RbPbPS₄: a promising IR nonlinear optical material achieved by lone-pair-cation-substitution-induced structure transformation

Abstract

When stereochemically-active-lone-pair (SCALP) cations are introduced into chalcogenide systems, it is beneficial to produce a remarkable second-harmonic generation (SHG) response (d_eff), but it also causes a narrow band gap (E_g), which ultimately results in negative two-photon and free-carrier absorption. Hence, how to obtain a wide E_g (>2.33 eV) while maintaining a strong d_eff remains a significant challenge in this domain. In this work, Rb is partially replaced by SCALP Pb in the known ternary centrosymmetric (CS) Rb₃PS₄ (space group: Pnma). This results in a quaternary non-centrosymmetric (NCS) RbPbPS₄ (space group: P2₁2₁2₁), which possesses distinct 2D [PbPS₄]⁻ layers and Rb⁺ occupies the interlayer spaces as the counter cations. Notably, RbPbPS₄ exhibits a promising overall performance, including strong d_eff (2.5 × AgGaS₂), wide IR transmittance cutoff edge (up to 18.1 μm) along with the large E_g (2.75 eV), resulting in an improved laser-induced damage threshold (7.5 × AgGaS₂). Theoretical calculations further indicated that the favorable balance between strong d_eff and large E_g in RbPbPS₄ can be attributed to the synergies of the [PbS₇] and [PS₄] nonlinear optical (NLO)-active units. This study not only presents a high-performance Pb-based IR-NLO candidate but also underscores the effectiveness of partial substitution of SCALP cations in inducing a CS-to-NCS structural transformation.

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Introduction

Nonlinear optical (NLO) materials have garnered unprecedented attention in laser science and technology because of their ability to facilitate frequency conversion in solid-state laser devices.¹ As widely recognized, an excellent NLO candidate should meet several crucial prerequisites: a sufficient second-harmonic generation (SHG) intensity (d_eff), a large energy gap (E_g), a wide optical transparent window, a moderate birefringence (Δn), chemical stability, and availability for obtaining large single crystals.² In the infrared (IR) region, numerous vital fields, including optoelectronic instruments, resource exploration, and remote laser communication, has sparked widespread attention and interest. Despite the strong d_eff exhibited by commercial IR-NLO crystals such as AgGaQ₂ (Q = S, Se)³ and ZnGeP₂,⁴ which make them suitable for applications in the IR region, they still suffer from limitations in high-power laser systems due to their low laser-induced damage thresholds (LIDT) or detrimental two-photon absorption, primarily attributed to their small E_g. However, integrating these optical performances into a single crystal is extremely challenging because they typically depend on competing structural requirements, such as the trade-off between wide E_g and strong d_eff.⁵ Therefore, it is of scientific and technological significance to explore new IR-NLO crystals with outstanding comprehensive performance to overcome these challenges.

In addition to the performance prerequisites mentioned above, a prerequisite of an IR-NLO crystal is that it has a non-centrosymmetric (NCS) structure.⁶ The addition of stereochemically-active-lone-pair (SCALP) cations, like As³⁺, Sb³⁺, Bi³⁺, Sn²⁺, and Pb²⁺, to chalcogenide systems has attracted the most attention among all the feasible approaches for creating IR-NLO materials because the majority of these chalcogenides exhibit exceptional IR-NLO performances.⁷ Among these cations, Pb²⁺ makes a significant contribution to the d_eff but adversely affects the optical E_g.⁸ As is known, narrow energy gaps (E_g < 2.33 eV) are unable to mitigate some harmful two-photon or free-carrier absorption under fundamental 1064 nm laser sources.⁹ Therefore, achieving a wide E_g (>2.33 eV) while maintaining a strong d_eff remains a significant challenge in Pb-based IR-NLO material design. On the other hand, partial chemical substitution in view of known centrosymmetric (CS) parent structures has shown to be a straightforward but incredibly successful approach in recent years for the design and synthesis of novel high-performance SCALP-based IR-NLO crystals.¹⁰ Successful examples include NCS Ba₂As₂Se₅ (parent structure: CS Ba₂GaAsSe₅),¹¹ NCS K₂Ag₃Sb₃S₇ (parent structure: CS K₂Sb₄S₇),¹² NCS ABiP₂S₆ (A = K, Rb) (parent structure: CS A₄P₂S₆),^13,14 NCS Sn₇Br₁₀S₂ (parent structure: CS SnBr₂),¹⁵ Sr_2−xPb_xGeSe₄ (parent structure: NCS Sr₂GeSe₄),¹⁶ and NCS Pb₄SeBr₆ (parent structure: CS PbBr₂).¹⁷ Considering these factors, our focus lies in identifying suitable CS parent structures with wide E_g and achieving CS-to-NCS structural transformation by introducing SCALP Pb for partial chemical substitution. This approach aims to obtain NCS materials with excellent, well-balanced IR-NLO performance.

