Equivalent cation-tuning to realize a new Ce(IV) fluoride with excellent comprehensive nonlinear optical performances

Abstract

Exploring nonlinear optical (NLO) halide materials has become a hot research field owing to their diverse structures and excellent optical properties. In this paper, a new inorganic tetravalent cerium fluoride NH₄Ce₃F₁₃ was obtained. It crystallizes in the polar space group of Pmc2₁ and exhibits a three-dimensional {[Ce₃F₁₃]⁻}_∞ framework, which is composed of {[CeF₈]⁴⁻}_∞ chains and {[CeF₆]²⁻}_∞ layers formed by CeF₉ polyhedra, with the NH₄⁺ cation balancing the charge. NH₄Ce₃F₁₃ exhibits a strong second-harmonic generation (SHG) response among inorganic metal fluorides of about 1.2 times greater than that of KH₂PO₄ (KDP) and a high laser-induced damage threshold (LIDT), which is 39 times more than that of AgGaS₂. Besides, NH₄Ce₃F₁₃ possesses the largest band gap among Ce(IV)-containing NLO materials. This work provides a good case for exploring high-performance NLO fluoride materials.

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Introduction

Metal halides play an important role in the field of photoelectronic functional materials. They are widely used in photovoltaics, light-emitting diodes (LEDs), nonlinear optical (NLO) materials, and laser technology on account of their diverse structural features and excellent photoelectric properties.^1–4 In the past several years, several NLO metal halides, including K₂SbF₂Cl₃, Pb₇F₁₂Cl₂, BaClBF₄, Ag₂HgI₄, HgBr₂, CsHgBr₃, Cs₂HgI₂Cl₂, Rb₂CdBr₂I₂, Rb₂CdBrI₃, and Rb₄Sn₃Cl₂Br₈, have been reported. Some of them exhibit strong SHG effects and high laser-induced damage thresholds (LIDTs), such as Pb₇F₁₂Cl₂, HgBr₂, and Rb₂CdBrI₃.^5–14 In addition, some metal halides with stereochemically active lone-pair electrons (LPEs) exhibit excellent optical anisotropy. For example, A₃SnCl₅, ASn₂Cl₅ (A = NH₄ and Rb), A₂Sn₂F₅Cl, and ASnFCl₂ (A = Rb and Cs) exhibit outstanding birefringence and a wide transparent region.^15,16

In recent years, NLO metal fluoride crystals have attracted more attention. The combination of the strongest electronegative F atom and metal cations can form compounds with excellent optical performances. Many NLO fluorides have been investigated, such as SbF₃, NaSb₃F₁₀, BaZnF₄, KBi₄F₁₃, SrAlF₅, KNa₂ZrF₇, K₃Ba₂Zr₆F₃₁, K₂BaM₂F₁₂, and Li₂CaMF₈ (M = Zr and Hf).^17–25 Evidently, Zr- and Hf-based fluorides show large optical band gaps and high LIDTs, such as KNa₂ZrF₇. Attractively, K₃Ba₂Zr₆F₃₁, K₂BaM₂F₁₂ and Li₂CaMF₈ (M = Zr and Hf) possess a wide transparency window below 200 nm. However, although fluorides have advantages in generating compounds with large band gaps, most acentric fluoride crystals show weaker SHG intensity than commercial NLO crystal KH₂PO₄ (KDP). Apart from group IVB metal fluorides, our group studied cerium(IV) fluorides owing to their similar ionic radii and valence states. Based on these studies, highly electropositive cations (Zr⁴⁺, Ti⁴⁺, Hf⁴⁺, Ce⁴⁺, etc.) could lead to diverse asymmetric structural units and thus produce many interesting crystal structures and promising NLO properties. To date, except for lone pair electronic metal fluorides, only Na₂CeF₆ exhibits an SHG intensity stronger than KDP (2.1 × KDP).²⁶ Clearly, tetravalent cerium fluorides have great potential for NLO performance. To date, among Ce(IV)-containing fluorides, only Na₂CeF₆ has been reported to show SHG effects. Hence, exploring new fluorides containing Ce(IV) is a meaningful task not just for exploring new NLO materials, but also for enriching the structural diversity of rare earth fluorides. Designing new acentric fluorides is the prerequisite for obtaining new NLO Ce(IV) fluoride materials. In current popular design strategies, the synthesis of new NLO materials using isovalent ion substitution based on non-centrosymmetric (NCS) or centrosymmetric (CS) parent compounds is an effective approach. Generally, different ionic radii may cause structural changes and variations in SHG activity. In recent years, several new NLO compounds have been discovered through equivalent ion regulation strategies. For instance, the NCS compounds CsNaTaF₇ were obtained from CS compound CsKTaF₇ by substituting the alkali–metal cation. CS-to-NCS structural transformation can be achieved from Cs₂M₃(P₂O₇)₂ (M = Zn and Mg) to Rb₂Zn₃(P₂O₇)₂, as well as from K₂YB₃O₆F₂ to A₂YB₃O₆F₂ (A = Cs, Rb), achieving CS to NCS structural transformation. The substitution of Li⁺ to K⁺ results in optimizing the optical properties of α-AZnPO₄ (A = Li, K). The physical properties vary due to the different cations based on the AB₄O₆F (A = NH₄, Na, K, Rb, and Cs) family. The NLO carbonates ABCO₃F (A = K, Rb, Cs; B = Ca, Sr, Ba) were designed by adjusting the metal cations. A series of NLO rare-earth borates, K₇MRE₂B₁₅O₃₀ (M = Zn, Cd, Pb; RE = Sc, Y, Gd, Lu), were also obtained by the substitution of isovalent cations.^27–38 Obviously, isovalent cation regulation is a preferred method for developing new NLO materials.

According to the above thoughts, a new ammonium cerium(IV) fluoride crystal, NH₄Ce₃F₁₃, was obtained by a hydrothermal reaction. It adopts the acentric space group of Pmc2₁ and shows a phase-matching SHG effect. Synthesis, crystal structure, and the relationship between structure and performance based on theoretical calculations are presented in this work.

