The exploration of new infrared nonlinear optical crystals based on the polymorphism of BaGa₄S₇

Abstract

Balancing the key performance metrics, such as a large second harmonic generation (SHG) response and a wide band gap, is an extremely important but intractable challenge for the development of infrared (IR) nonlinear optical (NLO) materials. Herein, we report two new polymorphs of BaGa₄S₇, β- and γ-BaGa₄S₇, both of which crystallize in the noncentrosymmetric and polar space groups, Pmc2₁ (No. 26) for β-BaGa₄S₇ and Cm (No. 8) for γ-BaGa₄S₇. They show an interesting structural evolution from AA′ [Ga₆S₁₆]_∞ chains to AA′A′A [Ga₆S₁₆]_∞ chains to AAA′AAA′ [Ga₆S₁₆]_∞ chains as their structures show a transition from the high-temperature phase to the low-temperature phase. More importantly, they both exhibit excellent NLO properties. In particular, β-BaGa₄S₇ exhibits the best balance along with a large phase-matching SHG response (1.2 × AgGaS₂) and a wide band gap (3.94 eV). These indicate that β-BaGa₄S₇ will be a promising IR NLO crystal for high-power laser application. The research also provides an insight into exploring new IR NLO crystals based on structural rearrangement.

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Introduction

Nonlinear optical (NLO) crystals, which can expand the spectral regions of solid-state lasers for generating coherent radiation at a variety of difficult to access wavelengths through a series of frequency conversion technologies, such as second harmonic generation (SHG), optical parametric oscillation (OPO), optical parametric amplification (OPA), etc., play crucial roles in the development of solid-state lasers.^1–5 In particular, ultraviolet (UV) and infrared (IR) coherent light is difficult or impossible to generate through direct lasing. In contrast, relying on the frequency conversion of NLO crystals is the best method for these laser outputs.^6,7 Currently, although a series of borate and phosphate crystals such as β-BaB₂O₄ (BBO),⁸ LiB₃O₅ (LBO),⁹ CsLiB₆O₁₀ (CLBO),¹⁰ KH₂PO₄ (KDP)¹¹ and KTiOPO₄ (KTP)¹² have been able to achieve a high-power laser output in the UV and visible regions, crystals that can be used in the IR region are still very limited. They are mainly chalcopyrite-type AgGaS₂ (AGS),¹³ AgGaSe₂ (AGSe)¹⁴ and ZnGeP₂ (ZGP),¹⁵ and some inherent performance defects, e.g. a low laser damage threshold (LDT) and two-photon absorption (TPA), also severely prohibit their performance in high-power laser output applications.¹⁶ Therefore, exploring new IR NLO crystals is still of current research interest.

Generally, an excellent IR NLO crystal needs to satisfy the following conditions, including (i) wide IR transmission windows, covering the atmospheric windows of 3–5 μm and 8–12 μm, (ii) large SHG coefficients (>0.5 × AGS), (iii) wide band-gaps and high LDTs (E_g >3.0 eV or >10 × AGS).¹⁷ Due to the merits of chalcogenides in IR optical transparency and SHG responses, they have been widely considered as the most promising materials class for the exploration of IR NLO crystals.¹⁸ In order to increase the band-gaps of chalcogenides, various strategies have been suggested, among which the most effective one is to introduce the electron-positive alkali or alkali-earth cations into structures.¹⁹ On the one hand, alkali or alkaline-earth metals have no d–d or f–f electronic transitions, so they can effectively widen the band gaps and reduce the TPAs, and thus enhance the LDTs of materials. On the other hand, the flexible coordination of alkali or alkali-earth cations is also helpful for adjusting the orientation of microscopic dipole moments of the chalcogenide MQ₄ (M = Zn, Cd, Ga, In, Si, and Ge; Q = S, Se) tetrahedra to make them have the additive manner and enhance the SHG responses.^20,21 Under the guidance of these ideas, lots of high-performance IR chalcogenide NLO crystals have been synthesized, including BaGa₄Q₇ (Q = S, Se),^22,23 BaGa₂GeQ₆ (Q = S, Se),²⁴ LiGaQ₂ (Q = S, Se),^25,26 Na₂BaMQ₄ (M = Ge, Sn; Q = S, Se),²⁷ Li₂Ga₂GeQ₆ (Q = S, Se),²⁸etc.

