KevinYager at 19:33, 27 July 2018

2018-07-27T19:33:46Z

KevinYager: Created page with "Consider a hexagonal lattice viewed end-on using scattering. For instance, hexgaonally-packed-cylinder block-copolymer moprhology that is oriente..."

2018-07-27T19:26:41Z

Created page with "Consider a hexagonal lattice viewed end-on using scattering. For instance, hexgaonally-packed-cylinder block-copolymer moprhology that is oriente..."

New page

Consider a [[Lattice:hexagonal|hexagonal]] lattice viewed end-on using [[scattering]]. For instance, hexgaonally-packed-cylinder [[block-copolymer]] moprhology that is oriented horizontally ('laying down'; i.e. cylinder long axes parallel to the substrate plane). There will be a peak along the specular at <math>(q_x, q_z) = (0, q_{l})</math>, where <math>q_l</math> corresponds to the cylinder layering distance in realspace (i.e. the distance between subsequent rows of cylinders). The full set of peaks is:
* <math>(q_x, q_z) = (0, +q_l)</math>
* <math>(q_x, q_z) = \left ( -\frac{\sqrt{3}}{2} q_l, +\frac{q_l}{2} \right )</math> and <math>(q_x, q_z) = \left ( +\frac{\sqrt{3}}{2} q_l, +\frac{q_l}{2} \right )</math>
* <math>(q_x, q_z) = \left ( -\frac{\sqrt{3}}{2} q_l, -\frac{q_l}{2} \right )</math> and <math>(q_x, q_z) = \left ( +\frac{\sqrt{3}}{2} q_l, -\frac{q_l}{2} \right )</math>
* <math>(q_x, q_z) = (0, -q_l)</math>
Since:
: <math>\cos 30^{\circ} = \frac{\sqrt{3}}{2}</math>
: <math>\sin 30^{\circ} = \frac{{1}}{2}</math>

The realspace layering distance is:
: <math>d_l = \frac{2 \pi}{q_l}</math>
And the realspace cylinder-cylinder distance is:
: <math>d_{cc} = </math>

@@ Line 1: / Line 1: @@
-Consider a [[Lattice:hexagonal|hexagonal]] lattice viewed end-on using [[scattering]]. For instance, hexgaonally-packed-cylinder [[block-copolymer]] moprhology that is oriented horizontally ('laying down'; i.e. cylinder long axes parallel to the substrate plane). There will be a peak along the specular at <math>(q_x, q_z) = (0, q_{l})</math>, where <math>q_l</math> corresponds to the cylinder layering distance in realspace (i.e. the distance between subsequent rows of cylinders). The full set of peaks is:
+Consider a [[Lattice:Hexagonal|hexagonal]] lattice viewed end-on using [[scattering]]. For instance, a hexagonally-packed-cylinder [[block-copolymer]] moprhology that is oriented horizontally ('laying down'; i.e. cylinder long axes parallel to the substrate plane). There will be a peak along the specular at <math>(q_x, q_z) = (0, q_{l})</math>, where <math>q_l</math> corresponds to the cylinder layering distance in realspace (i.e. the distance between subsequent rows of cylinders). Since:
 * <math>(q_x, q_z) = (0, +q_l)</math>
 * <math>(q_x, q_z) =  \left ( -\frac{\sqrt{3}}{2} q_l, +\frac{q_l}{2}  \right )</math> and <math>(q_x, q_z) =  \left ( +\frac{\sqrt{3}}{2} q_l, +\frac{q_l}{2}  \right )</math>
 * <math>(q_x, q_z) =  \left ( -\frac{\sqrt{3}}{2} q_l, -\frac{q_l}{2}  \right )</math> and <math>(q_x, q_z) =  \left ( +\frac{\sqrt{3}}{2} q_l, -\frac{q_l}{2}  \right )</math>
 * <math>(q_x, q_z) = (0, -q_l)</math>
 The realspace layering distance is:
 : <math>d_l = \frac{2 \pi}{q_l}</math>
 And the realspace cylinder-cylinder distance is:
-: <math>d_{cc} = </math>
+: <math>\begin{alignat}{2}

Extra:Hexagonal peaks - Revision history

KevinYager at 19:33, 27 July 2018

KevinYager: Created page with "Consider a hexagonal lattice viewed end-on using scattering. For instance, hexgaonally-packed-cylinder block-copolymer moprhology that is oriente..."