Asymmetric thermal vibrations of atoms and pyroelectricity in cancrinite

Abstract

The crystal structure of CO3-cancrinite was analyzed by applying a generalized structure factor expression of the Gram-Charlier expansion to the least-squares refinement performed by using the X-ray intensities measured on single crystals at 173, 293, 473, and 673 K. No satellite reflection or diffuse scattering was observed. The space group is P63 with unit cell a = 1.2604(3) and c = 0.51144(8) nm at 173 K, and a = 1.2709(4) and c = 0.5202(6) nm at 823 K. The temperature behavior for the dehydration and the unit cell dimensions were considerably different from those previously reported for CO3-cancrinite, which shows superstructure reflections.. Two position vectors were assigned to each of the framework atom sites or the CO3 site for examining its asymmetric probability density function—one for the free energy minimum and another for the potential energy minimum. Two polarization vectors were obtained for a unit cell from those position vectors and ion charges. The rigid ion contributions to the pyroelectric coefficients p(σ) (measured under a constant stress σ) and the secondary coefficient p(2) were finally estimated from the temperature dependences of the polarization vectors.