Pb_3.5GeS₄Br₃: the first phase-matching thiogermanate halide infrared nonlinear optical material

Abstract

Two new thiohalides Pb₃GeS₄Br₂ and Pb_3.5GeS₄Br₃ have been synthesized by introducing Pb²⁺ into the thiogermanate system. The compounds crystallize in centrosymmetric P2₁/c (Pb₃GeS₄Br₂) and non-centrosymmetric P6₃ (Pb_3.5GeS₄Br₃) space groups, respectively. To the best of our knowledge, Pb₃GeS₄Br₂ and Pb_3.5GeS₄Br₃ are the first Pb-containing thiogermanate halides, and the latter is the first phase-matching IR nonlinear optical material in the thiogermanate halide system. Due to the presence of Pb²⁺ with stereochemically active lone pair electrons, Pb₃GeS₄Br₂ exhibits a strong optical anisotropy with a birefringence of 0.131@1064 nm, while Pb_3.5GeS₄Br₃ shows a large second-harmonic generation response (0.8 × AgGaS₂) and high laser-induced damage threshold (3.0 × AgGaS₂). These results enrich the structural and chemical diversity of chalcohalides.

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Introduction

As a key device for frequency conversion in all-solid-state lasers, nonlinear optical (NLO) materials are widely applied in many fields, such as spectroscope technology, laser photolithography, photomedicine, environmental monitoring, and so on.^1–6 Based on their operating regions, NLO materials can be classified into deep-ultraviolet (DUV), ultraviolet-visible to near-infrared (UV-vis-NIR), and mid- to far-infrared (IR) NLO materials. In the past few decades, a large number of excellent oxide-based UV or DUV NLO materials, including β-BaB₂O₄,⁷ LiB₃O₅,⁸ KH₂PO₄,⁹ KTiOPO₄,^10,11 KBe₂BO₃F₂¹² and NH₄B₄O₆F,¹³ have been rationally designed and fabricated,^14–17 while for mid- and far-IR bands, the commercialized NLO materials are composed of chalcopyrite-like AgGaS₂ (AGS), AgGaSe₂ (AGSe) and ZnGeP₂ (ZGP).^18–20 Nevertheless, due to the intrinsic drawbacks of these materials, such as the low laser-induced damage threshold (LIDT) in AGS and AGSe,²¹ the non-phase matching behavior of AGSe and strong two-photon absorption in ZGP at around ∼1 μm, their applications are highly limited. Therefore, it is necessary to develop new IR NLO materials with high performance.^22–24

In general, an excellent IR NLO material should meet the following requirements: (1) large second-harmonic generation (SHG) response ≥ 0.5 × AGS, preferably ≥ 1.0 × AGS; (2) high LIDT ≥ 2.0 × AGS for high-power laser output; (3) wide optical transparent range that covers the two important atmospheric windows, 3–5 and/or 8–12 μm; (4) suitable birefringence (> 0.03) to achieve phase matching (PM), which is critical for the practical application of NLO materials; (5) good crystal growth habits and thermal stability.^25–33 However, it is challenging to satisfy these requirements in one compound. To explore new IR NLO materials, metal chalcohalides have received considerable attention due to their abundant structural diversity and adjustable optical properties.^34–36 Meanwhile, chalcohalides are expected to inherit the intrinsic advantages of both chalcogenides and halides. Recent results indicate that the salt-inclusion framework can effectively improve the optical band gap of chalcohalides,^37–39 resulting in balanced optical properties among these compounds. Hence, the salt-inclusion chalcogenides (SICs) have emerged as promising systems for the exploration of new IR NLO materials,^40–42 and a series of new SICs has been developed. It is worth noting that 9 compounds, [Ba₄Cl₂][Ge₃Se₉], [Ba₄Br₂][Ge₃Se₉], [Ba₄Cl₂][Ge₃S₉], [KSr₄Cl][Ge₃S₁₀], [NaSr₄Cl][Ge₃S₁₀], [KBa₄Cl][Ge₃S₁₀], [Sr₄Cl₂][Ge₃S₉], [NaBa₄Cl][Ge₃S₁₀], and [K₂Ba₃Cl₂][Ge₃S₉], have been reported with the thiogermanate halide system. Despite showing evident SHG responses, none of them possesses PM behavior,^43–48 which can be attributed to the small birefringence in these compounds.

