primitive cell, DFT-D2 phonon dispersion curve using
different q-point sampling densities. Figure from Ref. [2],
https://doi.org/10.1039/C8CP06161K. Copyright CC-BY . . . . . . 83
Fig. 3.9
Phonon dispersion curve calculated using PBE-D2 for the
primitive cell of a-NaN 3 . The zone centre frequencies
calculated with LO-TO correction are highlighted
as pink dots . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 85
Fig. 3.10 Tilting of the azido anion molecule showing a M 6 , b M 8 , c M 9
and d M 16 . Closed symbols are derived from rectilinear
application of eigenvectors, and open symbols result from
correction to the N-N bond lengths. The band gap is initially a
direct band gap (D), but becomes indirect (I) on perturbation.
Inset graphics show the distortion (green molecule) with
respect to the unperturbed (purple) molecular position. Band
gap based on HSE06 calculation. Figure from Ref. [2], https://
doi.org/10.1039/C8CP06161K. Copyright CC-BY . . . . . . . . . . . 86
Fig. 3.11 Calculated band gap for M 16 extended to large perturbation.
Band gap based on HSE06 calculation. Figure from Ref. [2],
https://doi.org/10.1039/C8CP06161K. Copyright CC-BY . . . . . . 87
Fig. 3.12 Comparison of the electronic band gap under equilibrium and
after imposing an a ¼ 8 fold perturbation of M 16 . a The partial
DOS is given for (black) N and (blue) Na species. The vertical
dotted line on (a) is given to indicate the Fermi surface ( F ),
and the red vertical line shows the energy of F relative to the
unperturbed structure. b The electronic band structure plotted
along high symmetry lines in the Brillouin zone for (left)
unperturbed and (right) a ¼ 8 structures. Figure from Ref. [2],
https://doi.org/10.1039/C8CP06161K. Copyright CC-BY . . . . . . 88
Fig. 3.13 Effect of external vibration normal coordinates on the energies
and band gap of a-NaN 3 . Mode numbers are indicated in
brackets in each plot. Modes are identified as, (Left)M 4 (-●-),
M 5 (-■-), M 7 (-▲-), M 10 (-♦-), (Right) M 11 (-■-), M 12 (-●-),
M 13 (-▲-), M 14 (-♦-), M 15 (-★-). Figure from Ref. [2], https://
doi.org/10.1039/C8CP06161K. Copyright CC-BY . . . . . . . . . . . 89
Fig. 3.14 Effect of M 17 (left) and M 19 (right) on the band gaps and
energies of a-NaN 3 . Band gap momentum conservation is
indicated as direct (D) or indirect (I). The arrow indicates
continuation of an indirect band gap. Band gaps from HSE06
calculation. 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 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 90
List of Figures
xxi
different q-point sampling densities. Figure from Ref. [2],
https://doi.org/10.1039/C8CP06161K. Copyright CC-BY . . . . . . 83
Fig. 3.9
Phonon dispersion curve calculated using PBE-D2 for the
primitive cell of a-NaN 3 . The zone centre frequencies
calculated with LO-TO correction are highlighted
as pink dots . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 85
Fig. 3.10 Tilting of the azido anion molecule showing a M 6 , b M 8 , c M 9
and d M 16 . Closed symbols are derived from rectilinear
application of eigenvectors, and open symbols result from
correction to the N-N bond lengths. The band gap is initially a
direct band gap (D), but becomes indirect (I) on perturbation.
Inset graphics show the distortion (green molecule) with
respect to the unperturbed (purple) molecular position. Band
gap based on HSE06 calculation. Figure from Ref. [2], https://
doi.org/10.1039/C8CP06161K. Copyright CC-BY . . . . . . . . . . . 86
Fig. 3.11 Calculated band gap for M 16 extended to large perturbation.
Band gap based on HSE06 calculation. Figure from Ref. [2],
https://doi.org/10.1039/C8CP06161K. Copyright CC-BY . . . . . . 87
Fig. 3.12 Comparison of the electronic band gap under equilibrium and
after imposing an a ¼ 8 fold perturbation of M 16 . a The partial
DOS is given for (black) N and (blue) Na species. The vertical
dotted line on (a) is given to indicate the Fermi surface ( F ),
and the red vertical line shows the energy of F relative to the
unperturbed structure. b The electronic band structure plotted
along high symmetry lines in the Brillouin zone for (left)
unperturbed and (right) a ¼ 8 structures. Figure from Ref. [2],
https://doi.org/10.1039/C8CP06161K. Copyright CC-BY . . . . . . 88
Fig. 3.13 Effect of external vibration normal coordinates on the energies
and band gap of a-NaN 3 . Mode numbers are indicated in
brackets in each plot. Modes are identified as, (Left)M 4 (-●-),
M 5 (-■-), M 7 (-▲-), M 10 (-♦-), (Right) M 11 (-■-), M 12 (-●-),
M 13 (-▲-), M 14 (-♦-), M 15 (-★-). Figure from Ref. [2], https://
doi.org/10.1039/C8CP06161K. Copyright CC-BY . . . . . . . . . . . 89
Fig. 3.14 Effect of M 17 (left) and M 19 (right) on the band gaps and
energies of a-NaN 3 . Band gap momentum conservation is
indicated as direct (D) or indirect (I). The arrow indicates
continuation of an indirect band gap. Band gaps from HSE06
calculation. 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 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 90
List of Figures
xxi