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Basic neutron scattering next up previous
Next: Basic understanding of instrument Up: McStas neutron ray-trace tutorial Previous: Goals and tasks

Basic neutron scattering

You may recall the Bragg law from your high school physics

\begin{displaymath}n\lambda=2d\sin(\theta),\end{displaymath}

giving the scattering condition for a wave of wavelength $\lambda$ against a series of lattice planes with lattice spacing $d$, rotated the angle $\theta$ off the lattice plane normal. $n$ is an integer giving the spectral order of the scattered wave. In neutron science one often refers to the scattering vector, $\vec{\kappa}$ of a given reflection, where

\begin{displaymath}\kappa=\vert\vec{\kappa}\vert=n\frac{2\pi}{d}.\end{displaymath}

This gives us the scattering vector formulation of the Bragg law

\begin{displaymath}\kappa=2k\sin(\theta),\end{displaymath}

where $k=\frac{2\pi}{\lambda}$. The Bragg law / scattering condition is illustrated in Figure 1.
Figure 1: Illustration of the Bragg Law.
\includegraphics[width=9cm]{pics/bragg.eps}
Most of the neutron processes we will study in this paper are elastic, meaning that the wavelength of the neutron is unaltered by the process.

Peter Kjær Willendrup 2015-11-12


Last Modified: Thursday, 12-Nov-2015 11:53:11 CET
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