To increase the optical anisotropy and birefringence, introducing Pb²⁺, Sb³⁺, and Sn²⁺ cations with stereochemically active lone pair (SCALP) electrons into the structure has been demonstrated as a feasible strategy.⁴⁹ In this work, by introducing Pb²⁺ into thiogermanate halides, the first Pb-containing thiogermanate halides, Pb₃GeS₄Br₂ and Pb_3.5GeS₄Br₃, have been rationally designed and fabricated by a high-temperature solution method. Pb₃GeS₄Br₂ crystallizes in the centrosymmetric (CS) P2₁/c space group and is composed of [PbS₄Br₄], [PbS₃Br₃], [PbS₈] and [GeS₄] units. It exhibits strong optical anisotropy and a large birefringence of 0.131@1064 nm due to the presence of Pb²⁺ with SCALP electrons. While Pb_3.5GeS₄Br₃ crystallizes in the non-centrosymmetric (NCS) P6₃ space group and is built from [PbS₄Br₄], [PbBr₆] and [GeS₄] units. Based on statistical analyses, Pb_3.5GeS₄Br₃ is the first thiogermanate halide IR NLO material with PM behavior. This compound shows a strong SHG response of 0.8 × AGS and has a high LIDT of 3 × AGS.

Experimental procedures

Reagents and syntheses

The raw reagents of PbBr₂ (≥ 99%), Ge (≥ 99.99%), and S (≥ 99.99%) were commercially purchased from Aladdin Industrial Inc. The small single crystals of Pb₃GeS₄Br₂ and Pb_3.5GeS₄Br₃ for structural determinations were prepared by the high-temperature solution method. The starting materials of PbBr₂, Ge and S were weighed and loaded into graphite crucibles with the ratio of 3 : 1 : 4 (Pb₃GeS₄Br₂) and 3.5 : 1 : 4 (Pb_3.5GeS₄Br₃), and then placed in silica tubes. The tubes were further sealed with methane–oxygen flame under a high vacuum of 10⁻³ Pa. After that, the sealed tubes were placed into a computer-controlled furnace and the heating program was set to 650 °C (Pb₃GeS₄Br₂) in 30 h, and 600 °C (Pb_3.5GeS₄Br₃) in 28 h, kept at that temperature for 48 h, and then cooled to room temperature at a rate of 1 °C h⁻¹. Finally, small orange single crystals of Pb₃GeS₄Br₂ and Pb_3.5GeS₄Br₃ (Fig. S1†) were harvested.

Single-crystal X-ray diffraction (SC-XRD)

A Bruker SMART APEX II CCD single-crystal X-ray diffractometer using graphite-monochromatized molybdenum Kα radiation (λ = 0.71073 Å) was utilized to collect the crystal data at 273 K. High-quality single crystals were selected under an optical microscope for collecting the X-ray diffraction data. The SADABS program⁵⁰ was used to perform the multiscan-type absorption correction. Then the XPREP program in the SHELX program package was used to determine the space group, and the SHELXT and XL programs⁵¹ were applied to solve and refine the structure data by direct methods and full-matrix least-squares on F². Finally, the PLATON program⁵² was used to check the possible missing symmetry elements, and no higher symmetry was found.

Powder XRD

A Bruker D2 PHASER diffractometer with Cu Kα radiation (λ = 1.5418 Å) was utilized to record the powder XRD patterns. The collected 2θ range was set to 10–70° with a scan rate of 0.02° s⁻¹. The theoretical patterns of the compounds were obtained by Mercury software based on the CIF file of Pb₃GeS₄Br₂ and Pb_3.5GeS₄Br₃.

