Giant Optical Anisotropy in a Covalent Molybdenum Tellurite via Oxyanion Polymerization

Abstract Large birefringence is a crucial but hard‐to‐achieve optical parameter that is a necessity for birefringent crystals in practical applications involving modulation of the polarization of light in modern opto‐electronic areas. Herein, an oxyanion polymerization strategy that involves the combination of two different types of second‐order Jahn–Teller distorted units is employed to realize giant anisotropy in a covalent molybdenum tellurite. Mo(H2O)Te2O7 (MTO) exhibits a record birefringence value for an inorganic UV‐transparent oxide crystalline material of 0.528 @ 546 nm, which is also significantly larger than those of all commercial birefringent crystals. MTO has a UV absorption edge of 366 nm and displays a strong powder second‐harmonic generation response of 5.4 times that of KH2PO4. The dominant roles of the condensed polytellurite oxyanions [Te8O20]8− in combination with the [MoO6]6− polyhedra in achieving the giant birefringence in MTO are clarified by structural analysis and first‐principles calculations. The results suggest that polymerization of polarizability‐anisotropic oxyanions may unlock the promise of birefringent crystals with exceptional birefringence.


Introduction
Birefringent materials capable of modulating polarized light are of great importance in many fields of modern opto-electronic technology such as linear optical devices, fiber optic sensors, and advanced optical communication systems. [1,2]Several well-DOI: 10.1002/advs.2023066703e] Unfortunately, drawbacks, such as inadequate crystal quality due to defects and impurities in natural crystals, significant anisotropic thermal expansion in -BaB 2 O 4 , weak UV transmittance in YVO 4 , and the relatively low birefringence of LiNbO 3 , [3] have significantly restricted their applications in high-tech demands.New birefringent materials with strong optical anisotropy are consequently urgently required.
The key to achieve large birefringence lies with high packing density and the aligned arrangement of the structural units that possess large polarizability anisotropy in a crystal lattice. [11]Of the possible crystalline constitutions, large optical anisotropy can be achieved in inorganic oxides [12a] in which appropriate oxyanions as well as their connection modes are carefully selected.In the present study, we propose an oxyanion polymerization strategy, in which three types of polarizability-anisotropic structural units [8,9] are employed in the construction of a condensed structure to maximize the optical anisotropy and achieve a large birefringence.4b] Materials constructed solely from SOJT-active cations without introducing alkali/alkali-earth counter-cations are beneficial in the pursuit of an optically anisotropic structure, owing to the resultant high-density of the SOJT-active cations.12c] By following the strategy outlined above, we have found that a combination of polymerized tellurium anions and molybdenum polyhedra leads to a new covalent molybdenum tellurite Mo(H 2 O)Te 2 O 7 (MTO) that exhibits the largest birefringence for an inorganic UV-transparent oxide crystal (Δn = 0.528 @ 546 nm), even surpassing those of the commercial birefringent crystals YVO 4 and TiO 2 .Furthermore, a UV absorption edge of 366 nm and a strong powder second-harmonic generation (SHG) response of 5.4 × KH 2 PO 4 (KDP) are observed for noncentrosymmetric MTO.The role of the polymerized functional units in enhancing the linear and nonlinear optical responses has been clarified by crystal structure analysis and first-principles simulations.This study not only affords a new birefringent crystal that is potentially of use in practical optical device applications but also unveils a new perspective for the development of high-performance next-generation birefringent crystalline materials.

Results and Discussion
The title compound MTO was synthesized by a straightforward hydrothermal method, with a mixture of MoO 3 , TeO 2 , CeO 2 , HF, and deionized water at 230 °C.The structure was determined by single-crystal X-ray diffraction (details are provided in the Supporting Information) and the purity of MTO was confirmed by powder X-ray diffraction studies (Figure S1, Supporting Information).Its chemical composition was determined by energydispersive X-ray diffraction (Figure S2, Supporting Information), with the results matching well with the formula suggested by the single-crystal X-ray diffraction data.Thermogravimetric analysis of MTO over the temperature range of 30-800 °C under N 2 revealed that MTO is thermally stable at 240 °C (Figure S3, Supporting Information).When MTO was further heated, the weight loss over the temperature range 240-340 °C was 3.74%, corresponding to the removal of one H 2 O molecule (calculated value: 3.74%).No further weight loss was observed over the temperature range 340-800 °C.