Experimental section

Synthesis

All commercial reagents of CeO₂ (Tansoole, 99.99%), NH₄F (Sinopharm, AR), ZnF₂ (Sinopharm, AR), and HF solution (40% in water, by weight) were used as received. Caution! Hydrofluoric acid is toxic and volatile. Proper precautions and extreme caution must be exercised during the experiment. The single crystals of NH₄Ce₃F₁₃ were obtained by applying the hydrothermal method. A mixture of NH₄F (0.9 mmol), CeO₂ (1.8 mmol), and ZnF₂ (0.3 mmol) was put into the 23 mL Teflon liners with adding 1.5 mL of HF and 3 mL of deionized water solution. Then, the sealed Teflon liners in the oven were heated to 230 °C for 1 day and cooled to room temperature for 2 days. Finally, colourless single crystals (inset of Fig. 3) of NH₄Ce₃F₁₃ were obtained with yields of 28–35% based on CeO₂.

Single crystal structure determination

The crystal data of NH₄Ce₃F₁₃ were collected by applying a Bruker D8 QUEST X-ray diffractometer with graphite-monochromated Mo-Kα radiation (λ = 0.71073 Å). The structures were solved using direct methods refined by full-matrix least-squares techniques on F² with anisotropic displacement parameters for all atoms. The PLATON program was used to check the correctness of the structure, and no errors were found.^39,40 The crystallographic data and refinement parameters of NH₄Ce₃F₁₃ are shown in Table 1. Bond lengths, bond angles, atomic coordinates and equivalent isotropic displacement parameters are summarized in Tables S1–S4,† respectively. CCDC number 2371443† was assigned to the deposition of NH₄Ce₃F₁₃.

Table 1 Crystal data and structure refinement parameters for NH₄Ce₃F₁₃

Empirical formula	NH4Ce3F13
a R 1 = ||Fo| − |Fc||/|Fo|. b wR2 = [w(Fo^2 − Fc^2)^2]/[w(Fo^2)^2]^1/2.
Mr (g mol^−1)	685.40
Cryst syst.	Orthorhombic
T (K)	296(2)
Space group	Pmc21
a (Å)	7.9167(8)
b (Å)	7.2697(7)
c (Å)	8.3413(7)
V (Å^3)	480.06(8)
Z	2
D c (g cm^−3)	4.742
μ(mm^−1)	14.161
F(000)	604.0
Crystal size/mm^3	0.12 × 0.11 × 0.1
Radiation	MoKα (λ = 0.71073)
2θ range for data collection/°	5.146 to 54.952
Index ranges	−6 ≤ h ≤ 10, −9 ≤ k ≤ 9, −10 ≤ l ≤ 9
Reflns collected	2327
Independent reflections	1046 [Rint = 0.0287, Rsigma = 0.0393]
Data/restraints/parameters	1046/10/99
Goodness-of-fit on F^2	1.047
Final R indexes [I ≥ 2σ(I)]^a^,^b	R 1 = 0.0178, wR2 = 0.0380
Final R indexes [all data]^a^,^b	R 1 = 0.0182, wR2 = 0.0382
Largest diff. peak/hole/e Å^−3	0.76/−1.35
Flack parameter	0.030(19)

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Energy-dispersive X-ray spectroscopy (EDS)

EDS analysis of selected several crystals was performed using a Bruker quantum dispersive X-ray spectroscope, which confirms the presence of N, Ce and F in the crystals. The EDS elemental analysis images for the single crystals and the molar ratios of N/Ce/F are shown in Fig. S2 and Table S5,† respectively.

Powder X-ray diffraction (PXRD) analysis

The PXRD characterization for the NH₄Ce₃F₁₃ sample was collected using a Smart Lab powder X-ray diffractometer for Cu Kα radiation (λ = 1.5406 Å), with the 2θ range of 10–70° and a scan speed of 0.1 s per step. The simulated patterns were generated on the Mercury v3.8 program using the single-crystal structure data of NH₄Ce₃F₁₃. The experimental and simulated PXRD patterns match well, suggesting that the obtained sample is pure (Fig. 1).

Fig. 1 Simulated and experimental powder X-ray diffraction patterns of NH₄Ce₃F₁₃.

Thermogravimetric analysis

Thermogravimetric characterization was performed on Netzsch STA 449 F3 in flowing N₂ gas. The powder sample was placed in an alumina crucible with a heating procedure ranging from 20 to 1000 °C at a rate of 15 °C per minute.

Optical properties

The IR spectrum was measured using a Magna 750 FI-IR spectrometer with a wavelength of 4000–400 cm⁻¹ with pure KBr as the background. The pure BaSO₄ sample was used as the standard reference. The UV–vis–NIR diffuse reflectance spectrum of NH₄Ce₃F₁₃ was collected using a Carry 5000 spectrometer in the range of 200–800 nm. The reflection spectrum was calculated using the Kubelka–Munk function to calculate the band gap.

Second-harmonic generation and laser-induced damage threshold (LIDT) measurements

The SHG response of the NH₄Ce₃F₁₃ powder sample was measured by applying the Kurtz and Perry method using a Q-switched Nd:YAG laser under 1064 nm. The frequency-doubling effect depended largely on the granular size, so the sample was sieved into six consecutive sizes (25–45, 45–75, 75–105, 105–150, 150–200 and 200–250 μm), with KDP samples of the same size used as the reference. The single-pulse measurement method was used to measure the LIDTs of NH₄Ce₃F₁₃, with AgGaS₂ (AGS) selected for comparison under the same conditions. The samples were radiated with a 1064 nm laser with a pulse width τ_p of 10 ns in a 1 Hz repetition. The laser emission energy was adjusted by a Nova II sensor display with a PE50-DIT-C energy sensor until the damaged spot was observed.

