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

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 were 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 Vogel-Fulcher 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 to instrumentation limits has a dramatic influence on the values obtained.