Deep-ultraviolet nonlinear-optical crystals LiBePO₄ and BeP₂O₆ synthesized by ionic potential modulation towards uniform arrangement of PO₄ groups

Abstract

The uniform arrangement of functional groups is a key factor in improving nonlinear properties in nonlinear-optical (NLO) materials, but currently there is no feasible and guiding strategy to modulate the uniform arrangement. Herein, we first apply the ionic potential concept to deep-ultraviolet (DUV, λ < 200 nm) NLO phosphates for a uniform arrangement of PO₄ tetrahedral functional groups. Adopting Cs₄LiBe₄P₇O₂₄ with a non-uniform arrangement of PO₄ as a structural model, by removing low ionic potential Cs⁺ and Li⁺ successively, two DUV NLO crystals LiBePO₄ and BeP₂O₆ were synthesized. LiBePO₄ features a [Be₃P₃O₁₈] six-membered ring constructed by alternate connection of BeO₄ and PO₄, while BeP₂O₆ exhibits two kinds of [PO₃]_∞ helical chains bridged by BeO₄. Remarkably, the arrangement of the PO₄ in LiBePO₄ and BeP₂O₆ exhibits uniform evolution. As a result, LiBePO₄ exhibits an enhanced second-harmonic-generation (SHG) effect up to 4.3 times that of Cs₄LiBe₄P₇O₂₄, while BeP₂O₆ shows an even more enhanced SHG effect, reaching 7.0 that of Cs₄LiBe₄P₇O₂₄ (2.1 × KDP). Moreover, BeP₂O₆ exhibits a short DUV absorption edge below 175 nm and the shortest SHG phase-matching output wavelength down to 211 nm. The universality of the new ionic potential modulation strategy is supported through analyzing known NLO materials containing alkali/alkaline-earth metal cations.

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Introduction

The exploration of deep-ultraviolet (DUV, λ < 200 nm or band-gap > 6.2 eV) nonlinear-optical (NLO) crystals with large second-harmonic-generation (SHG) effects is of tremendous academic interest,^1,2 as a large SHG effect is beneficial for high laser frequency-conversion efficiency, which can be widely applied in a series of optoelectronic fields, e.g., material micromachining, generation of entangled photon pairs, photoelectron spectroscopy, etc.^3–6 In particular, those crystals with both a large SHG effect and short SHG phase-matching output wavelength (preferably in the short-wave UV (λ ≤ 266 nm), and even DUV region) are popular research areas because of essential applications in frontier technology. However, a large SHG effect and wide band-gap are naturally incompatible due to the fact that the SHG effect is inversely proportional to the band-gap in principle. Over the past few decades, a common strategy for achieving a large SHG effect has been to introduce SHG-active π-conjugated groups such as [BO₃] and [CO₃] to construct DUV NLO crystals, and this strategy has produced many crystals, such as KBe₂BO₃F₂ (KBBF),⁷ NH₄Be₂BO₃F₂,⁸ β-Rb₂Al₂B₂O₇,⁹ NH₄B₄O₆F,¹⁰ and LiZn(OH)CO₃.¹¹

Recent studies show that non-π-conjugated tetrahedral groups such as [SiO₄], [PO₄], and [SO₄] with large HOMO–LUMO gaps can achieve high transmittance in the DUV region, and a series of tetrahedral DUV NLO crystals were thus synthesized, e.g. Li₂SrSiO₄,¹² Rb₆Si₁₀O₂₃,¹³ Ba₃P₃O₁₀Cl,¹⁴ Cs₆Mg₆(PO₃)₁₈,¹⁵ RbNaMgP₂O₇,¹⁶ Ba₅P₆O₂₀,¹⁷ (NH₄)₂Na₃Li₉(SO₄)₇,¹⁸ etc. However, most of these DUV NLO crystals exhibit a small SHG effect because the constituent tetrahedral groups show nearly nonpolar high symmetry and therefore exhibit weak SHG activity. In order to improve the SHG performance, some strategies have been proposed, mainly including the introduction of (i) second-order Jahn–Teller effect d⁰ cations (e.g. Mo⁶⁺, Ti⁴⁺) or ns² lone-pair cations (e.g. Pb²⁺, Sn²⁺),^19–22 (ii) anisotropic tetrahedral groups involving partially substituted oxygen atoms (e.g. [BO_4−xF_x], [PO_4−xF_x], [SO_4−x(NH₂)_x]),^23–26 and (iii) π-conjugated groups (e.g. [BO₃]).^27,28 However, the strategies all face seemingly insurmountable difficulties, such as an evident red-shift of the optical absorption edge, low thermal stability or returning to π-conjugated-characteristic NLO materials. Notably, that alkali/alkaline-earth metal cations with large HOMO–LUMO gaps have been only thought of as counterions for charge balance in these acentric structures, and their electrostatic interactions with surrounding tetrahedral groups are always overlooked. However, the interaction could affect the arrangement of tetrahedral groups, while a uniform arrangement can drive the generation of a large SHG effect according to anionic group theory.

