Polarized Raman, FTIR, and DFT study of Na2 Ti

R E S E A R C H A R T I C L E

Polarized Raman, FTIR, and DFT study of Na

₂

Ti

₃

O

₇

microcrystals

Fábio Lacerda Resende e Silva

_{| Adailton Azevedo Araújo Filho}

_|

Mauricélio Bezerra da Silva

_{| Karla Balzuweit}

_{| Jean}

‐

Louis Bantignies

|

Ewerton Wagner Santos Caetano

_{| Roberto Luiz Moreira}

_{| Valder Nogueira Freire}

_|

Ariete Righi

1_{Departamento de Física, Universidade}

Federal de Minas Gerais, Av. Antônio Carlos, 6627, Belo Horizonte 31270‐901, Brazil

2_{Departamento de Física, Universidade}

Federal do Ceará, Caixa Postal 6030, Fortaleza, CE 60455‐760, Brazil

3_{Place Eugène Bataillon, Université de}

Montpellier II, Montpellier 34095, France

4_{Instituto de Educação, Ciência e}

Tecnologia do Ceará, Universidade Federal do Ceará, Fortaleza, CE 60040‐531, Brazil

Correspondence

Ariete Righi, Departamento de Física, Universidade Federal de Minas Gerais, Av. Antônio Carlos, 6627, Belo Horizonte 31270‐901, Brazil.

Email: [email protected]

Funding information

FINEP; FAPEMIG; CAPES; CNPq, Grant/ Award Number: 304781/2016‐9

Abstract

Sodium trititanate Na2Ti3O7microcrystals were carefully prepared by sodium

carbonate and titanium dioxide solid‐state reaction and characterized by scan-ning and transmission electron microscopies, selected area electron diffraction, X‐ray powder diffraction, and Raman and Fourier transform infrared spectros-copies. Electron microscopic techniques revealed that the samples were formed by elongated particles several microns long with broad size distributions. The zone axis and crystal growth direction of the elongated particles were deter-mined by selected area electron diffraction. These results were useful for iden-tifying the symmetries of the optical vibrational modes obtained by infrared absorption and polarized Raman scattering of oriented crystals. For a complete assignment of the depicted phonon modes, Fourier transform infrared spectros-copy and Raman data were compared with theoretical data obtained from first‐ principles calculations within the framework of the density functional theory. A very nice agreement was established between the characteristic features of mea-sured and calculated vibrational modes. In particular, all optical phonon modes of Na2Ti3O7 could be experimentally observed and assigned to their correct

symmetries. These results must be useful for describing the physical behavior of the system and designing new technological applications.

K E Y W O R D S

DFT calculations, infrared spectra, polarized Raman spectra, sodium trititanate, solid‐state synthesis

1

|

I N T R O D U C T I O N

Layered titanates with the M2TinO2n+ 1formula, where

M is mainly H, Li, Na, and K, crystallize usually into a monoclinic structure. They are composed of edge‐sharing and strongly distorted TiO6 octahedra, yielding ribbons

whose thicknesses depend on thenvalue.[1]In this struc-ture, the alkaline metals are located in the interlayer

space. Forn < 6, these materials present an open struc-ture yielding a good ion exchange capacity,[2,3] and for n > 5, the adjacent layers are linked by corner sharing oxygen octahedra, forming a tunnel‐like structure with a poor ion exchange ability.[3] _{The tunnel}

‐like titanates exhibit better stability than the open ones.[1,2] _The

study of these materials has been motivated by their potential use in many technological applications, such as DOI: 10.1002/jrs.5316

photocatalysis,[4] _sensors,[5] _{dye adsorption,}[6] _{and ion}

exchange[7]. In particular, sodium trititanate Na2Ti3O7

has been demonstrated to be a good candidate as a matrix for lithium batteries[8]and also as the lowest voltage oxide insertion electrode for sodium ion batteries.[9]

Despite the advanced studies concerning their techno-logical applications, the fundamental physical properties of the layered titanates are still under debate. In view of this, optical vibrational spectroscopies (infrared and Raman) emerge as very appropriate tools for studying these systems. Unpolarized Raman and transmission infrared spectra of unoriented Na2Ti3O7polycrystals have

already been reported in the literature.[10–13] _Besides,

Raman measurements have shown to be very useful to study phase transitions[14]_{and structural changes due to}

the presence of different metals in similar interlayer mate-rials.[15,16]_{However, due to its complex crystal structure, a}

detailed study of sodium trititanate vibrational properties is still lacking. Because Raman spectroscopy requires rel-atively simple sample preparation procedures, a proper use of this technique using polarized light along with far‐and mid‐infrared spectra can bring new information about the vibrational properties of Na2Ti3O7. On the other

hand, the use of density functional theory (DFT) tech-niques along with Raman and infrared data, covering the entire vibrational range, can give information about the phonon characteristics of Na2Ti3O7, which will be

very useful for understanding its physical behavior and designing emerging optical applications of this material.