Energy-dispersive X-ray spectroscopy (EDS)

The EDS spectrum and mapping of the title compounds were characterized on a field emission scanning electron microscope (FE-SEM, JEOL JSM-7610F Plus, Japan) equipped with an energy-dispersive X-ray spectrometer (Oxford, X-Max 50), which was operated at 5 kV. The measurements were carried out on the small single crystals of Pb₃GeS₄Br₂ and Pb_3.5GeS₄Br₃. The EDS spectra and mappings confirm the presence of Pb, Ge, S and Br elements in the both compounds (Fig. S2a†).

Raman spectroscopy

The Raman spectra of Pb₃GeS₄Br₂ and Pb_3.5GeS₄Br₃ were recorded on a LABRAM HR evolution spectrometer equipped with a CCD detector using 532 nm radiation. The Raman spectra were collected in the 4000–100 cm⁻¹ region.

UV-vis-NIR diffuse-reflectance spectroscopy

A SolidSpec-3700 DUV spectrophotometer was used to determine the UV-vis-NIR diffuse-reflectance spectra of pure phase Pb_3.5GeS₄Br₃ powder samples at room temperature. The measured wavelength range is 200–2600 nm. To figure out the experimental band gap, the collected data were converted to absorbance by the Kubelka–Munk function⁵³F(R) = α/S = (1 − R)²/2R, where F(R) is the ratio of the absorption coefficient to scattering coefficient; α is the absorption coefficient; R is the reflectance; and S is the scattering coefficient.

Refractive index difference (RID) value measurement

The RID of Pb_3.5GeS₄Br₃ was measured on a polarizing microscope (ZEISS Axio Scope.5 Pol) equipped with a Berek compensator. The wavelength of the light source was 546 nm. The difference in the optical path (D) for one direction was determined according to the interference color with the maximum value of the crystal under polarized light. The RID can be calculated using eqn (1):

D = |N₂ – N₁| × T = Δn × T (1)

where Δn denotes the difference in the refractive index and T denotes the thickness of the crystal.

Theoretical calculations

The band structure, total/partial density of states, and optical properties of Pb₃GeS₄Br₂ were calculated by using the plane-wave pseudopotential method implemented in the CASTEP based on the density functional theory (DFT) method.⁵⁴ Perdew–Burke–Ernzerhof (PBE) exchange–correlation of generalized gradient approximation (GGA)^55,56 was applied in the calculations. The interactions between the core and electrons were described by the norm-conserving pseudopotential (NCP).⁵⁷ The Monkhorst–Pack scheme was set as 0.03 Å. The valence electrons were set as Pb 5d¹⁰ 6s² 6p², Ge 4s² 4p², S 3s² 3p⁴ and Br 4s² 4p⁵. The kinetic energy cutoffs were set to be 820 eV. The Heyd–Scuseria–Ernzerhof 06 (HSE06) hybrid functional⁵⁸ was performed using the PWmat code, which runs on graphics processing unit (GPU) processors. The pseudo-potential NCPP-SG15-PBE and 50 Ryd plane wave cut-off energy were used in the calculations:where α is the mixing parameter; μ is the adjustable parameter controlling the short-range interaction; E_X^HF,SR(μ) is the short-range Hartree–Fock exact exchange functional; E_X^PBE,SR(μ) and E_X^PBE,LR(μ) are the short- and long-range components of the PBE exchange functional; and E_C^PBE is the PBE correlation functional. In HSE06, the parameters are suggested as α = 0.25.

LIDT measurements

The resistance to laser damage of Pb_3.5GeS₄Br₃ was evaluated by a single-pulse LIDT method with an incident laser at 1064 nm (10 ns, 10 Hz). Micro-crystal samples of Pb_3.5GeS₄Br₃ with the particle size range ≤ 45 μm were applied for the measurements, and AGS samples with the same sizes were used as the reference. The laser directly irradiated the samples. The output energy of the laser was increased until the samples were damaged. The color change of the samples was carefully observed under an optical microscope. The damage energies were measured to ∼0.12 μJ for Pb_3.5GeS₄Br₃, and ∼0.04 μJ for AGS. The LIDT of Pb_3.5GeS₄Br₃ was calculated to be ∼3 × AGS from the following formula (3):where I is the laser damage energy of a single pulse.

