Structure evolution, dielectric, and conductivity behavior of (K0.5Na0.5)NbO3-Bi(Zn2/3Nb1/3)O3 ceramics

Abstract(1−x)K0.5Na0.5NbO3−xBi(Zn2/3Nb1/3)O3 ((1−x)KNN−xBZN, x = 0.010, 0.015, 0.020, 0.025, and 0.030) lead-free ceramics were fabricated via a traditional solid-state method. The crystal structure, microstructure, dielectric, and conductivity behavior of this system were studied. Combined with X-ray diffraction (XRD) patterns, Rietveld refinement, and dielectric spectroscopy, an orthorhombic phase was determined for x = 0.010, an orthorhombic-tetragonal mixed phase was identified for x = 0.015, and a rhombohedral symmetry appears in 0.020 ⩽ x ⩽ 0.030. Both 0.98KNN−0.02BZN and 0.975KNN−0.025BZN ceramics exhibit stable permittivity and low dielectric loss tangent (tanδ) in wide temperature ranges owing to the combination of rhombohedral-tetragonal step-like feature and the diffuse phase transition from tetragonal to cubic. The activation energies of dielectric relaxation and conductivity behavior at high temperatures initially decrease slightly, then drop sharply, and finally decline slowly, which could be attributed to microstructure morphologies and the concentration of oxygen vacancies.

No or Diffuse Phase-Transition With Temperature in One-dimensional Ising Model?

For nearly a century since Ising model was proposed in 1925, it is agreed that there is no phase-transition with temperature in the one-dimensional based on no global-spontaneous-magnetization in whole temperature region. In this letter, the exact calculation of local-spontaneous-magnetization shows that a diffuse phase-transition with temperature occurs in one-dimensional Ising model. In addition, although diffuse phase-transition phenomenon is common in the systems of heterogeneous-components and small-sizes etc., there is no accurate prediction of corresponding theoretical models so far, so the present works lay the theoretical foundation of this kind of phase-transition.