[Sn₃OF]PO₄vs. [Sn₃F₃]PO₄: enhancing birefringence by breaking the R3 symmetry and realigning lone pairs

Abstract

Tin(II)-containing phosphates are promising candidates for designing and studying materials with enhanced birefringence. Herein, we present a novel compound [Sn₃OF]PO₄ that exhibits significant birefringence (Δn_obv. = 0.117 at 546 nm), a five-fold improvement compared to that of the related compound [Sn₃F₃]PO₄ discovered nearly 40 years ago. The remarkable enhancement in birefringence is primarily attributed to the anisotropic [SnO₃F]⁵⁻ structure building unit. By simple regulation of the F/O ratio, the undesirable R3 symmetry in [Sn₃F₃]PO₄ is disrupted. This regulation also realigns the lone pairs, resulting in substantial optical anisotropy.

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10th anniversary statement

Congratulations on the 10th anniversary of ICF! These 10 years of ICF coincide with the second decade of my personal research career. As a founding member of the ICF editorial board, I have been actively involved in the forums organized by ICF.

Over the past decade, my collaborator Li-Ming Wu and I at BNU have made significant progress in the field of inorganic solid-state chemistry. We have explored the design and synthesis of novel compounds, studied the relationship between properties and crystal structures (focusing primarily on nonlinear optical and thermoelectric properties), and found ways to modify and enhance these properties.

Thank you for being with me throughout this journey!

Introduction

Birefringence (Δn) is a phenomenon that manifests in anisotropic media, particularly in non-cubic crystals.^1–4 It reflects the optical anisotropy of a crystal, which is one of the essential properties of optoelectronic functional crystals. A crystal with an appropriate birefringence is a crucial component of all-solid-state lasers, as it can modulate the polarized light for a single wavelength laser output. In fact, the birefringence phenomenon originates from the structural anisotropy of crystals. Therefore, effective and significant approaches are employed for enhancing birefringence to increase the anisotropy of the structure building units and optimize the arrangement in the crystal structure.

At present, there are several main methods to increase birefringence.^5–8 Firstly, introducing anisotropic building units (ABUs) with large birefringence is an effective approach for designing birefringent crystals, such as [BO₃]³⁻, [NO₃]⁻, [CO₃]²⁻, [C₄O₄]²⁻, and [C₃N₃O₃]³⁻.^5,6 Secondly, to broaden the range of available ABUs, a novel approach has recently emerged: designing ABUs by encompassing diverse chemical bonds (ABUCBs), which has garnered interest among researchers.⁹ The incorporation of ABUCBs into the crystal structure is likely to induce anisotropy in both the crystal structure and the spatial electron distribution. The latest experimental advancements indicate, for instance, that the introduction of P–F or B–F bonds enhances microscopic polarization anisotropy and hyperpolarization, eventually resulting in improved macroscopic properties, such as Δn.^10–18 Thirdly, the utilization of stereochemically active lone pairs could effectively increase the structural anisotropy, leading to a substantial Δn enhancement.^19–23 For instance, cations such as Pb²⁺, Sn²⁺, Sb³⁺, and Bi³⁺, serving as coordination centres, constitute the ABUs. For example, BaSn₂(PO₄)₂ exhibits a high Δn_cal. of 0.071,¹⁹ while Sn₂B₅O₉Cl demonstrates a Δn_obv. of 0.168.²⁰

Tin-based phosphates are excellent candidates for studying crystals with large birefringence. For example, Sn₂PO₄I²⁴ exhibits the largest Δn_obv. of ≥0.664 at 546 nm among the reported borates and phosphates to date. However, the presence of Sn²⁺ with stereochemically active lone pairs does not always lead to an increase in Δn. In particular, in high-symmetry crystal structures, Δn values are typically very small, as observed in compounds like KSn₄(PO₄)₃ ²⁵ (R3c, 0.013), NaSn₄(PO₄)₃ ²⁶ (R3c, 0.005) and [Sn₃F₃]PO₄ ²⁷ (R3, 0.011).^9,28–30 In these compounds, the Sn²⁺ ions are located along the C3 or 3₁ axes, forming a highly symmetric ABU arrangement that does not exhibit large anisotropy. We consider that in Sn²⁺-containing phosphates, the orientation of lone pairs plays a crucial role in determining the birefringence. However, controlling this orientation remains a challenge.

