An Introduction to Neutron Scattering - Spallation Neutron Source

so
or
ie
Coherent Elastic Scattering measures the Structure
Factor S(Q) I.e. correlations of atomic positions
dσ
=
dΩ
Now
where
b
∑
i
2
e
r
N.
S(
Q)
r r
−iQ.
R
r 1
S( Q)
=
N
∫
r
g( R)
=
i
=
∫
r
dr
'
∑
i≠0
r
dr.
e
∫
for an assembly of similar atomswhere
r r
−iQ.
r
∑
r r r
δ(
R−
R + R
i
i
r r
δ(
r −R
) =
0
∫
)
i
∫
r
dr.
e
r r
−iQ.
r
r
r 1 r r 2
−iQ.
r r
S(
Q)
= ∫ dr.
e ρN
( r)
N
r r r r
−iQ.(
r −r
')
r r 1
dr.
e ρN
( r)
ρN
( r')
=
N
r r r r r
−iQ.
R
S(
Q)
= 1+
dR.
g(
R)
. e
ρ
r
( r)
r
dR
∫ ∫
whereρ
r
dre
r
is a function of R only.
N
r 1
S(
Q)
=
N
r r
−iQ.
R
N
ρ
is
N
thenuclear
r
( r)
ρ
∑
N
i,
j
e
r r r
−iQ.(
R −R
r r
( r − R)
i
j
)
ensemble
number density
g(R) is known as the static pair correlation function. It gives the probability that there is an
atom, i, at distance R from the origin of a coordinate system at time t, given that there is also a
(different) atom at the origin of the coordinate system