An Introduction to Neutron Scattering - Spallation Neutron Source

Diffraction by a Lattice of Atoms
.
G
vector,
lattice
reciprocal
a
to
equal
is
Q,
r,
wavevecto
scattering
when the
occurs
only
lattice
(frozen)
a
from
scattering
So
.
2
)
.(
then
If
.
2
.
Then
ns.
permutatio
cyclic
and
2
Define
cell.
unit
the
of
on vectors
translati
primitive
the
are
,
,
where
can write
we
lattice,
Bravais
a
In
.
2
)
.(
such that
s
Q'
for
zero
-
non
only
is
S(Q)
s,
vibration
thermal
Ignoring
position.
m
equilibriu
the
from
thermal)
(e.g.
nt
displaceme
any
is
and
i
atom
of
position
m
equilibriu
the
is
where
with
1
)
(
hkl
*
3
*
2
*
1
*
3
2
0
*
1
3
2
1
3
3
2
2
1
1
,
)
.(
π
πδ
π
π
M
j
i
Q
a
l
a
k
a
h
G
Q
a
a
a
a
V
a
a
a
a
a
m
a
m
a
m
i
M
j
i
Q
u
i
u
i
R
e
N
Q
S
hkl
ij
j
i
i
i
i
i
i
i
j
i
R
R
Q
i j
i
=
−
+
+
=
=
=
∧
=
+
+
=
=
−
+
=
= ∑
−
−
r
r
r
r
r
r
v
r
r
r
r
r
r
r
r
r
r
r
r
v
r
r
r
r
r
r
r
r
r
v
r
r
a 1
a 2
a 3