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.

Effects of sintering temperature on structure and electrical properties of (Na0.48k0.473Li0.04Sr0.007)(Nb0.883Ta0.05Sb0.06Ti0.007)O3 piezoelectric ceramics

In this study, the effects of sintering temperature on microstructure, dielectric and piezoelectric properties are investigated for the non-stoichiometric (Na0.48K0.473Li0.04Sr0.007)(Nb0.883Ta0.05Sb0.06Ti0.007)O3 (NKLNTSST) piezoelectric ceramics. The results suggest that the piezoelectric properties are enhanced owing to the more normal ferroelectric characteristics, higher density, more uniform grains and presence of polymorphic phase transition regions, which are observed with an increase in the sintering temperature up to 1080?C. The piezoelectric properties are weakened owing to the larger degree of diffuse phase transition and more cationoxygen-vacancy pairs with an increase in the sintering temperature above 1080?C. The best piezoelectric properties including kp = 40%, d33 = 288 pC/N, ?max = 72.12, loss = 2.57%, Ec = 13.45 kV/cm and Pr = 10.23 ?C/cm2 are obtained at the sintering temperature of 1080?C.