Neutron Scattering

17.1 Introduction
Atomic and molecular motions in liquids and solids are driven by the thermal energy of the
sample . Fluctuations may concentrate kinetic energy on one atom, which then is able to cross
a potential barrier into a new site .
give rise to quasielastic scattering .
Such transport or orientational jumps occur randomly and
At low temperature the classical motion dies out on the timescale of neutron spectrometers .
The (classical) potentials are still prescrit, however . They now characterise the quantummechanical
excitations of the lattice object : librations and tunnelling . Theories used are mostly
single particle or mean field theories .
By studying both, classical quasielastic scattering and quantum excitations a detailed information
on the shape and the strength of potential barriers cari be obtained since neutron
properties allow a resolution in space and time . If the crystal structure of a material is known
one cari calculate the potentials from fundamental intermolecular interactions . The concept of
"transferable pair interactions" may finally allow to predict potentials of new materials .
Stochastic motions occur in many materials some of which attract technical interest.
Hydrogen
in metals is used for energy storage, microporous framework structures as zeolithes
offer catalytically active surfaces, polymers cari aggregate to secondary structures like micelles
with sometimes technically interesting properties . They mix or phase separate by diffusion.
Adsorbates, intercalates, molecular and liquid crystals, matrix isolated species and liquids
may bc studied this way. It was especially the invention of high resolution neutron scattering
instruments (since -1972) which gave an impact to this topic which still holds .
17 .1 .1 Gaussian approximation
The scattering function of a rare gas can be calculated exactly on the basis of plane wave
functions arid transition matrix elements . It happens to have the shape of a Gaussian . With
ß = k. B-1-1
and the recoil energy Er = 2M
( 4Er )2 CXP( - 4E, (hw - ET)2)
Fouriertransformation in space and time yields the correlation function (Chapter 5) :
r 2
Gs z (r,t) _ (2~Q2(t)) 2e :rp(-2Q2(t))
(17 .2)
with
a2(t) = t(t - i~,ß) / lll,ß (17 .3)
17-2