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Phase transition engineering to break the symmetry of diamond-like chalcogenide for second-order nonlinear optics†

Chunlan Tang^ab, Aoge Yao^c, Wenhao Xing^d, Wenwen Jiang^b, Jian Tang^b, Lei Kang^c, Jieyun Wu*^a, Wenlong Yin*^b and Bin Kang^b
aSchool of Optoelectronic Science and Engineering, University of Electronic Science and Technology of China, Chengdu 611731, P.R. China. E-mail: jieyunwu@uestc.edu.cn
^bInstitute of Chemical Materials, China Academy of Engineering Physics, Mianyang 621900, P.R. China. E-mail: wlyin@caep.cn
^cBeijing Center for Crystal Research and Development, Key Laboratory of Functional Crystals and Laser Technology, Technical Institute of Physics and Chemistry, Chinese Academy of Sciences, Beijing 100190, P.R. China
^dSchool of Mechanical and Electrical Engineering, Henan Institute of Science and Technology, Xinxiang 453003, P. R. China

First published on 9th June 2025

Introduction

The design of IR NLO crystals with outstanding NLO performance hinges on achieving a noncentrosymmetric (NCS) crystal structure, an essential yet highly challenging prerequisite.^11–15 Molecular engineering strategies, which focus on the selection of functional motifs and spatial optimization of NLO-active chromophores, have been extensively employed to develop novel NCS crystals. Traditional approaches for constructing NCS structures often rely on the partial substitution of elements or functional motifs within the CS structure^16–20 (e.g., CS: RbGaS₂ to NCS: [ABa₂Cl][Ga₄S₈] (A = Rb, Cs);²¹ CS: Rb₄P₂S₆ to NCS: RbBiP₂S₆;²² CS: ZnS to NCS: M[M₄Cl][Ga₁₁S₂₀](M = A/Ba, A = K, Rb)).²³ However, these methods frequently introduce structural and functional complexity that hinders the simultaneous optimization of the band gap and NLO properties. Notably, strong second-harmonic generation (SHG) effect is often accompanied by a narrowing of the band gap, presenting a fundamental challenge in material design.

Overcoming this limitation requires innovative strategies to break centrosymmetry while maintaining a wide band gap. One of the promising approaches is phase transition engineering, which enables the formation of NCS structures through gradual structural modifications driven by high energy barriers. This method stabilizes metastable phases and generates diverse coordination environments for structural ligands under external stimuli such as temperature, pressure, or atmospheric changes.^24,25 By leveraging phase transitions rather than chemical substitution, this strategy provides a more straightforward and controllable route to designing NCS materials.

Phase transitions can be classified as reversible and irreversible. Reversible phase transitions are predominantly explored in organic material systems, where they enable cyclic regulation of NLO switching function.^26,27 In contrast, inorganic compounds tend to undergo irreversible phase transitions due to their high thermodynamic stability (ΔG < 0) and significant phase transition barrier (>2 eV).^28,29 Such irreversible transitions offer key advantages: they not only facilitate the growth of large-size single crystals via the Bridgman–Stockbarger method, but also enhance the structural and optoelectronic stability of devices under extreme operating conditions, such as temperature fluctuations, mechanical stress, and radiation environment.

In chalcogenides, even minor rearrangements of the tetrahedral ligands in diamond-like (DL) structures can induce phase transitions, leading to significant modification in crystal structures. For instance, Cu₂ZnSiS₄ undergoes a transition between the α-phase (Pmn2₁) and the β-phase (Pn),³⁰ and Ga₂Se₃ exhibits multiple transitions (α: F3m; β: Cc; γ: F3m; σ: C222₁).³¹ Additionally, Ag⁺ cations, possessing a d¹⁰ closed-shell configuration, can couple filled d orbitals and empty s orbitals of similar energy due to the second-order Jahn–Teller (SOJT) effect, lowering the energy barriers, which is easily overwhelmed by thermal perturbations.^32–34

Building upon those insights, we propose a high-temperature-induced irreversible phase transition strategy to construct an NCS chalcogenide based on the ternary Ag/P/S system. This approach successfully led to the transformation of CS α-Ag₄P₂S₇ into a novel NCS phase, β-Ag₄P₂S₇, both of which adopt DL structures. The synthesis, crystal structures, phase transitions, NLO properties, and structure–property relationship were systematically investigated. The resulting β-Ag₄P₂S₇ exhibits a strong and phase-matching SHG response (1.02 × AgGaS₂), a wide band gap (2.9 eV), large birefringence (Δn = 0.045), and excellent thermal/chemical stability. Moreover, the ternary Ag/P/S system offers significant advantages over quaternary or quinary systems, particularly in terms of large-scale crystal growth. Its relatively simple composition facilitates better control over crystallization processes, making it a highly attractive platform for developing next-generation IR NLO materials.

