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:

Authors and contacts

1.
College of Physical Science and Technology, Yili Normal University, Yining 835000, China
2.
Xinjiang Laboratory of Condensed Matter Phase Transition and Microstructure, Yili Normal University, Yining 835000, China

Corresponding author: SU Xin, suxin_phy@sina.com ; HUANG Yineng, ynhuang@nju.edu.cn

Funds: Project supported by the Open Project of Key Laboratory of Xinjiang Uygur Autonomous Region, China (Grant No. 2023D04074), the Scientific Research Project of Yili Normal University, China (Grant No. 22XKZZ21), and the Innovation Training Project for College Students of Yili Normal University, China (Grant Nos. S202210764014, S202210764015, S202210764016).

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References

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Cited By

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

DownLoad: CSV

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)的响应电子分布各向异性指数(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

DownLoad: CSV

[1]	Pedrotti F L, Pedrotti L M, Pedrotti L S 2018 Introduction to optics (England: Cambridge University Press) pp333–360
[2]	Li X Z, Wang C, Chen X L, Li H, Jia L S, Wu L, Du Y X, Xu Y P 2004 Inorg. Chem. 43 8555 Google Scholar
[3]	Nomura H, Furutono Y 2008 Microelectron. Eng. 85 1671 Google Scholar
[4]	Aoki K, Miyazaki H T, Hirayama H 2003 Nat. Mater. 2 117 Google Scholar
[5]	Lancry M, Desmarchelier R, Cook K, Poumellec B, Canning J 2014 Micromachines-Basel 5 825 Google Scholar
[6]	Li R 2013 Z. Krist-Cryst. Mater. 228 526 Google Scholar
[7]	Levy M, Jalali A A, Huang X 2009 J. Mater. Sci. Mater. El. 20 43 Google Scholar
[8]	Zhang H, Zhang M, Pan S L, Yang Z H, Wang Z, Bian Q, Hou X L, Yu H W, Zhang F F, Wu K, Yang F, Peng Q J, Xu Z Y, Chang K B, Poeppelmeier K R 2015 Cryst. Growth Des. 15 523 Google Scholar
[9]	Ghosh G 1999 Opt. Commun. 163 95 Google Scholar
[10]	Luo H, Tkaczyk T, Sampson R, Dereniak E L 2006 Proc. SPIE 6119 136 Google Scholar
[11]	Guoqing Z, Jun X, Xingda C, Heyu Z, Siting W, Ke X, Fuxi G 1998 J. Cryst. Growth 191 517 Google Scholar
[12]	Appel R, Dyer C D, Lockwood J N 2002 Appl. Opt. 41 2470 Google Scholar
[13]	Cyranoski D 2009 Nature 457 953 Google Scholar
[14]	Krainer L, Paschotta R, Lecomte S, Moser M, Weingarten K J, Keller U 2002 IEEE J. Quantum Electron. 38 1331 Google Scholar
[15]	Lisinetskii V A, Grabtchiko A S, Demidovich A A, Burakevich V N, Orlovich V A, Titov A N 2007 Appl. Phys. B 88 499 Google Scholar
[16]	Vodchits A I, Orlovich V A, Apanasevich P A 2012 J. Appl. Spectrosc. 78 918 Google Scholar
[17]	Yu H, Liu J, Zhang H, Kaminskii A A, Wang Z, Wang J 2014 Laser Photonics Rev. 8 847 Google Scholar
[18]	Lei B H, Kong Q, Yang Z H, Yang Y, Wang Y J, Pan S L 2016 J. Mater. Chem. C 4 6295 Google Scholar
[19]	Li K X, Zhang X Y, Chai B Q, Yu H W, Hu Z G, Wang J Y, Wu Y C, Wu H P 2025 Chem. Eur. J. 31 e202403515 Google Scholar
[20]	Li K X, Wu H P, Yu H W, Hu Z G, Wang J Y, Wu Y C 2024 Chem. Commun. 60 12734 Google Scholar
[21]	Lei B H, Yang Z H, Pan S L 2017 Chem. Commun. 53 2818 Google Scholar
[22]	Huang Y, Zhang X Y, Zhao S G, Mao J G, Yang B P 2024 J. Mater. Chem. C 12 7286 Google Scholar
[23]	Zhang S Z, Dong L F, Xu B H, Chen H G, Huo H, Liang F, Wu R, Gong P F, Lin Z S 2024 Inorg. Chem. Front. 11 5528 Google Scholar
[24]	Cheng J L, Xu D, Lu J, Zhang F F, Hou X L 2023 Inorg. Chem. 62 20340 Google Scholar
[25]	Chen Z X, Xu F, Cao S N, Li Z F, Yang H X, Ai X P, Cao Y L 2017 Small 13 1603148 Google Scholar
[26]	Cao X Y, Yang Q, Zhu L M, Xie L L 2018 Ionics 24 943 Google Scholar
[27]	Yang H, Li J, Zhang X G, Jin Y L 2008 J. Mater. Process. Technol. 207 265 Google Scholar
[28]	Zhu L M, Li W X, Xie L L, Yang Q, Cao X Y 2019 Chem. Eng. J. 372 1056 Google Scholar
