.99(8) × 1, 110.38(3) × 4, 106.34(9)° × 1; average [6] = 109.47(2)°] and S-O distances indicate that the geometry of the SO ₄ group is quite distorted in anhydrite. The four anhydrite samples have structural trends where the a , b , and c unit-cell parameters increase linearly with increasing unit-cell volume, V , and their average and distances are nearly constant. The grand mean = 2.4660(2) Å, and grand mean = 1.4848(3) Å, the latter is longer than 1.480(1) Å in celestite, SrSO ₄ , as expected.