Scherrer Equation

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Masahisa Wada - One of the best experts on this subject based on the ideXlab platform.

  • thermal decomposition of native cellulose influence on crystallite size
    Polymer Degradation and Stability, 2010
    Co-Authors: Masahisa Wada
    Abstract:

    Abstract The thermal degradation behavior of crystalline cellulose has been investigated using thermogravimetry, differential thermal analysis, and derivative thermogravimetry in a nitrogen atmosphere. Three cellulose samples, Halocynthia , cotton, and commercial microcrystalline cellulose Funacel, were used in this study to analyze the influence on crystallite size. They all belongs to cellulose I β type and those crystallite sizes calculated from the X-ray diffractometry profiles by Scherrer Equation were very different in the order Halocynthia  > cotton > Funacel. The thermal decomposition of cellulose shifted to higher temperatures with increasing crystallite size. However, activation energies for the thermal degradation were the almost the same among the samples: 159–166 kJ mol −1 . These results indicated that the crystal structure does not affect the activation energy of the thermal degradation but the crystallite size affects the thermal degradation temperature.

Ignatius Y Chan - One of the best experts on this subject based on the ideXlab platform.

Bonex W. Mwakikunga - One of the best experts on this subject based on the ideXlab platform.

  • Strain and grain size of TiO2 nanoparticles from TEM, Raman spectroscopy and XRD: The revisiting of the Williamson-Hall plot method
    Results in Physics, 2018
    Co-Authors: Pierre M. Kibasomba, Simon Mokhotjwa Dhlamini, Malik Maaza, Chuan-pu Liu, Mohamed M. Rashad, D. A. Rayan, Bonex W. Mwakikunga
    Abstract:

    Abstract 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
    Elsevier, 2018
    Co-Authors: Pierre M. Kibasomba, Simon Mokhotjwa Dhlamini, Malik Maaza, Chuan-pu Liu, Mohamed M. Rashad, D. A. Rayan, Bonex W. Mwakikunga
    Abstract:

    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. Keywords: Williamson-Hall, Scherrer, Particle, Crystallite, Strain, Siz

Allen W Burton - One of the best experts on this subject based on the ideXlab platform.

John R Lombardi - One of the best experts on this subject based on the ideXlab platform.

  • raman investigation of nanosized tio2 effect of crystallite size and quantum confinement
    Journal of Physical Chemistry C, 2012
    Co-Authors: Wei Ji, Yue Wang, Xu Wang, Weidong Ruan, Bing Zhao, John R Lombardi
    Abstract:

    The influence of the TiO2 particle size on the enhanced Raman spectroscopy properties was systematically investigated on the nanometer-size scale. We report on the enhanced Raman spectrum of 4-mercaptobenzoic acid adsorbed on TiO2 nanoparticles. The results presented in this study highlight the major findings that the intensities of both the molecular lines and the phonon modes of TiO2 are strongly size-dependent. The TiO2 crystallite size estimated using the Scherrer Equation varied from 6.8 to 14.2 nm; as a function of crystal size, a large increase in intensity is observed, with a maximum near 10.9 nm and a subsequent decline at larger sizes. Moreover, we have investigated quantum confinement effects between TiO2 and the adsorbed molecules and attribute this to a charge-transfer resonance, which is responsible for the Raman enhancement.