Heteroanionic [VO_xS_4−x] groups: tetrahedral units with large birefringence for mid-infrared nonlinear optical crystals

Abstract

Tetrahedral groups can possess a wide bandgap and large second harmonic generation (SHG) response in nonlinear optical (NLO) materials; however, they usually exhibit a small optical birefringence owing to the low structural anisotropy, which would deteriorate the NLO performance. Herein, the [VO_xS_4−x] (x = 0–4) tetrahedra that combine the V⁵⁺ cation with oxygen–sulfur hybrid anions are highlighted as a type of good structural group to overcome the above problem. Using theoretical calculations, we systematically investigate the optical and NLO properties of all reported V⁵⁺-based thiovanadates. The calculated results reveal the largest birefringence (∼0.37 in Ba₅V₂O₄S₈) among the pure tetrahedron-based compounds and indicate the potential of [VO_xS_4−x] units in enhancing the birefringence and well-balanced NLO performance suitable for the mid-infrared (mid-IR) region. Furthermore, Na₃VOS₃ in this family is selected for experimental synthesis and measurements to verify our strategy and calculations. This work demonstrates that the [VO_xS_4−x] (x = 0–4) tetrahedral groups, which had been overlooked for a long time, are a good type of birefringent and NLO unit for the exploration of mid-IR NLO materials.

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Introduction

Mid-infrared (mid-IR) nonlinear optical (NLO) crystals are the key components in all-solid-state infrared tunable lasers, and they can convert the laser radiation from the common near-IR spectral region (e.g., Nd:YAG laser @ 1064 nm) to the mid-IR regions.^1–4 This significantly expands the laser application range in many civil and military fields such as medical imaging, laser displays, remote communications, and environmental monitoring.^5–13 To reach the practical applications, a mid-IR crystal should satisfy the high-performance criteria including^14,15 (i) a wide IR transparency covering the atmospheric windows, (ii) large NLO coefficient d_eff for high conversion efficiency, (iii) wide band gap to achieve a high laser-induced damage threshold (LDT) during the high power laser input, (iv) sufficient birefringence for IR phase-matching and (v) good crystal growth habit and chemical stability. Up to now, only AgGaS₂ (AGS),¹⁶ AgGaSe₂,¹⁷ and ZnGeP₂ ¹⁸ are commercially available; however, these crystals all have their own drawbacks such as low LDT in AGS and strong two-photon absorption in ZnGeP₂ pumping using Nd:YAG lasers. Therefore, it is urgent to explore novel mid-IR NLO crystals with well-balanced performance.

After extensive efforts for decades, dozens of promising mid-IR NLO candidates such as BaGa₄Se₇, LiGaS₂, LiInS₂, CdSiP₂, AMgAgGa₆S₁₁ (A = K, Rb), BaZnGeS₄, Zn₂NX (X = Cl, Br), Li₂K₄TiOGe₄O₁₂, KYGeS₄, and Hg₇P₂Se₁₂ have been reported.^19–28 Through systematic structure–property analysis, the tetrahedral units were highlighted as good IR NLO-active “material genes” to realize the balance between the large NLO coefficients and wide band gaps.^29,30 In addition, the polar arrangement of these tetrahedral units, e.g., in the diamond-like structures, would result in a tightly packed framework with the tetrahedra pointing in a special crystallographic axis, which is conducive to the large NLO effects.^31–37 However, the birefringence of the tetrahedron-based NLO crystals are usually rather small with the value ranging from 0.01 to 0.03. Such small optical birefringence can be attributed to the low structural anisotropy of the tetrahedral groups. Thus, it is urgent and necessary to improve the birefringence while keeping the balanced NLO performance in tetrahedron-based NLO crystals.

