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

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, c lattice 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 Fmeas. 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.