Neutron Scattering

10 . Time-of-flight spectrometers
Michael Monkenbusch
10 .1 Introduction
The information that may be extracted from a neutron scattering experiment can be expressed
in terras of the scattering function S(Q, w) .
of scattering experiments are contained in S(Q, cw) .
All properties accessible by these kinds
The resulting intensity represents the
double differential cross section :
2 r
_ 2
dS2dE'
N k b
(Qiw)
where k', k is the modulus of the scattered and incoming neutrons respectively.
N denotes
the number of atoras in the sample and b is the scattering length' .
The energy transfer
during scattering is hw = (E - E'), here E ,
E' denote the energies of the incoming and
scattered neutrons respectively. The variables of the scattering function depend on k, k' ;
Q - 1 - l' is the momentum. transfer and
hw = (h2/2mn )(k 2 - k'2 ) (l0 .2)
the energy transfer that occurred during the scattering process .
Since the modulus of the
wavevector k of the neutron is related as well to the neutron velocity, v_ (momentum) as
to the wavelength (1/wavenumber) :
v_m, = hk (10 .3)
27r
= k (10 .4)
it is possible to deterraine the energy transfer (10 .2) as well -by employing the wave
properties of the neutron- by analysis of the wavelength A' as -by using the particle
character- by measurement of the velocity v' of the scattered neutrons .
The first method
is applied in crystal-spectrometers like the classical triple-axis-spectrometer or the
'For compounds containing different types of atours (elements or isotopes the corresponding expression
consists of the sum of partial structure factors multiplied by the corresponding scattering lengths
bibj in bilinear combination . For the discussion of instruments the simple version is sufficient .
10-1