Normally, the birefringence of a crystal is positively related to the polarization anisotropy of its microscopic units. One could reach a large birefringence by increasing the polarization anisotropy. Introducing distorted polyhedra with d⁰ cations has been proven to be an efficient way to improve the polarization anisotropy and birefringence, and the degree of distortion generally follows the order V⁵⁺ > W⁶⁺ > Ti⁴⁺ > Nb⁵⁺ > Ta⁵⁺ > Zr⁴⁺.³⁸ Thus, polyhedra containing the V⁵⁺ ion are likely to produce a large birefringence. For instance, NaCa₄V₅O₁₇ with [V₂O₇] units and [V₃O₁₀] units exhibits a large birefringence of about 0.1 at 1064 nm,³⁹ and YVO₄ with [VO₄] tetrahedra possesses an ultra-large birefringence of 0.225 at 633 nm.⁴⁰ Therefore, V⁵⁺ cations can be regarded as good central cations to improve the birefringence of tetrahedron-based NLO crystals.

Constructing heteroanionic tetrahedra by coordinating with different electronegative ligands is also an efficient way to enhance the structural anisotropy for a large birefringence. In a recent review, Chen et al. investigated typical and emerging compounds, and demonstrated that the presence of an anisotropic structure building unit that encompasses diverse chemical bonds (ABUCB) in DUV/UV NLO compounds contributes to an increase in birefringence.⁴¹ For example, Pan et al. introduced the [PO₃F] unit into phosphates, and realized a large birefringence of 0.03 @ 1064 nm and 0.05 @ 589.3 nm in (NH₄)₂PO₃F ⁴² and NaNH₄PO₃F·H₂O, respectively.⁴³ Ye et al. tuned the ligands of [SO₄] units, and achieved a large birefringence in C(NH₂)₃SO₃F ⁴⁴ with [SO₃F] and M(SO₃NH₂)₂ (M = Sr, Ba) with [SO₃NH₂].⁴⁵ Our group also realized a large birefringence in CsSO₃CF₃ by constructing the heteroanionic [SO₃CF₃] unit.⁴⁶ Very recently, oxychalcogenides with heteroanionic units were developed to be promising IR NLO materials. The heteroanionic tetrahedral groups, e.g., [PO₃S] unit in Na₃PO₃S,⁴⁷ [SbOS₄] unit in Sr₆Cd₂Sb₆O₇S₁₀,⁴⁸ and [GeO₂Se₂] unit in BaGeOSe₂,⁴⁹ with a large structural anisotropy can possess enhanced hyperpolarizability and polarization anisotropy, which would result in large NLO effects and birefringence in the mid-IR region.

To improve the birefringence while keep the balanced NLO performance of the tetrahedral NLO chalcogenides, we propose to combine the above-mentioned two material design strategies. In this work, the V⁵⁺ cation is chosen as the tetrahedrally coordinated cation, and heteroanions (O²⁻ and S²⁻) are used as the ligands, thus forming the thiovanadates containing [VO_xS_4−x] (x = 0–4) groups (Fig. 1a). It should be noted that the linear and NLO properties in the [V–O–S] system were overlooked for a long time, and there has been no systematic research on this series yet. Our first-principles calculations show that the [V–O–S] series of compounds, not only with the [VO_xS_4−x] tetrahedra, but also with other types of [V–O–S] polyhedra, possess a large birefringence, verifying the validity of our strategy. The birefringence record of the pure tetrahedron-based compounds was found to be about 0.37 in Ba₅V₂O₄S₈. Furthermore, β-Na₃VOS₃ containing the [VO_xS_4−x] tetrahedra was selected for further experimental verification. In addition, materials design and structure–property correlation analysis based on β-Na₃VOS₃ were carried out. It is concluded that the [VO_xS_4−x] (x = 0–4) tetrahedral groups are a type of NLO unit with good birefringence in the mid-IR NLO materials.

Fig. 1 (a) Schematic of our design strategy for enlarging the birefringence of the tetrahedral group; (b) balanced performance coordinate of the Δn and energy band gap in the tetrahedral-based sulfides, halides and V⁵⁺-based thiovanadates (the data of the tetrahedral-based sulfides and halides are from ref. 33 and 50, and compounds are listed in Table S1†).

