Structural Features of Y2O2SO4 via DFT Calculations of Electronic and Vibrational Properties

The traditional way for determination of molecular groups structure in crystals is the X-Ray diffraction analysis and it is based on an estimation of the interatomic distances. Here, we report the analysis of structural units in Y2O2SO4 using density functional theory calculations of electronic properties, lattice dynamics and experimental vibrational spectroscopy. The Y2O2SO4 powder was successfully synthesized by decomposition of Y2(SO4)3 at high temperature. According to the electronic band structure calculations, yttrium oxysulfate is a dielectric material. The difference between the oxygen–sulfur and oxygen–yttrium bond nature in Y2O2OS4 was shown based on partial density of states calculations. Vibrational modes of sulfur ions and [Y2O22+] chains were obtained theoretically and corresponding spectral lines observed in experimental Infrared and Raman spectra.

Since the chemical formula contains trivalent rare-earth (Re 3+ ) ions, the common way for doping is a partial substitution of Re 3+ with Ln 3+ (Ln 3+ = Ce, Pr, Nd, Sm, Eu, Tb, Dy, Ho, Er, Tm, Yb, Lu) ions. Recently, Re 2 O 2 SO 4 oxysulfate was studied as a host for optical materials and it has been shown that the luminescent efficiency of Re 2 O 2 SO 4 :Ln 3+ phosphorous depends on the size and shape of particles [17], for example, the Eu 3+ doped nanosized Y 2 O 2 SO 4 samples (18-89 nm, C2/c) show the quantum efficiencies ranging from η = 44-70% [18]. The 2-3 µm in diameter Y 2 O 2 SO 4 :Eu 3+ was synthesized using a urea-based homogeneous precipitation technique based on a urea-ammonium sulfate system [19]. The Y 2 O 2 SO 4 :Tb 3+ microflakes were prepared via an electrospinning process followed by calcination treatment [20]. The biomolecule-assisted hydrothermal route followed by calcination was used for the production of yttrium oxysulfate hollow spheres doped with Yb 3+ and Eu 3+ or Er 3+ [21].
Traditionally, the search of nonlinear optical (NLO) materials focused on borate systems [22], on the other hand, several NLO sulfate crystals were synthesized in recent years [23][24][25][26][27]. As to the Re 2 O 2 SO 4 oxysulfates, the crystal structure of Nd 2 O 2 SO 4 [28] was solved in the non-centrosymmetric (I222) space group and thus this class of compounds can be a candidate for NLO materials. On the other hand, the crystal structure of Sm 2 O 2 SO 4 [29] and Eu 2 O 2 SO 4 [30] was solved in the centrosymmetric (C2/c) space group. 2 of 9 Determination of non-centrosymmetric or centrosymmetric space groups in Re 2 O 2 SO 4 :Ln 3+ can be easily done with Infrared spectroscopy as has been shown in work by Yu.G. Denisenko [30]. The focus of such study must be pointed to the presence of the peak related to the symmetric stretching vibration of SO 4 tetrahedra in case of the C2/c space group. However, it should be noted that while the interpretation of the spectral peaks related to vibrations of sulfate groups is beyond doubt, vibrations of rare-earth ions were explained as just Y-O vibrations and detailed description of these vibrations is completely absent in the literature. The spectral bands at 1220, 1130, 1060, 1000, 880, 660 and 610 cm −1 were observed in Infrared spectra of Y 2 O 2 SO 4 :Eu 3+ and attributed to vibrations of SO 4 2− ions, while the peak at 530 cm −1 was described as Y-O bond vibration [19]. In nanometer-sized Y 2 O 2 SO 4 :Eu 3+ , the Y-O bond peak was found at 560 cm −1 [31]. In Infrared spectra of Y 2 O 2 SO 4 doped with Tb 3+ ions, characteristic spectral bands related to sulfate vibrations and the Y-O stretching (at 539 cm −1 ) were observed [20]. Spectral peak related to the stretching vibrations of O-Y was found at 545 cm −1 in Y 2 O 2 SO 4 [32]. The spectral bands in Y 2 O 2 SO 4 nanoparticles at 1064, 1122, 133 and 664 have been attributed to SO 4 2-ions while bands at 621 and 534 to Y-O vibrations [33]. There is no information at all about Raman spectra.
In this paper, we report the synthesis of Y