[29]	Feng L L, Zhang W, Xu L N, Li D Z, Zhang Y Y 2020 Solid State Sci. 103 106187 Google Scholar
[30]	Kim H J, Jo J H, Choi J U, Voronina N, Myung S T 2020 J. Power Sources 478 229072 Google Scholar
[31]	Shchelkanova M, Shekhtman G, Pershina S, Vovkotrub E 2021 Materials 14 6976 Google Scholar
[32]	Wu W Z, Ding J, Peng H R, Li G C 2011 Mater. Lett. 65 2155 Google Scholar
[33]	Zhu J Z, Li X L, Chen S Y, Huang C M, Feng J J, Kuang Q, Fan Q H, Dong Y Z, Zhao Y M 2020 Electrochim. Acta 355 136799 Google Scholar
[34]	Wadsley A D 1957 Acta Crystallogr. 10 261 Google Scholar
[35]	Bachmann H G, Barnes W H 1962 Can Mineral 7 219
[36]	Baddour-Hadjean R, Boudaoud A, Bach S, Emery N, Pereira-Ramos J P 2014 Inorg. Chem. 53 1764 Google Scholar
[37]	Oka Y, Yao T, Yamamoto N 1997 Mater. Res. Bull. 32 1201 Google Scholar
[38]	Segall M D, Lindan P J D, Probert M J 2002 J. Phys. : Condens. Matter 14 2717 Google Scholar
[39]	Payne M C, Teter M P, Allan D C, Arias T A, Joannopoulos A J 1992 Rev. Mod. Phys. 64 1045 Google Scholar
[40]	Srivastava G P, Weaire D 1987 Adv. Phys. 36 463 Google Scholar
[41]	Monkhorst H J, Pack J D 1976 Phys. Rev. B 13 5188 Google Scholar
[42]	Perdew J P, Burke K, Ernzerhof M 1996 Phys. Rev. Lett. 77 3865 Google Scholar
[43]	Hamann D R, Schlüter M, Chiang C 1979 Phys. Rev. Lett. 43 1494 Google Scholar
[44]	Kong Q R, Yang Y, Liu L L, Bian Q, Lei B H, Li L P, Yang Z H, Su Z, Pan S L 2016 J. Mater. Res. 31 488 Google Scholar
[45]	阎守胜 2011 固体物理基础(北京: 北京大学出版社) Yan S S 2011 Fundamentals of Solid-state Physics (Beijing: Peking University Press
[46]	Hiscocks J, Frisch M J 2009 Gaussian 09: IOps Reference 9 (USA: Gaussian
[47]	Riffet V, Contreras-Garcıa J, Carrasco J, Calatayud M 2016 J. Phys. Chem. C 120 4259 Google Scholar
[48]	Mulliken R S 1931 Chem. Rev. 9 347 Google Scholar
[49]	张博, 王云杰, 齐亚杰, 和志豪, 丁家福, 苏欣 2024 人工晶体学报 53 999 Google Scholar Zhang B, Wang Y J, Qi Y J, He Z H, Ding J F, Su X 2024 J. Synth. Cryst. 53 999 Google Scholar
[50]	Su X, Wang Y J, Yang Z H, Huang X C, Pan S L, Li F, Lee M H 2013 J. Phys. Chem. C 117 14149 Google Scholar
[51]	Tudi A, Han S, Yang Z H, Pan S L 2022 Coord. Chem. Rev. 459 214380 Google Scholar
[52]	Wang X Y, Zhang B B, Yang D Q, Wang Y 2022 Dalton Trans. 51 14059 Google Scholar
[53]	Bai S, Yang D Q, Zhang B B, Li L, Wang Y 2022 Dalton Trans. 51 3421 Google Scholar
[54]	Chu Y, Wang H S, Chen Q, Su X, Chen Z X, Yang Z H, Li J J, Pan S L 2024 Adv. Funct. Mater. 34 2314933 Google Scholar
[55]	Ding Y Y, Zhu M M, Wang J B, Li B, Qi H X, Liu L L, Chu Y Q 2024 Inorg. Chem. 63 20003 Google Scholar
[56]	Lin L, Jiang X X, Wu C, Lin Z S, Huang Z P, Humphrey M G, Zhang C 2021 Dalton Trans. 50 7238 Google Scholar
[57]	Su X, Chu Y, Yang Z H, Lei B H, Cao C, Wang Y, Pan S L 2020 J. Phys. Chem. C 124 24949 Google Scholar
[58]	Bai S, Zhang X, Zhang B B, Li L, Wang Y J 2021 Inorg. Chem. 60 10006 Google Scholar
[59]	Li S, Dou D, Chen C, Shi Q, Zhang B B, Wang Y J 2024 Inorg. Chem. 63 24076 Google Scholar
[60]	Chu Y, Wang H S, Abutukadi T, Li Z, Mutailipu M, Su X, Yang Z H, Li J J, Pan S L 2023 Small 19 2305074 Google Scholar
[61]	Liu H J, Liang C W, Liang W I, Chen H J, Yang J C, Peng C Y, Chu Y H 2012 Phys. Rev. B Condens. Matter Mater. Phys. 85 014104 Google Scholar
[62]	王云杰, 和志豪, 丁家福, 苏欣 2025 人工晶体学报 54 85 Google Scholar Wang Y J, He Z H, Ding J F, Su X 2025 J. Synth. Cryst. 54 85 Google Scholar
[63]	丁家福, 和志豪, 王云杰, 苏欣 2025 人工晶体学报 54 95 Google Scholar Ding J F, He Z H, Wang Y J, Su X 2025 J. Synth. Cryst. 54 95 Google Scholar
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Vol. 74, Issue 10 - 2025-05-20

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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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Corresponding author: SU Xin, suxin_phy@sina.com ; HUANG Yineng, ynhuang@nju.edu.cn

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