Results and discussion

	Fig. 1 (a) 2D [Ag2PS4]4− layer in α-Ag4P2S7; (b) crystal structure along the b-axis of α-Ag4P2S7.

The thermal behavior of α-Ag₄P₂S₇ was studied by differential scanning calorimetry (DSC) measurements (Fig. 2a). It showed three absorption peaks at 421 °C, 463 °C, and 558 °C, and only one exothermic peak at 490 °C during the entire heating and cooling process. In addition, to gain a comprehensive insight into the relationship between the phase transitions and temperatures, a series of solid-state reactions at different calcination temperatures was performed in sealed silica tubes (Fig. 2b) based on the DSC results. For α-Ag₄P₂S₇, it is stable until 420 °C. Phase transition begins at 420 °C. The β-phase content increases progressively between 420–570 °C. Notably, Ag₇P₃S₁₁ emerges as a byproduct through peritectic reaction with the melt (Fig. S2†).³⁹ When the temperature exceeds 570 °C, a pure phase of β-Ag₄P₂S₇ is obtained. When the temperature begins to decrease, the β-Ag₄P₂S₇ fails to transform into the α-Ag₄P₂S₇, indicating the irreversible phase transition. Once the irreversible phase transition occurs, the system will move towards more stable thermal properties, leading to a decrease in the free energy, implying that the new phase β-Ag₄P₂S₇ is resistant to thermal perturbations and can maintain the stability of the phases and properties over a certain temperature range. In addition, irreversible phase transitions may lead to significant changes in the energy band structure of the material, such as an increase or decrease in the band gap. It is therefore necessary to probe the band gap of α-Ag₄P₂S₇, which has an absorption edge at 430 nm (Fig. S3†) and a band gap of about 2.65 eV (Fig. 2c), which fits well with the yellow color of the crystals.

	Fig. 2 (a) DSC curve of the α-Ag4P2S7; (b) the variable-temperature powder X-ray diffraction patterns of the Ag4P2S7; (c) Eg of α-Ag4P2S7.

Single-crystal XRD analysis indicates that β-Ag₄P₂S₇ crystallizes in the trigonal chiral space group P3₂21 (no. 154) (cell parameters: a = b = 6.3563(5), c = 23.3477(18) Å and Z = 3). The energy-dispersive spectroscopy (EDS) measurement corroborated the homogenous distribution of Ag/P/S with an approximate molar ratio of 4:2:7 (Fig. S4†). Its asymmetric unit also consists of two crystallographically independent Ag atoms, one P atom, and four S atoms, all at the Wyckoff position 6c except S2 at 3a (Table S4†). It is found that the structure of β-Ag₄P₂S₇ is composed of the typical [Ag1S₄]⁷⁻ tetrahedra with d(Ag–S) = 2.51(3)–2.882(3) Å, [Ag2S₄]⁷⁻ tetrahedra with d(Ag–S) = 2.526(3)–2.812(3) Å, and the [PS₄]³⁻ tetrahedra with d(P–S) = 1.996(3)–2.123 (3) Å (Table S5 and Fig. S1†), which are in accordance with those of related compounds.^36–38 The crystal structure of β-Ag₄P₂S₇ is shown in Fig. 3b and can be regarded as 3D anionic networks consisting of 2D [Ag2PS₄]²⁻ layers and [Ag1S₄]⁷⁻ tetrahedra, which are interconnected by sharing S atoms. Similar to α-Ag₄P₂S₇, the [Ag2PS₄]²⁻ layers of β-Ag₄P₂S₇ are bridged by 1D [Ag2S₃]⁵⁻ chains of [Ag2S₄]⁷⁻ tetrahedra linked by corner-sharing and isolated [P₂S₇]⁴⁻dimers constructed from two [PS₄]³⁻ tetrahedra via corner-sharing (Fig. 3d). Different from α-Ag₄P₂S₇, however, [Ag2PS₄]²⁻ layers adopt a more complex alternating stacking manner, i.e., AA′A′′AA′A′′…, leading to a superposition of microscopic SHG coefficients and macroscopically enhancing the NLO effect. So, a larger unit cell is necessary for β-Ag₄P₂S₇. In addition, the bond valence calculations resulted in values of 0.96–1.05 for the Ag⁺ cation, 5.26 for the P⁵⁺ cation, and 1.97–2.13 for the S²⁻ anion (Table S4†). All of these are consistent with their respective ideal oxidation states.