In 2020, we reported two isostructural DUV NLO crystals M₄LiBe₄P₇O₂₄ (M = Cs, Rb) by combining alkali and alkaline-earth metal cations. Unfortunately, both crystals exhibit a weak SHG effect (∼0.3 × KDP).²⁹ Structurally, the weak SHG effect is mainly caused by a non-uniform arrangement of PO₄ groups (Fig. S1†). Additionally, it is found that the characteristic differences between the three metal cations Cs⁺, Li⁺ and Be²⁺ in Cs₄LiBe₄P₇O₂₄ (as an example) are size and charge number. The influence of the size and charge number on the electrostatic interactions of the respective ions is consistent with the ionic potential concept. In this regard, we take Cs₄LiBe₄P₇O₂₄ as a structural model and put forward an ionic potential modulation strategy towards uniform arrangement of PO₄. By removing low ionic potential Cs⁺ and Li⁺, two NLO-active crystals LiBePO₄ and BeP₂O₆ were synthesized successively, and the arrangement of the PO₄ exhibits uniform evolution. An increased SHG effect from Cs₄LiBe₄P₇O₂₄ to LiBePO₄ to BeP₂O₆ is thus displayed. Notably, BeP₂O₆ exhibits a large SHG effect of 7.0 × Cs₄LiBe₄P₇O₂₄ (2.1 × KDP) and the shortest SHG phase-matching output down to the short-wave UV region of 211 nm. Furthermore, the universality of the ionic potential modulation strategy is supported through investigating known alkali/alkaline-earth metal NLO structures.

Experimental

Reagents

BeO (99.99%), NH₄H₂PO₄ (99.9%), Li₂CO₃ (99.99%), MoO₃ (99.9%) and Li₂MoO₄ (99.9%) were commercially available and used as received. Caution: due to the high toxicity of BeO upon inhalation, all experiments were performed with sufficient ventilation.

Synthesis

A polycrystalline sample of LiBePO₄ was synthesized by a solid-state reaction method. Stoichiometric amounts of Li₂CO₃, BeO, and NH₄H₂PO₄ were mixed, ground completely, put in a platinum crucible, and heated in a muffle furnace at 350 °C for 10 h. Then, the material was reground thoroughly, pressed into a pellet, and heated at 850 °C for 3d with several intermittent grindings.

Crystal growth

We used a high-temperature solution method to grow the crystals of LiBePO₄ and BeP₂O₆. For LiBePO₄, a mixture of LiBePO₄ polycrystalline powder (0.5 mmol, 0.055 g), MoO₃ (4 mmol, 0.576 g), and Li₂MoO₄ (3 mmol, 0.522 g) was melted at 850 °C, then quickly cooled to 750 °C and held for 10 h. Then, the melt was cooled to 550 °C at a rate of 3 °C h⁻¹ and finally cooled to 350 °C at a rate of 20 °C h⁻¹, and we switched off the furnace. Colorless millimeter-crystals were obtained after dissolving the material in water.

For BeP₂O₆, a mixture of Li₂CO₃ (0.5 mmol, 0.037 g), BeO (1 mmol, 0.025 g) and NH₄H₂PO₄ (3 mmol, 0.345 g) was melted at 850 °C and held for 12 h. Then, the melt was cooled down to 400 °C at a rate of 1 °C h⁻¹. Finally, the melt was cooled down to 350 °C at a rate of 10 °C h⁻¹, and we switched off the furnace. Colorless millimeter-crystals were obtained after dissolving the material in water.