Beyond these, polymorphism is also an effective strategy for exploring new IR NLO crystals because the rearrangement of the basic building units in the structure can further optimize the functional properties of materials.²⁹ The typical examples consist of BaB₂O₄ (α: R-3c, β: R3),⁸ BaTeMo₂O₉ (α: Pca2₁, β: P2₁, γ: P2₁),³⁰ Li₂ZnGeS₄ (α: Pna2₁, β: Pn),^31,32 K₂Hg₃Ge₂S₈ (α: Aba2; β: C2),³³ and Ba₂[VO₂F₂(IO₃)₂]IO₃ (α: Pna2₁, β: P2₁).³⁴ In our recent research, the highly symmetric NCS β-BaGa₄Se₇ and β-BaGa₂Se₄ have been synthesized and they exhibit more excellent NLO properties than the previously reported α-phases.^35,36 These indicate that structural rearrangement is indeed an ideal strategy for rationally synthesizing high-performance NLO crystals. Inspired by these, our current attention has been focused on another important IR NLO crystal, BaGa₄S₇, which can exhibit a larger band-gap (3.54 eV, from the crystal sample) and LDT (1.2 J cm⁻² at 1.064 μm and a 15 ns pulse width)²³ than β-BaGa₄Se₇ and β-BaGa₂Se₄. Our research has resulted in the discovery of two new polymorphs of BaGa₄S₇, which crystallize in orthorhombic (Pmc2₁) and monoclinic (Cm) space groups, respectively. Based on the orders they were discovered, these two new polymorphs of BaGa₄S₇ are named β-BaGa₄S₇ (Pmc2₁) and γ-BaGa₄S₇ (Cm), respectively, and the previously reported phase is named α-BaGa₄S₇ (Pmn2₁).²³ As far as we know, α-, β- and γ-BaGa₄S₇ represent the first ternary chalcogenides with three polar and non-centrosymmetric (NCS) polymorphs. The further structural analyses show that the phase-transitions among α-, β- and γ-BaGa₄S₇ are caused by the rearrangement of [Ga₆S₁₆]_∞ chains in their structures, which also represents the new phase-transition mechanism. More importantly, β-BaGa₄S₇ exhibits excellent NLO properties, including large phase-matching SHG responses (∼1.2 × AGS) and wide band gaps (E_g = 3.94 eV), indicating that they are promising IR NLO crystals. Herein, we will report their syntheses, crystal structures, phase transitions and NLO properties.

Experimental section

Materials

Barium (Ba, 99%, Aladdin), barium sulfide (BaS, 99.9%, Beijing Hawk Science and Technology Co. Ltd), gallium (Ga, 99.99%, Aladdin), gallium sulfide (99.9%, Beijing Hawk Science and Technology Co. Ltd), sulfide (S, 99.99%, Aladdin), and germanium (Ge, 99.99%, Beijing Hawk Science and Technology Co. Ltd) all were commercially purchased without further refinement.

Syntheses

α-, β- and γ-BaGa₄S₇ are polymorphous. Their pure polycrystalline samples were synthesized through a series of solid-state reactions in sealed silica tubes. The stoichiometric Ba (0.48 mmol, 0.0663 g), BaS (0.32 mmol, 0.0385 g), Ga (3.22 mmol 0.2246 g) and S (6.07 mmol, 0.1704 g) were firstly loaded into graphite crucibles. Then the graphite crucibles were put into silica tubes and flame-sealed under 10⁻³ Pa. These tubes were heated to 720 °C in 30 h and kept at this temperature for about 100 h. Then they were cooled to room temperature and the mixture in the tube was thoroughly ground and sealed into new silica tubes again. The new silica tubes were further heated to a higher temperature, 720 °C for 30 h and the temperature was maintained for 100 h. By repeating the above process with a 20 °C higher calcination temperature than the last reaction, the phase-transition temperature from β- to α-BaGa₄S₇ has been determined. And the pure polycrystalline samples of α- and β-BaGa₄S₇ were also obtained. Furthermore, their millimeter-sized crystals were also obtained by melting the pure polycrystalline sample (for α-BaGa₄S₇) or with the BaS and Ge as the flux for β- and γ-BaGa₄S₇ at 1100, 1000 and 950 °C, respectively.

Structural refinement and crystal data

The single-crystal structure data of α-BaGa₄S₇ were reported by Eisenmann et al. in 1983.³⁷ For new β- and γ-BaGa₄S₇, their single-crystal data were collected at 293(2) K by using a Bruker D8 VENTURE CCD diffractometer with a Mo Kα source (λ = 0.71073 Å).³⁸ All data were integrated with SAINT and a numerical absorption correction using SADABS was applied.³⁹ The structures were solved by direct methods using SHELXT and refined by full-matrix least-squares methods against F² by SHELXL-2019/1.⁴⁰ Crystallographic data for the structures were deposited with the Cambridge Crystallographic Data Centre. CCDC 2132789 and 2132787† contain the supplementary crystallographic data. Crystal data, data collection and structure refinement are summarized in Table 1. The final refined atomic coordinates, equivalent isotropic displacement parameters and the calculated bond valence sums (BVSs) are listed in Table S1,†⁴¹ and the selected bond distances are given in Table S2.†

