Complex dielectric, electric modulus, impedance, and optical conductivity of Sr<sub>3−<i>x</i> </sub>Pb<sub> <i>x</i> </sub>Fe<sub>2</sub>TeO<sub>9</sub> (<i>x</i> = 1.50, 1.88 and 2.17)
Abdelhadi El Hachmi, Bouchaib Manoun
Abstract
Abstract Sr 3− x Pb x Fe 2 TeO 9 ( x = 1.50, 1.88 and 2.17) were synthesized in polycrystalline form via the solid-state reaction route in air, and were studied at room temperature using powder X-ray diffraction and ultraviolet visible spectroscopy techniques. The crystal structures were resolved by the Rietveld refinement method; x = 1.50 and 1.88 adopt a tetragonal phase (space group I 4/ mmm ) while x = 2.17 adopts a hexagonal phase (space group R <m:math xmlns:m="http://www.w3.org/1998/Math/MathML"> <m:mrow> <m:mover accent="true"> <m:mrow> <m:mn>3</m:mn> </m:mrow> <m:mo>̄</m:mo> </m:mover> </m:mrow> </m:math> $\bar{3}$ m ). The direct bandgap energy ( E g ) of ∼1.89 eV for ( x = 1.50), ∼1.87 eV for ( x = 1.88) and ∼1.74 eV for ( x = 2.17) was estimated from the Tauc plots of ( αhʋ ) 2 versus photon energy. The Urbach energy ( E U ) was determined from the plots of logarithmic absorption coefficient versus hυ . Plots of the incident photon energy dependence of optical parameters such as refractive index, extinction coefficient, real and imaginary parts of the dielectric function, dielectric loss, real and imaginary parts of the complex optical conductivity, linear and nonlinear optical susceptibilities, real and imaginary parts of the electric modulus, real and imaginary parts of the impedance were obtained by means of ultraviolet visible spectrophotometer experiments. Additionally, the estimated values of the single oscillator energy, dispersion energy, static refractive index and high-frequency dielectric constant were obtained from the linear portion of the ( n 2 − 1) −1 versus ( hυ ) 2 plots using the Wemple–DiDomenico model.