Neutron Scattering

Back to the "bottled" neutrons : in this case it is the half life time of the free neutron of about
13 minutes which fmally limits the variance ofthe energy .
The probability for a k-vector to obey the Bragg condition is both given by the "thickness" of
thé bisecting plane (constructive interférence ofthé contribution of thé lattice planes) and by
thé variance of thé orientation of G . The former condition means a relative sharpness of thé
modulus of CL in thé range of 10 -° to 10 - ', whereas thé latter is fulfllled with an accuracy of
about 10 -8 for an illuminated crystal surface in thé order of cm2 . Simultaneously, eq. (12)
expresses thé dependence of thé résolution on thé material of thé crystal, i .e . thé lattice parameter.
This is exemplified in Fig . 6). The smallest variance in k (or ' ) results for a Bragg
angle of 90° . This range of O - 90° is not accessible for usual triple-axis spectrometers .
Ideal crystals would be nearly prohibitive for measurements with the triple-axis spectrometer
since their variances in the lattice vector are too small as to reflect sufficient intensity . Therefore,
the perfection of the crystals is artificially degraded by various methods . Possible methods
are elastic bending of the crystals or a continuous variation of the lattice parameter in socalled
gradient crystals . The breakthrough in the successful preparation of gradient crystals
which implies a complicated and costly procedure was achieved satisfactorily in 1995 in Berlin-Adlershof
with Ge-Si crystals . A comparably wide-spread method is the deformation of
perfect crystals, thereby generating an imperfect mosaic crystal by introducing dislocations .
On may imagine such a crystal as being composed of small perfectly crystalline blocks - the
1
Fig . 8) Bragg-reflexi onby a
crystal width mosaic spread il
and collimations ŒO und a,
mosaic pebbles - whose orientation is normally
distributed. A common full-width-half-maximum
or mosaic spread is in thé Order of 30' .
Fig. 8) illustrates the operation of such a crystal as
monochromator . The neutron beam incident on the
crystal is given a divergence a. . A perfect crystal
would reflect just one wavelength for each angle
OM , as expressed by the section of the dashed line
(bisecting plane) limited by a, (