Results and discussion

Although vanadates are widely used as important optoelectronic functional materials in such fields as photocatalysis, nonlinear optics, and solar energy utilization,^51–53 their thio-derivatives, i.e., thiovanadate, have not been extensively studied yet. Our survey in the Inorganic Crystal Structure Database (ICSD, version 5.1.0) shows that there only exist ten V⁵⁺-based thiovanadates from experimental studies. Their main structural features, including the microscopic structural groups, are listed in Table 1. Clearly, most of the reported thiovanadates consist of [VO_xS_4−x] tetrahedra, except Cs₅V₃O₃S₁₅ and Cs₄V₂O₂S₁₀, which contain [VOS₅] octahedra. By the self-consistent ab initio approach, the band gaps E_g, birefringence Δn and NLO coefficients d_ij of these thiovanadates are investigated for the first time, although their structures have been known for decades. The calculated birefringence of the selected thiovanadates is displayed in Fig. 1b. Compared with traditional tetrahedral sulfides and halides, it is clear that the birefringence values of the V⁵⁺-based thiovanadates are much larger, as shown in the pink field. Notably, the new birefringence record of the pure tetrahedron-based compounds is improved to 0.37 in Ba₅V₂O₄S₈ and it verifies our birefringence enhancing strategy (for the refractive indices for all compounds, see Table S1†).

Table 1 Calculated linear and nonlinear optical properties of the V⁵⁺-based thiovanadates. CS: centrosymmetric, NCS: non-centrosymmetric. Experimental values are shown in brackets

Compounds	Space groups	Groups	CS/NCS	E g (eV)	Δn @ 1 μm	d ij (pm V^−1)	ICSD no.
Cs5V3O3S15	P21/c	[VOS5]	CS	2.6	0.05	—	280814
Cs4V2O2S10	P21/n	[VOS5]	CS	2.4	0.33	—	280815
Ba5V2O4S8	Cmce	[VO2S2]	CS	2.1 (2.2 ^55)	0.37	—	18731
Ba10V6O18S7	P63	[VO3S]	NCS	2.2 (2.2 ^56)	0.03	d 33 = 4.2	235360
Ba6V4O5S11	Pnma	[VS4], [VOS3], [VO2S2]	CS	2.8	0.09	—	59294
K3VO2S2	P21/c	[VO2S2]	CS	3.6	0.12	—	419398
K3VO3S	P21/m	[VO3S]	CS	4.5	0.06	—	419400
Na3VO2S2	Pbca	[VO2S2]	CS	3.1	0.20	—	174237
Na3VOS3 (α-phase)	Pnma	[VOS3]	CS	3.1	0.29	—	415218
Na3VOS3 (β-phase)	Cmc21	[VOS3]	NCS	3.1	0.28	d 15 = 10.6	415217
Designed Na3VS4	Cmc21	[VS4]	NCS	2.7	0.21	d 33 = 53.5	This work
Designed Na3VOS3	Cmc21	[VOS3]	NCS	2.9	0.23	d 33 = 22.9	This work
Designed Na3VO2S2	Cmc21	[VO2S2]	NCS	3.2	0.16	d 33 = 17.3	This work
Designed Na3VO3S	Cmc21	[VO3S]	NCS	4.0	0.18	d 33 = 18.3	This work
Designed Na3VO4	Cmc21	[VO4]	NCS	5.6	0.05	d 33 = 5.4	This work

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At the same time, the band gaps of the thiovanadates are evaluated by hybrid sx-LDA functionals, whose results match well with the available experimental values and the previous research studies.^29,33,54 As shown, the alkali metal thiovanadates exhibit wide band gaps, some of which can even exceed 3.0 eV and are favorable for high LDT. In all known thiovanadates, there are only two non-centrosymmetric compounds containing [VO_xS_4−x] groups, i.e., Ba₁₀V₆O₁₈S₇ with the space group P6₃ and Na₃VOS₃ with Cmc2₁ (β-phase), whose SHG potentials were neglected for a long time. By the theoretical investigation, their NLO properties are firstly studied. Remarkably, the latter compound has large SHG coefficients with the largest component of 10.6 pm V⁻¹, making it a promising crystal for mid-IR NLO applications. For this reason, we further investigated its NLO origin and performed experimental verification.