In this work, a detailed study of vibrational features of the trititanate Na2Ti3O7crystalline sample was performed

by polarized Raman and infrared absorption (IR) spectroscopic techniques. The samples were synthesized by solid state reaction, and their crystal structure and morphology were investigated by electron and X‐ray powder diffraction (XRD), scanning (SEM) and transmis-sion electron (TEM) microscopy. Experimental results were compared and interpreted according to DFT first‐ principles calculations.

2

|

E X P E R I M E N T A L

2.1

|

Synthesis and growth of Na

Ti

O

microcrystals

Na2Ti3O7 samples were carefully produced by

conven-tional solid state reaction as reported in the literature.[2]

Sodium carbonate (99.5%) and anatase titanium dioxide (99%) were purchased from VETEC and Sigma‐Aldrich, respectively. All reagents were of analytical grade and used as received without further purification. A mixture of Na2CO3 and TiO2 with the molar ratio 1:3 was

heated at 1,073 K in air for 20 hr. The resulting powder

was grounded in a mortar, and the heat treatment was repeated twice.

2.2

|

Structural and spectroscopy

characterization

SEM images were obtained in a Quanta 200 FEI micro-scope. TEM images and electron diffraction patterns were acquired in a Tecnai G2‐20 SuperTwin FEI‐200 kV. The samples were prepared dispersing by sonication in etha-nol and dropping on a silicon substrate for SEM and on a holey carbon copper grid for TEM and electron diffrac-tion. The XRD patterns of the samples were collected in the 5–80o(2θ) range using a PANanalytical Empyrean dif-fractometer equipped with a Cu Kαsource and operating

with a 45 kV X‐ray tube voltage. In order to obtain the lattice parameters, the diffraction data were treated by profile matching with constant scale factor (Le Bail method) using the GSAS Expegui software[17,18] _based

on the monoclinic structure of Na2Ti3O7(ICSD‐250000).

Micro‐Raman spectroscopic measurements were per-formed in the backscattering configuration using the tri-ple spectrometer Horiba‐Jobin Yvon T64000 equipped with nitrogen‐cooled CCD. The 514.5‐nm line from an Ar/Kr ion laser was used as the excitation source, and the laser power was about 3.5 mW. Polarized Raman mea-surements were performed in an isolated small crystal. The spectra were collected with the electric field of the incident light perpendicular or parallel to the crystal growth direction and that of the scattered light perpendic-ular to this direction, which we called polarized VV and YV scattering configurations, respectively.

Fourier transform infrared (FTIR) spectroscopy exper-iments were performed from 50 to 1,000 cm−1. In the far‐

infrared region (50–700 cm−1), we used a Bruker IFS

113 V Fourier Transform spectrometer equipped with a Si‐bolometer detector cooled at 4 K. The spectrum in the mid‐infrared region 400–1,000 cm−1 was obtained in a

Bruker Vertex 70 spectrometer equipped with a pyroelec-tric DLaTGS detector. The sample was mixed either with polyethylene (for far‐IR measurements) or caesium iodide (for mid‐IR spectra) and pressed under high pressure to form pellets.

2.3

|

Computational procedures

The initial structure for the DFT simulations was the X‐ray crystal data for Na2Ti3O7(monoclinic, space group P21/m) published by Yakubovich and Kireev,[19] who

refined the previous measurements of Andersson and Wadsley.[20] _{Bulk sodium trititanate crystals consist of}

