Analysis of the extended defects in 3C-SiC.pdf - Nelson Mandela ...
Analysis of the extended defects in 3C-SiC.pdf - Nelson Mandela ...
Analysis of the extended defects in 3C-SiC.pdf - Nelson Mandela ...
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37<br />
Fig. 4.1. (a) A wave <strong>in</strong>cident on a set <strong>of</strong> hkl planes at an angle θ, (b) <strong>the</strong> <strong>in</strong>cident and<br />
diffracted directions and <strong>the</strong> plane normal must lie <strong>in</strong> a planar section through a<br />
conical surface with its top <strong>in</strong> <strong>the</strong> plane (from De Graef (2003))<br />
A wave is <strong>in</strong>cident on a set <strong>of</strong> planes with <strong>in</strong>dices (hkl) at an angle θ. Assum<strong>in</strong>g <strong>the</strong><br />
planes to be semi-transparent mirrors, part <strong>of</strong> <strong>the</strong> <strong>in</strong>tensity <strong>of</strong> <strong>the</strong> wave will be<br />
transmitted through <strong>the</strong> first plane and part <strong>of</strong> it reflected. If Snell’s law is applied<br />
s<strong>in</strong>ce an ideal mirror was assumed, <strong>the</strong> <strong>in</strong>cident and reflected angles must be <strong>the</strong> same,<br />
and both directions <strong>of</strong> <strong>the</strong> wave must be coplanar about a normal n to <strong>the</strong> (hkl) planes.<br />
Next, if <strong>the</strong> reflected waves from <strong>the</strong> first and second planes are considered it is seen<br />
that <strong>the</strong>re is a difference <strong>in</strong> path length between <strong>the</strong> two which relate to <strong>the</strong> waves<br />
be<strong>in</strong>g <strong>in</strong> or out <strong>of</strong> phase. This path length difference is given by <strong>the</strong> sum <strong>of</strong> <strong>the</strong><br />
distance PO’ and O’Q which <strong>in</strong> turn is related to <strong>the</strong> <strong>in</strong>terplanar spac<strong>in</strong>g dhkl and <strong>the</strong><br />
angle θ as follows:<br />
PO'O'Q d<br />
hkl<br />
2d<br />
s<strong>in</strong> d<br />
hkl<br />
s<strong>in</strong> <br />
hkl<br />
s<strong>in</strong> <br />
(4.1)<br />
For <strong>in</strong>-phase propagation <strong>of</strong> <strong>the</strong> two reflected waves, known as constructive<br />
<strong>in</strong>terference, <strong>the</strong> path length difference should be an <strong>in</strong>tegral number <strong>of</strong> wavelengths<br />
and thus for constructive <strong>in</strong>terference <strong>the</strong> relation is,<br />
2 s<strong>in</strong> n<br />
(4.2)<br />
d hkl