The single crystals of β-Na₃VOS₃ were obtained by traditional high-temperature solid-state reaction, and its structure was resolved by single crystal X-ray diffraction (CCDC no. 2366824†). Related structural information, including the structural refinement information, are summarized in Tables S2–S4.† The resolved crystal structure is in good agreement with that reported by Schnabel et al.⁵⁷ β-Na₃VOS₃ belongs to the non-centrosymmetric space group Cmc2₁, and its structure is shown in Fig. 2a with cell parameters a = 9.5667(7) Å, b = 11.8659(9)(2) Å, c = 5.8806(4) Å, with α = β = γ = 90° and Z = 6. This structure contains two Na atoms, one V atom, one O atom, and two S atoms in the symmetric unit. All of the V atoms are tetra-coordinated with three S atoms and one O atom to form the [VOS₃] tetrahedra. The V–O bond length is 1.673 Å, while the V–S bond lengths vary from 2.175 to 2.197 Å. The S–V–S/O bond angles range from 109.97° to 115.16°. The large structural distortion in the [VOS₃] tetrahedra would result in a large microscopic polarization anisotropy. In addition, all of these tetrahedra are distributed discretely in the lattice, and exhibit a relatively ordered arrangement with the O atoms pointing along the c-axis. Such a polarity-enhanced arrangement is favorable for realizing a large NLO response and birefringence, which will be further analyzed below. The two crystallographically independent Na⁺ cations are inserted in the space between the [VOS₃] tetrahedra to balance the charge, and they are surrounded by the neighboring S and O atoms. The distance between Na and S/O ranges from 2.283 Å to 3.212 Å. Each oxygen atom connects to three Na⁺ and one V⁵⁺ cations, with the V–O–V angles varying from 106.09° to 119.48°. Detailed crystal data, including the fractional atomic coordinates, isotropic/anisotropic displacement parameters, and bond lengths are listed in Tables S2–S5.†

Fig. 2 (a) Unit cell in β-Na₃VOS₃; (b) band structures (left panel), PDOS (middle panel) and band-resolved d₁₅ (right panel); (c) dispersion curves of the refractive indices and birefringence of β-Na₃VOS₃; (d) HOMO and LUMO; SHG-weighted density for occupied and unoccupied (e) VE process; (f) VH process.

The calculated electronic band structure and partial density of states (PDOS) in β-Na₃VOS₃ are shown in Fig. 2b. The band structure indicates that β-Na₃VOS₃ is an indirect bandgap semiconductor with a band gap of 3.1 eV. As PDOS shows, the top of the valence band (VB) is primarily occupied by S-3p and O-2p orbitals, while the bottom of the conduction band (CB) has contributions from the V-3d and S-3p orbitals. Both parts of the orbitals exhibit significant dispersion, indicating the strong hybridization between V and O/S in the [VOS₃] tetrahedra. Meanwhile, the VB maximum and CB minimum, i.e., the highest occupied molecular orbitals (HOMO) and the lowest unoccupied molecular orbitals (LUMO), predominantly have contributions from the p-orbitals of S and d-orbitals of V, as shown in Fig. 2d. As the optical properties are mainly dependent on the electronic transition between the top of VB and the bottom of CB, the [VOS₃] tetrahedra determine the optical properties of the title compound. In addition, the refractive index dispersion (displayed in Fig. 2c) reveals that β-Na₃VOS₃ is a biaxial crystal, and it possesses a very large birefringence of 0.28 at 1064 nm.