Second-harmonic generation measurements

The SHG responses of Pb_3.5GeS₄Br₃ were evaluated by the Kurtz–Perry method,⁵⁹ and AGS was used as the reference. The powder samples of Pb_3.5GeS₄Br₃ and AGS were ground and sieved into distinct particle size ranges (≤45, 45–63, 63–90, 90–125, 125–180 and 180–212 μm). The experiments were carried out using a 2.09 μm Q-switch laser. The SHG signals were detected by a photomultiplier tube and recorded on an oscilloscope.

Results and discussion

The Pb₃GeS₄Br₂ and Pb_3.5GeS₄Br₃ single crystals for structural determination were fabricated by the high-temperature solution method in a sealed carbon crucible. To avoid high vapour pressure-induced experimental failures, a slow heating rate from room temperature to 650 °C (Pb₃GeS₄Br₂) or 600 °C (Pb_3.5GeS₄Br₃) was utilized (for the detailed experimental process, see the Experimental sections). The results of SC-XRD show that Pb₃GeS₄Br₂ crystallizes in the monoclinic system with the P2₁/c space group, with cell parameters a = 12.8452(9) Å, b = 8.0502(5) Å, c = 11.4712(8) Å, β = 116.129(2)° and Z = 4. Pb_3.5GeS₄Br₃ crystallizes in the hexagonal system with the P6₃ space group, with cell parameters a = b = 11.0145(2) Å, c = 6.0539(2) Å, and Z = 2. The crystal data and structure refinement information, including the atomic coordinates and equivalent isotropic displacement parameters, bond lengths and angles information, are given in the ESI† (Tables 1 and S1–S8†).

Table 1 Crystal data and structure refinements of Pb₃GeS₄Br₂ and Pb_3.5GeS₄Br₃

Empirical formula	Pb3GeS4Br2	Pb3.5GeS4Br3
a R 1 = ∑||Fo| − |Fc||/∑|Fo| and wR2 = [∑w(Fo^2 – Fc^2)^2/∑wFo^4]^1/2 for Fo^2 > 2σ(Fo^2).
Formula weight (Da)	982.22	1165.73
Temperature (K)	273.15	273.15
Crystal system, space group	Monoclinic, P21/c	Hexagonal, P63
Unit cell dimensions (Å)	a = 12.8452(9)	a = b = 11.0145(2)
	b = 8.0502(5)	c = 6.0539(2)
	c = 11.4712(8)
	β = 116.129(2)°
Volume (Å^3)	1064.97(13)	636.06(3)
Z	4	2
Calculated density (Mg m^−3)	6.126	6.087
Completeness (%)	99	97
Absorption coefficient (mm^−1)	58.296	58.535
F(000)	1648.0	976.0
2θ range for data collection/°	3.532 to 55.026	4.27 to 50.578
Index ranges	−16 ≤ h ≤ 16, −10 ≤ k ≤ 10, −14 ≤ l ≤ 14	−13 ≤ h ≤ 13, −13 ≤ k ≤ 13, −7 ≤ l ≤ 7
Reflections collected	12 072	8186
Independent reflections	2426 [Rint = 0.0780, Rsigma = 0.0593]	751 [Rint = 0.0516, Rsigma = 0.0300]
Observed reflections [I > 2σ(I)]	2269	743
Data/restraints/parameters	2426/0/91	751/1/38
Absorption correction type	Multi-scan	Multi-scan
Goodness-of-fit on F^2	1.079	1.014
Final R indices (Fo^2 > 2σ(Fo^2))^a	R 1 = 0.0372, wR2 = 0.0853	R 1 = 0.0136, wR2 = 0.0311
R indices (all data)^a	R 1 = 0.0395, wR2 = 0.0869	R 1 = 0.0140, wR2 = 0.0312
Largest diff. peak and hole (e Å^−3)	3.48 and −2.10	0.47 and −0.5
Flack parameter	—	0.023(8)