Table 1 Crystal data and structure refinement for α-, β- and γ-BaGa₄S₇

a R 1 = S||Fo| − |Fc||/S|Fo| and wR2 = [Sw(Fo^2 − Fc^2)^2/Sw Fo^4]^1/2 for Fo^2 > 2s(Fo^2).
Empirical formula	α-BaGa4S7 ^23	β-BaGa4S7	γ-BaGa4S7
Formula weight	640.64
Space group (number)	Pmn21 (31)	Pmc21 (26)	Cm (8)
a [Å]	14.755(5)	14.6922(9)	18.347(3)
b [Å]	6.228(2)	6.2291(4)	14.719(3)
c [Å]	5.929(2)	11.9041(7)	6.2295(9)
β [°]			103.921(5)
Volume [Å^3]	544.8(3)	1089.45(12)	1632.9(4)
Z	2	4	6
ρ calc [g cm^−3]	3.905	3.906	3.909
μ [mm^−1]	14.601	14.603	14.615
F (000)	584	1168	1752
Crystal colour	Yellow	Colourless	Yellow
Completeness	99.9%	99.9%	99.9%
Data/Parameters	1159/59	3211/117	2705/174
Goodness-of-fit on F^2	0.947	1.033	1.007
Final R indexes [Fo^2 > 2s(Fo^2)]^a	R 1 = 0.0201, wR2 = 0.039	R 1 = 0.0392, wR2 = 0.0579	R 1 = 0.0435, wR2 = 0.0785
Flack X parameter	0.032(13)	0.06(2)	0.07(3)

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Powder X-ray diffraction

The powder X-ray diffraction (PXRD) analysis was performed on a SmartLab 9KW X-ray diffractometer at room temperature (Cu-Kα radiation). The collected data are within the 2θ range of 10–70°, with a step size of 0.01° and a step time of 2 s. As seen in Fig. S1,† the polycrystalline XRD patterns are in good agreement with the calculated ones.

Energy-dispersive spectroscopy

Microprobe elemental analyses and the elemental distribution maps were measured on a field-emission scanning electron microscope (Quanta FEG 250) made by FEI. The energy-dispersive spectroscopy measurement corroborated the existence of Ba/Ga/S with an average atomic ratio of 21.39% : 43.56% : 35.05% and 21.39% : 43.46% : 35.15% for β- and γ-BaGa₄S₇, respectively, which are approximately equal to the theoretical one, 21.43%, 43.53%, and 35.03% (Fig. S2†).

UV-Vis-near-IR (NIR) diffuse-reflectance and IR spectra

The UV/Vis/NIR diffuse reflectance spectrum was recorded with a Shimadzu SolidSpec-3700DUV UV/Vis/NIR Spectrophotometer at room temperature. The measurement range was from 300 to 2000 nm and barium sulfate was used as the diffuse reflection standard. The IR spectra were recorded on a Nicolet iS50 Fourier transform infrared spectrometer in the range 500–4000 cm⁻¹.

Raman spectroscopy

Raman spectra of the crushed crystals of the title compounds were obtained using a LABRAM HR Evolution spectrometer equipped with a CCD detector using 532 nm radiation from a diode laser. For each sample, crystals were placed on a glass slide and a 50× objective lens was used to choose the area of the crystal specimens to be measured. The grating was set to be 600 g mm⁻¹. The maximum power of 60 mW and a beam diameter of 35 μm were used. The spectrum was collected using an integration time of 5 s.

Power SHG measurement

The SHG responses were measured according to the method proposed by Kurtz and Perry with laser radiation at an optical wavelength of 2090 nm.⁴² Powder samples of polymorphs of BaGa₄S₇were graded into several distinct particle size ranges of 25–53, 53–75, 75–106, 106–120, 120–150, 150–180, and 180–212 μm. At the same time, a powder AGS sample with the same particle size range was used as a reference.

The details of computational methods

The electronic band structures, the partial density of states and optical properties for α-, β- and γ-BaGa₄S₇ were carried out using the CASTEP package based on density functional theory (DFT).⁴³ Generalized gradient approximation (GGA) parametrized by the Perdew–Burke–Ernzerhof (PBE) functional was chosen for the exchange–correlation energy, and the pseudopotential was set as norm-conserving pseudopotential (NCP).⁴⁴ The valence electrons were set as: Ba 4d¹⁰5p⁶6s², Ga 4s²4p¹, and S 3s²3p⁴. The plane-wave energy cutoff value was set at 860.0 eV. The corresponding Monkhorst–Pack κ-point meshes were adopted 2 × 5 × 6, 2 × 5 × 3 and 2 × 2 × 6 for α-, β- and γ-BaGa₄S₇, respectively.⁴⁵

The SHG coefficients were calculated from the band wave functions using the so-called length-gauge formalism derived by Aversa and Sipe at a zero frequency limit. The static second-order nonlinear susceptibilities χ⁽²⁾_αβγ can be reduced as:^46–48

χ⁽²⁾_αβγ = χ⁽²⁾_αβγ (VE) + χ⁽²⁾_αβγ (VH)

Virtual-Hole (VH), Virtual-Electron (VE) and Two-Band (TB) processes play an important role in the total SHG coefficient χ⁽²⁾. The TB process can be neglected owing to the little contribution for SHG. The formulas for calculating χ⁽²⁾_αβγ (VE) and χ⁽²⁾_αβγ (VH) are as follows:

Here, α, β, γ are Cartesian components, v and v′ denote valence bands, c and c′ refer to conduction bands, and P(αβγ) denotes the full permutation. The band energy difference and momentum matrix elements are denoted as ℏω_ij and P^α_ij, respectively. As we know, the virtual electron (VE) progress of the occupied and unoccupied states is the main contribution to the overall SHG effect.⁴⁹

On account of the electron transition from the valence band (VB) to the conduction band (CB), we inferred the imaginary part of the dielectric function. Then, by adopting the Kramers–Kronig transform, we calculated the real part of the dielectric function. The refractive indices n (and the birefringence Δn) were achieved from the real part of the dielectric function.

Results and discussion

Crystal structures and phase transitions

The structural data of α-, β- and γ-BaGa₄S₇ are listed in Table 1. It is clear that the unit cells gradually increase from α-, β- to γ-BaGa₄S₇. And γ-BaGa₄S₇ crystallizes in the lowest space group (Cm) and has the largest density (3.910 g cm⁻³). Therefore, γ-BaGa₄S₇ should be the low-temperature phase according to the principle of the thermal expansion and contraction, while α-BaGa₄S₇ is the high-temperature phase.

α-BaGa₄S₇. The structure of α-BaGa₄S₇ has been reported previously.²³ But in order to better compare it with other polymorphs, its structure is still shown in Fig. 1. Its asymmetric unit contains one unique Ba, two unique Ga, and four unique S atom(s). In the structure, the Ga atoms are coordinated by the four S atoms to form [GaS₄] tetrahedra with the Ga–S bond distances ranging from 2.242(6) to 2.335(6) Å. These [GaS₄] tetrahedra further connect with each other by corner-sharing to form one-dimensional (1D) [Ga₆S₁₆]_∞ chains (Fig. 1a). The adjacent [Ga₆S₁₆]_∞ chains adopt the opposite and staggered stacking along the c-axis, and they are connected to form the 3D [Ga₄S₇]_∞ framework. So, if the 1D [Ga₆S₁₆]_∞ chains with the different orientation are marked as A and A′ (Fig. 1b), respectively, the structure of α-BaGa₄S₇ could be written as AA′AA′AA′… Thus, AA′ can be as the minimum stacking length of [Ga₆S₁₆]_∞ chains in α-BaGa₄S₇. And owing to the different orientation of A- and A′-[Ga₆S₁₆]_∞ chains, the microscopic polarization in the a–b plane is offset. Only the polarization along the stacking direction (c-axis) will be retained. For Ba²⁺ cations, they are all filled in the stacking space of [Ga₆S₁₆]_∞ chains and have the sole coordinated environment, [BaS₁₂] polyhedral with the Ba–S distances ranging from 3.417(9) to 3.672(10) Å (Fig. S3a†). They are consistent with other reported ones.¹⁹ The bond valence calculations show the bond valence sums (BVSs) for Ba²⁺, Ga³⁺ and S²⁻ are 1.81, 3.04–3.06 and 1.90–2.20, respectively.⁴¹ They are all in agreement with their ideal oxidation states.

Fig. 1 Crystal structure of α-BaGa₄S₇. (a) The total crystal structure framework along the b direction, it is formed by the adjacent [Ga₆S₁₆]_∞ chains adopting the opposite and arrangement in the AA′AA′…… manner. (b) The 1D [Ga₆S₁₆]_∞ chains with different orientations as the A and A′, respectively.

β-BaGa₄S₇. The structure of β-BaGa₄S₇ is shown in Fig. 2. Its lattice parameter along the c-axis is around twice of α-BaGa₄S₇. In its asymmetric unit, there are two unique Ba, four unique Ga, and eight unique S atom(s). All the Ga atoms in β-BaGa₄S₇ are also coordinated by four S atoms to form the GaS₄ tetrahedra, and these GaS₄ tetrahedra are also connected to form the 1D [Ga₆S₁₆]_∞ chains (Fig. 2a). Different from α-BaGa₄S₇, however, the adjacent [Ga₆S₁₆]_∞ chains are arranged into the framework of β-BaGa₄S₇ in a manner of AA′A′AAA′A′A…(Fig. 2b). So, the minimum stacking length of [Ga₆S₁₆]_∞ chains in β-BaGa₄S₇ is AA′A′A, which is twice that in α-BaGa₄S₇. Accordingly, the Ba²⁺ cations in β-BaGa₄S₇ have two different coordination environments, [BaS₁₂] and [BaS₁₁] polyhedra with the Ba–S distances ranging from 3.456(3) to 3.642(3) Å (Fig. S3b†). The BVSs for Ba²⁺, Ga³⁺ and S²⁻ can be calculated as 1.78–1.80, 3.03–3.08 and 1.91–2.18, respectively. They are consistent with their respective ideal oxidation states.