The ternary chalcophosphate Rb₃PS₄ has piqued our interest due to its CS space group of Pmna and unique zero-dimensional (0D) cluster structure.¹⁸ By incorporating distorted Pb-based motifs, it is possible to disrupt symmetric centers, leading to structural reconstruction and the formation of NCS compounds. Furthermore, Rb₃PS₄ boasts a sufficiently large E_g (>3.5 eV), which can help offset the potential decrease in E_g resulting from the introduction of SCALP Pb²⁺ cations into new compounds. Following this approach, we have designed and synthesized the quaternary Pb-based thiophosphate RbPbPS₄, featuring a two-dimensional (2D) layered structure composed of [PbS₇] polyhedra and [PS₄] tetrahedra. Remarkably, RbPbPS₄ demonstrates comprehensive IR-NLO performance, including a strong d_eff (3.2 times that of AgGaS₂), one of the widest E_g among Pb-based NCS chalcogenides, high LIDT (7.5 times that of AgGaS₂), a broad transmittance range (up to 18.1 μm), and suitable Δn (0.112@2050 nm). In this report, we provide detailed insights into the CS-to-NCS structural transformation and the related optical properties of RbPbPS₄. Additionally, theoretical calculations are employed to further elucidate its linear optical and NLO performances.

Results and discussion

There are reports of RbPbPS₄'s crystal structure exhibiting two distinct phases.¹⁹ However, we meticulously determined the structure of the title compound to explore the intricate relationship between its NCS crystal structure and NLO properties. Light yellow lamellar crystals of RbPbPS₄, with sizes reaching the millimeter level, were grown using a simple boron–chalcogen method.²⁰ This method differs from previously reported techniques, which often necessitate complex experimental procedures or involve the use of costly and hazardous elemental Rb as a raw material. Elemental distribution maps indicate that Rb, Pb, P, and S are uniformly distributed throughout the crystals (Fig. 1a). Furthermore, EDX results confirmed that the average molar ratios of the title compound correspond to the formula determined by single-crystal XRD analysis (Fig. S1†). Powder XRD testing validated the phase purity of the title compound, as the experimental patterns closely matched the simulated data obtained from single-crystal XRD analyses (Fig. 1b). The UV-vis diffuse reflectance spectrum of RbPbPS₄ is depicted in Fig. 1c, and absorption data were derived using the Kubelka–Munk equation.²¹ With an experimental optical E_g of 2.75 eV, RbPbPS₄ exhibits the second-highest recorded value among Pb-based IR-NLO chalcogenides. Additionally, RbPbPS₄ demonstrates broad optical transparency across the 0.38–18.1 μm range (Fig. 1d). Thermogravimetric-differential thermal analysis (TG-DTA) was employed to assess the thermal stability of RbPbPS₄, revealing that the compound remains stable below 700 K (Fig. 1e).

Fig. 1 Experimental characterization results of PbPbPS₄: (a) SEM image and corresponding elemental distribution maps; (b) experimental (black) and simulated (red) powder XRD patterns; (c) UV–vis–NIR spectrum (inset: photograph of the title crystals); (d) optical transmittance spectrum; (e) TG-DTA test curves.

In the asymmetric unit, ternary Rb₃PS₄ has two independent Rb atoms (Wyckoff positions: 4c and 8d), one independent P atom (Wyckoff position: 4c), and two independent S atoms (Wyckoff positions: 4c and 8d). The P⁵⁺ cation is located in the center of its common tetrahedron, with P–S bond lengthes ranging from 2.043 to 2.055 Å and the bond angles in the range of 108.82–111.48°. Ternary Rb₃PS₄ belongs to the orthorhombic system [space group: Pnma (no. 62)] and the crystal structure consists of counterbalanced Rb⁺ cations situated in between discrete tetrahedral [PS₄] basic building units (BBUs) aligned parallel in opposing orientations (Fig. 2a). Unfortunately, Rb₃PS₄ lacks NLO activity due to its CS crystal structure.

Fig. 2 Structure evolution from ternary CS Rb₃PS₄ to quaternary NCS RbPbPS₄: view of the 2D layered structures of (a) Rb₃PS₄ and (b) RbPbPS₄ along the ab and bc plane, respectively; (c) a polyhedral 2D layer [PbPS₄]⁻ composed of (d) 2D Pb–S layer and (e) discrete tetrahedral [PS₄] motifs; (f and g) spatial symmetry operation changing from CS Pmna (no. 62) to NCS P2₁2₁2₁ (no. 19).

Quaternary RbPbPS₄ adopts the NCS orthorhombic space group P2₁2₁2₁ (no. 19, Table S1†), according to single-crystal XRD investigation. The cell lattice possesses dimensions of a = 6.3981(2) Å, b = 6.6888(2) Å, c = 17.2823(5) Å, and V = 739.61(4) ų. These crystal parameters are in good agreement with the NCS phase that was previously published. The compound has a 2D layered structure with discrete counterbalanced Rb⁺ cations inserted in the channels that are arranged in an “ABABAB” mode perpendicular to the ab-plane (Fig. 2b and c). With seven S atoms polyhedral coordinating each Pb atom in the structure, the highly distorted [PbS₇] BBUs with Pb–S bond lengths of 2.916–3.281 Å are formed. As shown in Fig. 2d, adjacent [PbS₇] BBUs are joined by apex-sharing S atoms to generate a 2D Pb–S layer. While the P–S bonds in RbPbPS₄ range in length from 2.031 to 2.069 Å and in bond angles from 106.56 to 111.62°, each P atom is comparable to that of Rb₃PS₄ and is encircled by four S atoms, forming the deformed [PS₄] tetrahedron (Table S2†). Subsequently, apex-sharing between these 2D Pb–S layers (Fig. 2d) and distinct [PS₄] BBUs (Fig. 2e) progressively linked them, resulting in the formation of a 2D [PbPS₄]⁻ anionic layer (Fig. 2c).

Fig. 2 shows the CS-to-NCS structural evolution via partial SCALP cation substitution from ternary CS Rb₃PS₄ to quaternary NCS RbPbPS₄. From a structural perspective, the following noteworthy modifications have been made following the partial replacement of Rb by SCALP Pb. First off, the initial highly symmetric structure is broken by the addition of SCALP [PbS₇] BBUs and the reassembly of discrete [PS₄] BBUs, which convert the 0D cluster structure into a 2D layered structure. Fig. 2f and g show the detailed symmetric operation modifications that occur after the substitution of SCALP Pb²⁺ cations, resulting in the removal of all center sites and the realization of the CS-to-NCS structural evolution. In particular, space group Pnma (no. 62) converts to P2₁2₁2₁ (no. 19) from the Bärnighausen tree via a translationengleiche reduction in index 2's symmetry (Fig. 3a).²² When Pb is substituted for Rb, the atomic positions (4c and 8d) in Rb₃PS₄ become 4a in RbPbPS₄ (see Table S3† for details). To put it briefly, the novel compound that was produced, RbPbPS₄, has good structural anisotropy, which helps to get a higher Δn for achieving PM feature. Secondly, the coordination number (CN) of the two crystallographically independent Rb atoms in Rb₃PS₄ differ (CN = 8 for Rb1 and CN = 9 for Rb2), but are identical in RbPbPS₄ (CN = 11) with Rb–S bond distances less than 4.4 Å (refer to Fig. S2 and S3 in ESI†). Finally, considering the flexible CN of Pb²⁺ cations, the integrated crystal orbital Hamilton population (ICOHP) curve was examined.²³ As depicted in Fig. 3b, it is evident that the short Pb–S bond lengthes of 2.916–3.114 Å exhibit stronger bonding interactions compared to the long Pb–S bond lengthes (3.647–3.825 Å), while the Pb–S bond distance of 3.281 Å falls between them, representing a medium interaction (see Table S2† for details). Based on the above analysis, it is reasonable to infer that the Pb atom forms a [PbS₇] mono-capped triangular prism. Research on the distinct [PbS₇] coordination mode in NCS chalcogenides is notably lacking, and a seven-coordinated example of this has been reported in Pb₅Ga₆ZnS₁₅.^8d Pb²⁺ cations in NCS chalcogenides are mostly five-coordinated (as in [Na₂PbI][Ga₇S₁₂]^8f) or six-coordinated (as in Pb₄Ga₄GeS₁₂ ^8a and Pb_0.65Mn_2.85Ga₃S₈ ^8b), among other compounds that have been found.

Fig. 3 (a) Group–subgroup relations between CS Rb₃PS₄ [space group: Pmna (no. 62)] and NCS RbPbPS₄ [space group: P2₁2₁2₁ (no. 19)]; (b) crystal orbital Hamilton population (COHP) curves for the Pb–S bond length in RbPbPS₄ (the inset figure is the coordination geometry of Pb atom).

Furthermore, through comparison with known ternary and quaternary chalcophosphates, it is determined that substituting SCALP Pb for partial alkali metal Rb is the most optimal and rational structural approach to accomplish the CS-to-NCS structural transformation of template structure Rb₃PS₄. Fig. S4† provides a detailed structural evolution. Roughly speaking, these replacements fall into three categories. In the first, three Rb atoms are completely substituted by one trivalent element or three monovalent elements in the absence of SCALP components. CS structures are displayed by the resultant compounds, including REPS₄ (space group: I4₁/acd),²⁴ BPS₄ (space group: Ibam),²⁵ GaPS₄ (space group: P2₁/c),²⁶ and Tl₃PS₄ (space group: Pnma).²⁷ The second category entails complete substitution of SCALP elements, as seen in SbPS₄ (space group: P1̄)²⁸ and BiPS₄ (space group: Ibca),²⁹ which also belong to the CS structures. The third category involves partial substitution, where Rb is partially replaced by monovalent or divalent elements. The resulting compounds, such as Rb₂AgPS₄ (space group: P1̄),³⁰ RbAg₅P₂S₈ (space group: Pbca),³¹ RbSrPS₄ (space group: Pnma),³² RbBaPS₄ (space group: Pnma),³³ RbPdPS₄ (space group: I4/mcm),³⁴ and RbHgPS₄ (space group: P2₁/n),³⁵ all adopt CS structures. Therefore, it is reasonable to replace partial Rb with SCALP elements to realize a structural transition from CS Rb₃PS₄ to NCS RbPbPS₄. Hence, employing established CS chalcophosphates as the parent structure and partially substituting them with SCALP-cation groups proves to be an effective chemical strategy for accomplishing the CS-to-NCS structural evolution.

As RbPbPS₄ belongs to the NCS space group P2₁2₁2₁ and possesses the NLO-active motifs [PbS₇] and [PS₄], a relatively strong d_eff could be expected. Powder SHG testing for RbPbPS₄ was conducted using the modified Kurtz–Perry technology,³⁵ with irradiation from a 2900 nm laser and commercial material AgGaS₂ as a reference. As depicted in Fig. 4a, the positive correlation between the particle size and SHG intensity indicates that RbPbPS₄ exhibits PM behavior. The SHG intensity of RbPbPS₄ is approximately 2.5 times that of benchmark AgGaS₂ in a particle size range of 150–210 μm (Fig. 4b). Based on d_eff = d_eff,_R (I²ω/I_R²ω)^1/2 (d_eff,_R = 13.4 pm V⁻¹ for AgGaS₂), the effective SHG coefficient d_eff of RbPbPS₄ at 2900 nm is 21.2 pm V⁻¹. In addition, powder LIDT measurement was employed to preliminarily evaluate the LIDT value,³⁶ with the increased optical E_g suggesting that the title crystal would exhibit higher LIDT. As illustrated in Fig. 4b, the LIDT of RbPbPS₄ (10.88 MW cm⁻²) is estimated to be 7.5 times that of AgGaS₂ (1.45 MW cm⁻²) under the same testing conditions. Compared with other reported Pb-based IR-NLO materials (Fig. 4c and Table S4†), RbPbPS₄ demonstrates a favorable balance between strong d_eff and large E_g. Notably, RbPbPS₄ represents the first quaternary Pb-based chalcogenide to overcome the incompatibility between a wide E_g (>2.56 eV, the E_g of AgGaS₂) and a sufficient d_eff (>1.0 × AgGaS₂). This balance IR-NLO performance can be compared to the recently reported quaternary NCS chalcogenides, such as α-Li₂ZnGeS₄,³⁷ Li₄CdSn₂S₇,³⁸ NaMg₃Ga₃S₈,³⁹ and (CuI)₃P₄S₄.⁴⁰

Fig. 4 (a) SHG intensities vs. particle size at λ = 2900 nm for PbPbPS₄ and AgGaS₂; (b) the relative SHG and LIDT intensities of PbPbPS₄ and reference commercial material AgGaS₂ in the particle size of 150–210 μm; (c) comparison of d_eff (×AgGaS₂) and E_g (eV) of reported Pb-based IR-NLO chalcogenides.

To gain further insights into the underlying structure–property relationship of the title compound, systematic theoretical calculations were conducted, encompassing band structure, densities of states (DOSs), and linear optical and NLO parameters, based on DFT. The calculated electronic band structure reveals a direct E_g of 2.27 eV for RbPbPS₄, as the valence band maximum (VBM) and conduction band minimum (CBM) coincide at the same high-symmetry k-points (Fig. 5a). The smaller calculated E_g can be attributed to underestimation by the DFT calculation.⁴¹ The partial DOSs of RbPbPS₄ are depicted in Fig. 5b, indicating that the tops of the VBs are predominantly composed of S-3p states, with a minor contribution from Pb-5s and P-3p states, while the bottoms of the CBs primarily consist of S-3p, Pb-5p, P-3s/3p, and Rb-5p states. Furthermore, the NLO coefficients of RbPbPS₄ can be calculated according to the electronic structure. In the light of Kleinman symmetry,⁴² RbPbPS₄ exhibits only one nonzero independent SHG coefficient, d₁₄ = 31.8 pm V⁻¹ at 2900 nm (ca. 0.43 eV) (Fig. 5c). Furthermore, the calculated d_eff of RbPbPS₄ is 26.88 pm V⁻¹, under 2900 nm irradiation,³⁵ which essentially coincides with the experimental findings. Additionally, the calculated Δn value of RbPbPS₄ is 0.109 at 2900 nm, significantly surpassing that of AgGaS₂ (Δn ∼ 0.04).⁴³ This suggests that RbPbPS₄ may be well-suited to achieve the PM condition for the SHG process. Furthermore, the line refractive dispersion diagrams indicate that the shortest type-I phase-matched output wavelength is 602 nm (Fig. 5d).⁴⁴

Fig. 5 Theoretical results of electronic structures and optical parameters of PbPbPS₄: (a) band structure; (b) partial density of states; (c) calculated nonzero independent SHG coefficient d₁₄ (pm V⁻¹) and calculated birefringence (Δn); (d) calculated refractive index dispersion curves with the shortest type-I PM cut-off wavelength.