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In Pb₃GeS₄Br₂, there are three crystallographically unique Pb atoms, one Ge atom, four S atoms and two Br atoms in its asymmetric unit. Pb1, Pb2, and Pb3 atoms are coordinated with S and Br atoms to form [Pb1S₄Br₄], [Pb2S₃Br₃] and [Pb3S₈] units, with bond lengths d_Pb–S = 2.760–3.601 Å and d_Pb–Br = 2.843–3.669 Å. The Ge atom is connected with four S atoms to form isolated [GeS₄] tetrahedral units with d_Ge–S = 2.193–2.218 Å (Fig. 1a). To further check the formed [Pb1S₄Br₄], [Pb2S₃Br₃], [Pb3S₈] and [GeS₄] units, the Raman spectra of the title compounds were investigated. As shown in Fig. S2b,† according to previous studies, the characteristic peaks of the [GeS₄] tetrahedral unit are located at ∼234 and ∼358 cm⁻¹.^46,60 The characteristic peaks of the Pb–Br bond are located at ∼61 and ∼134 cm⁻¹,⁶¹ and the peaks at ∼200 and ∼394 cm⁻¹ can be ascribed to the vibrations of Pb–S bonds.⁶² The formed [Pb1S₄Br₄], [Pb2S₃Br₃] and [Pb3S₈] groups are linked with each other to build a three-dimensional (3D) [Pb₃S₁₂Br₇] framework (Fig. 1b). The [GeS₄] tetrahedral units form a [GeS₄] pseudo-layer structure along the a axis (Fig. 1c). The [GeS₄] units are placed in the [Pb₃S₁₂Br₇] framework by sharing S atoms to result in the final 3D crystal structure of Pb₃GeS₄Br₂ (Fig. 1d).

Fig. 1 Crystal structure of Pb₃GeS₄Br₂. (a) Coordination environments of Pb, Ge, S and Br atoms; (b) the formed 3D Pb–S–Br framework; (c) the isolated [GeS₄] pseudo-layer structure; and (d) the whole structure of Pb₃GeS₄Br₂.

Pb_3.5GeS₄Br₃ crystallizes in the hexagonal system with the P6₃ space group. There are two crystallographically unique Pb atoms, one Ge atom, two S atoms and one Br atom in its asymmetric unit. The Pb1 atom is coordinated with four S atoms and four Br atoms to construct [Pb1S₄Br₄] units with d_Pb–S = 2.779–3.274 Å and d_Pb–Br = 3.203–3.598 Å. It is worth noting that the Pb2 atom is half-occupied and coordinated with four Br atoms to form a [Pb2Br₆] octahedron with d_Pb–Br = 2.961–2.970 Å. The Ge atom is connected with four S atoms to form isolated [GeS₄] tetrahedral units with d_Ge–S = 2.191–2.225 Å (Fig. 2a). Similarly, the Raman peaks at ∼252 and ∼363 cm⁻¹ can be attributed to the vibrations of the [GeS₄] tetrahedral unit,^46,60 while the peaks at ∼61 and ∼134 cm⁻¹ can be attributed to the vibrations of Pb–Br bonds,⁶¹ and the peaks at ∼200 and ∼397 cm⁻¹ can be attributed to the vibrations of Pb–S bonds,⁶² confirming the chemical bonding in the structure (Fig. S2b†). The formed [Pb1S₄Br₄] units are further connected to each other by sharing S and Br atoms to build a tunnel-like three-dimensional (3D) _∞[Pb₆S₂₁Br₁₂]_n framework (Fig. 2b). Each [Pb2Br₆] octahedron face shares three Br atoms along the c axis to form one-dimensional (1D) _∞[Pb2Br₃]_n chains (Fig. 2c). The isolated [GeS₄] tetrahedral units spiral around the _∞[Pb2Br₃]_n chains along the c axis (Fig. 2d) to form a [GeS₄] tunnel-like 0D framework (Fig. 2e). The Pb1 atoms and _∞[Pb2Br₃]_n 1D chains located within the [GeS₄] framework form the final 3D structure (Fig. 2e and f).