UV-Vis-NIR transmittance measurement of block single crystals of MTO reveals an absorption edge of 366 nm (Figure S4, Supporting Information), corresponding to a bandgap of 3.39 eV.This value is slightly larger than those of other tellurite-based d 0 -TM optical crystals [13] such as Ag 2 Te 3 Mo 3 O 16 (2.85eV), [13a] -BaTeMo 2 O 9 (2.95 eV), [13b] Na 2 Te 3 Mo 3 O 16 (2.9510a] The Infrared (IR) spectrum of MTO was measured over the rangel 4000-400 cm −1 at room temperature, the assignments of the IR absorption peaks being listed in Figure S5, Supporting Information.The absorption bands observed between 935 and 888 cm −1 are assigned to the stretching vibrations of the [MoO 6 ] 6− units, those from 820 to 690 cm −1 are attributed to Te─O stretching vibrations, and the peaks between 600 and 400 cm −1 are derived from Te─O─Te vibrations.Characteristic absorption bands at 3363 and 1621 cm −1 confirm the presence of H 2 O molecules in MTO.
To quantify its strong optical anisotropy, a birefringence measurement was performed using a high-quality cuboid single crystal under a cross-polarizing microscope equipped with a Berek compensator at 546 nm. [16]Single-crystal X-ray diffraction was employed to determine the crystal planes for MTO; (110), (1 " 10), and (00 " 1) are clearly observed (Figure 2a).For the birefringence measurement on the (110) crystal plane, the optical path difference at 546 nm was determined to be 12.20 μm with a thickness of 23.116 μm (Figure 2b,d).The derived birefringence of MTO for the (110) crystal plane is 0.528 @ 546 nm according to the formula R = d × Δn, where R represents the optical path difference and d denotes the thickness.The same birefringence measurement on the (1 " 10) crystal plane was also performed (Figure 2c,e).Given the optical path difference of 14.12 μm and thickness of 26.810 μm, the birefringence of MTO on the (1 " 10) plane is 0.527 @ 546 nm, coinciding with the birefringence characteristics of a uniaxial crystal.The refractive indexes of MTO along different crystal axes were calculated using the CASTEP package (Figure S7, Supporting Information).MTO exhibits unusually strong op-tical anisotropy with a calculated birefringence of 0.35 @ 546 nm, smaller than the experimental value.4b] The unusually large birefringence of MTO can be definitively attributed to its 3D covalent framework, which consists of three types of polarizability-anisotropic structural units ([TeO x ] (x = 3, 4) and [MoO 6 ] 6− ) without conventional alkali/alkali-earth counter-ions.To investigate the optical anisotropic property contributions from the different structural units in MTO, a real-space atom cutting technique was utilized, the calculated contributions being listed in Table S5, Supporting Information.The contributions are mainly from the [TeO 3 ] 2− (40.5%) and [TeO 4 ] 4− (37.7%) units, rather than the [MoO 6 ] 6− (17.4%) units  (30.2°and 29.9°) (Table S6, Supporting Information) which has the largest reported birefringence value (Δn = 0.305 @ 404.7 nm) for an extant optical d 0 -TM tellurite.The [TeO x ] units in MTO are almost uniformly arranged in the ac plane, and a larger optical anisotropy can be anticipated for MTO compared to those of other d 0 -TM tellurites (e.g., -BaTeMo 2 O 9 , [10a] Cs 2 TeW 3 O 12 , [19] Table 1.Experimental birefringences and densities of lone-pair cations (n V −1 ) (×10 −3 /Å 3 ) for optical d 0 -TM tellurites.and CdTeMoO 6 ) [17b] as a result of the high-density of [TeO x ] units, as well as their favorable aligned arrangement.
In order to develop an in-depth understanding of the exceptional birefringence of MTO, theoretical calculations were performed using the CASTEP package.Electronic bandgap predictions by density functional theory (DFT) gave an indirect bandgap We also analyzed electron localization function (ELF) maps of MTO.The (001)-projected ELF map shows the synergy between the [TeO 3 ] 2− , [TeO 4 ] 4− , and [MoO 6 ] 6− units (Figure 3d).In stark contrast to the electron density around the Mo atoms, the electron localization around the Te atoms is highly asymmetric owing to its lone-pair electron, and so they make a significant contribution to the optical properties.The directions of the lone-pair electrons of the [TeO 3 ] 2− and [TeO 4 ] 4− units oppose and are almost parallel, viewed along the [100] direction (Figure 3e), thereby making a strongly positive contribution to the birefringence of MTO.