(Ti3O7)2−layers held together by sodium ions occurring

independent Ti atoms have six anions in their closest neighborhood, forming strongly distorted edge‐sharing octahedra and creating ribbons extended along theb‐axis. Unit cell geometry optimization was performed using the Perdew–Burke–Ernzerhof[21,22] exchange‐correlation potential within the generalized gradient approximation (GGA). The CASTEP code[23,24] _{for electronic structure}

calculations was employed to optimize the unit cell geom-etry for each crystal under study, as well as to obtain their vibrational properties. A plane wave basis and a set of atomic pseudopotentials were employed to describe the valence and core electrons, respectively. Among the advantages of using a plane wave approach to describe Kohn–Sham orbitals, one can mention the consistency and ease to improve the quality of the calculations by changing a single number (the cutoff energy) and the absence of the basis set superposition errors observed for orbital‐based and Gaussian basis sets when evaluating dissociation energies. The plane wave energy cutoff was set to 1,000 eV for the system, and a 2 × 4 × 2 Monkhorst–Pack grid[25]was chosen to calculate integrals in reciprocal space, allowing the determination of an accurate and well‐converged Na2Ti3O7crystal structure,

as described in our previous work.[26]

Norm‐conserving pseudopotentials[27] were adopted for each atomic species with the following valence config-urations: Na: 2s2 2p6 3s1, Ti: 3s2 3p6 4s2 3d2, and O: 2s2 2p4, leading to 192 valence electrons per unit cell. The geometry optimization to a total energy minimum was performed using the Broyden–Fletcher–Goldfarb–Shanno quasi‐Newton scheme,[28,29] well‐known for its stability and efficiency. The unit cell volume was allowed to relax during the optimization process. Convergence thresholds for geometry optimization were the following: total energy variation smaller than 0.5 × 10−5eV/atom;

maxi-mum force per atom smaller than 0.1 × 10−1eV/Å;

max-imum atomic displacement smaller than 0.5 × 10−3 Å;

and maximum crystal stress component smaller than 0.2 × 10−1GPa. If these criteria are satisfied along two

successive optimization steps (convergence window), we consider that the crystal geometry well converged. On the other hand, the self‐consistent field calculations at each geometry optimization step obeyed the following convergence tolerances: total energy variation per atom smaller than 0.5 × 10−6 eV and electronic eigenenergy

variation smaller than 0.2875 × 10−6 eV. In this case,

the convergence window was chosen to be three self‐consistent field steps, as an accurate evaluation of the total energy of the system is critical for the geometry optimization process. The quality of the basis set was kept fixed notwithstanding unit cell volume changes during the geometry optimization (see Table S1 of the Supporting Information) using a finite basis set correction energy.

After finding the minimum energy structures, we obtained the infrared and Raman spectra within the linear response formalism.[30]_{All crystallographic figures}

were drawn using theVestasoftware.[31]

Simulated Raman integrated intensity (Ii) for each mode was calculated using the equation obtained by the theory of Raman scattering

Ii¼ f υ₀

−υi

ð Þ4

υ_i 1 −e−

hcυ_i

kT

Ai; (1)

whereAiis the calculated Raman activities (from the DFT output), υ₀ is the exciting wavenumber, υ_i is the

wave-number of the ith normal mode,f is a common scaling factor, h, c, and k are fundamental constants, and T is the room temperature.[32]_{Theoretical widths were taken}

as equals to the experimental ones. Symmetry‐averaged theoretical infrared absorption was simulated as follows: frequencies, oscillator strengths, and symmetries of the theoretical modes, along with the extrapolated compo-nents of the real dielectric tensors at low (zero) and high (infinity) frequencies, were provided by DFT calculations; damping constants were taken from the fits of the experi-mental FTIR spectra. Then, by using multi‐oscillator models, the dielectric responses (their real and imaginary parts as functions of the frequency) were generated sepa-rately for the Au and Bu modes (assuming arbitrary in‐

plane directions for the Bu phonons). From these

func-tions, we obtained the averaged functions <ε´ > = (1/3)

Trace{bε´} and <ε”> = (1/3)Trace{bε”}, wherebεmeans the

complex dielectric tensor function. From these functions, the averaged extinction index (κ, imaginary part of the

refractive index) and the absorption coefficient (α= 4πκ ν) were calculated.[33]

3

|

R E S U L T S A N D D I S C U S S I O N S

3.1

|

Morphology and crystal structure

as previously described for Na2Ti3O7[19] and similar

titanates.[34,35]

The crystal structure of sodium trititanate is presented in Figure 2a. It has a monoclinic symmetry belonging to the C2_2h(P21/m) space group. All atoms are located at 2e