Herein, we report a novel compound, [Sn₃OF]PO₄, obtained by a conventional hydrothermal synthesis method. Interestingly, this compound, together with [Sn₃F₃]PO₄ ²⁷ known for about 40 years, provides a compelling example demonstrating that a straightforward regulation of the F/O ratio leads to a remarkable five-time enhancement of Δn_obv. (0.117 vs. 0.027 at 546 nm). Furthermore, we delve deeper into how this simple regulation effectively disrupts the R3 high symmetry of the latter compound, causing all lone pairs to align consistently along the dielectric axis. As a result, a significant enhancement in birefringence is achieved. We believe that this strategy may offer new experimental guidelines for searching and designing effective birefringent crystals.

Experimental section

Synthesis of compounds

Reagents including NH₄HF₂ (Aladdin, 98%), CO(NH)₂ (Aladdin, 98%), SnF₂ (Bidepharm, 99%), H₃PO₄ (Aladdin, 99%), P₂O₅ (Aladdin, 99%) and B₂O₃ (Aladdin, 99.9%) were used as purchased.

Colourless block-like crystals of [Sn₃OF]PO₄ are obtained by hydrothermal synthesis. The raw materials, (NH₄)₂PO₃F, SnF₂ and B₂O₃, were well ground in a ratio of 1 : 2 : 4 and then put into PTFE pouches. The pouches were then enclosed in 1 mL autoclaves with PTFE inner linings, with addition of a little deionized water, and heated at 190 °C for 4 days. The pouches were cooled to room temperature at 0.5 °C min⁻¹. After cleaning with deionized water and alcohol, colorless block-like crystals were obtained. The yield of the [Sn₃OF]PO₄ product could not be calculated, because it is obtained by hydrothermal synthesis along with impurities, which cannot be separated.

The polycrystalline powder of [Sn₃OF]PO₄ is prepared by solid state synthesis. The raw materials, SnO, SnF₂ and P₂O₅, were well ground in a ratio of 5 : 1 : 1 and then loaded into a tidy silica tube (Φ 10 mm × 100 mm) washed with deionized water and dried at a high temperature to remove the impure phases, and then the tube was flame-sealed under 10⁻³ Pa. The tube was heated to 400 °C in 3 h and held at this temperature for 4 days. Afterwards, it was cooled slowly to 250 °C at a rate of 1.0 °C h⁻¹ and then cooled to room temperature quickly. Finally, the polycrystalline powder of [Sn₃OF]PO₄ is obtained and the yield is 100% without impurity.

In order to compare the birefringence and other optical performance, we have also synthesized [Sn₃F₃]PO₄ according to the literature,²⁷ and block-like colorless crystals and polycrystalline powders were obtained.

Single crystal X-ray diffraction and powder XRD analysis

A Bruker D8 Quest diffractometer with Mo Kα radiation (λ = 0.71073 Å) was used to collect the single-crystal X-ray diffraction (XRD) data at room temperature, and the data were integrated using the SAINT program.³¹ The direct methods and the SHELXTL system³² were used to solve and refine the crystal structure, respectively. All the atom positions were refined using full-matrix least-squares techniques. The purity of the sample was confirmed by powder XRD, which was performed on a Bruker Model D8 Advance diffractometer equipped with Cu Kα radiation at room temperature. The diffraction patterns were recorded with the 2θ range from 10 to 70°, the scanning step width was 0.02° and the scanning rate was 1 s per step. The simulated and experimental powder X-ray diffraction peaks of [Sn₃F₃]PO₄ and [Sn₃OF]PO₄ are consistent, ensuring the purity of the sample (Fig. S1†).

UV diffuse-reflectance spectroscopy

The UV-Vis-NIR diffuse reflectance spectra for [Sn₃F₃]PO₄ and [Sn₃OF]PO₄ were characterized using a Shimadzu UV-3600i Plus UV-Vis-NIR spectrophotometer at room temperature. The reflectance spectrum was transformed to absorbance using the Kubelka–Munk function.³³

Infrared (IR) spectroscopy

Infrared (IR) spectra were recorded on a Thermo Scientific Nicolet iS50 FT-IR spectrophotometer in the range from 500 to 2000 cm⁻¹ with a resolution of 1 cm⁻¹. The sample was mixed thoroughly with 500 mg of dried KBr.

