β-BaGa₄Se₇: a promising IR nonlinear optical crystal designed by predictable structural rearrangement

Abstract

Rationally designing new inorganic materials with specific functional properties is a fascinating challenge. This is particularly true with the nonlinear optical (NLO) crystals, which can expand the spectral ranges of solid-state lasers from ultraviolet (UV) to infrared (IR) through a second harmonic generation (SHG) or optical parametric oscillation (OPO) process. Herein, a high-performance IR NLO crystal, β-BaGa₄Se₇, has been successfully predicted and synthesized by the optimal rearrangement of the NLO-active basic structure units. The stability and functional properties of the material were simulated by first-principles calculations, and eventually it was also successfully synthesized via a high-temperature solid-state reaction in a sealed silica tube. More importantly, this material can exhibit exceedingly excellent NLO properties, including strong SHG response (5 × AgGaS₂), wide transmission range (0.44–20 μm) and high laser damage threshold (680 MW cm⁻², 20 × AgGaS₂), as well as stable physicochemical properties. These indicate that β-BaGa₄Se₇ is a promising IR NLO crystal. The discovery of β-BaGa₄Se₇ can also provide new insights into the rational design of IR NLO crystals based on the predictable structural rearrangement.

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Mid-infrared (mid-IR, 3 μm < λ < 20 μm) coherent radiation covering the atmospheric windows of 3–5 μm and 8–12 μm is urgently desired by a variety of important scientific and industrial applications, such as remote chemical sensing, free-space communication and high-resolution molecular fingerprint-region spectroscopy.^1–9 Relying on the frequency down-conversion of nonlinear optical (NLO) crystals, including difference-frequency generation (DFG), optical parametric oscillation (OPO) and optical parametric amplification (OPA), is the most effective way for solid-state lasers to achieve high-power output of the mid-IR coherent radiations.¹⁰ The developments of the above technologies strongly depend on the discoveries of high-performance IR NLO crystals. Currently, although a series of commercialized NLO crystals, such as β-BaB₂O₄ (β-BBO), LiB₃O₅ (LBO) and CsLiB₆O₁₀ (CLBO) as well as KTiOPO₄ (KTP) and LiNbO₃ (LN), have been used in the UV and visible (vis) regions,^11–14 the available NLO crystals in the IR region are still suffering from some intrinsic drawbacks, e.g. the low laser damaged threshold (LDT) of AgGaS₂ (AGS) and AgGaSe₂ (AGSe) (<30 MW cm⁻²) and the harmful two-photon absorption (TPA) of ZnGeP₂ (ZGP), which hamper their further practical applications under high power conditions.^15–17 As such, exploring new high-performance IR NLO crystals with large SHG coefficients (>0.5 × AGS), wide IR transmission window (3–12 μm) and high LDT (>1 × AGS or more than 30 MW cm⁻² for 10 ns pulse laser) that usually corresponds to a large energy band gap are urgently needed.^18–21

It is well known that the functional properties of a material are mainly determined by its structure, which involves not only the composition of materials, i.e. the types of the basic building units (BBUs), but also the arrangement of the BBUs.^22,23 In particular, the arrangement of the BBUs often has a critical effect on the properties of materials. A typical example is the polymorphism of BBO crystals (an α-phase with the group space of R3̄c vs. β-phase with R3). Although both phases have the same BBUs of [B₃O₆]³⁻ groups, they exhibit very different functional properties owing to the different BBU arrangements.^10,24 α-BBO is composed of oppositely aligned [B₃O₆]³⁻ groups and does not have an SHG response but exhibits a quite large birefringence, so it has been widely used as an excellent birefringent crystal. For β-BBO the parallel arranged [B₃O₆]³⁻ groups result in a large SHG response, and thus this crystal has been widely used in the frequency conversion of UV coherent light. Therefore, the optimization of the spatial arrangement of BBUs would be significant for the design of a high-performance NLO crystal.