Wyckoff position, which are symmetric under unitary transformation and reflection. There are three Ti atoms at non‐equivalent positions, each one with six oxygens as first neighbors, yielding a strongly distorted edge shar-ing TiO6octahedra. As Figure 2a shows, these octahedra

form {Ti3O7}−2ribbons that are connected by the oxygens

in the equatorial vertices, giving rise to stepped‐like layers. These layers have a zigzag format and are extended in [0 1 0] direction as shown in Figure 2b where one can see that the sodium atoms are located between the layers. The XRD pattern of the synthesized material is shown in Figure 2c and confirms that the sample is mostly sodium trititanate. A small amount of sodium hexatitanate (Na2Ti6O13) is present in the sample as a

sec-ondary phase, being identified by the peaks at 11.8° and 14.1° (marked by *) assigned to the (200) and 201 lattice planes, respectively. The presence of this phase was also previously reported by other authors.[11,13]_{The obtained}

lattice parameters for Na2Ti3O7 are a = 9.1281(1) Å, b= 3.80222(5) Å,c= 8.56254(9) Å, andβ= 101.603(5)°,

which are in agreement with the literature.[2,19,20] _They

were obtained using Le Bail method. Reliability factors were Rwp= 0.140 and Rp= 0.108.

In order to ensure the quality of our structural calcula-tions, we have tested two exchange‐correlation func-tionals (LDA and GGA) with three distinct cutoff energy values (530, 830, and 1,000 eV) to obtain the optimized unit cell. The results are shown in Table S1 of the Supporting Information. From it, one can see that the lat-tice parameters calculated at the LDA level for the sodium trititanate are close to those presented in literature.[2,19,20]

The best agreement with our experimental results. However, it was obtained using the GGA functional with cutoff energy of 830 eV, being identical to those found at 1,000 eV with a smaller computational cost. The unit cell parameters found at this level are a = 9.19 Å, b = 3.79 Å, c = 8.65 Å, andβ= 101.75°. It is worth mentioning that the DFT‐GGA method describes well the electronic and optical properties of sodium trititanate.[26]

3.2

|

Vibrational properties

The trititanate primitive cell contains two Na2Ti3O7

chemical formulas resulting in 24 atoms. Based on group theory, 72 vibrational modes at the Γ point of the first

Brillouin zone are expected. These modes can be decomposed into irreducible representations as follows:

ΓTotal¼24Agþ12Auþ12Bgþ24Bu;

where the acoustic modes are Au + 2Bu. The remaining optical modes have 24Ag+ 11Au+ 12Bg+ 22Bu irreduc-ible representations, whereAg and Bgare Raman active andAuandBuare IR active. Raman modes are symmetric under inversion with theAgmodes being completely sym-metric, whereas theBg are antisymmetric relative to the C2 screw axis (21 // [010]) and σh (m // (010)) mirror

plane. Infrared active modes are antisymmetric under inversion, Au being antisymmetric relative to the σh

mirror plane andBu being antisymmetric relative to the C2screw axis.

A high quality Raman spectrum of the sodium trititanate sample is presented in Figure 3a. This spectrum is in good agreement with to those presented by Peng et al.[12]and by Viana et al.[13], although, none of the cited authors had done a detailed analysis of their Raman spectra. In our case, by using peak fitting procedures, the unpolarized Raman spectrum of the Na2Ti3O7

sample could be adjusted with 36 Lorentzian lines, in complete agreement with group theory predictions. The wavenumbers and full‐widths at half‐maxima of all experimental Raman modes are listed in Table 1. The most intense modes are located around 83, 302, 849, and 884 cm−1.

In order to identify the symmetry of Raman normal modes, polarized Raman measurements were carried out on isolated trititanate particles along the main crystallog-raphy directions obtained from the electron diffraction data. The resulting spectra of this material in the VV and YV configurations are presented in Figure 4, where V and Y are related to the [101] and [010] directions, respectively. At our knowledge, these are the first polarized Raman spectra available so far. For sake of FIGURE 3 (a) Experimental (open circles) and adjusted (solid red line) Raman spectra of the sodium trititanate sample. The individual Lorentz lines for the adjustment are shown in solid black lines (b) simulated Raman spectrum by means of density functional theory at the generalized gradient approximation level with the cutoff energy of 1,000 eV [Colour figure can be viewed at wileyonlinelibrary.com] FIGURE 2 Na2Ti3O7crystal structure belonging to monoclinicC2_2h(P21/m) in the (a) [0 1 0] zone axis (ac‐plane) showing the stepped‐layer and lamellar format and (b)

comparison, the unpolarized Raman spectrum is also pre-sented in Figure 4. The polarizability Raman tensors for theC2_2hspace group reveal that theAgandBgmodes are expected to be observed in VV and YV polarized Raman measurements, respectively. This analysis is presented in the Supporting Information.

