Fig. 4.25 Vibrational up-pumping based on zone-centre phonon DOS.
(Left) calculation of the temperature independent overtone
contribution to N = 3. (Right) Two-level system with
equilibrium temperature 300 K. The addition of temperature in
the latter is responsible for the large increase in the y-axis . . . . . 149
Fig. 4.26 a Molecular structure of TATP. b Crystallographic structure of
TATP. c Zone-centre g x
ð Þ for TATP, and d X
2
ð Þ , with the
restriction that x 2 \ X max . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 150
Fig. 5.1
Structure of HMX. a Schematic representation of the HMX
molecule. b Crystal structure of b-HMX P2 1 =c (CCDC Ref:
OCHTET01). (C) Crystal structure of d-HMX P6 1 (CCDC
Ref: OCHTET03). Atoms are coloured as (red) oxygen, (blue)
nitrogen, (grey) carbon, and (white) hydrogen . . . . . . . . . . . . . . 158
Fig. 5.2
Structure of FOX-7. a Schematic representation of the FOX-7
molecular structure. (B) Crystal structure of a-FOX-7 P2 1 =n
(CCDC Ref: SEDTUQ03). c Crystal structure of b-FOX-7
P2 1 2 1 2 1 (CCDC Ref: SEDTUQ06). c Crystal structure of
c-FOX-7 P2 1 =n (From Crawford et al. [25]). The angle
between FOX-7 molecules (∠(FOX-7)) is given in each case.
Atoms are coloured as (red) oxygen, (blue) nitrogen, (grey)
carbon and (white) hydrogen . . . . . . . . . . . . . . . . . . . . . . . . . . . 159
Fig. 5.3
Inelastic neutron scattering spectra of d-HMX at ca. 10 K.
(top) The experimental pattern and (bottom) simulated patterns
are given. The latter is generated from C-point frequencies
only. The vertical dotted line indicates X max in each case . . . . . 164
Fig. 5.4
Comparison of the vibrational structure of two HMX
polymorphs. (Top) g x
ð Þ and X
2
ð Þ for b-HMX, and (bottom)
g x
ð Þ and X
2
ð Þ for d-HMX. 0 ! X max and X max ! 2X max are
identified in g x
ð Þ by yellow and purple, respectively. Note that
X
2
ð Þ have been normalised by
R
g x
ð Þ to account for a different
number of atoms (and hence vibrational modes) in the unit cell
according to the indirect up-pumping mechanism . . . . . . . . . . . . 166
Fig. 5.5
Overtone contributions to vibrational up-pumping in HMX
polymorphs. The overtones are shown for (blue) N ¼ 2 and
(green) N ¼ 3, and overlain by g x
ð Þ (black) . . . . . . . . . . . . . . . 167
Fig. 5.6
XRPD profiles for FOX-7 before and after BAM hammer
treatment. Experimental patterns (black) are compared to
simulated (blue) a-FOX-7 and (green) c-FOX-7 in all cases.
Note a small offset in the position of the experimental peak of
c-FOX-7 at d % 5.5 Å, which corresponds to the
crystallographic (0 0 2) plane. This offset is due to minor
misalignment of the diffractometer and sample geometry . . . . . . 169
xxvi
List of Figures
(Left) calculation of the temperature independent overtone
contribution to N = 3. (Right) Two-level system with
equilibrium temperature 300 K. The addition of temperature in
the latter is responsible for the large increase in the y-axis . . . . . 149
Fig. 4.26 a Molecular structure of TATP. b Crystallographic structure of
TATP. c Zone-centre g x
ð Þ for TATP, and d X
2
ð Þ , with the
restriction that x 2 \ X max . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 150
Fig. 5.1
Structure of HMX. a Schematic representation of the HMX
molecule. b Crystal structure of b-HMX P2 1 =c (CCDC Ref:
OCHTET01). (C) Crystal structure of d-HMX P6 1 (CCDC
Ref: OCHTET03). Atoms are coloured as (red) oxygen, (blue)
nitrogen, (grey) carbon, and (white) hydrogen . . . . . . . . . . . . . . 158
Fig. 5.2
Structure of FOX-7. a Schematic representation of the FOX-7
molecular structure. (B) Crystal structure of a-FOX-7 P2 1 =n
(CCDC Ref: SEDTUQ03). c Crystal structure of b-FOX-7
P2 1 2 1 2 1 (CCDC Ref: SEDTUQ06). c Crystal structure of
c-FOX-7 P2 1 =n (From Crawford et al. [25]). The angle
between FOX-7 molecules (∠(FOX-7)) is given in each case.
Atoms are coloured as (red) oxygen, (blue) nitrogen, (grey)
carbon and (white) hydrogen . . . . . . . . . . . . . . . . . . . . . . . . . . . 159
Fig. 5.3
Inelastic neutron scattering spectra of d-HMX at ca. 10 K.
(top) The experimental pattern and (bottom) simulated patterns
are given. The latter is generated from C-point frequencies
only. The vertical dotted line indicates X max in each case . . . . . 164
Fig. 5.4
Comparison of the vibrational structure of two HMX
polymorphs. (Top) g x
ð Þ and X
2
ð Þ for b-HMX, and (bottom)
g x
ð Þ and X
2
ð Þ for d-HMX. 0 ! X max and X max ! 2X max are
identified in g x
ð Þ by yellow and purple, respectively. Note that
X
2
ð Þ have been normalised by
R
g x
ð Þ to account for a different
number of atoms (and hence vibrational modes) in the unit cell
according to the indirect up-pumping mechanism . . . . . . . . . . . . 166
Fig. 5.5
Overtone contributions to vibrational up-pumping in HMX
polymorphs. The overtones are shown for (blue) N ¼ 2 and
(green) N ¼ 3, and overlain by g x
ð Þ (black) . . . . . . . . . . . . . . . 167
Fig. 5.6
XRPD profiles for FOX-7 before and after BAM hammer
treatment. Experimental patterns (black) are compared to
simulated (blue) a-FOX-7 and (green) c-FOX-7 in all cases.
Note a small offset in the position of the experimental peak of
c-FOX-7 at d % 5.5 Å, which corresponds to the
crystallographic (0 0 2) plane. This offset is due to minor
misalignment of the diffractometer and sample geometry . . . . . . 169
xxvi
List of Figures