172
5 Vibrational Up-Pumping in Polymorphic Materials
decreases in the sequence α-FOX-7 (~ 4.67 states per atom) > β-FOX-7 (~4.20 states
per atom) > γ-FOX-7 (~2.52 states per atom).
While it was not possible to isolate the β-form, the γ-form could be quench cooled,
and analysed by INS spectroscopy, Fig. 5.9. The calculated vibrational structure for
γ-FOX-7 yields a simulated INS spectrum that generally agrees well with the experimental spectrum. The most notable difference is the underestimation of max in
the simulated spectrum ( max is 160 cm
−1 from simulation, and 171 cm
−1 from
INS). While this is likely to have some consequence on the calculation of the uppumping model, it is important to note that the experimental max is still approximately 20 cm
−1 lower than the experimental max value for α-FOX-7 presented
in Chap. 4. The remainder of the INS spectra exhibit the same expected features,
with discrepancies in the calculated frequencies <6%. While this does suggest some
difficulty with reproducing the vibrational structure of γ-FOX-7, it is overall representative of the experimental frequencies and is therefore carried forward for data
processing in the up-pumping model.
As described for the HMX polymorphs, the FOX-7 polymorphs were analysed
within the framework of the two most successful models of Chap. 4. This first required
generation of g(ω) (for this system, sampling could be obtained from across the
Brillouin zone) and
(2) for the three polymorphs, Figs. 5.8, respectively. Across
all three polymorphs,
(2) adopts a very similar structure. The onset wavenumber is
approximately 270 cm
−1 in each case, which reflects the generally similar structure
of the doorway modes. Furthermore, all three polymorphs exhibit
(2)
= 0 just
above 1000 cm
−1 , and feature the same groupings of density. With very similar
vibrational structures, it follows that the main difference in understanding the uppumping between these polymorphs will be max and the relative rates at which
energy can up-pump into these nearly identical structures.
If the three FOX-7 polymorphs are analysed first using the overtone-based model,
built on the first two overtones, Fig. 5.10, the relative sensitivity ordering that was
determined by doorway density is recovered: α-FOX-7 ≈ β-FOX-7 > γ-FOX-7,
with the overtone up-pumped density equal to ~6.0, ~6.1 and ~4.9, respectively. This
places the two FOX-7 polymorphs that exhibit herringbone packing at approximately
the same sensitivity, with the layered γ-form predicted to have a lower sensitivity.
It is finally worth considering the three FOX-7 polymorphs using the two-layered
model, and an equilibrium temperature of 300 K. Despite the projection of the overtone pathways onto the doorway modes leading to considerably fewer doorway
contributions for γ-FOX-7, Fig. 5.8, the larger number of populated modes available in the phonon bath for this polymorph greatly reduces this effect. According
to discussions in Chap. 4, all three polymorphs exhibit
(2)
= 0 at approximately
1000 cm
−1 (Fig. 5.8). Hence, this is taken to be the upper limit for integration in the
two-layered model. The values of ∫
(2) for the three polymorphs are found to be
14.5, 12.6 and 12.2 a.u. for the α-, β- and γ-polymorphs, respectively. The results of
Chap. 4 (Fig. 4.20) suggest that this corresponds to a sizeable difference in predicted
sensitivity between the α- and γ-forms, with the latter being less sensitive.
Both the overtone and the two-layered models therefore suggest that flattening
the crystal layers of an energetic compound should decrease the impact sensitivity.
5 Vibrational Up-Pumping in Polymorphic Materials
decreases in the sequence α-FOX-7 (~ 4.67 states per atom) > β-FOX-7 (~4.20 states
per atom) > γ-FOX-7 (~2.52 states per atom).
While it was not possible to isolate the β-form, the γ-form could be quench cooled,
and analysed by INS spectroscopy, Fig. 5.9. The calculated vibrational structure for
γ-FOX-7 yields a simulated INS spectrum that generally agrees well with the experimental spectrum. The most notable difference is the underestimation of max in
the simulated spectrum ( max is 160 cm
−1 from simulation, and 171 cm
−1 from
INS). While this is likely to have some consequence on the calculation of the uppumping model, it is important to note that the experimental max is still approximately 20 cm
−1 lower than the experimental max value for α-FOX-7 presented
in Chap. 4. The remainder of the INS spectra exhibit the same expected features,
with discrepancies in the calculated frequencies <6%. While this does suggest some
difficulty with reproducing the vibrational structure of γ-FOX-7, it is overall representative of the experimental frequencies and is therefore carried forward for data
processing in the up-pumping model.
As described for the HMX polymorphs, the FOX-7 polymorphs were analysed
within the framework of the two most successful models of Chap. 4. This first required
generation of g(ω) (for this system, sampling could be obtained from across the
Brillouin zone) and
(2) for the three polymorphs, Figs. 5.8, respectively. Across
all three polymorphs,
(2) adopts a very similar structure. The onset wavenumber is
approximately 270 cm
−1 in each case, which reflects the generally similar structure
of the doorway modes. Furthermore, all three polymorphs exhibit
(2)
= 0 just
above 1000 cm
−1 , and feature the same groupings of density. With very similar
vibrational structures, it follows that the main difference in understanding the uppumping between these polymorphs will be max and the relative rates at which
energy can up-pump into these nearly identical structures.
If the three FOX-7 polymorphs are analysed first using the overtone-based model,
built on the first two overtones, Fig. 5.10, the relative sensitivity ordering that was
determined by doorway density is recovered: α-FOX-7 ≈ β-FOX-7 > γ-FOX-7,
with the overtone up-pumped density equal to ~6.0, ~6.1 and ~4.9, respectively. This
places the two FOX-7 polymorphs that exhibit herringbone packing at approximately
the same sensitivity, with the layered γ-form predicted to have a lower sensitivity.
It is finally worth considering the three FOX-7 polymorphs using the two-layered
model, and an equilibrium temperature of 300 K. Despite the projection of the overtone pathways onto the doorway modes leading to considerably fewer doorway
contributions for γ-FOX-7, Fig. 5.8, the larger number of populated modes available in the phonon bath for this polymorph greatly reduces this effect. According
to discussions in Chap. 4, all three polymorphs exhibit
(2)
= 0 at approximately
1000 cm
−1 (Fig. 5.8). Hence, this is taken to be the upper limit for integration in the
two-layered model. The values of ∫
(2) for the three polymorphs are found to be
14.5, 12.6 and 12.2 a.u. for the α-, β- and γ-polymorphs, respectively. The results of
Chap. 4 (Fig. 4.20) suggest that this corresponds to a sizeable difference in predicted
sensitivity between the α- and γ-forms, with the latter being less sensitive.
Both the overtone and the two-layered models therefore suggest that flattening
the crystal layers of an energetic compound should decrease the impact sensitivity.