Theoretical calculation

The theoretical calculations of electronic structure, optical properties and the density of states (DOS) were carried out on the CASTEP mode based on the density functional theory (DFT) method. The generalized gradient approximation (GGA) and the Perdew–Burke–Ernzerhof (PBE) function were applied for the exchange–correlation energy.^41–43 The orbital electrons of each atom as valence electrons were H 1s¹, N 2s²2p³, F 2s²2p⁵ and Ce 4f¹5d¹6s². The cut-off kinetic energy of 410 eV was adopted, and the Brillouin zone numerical integration was implemented by employing 4 × 3 × 3 for Monkhorst–Pack k-point sampling to determine the numbers of plane waves, with the Fermi level setting at zero as the energy reference.

Results and discussion

Crystal structure

NH₄Ce₃F₁₃ crystallizes in the orthorhombic space group Pmc2₁, which includes two kinds of Ce, one unique N, and nine types of F atoms in the asymmetric unit. The crystal structure of NH₄Ce₃F₁₃ consists of NH₄⁺ cations and the 3D {[Ce₃F₁₃]⁻}_∞ anion framework. Both Ce(1) and Ce(2) atoms are connected with nine F atoms to construct the CeF₉ polyhedra (Fig. S1†). The Ce(1)F₉ polyhedra are linked together via corner-sharing F(2) atoms along the c axis to form {[Ce(1)F₈]⁴⁻}_∞ chains (Fig. 2a), whereas the Ce(2)F₉ polyhedra are bonded together via edge-sharing to make up {[Ce(2)F₆]²⁻}_∞ layers in the ac plane (Fig. 2b). Furthermore, the {[Ce(1)F₈]⁴⁻}_∞ chains are corner- and edge-shared with {[Ce(2)F₆]²⁻}_∞ layers to construct the 3D {[Ce₃F₁₃]⁻}_∞ framework, with NH₄⁺ distributed in the cavity to balance the charge (Fig. 2c). The Ce–F and N–H bond distances are in the ranges of 2.197(6)–2.455(4) Å and 0.847(7)–0.851(1) Å, respectively.

Fig. 2 Crystal structure of NH₄Ce₃F₁₃. The arrangements of {[Ce(1)F₈]⁴⁻}_∞ chains along the c axis (a). {[CeF₆]²⁻}_∞ layers in the ac plane (b). The whole three-dimensional crystal structure viewed along the c direction (c). Unit-cell structures of Na₂CeF₆ (d) and NH₄Ce₃F₁₃ (e).

The reported inorganic monovalent cation Ce(IV)-based fluorides are summarized in Table S6† for comparison with NH₄Ce₃F₁₃. In Na₂CeF₆ (P6̄2m) and LiCeF₅ (I4₁/a), Ce atoms also form CeF₉ polyhedra.^26,44 Cs₃CeF₇ (Fm3̄m) and Rb₃CeF₇ (Fm3̄m) feature 3D frameworks composed of CeF₆ polyhedra. CsCeF₅ (P2₁/c), Na₃CeF₇ (I4/mmm), Li₄CeF₈ (Pnma), (NH₄)₇Ce₆F₃₁ (R3̄), (NH₄)₂CeF₆ (Pbcn) and (NH₄)₄CeF₈ (C2/c) comprised CeF₈ polyhedra to display 3D frameworks.^45–50 In the structure of LiCeF₅, the distorted CeF₉ polyhedra form {[CeF₆]²⁻}_∞ chains by edge-sharing along the c axis. Then, these chains are linked together via corner sharing to build a 3D {[CeF₅]⁻}_∞ framework. To date, only Na₂CeF₆ has been reported as an NLO material. Although the two compounds are composed of CeF₉ polyhedra, it is noteworthy that the arrangements of CeF₉ polyhedra have transformed. Na₂CeF₆ only contains one Ce atom, which forms {[CeF₆]²⁻}_∞ chains, with the 3D {[Na₆F₁₈]¹²⁻}_∞ framework to build the whole structure (Fig. S3†). However, there are two kinds of Ce atoms in NH₄Ce₃F₁₃, showing two different structural parts, {[CeF₈]⁴⁻}_∞ chains and {[CeF₆]²⁻}_∞ layers, and then further to build a 3D {[Ce₃F₁₃]⁻}_∞ framework. Besides, the Na–F bond distances are in the range of 2.2748(11)–2.6453(6) Å, which are close to the bond distances of Ce–F in the range of 2.182(2)–2.370(2) Å, so it can be observed that the structure of Na₂CeF₆ is composed of MF₉ (M = Na, Ce) polyhedra. When the Na⁺ cation is substituted by an NH₄⁺ cation with a larger ionic radius, NH₄⁺ cations are further away from CeF₉ polyhedra, resulting in the CeF₉ polyhedra adopting different configurations to fit different cations, from 1D chains in Na₂CeF₆ to a 3D framework in NH₄Ce₃F₁₃, which further leads to structural transformation. On the other hand, fluorides with the same number of fluorine atoms in the formulae are summarized in Table S7,† including KBi₄F₁₃ (I4̄), NH₄Sb₄F₁₃ (I4̄), KSb₄F₁₃ (I4̄), RbU₃F₁₃ (Pmc2₁), NH₄UF₁₃ (Pmc2₁), RbTh₃F₁₃ (Pmc2₁) and [(C₅H₆N₂)₂H](Sb₄F₁₃) (P1).^20,51–56 RbU₃F₁₃, NH₄UF₁₃ and RbTh₃F₁₃ are isotypes with the title compound, but these compounds are radioactive and have only been reported on their structures without studying the SHG effects. The structures of the three compounds also feature a combination of layers and chains consisting of edge- and corner-shared MF₉ (M = U and Th) polyhedra.

