Energy harvesting in core-shell ferroelectric ceramics: Theoretical approach and practical conclusions

Abstract

We have made a quantitative evaluation of the possibility to store electrical energy using ferroelectric supercapacitor built on core-shell nanoceramics. We have first solved the Laplace equation for a single core-shell particle and used afterward an effective medium approximation to get in a self consistent way the equations for the different internal electric field, the permittivity and the polarization of a nanoceramic constituted of such core-shell particles. A numerical calculation was performed to check these results. We could generalize these results in the case of a ceramic made of core-n shells particles, and for different cases of anisotropic shapes of particles. We have introduced afterward the expression of the core-shell polarization into the Landau potential for nanoceramics by Li et al. [J. Appl. Phys. 98, 064101 (2005)] which allows us to get the phases diagrams for different cases of nanoparticles shapes. Numerical minimization of the Landau potential results in curves of polarization versus external electric field, which were numerically integrated to obtain the maximum density of energy that can be stored in the nanoceramic. The influence of several parameters such as the maximum applied electric field or the breakdown field, the permittivity of the shell, and the anisotropy of particles has been considered for different types of dielectric materials. A final table condensates these results, which shows that the possibility of ferro-supercapacitor is fair but one or two order of magnitude lower than those of electrolytic-supercapacitor. However if some limitations like the breakdown field in the ceramics could be overcome, middle-density ferro-supercapacitors could be built and eventually replace current hybrid supercapacitors.