Fig. 4.18 Complete temperature independent X
2
ð Þ for the molecular
energetic materials, generated under the single restriction of
x 2 \ X max . For NTO, the curves are shown for X max of (green)
240 and (black) 200 cm
−1 . It is encouraging to find that apart
from the onset frequency, little changes as a function of X max . . . . . 141
Fig. 4.19 Predicted sensitivity based on T = 300 K, based purely on
combination pathways (i.e. integration of P X
2
ð Þ
). X
2
ð Þ are
generated under the restriction x 2 \ X max and integration
restricted by where X
2
ð Þ
¼ 0 . . . . . . . . . . . . . . . . . . . . . . . . . . . . 142
Fig. 4.20 Temperature dependent two-layer model to predict impact
sensitivity of the molecular EMs. The equilibrium temperature
is set at 300 K and integration of X
2
ð Þ is upper bound by the
limiting frequencies given in Table 4.5. Note NTO
(X max = 200) has X
2
ð Þ = 120 cm
−1 . Lifting these integration
restrictions lead to only minor increases in the integrations:
HBT (+10); a-FOX-7 (+3), TATB (+1). The relative ordering
therefore remains unchanged. . . . . . . . . . . . . . . . . . . . . . . . . . . . 143
Fig. 4.21 Variable temperature P(X
2
ð Þ ) for b-HMX. The initial excitation
temperature for the phonon bath modes (below
X max = 195 cm
−1 ) is taken to be 2000 K. The temperature
of the remaining states is then plotted over the temperature
range 10–300 K. Note the phonon bath has been omitted from
the x-axis . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 144
Fig. 4.22 Predicting impact sensitivity using the two-layered model at
ambient temperature of 300 K. The phonon modes are initially
excited to shock temperature T sh . In all cases X max for NTO is
240 cm
−1 . The y-axes are comparable and reflect an increase in
reactivity with increased shock temperature (and hence
stronger impact). Figure from Ref. [64], https://doi.org/10.
1039/C9TA06209B. Copyright CC-BY . . . . . . . . . . . . . . . . . . . 146
Fig. 4.23 Variable temperature INS spectra for a b-HMX and b TATB
from 10 K to 200 K. All spectra have been corrected for
sample container contributions and background. The
intensities of each system have been normalised to a wellresolved isolated peak (ca. 246 cm
−1 for HMX and ca. 446
cm
−1 for TATB). Note that this does introduce errors in the
absolute comparison of intensities across the spectra. The
change in intensities across the INS spectra reflects increasing
vibrational amplitude (populations) of these vibrational modes
in line with Eq. 2.47. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 147
Fig. 4.24 Variable temperature INS spectra for a-FOX-7 from 10 K to
150 K. All spectra have been normalised to the peak
at ca. 385 cm
−1 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 148
List of Figures
xxv
2
ð Þ for the molecular
energetic materials, generated under the single restriction of
x 2 \ X max . For NTO, the curves are shown for X max of (green)
240 and (black) 200 cm
−1 . It is encouraging to find that apart
from the onset frequency, little changes as a function of X max . . . . . 141
Fig. 4.19 Predicted sensitivity based on T = 300 K, based purely on
combination pathways (i.e. integration of P X
2
ð Þ
). X
2
ð Þ are
generated under the restriction x 2 \ X max and integration
restricted by where X
2
ð Þ
¼ 0 . . . . . . . . . . . . . . . . . . . . . . . . . . . . 142
Fig. 4.20 Temperature dependent two-layer model to predict impact
sensitivity of the molecular EMs. The equilibrium temperature
is set at 300 K and integration of X
2
ð Þ is upper bound by the
limiting frequencies given in Table 4.5. Note NTO
(X max = 200) has X
2
ð Þ = 120 cm
−1 . Lifting these integration
restrictions lead to only minor increases in the integrations:
HBT (+10); a-FOX-7 (+3), TATB (+1). The relative ordering
therefore remains unchanged. . . . . . . . . . . . . . . . . . . . . . . . . . . . 143
Fig. 4.21 Variable temperature P(X
2
ð Þ ) for b-HMX. The initial excitation
temperature for the phonon bath modes (below
X max = 195 cm
−1 ) is taken to be 2000 K. The temperature
of the remaining states is then plotted over the temperature
range 10–300 K. Note the phonon bath has been omitted from
the x-axis . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 144
Fig. 4.22 Predicting impact sensitivity using the two-layered model at
ambient temperature of 300 K. The phonon modes are initially
excited to shock temperature T sh . In all cases X max for NTO is
240 cm
−1 . The y-axes are comparable and reflect an increase in
reactivity with increased shock temperature (and hence
stronger impact). Figure from Ref. [64], https://doi.org/10.
1039/C9TA06209B. Copyright CC-BY . . . . . . . . . . . . . . . . . . . 146
Fig. 4.23 Variable temperature INS spectra for a b-HMX and b TATB
from 10 K to 200 K. All spectra have been corrected for
sample container contributions and background. The
intensities of each system have been normalised to a wellresolved isolated peak (ca. 246 cm
−1 for HMX and ca. 446
cm
−1 for TATB). Note that this does introduce errors in the
absolute comparison of intensities across the spectra. The
change in intensities across the INS spectra reflects increasing
vibrational amplitude (populations) of these vibrational modes
in line with Eq. 2.47. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 147
Fig. 4.24 Variable temperature INS spectra for a-FOX-7 from 10 K to
150 K. All spectra have been normalised to the peak
at ca. 385 cm
−1 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 148
List of Figures
xxv