Single-crystal X-ray diffraction (XRD)

Single-crystal XRD data for LiBePO₄ and BeP₂O₆ were collected at 293 K on a Bruker D8 Venture diffractometer equipped with a graphite monochromator using Mo K_α radiation (λ = 0.71073 Å). Empirical absorption correction using spherical harmonics was performed using the SCALE3 ABSPACK scaling algorithm. The structure was solved by direct methods with the program SHELXS and refined by the full-matrix least-squares program SHELXL.³⁰ The structure was carefully checked using the program PLATON and no higher symmetries were found.³¹ The details of relevant crystallographic data are summarized in Table 1. The atomic coordinates and equivalent isotropic displacement parameters are listed in Table S1.† The selected bond distances and angles are shown in Table S2.†

Table 1 Crystal data and structure refinements for LiBePO₄ and BeP₂O₆

a R1 = ∑||Fo|–|Fc||/∑|Fo|, and wR2 = [w(Fo^2−Fc^2)^2/w(Fo^2)^2]^1/2.
Empirical formula	LiBePO4	BeP2O6
Formula weight	221.84	166.95
Temperature/K	293(2) K	293(2) K
Crystal system	Monoclinic	Monoclinic
Space group	Cc	P21
a/Å	16.331(1)	7.084(2)
b/Å	9.151(1)	8.586(3)
c/Å	15.965(1)	14.092(7)
α/°	90	90
β/°	111.62(1)	94.06(3)
γ/°	90	90
Volume/Å^3	2218.34(9)	855.0(6)
Z	16	8
ρcalc/g cm^−3	2.117	2.594
μ/mm^−1	0.788	0.953
F(000)	1728	656
Goodness-of-fit on F^2	1.03	1.036
R1, wR2 [I ≥ 2 σ(I)]^a	0.0261, 0.0674	0.0328, 0.0793
R1, wR2 (all data)^a	0.0316, 0.0717	0.0381, 0.0823
Flack parameter	0.02(3)	−0.01(5)

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Powder X-ray diffraction (XRD)

Powder XRD data of LiBePO₄ and BeP₂O₆ were collected using a Rigaku MiniFlex600 powder diffractometer equipped with Cu K_α radiation (λ = 1.5418 Å) in the 2θ angular range of 5–80° with a scan step width of 0.01° at 293 K. These experimental XRD patterns were in good agreement with the calculated patterns (Fig. S2 and S3†).

Element analysis

Element analysis was performed by using a PerkinElmer Optima 8000 DV inductively coupled plasma optical emission spectrometer (ICP-OES). Two crystal samples were dissolved in perchloric acid at the boiling point for 0.5 h. ICP-OES measurements give molar ratios of 1.08(Li) : 0.95(Be) : 1.00(P) for LiBePO₄ and 1.00(Be) : 2.11(P) for BeP₂O₆, which are consistent with their formulae.

X-ray photoelectron spectroscopy (XPS)

The chemical states and surface compositions of LiBePO₄ and BeP₂O₆ were analyzed by a Thermo Scientific K-Alpha⁺ X-ray photoelectron spectrometer with a monochromatic Al K_α X-ray source (1486.6 eV) operating at 72 W (12 kV, 6 mA). All of the XPS spectra underwent background subtraction and were fitted using mixed Gaussian-Lorentzian peak shapes.

As seen in Fig. S4,† XPS spectra of LiBePO₄ and BeP₂O₆ demonstrate the presence of Li (for LiBePO₄), Be, P, and O (Fig. S4a and f†). For LiBePO₄, a peak is observed at 55.38 eV for Li 1s, ascribed to the Li(I) oxidation state (Fig. S4b†). The Be 1s XPS spectrum (Fig. S4c†) shows a peak at 113.50 eV, which is attributed to the Be(II) oxidation state. The peak at 133.46 eV (Fig. S4d†) corresponds to the P 2p binding energy for the +5 oxidation state. The O 1s XPS spectrum exhibits a peak at 531.54 eV (O²⁻) (Fig. S4e†). For BeP₂O₆, the Be 1s XPS spectrum (Fig. S4g†) shows a peak at 114.20 eV, which is attributed to the Be(II) oxidation state. The peak at 133.56 eV (Fig. S4h†) corresponds to the P 2p binding energy for the +5 oxidation state. The O 1s XPS spectrum exhibits a peak at 531.74 eV (O²⁻) (Fig. S4i†).

Thermal behavior

Thermogravimetry (TG) and differential scanning calorimetry (DSC) analysis of LiBePO₄ and BeP₂O₆ were carried out on a NETZSCH STA 449 F5 Jupiter simultaneous analysis system under flowing N₂. About 15 mg of polycrystalline samples of LiBePO₄ and BeP₂O₆ were separately placed in Pt crucibles, and heated from room temperature to 1300 °C (for LiBePO₄) or 1100 °C (for BeP₂O₆) at a rate of 10 °C min⁻¹ under a flowing N₂ atmosphere.

