The Williamson-Hall (W-H) equation, which has been used to obtain relative crystallite sizes and strains between samples since 1962, is revisited. A modified W-H equation is derived which takes into account the Scherrer equation, first published in 1918, (which traditionally gives more absolute crystallite size prediction) and strain prediction from Raman spectra. It is found that W-H crystallite sizes are on average 2.11 ± 0.01 times smaller than the sizes from Scherrer equation. Furthermore the strain from the W-H plots when compared to strain obtained from Raman spectral red-shifts yield factors whose values depend on the phases in the materials – whether anatase, rutile or brookite. Two main phases are identified in the annealing temperatures (350 °C–700 °C) chosen herein – anatase and brookite. A transition temperature of 550 °C has been found for nano-TiO2 to irreversibly transform from brookite to anatase by plotting the Raman peak shifts against the annealing temperatures. The W-H underestimation on the strain in the brookite phase gives W-H/Raman factor of 3.10 ± 0.05 whereas for the anatase phase, one gets 2.46 ± 0.03. The new βtot2cos2θ-sinθ plot and when fitted with a polynomial yield less strain but much better matching with experimental TEM crystallite sizes and the agglomerates than both the traditional Williamson-Hall and the Scherrer methods. There is greater improvement in the model when linearized – that is the βtotcos2θ-sinθ plot rather than the βtot2cos2θ-sinθ plot.

Strain and grain size of TiO2 nanoparticles from TEM, Raman spectroscopy and XRD: The revisiting of the Williamson-Hall plot method

Uniform and monodisperse Co-doped In2O3 nanorods were fabricated by a facile and environmentally friendly hydrothermal strategy that combined the subsequent annealing process, and their morphology, structure, and formaldehyde (HCHO) gas sensing performance were investigated systematically. Both pure and Co-doped In2O3 nanorods had a high specific surface area, which could offer abundant reaction sites to gas molecular diffusion and improve the response of the gas sensor. Results revealed that the In2O3/1%Co nanorods exhibited a higher response of 23.2 for 10 ppm of HCHO than that of the pure In2O3 nanorods by 4.5 times at 130 °C. More importantly, the In2O3/1%Co nanorods also presented outstanding selectivity and long-term stability. The superior gas sensing properties were mainly attributed to the incorporation of Co, which suggested the important role of the amount of oxygen vacancies and adsorbed oxygen in enhancing HCHO sensing performance of In2O3 sensors.

One-Step Synthesis of Co-Doped In2O3 Nanorods for High Response of Formaldehyde Sensor at Low Temperature

The influence of the particle size of an active material on its performance as a supercapacitor electrode was reported. Nickel oxide nanoparticles (NiO NPs) with a uniform particle size were synthesized via a facile sol–gel method, and various sizes of NiO NPs (8, 12, and 22 nm) were achieved by calcination at various temperatures (300, 400, and 500 °C). TEM observations and XRD analysis were used to determine the particle size of the NiO NPs. The field emission scanning electron microscopy (FESEM) and transmission electron microscopy (TEM) images showed flake-like morphologies, which consisted of interconnected nanoparticles with a porous channel to facilitate the diffusion of the electrolyte. The NiO NPs with an average particle size of 8 nm gave the highest specific capacitance value of 549 F g−1 at a scan rate of 1 mV s−1 compared to the NiO NPs with average particle sizes of 12 and 22 nm. These results suggest that the particle size of the NiO nanostructure plays an important role because of the presence of a higher number of active sites for a faradaic reaction.

Influence of particle size on performance of a nickel oxide nanoparticle-based supercapacitor

Barium fluoride (BaF2) nanoparticles (NPs) with different sizes were produced through a hydrothermal microwave method (HTMW) The microstructural and electronic properties of the synthesized BaF2 NPs were investigated using X-ray powder diffraction combined with the Rietveld refinement method and Williamson–Hall formalism, X-ray photoemission spectroscopy (XPS) and scanning electron microscopy (SEM) From the Rietveld method, we have found that the lattice parameter of BaF2 NPs is smaller than that observed for BaF2 in its crystal bulk form These results demonstrated that the lattice parameter shows dependence on size of particle, increasing for larger particles, reducing strain-surface effects XPS analyses showed that no other elements were present in the material Photoluminescence (PL) studies in the vacuum ultraviolet (VUV) and visible (VIS) range were also performed to investigate the luminescence properties The PL results showed a slight shift in the self-trapped exciton (STE) edge for samples with higher particle sizes In addition, the band gap energy (Eg) was found to be around 105 eV for all samples The observed lattice contraction/expansion was in concordance with the bond-order-length strength (BOLS) correlation mechanism Therefore, we concluded that this behavior was purely due to surface stress as a result of particle size decreasing

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Particle size effects on structural and optical properties of BaF2 nanoparticles

Nanocomposite films of CeO2 doped polyvinyl alcohol (PVA) of varying concentrations were prepared by a solution casting technique using nanoparticles synthesized by a solution combustion method. Energy Dispersive X-ray (EDX) confirmed the presence of constituent elements in the composite films. The characterization by X-ray Diffraction (XRD) gave the structure of the CeO2 nanoparticles as cubic fluorite and the size of the nanoparticles in the composites as 6.5–44 nm. Scanning Electron Microscopy (SEM) and High Resolution Transmission Electron Microscopy (HRTEM) show homogenous dispersion of nanoparticles with increasing size and some agglomeration for concentrations upto 12.5 wt% while the 25 wt% film is radically different showing a tape-like structure in SEM images and a string of beads-like formation of nanoparticles in the HRTEM images. Raman spectra exhibit shifts as well as new bands in the composites confirming structural change and formation of a new material. The UV-Visible spectrum of the composites exhibit a red shift in the optical band gap with respect to pure PVA and both red and blue shift with respect to nano CeO2 depending on the concentration of the filler. Good absorption in the UV (2.5 wt% and 25 wt%) and visible range (12.5 wt% and 25 wt%) suggest possible use in filters and solar cells. Photoluminescence studies reveal three emission peaks corresponding to the UV region and blue–green regions of the visible range. The maximum PL intensity, nearly equal to that of nano CeO2, was observed for 2.5 wt% films suggesting that this concentration is most suitable for optoelectronic applications.

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J.A. Carvalho

Papers

Size–strain study of NiO nanoparticles by X-ray powder diffraction line broadening