engleski

The Rietveld refinement of XRD data obtained on nanocrystalline TiO2

TiO2 is used in many applications such as photovoltaic devices, integrated wave guides, gas and humidity sensors, inorganic membranes, catalyst supports and electrochemical displays. Due to the grain-size dependence of structural parameters of nanocrystalline TiO2 such as: lattice parameters, Debye-Waller factors, microstrain, etc..., it seems obvious to explore this dependence and find smooth function which matches to experimental data. In this work we examined different (undoped and iron-doped) TiO2 samples prepared by the sol-gel route. They were characterised by means of X-ray diffraction measurements (XRD) on a Philips powder diffractometer (PW 1820) and selected area electron diffraction (SAED) by using JEOL JEM 2010 200 kV microscope, Cs=0.5 mm, point resolution of 0.19 nm. The Rietveld refinement of XRD and SAED data was applied in order to extract structural parameters such as unit cell parameters, bond lengths and angles. The obtained XRD patterns were analyzed by the Rietveld method using program FULLPROF [J. Rodriguez-Carvajal, FULLPROF- A program for Rietveld Refinement, Laboratoire Leon Brillouin, CEA-Saclay, France]. The values of refined unit cell parameters a and c of anatase are above/below ICDD values (a0=0.37852 nm, c0=0.95139 nm) within our grain size range (5-12 nm). By the increase of average grain size, the anatase unit cell parameters are approaching to ICDD values obtained from conventional polycrystalline materials. Fitting the relative deviations from ICDD values  a,  c ( a=(a-a0)/a0) to the inverse average grain size 1/D, asumming potential scaling law  a,  c 1/D , we obtained almost linear dependence for parameter c ( =0.9 0.2) and almost squared dependence for parameter a ( =2.0 0.6). Similarly, the fitting of r.m.s. microstrain   2 0.5 to the inverse average grain size yielded to exponent value  =0.7 0.2. The relative deviations from ICDD values  a,  c and r.m.s. microstrain   2 0.5 could be identified as a measure of defects, or more precisely defect concentration cd in nanocrystalline material. A model in which defects are uniformly distributed throughout individual grains, but present in larger concentration with smaller grain-sizes, such that cd 1/D, could be the model which gave the best description of observed grain-sized behaviour of TiO2 prepared by the sol-gel method [Eastman  Fitzsimmons, J. Appl. Phys. 77 (2), (1995) 522-527]. Significant changes of lattice parameters were found between undoped and iron doped samples in parameter a for 0.08 % and c 0.69 % (XRD) and a 1.6 %, c 0.5 % (SAED). The changes are observed in bond lengths and angles.

Rietveld; nanocrystalline

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