TG and DSC curves of LiBePO₄ and BeP₂O₆ (Fig. S5†) show that weight losses in the TG curves were not obviously observed up to 1300 °C for LiBePO₄ and 1100 °C for BeP₂O₆. An endothermic peak at 1263 °C in the DSC curve for LiBePO₄ was detected, while the endothermic peak of BeP₂O₆ was not observed until 1068 °C, indicating the excellent thermostability. Further, polycrystalline samples of LiBePO₄ and BeP₂O₆ were separately calcined at 1300 °C and 1100 °C for 0.5 h under an air atmosphere. Powder XRD of the residues (Fig. S2 and S3†) suggests that LiBePO₄ samples before and after melting are consistent, showing that it is a congruently melting compound, while BeP₂O₆ samples before and after melting are inconsistent. According to the powder XRD pattern of the residue, BeP₂O₆ after melting is transformed into another known polymorph BeP₂O₆ and an unknown phase (Fig. S3b†), demonstrating that BeP₂O₆ is an incongruently melting compound.

Infrared (IR) spectroscopy

Fourier transform infrared (FTIR) spectra of LiBePO₄ and BeP₂O₆ were recorded from KBr pellets in the range 4000–400 cm⁻¹ on a Nicolet Model 5DX spectrometer. As shown in Fig. S6,† the IR spectrum of LiBePO₄ indicates that the peak at 1055 cm⁻¹ is attributed to the P–O asymmetric stretching vibration of PO₄. The peaks at 789, 715, and 611 cm⁻¹ are attributed to the P–O symmetric stretching vibrations of PO₄. The peaks at 577 and 508 cm⁻¹ are attributed to the P–O bending vibrations of PO₄. The IR spectrum of BeP₂O₆ indicates that the peaks at 1287, 1174, 1109, 1030, and 995 cm⁻¹ are attributed to the P–O asymmetric stretching vibrations of PO₄. The peak at 735 cm⁻¹ is attributed to the P–O symmetric stretching vibration of PO₄. The peaks at 518 and 438 cm⁻¹ are attributed to the P–O bending vibrations of PO₄. The IR spectra further indicate the presence of P–O units of LiBePO₄ and BeP₂O₆.

SHG measurement

Powder SHG measurements of LiBePO₄ and BeP₂O₆ were performed by the Kurtz–Perry method at 298 K. The measurement was carried out using a Q-switched Nd:YAG solid-state laser at 1064 nm and 532 nm, and the intensity of the frequency-doubled output emitted from the samples was measured using a photomultiplier tube. Polycrystalline samples LiBePO₄ and BeP₂O₆ were sieved into a series of distinct size ranges: 20–40 μm, 40–60 μm, 60–80 μm, 80–120 μm, 120–150 μm, 150–200 μm, and 200–300 μm. Polycrystalline KH₂PO₄ (KDP) and β-BaB₂O₄ (BBO) with the same particle size ranges were used as references. The SHG signal intensity of the LiBePO₄/KDP and BeP₂O₆/KDP (or BBO) ratio was identified based on the same size (150–200 μm).

Optical transmission spectrum

Optical transmission spectra of LiBePO₄ and BeP₂O₆ were measured using a Shimadzu SolidSpec-3700 DUV spectrometer in the 175–800 nm region. Two polished single-crystals with sizes of 2.0 × 1.2 × 0.3 mm³ for LiBePO₄ and 1.8 × 1.1 × 0.3 mm³ for BeP₂O₆ were separately used to perform the measurements.

Birefringence measurement

Birefringences of LiBePO₄ and BeP₂O₆ were measured on a CNOPTEC cross-polarizing microscope BK-POLR with an LED light filter. The LED light source has an optical wavelength of 590 ± 3 nm. The birefringence was calculated by using the following equation: R = d × |N_e − N₀| = d × Δn, where R, d, and Δn represent the optical retardation, thickness of the crystal, and birefringence, respectively.

Interference colors of the selected LiBePO₄ and BeP₂O₆ single-crystal samples are second-order yellow and second-order green based on a Michel–Levy diagram, and complete extinction can be achieved (Fig. S7a and S7b†). The tested crystals have retardations (R) of 810 and 710 nm, with thicknesses (d) of 45.13 and 25.23 μm, respectively. Accordingly, the measured birefringences are 0.018 and 0.028 for LiBePO₄ and BeP₂O₆, respectively.

