Piezoelectric langbeinite-type K2Cd2(SO4)3 structure at four temperatures below and one above the 432°K ferroelastic–paraelastic transition

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Abstract
K2Cd2(SO4)3 is orthorhombic below 432°K, with space group P212121, and cubic above with space group P213. A structural study has been completed at 298, 351, 390.5, 417.5, and 443.5°K based, respectively, on 3383, 1377, 1803, 1724, and 1022 symmetry‐independent structure factors. Measurement of integrated intensities was made using a CAD‐4 diffractometer with Nb‐filtered MoKα radiation. An air‐flow microfurnace with temperature controller provided a thermal stability better than ±1°. The a, b, clattice constants in the orthorhombic phase are 10.2084(8), 10.2813(8), 10.1684(8) Å at 298°K; 10.2239(8), 10.2897(8), 10.1821(8) Å at 351°K; 10.2386(8), 10.2951(8), 10.1981(8) Å at 390.5°K; and 10.2501(10), 10.2972(8),10.2132(9) Å at 417.5°K. In the cubic phase, a=10.2704(10) Å at 443.5°K. The model previously obtained at room temperature [J. Chem. Phys. 67, 2146(1977)] was refined by the method of least squares using the new sets of measurements. The final agreement factors are R=0.028 (298°K), 0.032(351°K), 0.026(390.5°K), 0.037(417.5°K), and 0.026(443.5°K). Normal probability plot analysis shows the furnace does not introduce new systematic error in the F m e a s. The amplitudes of thermal vibration for the oxygen atoms increase gradually between 298 and 417.5°K and sharply between 417.5 and 443.5°K. The metal atom vibrations have smaller increases. The metal ions undergo displacements averaging 0.16 Å at the transition, with displacements in the orthorhombic phase averaging 0.05 Å over a 120°K interval. The sulfur atom displacements are comparable, with simultaneous rotations of the SO2− 4 tetrahedra. Two K–O contacts are broken and one is made in the K1+ coordination polyhedra at the phase transition. The Cd–O coordination polyhedra remain unchanged.