	Fig. 3 The structural evolution from α- to β-Ag4P2S7. (a) Crystal structure along the b-axis of α-Ag4P2S7; (b) crystal structure along the b-axis of β-Ag4P2S7; (c) 2D [Ag2PS4]4− layer in α-Ag4P2S7; (d) 2D [Ag2PS4]4− layer in β-Ag4P2S7; (e) spatial symmetry operation of α-Ag4P2S7; and (f) spatial symmetry operation of β-Ag4P2S7.

Further structural comparisons of α- and β-Ag₄P₂S₇ were performed to gain insight into the phase transition behavior (Fig. 3). The density of high-temperature phase β-Ag₄P₂S₇ (4.377 g cm⁻³) is lower than that of low-temperature phase α-Ag₄P₂S₇ (4.381 g cm⁻³), which is consistent with the principle of thermal expansion and contraction. Moreover, the unit cells gradually decrease from α- to β-Ag₄P₂S₇, that is, a_(α) = 10.7634(8) Å ≈ 1.69 × b_(β), b(α) = 6.5280(4) Å ≈ b_(β), and c_(α) = 23.3477(18) Å ≈ 0.69 × c_(β). As shown in Fig. 3a and b, along the a-axis, the a-Ag₄P₂S₇ unit cell can accommodate two [P₂S₇]⁴⁻ dimers, while that of β-Ag₄P₂S₇ can only accommodate one [P₂S₇]⁴⁻ dimer. Along the c-axis, the unit cell of a-Ag₄P₂S₇ can accommodate two [P₂S₇]⁴⁻ dimers, whereas that of β-Ag₄P₂S₇ can accommodate three [P₂S₇]⁴⁻ dimers. Those indicate that the phase transition from α- to β-Ag₄P₂S₇ has an abnormal anisotropic thermal expansion, such as contraction along the a direction and expansion along the c direction. In addition, the Ag1–S distances of in the [Ag1S₄]⁷⁻ bridges of β-Ag₄P₂S₇ (2.551–2.882 Å) are longer than the Ag1–S distances of a-Ag₄P₂S₇ (2.538–2.876 Å) (Fig. S5†), facilitating the rotation of the [Ag2PS₄]²⁻ layer and constructing to NCS structure accompanied by a significant SHG response. Intriguingly, the [Ag2PS₄]²⁻ layer shows a higher symmetry of the 3₂ screw axis in β-Ag₄P₂S₇ compared to the 2-fold axis in α-Ag₄P₂S₇ (Fig. 3c and d). As can be seen in Fig. 3e and f, the spatial symmetry operation increases from four (in α-Ag₄P₂S₇) to six (in β-Ag₄P₂S₇).