Birefringence measurement

The refractive index differences of [Sn₃F₃]PO₄ and [Sn₃OF]PO₄ were characterized using a polarizing microscope (ZEISS Axis Scope. 5 pol) equipped with a Berek compensator. The average wavelength of the light source was 546 nm. The formula for calculating the birefringence is as follows:

R = |N_g − N_p| × d = Δn × d (1)

where R represents the optical path difference; N_g, N_p and Δn mean the refractive index of fast light, that of slow light, and the difference value of the refractive index, respectively; and d denotes the thickness of the crystal.

Thermal analysis

A NETZSCH STA 449F5 instrument was used to examine the thermal stability of [Sn₃F₃]PO₄ and [Sn₃OF]PO₄ under static N₂ conditions. The sample and reference (Al₂O₃) were encapsulated in a Pt crucible, which was heated up to 800 °C at a rate of 10 °C min⁻¹ and then cooled to room temperature.

DFT calculations

Density functional theory^34,35 (DFT) calculations on the electronic structures and linear optical properties of [Sn₃F₃]PO₄ and [Sn₃OF]PO₄ were carried out using the Vienna Ab initio Simulation (VASP) Package.^36,37 The projector augmented wave (PAW) method was used to treat the valence–core interactions. The 5s and 5p states of Sn atoms, the 3s and 3p states of P atoms, the 2s and 2p states of O atoms, and the 2s and 2p states of F atoms were treated as valence states. The kinetic energy cutoff of the plane wave basis was set to be 500 eV. The Perdew–Burke–Ernzerhof^38,39 (PBE) functional within the generalized gradient approximation (GGA) was chosen to account for exchange–correlation effects. The Brillouin zone was sampled using a Gamma-centered mesh with a minimum spacing of 0.4 Å⁻¹ between k points. The convergence criterion for self-consistent field (SCF) iterations and structural relaxation was set to be 10⁻⁶ and 10⁻⁵ eV, respectively. The frequency-dependent dielectric matrix was calculated using the summation-over-states approach, and then linear optical properties, including the refractive index n and the birefringence Δn, can be assessed accordingly. Recognizing the inherent underestimation of band gaps by GGA, a scissor value was applied to align calculated and experimental band gaps. The refractive indices along the crystallographic axes n_a, n_b and n_c, as well as n_x, n_y and n_z along the dielectric axes, were calculated using the ellipsoid formula, with the aid of included angles between the dielectric and crystallographic axes.

Results and discussion

Crystal structure description and comparison

[Sn₃OF]PO₄ is first reported herein and crystallizes in the monoclinic space group P2₁/c (no. 14), with a = 4.8865(2) Å, b = 11.4484(5) Å, c = 11.9947(5) Å, β = 97.286(1)°, V = 665.60(5) ų, and Z = 4 (Fig. 1 and Tables S1–S3†). Another related yet different compound established nearly 40 years ago,²⁷ [Sn₃F₃]PO₄, crystallizes in a higher symmetry trigonal space group R3 (no. 146), with a = 11.8537(3) Å, c = 4.6271(2) Å, V = 563.05 (4) ų, and Z = 3. Herein, the crystallographic asymmetric unit consists of one unique 9b site occupied by Sn, one unique 3a site occupied by P, one unique 9b site and one unique 3a site occupied by O and one unique 9b site occupied by F in [Sn₃F₃]PO₄, respectively. Because the P(1) atom is located on the triad axis, an independent P(1) and O(1) and O(2) atoms form a C₃ [PO₄]³⁻ tetrahedron. There are three same P(1)–O(1) bonds with a length of 1.523 Å. Meanwhile, a longer P(1)–O(2) bond with a length of 1.557 Å can be found along the triad axis. All the P–O bond lengths are within a reasonable range (Fig. S2†).

Fig. 1 The structures of [Sn₃F₃]PO₄ and [Sn₃OF]PO₄F. Tin: gray, phosphorus: dark blue, oxygen: red, fluorine: dusty blue, and [PO₄]³⁻ dusty blue. (a) The spiral chain [SnO₂F]³⁻_∞. (b) The 3D structure of [Sn₃F₃]PO₄. (c) The [Sn₃O₄F₆]⁸⁻ polyhedron with the attached [PO₄]³⁻. (d) The 3D structure of [Sn₃OF]PO₄F. (e) The [Sn₃O₅F]⁵⁻_∞ layer. (f) [Sn₃O₆F₂]⁸⁻.

In addition, there is one unique crystallographic Sn atom that coordinates with O(1), O(2) and two F(1) atoms to form a distorted [SnO₂F₂]⁴⁻ tetrahedron in [Sn₃F₃]PO₄ (Fig. 1c). In the [SnO₂F₂]⁴⁻ tetrahedron, the lengths of Sn–O bonds are 2.098 and 2.567 Å and Sn–F bonds are 2.058 and 2.264 Å within a reasonable bond length range. Furthermore, each [SnO₂F₂]⁴⁻ tetrahedron is linked with the adjacent one by a shared F atom to form a 3₁ counterclockwise spiral chain [SnO₂F]³⁻_∞ which is along the c direction (Fig. 1a). The spiral chains are connected by shared O atoms to form a 3D network structure, within which the [PO₄]³⁻ tetrahedra are incorporated. Observing this structure, a hole with a diameter of 2.35 Å can be found. However, it's smaller than the diameter 2.75 Å of a H₂O molecule reported in the literature,⁴⁰ and it's assumed that the H₂O molecule couldn't be filled in. This observation is in line with the experimental result that regardless of changing the experimental conditions, the crystalline hydrate of [Sn₃F₃]PO₄ can't be obtained.

Besides, the [Sn₃OF]PO₄ compound can be transformed from the [Sn₃F₃]PO₄ compound by substituting two F⁻ with one O²⁻. To be specific, the change in the crystal structure begins with the conversion from the [Sn₃O₄F₆]⁸⁻ polyhedron in [Sn₃F₃]PO₄ to the [Sn₃O₆F₂]⁸⁻ polyhedron in [Sn₃OF]PO₄. As shown in Fig. 1c, the three same [SnO₂F₂]⁴⁻ polyhedra in the [Sn₃F₃]PO₄ compound form a [Sn₃O₄F₆]⁸⁻ trimer by sharing the O(2) atom. Moreover, it is found that the [Sn₃O₄F₆]⁸⁻ polyhedron is similar to the [Sn₃O₆F₂]⁸⁻ polyhedron in the [Sn₃OF]PO₄ compound. Therefore, what can force the structure transformation? Actually, as illustrated in Fig. 1c and f, a [SnO₂F₂]⁴⁻ polyhedron remains and the other two [SnO₂F₂]⁴⁻ polyhedra rotate along the Sn(1)–O(2) bonds. The rotation ultimately leads to a change in the polyhedral structure from [Sn₃O₄F₆]⁸⁻ in [Sn₃F₃]PO₄ to [Sn₃O₆F₂]⁸⁻ in [Sn₃OF]PO₄. Then, through the substitution of O and F atoms, the transformation can be achieved.

Herein, [Sn₃O₆F₂]⁸⁻ as the Sn-centered structure framework unit forms a [Sn₃O₅F]⁵⁻_∞ 2D layer (Fig. 1e) through the edge-sharing O(1) atom along the b direction and the corner-sharing F(1) atom along the c direction. Linked with the [PO₄]³⁻ tetrahedra along the a direction, the adjacent layers are connected to form a 3D [Sn₃OF]PO₄ network structure (Fig. 1d). In [Sn₃OF]PO₄, each crystallographic symmetric unit consists of three unique 4e sites occupied by Sn, one unique 4e site occupied by P, five unique 4e sites occupied by O and one unique 4e site occupied by F. All the bonds are within a reasonable range, of which the Sn–O bond is from 2.067 Å to 2.740 Å, the Sn–F bond is from 2.259 Å to 2.283 Å and the P–O bond is from 1.532 Å to 1.559 Å (Fig. 1f and S2†).

Because of the transformation of the crystal structure from [Sn₃F₃]PO₄ to [Sn₃OF]PO₄, the space group changes from R3 to P2₁/c, that is to say, from a high symmetry to a low symmetry. What causes it? From Fig. 2a viewed along the ab plane, it can be observed that the [Sn₃F₃]PO₄ compound has two kinds of symmetric axes, C₃ and 3₁ axes. For instance, the [PO₄]³⁻ polyhedron is located on the C₃ axis, and the [SnO₂F]³⁻_∞ chain is parallel to the 3₁ axis. However, due to the abovementioned rotation (Sn(1)–O(2)) in Sn-centered structure framework units and the assistance from the O atom which results in asymmetric components from [Sn₃F₃]PO₄ to [Sn₃OF]PO₄, the higher symmetric 3₁ and C₃ axes are destroyed, resulting in a transformation from a high symmetry (R3) to a low symmetry (P2₁/c).

