Constructing ultraviolet nonlinear optical crystals with large second harmonic generation and short absorption edges by using polar tetrahedral S₂O₃ groups

Abstract

It is generally considered difficult for traditional sulfates to exhibit strong second harmonic generation (SHG) responses and large birefringence values because SO₄ groups are nonpolar tetrahedral structures. However, by theoretical calculations, we found that polar tetrahedral S₂O₃ shows great improvements in anisotropy and second order polarizability compared to SO₄ while the wide band gap can be preserved. On this basis, a nonlinear optical (NLO) crystal (NH₄)₂S₂O₃ with excellent performance was synthesized. As expected, it exhibited a strong SHG response (3.3× that of KDP), suitable birefringence (0.077@546 nm) and a short absorption edge (238 nm). According to the first principles calculations, the polar tetrahedral S₂O₃ group is the main source for the SHG response of (NH₄)₂S₂O₃. These findings indicate that the polar S₂O₃ group is a kind of NLO functional group with superior comprehensive properties, and has great potential to develop more NLO crystals with superior comprehensive properties.

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Introduction

As the core materials of all-solid-state lasers, nonlinear optical (NLO) crystals have been widely applied to laser medical treatment, modern laser micromachining, laser communication, etc.^1–7 In the past several decades, the exploration of UV (ultraviolet) NLO crystals with excellent comprehensive properties has always been a research hotspot in this field. Generally, a high-performance UV NLO crystal should meet the following conditions: a large second-harmonic generation (SHG) coefficient, appropriate birefringence and short UV cut-off edge. According to the anionic group theory,⁸ π-conjugated anionic groups, such as NO₃, CO₃, and BO₃, are ideal functional units for UV NLO crystals.⁴⁵ Through lots of research studies into the π-conjugated systems, many excellent UV NLO crystals were developed including β-Rb₂A_l2B₂O₇,⁹ KBe₂BO₃F₂,^10,11 MB₅O₇F₃ (M = Ca, Sr),^12,13 NH₄B₄O₆F,¹⁴ ABCO₃F (A = K, Rb; B = Mg, Ca, Sr),^15–17 and M₂(NO₃)(OH)₃ (M = Sr, Ba).^18,19 In recent years, non-π-conjugated tetrahedral groups, such as SO₄ and PO₄ groups, which are beneficial for enlarging the band gaps, have also attracted researchers’ attention. However, since the tetrahedral groups SO₄ and PO₄ have approximately nonpolar T_d symmetry, their contributions to SHG coefficients and birefringence are limited. In fact, most reported NLO sulfates and phosphates either show small birefringence or weak SHG responses. Therefore, one of the most attractive research directions is enhancing the polarizability anisotropy or hyperpolarizability of sulfates and phosphates.

Recently, it was considered an effective strategy to design polar tetrahedral anionic groups with enlarged polarizability anisotropy and enhanced hyperpolarizability by the elemental substitution method. In 2019, Lu et al. first reported the optimization of birefringence with a polar tetrahedral anionic group.⁴⁶ Accordingly, SO₃F,^20,21 PO₃F ^22,23 and PO₂F₂ ²⁴ groups have been successively uncovered as excellent NLO functional groups. Compared to nonpolar tetrahedral groups, these polar tetrahedral groups not only could retain the wide band gap, but also could improve the SHG effect and birefringence. Taking steps along this path, the polar S₂O₃ tetrahedral group which is obtained by replacing an oxygen atom with a sulfur atom in SO₄ could be expected to be a new NLO tetrahedral unit. The NLO-related properties of the S₂O₃ group and SO₄ group were calculated and are listed for comparison (Table 1). It is noteworthy that the hyperpolarizability (β_ijk) of the S₂O₃ group was more than 12 times that of SO₄ and the polarizability anisotropy of the S₂O₃ group was much superior to that of SO₄, indicating that the S₂O₃ group indeed has more potential for developing strong SHG and large birefringence.

Table 1 Calculated NLO-related properties of isolated ideal S₂O₃ and SO₄ tetrahedra

	P x , Py, Pz	δ	[βmax]	E g (eV)
SO4	0.00, 0.00, 0.00	45.1	47.8	6.98
S2O3	62.7, 62.7, 95.6	73.6	578	5.79

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In addition to strong SHG response and large birefringence, excellent UV NLO materials also require a short UV absorption edge. Although the S₂O₃ group exhibits a wide band gap, the introduction of NLO-active cations with d–d or f–f transitions would cause a significant redshift of the UV absorption edge of the material, which should be avoided. Based on these considerations, ammonium thiosulfate was discovered by screening the ICSD database⁴⁷ and is expected to be an excellent UV NLO material. First, (NH₄)₂S₂O₃ crystallized in the polar non-centrosymmetric (NCS) space group, C2, which is a basic requirement for producing SHG responses. Second, in (NH₄)₂S₂O₃, the polar S₂O₃ group aligned along a specific orientation is conducive to a large SHG response and birefringence. Third, the ammonium ion group without a d orbital is an ideal cation for maintaining the short absorption edge of the UV material.

