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

Abstract

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.

1. Introduction

The rising in experimental and theoretical studies of rare-earth-activated phosphors over the past decades is primarily associated with their applications in lighting, electronic displays, temperature sensing, etc. [1]. A large variety of rare-earth doped inorganic compounds have been synthesized, such as molybdates [2,3,4], tungstates [5,6,7], phosphates [8,9,10], aluminates [11,12,13] and silicates [14,15,16].

Since the chemical formula contains trivalent rare-earth (Re³⁺) ions, the common way for doping is a partial substitution of Re³⁺ with Ln³⁺ (Ln³⁺ = Ce, Pr, Nd, Sm, Eu, Tb, Dy, Ho, Er, Tm, Yb, Lu) ions. Recently, Re₂O₂SO₄ oxysulfate was studied as a host for optical materials and it has been shown that the luminescent efficiency of Re₂O₂SO₄:Ln³⁺ phosphorous depends on the size and shape of particles [17], for example, the Eu³⁺ doped nanosized Y₂O₂SO₄ samples (18–89 nm, C2/c) show the quantum efficiencies ranging from η = 44–70% [18]. The 2–3 μm in diameter Y₂O₂SO₄:Eu³⁺ was synthesized using a urea-based homogeneous precipitation technique based on a urea-ammonium sulfate system [19]. The Y₂O₂SO₄:Tb³⁺ 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 Yb³⁺ and Eu³⁺ or Er³⁺ [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 Re₂O₂SO₄ oxysulfates, the crystal structure of Nd₂O₂SO₄ [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 Sm₂O₂SO₄ [29] and Eu₂O₂SO₄ [30] was solved in the centrosymmetric (C2/c) space group.

Determination of non-centrosymmetric or centrosymmetric space groups in Re₂O₂SO₄:Ln³⁺ 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:Eu³⁺ and attributed to vibrations of SO₄²⁻ ions, while the peak at 530 cm⁻¹ was described as Y-O bond vibration [19]. In nanometer-sized Y₂O₂SO₄:Eu³⁺, the Y-O bond peak was found at 560 cm⁻¹ [31]. In Infrared spectra of Y₂O₂SO₄ doped with Tb³⁺ 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 [Y₂O₂²⁺] structural units.

2. Materials and Methods

2.1. 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:

Y₂(SO₄)₃ → Y₂O₂SO₄ + 2SO₂ + O₂

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.

2.2. Calculation Details

All the density functional theory calculations [34,35] were performed with the CASTEP code (version 19.1.1) [36]. The 4s²4p⁶4d¹5s², 3s²3p⁴ and 2s²2p⁴ 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.

3. Results and Discussion

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. DFT calculated structural parameters for Y₂O₂SO₄ in comparison to ICDD PDF 53-0168.

Lattice Dimensions, Å	a	b	c
Calc. (this work)	13.1242	4.0956	7.8734
ICDD PDF 53-0168	13.3076	4.1465	8.0204
Lattice Angles, Degrees	α, γ	β
Calc. (this work)	90	107.292
ICDD PDF 53-0168	90	107.64
Fractional Coordinates	x	y	z
Y	0.17153	0.48979	0.08471
O1	0.24427	0.97988	0.12243
O2	0.9997	0.26714	0.09789
O3	0.09659	0.84802	0.29921
S	0	0.05146	0.25

and compared with experimental data from ICDD PDF 53-0168.

The Brillouin zone (BZ) of Y₂O₂SO₄ 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: Γ–C|C₂–Y₂–Γ–M₂–D|D₂–A–Γ|L₂–Γ–V₂. Coordinates of these points are: Γ(0, 0, 0), C(−0.276, 0.276, 0), C₂(−0.724, −0.276, 0), Y₂(−0.5, −0.5, 0), M₂(−0.5, −0.5, 0.5), D(−0.737, −0.263, 0.5), D₂(−0.263, 0.263, 0), A(0, 0, 0.5), L₂(−0.5, 0, 0.5), V₂(−0.5, 0, 0) (Figure 3a). The conduction band minimum (CBM) is located at the Γ point, while the valence band maximum (VBM) is located between M₂ and D k-point, thus making the Y₂O₂SO₄ an indirect band gap material, the E_gⁱ = 5.32 eV (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 Y₂O₂SO₄ 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 p-electron 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 SO₄ 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 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 C⁶_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 Y₂O₂SO₄, the SO₄ tetrahedra occupy the positions with C₂ symmetry and relation between free [SO₄]²⁻ ion with T_d symmetry, its site symmetry and the factor group symmetry of the monoclinic cell are presented in

Table 2. Correlation between internal vibrations of SO₄ tetrahedra in Y₂O₂SO₄.

