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The crystallite size (P) of Dy doped samples were roughly estimated from the broadening of a few XRD peaks (in a wide 2θ range) using the Scherrer's equation [19], (P = Klambda (beta_{{frac{1}{2}}} cos theta_{text{hkl}} )) (where K = constant = 0.89, λ = 1.5405 Å and β 1/2 = peak width of the reflection at half intensity).
The positions of the equatorial 1 10, 110, and 200 reflections were each fit with a linear baseline and an asymmetric function of the form where k is a scaling constant, Io is the maximal intensity at 2θ = 2θo, σ is a constant describing the radial width of the reflection, and f(2θ) = 0.3(2θ – 2θo) when 2θ < 2θo but zero when 2θ > 2θo.
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The effects of the wave steepness, the blockage coefficient of perforated wall and the relative wave chamber width on the reflection coefficient are clarified.
Sample 1 NA, however, exhibits a better pore arrangement than sample 2 NA according to the higher intensity and smaller width of the (100) reflection.
The width of the 200 reflection was slightly less than was observed by WAXS implying, if anything, a slightly greater Scherrer dimension perpendicular to the sheets of chains.
The width of the 006 reflection in gave a strain distribution of on the grating, in direct agreement with Yang & Mohideen, who estimated a shear strain perpendicular to a domain wall in the LN analogue, LiTaO, of (Yang & Mohideen, 1998 ▶).
Both tilting and nontilting modes were therefore used to collect the unit cell dimensions presented here, but only the tilting mode was used to measure any changes in the radial width of the 004 reflection that might indicate a redistribution of stress between microfibrils when the sample was stretched.
The grain growth is observed by analysing the thermal evolution of the width of the XRD reflections.
(The width of the KTA reflections in was not measured, so the strain distribution contained in the sample was unknown).
Wide intersheet spacing and a small monoclinic angle are features normally associated with primary-wall celluloses [ 13, 15, 28], but the radial width of the equatorial reflections from bamboo cellulose was considerably less than has been observed from primary-wall celluloses, indicating either greater crystallite dimensions or less disorder.
It is found that such a structure has wider reflection bands in comparison to a conventional dielectric PC structure and the width of the omni-directional reflection (ODR) bands can be enlarged by increasing the value of the gradual constant δ.
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