Neutron Scattering

10 .1 Common features of crystal spectrometers
One of the most important properties describing and characterizing spectrometers is the resolution
function . It is essential to determine and to optimize this function since it determines
the type of dynamical behaviour which may successfully be measured . For a substance to be
investigated, this might mean that several différent spectrometers are to be employed in order
to determine thé whole range of interesting excitations . According to thé expected excitation
energies not only a change in thé modération of thé neutron source but also switching to a
conceptually différent spectrometer might become necessary . However, already for a given
spectrometer, resolution and flux may be varied by an order ofmagnitude taking advantage of
available measures . Amongst other aspects, thé knowledge of thé instrumental resolution
function is of central importance in view of thé rather limited neutron flux, since - for example
- thé size of thé measured signal varies proportional to thé inverse fourth power of thé
chosen average collimation for a triple-axes spectrometer. Thus, for each experiment, a suitable
compromises between resolution and intensity have to be chosen . A comparison might
elucidate this point : e .g . 10 17 - 1021 quanta/s are typical for a LASER beam whereas a reactor
like thé DIDO offers normally 10 6 - 10 7 neutrons /cm2- s (monochromatic) at thé sample
position . In order to make thé most efficient use of those neutrons, différent strategies - discussed
below - are pursued by thé various crystal spectrometers .
For a crystal spectrometer one may Write thé measured intensity scattered into thé solid angle
Abt with thé energy spread Ahoi in thé form :
Nd2a
AI = A(k) - k - p(k) - AV .
- p ' (k ' ) - AS2 . AhùL) .
- dMdw
pximaryside
sample '
--dry side
The frst part ofeq . (3) up to thé cross section of thé sample represents information about thé
spectrum of thé neutron source A (k) and thé reflectivity of thé monochromator p(kb ; thé number
of scatterers in thé sample is N. The last part refers to thé signal measured by thé secondary
spectrometer . Since monochromator (primaiy side) and analyzer (secondary side) act by
thé saine physical principles it is advantageous to describe thé instrumental factors and thus
thé resolution in eq . (3) more symmetrically . To this end we use thé already introduced relation
between cross section and scattering function
d Za
df2dc L)
k'
= S(g,0 )
k
hz
h,
and with the hel of
4k~ Akl
AS2~ ~CAw
~ Z '
p =
AV we can rewrite eq.
=
k z ~ m kAki m . k'
(3) to
AIccA(k)-N-S(Q, üL )-p(1)AV-p(,L)AV' ,
where - as will be shown below - the volume elements in
AV = Ak11 . Ak . Aki .
wave vector space are given by
In this section, now, the most important elements for the triple-axis and the backscattering
spectrometer shall be introduced . It will become obvious that exploiting an essentially identical
principle leads to quite différent set-ups and properties . As a first step the general influence
of various components on the resolution will be descrbbnd by means of the triple-axis
9-2