Fig. 3.15 a Partial electronic density of states as a function of M 17 , with
contributions from N 3
− (black) and Na
+ (blue). The relative
energy of F at h NNN = 180
o is shown as a red vertical line in
the perturbed structures. b Electronic band structures for NaN 3
with h NNN ¼ 180
and h NNN ¼ 110
. F is marked with a
dotted line. Figure from Ref. [2], https://doi.org/10.1039/
C8CP06161K. Copyright CC-BY . . . . . . . . . . . . . . . . . . . . . . . . 91
Fig. 3.16 Effect of M 22 and M 24 (i.e. d R s and d R as , respectively) on the
electronic band gap. The latter is plotted as a, defined as in
Fig. 3.5. Band gaps are defined as direct (d) or indirect (i) and
the arrow indicates that the indirect band gap continues. To
reflect perturbation of two azido anions (in the conventional
cell), energy is given per molecule. Figure from Ref. [2],
https://doi.org/10.1039/C8CP06161K. Copyright CC-BY . . . . . . 92
Fig. 3.17 Phonon dispersion curves for the energetic azides. All are
given for the primitive cell except AgN 3 . . . . . . . . . . . . . . . . . . 95
Fig. 3.18 The phonon density of states for the crystalline azide materials
studied here. The vertical dotted line indicates X max , and the
blue rectangle highlights the position of x T . Red indicates
azido anion partial DOS. Figure from Ref. [1], https://doi.org/
10.1021/acs.jpcc.8b05285. Copyright 2018 American
Chemical Society . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 96
Fig. 3.19 Identification of target modes. The azide bend at each C-point
normal mode is highlighted . . . . . . . . . . . . . . . . . . . . . . . . . . . . 97
Fig. 3.20 Overtone pathways for phonon up-pumping. a Example of
overtone coupling in AgN 3 , showing the (black) PDOS, (blue)
N = 2 overtone, (green) N = 3 overtone and (pink) N = 4
overtone. b Integration over x T Æ 10 cm
−1 for the overtone
pathways available in the crystalline azide materials, arranged
in approximate order of increasing sensitivity. Values are
given as sums across all target modes. Overtones N = 2
(black), N = 3 (red) and N = 4 (blue) are shown, alongside
N2 + N3 (green), as well as N2 + N3 + N4 (orange).
c Renormalisation of the N2 + N3 overtone curve by the
number of N
À
3 molecules in the unit cell . . . . . . . . . . . . . . . . . . 100
Fig. 3.21 Two phonon density of states (2PDOS; X
(2) ) for the azides,
calculated by enforcing both x q 0 j 0 and x q 00 j 00 < 2X max (black).
The difference between this restricted 2PDOS and that
produced by considering all combination modes is also shown
(blue). The PDOS is given in red. X max is given as a vertical
dotted line, and x T is indicated with an arrow . . . . . . . . . . . . . . 102
xxii
List of Figures
contributions from N 3
− (black) and Na
+ (blue). The relative
energy of F at h NNN = 180
o is shown as a red vertical line in
the perturbed structures. b Electronic band structures for NaN 3
with h NNN ¼ 180
and h NNN ¼ 110
. F is marked with a
dotted line. Figure from Ref. [2], https://doi.org/10.1039/
C8CP06161K. Copyright CC-BY . . . . . . . . . . . . . . . . . . . . . . . . 91
Fig. 3.16 Effect of M 22 and M 24 (i.e. d R s and d R as , respectively) on the
electronic band gap. The latter is plotted as a, defined as in
Fig. 3.5. Band gaps are defined as direct (d) or indirect (i) and
the arrow indicates that the indirect band gap continues. To
reflect perturbation of two azido anions (in the conventional
cell), energy is given per molecule. Figure from Ref. [2],
https://doi.org/10.1039/C8CP06161K. Copyright CC-BY . . . . . . 92
Fig. 3.17 Phonon dispersion curves for the energetic azides. All are
given for the primitive cell except AgN 3 . . . . . . . . . . . . . . . . . . 95
Fig. 3.18 The phonon density of states for the crystalline azide materials
studied here. The vertical dotted line indicates X max , and the
blue rectangle highlights the position of x T . Red indicates
azido anion partial DOS. Figure from Ref. [1], https://doi.org/
10.1021/acs.jpcc.8b05285. Copyright 2018 American
Chemical Society . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 96
Fig. 3.19 Identification of target modes. The azide bend at each C-point
normal mode is highlighted . . . . . . . . . . . . . . . . . . . . . . . . . . . . 97
Fig. 3.20 Overtone pathways for phonon up-pumping. a Example of
overtone coupling in AgN 3 , showing the (black) PDOS, (blue)
N = 2 overtone, (green) N = 3 overtone and (pink) N = 4
overtone. b Integration over x T Æ 10 cm
−1 for the overtone
pathways available in the crystalline azide materials, arranged
in approximate order of increasing sensitivity. Values are
given as sums across all target modes. Overtones N = 2
(black), N = 3 (red) and N = 4 (blue) are shown, alongside
N2 + N3 (green), as well as N2 + N3 + N4 (orange).
c Renormalisation of the N2 + N3 overtone curve by the
number of N
À
3 molecules in the unit cell . . . . . . . . . . . . . . . . . . 100
Fig. 3.21 Two phonon density of states (2PDOS; X
(2) ) for the azides,
calculated by enforcing both x q 0 j 0 and x q 00 j 00 < 2X max (black).
The difference between this restricted 2PDOS and that
produced by considering all combination modes is also shown
(blue). The PDOS is given in red. X max is given as a vertical
dotted line, and x T is indicated with an arrow . . . . . . . . . . . . . . 102
xxii
List of Figures