An Introduction to Neutron Scattering - Spallation Neutron Source

Phonons – the Classical Use for Inelastic Neutron Scattering
• Coherent scattering measures scattering from single phonons
2 ⎛ d σ
⎞
⎜
d dE ⎟
⎝ Ω ⎠
coh±
1
= σ
coh
• Note the following features:
k
k
– Energy & momentum delta functions => see single phonons (labeled s)
– Different thermal factors for phonon creation (n s +1) & annihilation (n s )
– Can see phonons in different Brillouin zones (different recip. lattice vectors, G)
– Cross section depends on relative orientation of Q & atomic motions (e s )
– Cross section depends on phonon frequency (ω s ) and atomic mass (M)
– In general, scattering by multiple
excitations is either insignificant
or a small correction (the presence of
other phonons appears in the Debye-
Waller factor, W)
'
2
π
MV
0
e
− 2W
∑ ∑
r r
( Q.
e
ω
s G s
s
)
2
( n
s
1 ± 1
+ ) δ ( ω m ω
2
s
r r r
) δ ( Q − q − G )