Fig. 2 (a) [Sn₃F₃]PO₄ viewed along the ab plane and the [001] projection of the symmetry elements of the space group R3. (b) [Sn₃OF]PO₄F viewed along the ac and bc planes and the [010] projection of the symmetry elements of the space group P2₁/c. (c and e) The orientation of Sn-based polyhedra in [Sn₃F₃]PO₄ and [Sn₃OF]PO₄F, respectively. (d and f) The calculated birefringence and the observed birefringence at 546 nm for [Sn₃F₃]PO₄ and [Sn₃OF]PO₄F, respectively.

Optical and thermal properties

The UV/Vis-NIR diffuse reflection spectrum was obtained and is shown in Fig. S3.† It presents the UV cutoff edges of [Sn₃F₃]PO₄ and [Sn₃OF]PO₄, which are 258 nm and 306 nm, respectively. The converted absorption pattern indicates that the corresponding band gaps of [Sn₃F₃]PO₄ and [Sn₃OF]PO₄ are 4.31 eV and 3.62 eV, respectively, and the distinction derives from that [Sn₃F₃]PO₄ has more F atoms that are more electronegative than the O atom.⁴¹

Combining the IR absorption spectrum in Fig. S4,† it could be indicated that 1058, 997, and 940 cm⁻¹ for [Sn₃F₃]PO₄ and 1039, 981, and 948 cm⁻¹ for [Sn₃OF]PO₄ are from the asymmetric stretching vibrations of [PO₄]³⁻ groups, while 586 and 555 cm⁻¹ for [Sn₃F₃]PO₄ and 610, 579, and 533 cm⁻¹ for [Sn₃OF]PO₄ are from the asymmetric bending vibrations of [PO₄]³⁻ groups. This demonstrates that there are [PO₄]³⁻ groups in the title compounds.

The second harmonic generation (SHG) signal of [Sn₃F₃]PO₄ at a 1064 nm light source with a different particle size is shown in Fig. S5.† The result illustrates that [Sn₃F₃]PO₄ is phase-matchable at 1064 nm and features a weak SHG response, about 0.3 × KDP. Besides, energy dispersive spectroscopy (EDS) confirmed the existence of Sn, P, O and F elements in both [Sn₃F₃]PO₄ and [Sn₃OF]PO₄ (Fig. S6†). The thermogravimetric analysis (TG) and differential scanning calorimetry (DSC) curves indicated that [Sn₃F₃]PO₄ and [Sn₃OF]PO₄ are relatively stable before 300 °C and gradually decompose after that (Fig. S7†).

In addition, for linear optical properties of [Sn₃F₃]PO₄ and [Sn₃OF]PO₄, according to crystal thicknesses d (38.6 and 31.0 μm, respectively) and delay values for full extinction R at 546 nm (1.06 and 3.62 μm, respectively) (Fig. S8†), the birefringences of [Sn₃F₃]PO₄ and [Sn₃OF]PO₄ are larger than 0.027 and 0.117 at 546 nm based on formula (1), respectively. The birefringence of [Sn₃OF]PO₄ exceeds that of many tin(II) phosphates, such as Sn₃(PO₄)₂ (0.052 at 1064 nm), Rb(Sn₃O)₂(PO₄)₃ (0.081 at 1064 nm), and NH₄(Sn₃O)₂(PO₄)₃ (0.082 at 1064 nm). Moreover, the calculated birefringences of [Sn₃F₃]PO₄ and [Sn₃OF]PO₄ are 0.025 and 0.104 at 546 nm, respectively, which are in good agreement with the experimental data (Fig. 2d and f). Furthermore, the birefringence of [Sn₃OF]PO₄ is almost five times that of [Sn₃F₃]PO₄. But why is the optical anisotropy so different for the title compounds that contain the same element and why is there such a large birefringence gain?

