Neutron Scattering

9 . Crystal spectrometer :
triple-axis and back-scattering spectrometer
F .
Güthoff, H.Grimm
It has been emphasized in the preceding lectures that thermal neutrons provide wavelengths
k comparable to inter-atomic distances and energies hw in the order of collective excitations
of condensed matter. In order to determine the properties of a sample - as represented by the
scattering function s(_Q>ü) °c dZ6 /dÇ2dE' - a variety of instruments may be used . The evaluation
ofthe single differential cross section represented by d6 / dÇ2 is the topic of diffractometers
. However, since - in general - the scattering ofneutrons by the sample is connected with
an energy transfer it suggests itself to analyze the neutrons scattered into the solid angle dS2
in addition with regard to their energy . Introducing and investigating the double differential
cross section dZG / dS2dE' thus corresponds to the switching from diffractometer to spectrometer.
In order to determine which energy transfer E - E' = ho) is associated with which
momentum transfer _Q, the neutrons have to bc characterized before hitting the sample by
means of the so-called primary spectrometer and after leaving the sample by the secondary
spectrometer . It will be shown in the lecture on time-of-flight spectrometers that the energy
of neutrons can be determined via selection of velocity and travel time . Recall that thermal
neutrons (300K) having an energy of kBT =%2 mv2 - 25 meV travel with a speed of about
2200m/s . According to de Broglie one may associate a wavelength ;, to a moving particle
with mass m . This fact is used by crystal spectrometers which - by means ofBragg scattering
select neutrons of energy
n- ;, =2dsin0 (1)
h 2k2
2m
h z
2
2M;`,
(2)
under Bragg angle 0 for given spacing d of the selected atomic planes .
wave vector is related to the wavelength by k = 2n / ;, .
The modulus of the
Two types of crystal spectrometers will bc introduced in this lecture . The triple-axes spectrometer
represents one of the earliest neutron spectrometer types . It was developed by B . N .
Brockhouse . By means of this facility his essential studies [I] resulted by the end of the
fifthies laying ground for his winning of the Nobel prize for physics in 1995 . In contrast, the
backscattering spectrometer is of more recent origin (the first facility of this type was put into
operation in Jülich at the beginning of the seventieths by B .Alefeld) and was stimulated by
ideas of Maier-Leibnitz [2] .
Both types of spectrometers can be - similar to time-of-flight machines - positioned at cold
and thermal neutron sources . Especially for triple-axes spectrometers the possibility is realized
to use them at hot sources where neutron energies range up to leV .