Neutron Scattering

8 . Small-angle Scattering and Reflectometry
Dietmar Sehwahn
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8 .1 . Introduction
The methods of elastic scattering with neutrons deliver structural information from
arrangements of atoms and magnetic moments in condensed material . Those arrangements
can be precipitated phases in mixtures of metals, low molecular liquids or polymers and one
gets information about size, number density and corrélations between thé objects . In
scattering experiments thé intensity of neutrons is measured as a function of momentum
transfer Q
Q = 4n sirr 0
with thé Scattering angle 20 and thé wavelength k of thé neutrons. Q is thé différence of thé
wave numbers k (absolute value k=2n/A,) of incoming and scattered neutrons . The
momentum transfer is inversely proportional te, thé length scale of investigation ; at Q of thé
order of 1 A - 'one measures inter atomic distances and in thé région 10 - A-' _1()-4Â- '
mesoskopic objects of sizes between l0A _1()4Â . For all these investigations specialized
instruments have been developed . In this lecture we will introduce instruments for small angle
scattering and reflectometly with neutrons . With these instruments objects within thé bulk and
at thé surface are investigated. The main elements of these elastic methods will be separately
introduced in thé last part of thé lecture . We will discuss instruments working at stationary
nuclear research reactors . In future spallation sources will become thé more important sources
as they show a larger neutron flux with a periodic time structure ; those instruments need quite
différent conditions for optimization .
8 .2 . Intensity at Sample and Detector
In Fig . 8 .1 thé traces of neutrons for elastic Scattering are depicted in real and reciprocal
space. The intensity at thé sample (in linguistic usage : primary intensity) is determined
according te,
AI, =L-F-M2 (8 .2)
by thé luminosity ofthé source given in units [CM-2 s 1 steradian 1]