Since β-Na₃VOS₃ crystallizes in the mm2 point group, under the Kleinman's symmetry constraints, there are three independent SHG coefficients; they are calculated to be d₁₅ = −10.6 pm V⁻¹, d₂₄ = 8.3 pm V⁻¹, and d₃₃ = 4.2 pm V⁻¹. To further analyze the origin of such strong NLO effect, the band-resolved d₁₅, the largest SHG coefficient, was plotted and is shown in Fig. 2b. Clearly, the orbitals at the top VB and the CB bottom play predominant roles in determining the SHG responses. In order to clearly exhibit the contribution from the orbitals in real-space, the SHG-weighted densities of the virtual electron (VE) process and virtual hole (VH) process for d₁₅ are plotted in Fig. 2e and f, respectively. As expected, the large NLO effect of β-Na₃VOS₃ mainly originates from the large microscopic second-order polarization of the [VOS₃] tetrahedral, as well as their polarization superposition arrangement, while that from the Na⁺ ions can be neglected.

To verify the good NLO performance of β-Na₃VOS₃, we synthesized its polycrystalline powders and carried out the measurements. The X-ray diffraction patterns of the obtained powders agree well with the calculated diffraction patterns, indicating the high purity of the compound that we obtained (as shown in Fig. 3a). The UV-vis-NIR diffuse reflectance spectrum in Fig. 3b shows that the optical band gap of β-Na₃VOS₃ is about 2.1 eV, slightly lower than the theoretical value. This might be attributed to some impurities presented in the sample. The powder SHG measurements based on the Kurtz–Perry method⁵⁸ was carried out to investigate the NLO effects of β-Na₃VOS₃. Fig. 3c and d show the SHG responses of β-Na₃VOS₃ (and benchmark AgGaS₂), and they increase gradually with the increase of the particle sizes, indicating the phase matching ability of this compound. In the particle size range of 105–150 μm, the SHG response of β-Na₃VOS₃ is 0.61 times that of AgGaS₂, corresponding to a NLO effect of ∼7.9 pm V⁻¹, matching well with the calculated result. This value is larger than that for α-Na₃PO₃S (0.2 × SiO₂)⁵⁹ and comparable to other NLO oxychalcogenides, like Ba₂SnSi₂O₇S (0.6 × AGS),⁶⁰ Sr₂CdGe₂OS₆ (0.6 × AGS),⁶¹ Sr₂ZnSn₂OS₆ (0.7 × AGS),⁶² BaGeOS₂ (0.5 × AGS),⁶³ and Sr₅Ga₈O₃S₁₄ (0.8 × AGS).⁶⁴ In addition, Raman spectra and photoluminescence (PL) properties were measured and the results are shown in Fig. S2 and S3,† respectively. β-Na₃VOS₃ exhibits four Raman peaks at 216, 419, 454 and 479 cm⁻¹, which can be attributed to the vibrations of the [VOS₃] units, and this compound possesses a wide PL emission with the PL maximum located at 710 nm.

Fig. 3 (a) The experiment powder X-ray diffraction pattern and calculated diffraction pattern of β-Na₃VOS₃; (b) UV-vis/NIR diffuse reflectance spectrum (inset is the photograph of the β-Na₃VOS₃ crystal); (c) the measured SHG signals of β-Na₃VOS₃ and AgGaS₂ (reference) in a particle size range of 100–150 μm; (d) the SHG intensities versus particle sizes with AGS as the references under 2.09 μm irradiation.

To further investigate the NLO performance of the [VO_xS_4−x] (x = 0–4) units with respect to the O/S ratio, we designed a series of Na₃[VO_xS_4−x] (x = 0–4) compounds using β-Na₃VOS₃ as the parent structure. In the structures, the O/S positions and their ratio in the tetrahedral [VO_xS_4−x] groups are modified. These theoretically optimized structures, as well as their phonon spectra, are shown in Fig. S4 and S5.† The calculated band gaps, NLO coefficients, refractive index and birefringence of the designed compounds are displayed in Table 1 and Fig. 4a. On the basis of the calculated results, two conclusions can be drawn: (i) the positions of the S atoms in the tetrahedra can strongly influence the NLO coefficients. In β-Na₃VOS₃, the S atoms are located at the three bottom corner positions of the tetrahedra, while the O atom is located at the top corner position along the c-axis. As the top corner position is occupied by the S atom in the designed Na₃VOS₃, the maximum SHG coefficient can be increased from d₁₅ (10.6 pm V⁻¹) to d₃₃ (22.9 pm V⁻¹). (ii) The balanced IR NLO performance is strongly affected by the O/S ratio. A higher ratio results in larger band gaps and smaller NLO coefficients, and vice versa. Clearly, the band gap increases from 2.7 eV to 5.6 eV, while the NLO coefficients decrease from 53.5 pm V⁻¹ to 5.4 pm V⁻¹ as the O/S ratio increases. Such trend is reasonable and consistent with common tendency.^65,66 Notably, all five designed compounds exhibit a large birefringence, verifying the validity of our strategy of using the [VO_xS_4−x] tetrahedra to achieve a large birefringence. According to the above discussion, it is clear that the [VO_xS_4−x] tetrahedra are good birefringent and NLO active units in the IR region.

