Mathematical aspects of Rietveld refinement and crystal structure studies on PbTiO3 ceramics

Abstract

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 3 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) Å 3. Bond lengths and angles are calculated using the cell parameters. Using the Rietveld refinement parameters a stable PbTiO 3 structure is suggested.

Crystal growth, luminescence, and scintillation properties of Zn2Te3O8 crystal for 0νββ decay search

“…Details about the Rietveld refinement method can be found elsewhere in ref. 30. The w R p values obtained in this analysis were less than 15% and are in the acceptable range (w R p < 15%) for a monoclinic complex.…”

PbMoO4 Synthesis from Ancient Lead and Its Single Crystal Growth for Neutrinoless Double Beta Decay Search

“…These parameters are mentioned in Figure 4a,b, respectively, and used to calculate the GOF. Details about the Rietveld refinement method can be found elsewhere in [32].The wR p values were less than 9% for both PMO crystals, which are in the acceptable (wR p < 10%) range for a medium complex phase such as tetragonal [14]. Moreover, the GOF of 1.09 and 1.15 were obtained for PMO-K1 and PMO-K2, respectively, showing good quality of the refinement.…”

Structural, Microstructural, and Electrical Properties Study of Pb(Sn0.45Ti0.55)O3 Ceramics

“…The visual inspection confirm very good matching of the experimental XRD profile with the calculated graph from Rietveld refinement. The Rietveld parameters like the profile residual (Rp), the weighted profile factor (Rwp), the expected weighted profile factor (R exp ) and the goodness of fit ( ) 34 The unit cell of PST is modeled by VESTA software using the parameters obtained from Rietveld refinement of XRD data. In the unit cell of PST, the Pb atom occupies 1a (0, 0, 0) site, Ti and Sn occupies 1b (0.5, 0.5, 0.55) site, O1 occupies1b (0.5, 0.5, 0.05) site and O2 occupies 2c (0.5, 0, 0.57) site.…”