Fig. 2 Crystal structure of Pb_3.5GeS₄Br₃. (a) Coordination environments of Pb, Ge, S and Br atoms; (b) the 3D _∞[Pb₆S₂₁Br₁₂]_n tunnel-like 3D framework; (c) the _∞[Pb2Br₃]_n column configurations; (d) the isolated [GeS₄] tetrahedra arranged around the 6₃ axis; (e) The Pb1 atoms and _∞[Pb2Br₃]_n column configurations located within the [GeS₄] tunnel-like 0D framework; and (f) the whole structure of Pb_3.5GeS₄Br₃.

To clearly show the structural difference, a detailed structural comparison between the two compounds was carried out. It worth noting that the [GeS₄] tetrahedra are isolated in both compounds. However, in Pb₃GeS₄Br₂, the [GeS₄] tetrahedra are located in the glide plane with antiparallel orientation (Fig. S3a†). Accompanied by an increase in the Pb and Br ratios in Pb_3.5GeS₄Br₃ (Fig. S3c†), the [GeS₄] tetrahedra are arranged around a columnar configuration formed by the [PbBr₆] octahedron, showing a more consistent orientation. Moreover, in [Pb₃GeS₄Br₂], the [Pb2S₃Br₃] units show an umbrella-like morphology, indicating that the Pb2²⁺ ion has a strong lone pair effect; meanwhile, in Pb_3.5GeS₄Br₃, ball-shaped units [Pb1S₄Br₄] without lone pair electrons are observed.

To evaluate the optical properties of the title compounds, the syntheses of pure phase powder samples were attempted. Pb_3.5GeS₄Br₃ powder samples were synthesized at 550 °C with a starting mixture of PbBr₂ : Ge : S = 3.5 : 1 : 4. The experimental powder XRD patterns indicate that the main phase of the synthesized polycrystalline powder samples is noncentrosymmetric Pb_3.5GeS₄Br₃. However, there is a small amount of the centrosymmetric Pb₃GeS₄Br₂ secondary phase in the samples (Fig. S4a†), confirming the purity of Pb_3.5GeS₄Br₃. The synthesis of Pb₃GeS₄Br₂ polycrystalline samples was carried out at different temperatures (500, 600 and 700 °C) with diverse starting materials, but it resulted in low yields (the secondary phase is Pb_3.5GeS₄Br₃, Fig. S4b†). Since Pb_3.5GeS₄Br₃ crystallizes in the NCS P6₃ space group, the NLO response of the compound was evaluated by the Kurtz–Perry method under a 2.09 μm solid-state laser by using the polycrystalline samples. As shown in Fig. 3a, the SHG response of Pb_3.5GeS₄Br₃ was found to be ∼0.8 times than that of the benchmark AGS (Fig. S5†), comparable with the value of 0.7 × AGS in the recently reported salt-inclusion chalcogenide IR NLO material Li[LiCs₂Cl][Ga₃S₆].⁴² Meanwhile, the SHG intensities are increased with particle size augmentation until saturation occurs, indicating that Pb_3.5GeS₄Br₃ is a PM compound at the 2.09 μm pumping, which is critical for practical applications. Based on statistical analyses (Table 2), and to the best of our knowledge, it is the first thiogermanate halide IR NLO material with PM behavior. To explain the origin of PM in this compound, the RID (usually Δn ≥ RID) of Pb_3.5GeS₄Br₃ was investigated, and the measured RID is ∼0.05 at 546 nm (Fig. S6†). This means that the birefringence Δn of the compound should be larger than 0.05 at 546 nm,^23,26,63,64 which is consistent with the PM behavior as shown in Fig. 3a. These results indicate the feasibility for the exploration of PM NLO materials by introducing Pb²⁺ into the structure.

