Simulation of XRD data by modified Arrhenius and Lorentz equations for (Na0.5Bi0.5)0.94Ba0.06(Ti1-2xZrxCex)O3 ferroelectric ceramics having rhombohedral crystal structure

Abstract

In the present paper ferroelectric ceramics with chemical formula (Na0.5Bi0.5)0.94Ba0.06(Ti1-2xZrxCex)O3 (x = 0.01, 0.02, 0.03 & 0.04) were prepared by calcinations at 900 °C for 2 h. X-ray diffraction (XRD) patterns were obtained on these ceramic samples. For the first time we have shown a procedure to obtain Lattice parameters (a, αo) and activation energy by simulation of XRD data with modified Arrhenius and Lorentz equations. The modified Arrhenius and Lorentz equation is found to best fit to the experimental XRD data. From this simulation studies we have obtained lattice parameters and activation energy for various range of two theta values. The average values of lattice parameters are 6.0933 Ao, 6.1050 Ao, 6.2372 Ao, & 6.3154 Ao for x = 0.01, 0.02, 0.03 & 0.04 respectively. The average values of angle in degrees are 89.20, 87.67, 89.99 & 89.27 for x = 0.01, 0.02, 0.03 & 0.04 respectively. The average values of activation energy are 345 meV, 483 meV, 557 meV & 709 meV for x = 0.01, 0.02, 0.03 & 0.04 respectively. The simulation of XRD data shown in this paper can also be extended to other compounds to obtain the lattice parameters and activation energy.