Optical measurements

The IR spectrum shows two distinct absorption peaks (Fig. 3). The peaks at 3240 and 1417 cm⁻¹ are related to the N–H vibrations of NH₄⁺, which is close to the reported compounds containing NH₄⁺.^57,58 As the UV–vis–NIR diffuse reflectance spectrum shown in Fig. 4, the optical band gap of NH₄Ce₃F₁₃ is determined to be 4.26 eV, which is the largest among Ce(IV)-containing NLO materials, including Na₂CeF₆ (3.89 eV),²⁶ CeF₂(SO₄) (2.71 eV), Ce(IO₃)₂(SO₄) (2.42 eV), CeF₂(IO₃)₂ (2.17 eV), Ce(IO₃)₂F₂·H₂O (2.60 eV), Ce₃F₄(SO₄)₄ (2.5 eV), Ba₂Ce(IO₃)₈(H₂O) (2.44 eV), and Rb₂Ce(IO₃)₅F (2.35 eV).^59–65

Fig. 3 IR spectrum of NH₄Ce₃F₁₃.

Fig. 4 UV–vis–NIR diffuse reflectance spectrum of NH₄Ce₃F₁₃. Inset: band gap of NH₄Ce₃F₁₃.

Thermal properties

The TG–DTA curves of NH₄Ce₃F₁₃ are presented in Fig. 5. From the curves, we can observe that NH₄Ce₃F₁₃ can be stable at temperatures below about 260 °C.

Fig. 5 TG–DTA curves of NH₄Ce₃F₁₃.

SHG activity and LIDT

Due to the acentric structure of NH₄Ce₃F₁₃, its SHG measurement was performed using the Kurtz–Perry method under a 1064 nm laser. The result shows that NH₄Ce₃F₁₃ exhibits an SHG efficiency of about 1.2 times that of KDP and can achieve phase-matching (Fig. 6), which is larger than most of the NLO fluoride crystals, including BaZnF₄ (0.16 × KDP), KBi₄F₁₃ (0.5 × KDP), SrAlF₅ (0.65 × KDP), KNa₂ZrF₇ (0.4 × KDP), K₃Ba₂Zr₆F₃₁ (0.5 × KDP),^19–23 CsNaTaF₇ (0.2 × KDP),²⁷ and Na₂SbF₅ (0.17 × KDP).⁶⁶ Since NH₄Ce₃F₁₃ exhibits a large band gap and good SHG effect, the LIDTs of NH₄Ce₃F₁₃ and AgGaS₂ were measured under the same conditions. The LIDT measurement results show that NH₄Ce₃F₁₃ possesses a large LIDT value of 169.4 MW cm⁻², which is 39 times that of AGS (4.3 MW cm⁻²). The LIDT value of NH₄Ce₃F₁₃ is much enhanced compared to other NLO halides (Table S8†), such as Na₂CeF₆ (20 × AGS), Pb₇F₁₂Cl₂ (15.4 × AGS), and KBi₄F₁₃ (24 × AGS). Although the SHG signal is not stronger than Na₂CeF₆ (2.1 × KDP), NH₄Ce₃F₁₃ shows a larger band gap and higher LIDT than Na₂CeF₆. Hence, NH₄Ce₃F₁₃ exhibits balanced NLO performance.

Fig. 6 (a) Size-dependence SHG responses of NH₄Ce₃F₁₃ and KDP under 1064 nm radiation, and (b) SHG responses of 200–250 μm particles of NH₄Ce₃F₁₃ and KDP.

Theoretical studies

Based on the first principles calculations, we further study the relationship between structures and optical performances.⁶⁷ The calculated results indicate that the theoretical band gap of NH₄Ce₃F₁₃ is 2.47 eV (Fig. 7a). Due to the derivative discontinuity of the exchange–correlation function of GGA-PBE, the calculated band gap is smaller than the measured band gap. From the partial density of state (PDOS) graphs of NH₄Ce₃F₁₃ shown in Fig. 7b, the top of the valence band is mainly contributed by the F-2p orbitals. The bottom of the conduction band is mainly composed of Ce-4f and partial F-2p orbitals. Therefore, it can be observed that the charge transfer between the valence and conduction bands is mainly determined by the Ce and F atoms.

Fig. 7 Calculated (a) band gap and (b) density of states (DOS) of NH₄Ce₃F₁₃. The Fermi level is set at 0 eV.

We deeply explore the NLO properties of NH₄Ce₃F₁₃ by calculation. As crystallized in the mm2 point group and considered Kleinman symmetry, NH₄Ce₃F₁₃ has three independent SHG tensors (χ₃₁, χ₃₂, and χ₃₃), which are calculated to be 0.50, 0.53, and 0.57 pm V⁻¹ under a 1064 nm laser, respectively (Fig. 8a). The largest value is 0.7 times that of the KDP (d₃₆ = 0.39 pm V⁻¹), which is relatively smaller than the experimental value. The underestimation is a deviation between the experiment and calculation, and similar cases have been reported in other works.^68,69 As the calculated refractive index dispersion curves of NH₄Ce₃F₁₃ shown in Fig. 8b, the calculated birefringence is 0.03@1064 nm, which is suitable for the phase-matching requirement. The phase-matching wavelength condition was also calculated (Fig. 8c), indicating that the shortest SHG phase-matching wavelength of NH₄Ce₃F₁₃ is 685 nm, which confirms the experimental results.

Fig. 8 Energy-dependent SHG tensors (a), calculated refractive index dispersion curves (b), and phase-matching conditions of NH₄Ce₃F₁₃ (c).

To further study the contribution of the groups in NH₄Ce₃F₁₃ to optical properties, the calculation of the electronic density difference is carried out. As presented in Fig. 9, the electron density of the F⁻ anion connected by the Ce⁴⁺ cation is higher. Therefore, the electron density difference map confirms that the CeF₉ polyhedra in NH₄Ce₃F₁₃ are the main contributors to NLO performance. Besides, the degree of distortion of the total CeF₉ polyhedra is also calculated, as shown in Table S9.† The calculation results reveal that CeF₉ polyhedra have a relatively large degree of distortion, which is beneficial for NLO properties. The dipole moments of two types of CeF₉ units and the total structure in one unit cell of NH₄Ce₃F₁₃ were calculated to analyse the contribution to the NLO effects. The results are shown in Fig. 10 and Table S10,† indicating that the dipole moments of CeF₉ units are arranged in almost the same orientation ranging from 0.55 to 1.10 D and the total dipole moment of CeF₉ units is 2.40 D, which results in SHG performance for NH₄Ce₃F₁₃. Obviously, the optical properties of NH₄Ce₃F₁₃ are determined by CeF₉ units.