Fig. 3 The SHG intensity versus particle sizes (a) and experimental band gap (b) of Pb_3.5GeS₄Br₃. The density of states (DOS), partial DOS (c) and the calculated birefringence (d) of Pb₃GeS₄Br₂.

Table 2 The space group, band gaps, SHG efficiency PM behavior and Δn (cal) of title compound and typical Ge-containing salt-inclusion chalcohalides NLO materials

Compounds	Space group	E g (eV)^a	SHG efficiency (× AGS)	PM/NPM^b	Δn	Ref.
a Experimental value. b PM = phase-matching, NPM = non-phase-matching. c Calculated value.
Pb 3.5 GeS 4 Br 3	P6 3 (no. 173)	2.6	0.8 (@2090 nm, 180–212 μm)	PM	> 0.05 @ 546 nm	This work
[Ba4Cl2][Ge3Se9]	P63 (no. 173)	1.89	0.4 (@2050 nm, 30–46 μm)	NPM	Unknown	43
[Ba4Cl2][Ge3S9]	P63 (no. 173)	2.91	2.4 (@2050 nm, 46–74 μm)	NPM	0.019	43
[Ba4Br2][Ge3Se9]	P63 (no. 173)	2.6	3.5 (@2090 nm, 20–40 μm)	NPM	0.028 (@2090 nm)^c	44
[NaSr4Cl][Ge3S10]	P63 (no. 173)	3.51	0.91 (@2090 nm, 54–100 μm)	NPM	Unknown	45
[KSr4Cl][Ge3S10]	P63 (no. 173)	3.54	1.08 (@2090 nm, 54–100 μm)	NPM	Unknown	45
[KBa4Cl][Ge3S10]	P63 (no. 173)	3.57	0.82 (@2090 nm, 54–100 μm)	NPM	Unknown	45
[Sr4Cl2][Ge3S9]	P63 (no. 173)	3.71	0.97 (@2090 nm, 54–100 μm)	NPM	0.005 (@2050 nm)^c	46
[NaBa4Cl][Ge3S10]	P63 (no. 173)	3.49	0.33 (@2090 nm, 80–100 μm)	NPM	0.005 (@2050 nm)^c	47
[K2Ba3Cl2][Ge3S9]	P63 (no. 173)	3.69	0.34 (@2100 nm, 75–110 μm)	NPM	0.032 (@2100 nm)^c	48

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Beyond the NLO response, the band gap is another important parameter for an excellent IR NLO material. To detect the experimental optical band gap, the UV-vis-NIR diffuse reflectance spectrum of Pb_3.5GeS₄Br₃ was recorded on a SolidSpec-3700 DUV spectrophotometer. The band gap of Pb_3.5GeS₄Br₃ was found to be ∼2.6 eV (Fig. 3b). It is comparable with the band gaps of recently developed Pb-containing chalcogenide IR NLO materials such as Pb₂P₂S₆ (2.6 eV),⁶⁵ Pb₄SeBr₆ (2.62 eV),⁶⁶ and PbGa₂GeS₆ (2.64 eV),⁶⁷ and larger than those of α-Pb₂GeSe₄ (1.42 eV),⁶⁸ Sr_0.25Pb_1.75GeSe₄ (1.48 eV),⁶⁸ Sr_1.3Pb_0.7GeSe₄ (1.65 eV),⁶⁸ Pb_0.72Mn_2.84Ga_2.95Se₈ (1.65 eV),⁶⁹ Pb₄Ga₄GeSe₁₂ (1.91 eV),⁷⁰ Ag₂Pb₃Si₂S₈ (1.95 eV),⁷¹ PbGa₂GeSe₆ (1.96 eV),⁷² PbSnSiS₄ (2 eV),⁷³ Pb₃SBrI₃ (2.16 eV),⁷⁴ Pb₅Ga₆ZnS₁₅ (2.32 eV),⁷⁵ β-PbGa₂S₄ (2.46 eV),⁷⁶ and Li₂PbSiS₄ (2.51 eV).⁷⁷ Usually, the LIDT is proportional to the band gap, thermal conductivity, and the sample quality. The LIDT of Pb_3.5GeS₄Br₃ was found to ∼3 times than that of AGS. However, for practical applications, obtaining a single crystal of large size is essential. Since Pb_3.5GeS₄Br₃ belongs to the chalcogenide group, to increase the single crystal size, the Bridgman–Stockbarger method could be a good choice for the growth of its single crystal. Meanwhile, to improve the crystalline quality, the crystal growth process should be optimized.

