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双折射作为光学晶体的基本参数, 在相位调制、分光、偏振等许多光学应用中发挥着重要的作用, 是激光科学与技术中的关键材料, 而钒酸盐多面体较大双折射率为开发双折射材料提供了一条新的途径. 本文采用第一性原理研究4种碱金属钒酸盐AV3O8 (A = Li, Na, K, Rb)晶体的能带结构、态密度、电子局域函数和双折射率. 计算结果表明碱金属钒酸盐AV3O8 (A = Li, Na, K, Rb)均为间接带隙, 带隙值分别为1.695, 1.898, 1.965和1.984 eV. 对态密度分析可知在费米能级附近, 碱金属钒酸盐AV3O8 (A = Li, Na, K, Rb)导带底主要被V原子的最外层轨道所占据, 价带顶的主要贡献者是O-2p轨道, O原子的2p轨道还在费米能级附近表现出较强的局域性, 结合HOMO和LUMO以及布居分析说明在4种晶体中主要由V-3p轨道与O的2p轨道成键, V—O表现为强的共价键. 通过对晶体结构与光学性质关系的分析, 晶体较大的各向异性, 较高水平的响应电子分布各向异性指数, 阴离子基团的特殊排列和V-3d和O-2p轨道形成的d-p轨道杂化都是导致其大双折射率的主要原因, 经计算所得LiV3O8, NaV3O8, KV3O8和RbV3O8在1064 nm处的双折射率分别为0.28, 0.30, 0.28和0.27.Birefringence, as a fundamental parameter of optical crystals, plays a vital role in numerous optical applications such as phase modulation, light splitting, and polarization, thereby making them key materials in laser science and technology. The significant birefringence of vanadate polyhedra provides a new approach for developing birefringent materials. In this study, first-principles calculations are used to investigate the band structures, density of states (DOS), electron localization functions (ELFs), and birefringence behaviors of four alkali metal vanadate crystals AV3O8 (A = Li, Na, K, Rb). The computational results show that all AV3O8 crystals have indirect band gaps, whose values are 1.695, 1.898, 1.965, and 1.984 eV for LiV3O8, NaV3O8, KV3O8, and RbV3O8, respectively. The DOS analysis reveals that near the Fermi level, the conduction band minima (CBM) in these vanadates are predominantly occupied by the outermost orbitals of V atoms, while the valence band maxima (VBM) are primarily contributed by O-2p orbitals. The O-2p orbitals also exhibit strong localization near the Fermi level. Combined with highest occupied molecular orbital-lowest unoccupied molecular orbital (HOMO-LUMO) analysis and population analysis, the bonding interactions in all four crystals mainly arise from the hybridization between V-3p and O-2p orbitals, indicating strong covalent bonding in V—O bonds. Through the analysis of structure-property relationships, the large birefringence is primarily attributed to the pronounced structural anisotropy, high anisotropy index of responsive electron distribution, unique arrangement of anionic groups, and d-p orbital hybridization between V-3d and O-2p orbitals. The calculated birefringence values at a wavelength of 1064 nm for LiV3O8, NaV3O8, KV3O8, and RbV3O8 are 0.28, 0.30, 0.28, and 0.27, respectively.
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Keywords:
- alkali metal vanadate /
- first principles /
- electronic structure /
- birefringence
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图 1 四种物质的晶体结构 (a) LiV3O8; (b) NaV3O8; (c) KV3O8; (d) RbV3O8
Fig. 1. Four types of crystal structures of substances: (a) LiV3O8; (b) NaV3O8; (c) KV3O8; (d) RbV3O8.
图 2 四种化合物的能带结构图 (a) LiV3O8; (b) NaV3O8; (c) KV3O8; (d) RbV3O8
Fig. 2. Band structure diagrams of four compounds: (a) LiV3O8; (b) NaV3O8; (c) KV3O8; (d) RbV3O8.
