Neutron Scattering

ALQ) = Y-bfe'Q'-rB(r-(n .a+m .b+p»ç »d 3r
n,m,p
1 inQ .IM-1 i-Q .b p-1 ipQ .ç
=b Y- e - Y, e - Y, e -
n=0 m-0 p=0
geometrical series (3 .28)
Summing up the geometrical series, we obtain the scattered intensity :
sing
2 NQ - a sing 2 MQ - b sing 2 pQ . ç
I(Q ) - = Ibl2
ALQI2
sin21Q 2- . - 2- . b_ sin21Q 2- - c
(3 .29)
As expected, the scattered intensity is proportional to the magnitude square of the scattering
length b . The dependence on the scattering vector Q is given by the so-called Lauefunction .
The latter is plotted along one lattice direction a in figure 3 .5 .
30
"Laue" function N=5 and N=10
Fil Lauefunction along the lattice
respectively .
direction a for a lattice with 5 and 10 periods,
The main maxima are found at the positions Q = n -- .
a
The maximum intensity scales with
the square of the number of periods, the half-width is given approximately by
2z . The
N-a
3- 13