Origin of birefringence

Generally speaking, a rigid tetrahedron, such as [PO₄]³⁻, with small polarizability anisotropy contributes little to birefringence.^42–44 Hence, the optical anisotropy of [Sn₃F₃]PO₄ and [Sn₃OF]PO₄ mainly hinges on the geometry of the asymmetric Sn-centered polyhedron ([SnO₂F₂]⁴⁻ for [Sn₃F₃]PO₄ and [SnO₃F]⁵⁻ for [Sn₃OF]PO₄) with stereochemically active lone pairs as well as the orientation. The orientation of lone pairs is consistent with the direction from the center of the polyhedron ([SnO₂F₂]⁴⁻ in [Sn₃F₃]PO₄ and [SnO₃F]⁵⁻ in [Sn₃OF]PO₄) to the Sn atom (Fig. 2c and e).⁴⁵ In fact, optical anisotropy originates from the different contributions of stereochemically active lone pairs towards the dielectric axis. Large contribution differences often correspond to large optical anisotropy.

On the one hand, since the [Sn₃F₃]PO₄ compound crystallizes in the higher symmetric space group R3, there are angles of 59.3° between all the lone pairs in Sn-centered polyhedra and the c-axis in the unit cell (Fig. 2c). Then the orientation of the lone pairs in Sn-based polyhedra can be projected on the ac plane and perpendicular to the ac plane, respectively. It is speculated that if the angle is 45° between the lone pairs and the c-axis, it can result in minimum anisotropy because there are the two approximate contributions of stereochemically active lone pairs to the optical anisotropy along the ac plane and perpendicular to the ac plane. Consequently, the contributions of stereochemically active lone pairs of [SnO₂F₂]⁴⁻ in [Sn₃F₃]PO₄ to the optical anisotropy along the ac plane and perpendicular to the ac plane are 5.46 and 4.29, respectively (detailed calculations are provided in Table S4†). Therefore, it demonstrates that there is a little difference in the contribution, which results in small optical anisotropy.

On the other hand, [Sn₃OF]PO₄ belongs to a lower symmetry (P2₁/c), and the dielectric axes are shown in Fig. 2e. The contributions of three unique crystallographic Sn-based polyhedra in [Sn₃OF]PO₄ are different, as for [Sn(1)O₃F]⁵⁻: 0.56, 0.48, and 3.44, [Sn(2)O₃F]⁵⁻: 0.16, 3.44, and 0.60, and [Sn(3)O₃F]⁵⁻: 2.08, 2.24, and 2.20 along the dielectric axis (n_x, n_y, and n_z), respectively. Compared with Sn(3), [Sn(1)O₃F]⁵⁻ and [Sn(2)O₃F]⁵⁻ have a greater distinction in contributions on the three axes, and it could be inferred that Sn(1) and Sn(2) may have a greater effect on optical anisotropy. At the same time, the total contributions are 2.80, 6.16 and 6.24 along the dielectric axis (n_x, n_y, and n_z), respectively (detailed calculations are provided in Table S4†). This agrees well with the relationship among the calculated refractive indices n_x, n_y and n_z, where n_z and n_y are far larger than n_x. Hence, a relatively large difference in the contribution drives large optical anisotropy, agreeing with the experimental birefringence.

Additionally, considering the aligned cooperativity of the asymmetric Sn-centered polyhedron, defined (θ_i represents the i^th angle between the polyhedra; n represents the number of angles per unit),⁴⁵ it is observed that asymmetric Sn-centered polyhedra in [Sn₃OF]PO₄ have more aligned cooperativity than those in [Sn₃F₃]PO₄ (0.54 vs. 0.47) (detailed calculations are provided in Tables S4 and S5†).

Thus, it can be inferred that a large birefringence enhancement is achieved by breaking the symmetry with disadvantage for optical anisotropy and reconstructing the aligned arrangement of the lone pairs. Combined with the above view, the explanation is represented for KSn₄(PO₄)₃ (R3c, 0.013 at 1064 nm) and NaSn₄(PO₄)₃ (R3c, 0.005 at 1064 nm) with high symmetry and small birefringence. The reason is that [SnO₃]⁴⁻ polyhedra in the two isostructural compounds, Sn-centered structure framework units, are coincidentally located on the C3 and 3₁ axes, as shown in Fig. S9.† It results in a small distinction in contributions of optical anisotropy.