Guided by the above ideas, we successfully grew (NH₄)₂S₂O₃ crystals by a simple solution method. The NLO properties and the relationship between the structure and the NLO properties of the crystal were also studied. It exhibited super comprehensive properties, including a strong SHG effect of 3.3× that of KDP, a suitable birefringence of 0.077@546 nm, and a short UV absorption edge of 238 nm. These results showed that (NH₄)₂S₂O₃ is an excellent UV NLO crystal and the polar tetrahedron S₂O₃ group is a promising group for constructing UV NLO materials.

Experimental

Regents and synthesis

Chemicals including Na₂S₂O₃ (0.791 g, 5 mmol, 99%, Sinopharm) and NH₄Cl (0.535 g, 10 mmol, 99%, Sinopharm) were of analytical grade and used without further purification and were purchased from commercial sources. Single crystals of (NH₄)₂S₂O₃ were synthesized via a facile water solution method. A mixture of NH₄Cl and Na₂S₂O₃ was dissolved in 10 mL of deionized water. This solution was stirred until it became clear. The solution was evaporated at 298 K and after several days, bulk colorless single crystals of (NH₄)₂S₂O₃ were obtained.

Powder X-ray diffraction

Powder X-ray diffraction measurements of (NH₄)₂S₂O₃ were carried out at room temperature with a Miniflex600 powder X-ray diffractometer set with Cu Kα radiation (λ = 1.5418 Å) in the range of 2θ = 5–75° and a 0.02° scan step. The experimental X-ray powder patterns of the pure sample of (NH₄)₂S₂O₃ agree well with the simulated X-ray powder patterns of the (NH₄)₂S₂O₃ single crystal models (Fig. S1†).

Single crystal X-ray diffraction

A colorless single crystal of (NH₄)₂S₂O₃ was selected using an optical microscope to determine its crystal structure. The diffraction data were collected by using graphite-monochromatic Mo Kα radiation (λ = 0.71073 Å) on a Rigaku Mercury CCD diffractometer at room temperature. Then the data were integrated using the CrystalClear program, and based on the multi-scan method the data were corrected for absorption and refinement.²⁵ The crystal structure of (NH₄)₂S₂O₃ was solved using the SHELXTL program in OLEX2 ²⁶ with the direct methods. Besides, the PLATON²⁷ program was used to check for higher symmetry elements, and none was found. The crystallographic data and structural refinement information of (NH₄)₂S₂O₃ are summarized in Table 2. Atomic coordinates and equivalent isotropic displacement parameters, bond lengths and angles, and anisotropic displacement parameters (Ų × 10³) for (NH₄)₂S₂O₃ are listed in Tables S1–S3.†

Table 2 Crystallographic data and structural refinement for (NH₄)₂S₂O₃

a R 1(F) = ∑||Fo| − |Fc||/∑|Fo|wR2(Fo^2) = [∑w(Fo^2 − Fc^2)^2/∑w(Fo^2)^2]^1/2.
Formula	(NH4)2S2O3
Formula mass (amu)	70.07
Temperature (K)	293(2)
λ (Å)	1.34139
Crystal system	Monoclinic
Space group	C2
a (Å)	10.1484(7)
b (Å)	6.4862(5)
c (Å)	8.7175(7)
α (°)	90
β (°)	93.570(7)
γ (°)	90
V (Å^3)	572.71(8)
Z	8
ρ (calcd) (g cm^−3)	1.625
μ (mm^−1)	5.089
F(000)	280
θ (°)	4.421–60.581
Index range	−13 ≤ h ≤ 13
	−8 ≤ k ≤ 7
	−10 ≤ l ≤ 11
Reflections collected/unique	3357/1084
R int	0.0493
Completeness to θ = 27.42° (%)	100.0
GOF on F^2	1.123
R 1/wR2 [Fo^2 > 2σ(Fo^2)]^a	0.0432/0.1186
R 1/wR2 (all data)	0.0442/0.1194
Absolute structure parameter	0.08(3)

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Energy-dispersive X-ray spectroscopy analysis

Energy dispersive X-ray spectroscopy (EDS) analyses were performed on a scanning electron microscope (FESEM, SU-8010) equipped with an energy dispersive X-ray spectroscope. The (NH₄)₂S₂O₃ crystals were fixed on an aluminum sample table by using carbon conductive adhesive and tested with a focused beam with 12 μA emission current and 20 kV accelerating voltage (Fig. S2†).

