Ferroelectric phase transitions studies in 0.5Ba(Zr0.2Ti0.8) O3-0.5(Ba0.7Ca0.3)TiO3 ceramics

The ferroelectric phase transitions in 0.5Ba(Zr0.2Ti0.8)O3-0.5(Ba0.7Ca0.3)TiO3 (BCZT 50/50) ceramics,fabricatedbyasolidstatereaction,werestudiedbyusing X-Ray diffraction, Raman spectroscopy, and measuring electric polarization, dielectric permittivity and pyroelectric current. Xraydiffraction(XRD)confirmsthecoexistenceoftetragonal(T) andrhombohedral(R)phasesatroomtemperature.Thetemperature dependence of the Raman modes frequency reveals the existenceoftwophasetransitionscorrespondingtotherhombohedral – tetragonal, and tetragonal - cubic close to 30 and 100 °C, respectively. The temperature dependence of electric polarization,pyroelectriccurrent,anddielectricpermittivityfurther supports theferroelectric (tetragonal) toparaelectric (cubic) phasetransition.Moreover,thedielectricpermittivityrevealsthe diffuseness of the phase transition and is attributed to the compositional fluctuations of different polar micro-regions.

Rényi entropy and the thermodynamic stability of black holes

Thermodynamic stability of black holes, described by the Rényi formula as equilibrium compatible entropy function, is investigated. It is shown that within this approach, asymptotically flat, Schwarzschild black holes can be in stable equilibrium with thermal radiation at a fixed temperature. This implies that the canonical ensemble exists just like in anti-de Sitter space, and nonextensive effects can stabilize the black holes in a very similar way as it is done by the gravitational potential of an anti-de Sitter space. Furthermore, it is also shown that a Hawking–Page-like black hole phase transition occurs at a critical temperature which depends on the q-parameter of the Rényi formula.