Fig. 9 Electron-density difference map of NH₄Ce₃F₁₃.

Fig. 10 Calculated dipole moments of NH₄Ce₃F₁₃ (red: CeF₉, blue: total).

Conclusions

In conclusion, NH₄Ce₃F₁₃, a Ce(IV)-based fluoride NLO crystal, was synthesized using a hydrothermal reaction. It displays a three-dimensional framework comprising corner- and edge-shared CeF₉ polyhedra. NH₄Ce₃F₁₃ exhibits a strong SHG response and high LIDT. Besides, NH₄Ce₃F₁₃ possesses the largest band gap among all the reported Ce(IV)-based NLO materials. This study provides a good route to explore Ce(IV) halides with NLO effects. We will continue to develop more new promising NLO rare earth halide compounds.

Data availability

The data supporting the research findings of this work are available from the corresponding author on reasonable request.

Conflicts of interest

The authors declare that they have no conflict of interest.

Acknowledgements

The authors acknowledge financial support from the National Natural Science Foundation of China (22101248), the Lvyangjinfeng Talent Program of Yangzhou (YZLYJFJH2021YXBS083), and the Qinglan Project of Yangzhou University.

References

1. P. F. Gong, F. Liang, L. Kang, X. G. Chen, J. G. Qin, Y. C. Wu and Z. S. Lin, Recent advances and future perspectives on infrared nonlinear optical metal halides, Coord. Chem. Rev., 2019, 380, 83–102.
2. Y. Pan, S. P. Guo, B. W. Liu, H. G. Xue and G. C. Guo, Second-order nonlinear optical crystals with mixed anions, Coord. Chem. Rev., 2018, 374, 464–496.
3. H. Cho, S. H. Jeong, M. H. Park, Y. H. Kim, C. Wolf, C. L. Lee, J. H. Heo and A. Sadhanala, Overcoming the electroluminescence efficiency limitations of perovskite light-emitting diodes, Science, 2015, 350, 1222–1225.
4. F. G. You, F. Liang, Q. Huang, Z. G. Hu, Y. C. Wu and Z. S. Lin, Pb₂GaF₂(SeO₃)₂Cl: Band Engineering Strategy by Aliovalent Substitution for Enlarging Bandgap while Keeping Strong Second Harmonic Generation Response, J. Am. Chem. Soc., 2019, 141, 748–752.
5. Y. Huang, X. G. Meng, P. F. Gong, Z. S. Lin, X. G. Chen and J. G. Qin, A Study on K₂SbF₂Cl₃ as A New Mid-IR Nonlinear Optical Material: New Synthesis and Excellent Properties, J. Mater. Chem. C, 2015, 3, 9588–9593.
6. Q. Wu, X. Liu, F. Liang, S. R. Xu, H. B. Pi, X. Han, Y. Liu, Z. S. Lin and Y. J. Li, Pb₇F₁₂Cl₂: A Promising Infrared Nonlinear Optical Material with High Laser Damage Threshold, Dalton Trans., 2019, 48, 13529–13535.
7. M. Zhang, S. L. Pan, Z. H. Yang, Y. Wang, X. Su, Y. Yang, Z. J. Huang, S. J. Han and K. R. Poeppelmeier, BaClBF₄: a new noncentrosymmetric pseudo-Aurivillius type material with transparency range from deep UV to middle IR and a high laser damage threshold, J. Mater. Chem. C, 2013, 1, 4740–4745.
8. C. Yang, X. Liu, C. Teng, X. Cheng, F. Liang and Q. Wu, Hierarchical molecular design of high-performance infrared nonlinear Ag₂HgI₄ material by defect engineering strategy, Mater. Today Phys., 2021, 19, 100432.
9. Q. Wu, C. Yang, J. Ma, X. Liu and Y. J. Li, Halogen-Ion-Induced Structural Phase Transition Giving a Polymorph of HgBr₂ with Balanced Nonlinear Optical Properties, Inorg. Chem., 2021, 60, 19297–19303.
10. S. W. Lv, Q. Wu, X. G. Meng, L. Kang, C. Zhong, Z. S. Lin, Z. G. Hu, X. G. Chen and J. G. Qin, A promising new nonlinear optical crystal with high laser damage threshold for application in the IR region: synthesis, crystal structure and properties of noncentrosymmetric CsHgBr₃, J. Mater. Chem. C, 2014, 2, 6796–6801.
11. G. Zhang, Y. J. Li, K. Jiang, H. Y. Zeng, T. Liu, X. G. Chen, J. G. Qin, Z. S. Lin, P. Z. Fu, Y. C. Wu and C. T. Chen, A New Mixed Halide, Cs₂HgI₂Cl₂: Molecular Engineering for a New Nonlinear Optical Material in the Infrared Region, J. Am. Chem. Soc., 2012, 134, 14818–14822.
12. Q. Wu, X. G. Meng, C. Zhong, X. G. Chen and J. G. Qin, Rb₂CdBr₂I₂: A New IR Nonlinear Optical Material with a Large Laser Damage Threshold, J. Am. Chem. Soc., 2014, 136, 5683–5686.
13. Q. Wu, X. Liu, Y. S. Du, C. L. Teng and F. Liang, Abnormal bandgap enlargement resulted in a promising mid-infrared nonlinear optical material Rb₂CdBrI₃ with an ultrahigh laser damage threshold, J. Mater. Chem. C, 2020, 8, 9005–9011.