Bond-valence-sum (BVS) calculation

BVS calculations for LiBePO₄ and BeP₂O₆ were performed to further validate the structural model, and the bond valence sums were calculated using the formula V_i = ∑S_ij = ∑exp[(r₀ − r_ij)/B], where S_ij is the bond valence associated with the bond length r_ij, and r₀ and B (usually 0.37) are empirically determined parameters.

Computational method

Single-crystal structural data of LiBePO₄ and BeP₂O₆ were used for the theoretical calculations. The electronic structures and optical properties were calculated using a plane-wave pseudopotential method within density functional theory (DFT) implemented in the total energy code CASTEP.^32,33 Generalized gradient approximation (GGA) Perdew–Burke–Ernzerhof (PBE) was used as the exchange and correlation functional.³⁴ The norm-conserving pseudopotential was applied to present the core–electron interactions.³⁵ Li 2s¹, Be 2s², O 2s² 2p⁴, and p 3s² 2p³ orbital electrons were considered as valence electrons. A cutoff energy of 850 eV determined the number of plane waves included in the basis sets. Monkhorst–Pack k-point sampling of 2 × 1 × 4 was used to perform the numerical integration of the Brillouin zone. During the optical property calculations, about 540 empty bands were set to ensure the convergence of SHG coefficients. Birefringence is calculated by subtracting the minimum refractive index from the maximum refractive index. The theoretical birefringences of LiBePO₄ and BeP₂O₆ are 0.016 and 0.024, respectively, at 590 nm, which are close to the experimental results. The calculations of second-order NLO susceptibilities were based on length-gauge formalism within the independent particle approximation.^36,37

Results and discussion

Crystal structures

LiBePO₄ and BeP₂O₆ single-crystals were synthesized through high-temperature molten reactions, and both crystal structures were characterized by single-crystal XRD. LiBePO₄ crystallizes in acentric and polar monoclinic space group Cc (no. 9), and contains eight crystallographically independent Li atoms, eight Be atoms and eight PO₄ groups, all of which are localized on crystallographically general positions with site occupancies of 1. Basic tetrahedral BeO₄ and PO₄ show typical bond distances of 1.606(3)–1.645(3) Å for Be–O and 1.525(1)–1.542(1) Å for P–O bonds. The material features a [Be₃P₃O₁₈] six-membered ring constructed by alternate connection of BeO₄ and PO₄. The six-membered rings are fused by shared oxygen to generate [BePO₄]_∞ two-dimensional (2D) pseudo layers in the ac plane (Fig. 1a). The pseudo layers are interconnected through Be–O–P bonds to form a 3D structure with pores (Fig. 1b). It should be noted that c glide planes in the structure cause polarization cancellation along the b-axis and net polarization in the ac plane. Small four-coordinated Li⁺ fills in pores to balance charge (Fig. 1b). In comparison, in Cs₄LiBe₄P₇O₂₄, large high-coordinated Cs⁺ requires large coordination space that induces four-coordinated Li⁺ on large [LiBe₄P₇O₂₄] twelve-membered rings of framework layers (Fig. S1†).

Fig. 1 Crystal structures of LiBePO₄ and BeP₂O₆. LiBePO₄: (a) [BePO₄]_∞ 2D pseudo layer formed by [Be₃P₃O₁₈] six-membered rings. (b) 3D stacking of [BePO₄]_∞ pseudo layers viewed along the a-axis. BeP₂O₆: (c) two kinds of [PO₃]_∞ chains with 2₁ helices along the b-axis. (d) 3D stacking of [PO₃]_∞ chains bridged by BeO₄ viewed along the b-axis.

BeP₂O₆ crystallizes in acentric and polar monoclinic space group P2₁ (no. 4). There are four crystallographically independent Be atoms and eight PO₄ groups, all of which are localized on crystallographically general positions with Wyckoff letter 2a. These PO₄ by corner-sharing generate two kinds of [PO₃]_∞ helical chains with a 2₁ axis along the b-axis (Fig. 1c). Adjacent [PO₃]_∞ chains are bridged by BeO₄ to produce a 3D structure. Net polarization of the structure is along the b-axis, as deduced from its P2₁ space group. Viewed along the b-axis (Fig. 1d), two [PO₃]_∞ chains both exhibit almost uniform stacking. In all BeO₄ and PO₄ unis, Be–O (1.579(6)–1.633(6) Å) and P–O (1.434(4)–1.603(3) Å) bond lengths both vary in reasonable ranges. Validity of both structure models is checked through BVS calculations and XPS measurements, revealing their constituent elements in rational oxide states (Table S1 and Fig. S4†).

