3.4 Methods
73
Band structures were generated along high symmetry paths. As GGA based band
gaps are known to provide poor agreement with experiment, further band structures were generated in CRYSTAL17 [64] using the HSE06 [65] hybrid DFT functional (with localised basis sets available from the CRYSTAL17 database: N-N_m-6311G(d)_Heyd_2005 [66]; Na, Li, C; H-TZVP [66]; Ba-HAYWSC-3111(2d)G [67];
Ag-From Ref. [68]; and Sn- DURAND-21G* [69]) which has been demonstrated
to offer reasonable agreement with experimental band gaps for a broad range of
materials [70]. Those presented here can therefore be regarded as accurate to within
a reasonable level of confidence. The wavefunction was converged to < 10
−8 , and
convergence criteria TOLINTEG 7 7 7 19 30, as recommended for this functional
and basis set [66]. The electronic structure was calculated at 172 k-points across a 7
× 7 × 7 Monkhorst-Pack grid [61]. Analysis of the crystal overlap Hamilton populations (COHP) [71] were performed using the properties code, as implemented in
the CRYSTAL17 suite. A minimal basis set (STO-6G) was used to avoid spurious
overlap of basis functions, which were found to contaminate the calculation. COHP
were calculated for directly bonded N atoms in the azido anion.
Inelastic Neutron Scattering Spectroscopy. All spectra were collected on the
TOSCA spectrometer at the ISIS Neutron and Muon source [72, 73]. A sample
of NaN 3 (ca. 1.5) was placed in an aluminium sample holder and cooled to ca. 10 K.
Data were collected for a total of ca. 400 μAh. Both forward and back-scattered data
were summed and corrected for scattering from the sample holder and background.
All data processing was done using Mantid [74]. Simulated spectrum was generated
using ABINS [75], as implemented in Mantid.
3.5 Results and Discussion
3.5.1 Bond Rupture of Explosophoric N
−
3
The initiation of an energetic material involves rapid release of chemical potential
energy. This process must therefore involve rupture of a covalent bond within the
explosophoric moiety of the material. Within the azide materials, this is rupture of an
N-N bond. In their ground state structures, the azide materials contain a closed-shell
N
−
3 molecule. It is therefore necessary to understand the reactivity of this molecule.
Due to the delocalised nature of electronic states in solids, however, there is an
intimate interaction between the electronic states of the counter-ion and the azido
anion. Further, with the unavoidable presence of intrinsic defects (e.g. vacancies),
the electronic band structures will likely include some additional states within the
band gap that may influence sensitivity [76, 77]. A variety of pathways are therefore
available for the reduction or oxidation of the azido anion species within the solid
state. Only those in the ideal crystal are considered through this Chapter.
73
Band structures were generated along high symmetry paths. As GGA based band
gaps are known to provide poor agreement with experiment, further band structures were generated in CRYSTAL17 [64] using the HSE06 [65] hybrid DFT functional (with localised basis sets available from the CRYSTAL17 database: N-N_m-6311G(d)_Heyd_2005 [66]; Na, Li, C; H-TZVP [66]; Ba-HAYWSC-3111(2d)G [67];
Ag-From Ref. [68]; and Sn- DURAND-21G* [69]) which has been demonstrated
to offer reasonable agreement with experimental band gaps for a broad range of
materials [70]. Those presented here can therefore be regarded as accurate to within
a reasonable level of confidence. The wavefunction was converged to < 10
−8 , and
convergence criteria TOLINTEG 7 7 7 19 30, as recommended for this functional
and basis set [66]. The electronic structure was calculated at 172 k-points across a 7
× 7 × 7 Monkhorst-Pack grid [61]. Analysis of the crystal overlap Hamilton populations (COHP) [71] were performed using the properties code, as implemented in
the CRYSTAL17 suite. A minimal basis set (STO-6G) was used to avoid spurious
overlap of basis functions, which were found to contaminate the calculation. COHP
were calculated for directly bonded N atoms in the azido anion.
Inelastic Neutron Scattering Spectroscopy. All spectra were collected on the
TOSCA spectrometer at the ISIS Neutron and Muon source [72, 73]. A sample
of NaN 3 (ca. 1.5) was placed in an aluminium sample holder and cooled to ca. 10 K.
Data were collected for a total of ca. 400 μAh. Both forward and back-scattered data
were summed and corrected for scattering from the sample holder and background.
All data processing was done using Mantid [74]. Simulated spectrum was generated
using ABINS [75], as implemented in Mantid.
3.5 Results and Discussion
3.5.1 Bond Rupture of Explosophoric N
−
3
The initiation of an energetic material involves rapid release of chemical potential
energy. This process must therefore involve rupture of a covalent bond within the
explosophoric moiety of the material. Within the azide materials, this is rupture of an
N-N bond. In their ground state structures, the azide materials contain a closed-shell
N
−
3 molecule. It is therefore necessary to understand the reactivity of this molecule.
Due to the delocalised nature of electronic states in solids, however, there is an
intimate interaction between the electronic states of the counter-ion and the azido
anion. Further, with the unavoidable presence of intrinsic defects (e.g. vacancies),
the electronic band structures will likely include some additional states within the
band gap that may influence sensitivity [76, 77]. A variety of pathways are therefore
available for the reduction or oxidation of the azido anion species within the solid
state. Only those in the ideal crystal are considered through this Chapter.