Determination of local high-frequency dielectric function during the cubic-to-tetragonal phase transformation in barium titanate

Abstract

Transmission electron energy loss spectroscopy was used to obtain local dielectric properties in barium titanate. The high frequency dielectric function of the material was studied dynamically during the cubic-to-tetragonal (c → t) phase transformation in conjunction with the effect of a small amount (0.9%) of donor dopant (niobium). In order to obtain the local dielectric function during the phase transformation, Kramers–Kronig relations were applied to the energy loss measurements. The optical excitations in the energy loss spectra were consistent with band structure results from the literature. The Re (1/∈), real part of the inverse dielectric function, obtained from the energy loss data indicated a change at the phase transformation. Specifically, a broadening of the valence plasmon excitation is observed which is attributed to the order-disorder nature of the t → c transformation. A 0.4 eV shift in the volume plasmon was observed in the Nb-doped sample in all regions (within grains as well as at grain boundaries), indicating a uniform incorporation of the dopant in the lattice. In this paper, the changes in the dielectric function, such as shifts in collective excitations, are attributed to a large contribution from loosely bound Nb electrons. Furthermore, it is demonstrated that it is possible to obtain local (≈10 nm) physical property of a complex material dynamically at relatively high temperature.