Ionic potential modulation model of PO₄ arrangement

Arrangement changes of the PO₄ from Cs₄LiBe₄P₇O₂₄ to LiBePO₄ to BeP₂O₆ are related to the respective counter-balance cations Cs⁺, Li⁺ and Be²⁺. The Pauling electronegativity of these elements increases in turn from Cs (0.79) to Li (0.98) to Be (1.57). In Cs₄LiBe₄P₇O₂₄, Cs⁺ has the strongest ionic bonding character and thus is regarded as the counter-balance cation of the structure, and the remaining ions Li⁺ and Be²⁺ mainly act as local charge balancing cations in the structure. Similarly, in LiBePO₄, Li⁺ is counter-balance cation of the structure and Be²⁺ mainly acts as a local charge balancing cation. The size and charge number are the main differences between these cations. Their effect on PO₄ arrangement is studied using an ionic potential modulation model. According to the equation φ = z/r (φ, ionic potential; z, ionic charge number; r, ionic radius), z values of Cs⁺, Li⁺ and Be²⁺ are 1, 1 and 2, respectively, and r values (effective ionic radii) of these cations in Cs₄LiBe₄P₇O₂₄, LiBePO₄ and BeP₂O₆ are 0.18, 0.059 and 0.027 nm, respectively. φ_Li⁺ and φ_Be²⁺ are calculated to be 16.95 and 74.07, 3.1 and 13.4 times greater, respectively, than 5.52 for φ_Cs⁺. The impacts of the alkali/alkaline-earth metal cations on the respective PO₄ groups are depicted in the radar maps in Fig. 2. As shown in Fig. 2, with increasing φ from φ_Cs⁺ to φ_Li⁺ to φ_Be²⁺, the arrangement of these PO₄ groups around the cations exhibits uniform evolution. The uniform evolution can bring the following advantages: (i) the number of PO₄ groups per unit volume increases, which is confirmed by calculating the packing density (ρ) of PO₄, showing that ρ_[PO4] increases from 1.2 × 10⁻² to 1.5 × 10⁻² to 1.9 × 10⁻² per ų; (ii) favorable superposition of microscopic hyperpolarizability of PO₄ that is beneficial for increasing the overall SHG effect is generated, and it is verified by calculating the dipole moment (μ) of PO₄, revealing that μ_[PO4] increases from 0, 0.7 × 10⁻³ to 4.5 × 10⁻³ Debye (D) Å⁻³. Essentially, ionic potential modulation is mainly due to electrostatic interactions between alkali/alkaline-earth metal cations and surrounding ions. The electrostatic interaction can be estimated using Coulomb's law based on a simple point-charge model, revealing that the electrostatic interactions between Li⁺ and P⁵⁺ in LiBePO₄ and between Be²⁺ and P⁵⁺ in BeP₂O₆ are 1.8 and 3.7 times that between Cs⁺ and P⁵⁺ in Cs₄LiBe₄P₇O₂₄ (average distances of Cs and P, Li and P, and Be and P are 3.99, 3.00 and 2.93 Å according to Fig. 2). In addition, within the same structure, the ionic potential concept remains effective and applicable. In Cs₄LiBe₄P₇O₂₄ and LiBePO₄, the arrangement uniformity of the PO₄ surrounding Cs⁺/Li⁺/Be²⁺ and Li⁺/Be²⁺ is improved in turn (Fig. S8 and S9†).

Fig. 2 Ionic potential (φ) modulation model of PO₄ arrangement. In the radar maps, the numbers and arrows represent the distance (Å) between the cations and dipole moment direction of PO₄. Only PO₄ tetrahedra are displayed for clarity.