Thermal analysis

Thermogravimetric analysis (TGA) was performed using a NETZSCH STA449F3 simultaneous analyzer. Clean crystals of (NH₄)₂S₂O₃ were ground into powder, and then the powder was placed in an Al₂O₃ crucible. With an empty Al₂O₃ crucible as a reference, the sample was heated from 30 °C to 800 °C at a rate of 10 °C min⁻¹ in an atmosphere of flowing N₂ (Fig. S3†).

UV-vis diffuse reflectance spectroscopy

By using BaSO₄ powder as the standard (100% reflectance), UV-vis-NIR diffuse reflection data were measured and recorded using a PerkinElmer Lamda-950 UV/vis/NIR spectrophotometer at room temperature in the scan range of 200–2000 nm. In accordance with the Kubelka–Munk function, the reflection value was converted to an absorption value (Fig. S4†).^28,29

Birefringence

The birefringence of (NH₄)₂S₂O₃ was measured by using a Nikon ECLIPSE LV100 POL polarizing microscope equipped with a Berek Compensator and a 546 nm light source (Fig. S5†). The birefringence was calculated using the following formula:

ΔR = Δn × T

ΔR represents the optical path difference, Δn represents the birefringence, and T represents the thickness of the crystal.

Second harmonic generation

Polycrystalline SHG signals of the (NH₄)₂S₂O₃ samples were investigated by using the Kurtz–Perry method³⁰ and measured by using a Q-switched Nd:YAG solid-state laser with a fundamental wavelength of 1064 nm. Owing to the significant correlation between the SHG efficiency and the particle size of the powder, the (NH₄)₂S₂O₃ crystals were ground and divided into several different particle size ranges including 25–45,45–62, 62–75, 75–109, 109–150, and 150–212 μm. As a reference, the KDP crystals were also ground and sieved following the above procedures. Then they were placed in a fixed position and irradiated by using a pulsed laser (λ = 1064 nm). The outputs of second harmonic intensity from the samples and KDP were collected by using a RIGOL DS1052E 50 MHz oscilloscope.

First-principles calculations

First-principles calculations of crystal (NH₄)₂S₂O₃ were performed by using a CASTEP package based on density functional theory (DFT) in Material Studio software. The exchange–correlation energy was described by Perdew–Burke–Ernzerhof (PBE) in the generalized gradient approximation (GGA).³¹ To model the effective interaction between atomic nuclei and valence electrons of all the elements in (NH₄)₂S₂O₃, the optimized norm-conserving pseudopotentials in the Kleinman–Bylander form were used.³² The valence configurations of (NH₄)₂S₂O₃ including N 2s²2p³, H 1s¹, S 3s²3p⁴, and O 2s²2p⁴ were observed using a relatively small basis set without compromising calculation accuracy. A high kinetic energy cut-off of 274 eV and 1 × 2 × 2 Monkhorst–Pack³³k-point meshes were selected for the numerical integration calculation of (NH₄)₂S₂O₃ in the Brillouin zone. According to the transition from valence bands to conduction bands of the electron, the imaginary part of the dielectric function was calculated. Based on the Kramers–Kronig³⁴ transform the real part of the dielectric function was obtained and the refractive index was determined. The calculation results of SHG coefficients d_ij were obtained using a formula developed by Lin's group.³⁵

Results and discussion

Crystal structure

Single crystals of (NH₄)₂S₂O₃ crystallized in the NCS space group C2 (no. 5) of the monoclinic crystal system. The crystal structure of (NH₄)₂S₂O₃ was composed of isolated NH⁴⁺ and S₂O₃²⁻ anionic groups. Within an asymmetric unit, there were three N atoms, two S atoms and three O atoms. Every S₂O₃ group was formed by one central S⁶⁺ atom coordinating with three O atoms and one S²⁻ atom, in which the S–O bond lengths ranged from 1.465(2) to 1.485(3) Å and one S=S bond was 1.975(2) Å. It is clear from Fig. 1a that there are two different orientations of S₂O₃ in the structure, S₂O₃(1) group and S₂O₃(2) group, both of which are arranged neatly along the b-axis. Obviously, in the a-axis and c-axis, the polarity of the S₂O₃(1) group and S₂O₃(2) group canceled each other out, respectively. The polarity of both S₂O₃ groups in the b-axis was superimposed, which was conducive to increasing the SHG effect. Looking at the crystal structure from the ac plane (Fig. 1b), there were three kinds of ammonium ions, NH₄(1), NH₄(2), and NH₄(3), next to the S₂O₃ groups, which were connected by hydrogen bonds, and the adjacent S₂O₃ groups were connected by hydrogen bonds of the NH₄(1) group and NH₄(3) group. In contrast, the NH₄(2) groups were dispersed among those [S₂O₃NH₄]₂ structures. The NH₄(2) groups were connected to the S₂O₃ groups above or below them by hydrogen bonds to form a three-dimensional structure of (NH₄)₂S₂O₃ (Fig. 1c).

