Article pubs.acs.org/JPCC
Lattice Dynamics of β‑SnWO4: Experimental and Ab Initio Calculations Justyna Wojcik,†,‡ Florent Calvayrac,† François Goutenoire,† Noureddine Mhadhbi,†,§ Gwenael̈ Corbel,† Philippe Lacorre,† and Alain Bulou*,† †
LUNAM Université, Université du Maine, CNRS UMR 6283, Institut des Molécules et Matériaux du Mans (IMMM), Avenue Olivier Messiaen, 72085 Le Mans Cedex 9, France ‡ Institute of Physics, Jan Dlugosz University, Czestochowa, Poland § Laboratoire de Chimie de l’Etat Solide, Faculté des Sciences de Sfax, B.P. 1171, Sfax 3000, Tunisia ABSTRACT: The vibrational properties of β-SnWO4 at center of the Brillouin zone are investigated by Raman at low temperature and infrared spectroscopies in connexion with ab initio calculations. In this cubic structure archetype of new materials with ionic conductivity properties, all 29 optical modes predicted by group theory are Raman-active. All lines have been unambiguously identified on the basis of depolarization ratio measurements. The phonon spectrum is calculated at the center of the Brillouin zone by GGA pseudopotentials within the PWSCF/QE suite. A remarkable agreement is obtained with the experimental frequencies, and a fairly good one is also observed with the Raman scattering cross sections calculated using LDA pseudopotentials for the internal modes of WO42− tetrahedra and the lattice modes as well. All Raman lines are assigned for the first time, and the normal coordinates characteristics are described. The whole results give a large credit to the calculation of the phonon spectra in this structural arrangement with such ions. The phonon density of states is deduced, and the characteristics are explained on the basis of the phonon dispersions curves along the [ξ00] and [ξξ0] high-symmetry directions of the Brillouin zone. set in a rocksalt-like structure. The 5s2 lone pair (E) of divalent tin directed along the three-fold axis involves the off-centering of Sn ion toward the triangular face formed by O1 atoms of its coordination octahedron to minimize the oxide ion-lone pair repulsions (Figure 1).3 The phase stable below 670 °C (αSnWO4)2 consists of WO6 octahedra two-dimensionnally connected and separated by Sn layers. However, Jeitschko and Sleight1 showed that β-SnWO4 can be obtained also at room temperature by rapidly quenching the stable high-temperature phase, and temperatures as high as 500 °C for 0.5 h are necessary for conversion into the α-phase; the β-SnWO4 reported structure was actually determined in this metastable phase.1 Jeitschko and Sleight pointed out that the two phases are entirely different2 and so the mechanism of this reversible β/α phase transition involving a switch between coordinance IV and coordinance VI for W6+ is strongly puzzling. It must be emphasized that materials with the α-SnWO4 structural arrangement2,4,5 have been shown to exhibit many kinds of transitions, displacive,6 order−disorder displacive induced,7 or even martensitic phase transitions8 (including a premartensitic phase with explained origin).9 All of them have been explained by singularities of the phonon spectra at various points or branches of the Brillouin zone of the
I. INTRODUCTION SnWO4 exhibits two very different structural arrangements with a reversible phase transition at ∼ 670 °C.1,2 The structure of the high -temperature phase (β-SnWO4), from 670 °C to the melting point (782 °C) consists of fairly regular WO4 tetrahedra isolated from one to each other by Sn atoms (Figure 1).1 The two entities
Figure 1. (a) Projection along the c axis of the β-SnWO4 cubic structure showing the connection between regular WO4 tetrahedra (in blue) and highly distorted SnO6 octahedron. (b) Spatial orientation of 5s2 lone pair (E) of divalent tin along the three-fold axis of the structure. The main bond distances and bond angles are given in Table 2. © 2013 American Chemical Society
Received: October 7, 2012 Revised: February 7, 2013 Published: February 13, 2013 5301
dx.doi.org/10.1021/jp3099126 | J. Phys. Chem. C 2013, 117, 5301−5313
The Journal of Physical Chemistry C
Article
powder diffraction patterns showed that the compound is pure βSnWO4.