The metal chalcogenides are often chosen as the IR NLO candidates because they can exhibit a wide IR transmission region and large SHG responses, originating from their weaker interatomic bonds and stronger polarizability of chalcogen atoms than oxygen.^25–28 The reported metal chalcogenides with excellent NLO properties consist of BaGa₄Q₇ (Q = S, Se),^29,30 BaGa₂GeQ₆ (Q = S, Se),^31,32 LiGaQ₂ (Q = S, Se),³³ Na₂BaMQ₄ (M = Ge, Sn; Q = S, Se),²⁴ Li₂Ga₂GeQ₆ (Q = S, Se),^34,35 Ba₃AGa₅Se₁₀Cl₂ (A = Cs, Rb, K),³⁶ and [A₃X][Ga₃PS₈] (A = K, Rb; X = Cl, Br).³⁷ Among them, BaGa₄Se₇ has caught particular attention owing to its outstanding comprehensive performances, including strong SHG response (2–3 × AGS),³⁰ wide transparency range (0.47–18 μm) and high LDT (557 MW cm⁻²).³⁸ Based on the OPO technique, the BaGa₄Se₇ crystal has achieved the output of IR coherent radiation at the wavelengths of 3–17 μm with a high conversion efficiency.³⁹ It should be noted, however, that BaGa₄Se₇ crystallizes in a low symmetric monoclinic space group Pc (named as α-BaGa₄Se₇ phase) resulting from the arrangement of the [GaSe₄] BBUs, which makes the properties’ measurements and applications difficult because the optical axes, crystallographic axes and dielectric axes do not coincide with each other.^40,41

Analyzing the crystal structure of α-BaGa₄Se₇, one may find that its structure is composed of [GaSe₄] tetrahedra (Fig. 1a and b). Clearly, the [GaSe₄] BBUs connect with one another in the a–b plane to form [Ga₃Se₁₀]_∞ layers (Fig. 1b), which stack along the c-axis and are linked together with Ga(2)Se₄ tetrahedra through sharing the Se(1), Se(2) and Se(3), as shown in Fig. 1a. The arrangement of BBUs produces the [Ga₄Se₁₁] C₂-type supertetrahedra structures with a C_3v local symmetry in α-BaGa₄Se₇ (see the red dashed boxes in the upper left corner in Fig. 1a and the left side in Fig. 1b). By analyzing the packing pattern of the [Ga₃Se₁₀]_∞ layers, we propose that actually there is another layer-to-layer connection manner, i.e., the adjacent [Ga₃Se₁₀]_∞ layers can be shifted by 1/2 cell parameter along the b-axis with respect to each other and linked by sharing Se(1), Se(2)′ and Se(3) atoms (see the blue dashed box at the right side in Fig. 1b), rather than by sharing the Se(1), Se(2) and Se(3) atoms. The newly constructed structure is shown in Fig. 1c. More importantly, in this structure the [GaSe₄] BBUs are arranged to form supertetrahedral [Ga₄Se₁₀] groups (see the blue dashes boxes in the upper right corner in Fig. 1c). Clearly, compared with [Ga₄Se₁₁] C₂-type supertetrahedra, [Ga₄Se₁₀] supertetrahedra have a higher symmetric T_d local symmetry, which would be beneficial for the structure to crystallize in the higher symmetric space group. Moreover, the supertetrahedral configuration is favorable for generating large SHG effects and band gaps due to the balanced structural feature.²³

Fig. 1 The layer structure of α-BaGa₄Se₇ and the predictable structural rearrangement: (a) the structure of α-BaGa₄Se₇ was composed by the [Ga₃Se₁₀]_∞ layer bridged Ga(2)Se₄ through sharing Se(1), Se(2) and Se(3) atoms to form the [Ga₄Se₁₁] C₂-type supertetrahedra; (b) beyond sharing Se(1), Se(2) and Se(3) atoms in the red dashed box, the adjacent [Ga₃Se₁₀]_∞ layers can also be linked by sharing Se(1), Se(2)′ and Se(3) atoms in the blue dashed box; (c) the [Ga₄Se₁₀] T₂-type supertetrahedra composed by the [Ga₃Se₁₀]_∞ layers bridged Ga(2)Se₄ through sharing Se(1), Se(2)′ and Se(3) atoms.