Fig. 1 (a) S₂O₃ group aligned along the b axis. (b) Crystal structure representations of (NH₄)₂S₂O₃ in the ac plane and (c) in the bc plane.

Thermal analysis

As shown in Fig. S3,† the title compound decomposed around 170 °C, and there was only one-step decomposition of (NH₄)₂S₂O₃ in the range of 170–390 °C. The 99.23% (cal. 100%) weight loss can be assigned to the complete decomposition of (NH₄)₂S₂O₃ into NH₃, SO₂, S and H₂O with the evaporation of S.

UV-vis diffuse reflectance spectra

As shown in the UV-vis diffuse reflectance spectra (Fig. S4†), the absorption edge of (NH₄)₂S₂O₃ was down to 238 nm. According to the Kubelka–Munk function,²⁹ the optical band gap of (NH₄)₂S₂O₃ was deduced to be 4.44 eV, which was much larger than the band gap of Na₁₀Cd(NO₃)₄(SO₃S)₄ (E_g = 3.74 eV).³⁶

Birefringence

The single crystal of (NH₄)₂S₂O₃ was chosen for the measurement of birefringence (Fig. S5†). The retardation value of the (NH₄)₂S₂O₃ crystal which was measured using a polarizing microscope (ZEISS Axio Scope A1) at a wavelength of 546 nm is 808.1 nm. Meanwhile, the thickness of the measured sample was 10.5 μm. Based on the formula ΔR = Δn × T, the experimental birefringence of (NH₄)₂S₂O₃ was 0.077 at 546 nm. The theoretical birefringence value calculated through the first-principles method (Δn = |n_x − n_z|) was 0.08 at 546 nm (Fig. 2b) which was perfectly matched with the experimental birefringence value. Compared to other NLO sulfates, such as Rb₂Bi₂(SO₄)₂Cl₄ (calc. 0.047 at 1064 nm),³⁷ (NH₄)₂Bi₂(SO₄)₂Cl₄ (calc. 0.055 at 1064 nm),³⁷ K₂Bi₂(SO₄)₂Cl₄ (calc. 0.056 at 1064 nm),³⁷ and Nb₂O₃(IO₃)₂(SO₄) (calc. 0.220 at 1064 nm),³⁸ the birefringence of (NH₄)₂S₂O₃ was well suitable and could be more in line with the requirements of the phase matching ability of crystals.

Fig. 2 (a) SHG intensity measurements of (NH₄)₂S₂O₃. (b) Dispersion curves of the refractive index of (NH₄)₂S₂O₃.

NLO properties

The powder SHG measurement was performed by the Kurtz–Perry method.³⁰ As shown in Fig. 2a, with KDP of the same particle size as the reference, the SHG response of (NH₄)₂S₂O₃ was approximately 3.3 times that of KDP at 1064 nm. As shown in Fig. 2a, the SHG responses increased when the particle sizes became larger, showing that (NH₄)₂S₂O₃ was phase-matchable. It is notable that the SHG effect of (NH₄)₂S₂O₃ was superior to those of NLO sulfates containing non-polar SO₄ groups, such as Cs₄Mg₆(SO₄)₈ (0.2 × KDP),³⁹ Li₈NaRb₃(SO₄)₆·2H₂O (0.5 × KDP),⁴⁰ (NH₄)₂Na₃Li₉(SO₄)₇ (0.5 × KDP),⁴¹ NH₄NaLi₂(SO₄)₂ (1.1 × KDP),⁴¹ and Li₉Na₃Rb₂(SO₄)₇ (1.3 × KDP).⁴² The stronger SHG response of (NH₄)₂S₂O₃ should be due to its polar S₂O₃ groups with enhanced microscopic second order polarizability. Furthermore, as depicted in Fig. 1a, S₂O₃ was neatly arranged, which was also beneficial for improving the SHG effect of the title compound.

