Difference between revisions of "Talk:Scattering"

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(cont)
(cont)
Line 77: Line 77:
 
     & = \frac{d^2x^2+d^2z^2 + d^6 -2d^3\sqrt{d^2+x^2+d^2z^2} + d^2+x^2+d^2z^2}{d^2+x^2+d^2z^2}  \\
 
     & = \frac{d^2x^2+d^2z^2 + d^6 -2d^3\sqrt{d^2+x^2+d^2z^2} + d^2+x^2+d^2z^2}{d^2+x^2+d^2z^2}  \\
 
     & = \frac{d^6 + d^2 + d^2x^2 + x^2 + 2d^2z^2 -2d^3\sqrt{d^2+x^2+d^2z^2}}{d^2+x^2+d^2z^2}  \\
 
     & = \frac{d^6 + d^2 + d^2x^2 + x^2 + 2d^2z^2 -2d^3\sqrt{d^2+x^2+d^2z^2}}{d^2+x^2+d^2z^2}  \\
     & = ? \\
+
     & = \frac{ (x^2 + z^2) } {(d^2 + x^2 + z^2)} \frac{(d^2 + x^2 + z^2)}{ (x^2 + z^2) } \frac{d^6 + d^2(1+x^2+2z^2) + x^2 -2d^3\sqrt{d^2(1+z^2)+x^2}}{d^2(1+z^2)+x^2}  \\
    & = ? \\
 
 
     & = ? \\
 
     & = ? \\
 
     & = \frac{ x^2 + z^2 } {d^2 + x^2 + z^2} \\
 
     & = \frac{ x^2 + z^2 } {d^2 + x^2 + z^2} \\

Revision as of 09:32, 30 December 2015

TSAXS 3D

The q-vector in fact has three components:

Consider that the x-ray beam points along +y, so that on the detector, the horizontal is x, and the vertical is z. We assume that the x-ray beam hits the flat 2D area detector at 90° at detector (pixel) position . The scattering angles are then:

where is the sample-detector distance, is the out-of-plane component (angle w.r.t. to y-axis, rotation about x-axis), and is the in-plane component (rotation about z-axis). The alternate angle, , is the elevation angle in the plane defined by . Also note that the full scattering angle is:

The momentum transfer components are:

Check

As a check of these results, consider:

Where we used:

And, we further note that:

cont

Continuing: