Lattice dynamics and dielectric properties of yttrium oxysulfide
Rare-earth oxysulfide (M2O2S, with M5yttrium and lanthanide atoms!, famous as efficient bulk for phosphors,1 has an interesting crystal structure from a scientific aspect. The crystal symmetry is trigonal, with the space group P3¯m1 (D3d 3 ).2 Both M and O atoms have the same site symmetry, C3v . Each metal atom M is coordinated by four oxygen atoms and three sulfur atoms in its nearest neighbor, i.e., a rare seven-coordinated geometry. In more detail, four M atoms tetrahedrally coordinate around one oxygen atom.
The S site is coordinated octahedrally by six M atoms, havinga symmetry of D3d . Further observation of the atomic structure reveals that M-atom planes, O-atom planes, and S-atom planes are all perpendicular to the c axis of the trigonal crystal. This characteristic uniaxial structure may cause anisotropy in some physical properties, such as lattice vibration modes or dielectric tensor components. Although this industrially important material attracts such scientific interest, the lattice dynamics and the optical properties have been little studied. This is mainly because the synthesis of large-sized single crystals, necessary for elaborate optical measurements, is practically difficult owing to the high vapor pressure of sulfur species.3 No reliable data on the dielectric constants of M2O2S have been reported so far. The high-frequency dielectric constant was estimated as 4.67 for La2O2S, simply from the square of the refractive index at a wavelength ;1 mm.3 The static dielectric constant was roughly estimated to be 18, as the mean of those for Y2O3 and BaS.4 Of course, the anisotropic properties of the dielectric constants were not discussed from either theoretical or experimental viewpoints. To the best knowledge of the present authors, the Raman experiment with several powdered oxysulfides performed by Yokono, Imagana, and Hoshina was the only one for the lattice vibration of Y2O2S.5 Recent band-structure calculations based on densityfunctional theory6 were so established as to quantitatively discuss physical properties of materials without any parametrization to experimental data. In fact, ab initio theory is able to generate the lattice parameters and atomic positions to within 1–2%, and the phonon frequencies, elastic constants, and dielectric tensors to within 5–10%.7 In this paper, as a natural extension of our previous theoretical investigations,8–10 we study the lattice dynamics and optical properties of yttrium oxysulfide quantitatively, by employing density-functional perturbation theory ~DFPT!,11–15 that was successfully applied to many cases.11,16–20 We also measure Raman spectra on single crystals of Y2O2S. It is claimed that the present calculation of lattice vibration modes is in fairly good agreement with the experimental data.
II. CALCULATION METHOD
The present calculations are performed with use of the ABINIT code,21 which is based on first-principles pseudopotentials and plane waves in the framework of the densityfunctional formalism. It relies on an efficient fast Fourier transform algorithm22 for the conversion of wave functions between real and reciprocal spaces, on an adaptation to a fixed potential of the band-by-band conjugate gradient method,23 and on a potential-based conjugate-gradient algorithm24 for the determination of the self-consistent potential. Our calculations are based on the crystal structure optimized in the previous theoretical work:8 the lattice constants a and c are 3.750 and 6.525 Å, respectively. Troullier-Martins-type pseudopotentials,25 generated thanks to the FHI98PP code,26 are adopted in this work. The parameters necessary to make such pseudopotentials, cutoff radii, and electronic configurations follow the previous works performed in Refs. 8–10. The DFPT was reviewed in Ref. 11. Technical details employed in the present computation of the second-order responses to atomic displacements and homogeneous electric fields can be found in Ref. 14, while Ref. 15 presents a subsequent computation of dynamical matrices, Born effective charges, dielectric permittivity tensors, and interatomic force constants ~IFC's!. The exchange-correlation energy is evaluated within the local-density approximation ~LDA! by using Ceperley-Alder homogeneous electron-gas data.27 The wave functions are expanded in plane waves up to a kinetic-energy cutoff of 30 Hartree.
Integrals over the Brillouin zone ~BZ! are replaced by a sum on a Monkhorst-Pack grid of 43434 special k points.28 In order to obtain the phonon band structure, dynamical matrices are computed ab initio for q wave vectors belonging to the 43432 Monkhorst-Pack grid, which shows good convergence within 2% error in comparison with the result of the 63634 Monkhorst-Pack grid. Then the short-ranged parts are Fourier transformed for generating real-space IFC's. The long-ranged parts are described by an analytical expression (see Ref. 15).
III. CALCULATED RESULTS OF LATTICE DYNAMICS
AND OPTICAL PROPERTIES
First we present the phonon frequencies at the G point. The calculated mode frequencies are summarized in Table I, along with the experimental data. Since there are five atoms in the unit cell, there are 12 optical modes (Gopt) and three acoustic modes. From the factor group analysis for this unit cell (D3d), the optical modes at the G point are classified into the following symmetry species:29
From the crystal symmetry, the one-dimensional modes (A1g , A2u) are the atomic motions parallel to the c axis, while the two-dimensional modes (Eg , Eu) are those perpendicular to it. The even modes (A1g , Eg) are Raman active, and the odd modes (A2u , Eu) are infrared (IR) active. Notice that the IR modes include sulfur atom motion,whereas the Raman modes do not. Owing to the above consideration, a diagonalization of the dynamical matrix leads to a rigorous assignment of the lattice vibration modes.