Fig. 2 Crystal structure of β-BaGa₄S₇. (a) The total crystal structure framework along the b direction, it is formed by the adjacent [Ga₆S₁₆]_∞ chains that adopt the opposite and arrangement in the AA′A′A… manner. (b) The 1D [Ga₆S₁₆]_∞ chains with different orientations as the A and A′, respectively.

γ-BaGa₄S₇. The structure of γ-BaGa₄S₇ is shown in Fig. 3. γ-BaGa₄S₇ has the largest unit cell among three polymorphs. It is around three times that of α-BaGa₄S₇. Accordingly, in the asymmetric unit of γ-BaGa₄S₇, it contains three unique Ba, six unique Ga, and twelve unique S atom(s). In its structure (Fig. 3a), all the Ga atoms are also coordinated to form the GaS₄ tetrahedra, and these GaS₄ tetrahedra are also connected to form the 1D [Ga₆S₁₆]_∞ chains (Fig. 3b). Notably, when these [Ga₆S₁₆]_∞ chains are connected into the 3D framework, they adopt a more complex stacking manner, i.e. AAA′AAA′… (Fig. 3a). So, a larger unit cell is necessary for γ-BaGa₄S₇. And owing to the complex stacking of [Ga₆S₁₆]_∞ chains, three different polyhedra are also built for three different coordinated Ba²⁺ cations in γ-BaGa₄S₇. Ba(1) and Ba(3) are coordinated into [BaS₁₂] polyhedra with Ba–S distances ranging from 3.451(8) to 3.641(6) Å, and Ba(2) are coordinated into [BaS₁₁] polyhedra with the Ba–S distance in the range of 3.423(6) to 3.649(6) Å (Fig. S3c†). Clearly, these bond distances for all Ga–S bonds and Ba–S bonds are consistent with other reported ones. The BVSs for Ba²⁺, Ga³⁺ and S²⁻ are 1.74–1.80, 2.99–3.04 and 1.90–2.09, respectively. They are also consistent with their respective ideal oxidation states.

Fig. 3 Crystal structure of γ-BaGa₄S₇. (a) The total crystal structure frameworks along the b direction, it is formed by the adjacent [Ga₆S₁₆]_∞ chains that adopt the opposite and arrangement in the AAA′AAA′…… manner. (b) The 1D [Ga₆S₁₆]_∞ chains with different orientations as the A and A′, respectively.

The phase transitions. It is clear that the different crystal structures of α-, β- and γ-BaGa₄S₇ mainly originate from the different orientations and stacking manners of [Ga₆S₁₆]_∞ chains in their structures. In order to understand the relationship between the phase transitions and temperatures, a series of solid-state reactions with different calcined temperatures were performed in sealed silica tubes. As shown in Fig. 4a, when the calcination temperature is in the range of 720 to 800 °C, the main reaction product is β-BaGa₄S₇. When the temperature is higher than 800 °C, β-BaGa₄S₇ starts to transfer into α-BaGa₄S₇ (Fig. 4a). From 800 °C to the melting temperature (∼1100 °C), the stable phase is always α-BaGa₄S₇. That also indicates α-BaGa₄S₇ should be the high-temperature phase. The phase transition temperature from β- to α-BaGa₄S₇ is around 800 °C. However remarkably, calcining α-BaGa₄S₇ at 750 °C for 72 h (Fig. 4b), no phase-transition from α- to β-BaGa₄S₇ was observed, indicating that the phase-transition from β- to α-BaGa₄S₇ is irreversible. In addition, during the whole heating process, the main phase for γ-BaGa₄S₇ was not observed. That indicates γ-BaGa₄S₇ may be a substable phase, which can be attributed to the complex stacking of [Ga₆S₁₆]_∞ chains in the structure. In order to confirm the stabilities of α-, β- and γ-BaGa₄S₇. Their Bond Strain Index (BSI) and Global Instability Index (GII) were also calculated (Table S3a–c†). Generally, BSI and GII values imply the strain caused by electronic-induced and lattice-induced strains, respectively.^50,51 A value greater than 0.05 v.u. indicates the structure is strained, and a value greater than 0.2 v.u. indicates the structure is unable. Clearly, γ-BaGa₄S₇ has the largest BSI and GII values, which are 0.161 valence unit (v.u.) and 0.133 v.u. (Table S3c†), respectively. These indicate that γ-BaGa₄S₇ is strongly strained. When γ-BaGa₄S₇ transforms into α- and β-BaGa₄S₇, the electronic-induced and lattice-induced strains can be released with the decrease in the BSI and GII values (Tables S3a and 3b†).

Fig. 4 The powder XRD patterns of BaGa₄S₇. (a) The variable-temperature powder XRD patterns of the β-BaGa₄S₇. (b) The powder XRD patterns of the α-BaGa₄S₇ after 750 °C for 72 h.

