X-ray diffraction and dielectric temperature dependence study of the K2Cd2(SO4)3 paraelastic-ferroelastic phase transition

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Abstract
The thermal expansion coefficients of the orthorhombic a, b, and c axes in langbeinite-type K2Cd2(SO4)3 are α=24(2) ×10−6, 12(1) ×10−6, and 19(2) ×10−6 deg−1, β=5(1) ×10−8, 8(1) ×10−8, and 5(1) ×10−8 deg−2, γ=2(1) ×10−10, −6(1) ×10−10, and 6(1) ×10−10 deg−3, respectively, between 287 and 425 K. Above the first-order phase transition at Tc=432 K, α=19(1) ×10−6 deg−1. The sulfate tetrahedra angular rotations are less than 5° between 298 and 417.5 K but are as much as 20° between 417.5 and 443.5 K. Over 70% of the rotations are estimated to take place within 2–3 K of Tc. The room-temperature dielectric constants ε1, ε2, and ε3 are about 8, 8, and 16, respectively, at 1 kHz: a jump of about 5% occurs at Tc. Two spontaneous strains decrease markedly as Tc is approached, but all three remain greater than 2×10−3. The ferroelastic displacements decrease by as much as 0.25 Å between 298 and 417.5 K to values ranging from 0.22 to 0.91 Å. The absolute sense of the piezoelectric shear coefficient d14 has been measured as positive, i.e., a tensile stress along [011] generates positive polarity on (100), negative on (1̄00). The magnitude of d14 is about 7.3(5) ×10−12 C N−1, the electromechanical coupling factor k14 is 0.124(5), and the elastic compliance s11 is 1.72(2) ×10−11 m2 N−1.