By adopting the supertetrahedral [Ga₄Se₁₀] groups, we theoretically constructed a new structure of BaGa₄Se₇, and the constructed structure was relaxed by first-principles geometry optimizations, which generates a new phase, i.e. β-BaGa₄Se₇, with a higher symmetric structure, Pna2₁. The first-principles phonon vibration calculation demonstrates that there is no presence of an imaginary phonon mode in the whole Brillouin zone (Fig. S1, ESI†), indicating the dynamic stability of this designed structure. The total energy calculations reveal that the total energy of β-BaGa₄Se₇ is very close to that of α-BaGa₄Se₇, with an energy difference of only ∼3 meV/atom. Both calculated results strongly suggest that the designed β-BaGa₄Se₇ would truly exist. The further calculations show that the three independent nonzero SHG coefficients d₃₁, d₃₂ and d₃₃ in β-BaGa₄Se₇ are 37.91, −35.78 and 8.35 pm V⁻¹,^42,43 respectively, which are larger than d₃₆ (12.6 pm V⁻¹) of AGS and d₁₁ (24.3 pm V⁻¹) of α-BaGa₄Se₇.⁴⁰ The first-principles calculations have proven to be one of the most accurate methods for the computation of the electronic structure of solids.^44–46 This means that β-BaGa₄Se₇ would be a promising IR NLO crystal if it could be obtained in experiments.

In order to synthesize the designed β-BaGa₄Se₇ phase in experiments, a series of solid-state reactions with different calcination temperatures were performed in a sealing silica tube. After many attempts, it is very exciting that the β-BaGa₄Se₇ phase was successfully obtained when the calcination temperature is lower than 900 °C (Fig. S2, ESI†). When the calcination temperature is higher than 900 °C, β-BaGa₄Se₇ starts to transfer into α-BaGa₄Se₇ (Fig. S3, ESI†). These show that the β-BaGa₄Se₇ is a low-temperature phase. However, in contrast, the phase-transition from α-BaGa₄Se₇ to β-BaGa₄Se₇ did not occur when α-BaGa₄Se₇ was calcined at 850 °C for 72 h (Fig. S4, ESI†). This suggests that the phase-transition from β-BaGa₄Se₇ to α-BaGa₄Se₇ is irreversible. In addition, when β-BaGa₄Se₇ was soaked in water for one week, no obvious weight loss was observed and its powder X-ray diffraction pattern is also in good agreement with that before soaking. These results indicate that β-BaGa₄Se₇ has good thermal and environmental stabilities.

With Ga₂Se₃–Se as the flux, the millimeter-sized single crystals of β-BaGa₄Se₇ can also be successfully grown and used for single-crystal X-ray diffraction. This shows that β-BaGa₄Se₇ indeed crystallizes in the higher symmetric space group, Pna2₁, exactly the same as predicted. The crystal structure of β-BaGa₄Se₇ is shown in Fig. 2. In the asymmetric unit, there is one unique Ba, four unique Ga, and seven unique Se atom(s). The [GaSe₄] tetrahedra are connected to each other by corner-sharing to form a 3D framework with the Ba filled in the space to balance the residual changes (Fig. 2a). Thus, all the Ga atoms are four-coordinated with the Ga–Se bonds ranging from 2.356(2) to 2.500(2) Å, and the Ba atoms are eight-coordinated with the Ba–Se bonds ranging from 3.4893(17) to 3.7742(18) Å (Fig. 2b). The calculation results of the bond valence sums (BVSs) of each atom are Ba: 1.73, Ga: 3.04–3.13, Se: 1.91–2.21, which are all consistent with the results in other compounds, indicating that the structure of β-BaGa₄Se₇ is reasonable. In addition, as predicted above, the [GaSe₄] tetrahedra in β-BaGa₄Se₇ are interconnected to form the [Ga₄Se₁₀] T2-type supertetrahedral configuration (Fig. 2c). The [Ga₄Se₁₀] supertetrahedra may also be interesting for the catalyst material.⁴⁷