The microstructural characteristics of a material, such as atomic arrangement, crystal structure, phase composition, etc., fundamentally determine the material's various physical and chemical properties. We evaluated the NLO properties of the β-Ag₄P₂S₇ by using the Kurtz–Perry method under the Q-switched 2100 nm laser.⁴⁰ As illustrated in Fig. 4a, the SHG intensity tended to attain saturation with an increase in the particle size of the sample, which indicated that β-Ag₄P₂S₇ was phase-matchable. β-Ag₄P₂S₇ demonstrates a strong SHG intensity of about 1.02 times that of AgGaS₂ at 150–200 μm (Fig. S6†), and is comparable to previously reported IR NLO materials [RbBa₂Cl][Ga₄S₈] (1.0 × AgGaS₂),¹⁹ NaAgPS₄ (1.05 × AgGaS₂),⁴¹ NaMg₃Ga₃Se₈ (1.0 × AgGaS₂),⁴² and [K₄Cl][CdGa₉S₁₆] (0.9 × AgGaS₂).⁴³ The large SHG response of β-Ag₄P₂S₇ will be favorable for generating high application conversion efficiencies. Note that the key scientific issue in the design of promising IR NLO crystals, especially for high-power laser applications, is how to strike a balance between strong SHG effects and high LDT, which have opposite structural requirements. In general, the barrier of photon absorption increases with a larger optical band gap, and materials tend to have a higher LDT. However, Ag-based chalcogenides typically possess a shallow LDT further dramatically shortening the device longevity which stems from the 4d, 5s and 5p orbitals of Ag⁺ always occupying the bottom of the conduction band (CB) and the top of the valence band (VB) leading to the narrow band gap and the photodarkening effect of silver. The absorption edge of β-Ag₄P₂S₇ is at 414 nm (Fig. S7†) and the band gap of β-Ag₄P₂S₇ is deduced to be 2.90 eV based on the Kubelka–Munk equation, which is in good agreement with the buff color of the crystals (Fig. 4b) and, to our knowledge, is the largest band gap in the ternary Ag-based DL chalcogenides (Fig. 4e and Table S6†).^44–51 We hypothesize that the strong covalent P–S anionic frameworks promote the expansion of the band gap and drive the blue shift of the shortwave absorption edge, thus achieving high LDT, which is verified in subsequent theoretical calculations.

	Fig. 4 (a) Size-dependent SHG intensities of β-Ag4P2S7 and AgGaS2 under 2100 nm radiation; (b) Eg of β-Ag4P2S7. Inset: crystals of β-Ag4P2S7; (c) DSC curve of the β-Ag4P2S7; (d) PXRD patterns; (e) band gaps comparison of the Ag-based DL chalcogenides.

The thermal behavior of β-Ag₄P₂S₇ was investigated by DSC, as illustrated in Fig. 4c. There are two endothermic peaks at 460 °C and 558 °C, corresponding to the peritectic reaction of Ag₇P₃S₁₁ with the melt and melting point, respectively, and one exothermic peak at 489 °C during one heating/cooling cycle. In addition, the match of the powder X-ray diffraction (PXRD) patterns between the DSC measurement of β-Ag₄P₂S₇ and the β-Ag₄P₂S₇ sample further illustrates the melts congruence and the irreversible behavior of the phase transition (Fig. 4d). Thereby, β-Ag₄P₂S₇ is thermodynamically stable and can be grown as bulk single crystals by the Bridgeman–Stockbarger method. With its stable DL crystal structure, β-Ag₄P₂S₇ possesses desirable water resistance. After being immersed in water for over two weeks, PXRD analysis showed that the crystalline structure of β-Ag₄P₂S₇ remained stable for further practical applications (Fig. 4d). The Raman spectrum recorded on the β-Ag₄P₂S₇ powder sample is displayed in Fig. S8.† The peaks located at 450–600 cm⁻¹ correspond to vibration modes of the P–S bond, while peaks existing between 200 and 450 cm⁻¹ can be designated to vibrations of the Ag–S bond.^52,53

