Figure 4: Various modes of vibration at different frequencies:
(a-b) bending, (c) symmetrical stretching, (d) asymmetrical stretching,
(e-f) symmetrical stretching.
Electronic Properties
The electronic structure calculations have been carried out using CASTEP
simulation code. The electronic density of states and band structure
shown in figures (5-7) are calculated by utilizing LDA, PBE and HSE06
functionals, respectively. Figures (a) reveal band structures while
figures (b) demonstrate corresponding DOS plots. In all figures (5-7)
(a), it has been noticed that the electron-hole pair recombination took
place at Γ (gamma) symmetry point of the first Brillouin Zone with a
significant energy gap of magnitudes 6.35 eV, 6.81 eV and 7.58 eV using
LDA, PBE and HSE06 functionals respectively, leading to the direct band
gap insulating material. As depicted by the figure (5-7) (b), the
density of states are found in wide range of energy, i.e., from 13.96 eV
to -7.5 eV, 9.51 eV to -7.5 eV, and 15 eV to -7.5 eV for respective
functionals. The highest edge of the valence band (VBM) is found on the
Fermi level, which is set at zero energy, while lowest edges of the
conduction bands (CBM) are noted at 6.35 eV, 6.81 eV and 7.58 eV for
three different functionals, i.e., LDA, PBE and HSE06 respectively. 1s,
1s2 2s1, and 2s22p1 are the pseudo-states for H, Li, and B atoms
respectively which are contributing in conduction mechanism. The highest
value of band gap for HSE06 functional is due to underestimating the
lattice constants as mentioned in structural properties section 3.1.
Comparatively, it has been concluded that our theoretically estimated
value of the band gap of 6.81 eV using PBE functional is
~4.1% smaller than the former experimental value of 7.1
eV reported for LiBH4 [27], which is an acceptable
precision range. The value of band gap was found to be very close to the
previously reported values of 6.80 eV and 6.95 eV by Miwa et al.and Ghellab et al. [31-32] respectively using diverse
calculation codes. Figure 8 illustrates the behavior of atomic orbitals
of each element of the studied compound. From this figure, it is seen
that in the conduction band region, p -states of Li atoms mainly
contribute between the energy range 7.0 eV to 12.5 eV. However, denser
bands near the Fermi level and large peaks in density of states are seen
due to p -state of B atoms and s -states of H atoms in
energy range from -2.5 eV to 0 eV in the valence band. Thes -states of H and B atoms lie in lower region of the valence
bands in between -7.5 eV to -5.2 eV energy range which look exactly
similar to total density of states in this region of valence band.