First-principles study of mechanism of high birefringence in alkali metal vanadates AV3O8 (A = Li, Na, K, Rb)

WAN Fuhong; DING Jiafu; HE Zhihao; WANG Yunjie; CUI Jian; LI Jiajun; SU Xin; HUANG Yineng

doi:10.7498/aps.74.20241631

Abstract
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.

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

Figure 1. Four types of crystal structures of substances: (a) LiV₃O₈; (b) NaV₃O₈; (c) KV₃O₈; (d) RbV₃O₈.

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图 2 四种化合物的能带结构图　(a) LiV₃O₈; (b) NaV₃O₈; (c) KV₃O₈; (d) RbV₃O₈

Figure 2. Band structure diagrams of four compounds: (a) LiV₃O₈; (b) NaV₃O₈; (c) KV₃O₈; (d) RbV₃O₈.

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图 3 四种化合物的态密度图及HOMO&LUMO　(a) LiV₃O₈; (b) NaV₃O₈; (c) KV₃O₈; (d) RbV₃O₈

Figure 3. Density of states diagrams for four compounds and HOMO&LUMO: (a) LiV₃O₈; (b) NaV₃O₈; (c) KV₃O₈; (d) RbV₃O₈.

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图 4 四种化合物的电子局域函数　(a) LiV₃O₈; (b) NaV₃O₈; (c) KV₃O₈; (d) RbV₃O₈

Figure 4. Electron localization function of four compounds: (a) LiV₃O₈; (b) NaV₃O₈; (c) KV₃O₈; (d) RbV₃O₈.

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图 5 双折射原理示意图

Figure 5. Schematic diagram of the principle of birefringence.

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图 6 四种化合物的双折射率 (a) LiV₃O₈; (b) NaV₃O₈; (c) KV₃O₈; (d) RbV₃O₈

Figure 6. Birefringence of four compounds: (a) LiV₃O₈; (b) NaV₃O₈; (c) KV₃O₈; (d) RbV₃O₈.

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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

Figure 7. 3D plot of Young’s modulus anisotropy for four compounds: (a) LiV₃O₈; (b) NaV₃O₈; (c) KV₃O₈; (d) RbV₃O₈.

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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
LiV₃O₈	After	0.695	0.358	1.219	108.397	0.294	1.67%	0.288
NaV₃O₈	Before	0.512	0.855	0.744	101.993	1.148	3.92%	0.319
NaV₃O₈	After	0.531	0.877	0.795	113.173	1.103	3.92%	0.350
KV₃O₈	Before	0.500	0.839	0.767	98.135	1.094	4.84%	0.319
KV₃O₈	After	0.516	0.865	0.831	103.812	1.041	4.84%	0.361
RbV₃O₈	Before	0.501	0.842	0.791	96.943	1.064	2.16%	0.331
RbV₃O₈	After	0.516	0.865	0.831	100.581	1.041	2.16%	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 population	Length/Å
Substance	Species	s	p	d	Total	Charge/e	Bond	Bond population	Length/Å
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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First-principles study of mechanism of high birefringence in alkali metal vanadates AV₃O₈ (A = Li, Na, K, Rb)

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