The linear and NLO properties of α- and β-BaGa₄S₇

As described above, α-, β- and γ-BaGa₄S₇ have the same compositions and stoichiometric ratios. The different arrangements of their basic building units (BBUs) result in their different structures. Clearly, the different structures will make them exhibit different functional properties. In order to better show the difference of their properties, their linear and NLO properties have been measured and compared in the same conditions. Remarkably, as the pure phase for γ-BaGa₄S₇ was not obtained, only the properties of α- and β-BaGa₄S₇ will be characterized.

UV-Vis-NIR spectra. The UV-Vis-NIR spectra of α- and β-BaGa₄S₇ in the range from 300–2500 nm are shown in Fig. 5a. Their UV cut-off edges are 330 and 315 nm, respectively. Correspondingly, their band-gaps are 3.75 and 3.94 eV (from powder sample). Therefore, it is clear that the band gap of β-BaGa₄S₇ is a little larger than that of α-BaGa₄S₇. The larger band gap of β-BaGa₄S₇ can also be confirmed by the crystal colors (Fig. 5a). Clearly, β-BaGa₄S₇ is colorless, while the color of α-BaGa₄S₇ is pale yellow (Fig. 5a).

Fig. 5 Optical properties of BaGa₄S₇. (a) The UV/Vis-NIR diffuse reflectance spectrum of β-BaGa₄S₇. Inset: α- and β-BaGa₄S₇ crystal. (b) The FTIR spectrum. Inset: Raman spectrum of α- and β-BaGa₄S₇. (c) Particle size dependence of SHG intensities of β-BaGa₄S₇ and AGS. (d) The SHG signals for α- and β-BaGa₄S₇ in the same particle sizes.

IR and Raman spectra. The IR spectra of α- and β-BaGa₄S₇ are shown in Fig. 5b. It shows α- and β-BaGa₄S₇ have similar IR spectra. Both of them have no obvious absorption in a wide range from 4000 to 500 cm⁻¹ (i.e. 2.5–20 μm), implying their wide IR transmission region. Furthermore, the Raman spectra of α- and β-BaGa₄S₇ were also recorded (Fig. 5b). The strong absorptions at 241, 322, 339 and 387 cm⁻¹ for α-BaGa₄S₇ and 249, 345, 391 and 406 cm⁻¹ for β-BaGa₄S₇ are due to asymmetric and symmetric stretching vibrations of Ga–S–Ga modes, in GaS₄ tetrahedral units. For the two compounds, the other Raman peaks below 200 cm⁻¹ are due to the Ba–S vibrations. These are consistent with those of other related chalcogenides, such as BaGa₂S₄ and PbGa₂S₄.^52,53

Second harmonic generation properties. The powder SHG response of β-BaGa₄S₇ was studied through the Kurtz and Perry method with 2.09 μm radiation.⁴³ The data reveal that β-BaGa₄S₇ is type I phase-matchable (Fig. 5c), and the SHG response is around 1.2 × AGS and 1.3 × α-BaGa₄S₇ under the same conditions (Fig. 5d). Obviously, the SHG response can satisfy the requirement of IR NLO crystals (0.5 × AGS).

The structure–property relationships

The first principles calculations. To understand the origin of the NLO properties, we firstly carried out first-principles calculations for α- and β-BaGa₄S₇ with the same parameters, and the results show that α- and β-BaGa₄S₇ have similar electronic structures (Fig. 6). α- and β-BaGa₄S₇ have the following direct band gaps, 2.38 eV for α-BaGa₄S₇ and 2.48 eV for β-BaGa₄S₇ (Fig. 6). Clearly, their band gaps are both smaller than the experimental ones owing to the discontinuity of exchange–correlation energy.⁵⁴ The partial density of states analysis of transitions from occupied states to unoccupied states reveals the microcosmic origin of the optical properties from an electronic level insight. The 4s, 4p states of Ga, and 3s states of S construct the top region of valence states from −8 to 0 eV. Their wide hybridization in this area indicates that Ga–S bonds make the main contribution of the upper side of the valence band. The bottom region of conduction states mainly is composed of 4s, 4p states of Ga, 3s state of S, and 5d state of Ba. Thus, [GaS₄] tetrahedra have a significant effect on its optical properties, and Ga–S polyhedra determine the SHG effects of α- and β-BaGa₄S₇. In addition, the calculations show that the three independent nonzero SHG coefficients d₃₁, d₃₂ and d₃₃ in α-BaGa₄S₇ are −9.43, −8.05 and 26.83 pm V⁻¹; the three independent nonzero SHG coefficients d₃₁, d₃₂ and d₃₃ in β-BaGa₄S₇ are −11.24, −9.59 and −27.11 pm V⁻¹. Both of them are also consistent with the experimental results.

Fig. 6 The theoretical calculation for BaGa₄S₇. Band structures and density of states of α- and β-BaGa₄S₇ calculated using the PBE functional under the same conditions, the (a) and (b) for α- and β-BaGa₄S₇, respectively.

