Neutron Scattering

tribution of bisecting planes (ntosaic) which spans the hatched area being proportional to
k 2 cot0, . Together with the vertical divergence iß delivering a contribution of ßk there results
a resolution volume being proportional to k' cot 0,,, . The variance ofthe scattering angle
AO in eq . (12) follows to (without derivation) :
a 2 a 2 + a 2 2 + a2 172
2 2 2
ao+a, +41
(13)
This dependence shows that the gain in intensity by the mosaic crystal is not to be "paid" by a
worse energy resolution for ao = a, ! Generally, the influence of ri on AO is weak . (Fig . 9)
Which crystals should now be used as monochromators for neutron? Apart front the lattice parameters
further criteria are to be considered : those are the reflectivity, the suppression of
A,/2-contamination, and last not least the availability as given by the technical and fmancial effort
for their production in suitable quality and size . For example, for the saine reflected
wavelength, Cu bas a better resolution as graphite (PG means pyrolytic deposited graphite),
however, an appreciably lower reflectivity (see table 1) and Fig . 7)) . The elastic form factor of
the crystal
plays an important role saine it represents the coherent scattering length and the extinction
cules . Eq . (14) delivers for the diamond lattice the form factors :
2 h+k+1= 4n
F(Q)=_b 1±i = 2n + 1
0 = 2(2n + 1) !!
Thus Ge and Si have the desired property to suppress the ~,/2-contamination of the reflected
beam by means ofthe forbidden (222)-reflection when using the (111)-reflection.
1 .0
Fig . 10) transmission of
PG-filters [4]
0.8
a .s
0.4
0.2
0.5 1 .0 1 .5 2.0 2.5
wavelength ~ iA
9-9