Composite materials composed of multiferroelectric nanoparticles in dielectric matrixes have attracted enormous attention for their potential applications in developing future functional devices. However, the functionalities of ferroelectric nanoparticles depend on shapes, sizes, and materials. In this paper, a time-dependent Landau-Ginzburg method has been used and combined with a method as the coupled-physics finite-element-method-based simulations are used to illustrate the polarization behavior in isolated BaTiO3 or PbTiO3 octahedral nanoparticles embedded in a dielectric medium, like SrTiO3 (ST, high dielectric permittivity) and amorphous silica (a-SiO2, low dielectric permittivity). The equilibrium polarization topology of the octahedral nanoparticle is strongly affected by the choice of inclusion and the size of matrix materials. Also, there are three equilibrium polarization patterns, i.e., monodomain, vortex-like, and multidomain, because of the various sizes and material parameters combination. There is a critical particle size below which ferroelectricity vanishes in our calculations. This size of the PbTiO3 octahedral nanoparticle is 2.5 and 3.6 nm for high- and low-permittivity matrix materials, respectively. However, this size of the BaTiO3 octahedral nanoparticle is 3.6 nm regardless of the matrix materials.
Computing Protein pKas Using the TABI Poisson–Boltzmann Solver