14. P. F. Gong, S. Y. Luo, Y. Yang, F. Liang, S. Z. Zhang, S. G. Zhao, J. H. Luo and Z. S. Lin, Nonlinear Optical Crystal Rb₄Sn₃Cl₂Br₈: Synthesis, Structure, and Characterization, Cryst. Growth Des., 2017, 18, 380–385.
15. J. Y. Guo, J. B. Huang, A. Tudi, X. L. Hou, S. J. Han, Z. H. Yang and S. L. Pan, Birefringence Regulation by Clarifying the Relationship Between Stereochemically Active Lone Pairs and Optical Anisotropy in Tin-based Ternary Halides, Angew. Chem., Int. Ed., 2023, 62, e202304238.
16. J. B. Wang, M. M. Zhu, Y. Q. Chu, J. D. Tian, L. L. Liu, B. B. Zhang and P. S. Halasyamani, Rational Design of the Alkali Metal Sn-Based Mixed Halides with Large Birefringence and Wide Transparent Range, Small, 2024, 20, 2308884.
17. G. Zhang, T. Liu, T. X. Zhu, J. G. Qin, Y. C. Wu and C. T. Chen, SbF₃: A new second-order nonlinear optical material, Opt. Mater., 2008, 31, 110–113.
18. G. Zhang, J. G. Qin, T. Liu, Y. J. Li, Y. C. Wu and C. T. Chen, NaSb₃F₁₀: A new second-order nonlinear optical crystal to be used in the IR region with very high laser damage threshold, Appl. Phys. Lett., 2009, 95, 261104.
19. J. G. Bergman, G. R. Crane and H. Guggenheim, Linear and nonlinear optical properties of ferroelectric BaMgF₄ and BaZnF₄, J. Appl. Phys., 1975, 46, 4645.
20. Q. Wu, H. M. Liu, F. C. Jinang, X. G. Meng, X. G. Chen, L. Yang, Z. G. Hu and J. G. Qin, KBi₄F₁₃: An Infrared Nonlinear Optical Material with High Laser Damage Threshold, Inorg. Chem., 2015, 31, 1875–1880.
21. H. Huang, Z. S. Lin, L. Bai, R. He and C. T. Chen, Mechanism of the linear and nonlinear optical effects of SrAlF₅ and BaMgF₄ crystals, Solid State Commun., 2010, 150, 2318–2321.
22. X. Lian, W. D. Yao, W. L. Liu, R. L. Tang and S. P. Guo, KNa₂ZrF₇: A Mixed-Metal Fluoride Exhibits Phase-Matchable Second-Harmonic-Generation Effect and High Laser-Induced Damage Threshold, Inorg. Chem., 2021, 60, 19–23.
23. M. Yan, R. L. Tang, W. D. Yao, W. L. Liu and S. P. Guo, Exploring a new short-wavelength nonlinear optical fluoride material featuring unprecedented polar cis-[Zr₆F₃₄]¹⁰⁻ clusters, Chem. Sci., 2024, 15, 2883–2888.
24. M. Yan, R. L. Tang, W. D. Yao, W. L. Liu and S. P. Guo, From CaBaM₂F₁₂ to K₂BaM₂F₁₂ (M = Zr, Hf): Heterovalent Cation-Substitution-Induced Symmetry Break and Nonlinear-Optical Activity, Inorg. Chem., 2024, 63, 10949–10953.
25. M. Yan, R. L. Tang, W. Xu, W. L. Liu and S. P. Guo, Centrosymmetric CaBaMF₈ and Noncentrosymmetric Li₂CaMF₈ (M = Zr, Hf): Dimension Variation and Nonlinear Optical Activity Resulting from an Isovalent Cation Substitution-Oriented Design, Inorg. Chem., 2024, 63, 5260–5268.
26. R. L. Tang, W. Xu, X. Lian, Y. Q. Wei, Y. L. Lv, W. L. Liu and S. P. Guo, Na₂CeF₆: A Highly Laser Damage-Tolerant Double Perovskite Type Ce(IV) Fluoride Exhibiting Strong Second-Harmonic-Generation Effect, Small, 2024, 20, 2308348.
27. R. L. Tang, X. Lian, X. H. Li, L. Huai, W. L. Liu and S. P. Guo, From CsKTaF₇ to CsNaTaF₇: Alkali Metal Cations Regulation to Generate SHG Activity, Chem. – Eur. J., 2022, 28, e202201588.
28. Z. F. Song, H. W. Yu, H. P. Wu, Z. G. Hu, J. Y. Wang and Y. C. Wu, Syntheses, structures and characterization of non-centrosymmetric Rb₂Zn₃(P₂O₇)₂ and centrosymmetric Cs₂M₃(P₂O₇)₂ (M = Zn and Mg), Inorg. Chem. Front., 2020, 7, 3482–3490.
29. Y. Zheng, Z. J. Wei, H. P. Wu, Z. G. Hu, J. Y. Wang, Y. C. Wu and H. W. Yu, Breaking through the “200 nm deep-ultraviolet wall” of phase matching region by cation structural modulation, Mater. Today Phys., 2024, 46, 101529.
30. H. P. Wu, Z. J. Wei, Z. G. Hu, J. Y. Wang, Y. C. Wu and H. W. Yu, Assembly of π-Conjugated [B₃O₆] Units by Mer-Isomer [YO₃F₃] Octahedra to Design a UV Nonlinear Optical Material, Cs₂YB₃O₆F₂, Angew. Chem., Int. Ed., 2024, 63, e202406318.
31. X. M. He, L. Qi, W. Y. Zhang, R. X. Zhang, X. Y. Dong, J. H. Ma, M. Abudoureheman, Q. Jing and Z. H. Chen, Controlling the Nonlinear Optical Behavior and Structural Transformation with A-Site Cation in α-AZnPO₄ (A = Li, K), Small, 2023, 19, 2206991.
32. Z. Z. Zhang, Y. Wang, B. B. Zhang, Z. H. Yang and S. L. Pan, Polar Fluorooxoborate, NaB₄O₆F: A Promising Material for Ionic Conduction and Nonlinear Optics, Angew. Chem., Int. Ed., 2018, 57, 6577–6581.
