Dielectric properties of ferroelectric nanocomposites: effects of thermal stresses and filler shape anisotropy

Abstract

Ferroelectric nanocomposites are intriguing nonhomogeneous materials, which may have unusual phase states and specific physical properties useful for practical applications. Here we theoretically describe dielectric properties of nanocomposites comprising single-domain ferroelectric nanocrystals embedded into a linear dielectric medium. First, small-signal intrinsic permittivities of spheroidal PbTiO3 and BaTiO3 crystallites surrounded by an isotropic matrix with linear elastic properties are calculated with the aid of a nonlinear thermodynamic theory. It is shown that thermal stresses caused by differences in thermal expansion between the inclusions and the matrix may strongly influence the intrinsic permittivities of ferroelectric nanocrystals. Second, macroscopic dielectric responses of ferroelectric–dielectric composites are evaluated in the Maxwell Garnett approximation. For effective permittivities of such composites, generalized relations are derived, which allow for both the shape and dielectric anisotropies of ferroelectric nanocrystals. Numerical calculations of the effective permittivities are performed for composites comprising PbTiO3 and BaTiO3 nanocrystals embedded into representative dielectric matrices generating tensile (silica glass) or compressive (potassium silicate glass) thermal stresses inside ferroelectric inclusions. For nanocomposites involving randomly oriented and similarly aligned spheroidal inclusions, temperature dependences of the effective permittivities are determined with the account of phase transitions occurring in strained ferroelectric nanocrystals and suppression of their dielectric responses due to the depolarizing-field effect created by low-permittivity matrix. Our theoretical calculations show that effective permittivities of composites comprising needle-like or disc-shaped ferroelectric inclusions could strongly exceed the permittivity of the matrix. Most importantly, we predict that BaTiO3–K2O-SiO2 composites with such inclusions should exhibit a broad dielectric peak around the room temperature, which is associated with shifted structural transitions in strained BaTiO3 nanocrystals. The presented theory provides guidelines for the development of ferroelectric nanocomposites with enhanced dielectric responses, which could be suitable for applications in supercapacitors and other advanced electronic devices.