图 3 四种化合物的态密度图及HOMO&LUMO (a) LiV3O8; (b) NaV3O8; (c) KV3O8; (d) RbV3O8
Fig. 3. Density of states diagrams for four compounds and HOMO&LUMO: (a) LiV3O8; (b) NaV3O8; (c) KV3O8; (d) RbV3O8.
图 4 四种化合物的电子局域函数 (a) LiV3O8; (b) NaV3O8; (c) KV3O8; (d) RbV3O8
Fig. 4. Electron localization function of four compounds: (a) LiV3O8; (b) NaV3O8; (c) KV3O8; (d) RbV3O8.
图 6 四种化合物的双折射率 (a) LiV3O8; (b) NaV3O8; (c) KV3O8; (d) RbV3O8
Fig. 6. Birefringence of four compounds: (a) LiV3O8; (b) NaV3O8; (c) KV3O8; (d) RbV3O8.
图 7 四种化合物的杨氏模量各向异性三维图 (a) LiV3O8; (b) NaV3O8; (c) KV3O8; (d) RbV3O8
Fig. 7. 3D plot of Young’s modulus anisotropy for four compounds: (a) LiV3O8; (b) NaV3O8; (c) KV3O8; (d) RbV3O8.
表 1 结构优化前后的AV3O8 (A = Li, Na, K, Rb)晶格参数
Table 1. Lattice parameters of AV3O8 (A = Li, Na, K, Rb) before and after geometry optimization.
Compounds a/nm b/nm c/nm β/(°) b/c Error V/nm3 LiV3O8 Before 0.668 0.360 1.203 107.830 0.299 1.67% 0.275 After 0.695 0.358 1.219 108.397 0.294 0.288 NaV3O8 Before 0.512 0.855 0.744 101.993 1.148 3.92% 0.319 After 0.531 0.877 0.795 113.173 1.103 0.350 KV3O8 Before 0.500 0.839 0.767 98.135 1.094 4.84% 0.319 After 0.516 0.865 0.831 103.812 1.041 0.361 RbV3O8 Before 0.501 0.842 0.791 96.943 1.064 2.16% 0.331 After 0.516 0.865 0.831 100.581 1.041 0.365 
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表 2 AV3O8 (A = Li, Na, K, Rb)的布居数 (Mulliken)
Table 2. Population of AV3O8 (A = Li, Na, K, Rb) (Mulliken).
Substance Species Atomic population Total Charge/e Bond Bond
populationLength/Å s p d LiV3O8 Li –0.20 0.00 0.00 –0.20 1.20 Li—O –0.06 2.16 V 0.20 0.31 3.20 3.71 1.29 O—V 0.01 2.86 O 1.90 4.68 0.00 6.59 –0.59 O—V 0.92 1.66 NaV3O8 Na 2.07 5.95 0.00 8.01 0.99 Na—O 0.02 2.38 V 0.15 0.33 3.18 3.66 1.34 O—V 0.92 1.64 O 1.89 4.72 0.00 6.62 –0.62 O—V 0.33 1.99 KV3O8 K 2.03 5.91 0.00 7.95 1.05 K—O 0.04 2.72 V 0.15 0.34 3.32 3.72 1.28 O—V 0.97 1.64 O 1.89 4.74 0.00 6.63 –0.63 O—V 0.33 1.98 RbV3O8 Rb 2.04 5.86 0.00 7.90 1.10 Rb—O 0.04 2.97 V 0.16 0.35 3.23 3.74 1.26 O—V 0.98 1.64 O 1.89 4.74 0.00 6.64 –0.64 O—V 0.34 1.98
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表 3 AV3O8 (A = Li, Na, K, Rb)的响应电子分布的REDA
Table 3. REDA of AV3O8 (A = Li, Na, K, Rb) of the electron distribution.
Compounds Groups δ Δn LiV3O8 VO4 0.011 0.28 NaV3O8 V3O8 0.019 0.30 KV3O8 V3O8 0.013 0.28 RbV3O8 V3O8 0.012 0.27
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