33. G. Q. Shi, Y. Wang, F. F. Zhang, B. B. Zhang, Z. H. Yang, X. L. Hou, S. L. Pan and K. R. Poeppelmeier, Finding the Next Deep-Ultraviolet Nonlinear Optical Material: NH₄B₄O₆F, J. Am. Chem. Soc., 2017, 139, 10645–10648.
34. F. Liang, L. Kang, P. F. Gong, Z. S. Lin and Y. C. Wu, Rational Design of Deep-Ultraviolet Nonlinear Optical Materials in Fluorooxoborates: Toward Optimal Planar Configuration, Chem. Mater., 2017, 29, 7098–7102.
35. X. F. Wang, Y. Wang, B. B. Zhang, F. F. Zhang, Z. H. Yang and S. L. Pan, CsB₄O₆F: A Congruent-Melting Deep-Ultraviolet Nonlinear Optical Material by Combining Superior Functional Units, Angew. Chem., Int. Ed., 2017, 56, 14119–14123.
36. Y. Wang, B. B. Zhang, Z. H. Yang and S. L. Pan, Cation-Tuned Synthesis of Fluorooxoborates: Towards Optimal Deep-Ultraviolet Nonlinear Optical Materials, Angew. Chem., Int. Ed., 2018, 57, 2150–2154.
37. G. h. Zou, N. Ye, L. Huang and X. S. Lin, Alkaline-Alkaline Earth Fluoride Carbonate Crystals ABCO₃F (A = K, Rb, Cs; B = Ca, Sr, Ba) as Nonlinear Optical Materials, J. Am. Chem. Soc., 2011, 133, 20001–20007.
38. Z. Q. Xie, M. Mutailipu, G. J. He, G. P. Han, Y. Wang, Z. H. Yang, M. Zhang and S. L. Pan, A Series of Rare-Earth Borates K₇MRE₂B₁₅O₃₀ (M = Zn, Cd, Pb; RE = Sc, Y, Gd, Lu) with Large Second Harmonic Generation Responses, Chem. Mater., 2018, 30, 2414–2423.
39. V. Dolomanov, L. J. Bourhis, R. J. Gildea, J. A. K. Howard and H. Puschmann, OLEX2: A complete structure solution, refinement and analysis program, J. Appl. Crystallogr., 2009, 42, 339–341.
40. J. Tauc, R. Grigorovici and A. Vancu, Optical Properties and Electronic Structure of Amorphous Germanium, Phys. Status Solidi B, 1966, 15, 627–637.
41. S. K. Kurtz and T. T. Perry, A Powder Technique for the Evaluation of Nonlinear Optical Materials, J. Appl. Phys., 1968, 39, 3798–3813.
42. S. J. Clark, M. D. Segall, C. J. Pickard, P. J. Hasnip, M. J. Probert, K. Refson and M. C. Z. Payne, First Principles Methods Using CASTEP, Z. Kristallogr. - Cryst. Mater., 2005, 220, 567–570.
43. D. D. Macdonald and M. Urquidi-Macdonald, Application of Kramers-Kronig Transforms in the Analysis of Electrochemical Systems: I. Polarization Resistance, J. Electrochem. Soc., 1985, 132, 2316–2319.
44. A. Grzechnik, C. C. Underwood, J. W. Kolis and K. Friese, Crystal structures and stability of LiCeF₅ and LiThF₅ at high pressures: A comparative study of the coordination around the Ce⁴⁺ and Th⁴⁺ ions, J. Fluor. Chem., 2013, 156, 124–129.
45. R. Hoppe and K. M. Roedder, Fluorokomplexe des vierwertigen Cers, Z. Anorg. Allg. Chem., 1961, 313, 154–160.
46. A. Grzechnik, C. C. Underwood and J. W. Kolis, Twinned caesium cerium(IV) pentafluoride, Acta Crystallogr., Sect. B: Struct. Sci., 2014, 70, 112–113.
47. C. J. Windorff, A. T. Chemey, J. M. Sperling, B. E. Klamm and T. E. Albrecht-Schmitt, Examination of Molten Salt Reactor Relevant Elements Using Hydrothermal Synthesis, Inorg. Chem., 2020, 59, 4176–4180.
48. C. C. Underwood, C. D. Mcmillen and J. W. Kolis, Hydrothermal Synthesis and Crystal Chemistry of Novel Fluorides with A₇B₆F₃₁ (A = Na, K, NH₄, Tl; B = Ce, Th) Compositions, J. Chem. Crystallogr., 2014, 44, 493–500.
49. R. R. Ryan, A. C. Larson and F. H. Kruse, Crystal Structure of Ammonium Hexafluorocerate(IV), (NH₄)₂CeF₆, Inorg. Chem., 1969, 8, 33–36.
50. S. J. Patwe, B. N. Wani, U. R. K. Rao and K. S. Venkateswarlu, Synthesis and thermal study of tris(ammonium) hexafluoro metallates(III) of some rare earths, Can. J. Chem., 1989, 67, 1815–1818.
51. L. A. Zemnukhova, A. A. Udovenko, N. V. Makarenko, S. I. Kuznetsov and T. A. Babushkina, Crystal structure and Sb NQR Parameters of ammonium tridecafluorotetraantimonate(III) NH₄Sb₄F₁₃, J. Struct. Chem., 2017, 58, 694–699.
52. A. A. Udovenko, L. A. Zemnukhova, Y. E. Gorbunova, Y. N. Mikhailov and R. L. Davidovich, Crystal Structure of Thallium Tridecafluorotetraantimonate(III) TlSb₄F₁₃, Russ. J. Coord. Chem., 2003, 29, 310–311.
53. J. Yeon, M. D. Smith, J. Tapp, A. Möller and H. C. zur Loye, Mild Hydrothermal Crystal Growth, Structure, and Magnetic Properties of Ternary U(IV) Containing Fluorides: LiUF₅, KU₂F₉, K₇U₆F₃₁, RbUF₅, RbU₂F₉, and RbU₃F₁₃, Inorg. Chem., 2014, 53, 6289–6298.
