Mathematical aspects of Rietveld refinement and crystal structure studies on PbTiO ceramics.

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 PbTiO compound prepared by following solid-state route, suggests it to be in single crystal form. All the observed peaks could be indexed to P4 mm space group with tetragonal symmetry. XRD pattern is analysed by employing Rietveld method. The unit cell parameters are found to be a = b = 38987 (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) Å. Bond lengths and angles are calculated using the cell parameters. Using the Rietveld refinement parameters a stable PbTiO structure is suggested. [ABSTRACT FROM AUTHOR]