The dipole moment calculations based on the bond-valence modes. From the experimental and calculated results, it can be seen that β-BaGa₄S₇ exhibits more excellent NLO properties than the α-phase. In order to understand the structural origin resulting in their different functional properties, a more detailed structure comparison of the two polymorphs has been carried out based on the dipole moment calculations (Table 2).⁴¹ Clearly, α- and β-BaGa₄S₇ crystallize in the orthorhombic space group and possess a non-zero dipole moment along the c axis (Fig. 7).

Fig. 7 The microscopic dipole moments. The orientation of the microscopic dipole moments of the GaS₄ groups in α- and β-BaGa₄S₇ of (a) and (b). The total dipole moments along the −c axis (pink arrows).

Table 2 The dipole moments and flexibility indices (F) of [GaS₄]⁵⁻ groups in α- and β-BaGa₄S₇

Compound	Polyhedron	Dipole moment					F
		X-axis	Y-axis	Z-axis	Magnitude	Total
α-BaGa4S7	[Ga(1)S4]^5−	0	0	−11.04	11.04	0.059 (esu cm Å^−3)	0.216
	[Ga(2)S4]^5−	0	0	−5.16	5.16
	Unit cell	0	0	−16.20	16.20
β-BaGa4S7	[Ga(1)S4]^5−	0	0	−9.45	9.45	0.043 (esu cm Å^−3)	0.218
	[Ga(2)S4]^5−	0	0	1.42	1.42
	[Ga(3)S4]^5−	0	0	−5.42	5.42
	[Ga(4)S4]^5−	0	0	−10.14	10.14
	Unit cell	0	0	−23.59	23.59

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For α-BaGa₄S₇, it contains two crystallographically different GaS₄ tetrahedra, i.e. Ga(1)S₄ and Ga(2)S₄. The sum of their dipole moments in a unit cell is 16.20 D along the c-axis (Fig. 7a), and the total dipole moment is 0.059 esu cm Å⁻³. For β-BaGa₄S₇, four different GaS₄ tetrahedra can be observed in a unit cell, and their sum for the dipole moment is 23.59 D along the c-axis (Fig. 7b), the total dipole moment is 0.043 esu cm Å⁻³. It is clear that α-BaGa₄S₇ can exhibit stronger polarity in the unit cell than that of β-BaGa₄S₇. Generally, for the polar materials, a larger net dipole moment in the unit cell often results in a larger SHG response.⁵⁵ Therefore, the SHG response of α-BaGa₄S₇ should larger than β-BaGa₄S₇, but clearly this is contrary to the results of experimental and theoretical calculations. The cause of the heightened SHG response in β-BaGa₄S₇ is difficult to explain just based on the anionic groups, as shown by an examination of the dipole moments along the c direction (Table 2). Accordingly, different mechanisms must be investigated in order to further investigate the causes behind the β-BaGa₄S₇ enhanced SHG response. It is well known that the SHG responses of materials are related to not only the intrinsic dipole moments but also the induced dipole moments, which have been considered to have a more significant effect. The flexibility index was proposed to characterize the induced polarizability by valence electrons.⁵⁶ In 2014, Jiang et al. proposed a simple “flexible dipole model” to ‘quantify’ the induced dipole moments by calculating an empirical “flexibility index” F.⁵⁷ Clearly, the flexibility index calculations (Table 2) reveal that GaSe₄ tetrahedra in β-BaGa₄S₇ (F = 0.218) are more “flexible” than the α-BaGa₄S₇ (F = 0.216), indicating that the former groups are easier to generate the larger induced polarization compared with the latter, combined with the higher number of the GaSe₄ tetrahedra in the unit cell (α-BaGa₄S₇: 8 vs. β-BaGa₄S₇: 16), that makes the SHG response enhanced from α- to β-BaGa₄S₇.

The symmetry-adapted mode decomposition (SAMD) calculations. From the calculations above, β-BaGa₄S₇ exhibits a larger F-value than the α-phase. This indicates that the intrinsic dipole moments play important roles in the SHG enhancement of β-BaGa₄S₇. Beyond these, in order to further elucidate the contribution of atomic displancements from inversion center on NLO properties, we also performed a symmetry-adapted mode decomposition using the symmetry mode analysis tool of the Bilbao Crystallographic Server.^58–60