Synthesis and Experimental Details
Yttrium oxysulfate was obtained by decomposition of yttrium sulfate Y 2 (SO 4 ) 3 (99.99%, Novosibirsk Rare Metals Plant, Novosibirsk, Russia) in an argon atmosphere at a temperature of 700 • C. A schematic of an installation for carrying out high temperature decomposition processes is shown in Figure 1. Argon of high purity 99.9999% was used to create an inert atmosphere. Temperature control and regulation was carried out using a microprocessor controller ("Thermokeramika", Moscow, Russia). Temperature in the reaction zone was measured with a chromel-alumel thermocouple. A weighed portion of dry Y 2 (SO 4 ) 3 was placed in a quartz reactor and purged with argon for 30 min at a rate of 6 L/h. After that, the reactor was placed in a heated vertical furnace and held for 10 h. After the completion of the reduction process, the reactor was removed from the furnace and cooled to room temperature. The decomposition recovery process is described by the equation: Determination of non-centrosymmetric or centrosymmetric space groups in Re2O2SO4:Ln 3+ can be easily done with Infrared spectroscopy as has been shown in work by Yu.G. Denisenko [30]. The focus of such study must be pointed to the presence of the peak related to the symmetric stretching vibration of SO4 tetrahedra in case of the C2/c space group. However, it should be noted that while the interpretation of the spectral peaks related to vibrations of sulfate groups is beyond doubt, vibrations of rare-earth ions were explained as just Y-O vibrations and detailed description of these vibrations is completely absent in the literature. The spectral bands at 1220, 1130, 1060, 1000, 880, 660 and 610 cm −1 were observed in Infrared spectra of Y2O2SO4:Eu 3+ and attributed to vibrations of SO4 2− ions, while the peak at 530 cm −1 was described as Y-O bond vibration [19]. In nanometer-sized Y2O2SO4:Eu 3+ , the Y-O bond peak was found at 560 cm −1 [31]. In Infrared spectra of Y2O2SO4 doped with Tb 3+ ions, characteristic spectral bands related to sulfate vibrations and the Y-O stretching (at 539 cm −1 ) were observed [20]. Spectral peak related to the stretching vibrations of O-Y was found at 545 cm −1 in Y2O2SO4 [32]. The spectral bands in Y2O2SO4 nanoparticles at 1064, 1122, 133 and 664 have been attributed to SO4 2-ions while bands at 621 and 534 to Y-O vibrations [33]. There is no information at all about Raman spectra.
In this paper, we report the synthesis of Y2O2SO4, results of DFT (Density Functional Theory) calculations of electronic and vibrational properties and we demonstrated that spectral lines in Infrared and Raman spectra of Y2O2SO4 were associated with [SO4] 2− and [Y2O2 2+ ] structural units.

Synthesis and Experimental Details
Yttrium oxysulfate was obtained by decomposition of yttrium sulfate Y2(SO4)3 (99.99%, Novosibirsk Rare Metals Plant, Novosibirsk, Russia) in an argon atmosphere at a temperature of 700 °C. A schematic of an installation for carrying out high temperature decomposition processes is shown in Figure 1. Argon of high purity 99.9999% was used to create an inert atmosphere. Temperature control and regulation was carried out using a microprocessor controller ("Thermokeramika", Moscow, Russia). Temperature in the reaction zone was measured with a chromel-alumel thermocouple. A weighed portion of dry Y2(SO4)3 was placed in a quartz reactor and purged with argon for 30 min at a rate of 6 L/h. After that, the reactor was placed in a heated vertical furnace and held for 10 h. After the completion of the reduction process, the reactor was removed from the furnace and cooled to room temperature. The decomposition recovery process is described by the equation:  Fourier-transformed Infrared spectroscopy (IR) was carried out with the use of a Fourier Transform Infrared Spectrometer FSM 1201, (Infraspec Ltd., Borovliany, Minsk district, Belarus). The sample for the investigation was prepared in a tablet form with addition of annealed KBr. IR spectrum was recorded with spectral resolution 4 cm −1 . Raman spectrum was recorded using an i-Raman Plus spectrometer at a laser excitation wavelength of 785 nm and the spectral resolution was about 4 cm −1 . The Infrared as well as the Raman spectrum was obtained at room temperature.