SHG effect analysis

SHG effects based on the Kurtz–Perry method were measured at laser wavelengths 1064 and 532 nm, showing that the SHG effect of LiBePO₄ is 1.3 × benchmark KDP (KH₂PO₄) at 1064 nm (Fig. 3a), and 4.3 times that of Cs₄LiBe₄P₇O₂₄. The SHG effect of BeP₂O₆ further increases to 2.1 × KDP (Fig. 3a), reaching 7.0 times that of Cs₄LiBe₄P₇O₂₄, and meanwhile, BeP₂O₆ exhibits an SHG effect of 0.4 × BBO (β-BaB₂O₄) at 532 nm (Fig. 3c). The large SHG effect of BeP₂O₆ is compared not only with reported non-π-conjugated tetrahedral DUV NLO materials, such as Ba₂NaClP₂O₇ (0.9 × KDP),³⁸ KMg(H₂O)PO₄ (1.14 × KDP),³⁹ BPO₄ (2.0 × KDP),⁴⁰ Li₂SrSiO₄ (0.3 × KDP),¹³ Li₃AlSiO₅ (0.8 × KDP),⁴¹ Li₂NaNH₄(SO₄)₂ (1.1 × KDP),¹⁸ and LiKSO₄ (1.2× KDP),⁴² but also with well-known π-conjugated NLO materials, such as KBBF (1.21 × KDP),⁷ LiB₃O₅ (LBO, 3.0 × KDP),⁴³ CsB₃O₅ (CBO, 2.7 × KDP),⁴⁴ and CsLiB₆O₁₀ (CLBO, 2.2 × KDP).⁴⁵ Furthermore, LiBePO₄ reveals phase-matchable behavior in the visible region, whereas BeP₂O₆ exhibits phase-matchable behavior in both visible and ultraviolet (UV) regions, as shown by the increasing SHG intensities with increasing particle size (Fig. 3b and d).

Fig. 3 (a) SHG signals and (b) SHG signal intensity vs. particle size for LiBePO₄, BeP₂O₆, and benchmarks Cs₄LiBe₄P₇O₂₄ and KDP at 1064 nm. (c) SHG signals and (d) SHG signal intensity vs. particle size for BeP₂O₆ and benchmark BBO at 532 nm.

The phase-matching capacities of both structures are studied through experimental and theoretical methods. Calculated refractive index dispersions (Fig. 4a and b) reveal that the shortest SHG phase-matching output wavelengths are 317 and 211 nm for LiBePO₄ and BeP₂O₆, respectively, consistent with the corresponding experimental observations of phase-matching in the 1064-to-532 nm and 532-to-266 nm second-harmonic processes (Fig. 3b and d), confirming their phase-matching capacity. In addition, calculated birefringences of LiBePO₄ and BeP₂O₆ are 0.016 and 0.024, respectively, at 590 nm, and experimental birefringences determined using a cross-polarizing microscope at 590 ± 3 nm through an optical retardation method show that the tested birefringences are 0.018 for LiBePO₄ and 0.028 for BeP₂O₆ (Fig. S7†), in general agreement with the calculated results. Remarkably, the shortest SHG phase-matching output of BeP₂O₆ is down to the short-wave UV region of 211 nm, much better than non-phase-matching BPO₄, 450 nm of LiCs₂PO₄,⁴⁶ and well-known borates LBO (277 nm), CBO (273 nm) and CLBO (236 nm) (Table 2). BeP₂O₆ may be applied to frequency quadruple and quintuple the Nd:YAG laser output, producing 266 nm and 213 nm coherent light. In addition, optical transmission spectra show that LiBePO₄ and BeP₂O₆ both have short DUV absorption edges below 175 nm (Fig. 4c and d), comparable to that of Cs₄LiBe₄P₇O₂₄ (<190 nm).²⁹

Fig. 4 Refractive index dispersions of (a) LiBePO₄ and (b) BeP₂O₆. Single-crystal transmission spectra of (c) LiBePO₄ and (d) BeP₂O₆, with single-crystal photographs in the insets.

Table 2 Comparison of DUV absorption edges (λ_DUV), SHG effects at 1064 nm, and SHG phase-matching cutoff wavelengths (λ_PM) of well-known crystals

Material	λDUV (nm)	SHG effect (×KDP)	λPM (nm)
BPO4	134	2.0	Nonphase-matching
LiCs2PO4	174	2.6	450
LBO	158	3.0	277
CBO	167	2.7	273
CLBO	180	2.2	236
BeP2O6	<175	2.1	211

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Theoretical calculation

To gain deep insight into the origin of the good optical properties of LiBePO₄ and BeP₂O₆, first-principles calculations were implemented. Band structures calculated using the hybrid exchange–correlation functional of HSE06 (Fig. 5a and c) indicate that LiBePO₄ and BeP₂O₆ have very wide band-gaps of 8.33 and 8.20 eV, corresponding to DUV absorption edges of 149 and 151 nm, respectively, in good support of the experimental results. Partial densities of states (Fig. 5b and d) show that the upper part of the valence-band consists mainly of P 3p, O 2p, and Be 2p electronic states, and the bottom part of the conduction-band is mainly composed of unoccupied P 3s 3p, O 2p, Be 2s 2p, and Li 2s (for LiBePO₄) orbitals, revealing that all the chemical bonding interactions (including P–O, Be–O and Li–O) make contributions to the optical transitions of LiBePO₄ and BeP₂O₆.