Fig. 2 The structure of the title compound. (a) Ball-and-stick diagram of the β-BaGa₄Se₇ three dimensional (3D) network structure; (b) [BaSe₈] and [GaSe₄] polyhedra; (c) [Ga₄Se₁₀] T₂-type supertetrahedral configuration.

The UV-vis-NIR spectrum in the range from 300 to 2500 nm for β-BaGa₄Se₇ is shown in Fig. S5 (ESI†). The cut-off edge of β-BaGa₄Se₇ is about 440 nm. Correspondingly, its band-gap can be calculated as 2.82 eV, which is larger than commercialized AGS (2.70 eV), AGSe (1.83 eV) and ZGP (1.75 eV). The relatively large band-gap is generally helpful for generating a large LDT. Furthermore, we also measured the LDT of β-BaGa₄Se₇ on a powder sample with AGS and α-BaGa₄Se₇ as a reference by a 1.064 μm pulse laser. The results show that β-BaGa₄Se₇ has a high LDT, ∼680 MW cm⁻², which is ∼20 × AGS and is comparable with α-BaGa₄Se₇ (557 MW cm⁻²).

The IR spectrum of β-BaGa₄Se₇ is shown in Fig. S6 (ESI†). It shows that β-BaGa₄Se₇ has no absorption in a wide range from 4000 to 500 cm⁻¹ (i.e. 2.5–20 μm), implying that β-BaGa₄Se₇ may have a wide IR transmission region and covering two important atmospheric windows, 3–5 and 8–14 μm. Furthermore, the Raman spectrum of β-BaGa₄Se₇ was measured (Fig. S7, ESI†). The absorption between 180 and 240 cm⁻¹ can be assigned to the characteristic vibration of the Ga–Se mode, and other Raman peaks below 180 cm⁻¹ are due to the Ba–Se vibrations. These are consistent with those of other related chalcogenides, such as Ba₄CuGa₅Se₁₂ and Na₆Zn₃Ga₂Se₉.^48,49

The birefringence is also important for the application of NLO crystals. So the birefringence of β-BaGa₄Se₇ was measured by a cross-polarizing microscope.⁵⁰ The observed interference colors in cross-polarized light were first-order yellow for β-BaGa₄Se₇ (Fig. S8a, ESI†). On the basis of the Michel-Levy chart, the retardation (R values) is 350 nm.⁵¹ And the crystal thickness was measured as 7.8 μm (Fig. S8b, ESI†). Thus, the birefringence in the visible region can be calculated as 0.040 for β-BaGa₄Se₇, which is consistent with our calculated values (0.057–0.031@500–2000 nm) (Fig. S9, ESI†). This birefringence is also comparable with AGS, and ZGP. Additionally, we also calculated the phase matching (PM) wavelength ranges of β-BaGa₄Se₇ in the IR wavelength based on the calculated birefringence and added the results to Fig. S10 (ESI†). The results show that β-BaGa₄Se₇ is able to achieve PM in the whole Mid-IR wavelengths and cover two important atmospheric windows, 3–5 μm and 8–12 μm.

