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The calculation of the average grain size of nanocrystalline titania by means of electron microscopy and XRD

Nanocrystalline (NC) titania (TiO2) has enhanced mechanical, magnetic and transport properties in comparison to coarse-grained one. For such properties, the deviation from conventional behaviour is a sensitive function of the average grain size and its distribution [1]. Therefore, it is important to measure the average grain size and grain size distribution and correlate them with physical properties of nanocrystalline materials. Two kinds of nanocrystalline TiO2 samples were prepared by the sol-gel method: a) iron doped TiO2 (TiO2 anatase + Fe solid solution and poly(ethylene)glycol) ; b) undoped TiO2 containing anatase and a small amount of brookite [2]. The samples were annealed which gave the average grain size ranging from 3 to 12 nm. TEM and high-resolution transmission electron microscopy (HRTEM) investigations were carried out by using JEOL JEM 2010 200 kV microscope, Cs=0.5 mm, point resolution of 0.19 nm with a beryllium window energy-dispersive (EDS) detector. For each sample the dark-field (DF) image, bright-field (BF) and HRTEM image were recorded and the average grain size was determined by measuring individual grains from captured micrographs. The X-ray diffraction (XRD) measurements of the samples were carried out at room temperature on a Philips powder diffractometer (PW 1820) with monochromatized CuK radiation. The corrections due to the instrumental broadening of diffraction lines were done using XRD pattern of NIST LaB6 crystalline standard. The average grain size and its distribution were determined by means of the direct method using dark-field TEM images taken from (101) nanocrystalline ring of anatase (Figure 1a) by measuring grain diameters in one fixed direction [3]. The corresponding selected area electron diffraction pattern (SAED) consists of characteristic rings for NC materials (Figure 1b). The same analysis was done from complementary bright-field image (Figure 1c), while the average grain size from HRTEM images was determined by measuring grain diameters in a direction perpendicular to the direction of nanocrystalline planes. To calculate the average grain size from broadening of XRD peaks of TiO2 anatase, we applied Rietveld refinement of XRD pattern. The basic assumption for this size-strain analysis is representation of size broadening profile by Lorentzian function and microstrain broadening profile by Gaussian function. The obtained results for hkl dependence of average grain sizes and microstrains show isotropic character of line broadening. The goodnes of fitting was tested by means of values of Rwp, whose values were below 10 %, indicating satisfied fit, which is shown in Figure 1d. Good agreement between the average grain sizes determined by the Rietveld method and TEM (HRTEM) indicates the complementarity of direct and indirect method that we performed in the grain size analysis.

nanocrystalline; titania; average grain size

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