X-ray powder diffraction line broadening analysis of the nanocrystalline tin dioxide by the classical Warren-Averbach approach

In the present study, the X-ray diffraction line profile analysis technique has been applied to investigating the microstructure of nanocrystaline materials in terms of average crystallite sizes, size distributions and micro strains. We have calculated the size and strain Fourier coefficients by using classical Warren-Averbach method for the two (110) and (220) reflections. Assuming that the grain size distribution in the nanocrystaline SnO₂ can be approximated by a log normal function, the area- and volume-weighted average grain size value were estimated as $16.14\pm 0.23$ and $19.67\pm 0.23$ nm, respectively. To validate the results obtained from Warren-Averbach analysis, the obtained size was compared by the SEM results reported in our previous work and the results are in good agreement. The behavior of strain indicates the extent of the inhomogeneous strain distribution which causes the broadening of X-ray line profile in the crystalline lattice of tin dioxide nanoparticles.