60 K
30 K
0 K
-15
-10
-5
0
5
10
15
0.000
0.001
0.002
0.003
0.004
0.005
Energy (meV)
S 1 (E) (meV
- 1
)
40 K
0 K
(x10)
2- phonon
1- phonon
-20
-10
0
10
20
30
0.000
0.001
0.002
0.003
0.004
0.005
Energy (meV)
(
S
n E) (meV
-1
)
a
b
Fig. 10.9. Left: single-phonon excitation probabilities, S 1 (E), for a Debye model PVDOS with a
cutoff energy of 14 meV at different temperatures. Right: comparison of one-phonon and
two-phonon excitation probabilities for a Debye model as a function of temperature
Table 10.1 Quantities derived from sum rule analysis
Quantity
Fe metal (300 K) [449]
Goethite [490]
Lamb-Mössbauer factor f LM
0.796
0.78
Mean square displacement hz
2
i 10
À3 (Å
2
)
4.13
4.66
Average kinetic energy, T av (meV)
14.16
15.58
Average force constant, k av (N/m)
180
107.1
268
10 Nuclear Resonaynce Vibrational Spectroscopy