In order to further investigate the origin of the SHG contributions of the (NH₄)₂S₂O₃ crystal, the local dipole moments for the NH₄ and S₂O₃ groups were calculated. The calculated results are shown in the ESI (Table S5†). It is worth noting that the S₂O₃ polar tetrahedron has a large distortion and shows a large dipole moment of 13.67 Debye. It is even more important that in a unit cell of the title compound, the dipole moment of four S₂O₃ groups adopts a superimposed arrangement mode on the y-axis which results in a large dipole moment of −33.44 Debye, which is the key component for the whole dipole moment (−34.88 Debye). In polar materials, a large net dipole moment usually implies a large SHG response.^43,44 Therefore, the large SHG response of (NH₄)₂S₂O₃ can be attributed to the polar tetrahedron S₂O₃ groups with a large distortion and their superimposed dipole moments along the y-axis.

Theoretical calculations

In order to gain insight into the optical properties of (NH₄)₂S₂O₃, the first-principles calculations of (NH₄)₂S₂O₃ were carried out. The calculated band gap of (NH₄)₂S₂O₃ was about 4.106 eV (Fig. 3b), which was in good agreement with the experimental value of 4.44 eV. N 2s²2p³, H 1s¹, S 3s²3p⁴, and O 2s²2p⁴ were used for calculations of the total and partial densities of states (DOS and PDOS) of (NH₄)₂S₂O₃ as shown in Fig. 3a. The optical properties of the compounds depended largely on the states near the forbidden band; so only the valence band (VB) top and the conduction band (CB) bottom were analyzed. It was obvious that the VBs were mostly contributed by S 3p and O 2p and the CBs were mainly due to S 3p, O 2p, N 2P, and H 1s, respectively. From the above analysis, it was clear that the optical properties of (NH₄)₂S₂O₃ were attributed mainly to the S₂O₃ polar tetrahedral groups.

Fig. 3 (a) Total and partial DOS curves for (NH₄)₂S₂O₃. (b) Calculated electronic band structure for (NH₄)₂S₂O₃.

According to the formula proposed by Lin et al.,³⁵ the SHG coefficient d_ij of (NH₄)₂S₂O₃ was calculated. (NH₄)₂S₂O₃ crystallized in the 2 point group. Considering the Kleinman symmetry, four independent SHG tensors including d₂₁, d₂₂, d₂₃ and d₂₅ of (NH₄)₂S₂O₃ were calculated (Fig. S7†). The largest one was d₂₃ of −1.05 pm V⁻¹, which was about 2.69 times that of KDP (0.39 pm V⁻¹). It matched well with the experimental result. As shown in Fig. S6,† the occupied and unoccupied states of SHG-densities for the largest tensor d₂₃ were calculated to further confirm the contributions of the S₂O₃ group to the macroscopic hyperpolarizability. In Fig. S6a,† it is obvious that the sources of SHG densities in the occupied states were mainly contributed by the S₂O₃ group. For the unoccupied states, the SHG weighted densities were mostly contributed by the S₂O₃ group and NH₄ group (Fig. S6b†). It could be concluded that the S₂O₃ groups made great contributions to the SHG response in (NH₄)₂S₂O₃. Atom contributions to SHG coefficients were calculated to investigate the origin of the SHG effect intuitively.^48–50 The SHG-contribution of the S₂O₃ tetrahedron to the SHG response of (NH₄)₂S₂O₃ was 66.9%, which was about twice as much as that of NH₄. This result further confirmed that the S₂O₃ group played a major role in the improvement of the SHG response.

Conclusions

In a word, we have successfully synthesized a high-performance NLO thiosulfate (NH₄)₂S₂O₃via a water solution method under mild conditions. It exhibited a short cut-off edge of 238 nm, a large SHG effect that is 3.3 times that of KDP and sufficient birefringence for phase-matching. According to the theoretical calculations, the S₂O₃ group shows a great improvement in polarizability anisotropy and hyperpolarizability compared to SO₄, which indicates that the polar tetrahedral S₂O₃ group is an outstanding functional group for building NLO materials. These materials containing the polar tetrahedral S₂O₃ group might show great improvements in the SHG effect while retaining a short UV absorption edge. It is clear that the S₂O₃ group has great potential for the synthesis of high performance nonlinear optical crystals.

Conflicts of interest

There are no conflicts to declare.

Acknowledgements

This work was supported by the National Natural Science Foundation of China (Grant No. 22222510, 21975255 and 21921001), the Foundation of Fujian Science & Technology Innovation Laboratory (2021ZR202) and the Youth Innovation Promotion Association CAS (2019303).

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Footnote

† Electronic supplementary information (ESI) available. See DOI: https://doi.org/10.1039/d3qi00172e

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