Theoretical calculations

Both the geometric configuration and electronic structure are significant factors affecting the optical properties. The partial density of states (PDOS) of [Sn₃F₃]PO₄ and [Sn₃OF]PO₄ are illustrated in Fig. 3(a) and (d), respectively. For both [Sn₃F₃]PO₄ and [Sn₃OF]PO₄, the CBM (Conduction Band Minimum) is mainly composed of the 5p states of Sn atoms, while the VBM (Valence Band Maximum) is mainly composed of the 5s states of Sn atoms and the 2p states of O atoms. However, the contribution of O-2p states around the VBM in [Sn₃OF]PO₄ is larger than that in [Sn₃F₃]PO₄. This is consistent with the larger band gap of [Sn₃F₃]PO₄ (band gaps calculated using PBE are shown in Fig. S10†). To deeply understand the bonding feature of [Sn₃F₃]PO₄ and [Sn₃OF]PO₄, the negative partial crystal orbital Hamiltonian population^46–48 (pCOHP) is presented in Fig. 3(b) and (e). Below the Fermi level, a partition of the valence states appears as antibonding states for both Sn–O and Sn–F bonds. However, the antibonding interactions in [Sn₃F₃]PO₄ are smaller than those in [Sn₃OF]PO₄. Thus, the Sn–O and Sn–F bonds in [Sn₃F₃]PO₄ are stronger than those in [Sn₃OF]PO₄. Furthermore, it can be visualized from the electron localization function (ELF) diagrams (Fig. 3c and f) that Sn²⁺ has an asymmetric cloud of lone pairs, indicating that both [Sn₃F₃]PO₄ and [Sn₃OF]PO₄ show considerable strength of lone pairs under the same conditions. Therefore, there is no obvious difference in the electronic structure compared to the large observed birefringence difference between [Sn₃F₃]PO₄ and [Sn₃OF]PO₄. Therefore, the effect of the electronic structure on birefringence is relatively small. Hence, it can be inferred that the geometries rather than electronic structures play an important role in contributing to the optical properties.

Fig. 3 (a and d) Partial density of states (PDOS), (b and e) negative crystal orbital Hamiltonian population (–pCOHP), and (c and f) electron localization function (ELF) diagrams of [Sn₃F₃]PO₄ and [Sn₃OF]PO₄, respectively.

Conclusions

In conclusion, a novel compound [Sn₃OF]PO₄ is discovered, exhibiting significant birefringence (Δn_obv. = 0.117 at 546 nm), a five-fold improvement compared to that of a related compound [Sn₃F₃]PO₄. The remarkable enhancement in birefringence is primarily attributed to the anisotropic [SnO₃F]⁵⁻ structure building unit. By simple regulation of the F/O ratio, the undesirable R3 symmetry in [Sn₃F₃]PO₄ is disrupted. This regulation also realigns the lone pairs, resulting in substantial optical anisotropy. These strategies for designing compounds and optimizing performance could serve as an experimental guideline for discovering and optimizing effective birefringent crystals.

Author contributions

Y. H. H., J. Y. G. and L. M. W. conceived, designed and performed all the experimental work. X. X. and J. Y. H. performed the theoretical calculations. Y. H. H. and L. C. wrote the draft paper. All the authors discussed the results and commented on the manuscript. All authors contributed to the general discussion.

Data availability

The data supporting this article have been included as part of the ESI.†

Crystallographic data have been deposited at CCDC 2332572 and 2334179 for [Sn₃OF]PO₄ and [Sn₃F₃]PO₄, respectively.†

Conflicts of interest

There are no conflicts to declare.

Acknowledgements

This work was supported by the National Natural Science Foundation of China (22205024 and 22193043), Start-up Funding from Beijing Normal University (310432105) and the National Key R&D Program of China (2022YFB3803902). This work was also supported by the Interdisciplinary Intelligence SuperComputer Center of Beijing Normal University, Zhuhai.

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Footnote

† Electronic supplementary information (ESI) available: Experimental sections, computational methods, crystallographic data tables, powder XRD patterns, and optical property measurements. CCDC 2332572 ([Sn₃OF]PO₄) and 2334179 ([Sn₃F₃]PO₄). For ESI and crystallographic data in CIF or other electronic format see DOI: https://doi.org/10.1039/d4qi01203h

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