archetype structure, but no rearrangement like in SnWO4 has ever been reported. The two forms of SnWO4, semiconductors, have been more recently studied for applications as sensors10,11 or photoelectrochemical and photocatalytic properties,12 which even become much efficient in the nanocrystalline state.13 Twelve years ago, an oxide-ion conductivity higher than the best stabilized zirconia has been reported in the binary oxide La2Mo2O9 above its first-order α (monoclinic)−β (cubic) phase transition taking place at ∼580 °C.14,15 Numerous works were devoted to aliovalently or isovalently substitute La or Mo ions to stabilize the highly conducting β-form to lower temperatures, these derivatives belonging to the so-called LAMOX family.16 A close relationship between structures of β-SnWO4 and of β-La2Mo2O9 has been evidenced, which gave the structural origin of the fast oxide ion conduction in this lanthanum molybdate.17 In β-SnWO4 (Figure 1), the oxygen O1 and O2 atoms and both cations occupy the same type of positions as in β-La2Mo2O9. Substituting divalent tin with its lone pair E by trivalent lanthanum implies that extra oxygen ions and oxygen vacancies □ are incorporated in place of the original lone pair (Sn2W2O8E2 → La2Mo2O8+1□) to fulfill the lanthanum valence. The presence of intrinsic oxygen defects allows the migration of oxide ions in the structure of β-La2Mo2O9. An atomic-pair distribution function analysis of time-of-flight neutron data collected on both polymorphs of La2Mo2O918 revealed that the local structure of the cubic high temperature β-form is exactly the same as that of the monoclinic low temperature α-form, thus indicating that the structural α/β phase transition actually arises from a static to a dynamic distribution of the oxygen defects. In thermodynamically stable β-LAMOX, however, the evolution of conductivity upon heating exhibits a transition from a conventional Arrhenius-type behavior at low temperature to a phononassisted conduction regime above 400−450 °C.19 The subtle structural distortions and thermal vibrations of the cationic framework at the origin of, or correlated to, this change of the ionic conduction process has been recently identified thanks to a thorough temperature-controlled powder neutron diffraction study carried out on chemically β-stabilized LAMOX compound.20 The present article reports on the description of β-SnWO4 lattice dynamics structural arrangement that can be considered as reference both for the investigation of its β/α transition and for the transitions and dynamical properties in La2Mo2O9 and in β-stabilized LAMOX compounds. The investigations are experimentally based upon accurate polarized Raman scattering measurements at low temperature (extending a former investigation)21 and infrared (IR) absorption measurements in the high-frequency range. The results are used to probe and establish the accuracy of an ab initio approach to calculate vibrational spectra of such a structure with such elements. The whole characteristics of the normal modes and the phonon spectra along the main symmetry directions of the Brillouin zone are described.
III. SYMMETRIES OF THE NORMAL MODES OF VIBRATIONS In the structure of β-SnWO4,1 Sn, W, and oxygen O1 atoms set in the same 4a special position of the space group (P213 or T4) with three-fold symmetry, whereas the second oxygen O2 atom occupies the 12b site without any symmetry (Figure 1). Therefore, it can be predicted that the normal modes of vibration at the center of the Brillouin zone can be classified according to the following irreducible representations of the T point group:22 6A ⊕ 6E ⊕ 17T (optical modes) plus one T symmetry mode corresponding to the acoustic vibrations with zero frequency. All of these modes are Raman-active.23 Actually, the T optical modes are polar; therefore, two components (TO/LO) are associated with each of them. The 17 T symmetry optical modes are also IR-active.