Motivated by the noncentrosymmetric structure of MTO, the powder SHG response was assayed by the Kurtz and Perry method.MTO exhibits an SHG response of about 5.4 times that of KDP at 1064 nm laser radiation (particle size range 105-150 μm) (Figure S9a, Supporting Information).The SHG intensity signal gradually increases with particle size and finally reaches a constant value (Figure S9b, Supporting Information), indicating the phase-matching behavior of MTO at 1064 nm.20d] The SHG coefficients d ij were calculated by the method of Lin et al. [21] The nonzero independent SHG coefficients (d 14 and d 15 ) under the restriction of Kleinman symmetry [22a] are as follows: d 14 = 4.28 pm V −1 and d 15 = − 2.34 pm V −1 (Table S5, Supporting Information).The calculated average SHG coefficient is slightly larger than the experimental result, which can be attributed to the fact that the SHG calculations are based on an optimized single-crystal structure that may generate a larger SHG effect.22b] Specifically, the [MoO 6 ] 6− octahedron in MTO displays a strong out-of-center distortion toward an edge along the C2 direction, and these [MoO 6 ] 6− octahedra stack uniformly within a unit cell (Figure S6c, Supporting Information).The spatial arrangement of the [MoO 6 ] 6− octahedra with large local microscopic polarizability is beneficial for the enhancement of the SHG response.Although the lone-pair electrons on the [TeO 3 ] 2− and [TeO 4 ] 4− units are arranged in almost opposing directions (Figure 1f), the superimposed microscopic polarizability of the [TeO 3 ] 2− and [TeO 4 ] 4− units (with significant microscopic polarizabilities) also contribute to the global effect.The microscopic second-order susceptibilities associated with the [MoO 6 ] 6− , [TeO 3 ] 2− , and [TeO 4 ] 4− units constructively reinforce, leading to a large optical nonlinearity, which is confirmed by the powder SHG measurements on the crystalline MTO.The origin of the SHG response was explored further via an SHG-weighted electron density analysis.The SHG-weighted electron clouds of d 14 are mainly located on the [TeO 3 ] 2− , [TeO 4 ] 4− , and [MoO 6 ] 6− units (Figure S10a,b, Supporting Information).The Mo-4d orbitals and to a lesser extent Te-5p orbitals make the most significant contributions to the SHG response in the unoccupied states, while in the occupied states, the nonbonding O-2p orbitals afford the primary contribution to the SHG response.The SHG contributions from all units were calculated using a real-space atom-cutting method, the [TeO 3 ] 2− , [TeO 4 ] 4− , and [MoO 6 ] 6− units making the dominant contributions to the largest coefficient d 14 and these units accounting for 39%, 28.7%, and 30.1% for MTO, respectively.These results indicate that the [TeO 3 ] 2− , [TeO 4 ] 4− , and [MoO 6 ] 6− units are the main contributors to the SHG response of MTO under the perturbation of ambient optoelectronic fields.

Conclusion
In summary, the new molybdate tellurite MTO was synthesized by an oxyanion polymerization strategy and found to exhibit a strong SHG response (≈5.4 × KDP) and a UV absorption edge (366 nm).Its excellent NLO properties are attributed to cooperative contributions from the [TeO x ] (x = 3, 4) and [MoO 6 ] 6− units.Polymerization of the SOJT polyhedra [Te 8 O 20 ] and [MoO 6 ] 6− results in a giant birefringence (0.528 @ 546 nm), which is the largest for an inorganic UV-transparent oxide crystal and exceeds those of commercial birefringent crystals.Theoretical calculations suggest that the remarkable linear optical properties of MTO are driven by a favorable ordered alignment of the high-density [TeO x ], as well as synergetic [MoO 6 ] 6− polyhedra.The study demonstrates that giant optical anisotropy can be achieved by a combination of polymerized tellurium anions and molybdenum polyhedra and, accordingly, provides an outstanding paradigm for the future development of high-performance birefringent crystalline materials.