As it can be clearly seen by comparing the unpolarized and VV spectra in Figure 4, the Raman peaks located at 201, 260, 285, 302, 488, 587, and 655 cm−1(labelled with

*) present relatively low intensities in the VV spectrum. On the other hand, the peaks at 83, 117, 140, 230, 449, 684, 742, 849, and 884 cm−1present very similar relative

intensities compared to those of the unpolarized spectral curve. These results imply that the Raman modes in this second group have Ag symmetry, whereas the Raman vibrational modes in the first group would haveBg sym-metry. This assignment is supported by the YV spectrum in Figure 4, where the Raman modes located at 83, 117, 140, 230, 277, 684, 742, 849, and 884 cm−1show a clear

decrease of intensity, whereas the modes at 179, 201, 260, 285, 302, 488, 587, and 655 cm−1do not display the

same behavior. The incomplete extinction of the peaks is due to imperfect orientation and/or the presence of defects. A detailed analysis and comparison of the three spectra is presented in Figure 4, where all 36 Raman TABLE 1 Experimental and theoretical wavenumbers of Raman‐active normal modes of sodium trititanate with their respective assign-ments [Colour table can be viewed at wileyonlinelibrary.com]

Exp. (cm−1₎

FWHM (cm−1₎

Irred. Rep.

Theor.

(cm−1_{) Assignment}

Exp. (cm−1₎

FWHM (cm−1₎

Irred. Rep.

Theor.

(cm−1_{) Assignment} 83 6.0 Ag 68 αNa1 285 5.8 Bg 280 ωO3‐Ti2‐O4 92 4.0 Bg 101 τNa1‐Na2 302 6.0 Bg 294 ωO2‐Ti2‐O3 106 3.9 Bg 117 τO3‐Na1‐O6 320 7.0 Ag 296 δaO4‐Ti1‐O5

117 4.6 Ag 104 αNa2,Ti2 338 9.6 Ag 318 υaO2‐Ti2‐O4 123 6.7 Ag 132 αNa2 346 9.8 Ag 339 σO2‐Ti2‐O3 135 5.2 Bg 153 ωO1‐Na2‐O4 386 10.4 Ag 364 δaO6‐Ti3‐O7

140 6.0 Ag 147 ρO2‐Ti2‐O3 400 9.0 Ag 375 υsO4‐Ti2‐O5 155 5.9 Ag 165 αNa2 406 10.7 Ag 424 δaO6‐Ti3‐O7 166 8.0 Bg 166 τTi1‐O1‐Ti3 449 14.4 Ag 458 σO5‐Ti1‐O4 172 3.2 Ag 208 αNa2 488 10.4 Bg 433 υaTi2‐O6 179 4.2 Bg 186 τO4‐Ti2‐O5 506 10.0 Ag 477 υTi1‐O7

194 7.8 Ag 217 δaNa1‐O3 524 9.6 Ag 548 σO1‐Ti1‐O4 201 10.2 Bg 222 τO1‐Ti3‐O2 587 76.0 Bg 541 υaTi1‐O7 223 4.0 Ag 219 δaO3‐Ti2‐O4 655 13.5 Bg 610 υaTi1‐O7

230 8.6 Ag 244 δaNa1‐O3 684 14.4 Ag 658 δaO4‐Ti1‐O1 251 4.4 Ag 268 δaO1‐Ti3‐O2 742 11.6 Ag 716 υsO1‐Ti1‐O4 260 10.8 Bg 253 τTi1‐O1‐Ti3 849 20.5 Ag 810 υTi1‐O4 277 9.7 Ag 277 τO5‐Ti2‐O6 884 5.0 Ag 851 υsO3‐Ti2‐O5

Note. The full width at half maximum (FWHM) of the experimental Lorentzian curves is also listed.

modes of Na2Ti3O7 were classified according to their

vibrational symmetries, as shown in Table 1.