Wavenumber, cm−1 [44]	Td	C2	C2h
983	A1 (ν1)	A	Ag + Au
450	E (ν2)	2A	2Ag + 2Au
1105	F2 (ν3)	A+2B	Ag + Au + 2Bg + 2Bu
611	F2 (ν4)	A+2B	Ag + Au + 2Bg + 2Bu

. According to Table 2, nine internal vibrations of SO₄ should be observed in Raman as in Infrared spectra. The Infrared and Raman spectra of Y₂O₂SO₄ are presented in Figure 6. The total set of observed spectral lines, DFT calculated wavenumbers and mode assignments are presented in

Table 3. Calculated and experimental phonon wavenumbers (cm⁻¹) of Y₂O₂SO₄ with proposed assignments. Notations: Irreps.—irreducible representations, str.—stretching, tr.—translation, rot.—rotation, def.—deformation.

Infrared				Raman
Irreps.	Calc	Exp	Assignment	Irreps.	Calc	Exp	Assignment
Bu	1155.6	1219	ν3 SO4	Bg	1154.3	1180	ν3 SO4
Au	1095.9	1133		Bg	1123.3	1142
Bu	1030.4	1063		Ag	1096.3	1118
Au	969.0	1002	ν1 SO4	Ag	980.0	1009	ν1 SO4
Bu	636.0	666	ν4 SO4	Bg	632.0	651	ν4 SO4
Bu	592.1	621		Bg	629.3	648
Au	581.9	608		Ag	584.3	604
Au	546.7		ν2 SO4 + O1-O1 str.	Bg	533.1	500	O1-O1 str.
Bu	499.1	532	O1 tr.	Ag	505.3	480	O1 tr.
Au	481.7		ν2 SO4 + O1-O1 str.	Bg	492.9	448	O1-O1 str.
Au	461.9		ν2 SO4	Ag	492.6	448	ν2 SO4
Au	429.2		O1 tr.	Ag	476.2	432	ν2 SO4
Bu	416.3		O1 tr.	Ag	453.6	416	ν2 SO4 + O1-O1 str.
Bu	378.8		O1 tr.	Bg	383.2	374	O1-O1 tr.
Au	334.3		O1 tr.	Ag	352.5	344	O1-O1 tr.
Au	260.3		Y tr.	Bg	275.5		SO4 def.
Bu	231.2		SO4 rot.	Ag	248.3	240	Y tr.
Bu	216.2		SO4 rot.	Bg	240.2		Y tr.
Au	191.3		SO4 rot.	Bg	207.7		SO4 tr.
Bu	187.4		SO4 tr.	Bg	203.1		SO4 tr.
Bu	157.7		SO4 tr.	Ag	202.1	195	SO4 rot.
Au	151.6		SO4 def.	Ag	188.8		SO4 tr.
Bu	131.6		SO4 tr.	Bg	184.7		SO4 rot. + tr.
Au	96.7		Y tr.	Ag	172.5	172	Y tr.
				Bg	161.2	168	SO4 tr.
				Ag	151.9		Y tr.
				Bg	120.0		SO4 tr. + [Y2O22+] tr.

.

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 ν₁ symmetric stretching vibrations of SO₄ groups. Spectral bands above 1000 cm⁻¹ are antisymmetric stretching vibrations (ν₃). Bands at 650 and 604 cm⁻¹ in Raman spectrum are ν₄ antisymmetric bending of SO₄ tetrahedra. The ν₄ modes appeared in the Infrared spectrum at 666, 621 and 608 cm⁻¹. Spectral lines in Raman spectrum at 448 and 432 cm⁻¹ are defined as ν₂ symmetric bending of sulfur ions. The rotational vibration of SO₄ appeared in Raman spectrum as the peak at 195 cm⁻¹. The Raman peak at 168 cm⁻¹ is explained as translations of SO₄ in the SO₄ structural layer.

Connection of the OY₄ tetrahedra (Figure 5) into the chains creates the [Y₂O₂²⁺] layers as shown in Figure 7 and vibrations of these layers have been found in Raman spectra. Spectral band at 500 cm⁻¹ is related to O-O stretching, as shown in Figure 8a. The line at 480 cm⁻¹ is an antiphase translation of O atoms along the layer, Figure 8b. The spectral line at 374 cm⁻¹ is an antiphase vibration of O in [Y₂O₂²⁺] structural units as shown in Figure 8c. The strong band at 344 cm⁻¹ is an antiphase vibration of O atoms, Figure 8d. The A_u mode (Infrared active) with a calculated wavenumber value equal to 546.7 cm⁻¹ is a combination of ν₂ vibrations of SO₄ and O-O stretching, as shown in Figure 8e. The B_u mode at 499.1 cm⁻¹ is a translation of O, as shown in Figure 8f. Thus, we can conclude that the wide spectral band at 532 cm⁻¹ in Infrared spectra is devoted to oxygen vibration in [Y₂O₂²⁺] 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.

4. Conclusions

In summary, we have demonstrated that the lines in vibrational spectra of Y₂O₂SO₄ should be interpreted in terms of vibrations of SO₄ tetrahedra and layers composed of [Y₂O₂²⁺] structural units. Calculated partial density of states shows different electron distribution for s and p orbitals in case of oxygen atoms in [SO₄]²⁻ and in case of [Y₂O₂²⁺]. 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.