4.5 Results and Discussion
121
4.5.2 Vibrational Structure of Some Organic Energetic
Materials
Following from the theory presented in Chap. 3, the vibrational structure of the
molecular materials was considered. The full phonon dispersion curves were calculated along the high symmetry lines of the Brillouin zones and are given in Fig. 4.2.
As expected for molecular materials, it is generally seen that the branch dispersion
is relatively small across the Brillouin zone, and almost negligible for the internal
vibrational modes.
Slight instabilities are observed in the phonon dispersion curves of both NTO and
HNB, with frequencies of the lowest acoustic branch becoming negative at a small
set of wave vectors. Unfortunately, no attempts to rectify this were successful. As
both compounds are stable, this is unlikely to be indicative of dynamic instability of
the structures, but rather more likely to be attributed to a slight numerical error in the
calculated structures. However, this is not expected to result in any marked effect on
the remaining vibrational structure.
As a means to assess the ability of DFT to model the vibrational structure for these
types of compounds, experimental INS spectra for a subset of the test compounds
were collected. Calculated phonon dispersion curves were then used to simulated
INS spectra for direct comparison.
The simulated INS spectra for the most sensitive compound, β-HMX, Fig. 4.3,
generally shows good agreement with experiment. The frequencies of the lowest
region of the INS spectrum are well reproduced, with the calculated max underestimated by only ca. 5 cm
−1 . There appears to be a ca. 20 cm
−1 systematic underestimation of the vibrational frequencies in the ω > 200 cm
−1 region of the spectrum. The
intensities are not well reproduced for the lowest frequency modes, which suggests
some error surrounding the exact structure of the β-HMX phonon modes, or textured
powder. In contrast, comparison of the simulated and experimental INS spectra for
α-FOX-7, Fig. 4.3, shows excellent agreement. While the frequencies are well reproduced based on the zone-centre structure, increased sampling of the Brillouin zone
is required to obtain accurate intensities. By 0.08 Å
−1 , the full INS spectrum is very
well reproduced by simulation.
For NTO the simulations are an excellent reproduction of the experimental INS
spectra, Fig. 4.4, despite the small instability (negative frequencies) reported above.
Both the intensities and frequencies appear well reproduced across the spectrum,
particularly when a dense grid of phonon wave vectors is used. This strongly suggests
that this minor instability has negligible influence on the vibrational structure. The
INS spectrum of TATB is also well reproduced, Fig. 4.4, but there does appear to be a
slight disagreement between the higher frequency vibrational modes at ca. 800 cm
−1 .
Internal modes in this region are primarily NH 2 twisting modes. Overall, however,
the spectrum is very well reproduced in both frequencies and intensities.
In contrast to the case of α-NaN 3 presented in Chap. 3, INS spectra simulated from
zone-centre calculations generally perform well in reproducing both the frequencies and relative intensities observed in the experimental INS spectra of the organic
121
4.5.2 Vibrational Structure of Some Organic Energetic
Materials
Following from the theory presented in Chap. 3, the vibrational structure of the
molecular materials was considered. The full phonon dispersion curves were calculated along the high symmetry lines of the Brillouin zones and are given in Fig. 4.2.
As expected for molecular materials, it is generally seen that the branch dispersion
is relatively small across the Brillouin zone, and almost negligible for the internal
vibrational modes.
Slight instabilities are observed in the phonon dispersion curves of both NTO and
HNB, with frequencies of the lowest acoustic branch becoming negative at a small
set of wave vectors. Unfortunately, no attempts to rectify this were successful. As
both compounds are stable, this is unlikely to be indicative of dynamic instability of
the structures, but rather more likely to be attributed to a slight numerical error in the
calculated structures. However, this is not expected to result in any marked effect on
the remaining vibrational structure.
As a means to assess the ability of DFT to model the vibrational structure for these
types of compounds, experimental INS spectra for a subset of the test compounds
were collected. Calculated phonon dispersion curves were then used to simulated
INS spectra for direct comparison.
The simulated INS spectra for the most sensitive compound, β-HMX, Fig. 4.3,
generally shows good agreement with experiment. The frequencies of the lowest
region of the INS spectrum are well reproduced, with the calculated max underestimated by only ca. 5 cm
−1 . There appears to be a ca. 20 cm
−1 systematic underestimation of the vibrational frequencies in the ω > 200 cm
−1 region of the spectrum. The
intensities are not well reproduced for the lowest frequency modes, which suggests
some error surrounding the exact structure of the β-HMX phonon modes, or textured
powder. In contrast, comparison of the simulated and experimental INS spectra for
α-FOX-7, Fig. 4.3, shows excellent agreement. While the frequencies are well reproduced based on the zone-centre structure, increased sampling of the Brillouin zone
is required to obtain accurate intensities. By 0.08 Å
−1 , the full INS spectrum is very
well reproduced by simulation.
For NTO the simulations are an excellent reproduction of the experimental INS
spectra, Fig. 4.4, despite the small instability (negative frequencies) reported above.
Both the intensities and frequencies appear well reproduced across the spectrum,
particularly when a dense grid of phonon wave vectors is used. This strongly suggests
that this minor instability has negligible influence on the vibrational structure. The
INS spectrum of TATB is also well reproduced, Fig. 4.4, but there does appear to be a
slight disagreement between the higher frequency vibrational modes at ca. 800 cm
−1 .
Internal modes in this region are primarily NH 2 twisting modes. Overall, however,
the spectrum is very well reproduced in both frequencies and intensities.
In contrast to the case of α-NaN 3 presented in Chap. 3, INS spectra simulated from
zone-centre calculations generally perform well in reproducing both the frequencies and relative intensities observed in the experimental INS spectra of the organic