Calculation Details
All the density functional theory calculations [34,35] were performed with the CASTEP code (version 19.1.1) [36]. The 4s 2 4p 6 4d 1 5s 2 , 3s 2 3p 4 and 2s 2 2p 4 valence electron configurations were used for Y, S and O, respectively. The local density approximation (LDA) based on the Perdew and Zunger parametrization [37] of the numerical results of Ceperley and Alder [38], and nonlocal exchange-correlation HSE06 functional [39] were used for calculation of electronic properties. The on-the-fly-generated norm-conserving pseudopotentials were used and the cutoff energy for the plane basis was chosen as 1150 eV. The convergence criteria for geometry optimization were set to 5.0 × 10 −4 eV/Å for maximal force and 0.01 GPa for maximal stress. The density functional perturbation theory (DFPT) (linear response method) [40] was used to perform the calculation of vibrational properties. Different k-point density [41] was checked for Monkhorst-Pack sampling [42] and it was found that the 6 × 6 × 3 k-point set is enough.  Table 1 and compared with experimental data from ICDD PDF 53-0168.

Results and Discussion
The Brillouin zone (BZ) of Y 2 O 2 SO 4 and electronic band structure obtained using the local density approximation are shown in Figure 3. The path along high symmetry points of BZ was selected as:  (Figure 3b). However, the difference between indirect and direct electronic transition is small, the value of the calculated direct band gap is 5.37 eV. Taking into account that the experimental band gap value of Y 2 O 2 SO 4 has not yet been published and DFT calculations in LDA approximation generate a band structure which underestimates the gap [43], the electronic band structure was calculated using the HSE06 hybrid functional. The value of indirect and direct electronic transition obtained with HSE06 are 7.126 and 7.131 eV correspondingly. In the meantime, the electronic density of states (DOS) and partial DOS are shown in Figure 4. It is clearly seen from Figure 4 that the top of valence band is formed by pelectron of oxygen, while the bottom of the conduction band comprises Y's d-electrons. It is interesting to note that partial densities of states are different for oxygen ions in SO 4 tetrahedra and O1 ions located between Y layers (see Figure 2) and the VBM is formed with O1 atoms. Thus, the wide band gap dielectric behaviors (E g (HSE06) = 7.12 eV) of Y 2 O 2 SO 4 are connected with the structural layer formed with Y and O1 atoms. The electronic density of states of O2 and O3 atoms (in SO 4 tetrahedra) from −8 to −6 eV has contribution from 2s and 2p orbitals while the same region is empty in DOS of O1. We suppose that, in this case, the DOS of O1 in the range of −2.5-0 eV corresponds to the hybrid sp orbital, see Figure 4, and the OY 4 molecule can be distinguished as a separate structural unit, see Figure 5. Figure 2 presents the crystal structure of Y2O2SO4. Investigated sulfate presents a monoclinic structure with the C2/c space group (#15). As can be seen from Figure 2, the crystal structure consists of SO4 layers and layers formed with Y and O ions. Calculated values of lattice parameters and atomic coordinates are presented in Table 1 and com pared with experimental data from ICDD PDF 53-0168.    The Y 2 O 2 SO 4 belongs to the monoclinic space group with the factor group symmetry C 6 2h . Vibrational representation for the yttrium oxysulfate at the center of the Brillouin zone can be written as follow: Γ vibr = 13A g + 13A u + 14B g + 14B u . The A u + 2B u are acoustical translational modes while the remaining A u and B u modes are Infrared-active, the A g and B g are Raman-active vibrations. In the structure of Y 2 O 2 SO 4 , the SO 4 tetrahedra occupy the positions with C 2 symmetry and relation between free [SO 4 ] 2− ion with T d symmetry, its site symmetry and the factor group symmetry of the monoclinic cell are presented in Table 2. According to Table 2, nine internal vibrations of SO 4 should be observed in Raman as in Infrared spectra. The Infrared and Raman spectra of Y 2 O 2 SO 4 are presented in Figure 6. The total set of observed spectral lines, DFT calculated wavenumbers and mode assignments are presented in Table 3.