Electronic band structure calculations of α-Ag₄P₂S₇ and β-Ag₄P₂S₇ have been carried out to comprehensively understand the relationship between the structure and optical properties based on first principles. The α-Ag₄P₂S₇ undergoes an indirect transition from the M point to the other position points, corresponding to an indirect band gap value of 2.16 eV (Fig. 5a). The β-Ag₄P₂S₇ transitions directly from the M point to the M point, corresponding to a direct band gap of 2.42 eV (Fig. 5b). The calculated band gap value is significantly underestimated compared to the experimental result (2.65 eV and 2.90 eV, respectively) due to the discontinuity in the exchange–correlation potential.⁵⁴ It is generally accepted that optical properties are mainly determined by electronic transitions close to the band gap. To profoundly understand their band structure characteristics, partial densities of states (PDOS) are presented in Fig. 5a and b. Both structures have similar PDOS; the top of the valence band (VB) is predominantly dominated by Ag 4d and S 3p orbitals, while the bottom of the conduction band (CB) is primarily contributed by P 3p and S 3p orbitals. In addition, orbital analyses are carried out to understand the structure-performance relationship more intuitively. The partial charge density distributions of the highest occupied atomic orbitals (HOMO) and the lowest unoccupied atomic orbitals (LUMO) of α-Ag₄P₂S₇ and β-Ag₄P₂S₇ are plotted in Fig. 5c and d, respectively. It is observed that the HOMO states of α-Ag₄P₂S₇ are mainly composed of Ag 4d and S 3p orbitals, and the LUMO states of α-Ag₄P₂S₇ consist of unoccupied P 3p, and S 3p orbitals. The HOMO state of β-Ag₄P₂S₇ consists mainly of Ag2 4d and S 3p orbitals and the LUMO state consists mainly of unoccupied P 3p and S 3p orbitals. The stacking mode of the [Ag2PS₄]²⁻ layer change selectively strengthens the covalency of the anionic framework (e.g., P–S) and weakens the Ag1 4d–S 3p orbital hybridization. Therefore, the band gap increase induced by the CS to NCS structural phase transition is mainly altered by the stacking mode of the [Ag2PS₄]²⁻ layer. In addition, the charge transitions responsible for the SHG efficiency in β-Ag₄P₂S₇ are mainly dominated by the charge transfer from Ag2 4d and S 3p to P 3p and S 3p orbitals in the [Ag2PS₄]²⁻ layer. The calculated SHG coefficients of d₁₆ = d₂₂ = 6.7 pm V⁻¹ are much smaller than second-order nonlinear optical coefficient (d₃₆ = 13.7 pm V⁻¹) of the reference material AgGaS₂⁵⁵ and the experimental value (d_eff = 13.8 pm V⁻¹) of β-Ag₄P₂S₇, and a similar underestimate of the second-order susceptibilities has also been observed in other reports.^56,57 Furthermore, the birefringence of α-Ag₄P₂S₇ is slightly larger than that of β-Ag₄P₂S₇ at 2100 nm, which is consistent with the general rule that low crystal symmetry usually leads to higher birefringence (Fig. 5e).⁵⁸ The birefringence of β-Ag₄P₂S₇ is suitable for a mid-infrared material to achieve phase-matching conditions. To understand the contribution of NLO active electron states and units, the SHG-weighted electron density analysis of β-Ag₄P₂S₇ was adopted with electron-including occupied and unoccupied states (Fig. 5f).⁵⁹ The result shows that SHG efficiency in β-Ag₄P₂S₇ is mainly determined by the synergistic effect of the anionic groups [Ag2S₄]⁷⁻, [PS₄]³⁻, and the small contribution of [Ag1S₄]⁷⁻ tetrahedra. Furthermore, the dipole moments calculations for [Ag1S₄]⁷⁻, [Ag2S₄]⁷⁻, and [PS₄]³⁻ tetrahedra in the unit cell were calculated based on the bond valence method⁶⁰ to analyze the origin of the strong SHG effect, as displayed in Table 1. For per cell, the z components of the [Ag1S₄]⁷⁻, [Ag2S₄]⁷⁻, and [PS₄]³⁻ tetrahedral polarizations almost cancel out. The [PS₄]³⁻ tetrahedra possess a very large net dipole moment of 45.43 Debye (D), followed by [Ag2S₄]⁷⁻ tetrahedra with a net dipole moment of 18.78 D, whereas [Ag1S₄]⁷⁻ tetrahedra has the smallest net dipole moment of 4.35 D. Overall, the synergistic action of the [Ag2S₄]⁷⁻ and [PS₄]³⁻ tetrahedra in [Ag2PS₄]²⁻ layer contribute mainly to the net dipole moment, which facilitates the superposition of their polarizations. In other words, the temperature-induced changes in the alternating stacking pattern of the [Ag2PS₄]²⁻layers contribute to the superposition of microscopic SHG coefficients and macroscopically enhance the NLO effect.

	Fig. 5 (a) Electronic band structure and PDOS of α-Ag4P2S7; (b) electronic band structure and PDOS of β-Ag4P2S7; (c) HOMO and LUMO of α-Ag4P2S7; (d) HOMO and LUMO of β-Ag4P2S7; (e) the calculated refractive indices of α-Ag4P2S7 and β-Ag4P2S7; and (d) SHG density map. The blue, violet, and yellow balls represent Ag, P, and S atoms, respectively.

Conclusions

Data availability

Conflicts of interest

Acknowledgements

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