DFT-based ab initio study of structural and electronic properties of lithium fluorooxoborate LiB${}_6$O${}_9$F and experimentally observed second harmonic generation

An ab initio density functional theory–based study of the electronic band structure, the elastic, electric, elastoelectric, and linear and nonlinear optical properties of the new ion conductor LiB${}_6$O${}_9$F, has been performed. The computed band structure reveals a wide direct band gap. The coefficients of the second order nonlinear susceptibility χ${}^{\left(2\right)}$ were found to be comparable to those of KH${}_2$PO${}_4$. Corresponding experimental investigations of second harmonic generation comply with the respective ab initio calculations.

Figure 1

Repetition unit of the chainlike polyoxoanion (a) and crystal structure of LBOF with the margins of the unit cell (b). The B${}_3$O${}_3$ rings are emphasized in gray (Ref. 1).

Figure 2

Differences of calculated and experimental interatomic distances ($d_{\mathrm{calc}}$ − $d_{\exp }$) of the atoms of the LBOF unit cell as a function of the experimental $d_{\exp }$ in the range from 1.3 to 2.8 Å. The dashed line is an averaged magnitude of ($d_{\mathrm{calc}}$ − $d_{\exp }$). The standard deviation is SD $=$ 0.027 Å.

Figure 3

Electronic band structure of LBOF, ρ $=$ 2.1 g/cm${}^3$ (a), and of LBO, ρ $=$ 2.38 g/cm${}^3$ (b), for the optimized crystal structures, on the level of B3LYP.

Figure 4

Unit cell volume dependence of the absolute value of the polarization $P$($V$) of LBOF. The dashed line marks the computed equilibrium geometry.

Figure 5

Spectra of real (ε${}_1$) and imaginary (ε${}_2$) parts of the dielectric permittivity ε(ħω) of LBOF for light polarizations along the principal directions $X$, $Y$, and $Z$ of the optical indicatrix, obtained using the VASP code, with LDA.

Figure 6

Photon energy dependences of the refractive indices $n_a$(ħω), $n_b$(ħω), and $n_c$(ħω): LBOF computed with VASP (LDA) is indicated by thick lines in the range of 0–6 eV, LBO computed with VASP (LDA) is indicated by thin lines in the range of 0–6 eV, LBO computed with CRYSTAL (B3LYP, only for ħω $=$ 0) is indicated by horizontal lines, and experimental LBO (Ref. 3) is indicated by squares ($n_a$), circles ($n_b$), and triangles ($n_c$). $n_a$, $n_b$, and $n_c$ are refractive indices for the directions of the light polarization along the unit cell edges $a$, $b$, and $c$.

Figure 7

Phase matching angles of LBOF (LDA) for type I (PM1) and type II (PM2) for the first photon energy ħω $=$ 1.165 eV (λ $=$ 1064 nm), plotted on the first quadrant.