The present calculation predicts four Raman-active modes, in agreement with the experiment. From Table I, the comparison between the calculation and the experiment gives the maximum deviation of 50 cm21, a rms of absolute deviations of 27 cm21, and a rms of relative deviations of 5.9%. Hence the quantitative agreement seems fairly good.
Experimental wave numbers of the IR modes in Y2O2S are not available in the literature. There is only one paper by Golovin et al.,30 who found six IR modes in the other oxysulfide systems,.g., La2O2S. However, the conclusion is not understandable. The phonon frequencies of IR modes at the G point in ionic crystals exhibit a nonanalytical behavior due to the long-range Coulomb field. The negative ions ~O, S! and the positive ions ~Y! lie on separate planes perpendicular to the c axis; such a sequence of ionic planes can be found only along the c-axis direction. Thus the polarization by the LO-phonon mode parallel to the c axis is largely different
from that in the other directions. In addition, the degeneracy of Eu modes in the vicinity of the G point depends on the direction of wave vector q; the Eu modes with q along the c axis are doubly degenerate as TO modes, while the Eu mode in the other direction of q will be split due to the LO-TO splitting. The present calculation thus predicts the existence of eight IR modes for Y2O2S ~Table I!.
The phonon dispersion over the whole BZ is shown in Fig. 1. One can see the discontinuity in the vicinity of the G point31 and some flat optical branches along the A-G, M-L, and K-H directions. These features are typical in uniaxial crystal structures.32 The anisotropic crystal structure, therefore, essentially affects the phonon-band structure, just as it affects the electronic band structure.8 The high-frequency dielectric tensor components along the a and c axes are evaluated as 5.23 and 4.87, respectively ~Table II!. No experimental dielectric tensors have been reported for Y2O2S, although the dielectric constant of La2O2S was estimated as 4.67.3 By presuming that the dielectric constant of Y2O2S is close to that of La2O2S because of their chemical and structural similarities, we suppose that our calculated values are somewhat overestimated. This overestimate may be attributed to the LDA; the typical deviations are
known to be about 10%.15 The present result may still suggest that the dielectric constant of Y2O2S is larger than that of Y2O3 (3.64).4 The low-frequency ~static! LDA dielectric tensor components, for which experimental data are also not available, are evaluated as 12.51 along the a axis and 12.20 along the c axis. These values are considerably smaller than 18 estimated
by Robbins.4 The Born effective charge tensors are summarized in Table II. We notice that the absolute values of the effective charges become somewhat larger than those of the formal charges (Y: 13; O: 22; S:22). This tendency is similar to that in other inorganic materials such as perovskites.33 This tendency can be explained from the viewpoint that the Born effective charge depends on the electronic charge reorganization induced by atomic displacements, due to the definition as dynamical effective charge.33,34 More specifically, the presence of a large effective charge requires a modification of the interaction between occupied and unoccupied electronic state.33 In fact, a previous theoretical study (Ref. 8) indicated that weak but substantial covalent bonds exist in yttrium oxysulfide.
IV. RAMAN EXPERIMENT
Single crystals of Y2O2S were prepared by the sintering method at temperatures below the melting point of the compound (;2200°C). After a crucible was sealed by the arcwelding method using an argon-arc plasma flame, it was heated by radio frequency power. A large part of the crystals obtained was still rugged and colored. Among them, some transparent single crystals with uneven surfaces were picked up for microscopic Raman spectroscopy measurement. The samples could not be cut and polished because of the very
small size (,0.530.530.3 mm3).
small size (,0.530.530.3 mm3).
Raman spectra were taken at room temperature under ambient conditions using a Reinshaw Raman Image Microscope System 1000 ~Gloucestershire, U.K.!, equipped with a charged-coupled-device multichannel detector. The excitation source was a 514.5-nm Ar-ion laser line ~average power510 or 25 mW!. The laser spot size on the sample was about 0.8 mm in diameter. The scattered light was collected in a backscattering configuration, having a resolution of 1 cm21. The spectra were measured with unpolarized light due to the uneven surfaces of the sample. Figure 2 represents Raman spectrum in the range 0 –1000 cm21 for a single crystal of Y2O2S. The background noise in the present work is much more reduced than that in the previous work.5 Our spectroscopic parameters are summarized in Table I, along with those obtained by Yokono et al.5 The present result ensures that the Raman spectrum measured on powdered samples is indeed related to the bulk properties. The intensity ratios among the peaks in our spectrum are different from those in Ref. 5. This probably comes from the difference in sample configuration or quality between ours ~bulk crystal! and theirs ~pressed powder!, or both.
V. CONCLUSION
We have investigated lattice dynamics and optical properties of Y2O2S, mainly from the standpoint of a firstprinciples calculation. Our ab initio calculation reproduces the experimental Raman wavenumbers, with a maximum deviation of 50 cm21. We have also discussed IR modes, and pointed out the ambiguity in the previous experimental work.
The high-frequency and static dielectric tensor components have been quantitatively predicted. Furthermore, we observed that the phonon band structure and the dielectric permittivity tensors are affected by the anisotropic crystal structure. The effective charges are also discussed in view of covalency of the bonds. In addition, Raman experiments were carried out on single crystals synthesized by ourselves. The result confirms the earlier data on powdered samples, with a much improved signal-to-noise ratio. The present spectrum reveals several faint peaks, although their origin remains unclear. Higherorder perturbation theory generalized for evaluation of Raman tensors15,35–38 or phenomenological studies based on the DFPT39–41 could benefit future experimental studies .
Cesar Hernandez
19.502.806
Electronica de Estados Solidos
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