Experimental Section
Synthesis: Molybdenum trioxide (MoO 3 , 99.5%, Xiya Reagent), tellurium dioxide (TeO 2 , 99.8%, Xiya Reagent), cerium dioxide (CeO 2 , 99.99%, Xiya Reagent), and hydrofluoric acid (HF, 40%, Tansoole Chemical Reagent) were commercially available and used as received without further purification (Caution: hydrofluoric acid is toxic and corrosive!It must be handled with extreme caution and appropriate protective equipment and training).A mixture of TeO 2 (0.319 g, 2 mmol), MoO 3 (0.144 g, 1 mmol), CeO 2 (0.103 g, 0.6 mmol), HF (0.2 mL), and deionized water (1 mL) was placed in a tightly sealed 23 mL autoclave equipped with a Teflon liner.The autoclave was heated at 230 °C for 72 h and then cooled slowly to room temperature at a rate of 4 °C h −1 .The product was collected by vacuum filtration, washed with deionized water, and then dried in the air.Block colorless crystals of MTO were isolated in a yield of 65% (based on Te) using a microscope.The reaction starting materials and stoichiometry are critical for the synthesis of MTO.When the amount of starting material CeO 2 is less than 0.5 mmol, MTO cannot be obtained.It is noteworthy that using a small amount of CeO 2 and HF is conducive to enhancing the yield of the target compound.The pH of the solution also plays a vital role in the synthesis of compound MTO, with acidic conditions favoring its formation.
Single-Crystal Structure Determination: A block crystal of MTO with dimensions of 0.14 × 0.08 × 0.07 mm 3 was selected for the single-crystal structure determination.The diffraction data collection was carried out on a Bruker D8 VENTURE CMOS X-ray source with Mo K radiation ( = 0.71073 Å) at 293(2) K. Data collection and reduction were performed using the APEX II software, and absorption corrections were implemented based on a multiscan-type model.The crystal structure was solved by direct methods and refined on F 2 by full-matrix least squares methods using the SHELXTL-97 software package. [23]All non-hydrogen atoms were refined with anisotropic displacement parameters.On the basis of the requirements of charge balance and bond valence calculations, O(1) was assigned as being in a water molecule.The absolute structure was examined for missing symmetry elements using PLATON, and none were found. [24]Crystal data and structure refinement information for MTO are summarized in Table S1, Supporting Information.Atomic coordinates and equivalent isotropic displacement parameters, as well as calculated bond valence sums (BVS), are given in Table S2, Supporting Information, while selected bond distances and angles are collected in Table S3, Supporting Information.BVS calculations of 3.93-3.97,6.39, and 1.73-2.30for Te, Mo, and O atoms, respectively, are consistent with the expected valences.Hydrogen-bonding interactions for MTO are listed in Table S4, Supporting Information.
Powder X-ray Diffraction: Powder XRD data for MTO were collected using a Bruker D8 Advance X-ray diffractometer equipped with Cu K radiation ( = 1.5418Å) with a 2 range of 5°-70°and a scan step width of 0.02°.
Energy-Dispersive X-ray Spectroscopy: Microprobe elemental analyses were performed using energy-dispersive X-ray spectroscopy (EDS) with a field-emission scanning electron microscope (Hitachi S-4800, Japan).
UV-vis Transmission Spectrum: The UV-vis transmittance spectrum was measured at room temperature with crystal samples.Data were collected on a PerkinElmer Lambda-950 UV/Vis/NIR spectrophotometer scanning in the range of 200-2500 nm.
Thermal Stability: A Netzsch STA 409 PC thermal analyzer was used to analyze the thermal stability of MTO.The sample was heated from 30 to 800 °C with a heating rate of 15 °C min −1 in nitrogen gas.
Birefringence Measurements: The birefringence of crystalline sample MTO was assessed with a polarizing microscope (ZEISS AXIO Scope.A1) equipped with a Berek compensator.The wavelength of the light source was 546 nm.The birefringence was calculated according to Equation ( 1) where ΔR denotes the optical path difference, Δn represents the birefringence, and T is the thickness of the crystal.The positive and negative rotation of compensation affords the relative retardation.To improve the accuracy of the birefringence measurement, a transparent cuboid MTO crystal was chosen for the study.
Second-Harmonic Generation: Measurements of the powder frequency-doubling effect were carried out by the method of Kurtz and Perry, [25] employing a Q-switched Nd:YAG laser at 1064 nm laser radiation.The crystal samples were ground and sieved into seven distinct particle size ranges (<26, 26-50, 50-74, 74-105, 105-150, 150-200,  200-280 μm), which were pressed into disks with a diameter of 6 mm that were placed between glass microscope slides and secured with tape in a 1 mm thick aluminum holder.Crystalline KH 2 PO 4 (KDP) was ground and sieved into the same particle size ranges (<26, 26-50,  50-74, 74-105, 105-150, 150-200, 200-280 μm) which were used as references.The intensities of the frequency-doubled output emitted from the crystalline samples were measured using a photomultiplier tube.
