Vogel–Fulcher analysis of relaxor dielectrics with the tetragonal tungsten bronze structure: Ba6MNb9O30 (M = Ga, Sc, In)

Abstract

In-depth analysis of the relaxor behaviour of Ba6MNb9O30 (M = Ga, Sc, In) tetragonal tungsten bronze (TTB) ceramics was carried out. Powder X-ray diffraction and scanning electron microscopy were performed in order to confirm the formation of desired phases and to determine the microstructure. Low-temperature dielectric spectroscopy was used in order to characterise the dielectric properties of these materials; the degree of relaxor behaviour was investigated in relation with the increase of ionic radius of the M cation on the B-site of the TTB structure. The dynamics of dielectric relaxation of dipoles was studied by fitting the dielectric permittivity data to the Vogel–Fulcher (VF) model in order to monitor the reproducibility and validity of the physical results. Restrictions to the VF fit were attempted besides the regular “free-fit” by constraining some of the fundamental relaxation parameters to physically sensible values. We show that VF fits are very sensitive to the fitting range resulting in a large range of fundamental parameters for the dielectric relaxation processes, and that the restriction of the frequency domain due to experimental noise or instrumentation limits has a dramatic influence on the values obtained.