Fig. 3.22 Integrated X
(2) (x T ) for the azides. a Based on X
(2) generated
under the restriction of x q 0 j 0 and x q 00 j 00 < 2X max and
x q 0 j 0 \X max . b Based on X
(2) with x q 0 j 0 and x q 00 j 00 \x T .
c Recasting of (A) with addition of g
N x T
ð Þ for N = 2,3;
and d recasting of (b) with addition of g
N x T
ð Þ for N = 2,3 . . . . 103
Fig. 3.23 Recasting of Fig. 3.22 (c–d) normalising by the number of
azido anions in the unit cell . . . . . . . . . . . . . . . . . . . . . . . . . . . . 104
Fig. 4.1
Molecular diagrams and crystallographic unit cells for the
organic EMs used in this work. The space group (SG) is shown
in each case. The structure of TATP is considered
independently in Sect. 4.5.3.4 . . . . . . . . . . . . . . . . . . . . . . . . . . . 116
Fig. 4.2
Phonon dispersion curves for the molecular EMs discussed in
this work. Wavenumber is truncated at 600 cm
−1 to allow
visualisation of the low frequency modes that are important in
this work. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 122
Fig. 4.3
Inelastic neutron scattering spectra for b-HMX and a-FOX-7
at 10 K. The experimental pattern (black) is given in
comparison to (blue) simulated INS spectra at three different
sampling densities of the Brillouin zone. Only the first
quantum events are simulated. Figure from Ref. [64], https://
doi.org/10.1039/C9TA06209B. Copyright CC-BY . . . . . . . . . . . 123
Fig. 4.4
Inelastic neutron scattering spectra for NTO and TATB
at 10 K. The experimental pattern (black) is given, in
comparison to (blue) simulated INS spectra at three different
sampling densities of the Brillouin zone. Only the first
quantum events are simulated. Figure from Ref. [64],
https://doi.org/10.1039/C9TA06209B. Copyright CC-BY . . . . . . 124
Fig. 4.5
Vibrational density of states (g x
ð Þ) for the molecular energetic
materials arranged in order of decreasing impact sensitivity.
The segments of integer values of X max are indicated in each
case. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 126
Fig. 4.6
Predicted sensitivity order based on the vibrational frequency
‘energy gap’ criterion, distinguishing between compounds
containing −NO 2 groups (red squares) and those that do not
(black squares) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 127
Fig. 4.7
Comparison of doorway density of states and experimental
impact sensitivities. Doorway densities are normalized by 3N
to account for variations in the normalization of the DOS . . . . . 128
Fig. 4.8
Overtone-based prediction of impact sensitivity of molecular
energetic materials, P(X
2
ð Þ ). Data are given for (left) the first
overtone, N = 2, and (right) the second overtone, N = 2+3.
Molecules which contain explosophoric –NO 2 moieties are
List of Figures
xxiii
(2) (x T ) for the azides. a Based on X
(2) generated
under the restriction of x q 0 j 0 and x q 00 j 00 < 2X max and
x q 0 j 0 \X max . b Based on X
(2) with x q 0 j 0 and x q 00 j 00 \x T .
c Recasting of (A) with addition of g
N x T
ð Þ for N = 2,3;
and d recasting of (b) with addition of g
N x T
ð Þ for N = 2,3 . . . . 103
Fig. 3.23 Recasting of Fig. 3.22 (c–d) normalising by the number of
azido anions in the unit cell . . . . . . . . . . . . . . . . . . . . . . . . . . . . 104
Fig. 4.1
Molecular diagrams and crystallographic unit cells for the
organic EMs used in this work. The space group (SG) is shown
in each case. The structure of TATP is considered
independently in Sect. 4.5.3.4 . . . . . . . . . . . . . . . . . . . . . . . . . . . 116
Fig. 4.2
Phonon dispersion curves for the molecular EMs discussed in
this work. Wavenumber is truncated at 600 cm
−1 to allow
visualisation of the low frequency modes that are important in
this work. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 122
Fig. 4.3
Inelastic neutron scattering spectra for b-HMX and a-FOX-7
at 10 K. The experimental pattern (black) is given in
comparison to (blue) simulated INS spectra at three different
sampling densities of the Brillouin zone. Only the first
quantum events are simulated. Figure from Ref. [64], https://
doi.org/10.1039/C9TA06209B. Copyright CC-BY . . . . . . . . . . . 123
Fig. 4.4
Inelastic neutron scattering spectra for NTO and TATB
at 10 K. The experimental pattern (black) is given, in
comparison to (blue) simulated INS spectra at three different
sampling densities of the Brillouin zone. Only the first
quantum events are simulated. Figure from Ref. [64],
https://doi.org/10.1039/C9TA06209B. Copyright CC-BY . . . . . . 124
Fig. 4.5
Vibrational density of states (g x
ð Þ) for the molecular energetic
materials arranged in order of decreasing impact sensitivity.
The segments of integer values of X max are indicated in each
case. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 126
Fig. 4.6
Predicted sensitivity order based on the vibrational frequency
‘energy gap’ criterion, distinguishing between compounds
containing −NO 2 groups (red squares) and those that do not
(black squares) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 127
Fig. 4.7
Comparison of doorway density of states and experimental
impact sensitivities. Doorway densities are normalized by 3N
to account for variations in the normalization of the DOS . . . . . 128
Fig. 4.8
Overtone-based prediction of impact sensitivity of molecular
energetic materials, P(X
2
ð Þ ). Data are given for (left) the first
overtone, N = 2, and (right) the second overtone, N = 2+3.
Molecules which contain explosophoric –NO 2 moieties are
List of Figures
xxiii