82
3 Vibrational Up-Pumping: Predicting Impact Sensitivity of Some …
Table 3.5 Calculated
vibrational frequencies (ω)
for the primitive and
conventional unit cells of
α-NaN 3 using PBE-D2.
Values are given in cm -1
Mode ω Primitive ω Conventional Assignment
M 4
–
84.78
Lattice
M 5
–
88.61
Lattice
M 6
150.97
151.41
Lattice
M 7
–
154.47
Lattice
M 8
–
157.09
Lattice
M 9
177.99
184.34
Lattice
M 10
202.21
206.42
Lattice
M 11
214.51
219.05
Lattice
M 12
220.22
221.37
Lattice
M 13
–
221.54
Lattice
M 14
–
226.97
Lattice
M 15
–
230.22
Lattice
M 16
–
236.87
Lattice
M 17
606.27
610.35
In phase δθ NNN
M 18
609.71
614.72
In phase δθ NNN
M 19
–
617.49
Out of phase δθ NNN
M 20
–
618.24
Out of phase δθ NNN
M 21
–
1247.99
Out of phase δR S
M 22
1250.43
1250.25
In phase δR S
M 23
–
1929.65
Out of phase δR A
M 24
1959.81
1964.65
In phase δR A
and hence to neighbouring primitive cells being directly out of phase. This is often
the maximum energy state of these vibrational bands.
Experimental data regarding the lowest frequency modes (i.e. lattice modes) is
sparse. To explore the validity of DFT to model lattice modes in ionic azides, the
inelastic neutron scattering spectrum (INS) of α-NaN 3 was obtained, Fig. 3.8. Unlike
Raman and infrared spectroscopy, INS is not limited by quantum selection rules, and
therefore all vibrational modes are in principle visible. The INS spectrum reveals
the five lattice modes, the three highest with observed frequencies ~ 220, 210 and
196 cm
−1 . The calculated frequencies agree well with these experimental values,
occurring at 220, 214 and 202 cm
−1 . Two additional features are observed at ~
160 cm
−1 and 130 cm
−1 in the INS spectrum, which appear to be somewhat lower in
frequency than the calculated frequencies of 177 cm
−1 and 150 cm
−1 using the D2
dispersion correction. Low frequency vibrations are extremely sensitive to the weak
underlying potential of the surrounding crystal. The zone-centre vibrational modes
were therefore re-calculated using a second common dispersion correction scheme,
TS, which is somewhat less empirical than the D2 scheme.
3 Vibrational Up-Pumping: Predicting Impact Sensitivity of Some …
Table 3.5 Calculated
vibrational frequencies (ω)
for the primitive and
conventional unit cells of
α-NaN 3 using PBE-D2.
Values are given in cm -1
Mode ω Primitive ω Conventional Assignment
M 4
–
84.78
Lattice
M 5
–
88.61
Lattice
M 6
150.97
151.41
Lattice
M 7
–
154.47
Lattice
M 8
–
157.09
Lattice
M 9
177.99
184.34
Lattice
M 10
202.21
206.42
Lattice
M 11
214.51
219.05
Lattice
M 12
220.22
221.37
Lattice
M 13
–
221.54
Lattice
M 14
–
226.97
Lattice
M 15
–
230.22
Lattice
M 16
–
236.87
Lattice
M 17
606.27
610.35
In phase δθ NNN
M 18
609.71
614.72
In phase δθ NNN
M 19
–
617.49
Out of phase δθ NNN
M 20
–
618.24
Out of phase δθ NNN
M 21
–
1247.99
Out of phase δR S
M 22
1250.43
1250.25
In phase δR S
M 23
–
1929.65
Out of phase δR A
M 24
1959.81
1964.65
In phase δR A
and hence to neighbouring primitive cells being directly out of phase. This is often
the maximum energy state of these vibrational bands.
Experimental data regarding the lowest frequency modes (i.e. lattice modes) is
sparse. To explore the validity of DFT to model lattice modes in ionic azides, the
inelastic neutron scattering spectrum (INS) of α-NaN 3 was obtained, Fig. 3.8. Unlike
Raman and infrared spectroscopy, INS is not limited by quantum selection rules, and
therefore all vibrational modes are in principle visible. The INS spectrum reveals
the five lattice modes, the three highest with observed frequencies ~ 220, 210 and
196 cm
−1 . The calculated frequencies agree well with these experimental values,
occurring at 220, 214 and 202 cm
−1 . Two additional features are observed at ~
160 cm
−1 and 130 cm
−1 in the INS spectrum, which appear to be somewhat lower in
frequency than the calculated frequencies of 177 cm
−1 and 150 cm
−1 using the D2
dispersion correction. Low frequency vibrations are extremely sensitive to the weak
underlying potential of the surrounding crystal. The zone-centre vibrational modes
were therefore re-calculated using a second common dispersion correction scheme,
TS, which is somewhat less empirical than the D2 scheme.