3.1. Structural properties
The space group of tetragonal structure B3N3H6 is P43212. The crystal mode of B3N3H6 is shown in Fig. 1 after structural optimization, it is an equilibrium crystal structure of Borazine. The optimized structural parameters of B3N3H6 are given in Table 1 as well as experimental data. It can be seen that the values based on the GGA PBE-TS functional are in good agreement with the experimental results, indicating that this functional can well describe the crystal structure of Borazine. Hence, the physical properties of Borazine are solved by the GGA PBE-TS in the following work.
Table 1
The optimized structural parameters of B3N3H6 along with the results of previous experimental data.
|
This work
|
Experimental data [1]
|
LDA
|
GGA PBE-G
|
GGA PBE-TS
|
a (Å)
|
4.787
|
5.115
|
5.315
|
5.463
|
c (Å)
|
13.699
|
15.264
|
16.204
|
16.315
|
3.2. Electronic properties
The band structure of B3N3H6 calculated within the GGA PBE-TS is shown in Fig. 2. From the band structure, it is shown that B3N3H6 has an indirect band gap because the top of valence band is found at G point while the bottom of conduction band is found at A point. The band gap is calculated to be 5.007 eV, so we can know that B3N3H6 is an insulator. The calculated band gap value is smaller than the experimental value of 6.5 eV [27]. The discrepancy is due to the well-known underestimation of DFT calculations. In the band structure, the valence bands are roughly divided into three regions: -16.0 eV to -14.0 eV (lower), -7.5 eV to 6.0 eV (middle) and − 4.5 eV to 0 eV (higher). Figure 3 shows the total and the partial density of states (DOS) of B3N3H6. With the states between − 16 eV and − 12.5 eV, there is the interaction of N 2s, B 2p and H 1s. The states between − 8eV and − 5eV are predominantly composed of N 2p, B 2s and all hydrogen’s 1s. The valence bands basically arise from interaction of N 2p, B 2p and H 1s states in the Fermi level.
3.3. Optical properties
The optical properties such as the complex dielectric function, complex refractive index, complex conductivity function, reflectivity, loss function and absorption coefficient are important, which can be obtained from the complex dielectric function [28]:
![](data:image/png;base64,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)
In this section, we present our results of optical properties of B3N3H6 at the equilibrium lattice constants in Figs. 4–9, up to a photon energy of 35 eV. We resolve the optical properties into two independent components: the polarization direction (001) component and the polarization direction (100) component. The calculated real part and imaginary part of complex dielectric function of B3N3H6 are shown in Fig. 4. From this figure, the real part of complex dielectric function is ε1 (001) = 2.209 and ε1 (100) = 2.298. There is a peak (ω (001) = 7.735 eV, ω (100) = 7.577 eV) from 4.5eV to 9eV for imaginary part, which is attributed to transition from the valence bands to conduction bands (t2g). There is a peak (ω (001) = 13.225 eV, ω (100) = 12.863 eV) for the calculated imaginary part, which is due to transition from the valence bands to conduction bands (eg). The complex refractive index of B3N3H6 is shown in Fig. 5. As shown in Fig. 5, we find that the static refractive index are n (001) (0) = 1.486 and n (100) (0) = 1.516. The refractive index reaches a peak at energy of 6.979 eV in (001) component, while it reaches a peak at energy of 6.806 eV in (100) component. Figures 6–9 show the absorption coefficient α(ω), complex conductivity function σ(ω), energy-loss function L(ω) and optical reflectivity R(ω). In each figure, as we can see, the optical anisotropy corresponds to the space group of B3N3H6.
3.4. Vibrational properties
As shown in Fig. 10, there are 144 vibrations including 3 acoustic branches and 141 optical branches. The phonon spectra with no imaginary frequency reveal that B3N3H6 is dynamically stable. There is no significant splitting, which indicates that the B3N3H6 has no ability to change the strength of light as an optical device.
As shown in Fig. 10, the frequencies around 3450 cm− 1 are referred to the vibrations of B-H and N-H, which are parallel to plane
, including anti-symmetry and symmetry vibrations. It indicates that the B-H and N-H have a most dynamic strength. The frequencies around 2550 cm− 1 are B-N anti-symmetric and symmetric vibrations, which are also parallel to above four planes. According to the calculated results, the vibrations of the frequencies above 896 cm− 1 are parallel to four planes. The vibration of phonon is parallel to four planes at high frequencies, it shows that the crystal has a better dynamic stable when the optical radiation along those planes. Below 890 cm− 1, the vibrations begin to be perpendicular and parallel to four planes as well as group vibration. It corresponds to a weak covalent bond strength, so the crystal has a low mechanical modulus and thermal conductivity.