Neutron Scattering

2
0 0 2 4 6 8 10 12
0 (A -1 )
Figure 5 .4 : Structure factor S(Q) of liquid "Ar at 85 K . The points are frein a neutron
scattering experiment, the curve is generated by a molecular dynamics calculation using
a Lennard -Jones potential [7] .
5 .2 .2 Experiments on Liquid Argon
As an example of the structure factor S(Q) of a monatomic liquid we consider the neutron
scattering results of Yarnell et al . [7] from liquid Argon . The result of the experiment is
shown in figure 5 .4 . The wavelength of the incident neutrons was A = 0.978 f1 . Under
this condition the Placzek corrections vary between 0.0012 near Q = 0 and -0.0426 at
Q = 9 .08-Â -1 . The pair correlation function g(r) was obtained by numerical inverse
Fourier transform of S(Q) - 1 and is shown in figure 5 .5 . The oscillations at small r
are a consequence of cut-off effects on the Fourier transform . They eccur below the
atomic diameter r o and therefore do not impede the interpretation . The determination
of g(r) is important for the calculation of equilibrium properties of the liquid and allows
scrutinization of theoretical models for the interatomic forces .
Two methods of theery based calculation of g(r) have to be emphasized : (1) In Monte
Carlo (MC) calculations a large number of possible atomic configurations is created .
Their probability is determined by the Boltzmann factor on the basis of interatomic
potentials . Finally, the ensemble average is calculated . (2) In Molecular Dynamics (MD)
calculations one starts from an initial configuration and solves (numerically) the equations
5-7