To detect the optical properties of Pb₃GeS₄Br₂, DFT calculations were carried out. The calculated band structure indicates that Pb₃GeS₄Br₂ is an indirect band-gap compound with a theoretical GGA band gap of 2.27 eV (Fig. S7†), which is usually underestimated because the GGA served as an exchange–correlation functional. To ensure the calculated accuracy, the HSE06 method was applied.⁷⁸ The calculated HSE06 band gap is ∼2.74 eV. From the density of states (DOS) (Fig. 3c), the top of the valence band (VB) is predominately derived from the S-3p and Br-4p orbitals, while the bottom of the conduction band (CB) is occupied by the Pb-6p orbital. This means the band gap of Pb₃GeS₄Br₂ is mainly determined by the [PbS₄Br₄], [PbS₃Br₃] and [PbS₈] units. Since the compound shows evident structural anisotropy, the birefringence of Pb₃GeS₄Br₂ was studied by DFT calculations, and the computed birefringence is ∼0.131@1064 nm (Fig. 3d), higher than those of other thiogermanate halides like [K₂Ba₃Cl₂][Ge₃S₉] (0.032@2100 nm), [Ba₄Br₂][Ge₃Se₉] (0.028@2090 nm), [Sr₄Cl₂][Ge₃S₉] (0.005@2050 nm), and [NaBa₄Cl][Ge₃S₁₀] (0.005@2050 nm).^44,46–48 The birefringence of Pb₃GeS₄Br₂ is significantly larger than that of Pb_3.5GeS₄Br₃, because of the evident SCALP electrons of Pb2²⁺ in the compound.

Conclusions

In conclusion, by introducing the Pb²⁺ cation into thiogermanate halides, the first series of Pb-containing thiogermanate halides, Pb₃GeS₄Br₂ and Pb_3.5GeS₄Br₃, were successfully synthesized. The compounds show distinctive crystal structures. Compared to the Pb₃GeS₄Br₂, the higher Pb and Br ratios give rise to a columnar configuration along the 6₃ spiral axis direction of the structure in Pb_3.5GeS₄Br₃, resulting in a better arrangement of tetrahedral motifs and higher symmetry in the compound. More importantly, Pb_3.5GeS₄Br₃ exhibits a large SHG response (0.8 × AGS) with PM behaviour and a high LIDT (3 × AGS). Meanwhile, Pb₃GeS₄Br₂, containing Pb²⁺ with SCALP electrons, shows a large birefringence of ∼0.131@1064 nm, indicating that the Pb²⁺ cation with SCALP electrons can effectively enhance the birefringence of thiogermanate halides.

Author contributions

Xiangzhan Jiang, Jiale Qu and Yu Chu designed and guided the experiments and wrote the manuscript. Jiazheng Zhou synthesized the samples, characterized the properties, and wrote the manuscript. Hongshan Wang, Junjie Liu and Xin Su carried out the DFT calculations.

Conflicts of interest

The authors declare no conflict of interest.

Acknowledgements

This work was supported by the National Natural Science Foundation of China (61835014 and 51972336), the Xinjiang Tianshan Talent Program (2022TSYCTD0005), and the Scientific Foundation of Binzhou Medical University (No. 50012304488).

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Footnotes

† Electronic supplementary information (ESI) available. CCDC 2329605 and 2329606. For ESI and crystallographic data in CIF or other electronic format see DOI: https://doi.org/10.1039/d4qi00293h

‡ These authors contributed equally to this work.

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