26b,c] The correlation-exchange terms in the Hamiltonian were described by the functional developed by PBE [26d] in the generalized gradient approximation (GGA) [26e] form.The optimized norm-conserving pseudopotentials [26f] were adopted to model the effective interaction between the valence electrons and atom cores, which allowed the choice of a relatively small plane-wave basis set without compromising the computational accuracy.A kinetic energy cutoff of 800 eV and dense Monkhorst-Pack [26g] k-point meshes spanning less than 0.015 Å 3 in the Brillouin zone were chosen.
Due to the discontinuity of exchange-correlation in the framework of standard DFT, the calculated bandgap was usually smaller than the experimental value, and so a scissor operator [27a] was used to shift the conduction bands to match the values.Based on the scissor-corrected electron band structure, the imaginary part of the dielectric constants can be calculated by the electron transition from the VBs to the CBs.27b] The refractive indices n and the birefringence Δn were thereby obtained.21a,27c] To gain insight into the contribution of the constituent groups to the SHG coefficient, SHG-weighted electron density and real-space atom-cutting analyses were performed.27c] [CCDC 2 286 015 contains the supplementary crystallographic data for this paper.These data can be obtained free of charge from The Cambridge Crystallographic Data Centre via www.ccdc.cam.ac.uk/data_request/cif .].

Figure 1 .
Figure 1.a) [TeO 3 ] 2− and [TeO 4 ] 4− units.b) [Te 8 O 20 ] 8− polytellurite anion in Mo(H 2 O)Te 2 O 7 .c) Linking mode of the [Te 8 O 20 ] 8− unit of Mo(H 2 O)Te 2 O 7 and eight adjacent units.d) View of the 12-membered-ring channel in Mo(H 2 O)Te 2 O 7 .e) Perspective view of the 3D covalent framework of Mo(H 2 O)Te 2 O 7 along the c-axis.Hydrogen atoms and hydrogen bonds are omitted for clarity.f) Arrangement of the [Te 8 O 20 ] 8− polytellurite anion in Mo(H 2 O)Te 2 O 7 .Purple crescents indicate the approximate position of lone-pair electrons.Up and left arrows indicate the direction of the minimum and maximum refractive indices along the c-axis and a-axis, respectively.
and the H 2 O molecules.The largest contribution comes from the [TeO 3 ] 2− and [TeO 4 ] 4− groups, demonstrating that introducing highly polymerized SOJT oxyanions, that is, the polytellurite oxyanion [Te 8 O 20 ] 8− , to modulate the structure and function of oxides can be a promising way to develop birefringent materials.To clearly demonstrate the influences of the polymerized SOJT oxyanions on the optical anisotropy from a structural perspective, we first calculated the density of the lone-pair electron cation Te 4+ in extant optical d 0 -TM tellurites (Figure3aand Table1).The density of the lone-pair electron cation Te 4+ in MTO (0.0108 Å −3 ) is the highest for an optical d 0 -TM tellurites, and this can be attributed to the presence of the polytellurite oxyanion [Te 8 O 20 ] 8− .Second, the arrangement of the [TeO x ] units in MTO was quantified from bond valence calculations.We define  as the angle between the direction of the [TeO x ] maximum component's dipole moment and the direction of the total dipole moment.In principle, the smaller this angle is, the more uniform the alignment of the lone-pair electron on [TeO x ] units will be.The angles  between the direction of the total dipole moment and the direction of the maximum component dipole moments for [TeO 3 ] 2− and [TeO 4 ] 4− are 23.6°and22.7°(Figure1f), respectively.These values are significantly smaller than those of -BaTeMo 2 O 9[10a]

Figure 3 .
Figure 3. a) Birefringence and density of the functional units for Mo(H 2 O)Te 2 O 7 , Cs 2 TeW 3 O 12 , CdTeMoO 6 , and -BaTeMo 2 O 9 .b) Birefringence and bandgap for Mo(H 2 O)Te 2 O 7 , and some representative UV-transparent optical materials with bandgaps in the range of 3.1 to 6.2 eV.c) Total density of states and partial density of states of Mo(H 2 O)Te 2 O 7 ; Fermi levels (dotted lines) located at zero.The insets are electron density maps of the VBM (lower) and CBM (upper) in the primitive cell for Mo(H 2 O)Te 2 O 7 .The isosurface value is set to 0.001 eV Å −3 .Red: oxygen; yellow: molybdenum; green: tellurium; gray: hydrogen.d) Sliced-plane of the ELF diagram for Mo(H 2 O)Te 2 O 7 along the [001] direction.e) ELF diagram associated with the polytellurite anion [Te 8 O 20 ] 8− along the [100] direction, in which asymmetric lobe-like isosurface (pink) near each Te 4+ center is observed.