The powder SHG response of β-BaGa₄Se₇ was studied through the Kurtz and Perry method with 2.09 μm radiation.⁵² The data reveal that β-BaGa₄Se₇ can achieve type I PM (Fig. 3a), and the SHG response is around 5 × AGS (Fig. 3b). These results are in very good consistency with our first-principles calculations. The large SHG response of β-BaGa₄Se₇ will be favorable for generating high conversion efficiency in applications. In order to better understand the origin of the large SHG response in β-BaGa₄Se₇, the dipole moments of the [GaSe₄] polyhedra were calculated based on the bond valence method.⁵³ As listed in Table S4 (ESI†), the average dipole moments of the [GaSe₄] polyhedra in α- and β-BaGa₄Se₇ are 9.60 and 16.99 D respectively, thus the [GaSe₄] polyhedra in β-BaGa₄Se₇ exhibit stronger distortion. Additionally, the Ga–Se bond lengths, polarization directions and dipole moments in the [GaSe₄] polyhedra of the two compounds are also given in Fig. S11 (ESI†). Clearly, the range of dipole moments for [GaSe₄] polyhedra in β-BaGa₄Se₇ is from 5.02 D to 27.95 D, which is larger than that for [GaSe₄] polyhedra in α-BaGa₄Se₇, 6.82 D to 12.58 D. That indicates that the larger SHG response of polarity of β-BaGa₄Se₇ may be attributed to the larger distortion of the [GaSe₄] polyhedra in the structure. Furthermore, the dipole moments of α- and β-BaGa₄Se₇ in a unit cell are 15.64 and 45.07 D, respectively. This indicates that β-BaGa₄Se₇ can exhibit stronger polarity in the unit cell than that of α-BaGa₄Se₇. Generally, for the polar materials, a larger net dipole moment in the unit cell often means a larger SHG response,^54–56 and the SHG signal of β-BaGa₄Se₇ is around 1.5 times that of α-BaGa₄Se₇ under the same conditions (Fig. S12, ESI†). Therefore, the larger SHG response of β-BaGa₄Se₇ is attributed to its stronger structural polarity.

Fig. 3 (a) Phase-matching curves for AGS and β-BaGa₄Se₇ at 2090 nm, the solid curves are a guide for the eyes and not a fit to the data. (b) The SHG signals for β-BaGa₄Se₇ and AGS in the same particle sizes; β-BaGa₄Se₇ exhibits a strong SHG response of 5 × AGS.

Comparing β-BaGa₄Se₇ with the commercialized IR NLO crystals (Table 1), one can find that β-BaGa₄Se₇ exhibits excellent NLO properties and would be a promising IR NLO crystal. Firstly, β-BaGa₄Se₇ possesses a comparably large SHG response, suitable birefringence, and a wide IR transmission range compared with the commercialized AGS, AGSe and ZGP. These will enable the high laser conversion efficiency of β-BaGa₄Se₇ in applications. More importantly, β-BaGa₄Se₇ has a larger band gap than AGS, AGSe and ZGP, which results in its larger LDT (680 MW cm⁻², 20 times higher than that of AGS). Therefore, β-BaGa₄Se₇ is suitable for high-power applications, which are often limited for AGS, AGSe and ZGP. In addition, just like AGS, AGSe and ZGP, β-BaGa₄Se₇ also crystallizes in the higher symmetric space group of Pna2₁ than the monoclinic Pc of α-BaGa₄Se₇. This will also be favorable for its processing and practical applications.

Table 1 The structure and properties’ comparison of β-BaGa₄Se₇ with the commercial IR NLO crystals (sorted by SHG)

Crystal	Space group	Power SHG	d ij (pm V^−1)	Trans. rang (μm)	E g (eV)	Δn	LDT (MW cm^−2)	Ref.
a Measured SHG coefficients. b Calculated SHG coefficients. c Estimated from powder SHG data. d Powder test under the same conditions.
AgGaS2	I4̄2d	1 × AGS^a	d 36 = 12.6^a	0.47–13	2.73	0.039	34	57
AgGaSe2	I4̄2d	3 × AGS^a	d 36 = 39.5^a	0.76–18	1.83 (TPA)	0.02	13	58
β-BaGa4Se7	Pna21	5 × AGS^c	d 36 = 37.97^b	0.44–20	2.82	0.04	680^d	This work
ZnGeP2	I4̄2d	6 × AGS^a	d 36 = 75^a	0.7–13	2.00 (TPA)	0.04	55.6	59