First, a hypothetical high symmetry structure was identified for β-BaGa₄S₇ in centrosymmetric (CS) Pnma (No. 62) (Fig. S4†). Next, the pseudosymmetric structures subjected to structural relaxation by performing DFT calculation with lattice constants were fixed at the values in the corresponding experimental structures and the atomic forces were restricted to be <8 meV Å⁻¹. We then examined the relationship between the CS (Pnma) and NCS (Pmc2₁) phases in terms of orthonormal symmetry-adapted modes (Tables S4 and S5†). In these two structures, the Ba(1), Ga(1), Ga(2), S(1), S(2), S(3) and S(4) in the nonpolar Pnma structure are split into Ba(1)/Ba(2), Ga(1)/Ga(4), Ga(2)/Ga(3), S(1)/S(7), S(2)/S(5), S(3)/S(8) and S(4)/S(6), respectively, in the polar Pmc2₁ structure, with a single polar mode with a maximum atomic displacement of 3.05 Å (Table S6†). Table 3 lists the atoms that make up each Wyckoff position (WP) as well as the distortions of the atoms; Fig. S5† shows the distortions. The atomic displacements at WPs 8d contribute the most to the overall distortions of 12.34 Å, indicating that Ga and S displacements contribute the most to the local dipole. As a result, the GaS₄ groups play a vital role in inversion symmetry breaking and contribute significantly to the SHG intensity in β-BaGa₄S₇. Furthermore, we calculated the net mode-distortion vectors in the polar axis, A_p (Table 3). Values of A_p/A of 4c and 8d less than 1 indicate that there are no “fully polarized” WPs, but through the decomposition of linearity and orthogonality along the polar axis, the atomic displacements in those orbitals contribute to a local dipole and the asymmetry in the structure.

Table 3 The α- and β-BaGa₄S₇ atomic decompositions, total and polar-axis distortion model amplitudes (in Å)

Compound	WP	Atom(s)^a	A	A p	A/Ap	Total	SAMDs
a The atom shown in bold for each WP makes the greatest displacement.
β-BaGa4S7	4c	Ba1, S1	2.83	1.94	0.69	12.34	11.3 × 10^21 (Å cm^−3)
	8d	Ga1, Ga2, S2, S3, S4	12.01	7.21	0.60
α-BaGa4S7	2a	Ba1	0.20	0.20	1	1.54	2.84 × 10^21 (Å cm^−3)
	2b	S4	0.44	0.34	0.77
	4f	Ga1, Ga2, S1, S2, S3	1.47	1.47	1

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For comparison, we applied the same analysis to α-BaGa₄S₇ (see Tables S4–S6 and Fig. S3, S4†) and found the total distortions to be just 1.54 Å for α-BaGa₄S₇ (Table 3). It is clear that the atomic displacements in both compounds are contributed by the GaS₄ groups, and β-BaGa₄S₇ is much larger than α-BaGa₄S₇. To obtain the specific centric-mode displacements (SAMDs) and provide an unbiased measure of the amounts of polar distortion per unit volume in the two crystals, the values of SAMDs are also calculated, i.e., 2.84 × 10²¹ and 11.3 × 10²¹ Å cm⁻³ for α- and β-BaGa₄S₇ (Table 1), respectively. The values of SAMDs of β-BaGa₄S₇ are larger than α-BaGa₄S₇, which leads to a bigger SHG response in general and also correlates better with the experimental multiplicity intensity. These results suggest that the larger SHG responses of β-BaGa₄S₇ can be attributed to its larger atomic polar displacements and the easier polariability when it is radiated.

Conclusions

In summary, two new polymorphs of BaGa₄S₇, i.e., β- and γ-BaGa₄S₇, with excellent performances have been discovered and synthesized by high-temperature solution methods in sealed quartz tubes. Their phase transformations from the low-temperature phase to the high-temperature phase are systematically analyzed based on a series of solid-state reactions and the calculations of structural parameters. Furthermore, their functional properties were also measured and calculated under the same conditions. These show that all of materials are promising IR NLO materials. In particular, β-BaGa₄S₇ exhibits the best NLO properties among them, including the widest experimental band gap (3.94 eV) and the largest SHG response (1.2 × AGS) with phase-matching behavior. The study of the structure–property relationship reveals that the better NLO properties of β-BaGa₄S₇ can be attributed to the different arrangement of the GaS₄ tetrahedral structure's basic building units, which suggests that structural rearrangement is an effective strategy for optimizing and exploring new IR NLO crystals. Further research on the crystal growth of β-BaGa₄S₇ is ongoing.

Author contributions

Writing – original draft: Zhen Qian; Writing – review and editing: Haonan Liu, Yujie Zhang and Hongping Wu; Resources: Zhanggui Hu; Supervision: Jiyang Wang and Yicheng Wu; Funding acquisition and conceptualization – ideas: Hongwei Yu.

Conflicts of interest

There are no conflicts to declare.

Acknowledgements

This work is supported by the National Natural Science Foundation of China (Grant No. 52172006, 22071179, 51972230, 51890864 and 51890865) and the Natural Science Foundation of Tianjin (Grant No. 20JCJQJC00060 and 21JCJQJC00090).

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Footnote

† Electronic supplementary information (ESI) available: Atomic coordinates, equivalent isotropic displacement parameters, and the bond valence sums of each atom; selected bond distances and angles; experimental and calculated XRD patterns; elemental analysis; IR transmission; dipole moment calculations. CCDC 2132789 and 2132787. For ESI and crystallographic data in CIF or other electronic format see DOI: https://doi.org/10.1039/d2qi01263d

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