54. H. Abazli, A. Cousson, A. Tabuteau and M. Pages, Fluorure d'Ammonium et d'Uranium(IV): NH₄U₃F₁₃, Acta Crystallogr., Sect. B: Struct. Crystallogr. Cryst. Chem., 1980, 36, 2765–2766.
55. C. C. Underwood, M. Mann, C. D. McMillen and J. W. Kolis, Hydrothermal Descriptive Chemistry and Single Crystal Structure Determination of Cesium and Rubidium Thorium Fluorides, Inorg. Chem., 2011, 50, 11825–11831.
56. J. H. Wu, C. L. Hu, Y. F. Li, J. G. Mao and F. Kong, [(C₅H₆N₂)₂H](Sb₄F₁₃): a polyfluoroantimonite with a strong second harmonic generation effect, Chem. Sci., 2024, 15, 8071–8079.
57. Q. Wang, J. X. Ren, D. Wang, L. L. Cao, X. H. Dong, L. Huang, D. J. Gao and G. H. Zou, Low temperature molten salt synthesis of noncentrosymmetric (NH₄)₃SbF₃(NO₃)₃ and centrosymmetric (NH₄)₃SbF₄(NO₃)₂, Inorg. Chem. Front., 2023, 10, 2107–2114.
58. Q. Wu, C. Yang, X. Liu, J. Ma, F. Liang and Y. S. Du, Dimensionality reduction made high-performance mid-infrared nonlinear halide crystal, Mater. Today Phys., 2021, 21, 100569.
59. C. Wu, T. H. Wu, X. X. Jiang, Z. J. Wang, H. Y. Sha, L. Lin, Z. S. Lin, Z. P. Huang, X. F. Long, M. G. Humphrey and C. Zhang, Large Second-Harmonic Response and Giant Birefringence of CeF₂(SO₄) Induced by Highly Polarizable Polyhedra, J. Am. Chem. Soc., 2021, 143, 4138–4142.
60. T. H. Wu, X. X. Jiang, Y. R. Zhang, Z. J. Wang, H. Y. Sha, C. Wu, Z. S. Lin, Z. P. Huang, X. F. Long, M. G. Humphrey and C. Zhang, From CeF₂(SO₄)·H₂O to Ce(IO₃)₂(SO₄): Defluorinated Homovalent Substitution for Strong Second-Harmonic-Generation Effect and Sufficient Birefringence, Chem. Mater., 2021, 33, 9317–9325.
61. T. H. Wu, X. X. Jiang, C. Wu, H. Y. Sha, Z. J. Wang, Z. S. Lin, Z. P. Huang, X. F. Long, M. G. Humphrey and C. Zhang, From Ce(IO₃)₄ to CeF₂(IO₃)₂: fluorinated homovalent substitution simultaneously enhances SHG response and bandgap for mid-infrared nonlinear optics, J. Mater. Chem. C, 2021, 9, 8987–8993.
62. T. Abudouwufu, M. Zhang, S. C. Cheng, Z. H. Yang and S. L. Pan, Ce(IO₃)₂F₂·H₂O: The First Rare-Earth-Metal Iodate Fluoride with Large Second Harmonic Generation Response, Chem. – Eur. J., 2019, 25, 1221–1226.
63. T. H. Wu, X. X. Jiang, C. Wu, Z. S. Lin, Z. P. Huang, M. G. Humphrey and C. Zhang, Ce₃F₄(SO₄)₄: cationic framework assembly for designing polar nonlinear optical material through fluorination degree modulation, Inorg. Chem. Front., 2023, 10, 5270–5277.
64. X. Y. Zhang, X. H. Zhang, B. P. Yang and J. G. Mao, A new polar alkaline earth–rare earth iodate: Ba₂Ce(IO₃)₈(H₂O), Dalton Trans., 2023, 52, 4423–4428.
65. O. P. Grigorieva, T. B. Shatalova, A. N. Kuznetsov, P. S. Berdonosov, S. Yu. Stefanovich, K. A. Lyssenko and V. A. Dolgikh, New iodate fluoride Rb₂Ce(IO₃)₅F with nonlinear optical properties, Dalton Trans., 2024, 53, 7367–7375.
66. J. G. Bergman, D. S. Chemla, R. Fourcade and G. Mascherpa, Linear and nonlinear optical properties of Na₂SbF₅, J. Solid State Chem., 1978, 23, 187–190.
67. J. P. Perdew and M. Levy, Physical Content of the Exact Kohn-Sham Orbital Energies: Band Gaps and Derivative Discontinuities, Phys. Rev. Lett., 1983, 51, 1884–1887.
68. Y. Q. Wei, W. Xu, L. Huai, Y. L. Lv, W. L. Liu, S. P. Guo and R. L. Tang, From ZnF₂ to ZnF₂(H₂O)₄: Partial Substitution Achieves Structural Transformation and Nonlinear Optical Activity while Keeping Short Ultraviolet Cutoff Edge, Inorg. Chem., 2024, 63, 1714–1719.
69. M. Yan, C. L. Hu, R. L. Tang, W. D. Yao, W. L. Liu and S. P. Guo, KBa₃M₂F₁₄Cl (M = Zr, Hf): novel short-wavelength mixed metal halides with the largest second-harmonic generation responses contributed by mixed functional moieties, Chem. Sci., 2024, 15, 8500–8505.

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Footnotes

† Electronic supplementary information (ESI) available: Additional tables and figures. CCDC 2371443. For ESI and crystallographic data in CIF or other electronic format see DOI: https://doi.org/10.1039/d4qi02088j

‡ These authors contributed equally to this work.

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