For a complete assignment of the vibrational modes of sodium trititanate, their vibrational properties were simulated within the framework of density functional theory and compared with the experimental data. As described in our previous paper, the GGA functional pre-dicts lattice parameters and optical properties of sodium trititanate in good agreement with experiment.[26] _The

simulated Raman spectrum of sodium trititanate within these conditions is presented in Figure 3b. This calculated spectrum is in relative agreement with that obtained by

Łuczyńska‐Szymczak et al.,[36] with LDA functional. However, the cited authors kept the experimental lattice parameters fixed during the internal coordinates optimi-zation. As we have already mentioned, in the present computational procedures, the lattice parameters have been optimized for the calculations, aiming to obtain more realistic results (unrelaxed cells would lead to fre-quency shifts due to pressure effects). The energies (wavenumbers) of experimental and theoretical Raman modes are in good agreement, although a direct compari-son between their intensities must be only qualitative, because of experimental peculiarities in each particular measurement, which include the scattering geometry and crystal symmetry. In the case of our monoclinic sodium trititanate, because the crystals grew along the [010] direction, unpolarized Raman measurements have a larger contribution of YY + YV + VV configurations, whereas the simulated spectrum has equal contributions from all crystal directions.

Comparing the theoretical and experimental Raman modes, we could set their relationship considering the wavenumbers values and taking care with the agreement in the symmetry of the modes. These results are presented in Table 1. Some Raman modes like those at 83, 302, and 884 cm−1show a difference between their measured and

theoretically estimated wavenumber values of 15, 8, and 33 cm−1, respectively, which can be considered as a quite

good result (the calculated energies for theses modes are only 18%, 2.6%, and 3.7% higher than the experimental ones). The motion of all vibrational modes can be visual-ized by the “Trititanate_Efield.phonon”file provided in Supporting Information, using Jmol software.[37] The assignment of the vibrational modes is depicted in the last column of Table 1 and was performed considering the atomic displacements with largest amplitudes. The following convention was adopted to depict them: υ for bond stretching,δ for deformation,ωfor wagging,σ for

scissoring,τfor twisting,ρfor rocking, andαfor a com-plex lattice mode. Thesandasubscripts denote symmet-ric and antisymmetsymmet-ric movements, respectively. A scheme of some Raman vibrational modes is represented in

Figure 5. The atoms are labelled according to the descrip-tion contained in the ICSD‐250000 Crystallographic Information File,[26]_{as shown in Figure 5a,c. It is possible}

to note in Table 1 that the modes involving strong contri-bution from the sodium atoms occur in the low energy range, being the strongest one localized at 230 cm−1,

which is due to an antisymmetric deformation of the Na1‐O3 atoms. In the 410 and 890 cm−1range, only the

modes at 489 and 590 cm−1are related to displacements

of sodium atoms but with small amplitude. Two intense bands at around 280 and 310 cm−1 are attributed by

some authors to Na‐Ti‐O stretching vibrations in Na2Ti3O7,[14–16]which is in disagreement with our results.

As it was already mentioned, the vibrational modes belonging to Bg irreducible representation are antisym-metric with {C2|τb} and {σh|0} operations. Because the

mir-ror plane of theC2_2hspace group is parallel to (010) planes, all vibrational modes that are {σh|0} antisymmetric must

correspond to atomic motions along the [010] direction. Two examples ofBgmodes are presented in Figure 5a,b. The first one refers to the intense Raman mode experi-mentally located at 302 cm−1and is mainly related to a

wagging vibration involving the O2‐Ti2‐O3 atoms. The second mode at 655 cm−1is an antisymmetric stretching

of the Ti1–O7 and Ti3–O5 bonds. The Ag vibrational modes are invariant under all symmetry operations of the C2_2h space group, so the movements of the atoms in this group of vibrations must be parallel to the (010) planes. The last four images in Figure 5 represent Ag vibrational modes. The Raman mode experimentally observed at 851 cm−1 is represented in Figure 5e and is

assigned to Ti1‐O4 and Ti3‐O2 bond stretching motions. Some authors attributed the Raman mode around 900 cm−1 in some titanium oxides to a symmetric

stretching of short Ti–O bond in distorted TiO6

octahe-dra.[38,39] The smallest Ti–O bonding in the Na2Ti3O7

structure is 1.72 Å and is related to the Ti2‐O3 atoms, being the O3 oxygen atom located at the corner of the {Ti3O7}2− ribbon. A description of the most energetic

mode, observed at 886 cm−1in the experimental spectra,

can be seen in Figure 5f and is mainly due the symmetric bond stretching of the oxygen atom in corner of the ribbon, in agreement with previous studies.