Results and Discussion
band gap dielectric behaviors (Eg(HSE06) = 7.12 eV) of Y2O2SO4 are connected with the structural layer formed with Y and O1 atoms. The electronic density of states of O2 and O3 atoms (in SO4 tetrahedra) from −8 to −6 eV has contribution from 2s and 2p orbitals while the same region is empty in DOS of O1. We suppose that, in this case, the DOS of O1 in the range of −2.5-0 eV corresponds to the hybrid sp orbital, see Figure 4, and the OY4 molecule can be distinguished as a separate structural unit, see Figure 5.    The Y2O2SO4 belongs to the monoclinic space group with the factor group symmetry C 6 2h. Vibrational representation for the yttrium oxysulfate at the center of the Brillouin zone can be written as follow: Γvibr = 13Ag + 13Au + 14Bg + 14Bu. The Au + 2Bu are acoustical translational modes while the remaining Au and Bu modes are Infrared-active, the Ag and Bg are Raman-active vibrations. In the structure of Y2O2SO4, the SO4 tetrahedra occupy the positions with C2 symmetry and relation between free [SO4] 2− ion with Td symmetry, its site symmetry and the factor group symmetry of the monoclinic cell are presented in Table  2. According to Table 2, nine internal vibrations of SO4 should be observed in Raman as   The Y2O2SO4 belongs to the monoclinic space group with the factor group symmetry C 6 2h. Vibrational representation for the yttrium oxysulfate at the center of the Brillouin zone can be written as follow: Γvibr = 13Ag + 13Au + 14Bg + 14Bu. The Au + 2Bu are acoustical translational modes while the remaining Au and Bu modes are Infrared-active, the Ag and Bg are Raman-active vibrations. In the structure of Y2O2SO4, the SO4 tetrahedra occupy the positions with C2 symmetry and relation between free [SO4] 2− ion with Td symmetry, its site symmetry and the factor group symmetry of the monoclinic cell are presented in Table Materials 2021, 14, x FOR PEER REVIEW 6 of 9 Figure 6. Experimental Infrared and Raman spectra of Y2O2SO4. The weak spectral band at 969 cm −1 in the Infrared spectrum and strongest band at  The weak spectral band at 969 cm −1 in the Infrared spectrum and strongest band at 1009 cm −1 in the Raman spectrum are associated with ν 1 symmetric stretching vibrations  Figure 8f. Thus, we can conclude that the wide spectral band at 532 cm −1 in Infrared spectra is devoted to oxygen vibration in [Y 2 O 2 2+ ] chains, but not to Y-O vibrations as was stated earlier [19,20,[31][32][33]. The assignment of remain vibrational modes is presented in Table 3.  Figure 8f. Thus, we can conclude that the wide spectral band at 532 cm −1 in Infrared spectra is devoted to oxygen vibration in [Y2O2 2+ ] chains, but not to Y-O vibrations as was stated earlier [19,20,[31][32][33]. The assignment of remain vibrational modes is presented in Table 3.   Figure 8f. Thus, we can conclude that the wide spectral band at 532 cm −1 in Infrared spectra is devoted to oxygen vibration in [Y2O2 2+ ] chains, but not to Y-O vibrations as was stated earlier [19,20,[31][32][33]. The assignment of remain vibrational modes is presented in Table 3.

Conclusions
In summary, we have demonstrated that the lines in vibrational spectra of Y 2 O 2 SO 4 should be interpreted in terms of vibrations of SO 4  ]. The formation of hybrid sp orbital in yttrium-oxygen chains is supposed. The electronic structure and band gap value of yttrium oxysulfate was presented for the first time.

Data Availability Statement:
The data presented in this study are available on request from the corresponding author.

Conflicts of Interest:
The authors declare no conflict of interest.