IV. RAMAN SCATTERING STUDY As shown above, all optical normal modes are Raman-active, and they can be classified according to three kinds of symmetries. No single crystal was available to attribute the lines by standard polarization analysis. However, because of its cubic symmetry: (i) the material is optically isotropic and therefore it preserves the polarization state of light whatever the orientation of the crystallites and (ii) the Raman tensors for each symmetry are characterized by only a single parameter:23 ⎡a . . ⎤ A: ⎢ . a . ⎥ ⎢⎣ . . a ⎥⎦ ⎡− ⎢ E: ⎢ ⎢⎣ ⎡. T: ⎢ . ⎢ ⎣.
3 .b
. ⎤ .⎤ ⎡ b . ⎥ ⎥ ⎢ , 3 .b . ⎥ ⎢ . b . ⎥ . . ⎥⎦ ⎢⎣ . . −2b ⎥⎦ .
. . . .⎤ ⎡ . . d⎤ ⎡ . d . d⎥ , ⎢ . . . ⎥ , ⎢ ⎥ ⎢ ⎥ ⎢d . d . ⎦ ⎣d . . ⎦ ⎣ . .
.⎤ ⎥ .⎥ .⎦
As a consequence, polarization analysis measuring depolarization ratio on homogeneous powdered sample makes its possible to attribute the symmetry of each line. The theoretical depolarization ratios24 ρ between intensities measured in cross polarization and in parallel polarization take the smallest value (ρ = 0) for A symmetry modes and the highest value (ρ = 0.75) for E symmetry ones; with regard to the Raman tensors, ρ should also be 0.75 for the T modes, but deviations with such ratio could occur due to the polar character that leads to slight changes of the Raman shifts and intensities depending on the orientation of the scattering vector with respect to the crystallographic axes.25−27 A complete symmetry assignment of the lines is therefore expected just from depolarization ratio measurements.
II. SAMPLE SYNTHESIS AND CHARACTERIZATION The β-SnWO4 phase was prepared slightly differently from the previous process described by Jeitschko and Sleight.1 An equimolar mixture of SnO and WO3 was intimately mixed and placed in an alumina crucible. The preparation was introduced in a tubular furnace under a (N2/H2) flow with 6% of H2 at 750 °C for 12 h. The product then was quenched by removing the alumina crucible from the hot zone of the tubular furnace. X-ray
V. EXPERIMENTAL DETAILS The Raman scattering spectra were collected with a T64000 multichannel spectrometer (Horiba−Jobin−Yvon) using a Si-based CCD detector cooled to −133 °C (liquid-nitrogencooled). The experiments were performed under microscope, in the backscattering geometry, with a ×10 objective (numerical 5302
dx.doi.org/10.1021/jp3099126 | J. Phys. Chem. C 2013, 117, 5301−5313
The Journal of Physical Chemistry C
Article
Figure 2. (a) Experimental polarized Raman spectra of β-SnWO4 powder collected at 100 K in backscattering geometry. The symmetries of the different lines (A,E,T) are given as deduced from measurements of the depolarization ratios. The νi(WO4) give the spectral range of modes arising from WO42− internal modes, as deduced from calculated spectra. (b) Relative Raman scattering intensities calculated from LDA-NC pseudopotential (see text) and taking into account the scattering and temperature factors.
to renormalize the (relative) lines intensities, in the parallel polarization, according to their symmetries.
aperture 0.25) and using as excitation the 514.5 nm wavelength radiation (Ar/Kr Coherent Spectrum laser) with power limited to 3 mW on the sample. Measurements have been done under high resolution, starting 4 cm−1 from the Rayleigh (triple monochromator and 1800 tr/mm grating, 0.6 cm−1 instrument resolution). Spectra were calibrated with the 520.2 cm−1 line of a silicon wafer. The measurements have been performed on a powder to prevent for any stress effect that could occur from compaction process. The complete characterization has been done at low temperature (100 K) to improve the spectral resolution taking advantage of line-width reduction. The ν1 and ν4 lines of standard liquid carbon tetrachloride CCl4 (i.e., with natural isotopic abundance, for which the depolarization ratio is 0.72)28 have been used to perform depolarization calibration measurements and to quantify depolarization contaminations of the instrument under the geometries of analysis (which has been found to be
