Kramers–Kronig method for determination of optical properties of PZT nanotubes fabricated by sol–gel method and porous anodic alumina with high aspect ratio

Abstract

Ferroelectric Pb(ZrTi)O3 (PZT) nanotubes were prepared by sol–gel method and porous anodic alumina (PAA) membrane using spin-coating technique. This method is based on filling-pyrolysis-filling process and the use of one-stage alumina membranes. One of the advantages of this method is its rapidity, which takes only 1 h time before the calcination step. The effect of repeated pores filling was investigated to get the required size of nanotubes. The field emission scanning electron microscope (FE-SEM) images were shown that the PZT nanotubes have inner diameters in the range of 65–90 nm and length of about 50–60 [Formula: see text]m. This means that the samples have a significant aspect ratio (700–800). Also the FE-SEM image confirmed that the highly ordered, hexagonally distributed PAA membranes with the pore diameter about 140–150 nm were formed. The X-ray diffraction (XRD) results showed that the PZT nanotubes have a tetragonal structure. The metal oxide bands like ZrO6 and TiO6 of the final PZT nanotubes were detected by Fourier transform infrared (FT-IR) analysis and confirmed the formation of perovskite structure. By using FT-IR spectroscopy and Kramers–Kronig transformation method, the optical constants like real [Formula: see text]([Formula: see text]) and imaginary [Formula: see text]([Formula: see text]) parts of dielectric function, extinction coefficient k([Formula: see text]) and refractive index n([Formula: see text]) were determined. It was shown that the optical constants of PZT nanotubes are different from PZT nanoparticles.