The core mathematics, goodness-of-fit parameters of Rietveld refinement technique is introduced for structural analysis of crystalline materials not available as single crystals. X-ray diffraction (XRD) patterns of PbTiO₃ compound prepared by following solid-state route, suggests it to be in single crystal form. All the observed peaks could be indexed to $P4mm$ space group with tetragonal symmetry. XRD pattern is analysed by employing Rietveld method. The unit cell parameters are found to be 𝑎 = 𝑏 = 3.8987 (0.0008) Å and 𝑐 = 4.1380 (0.0009) Å. The axial ratio 𝑐/𝑎 and unit cell volume are found to be 1.0614 and 62.896 (0.023) ų. Bond lengths and angles are calculated using the cell parameters. Using the Rietveld refinement parameters a stable PbTiO₃ structure is suggested.

The polycrystalline samples of Pb(Zr_0.65−𝑥A_𝑥Ti_0.35)O₃ (A = Mn/Fe), (𝑥 = 0.00, 0.05) (PZM/FT) were synthesized by conventional solid-state reaction technique. X-ray diffraction (XRD) pattern was recorded at room temperature and the samples were found in single phase form. All the observed peaks could be indexed to 𝑅3𝑐 space group with rhombohedral symmetry. XRD pattern has been analysed by employing Rietveld method with the help of FullProf Program. The lattice parameters and unit cell volumes decrease from Mn³⁺ to Fe³⁺ ion concentrations. The bond lengths and angles have been calculated by using Powder Cell Programme. Microstructural analysis of the surface of the ceramic compound by scanning electron microscopy (SEM) exhibits that there is a significant change in grain size on introduction of Mn³⁺ and Fe³⁺ ions at the Zr-site of the compound. It is observed that both the substitutions (Mn³⁺ and Fe³⁺) at Zr site induce an increase in dielectric constant and a shift in Curie temperature (𝑇_c). From a.c. conductivity analysis, we have estimated the activation energy for both ferroelectric and paraelectric regions. Both the modified samples are obeying Jonscher power law. From Nyquist plots, the activation energy of grain resistance, relaxation time and bulk conductivity are compared. The grain resistance of the material decreases with rise in temperature which indicates a semiconducting behaviour of the material.