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Clearly, the excellent NLO properties of β-BaGa₄Se₇ are related to its T2-type [Ga₄Se₁₀] supertetrahedra in the structure. Generally, the Tn-type supertetrahedra are often observed in organic–inorganic hybrid materials, and they have achieved many interesting photochemical and electrochemical functional properties in organic–inorganic hybrid materials.^60,61 But for inorganic chalcogenides, the Tn-type supertetrahedra are still rare. Only several compounds are reported to contain the T2-type supertetrahedra, such as Ba₆Zn₇Ga₂S₁₆,⁶² Pb₆ZnGa₅S₁₅⁶³ and the halide-containing chalcogenides Ba₃AGa₅Se₁₀Cl₂ (A = K, Rb, Cs),³⁶ Ba₄MGa₄Se₁₀Cl₂ (M = Zn, Cd, Mn, Cu/Ga, Co, Fe)⁶⁴ and [A₃X][Ga₃PS₈](A = K, Rb; X = Cl, Br).³⁷ Remarkably, most of these materials exhibit excellent NLO properties. This indicates that the Tn-type supertetrahedra can be seen as an ideal structural gene for the design of new IR NLO crystals. The structural and property superiorities of Tn-type supertetrahedra are proved in β-BaGa₄Se₇. Structurally, the Tn-type supertetrahedra have the same local symmetry as the simple tetrahedra. Considering Tn-type supertetrahedra as four-connected nets, the Tn-type chalcogenides can exhibit a similar structural topology to the simple tetrahedral chalcogenides. For example, considering T2-type [Ga₄Se₁₀] supertetrahedra as the four-connected nets, we can find that β-BaGa₄Se₇ exhibits a similar structural topology to that of AGSe (Fig. S13, ESI†). As for properties, the Tn-type supertetrahedra can also make the structure possess a higher tetrahedral packing number in the unit cell, and larger “flexibility index” in β-BaGa₄Se₇ (Table S5, ESI†), which is generally helpful for materials to exhibit large SHG responses and birefringence, just as we have observed in β-BaGa₄Se₇.

Conclusions

In conclusion, a new polymorph of BaGa₄Se₇, β-BaGa₄Se₇ has been successfully predicted and synthesized. It features a typical supertetrahedral configuration. More importantly, it exhibits a large SHG response (5 × AGS), a wide IR transmission region (2.5–20 μm), a wide band gap (2.82 eV) and high LDT (680 MW cm⁻²) as well as moderate birefringence (∼0.04@visible region). Comparing these properties of β-BaGa₄Se₇ with some other excellent IR NLO crystals (Table 1), one can conclude that β-BaGa₄Se₇ will also be an excellent candidate for IR NLO crystals. In addition, this work will provide an effective strategy for exploring new NLO crystals through predictable structural rearrangement. Further research on the crystal growth of β-BaGa₄Se₇ is ongoing.

Author contributions

Z. Q. performed the experiments, data analysis, and paper writing. Q. B. developed the theoretical calculations. H. W. designed and supervised the experiments. H. Y. and Z. L. provided major revisions of the manuscript. Z. H. supervised the optical experiments. J. W. and Y. W. helped with the analyses of the crystallization process and the data. All the authors discussed the results and commented on the manuscript.

Conflicts of interest

There are no conflicts to declare.

Acknowledgements

This work was supported by the National Natural Science Foundation of China (Grant No. 51802217, 51972230, 61835014, 51890864, and 51890865), the Natural Science Foundation of Tianjin (19JCZDJC38200), the National Key R&D Program (Grant No. 2016YFB0402103) and Tianjin Science and technology plan Program (Grant No. 19ZYPTJC00070).

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Footnote

† Electronic supplementary information (ESI) available. CCDC 2048470. For ESI and crystallographic data in CIF or other electronic format see DOI: 10.1039/d1tc05436h

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