Fig. 5 Electronic band structures of (a) LiBePO₄ and (c) BeP₂O₆. Density of states diagrams for (b) LiBePO₄ and (d) BeP₂O₆.

Calculated SHG coefficients show that the maximum tensors d₁₅ for LiBePO₄ and d₂₃ for BeP₂O₆ are 0.42 and 0.57 pm V⁻¹, respectively, close to experimentally measured SHG effects. To intuitively determine the main SHG-contributed electronic orbitals, SHG-density analyses for both maximum SHG tensors were carried out. For LiBePO₄ and BeP₂O₆, in the valence-band (Fig. 6a and c), the dominant SHG-contributed orbitals are O 2p nonbonding states, while in the conduction-band (Fig. 6b and d), unoccupied P 3s 3p and O 2p orbitals have a crucial impact on SHG effects, while the unoccupied Be 2p orbitals make a small contribution to the SHG effects. Furthermore, SHG contributions of different groups are summed based on the SHG-density analysis results shown in Fig. 6e, showing that PO₄ is in both cases the leading group producing SHG effects, accounting for 62.1% in LiBePO₄ and 83.4% in BeP₂O₆. The BeO₄ groups make small contributions to the SHG effects, accounting for 25.6% in LiBePO₄ and 16.6% in BeP₂O₆, respectively. The applicability of the ionic potential modulation strategy is investigated for known NLO structures containing alkali/alkaline-earth metal cations (Fig. 6f and Table S3†), and it is found that the strategy can be applied to these NLO materials well.

Fig. 6 SHG density maps of the valence band (VB) and conduction band (CB) for (a and b) LiBePO₄ and (c and d) BeP₂O₆. (e) SHG contribution of different groups in LiBePO₄ and BeP₂O₆. (f) Applicability of the ionic potential modulation strategy in known alkali/alkaline-earth metal NLO materials. Blue represents cations with low ionic potential and their corresponding compounds, and red represents cations with high ionic potential and their corresponding compounds. ^a Represents the SHG effect based on benchmark AGS (AgGaS₂).

Conclusions

An ionic potential modulation strategy is applied to tetrahedral DUV NLO phosphates that have long suffered from a weak SHG effect. Taking Cs₄LiBe₄P₇O₂₄ as a structural prototype, through continuous removal of low ionic potential Cs⁺ and Li⁺, two DUV NLO crystals LiBePO₄ and BeP₂O₆ were successfully synthesized. LiBePO₄ exhibits a 3D structure constructed from [Be₃P₃O₁₈] six-membered rings composed of alternate BeO₄ and PO₄, while BeP₂O₆ features a 3D structure constructed from two kinds of [PO₃]_∞ helical chains bridged by BeO₄. Notably, the arrangement of PO₄ in LiBePO₄ and BeP₂O₆ exhibits uniform evolution. Thus, an increased SHG effect from Cs₄LiBe₄P₇O₂₄ to LiBePO₄ to BeP₂O₆ is generated. Furthermore, BeP₂O₆ exhibits a large SHG effect of 7.0 × Cs₄LiBe₄P₇O₂₄ (2.1 × KDP), the shortest SHG phase-matching output down to the short-wave UV region of 211 nm, and a short DUV absorption edge below 175 nm, showing that BeP₂O₆ is a potential short-wave UV NLO crystal. Moreover, the new modulation strategy is universally supported through known alkali/alkaline-earth metal NLO materials. This work may not only be used to update the possible roles of alkali/alkaline-earth metal cations in NLO materials but also provide new opportunities for the precise design of material structures and properties.

Author contributions

All authors have given approval to the final version of the manuscript.

Data availability

The detailed crystallographic information and ESI figures and tables can be found in the ESI.† Crystallographic data are available via the Cambridge Crystallographic Data Centre (CCDC): 2384142 and 2384141 for LiBePO₄ and BeP₂O₆. The data supporting this article have been included as part of the ESI.†

Conflicts of interest

There are no conflicts to declare.

Acknowledgements

This work was supported by the NSFC (21971155, 5207021329), Fundamental Research Program of Shanxi Province (202303021221153).

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Footnote

† Electronic supplementary information (ESI) available: Crystallographic data, XPS spectra, powder XRD, TG and DSC curves, IR spectra. CCDC 2384142 and 2384141 for LiBePO₄ and BeP₂O₆. For ESI and crystallographic data in CIF or other electronic format see DOI: https://doi.org/10.1039/d5qi00779h

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