Fig. 4 (a) Band gap E_g, largest SHG coefficient d_ij(Max), birefringence Δn; (b) IR spectra of Na₃VS₄, Na₃VOS₃, Na₃VO₂S₂, Na₃VO₃S, and Na₃VO₄.

The IR transmission is also an important factor for IR NLO applications. Thus, the IR spectra for the five designed compounds were calculated, and the vibrational characteristics of the [VO_xS_4−x] (x = 0–4) units were analyzed. It is known that there exists a strong correlation between the wavenumber of the IR absorption and the IR absorption cutoff in a compound.^67,68 With decreasing value of the highest wavenumber, there is a greater red-shift in the IR absorption cutoff. As shown in Fig. 4b, the highest wavenumber IR absorption peak of Na₃VS₄ is close to that of AGS, which indicates its good IR transmission. As O anions are introduced into the structure, the highest wavenumber of IR peaks in Na₃VO_xS_4−x (x = 1–4) appear at greater wavenumbers. These peaks can be attributed to the stretching vibration of the V–O bond, indicating the unfavorable role of O atoms in the IR transmission.

Conclusions

We proposed and examined the birefringence enhancing strategy that simultaneously introduces V⁵⁺ cations and constructs heteroanionic tetrahedra in thiovanadates for the comprehensive IR NLO performance. By this method, the new birefringence record of the pure tetrahedron-based compounds has been increased to 0.37 in Ba₅V₂O₄S₈. Combining the theoretical calculations and experimental measurements, the linear and NLO properties of β-Na₃VOS₃, which were highlighted by the systematical theoretical investigation, are reported herein with a strong NLO effect at about 0.6 × AGS, a large birefringence of 0.28, and a wide band gap of about 2.1 eV, indicating its potential for IR NLO applications. Furthermore, the structure–property relationships of β-Na₃VOS₃ and its derivatives were investigated, and they indicate the potential of the [VO_xS_4−x] units in enhancing the birefringence and NLO properties. This finding is significant for the development of materials in this system.

Author contributions

Shengzi Zhang: formal analysis, investigation, writing – original draft; Linfeng Dong: formal analysis, investigation, writing – original draft; Bohui Xu: formal analysis, validation; Huige Chen: investigation; Hao Huo: visualization; Fei Liang: conceptualization; Rui Wu: writing – review & editing; Pifu Gong: conceptualization, supervision, writing – review & editing; Zheshuai Lin: conceptualization, supervision, writing – review & editing.

Data availability

The authors confirm that the data supporting the findings of this study are available within the article and its ESI.†

Conflicts of interest

There are no conflicts to declare.

Acknowledgements

This work was supported by the National Natural Science Foundation of China (Grant No. 22275201 and 22133004). P. G. also acknowledges the support of the Youth Innovation Promotion Association CAS.

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Footnotes

† Electronic supplementary information (ESI) available: Experimental procedures, crystal structure data, photoluminescence spectroscopy, Raman spectra. CCDC 2366824. For ESI and crystallographic data in CIF or other electronic format see DOI: https://doi.org/10.1039/d4qi01442a

‡ These authors contributed equally.

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