To visually illustrate the contribution of the constituent BBUs to the SHG effect, the cutoff energy dependence of the static d₁₄ for RbPbPS₄ is calculated using a length-gauge formalism method.⁴⁵ As depicted in Fig. 6a, the d₁₄ values exhibit an upward trend in the VB-1, VB-3, CB-1, CB-3, and CB-5 intervals. This illustrates that the orbitals in these regions have a significant influence on the overall NLO response.⁴⁶ Moreover, by integrating the partial DOSs (Fig. 5b) with the relevant partial charge density maps (Fig. 6b), it is evident that the enhancement of the d_eff in RbPbPS₄ primarily stems from the strong hybridization of electron states at the top of the VBs and the substantial distortion of [PbS₇] and [PS₄] groups, indicative of the 2D [PbPS₄]⁻ alternating arrangement layer.

Fig. 6 Theoretical analysis of the intrinsic mechanism of SHG source for PbPbPS₄: (a) cut-off energy (eV) dependence of the static d₁₄ (pm V⁻¹); (b) distribution of the partial charge density maps with major contributions in the VB-1, VB-3, CB-1, CB-3 and CB-5 regions. Black atoms: Rb; blue atoms: Pb; pink atoms: P; yellow atoms: S.

Conclusions

In summary, building upon the parent ternary CS compound Rb₃PS₄, we implemented a strategy involving the partial substitution of Rb with SCALP Pb, resulting in the creation of a new quaternary NCS chalcophosphate, RbPbPS₄. This substitution also triggered a structural transformation from 0D clusters to 2D layers. As anticipated, experimental findings highlight RbPbPS₄ as a promising candidate for IR-NLO applications, boasting a large d_eff (2.5 × AgGaS₂ at 2900 nm), a broad transmittance cutoff window (0.38–18.1 μm), and a significant E_g (2.75 eV) conducive to a high LIDT (7.5 × AgGaS₂ at 1064 nm). Detailed structure–property analyses elucidate that the strong calculated d_eff (26.88 pm V⁻¹@2900 nm) and large calculated birefringence (0.109@2900 nm) in RbPbPS₄ primarily stem from the cooperative effects of [PbS₇] and [PS₄] NLO-active motifs. These findings underscore the efficacy of the lone-pair-cation substitution strategy in achieving both structural transformation and effectively balancing strong d_eff with a large E_g in SCALP-based chalcogenides.

Author contributions

A-Yang Wang: investigation, formal analysis, writing – original draft. Sheng-Hua Zhou: investigation, methodology, validation. Mao-Yin Ran: investigation, formal analysis, validation. Bingxuan Li: formal analysis, validation. Xin-Tao Wu: conceptualization, writing – review & editing. Hua Lin: supervision, conceptualization, writing – review & editing. Qi-Long Zhu: supervision, writing – review & editing.

Conflicts of interest

There are no conflicts to declare.

Acknowledgements

This work was supported by the National Natural Science Foundation of China (22175175), Natural Science Foundation of Fujian Province (2022L3092 and 2023H0041), Fujian Science & Technology Innovation Laboratory for Optoelectronic Information of China (2021ZR118), and the Youth Innovation Promotion Association CAS (2022303). The authors thank Prof. Yong-Fan Zhang at Fuzhou University for helping with the DFT calculations.

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Footnotes

† Electronic supplementary information (ESI) available: Additional experimental and theory results, together with additional tables and figures. CCDC 2347371. For ESI and crystallographic data in CIF or other electronic format see DOI: https://doi.org/10.1039/d4qi01040j

‡ A. Y. Wang and S. H. Zhou contributed equally to this work.

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