Influence of the Processes Parameters on the Properties of The ...
Influence of the Processes Parameters on the Properties of The ...
Influence of the Processes Parameters on the Properties of The ...
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Chapter 3.<br />
Analytical Methods and Designs <str<strong>on</strong>g>of</str<strong>on</strong>g> Experiments<br />
also caters <str<strong>on</strong>g>the</str<strong>on</strong>g> light refracti<strong>on</strong> with <str<strong>on</strong>g>the</str<strong>on</strong>g> particle (sec<strong>on</strong>dary scattering) which is very important when particle<br />
diameter is below 50 μm. This is also menti<strong>on</strong>ed in <str<strong>on</strong>g>the</str<strong>on</strong>g> standard for laser diffracti<strong>on</strong> measurements (ISO<br />
133201) [Kippax, 2005]. According to Lorenz-Mie’ <str<strong>on</strong>g>the</str<strong>on</strong>g>ory <str<strong>on</strong>g>the</str<strong>on</strong>g> scattering patterns <str<strong>on</strong>g>of</str<strong>on</strong>g> spheres are symmetric<br />
with axis <str<strong>on</strong>g>of</str<strong>on</strong>g> <str<strong>on</strong>g>the</str<strong>on</strong>g> incident light. Scattering minima and maxima are in different angles, if <str<strong>on</strong>g>the</str<strong>on</strong>g> properties <str<strong>on</strong>g>of</str<strong>on</strong>g> <str<strong>on</strong>g>the</str<strong>on</strong>g><br />
particles vary. Figure 3.9, shows <str<strong>on</strong>g>the</str<strong>on</strong>g> diffracti<strong>on</strong> patterns <str<strong>on</strong>g>of</str<strong>on</strong>g> two particles with different sizes [Xu, 2000].<br />
With large particle (solid line) <str<strong>on</strong>g>the</str<strong>on</strong>g> peak <str<strong>on</strong>g>of</str<strong>on</strong>g> intensity is str<strong>on</strong>ger than with small particle (dashed line) and <str<strong>on</strong>g>the</str<strong>on</strong>g><br />
minimum intensity is much closer to axis <str<strong>on</strong>g>of</str<strong>on</strong>g> <str<strong>on</strong>g>the</str<strong>on</strong>g> incident light. <strong>The</strong> intensity peaks are in <str<strong>on</strong>g>the</str<strong>on</strong>g> same locati<strong>on</strong>s<br />
in <str<strong>on</strong>g>the</str<strong>on</strong>g> both positive and negative angles because <str<strong>on</strong>g>the</str<strong>on</strong>g> symmetrical nature <str<strong>on</strong>g>of</str<strong>on</strong>g> scattering. Very illustrative way<br />
<str<strong>on</strong>g>of</str<strong>on</strong>g> displaying <str<strong>on</strong>g>the</str<strong>on</strong>g> intensity distributi<strong>on</strong> is also a radial graph as in Figure 3.9. <strong>The</strong> bold trace describes <str<strong>on</strong>g>the</str<strong>on</strong>g><br />
intensity <str<strong>on</strong>g>of</str<strong>on</strong>g> scattered light in different angles [Xu, 2000].<br />
Figure 3.9: Scattering patterns <str<strong>on</strong>g>of</str<strong>on</strong>g> two particles <str<strong>on</strong>g>of</str<strong>on</strong>g> a different size.<br />
[Xu, 2000]<br />
3.2.3 Fraunh<str<strong>on</strong>g>of</str<strong>on</strong>g>er’ <strong>The</strong>ory<br />
Fraunh<str<strong>on</strong>g>of</str<strong>on</strong>g>er’ <str<strong>on</strong>g>the</str<strong>on</strong>g>ory covers <str<strong>on</strong>g>the</str<strong>on</strong>g> light diffracti<strong>on</strong> in <str<strong>on</strong>g>the</str<strong>on</strong>g> aperture which is described in Fresnel-<br />
Kirch<str<strong>on</strong>g>of</str<strong>on</strong>g>f’ diffracti<strong>on</strong> integral [Brittain, 2003]. In Fresnel diffracti<strong>on</strong> (Figure 3.10-A), distances from <str<strong>on</strong>g>the</str<strong>on</strong>g><br />
point source and <str<strong>on</strong>g>the</str<strong>on</strong>g> screen to <str<strong>on</strong>g>the</str<strong>on</strong>g> obstacle forming <str<strong>on</strong>g>the</str<strong>on</strong>g> diffracti<strong>on</strong> pattern are relatively short. In Fraunh<str<strong>on</strong>g>of</str<strong>on</strong>g>er’<br />
diffracti<strong>on</strong> (Figure 3.10-B), <str<strong>on</strong>g>the</str<strong>on</strong>g> distances are much l<strong>on</strong>ger and all lines from <str<strong>on</strong>g>the</str<strong>on</strong>g> source to <str<strong>on</strong>g>the</str<strong>on</strong>g> obstacle and<br />
forward to <str<strong>on</strong>g>the</str<strong>on</strong>g> screen can be c<strong>on</strong>sidered parallel. In Figure 3.10-C, <str<strong>on</strong>g>the</str<strong>on</strong>g> lens forms smaller image <str<strong>on</strong>g>of</str<strong>on</strong>g> <str<strong>on</strong>g>the</str<strong>on</strong>g> same<br />
diffracti<strong>on</strong> pattern which would be formed <strong>on</strong> <str<strong>on</strong>g>the</str<strong>on</strong>g> screen extremely far without <str<strong>on</strong>g>the</str<strong>on</strong>g> lens [Young and<br />
Freedman, 2000].<br />
(A) (B) (C)<br />
Figure 3.10: Principles <str<strong>on</strong>g>of</str<strong>on</strong>g> Fresnel’ diffracti<strong>on</strong> (A) and Fraunh<str<strong>on</strong>g>of</str<strong>on</strong>g>er’ diffracti<strong>on</strong> (B and C).<br />
[Young and Freedman, 2000]<br />
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