As one can see in the YV spectrum of Figure 4, the sodium trititanate crystal has four considerable intense RamanBgbands at 201, 302, 488, and 655 cm−1. It is inter-esting to note that Raman spectra of monoclinic titanates with the composition M2TinO2n + 1 also have intense

Raman bands near these wavenumbers. We can cite for instance K2Ti4O9, which has bands at 206, 302, 478, and

663 cm−1,[40]sodium titanates nanoribbons, which have

bands at around 199, 280, 475, and 675 cm−1[13] and at

nanoribbons.[41]_{As it can be seen in Figure 5a,b, neither of}

the four Raman modes of sodium trititanate cited above are related to interlayer sodium displacements. Furthermore, due to theirBgsymmetry, they are related to movements along the [010] direction. Thus, they should not have a strong dependence on the interlayer ions neither on the nvalues in M2TinO2n+ 1, which is related to the number

of octahedra in the ribbons that form the lamellar titanate crystal structure. For such reasons, one can expect that the lamellar titanates would present similarBgmodes, which will not depend on the interlayer ions.

Figure 6a presents the IR absorbance spectrum of a pelletized trititanate sample in the far‐and mid‐infrared regions altogether. Above 250 cm−1, the spectrum is

similar to those presented in literature,[11,13] _{but below}

this value, it had not been reported yet. The experimental spectrum was adjusted using 33 lines, in perfect

agreement with group theory predictions. The best adjust-ment was performed with Lorentz‐type lines above 617 cm−1and Gaussian curves below this wavenumber.

Lorentz lines are expected in the absorption spectra for narrow bands. Gaussian broadening is a quite common effect in the case of inhomogeneous samples or due to size distribution. The individual lines used in the fit are also shown in Figure 6a.

The infrared absorption spectrum is composed by a set of 17 bands below 317 cm−1 with a remarkable intense

band at 301 cm−1, 11 bands between 350 and 617 cm−1,

a main band at 475 cm−1, and five bands in the range

676 to 930 cm−1. The list of all depicted infrared modes

is presented in Table 2. Experimental IR results were com-pared with DFT‐GGA simulated data, which are pre-sented in Figure 6b. Due to the absence of polarized infrared measurements, which cannot be realized in FIGURE 5 Raman normal modes corresponding to the experimental lines at (a) 302, (b) 655, (c) 346, (d) 406, (e) 849, and (f) 884 cm−1. The

polycrystalline samples, the symmetry of the IR modes could not be determined experimentally. Therefore, the proposed relationship between experimental and simu-lated infrared modes was done by using the energy sequence, as it can be seen in Table 2. If the symmetry

assignments of the Raman data were done considering only the energy sequence of the experimental and theoret-ical modes, disregarding their experimentally determined symmetries from the polarized spectra, we would mistook only six attributions, among the 36 Raman modes (namely, the pairs at 104–117 cm−1, 147–153 cm−1,

186–208 cm−1, 219

–222 cm−1, 253

–268 cm−1, and

433–458 cm−1 Raman modes), representing more than

80% of correctness. Therefore, we believe that the validity of our IR assignment by this procedure would also be around 80%.

The comparison between the experimental and theo-retical infrared spectra is not as good as the obtained for the Raman spectra. The largest absolute wavenumber dif-ference occurs for the IR modes at 676 (experimental) and 585 cm−1 (theoretical), representing a relative

disagree-ment of 14%. The most intense infrared lines, experimen-tally located at 301, 475, 711, and 930 cm−1, are predicted

theoretically with relative errors of 9%, 16%, 10%, and 6% in the peak positions, respectively. The assignment of the infrared normal modes is presented in the last column of Table 2. Similarly to what it was observed in the Raman data, the modes involving largest displacements of the sodium ions are all below 264 cm−1. Analogously to the

Bgvibrational modes, the IR‐activeAumodes are antisym-metric with respect to the mirror planes of theC2_2hgroup,

TABLE 2 Experimental and theoretical wavenumbers of infrared‐active normal modes of sodium trititanate with their tentative assign-ments [Colour table can be viewed at wileyonlinelibrary.com]

Exp. (cm−1₎

FWHM (cm−1₎

Irred. Rep.

Theor.

(cm−1_{) Assignment}

Exp. (cm−1₎

FWHM (cm−1₎

Irred. Rep.

Theor.

(cm−1_{) Assignment} 66 6.0 Bu 66 αNa1 350 24.0 Bu 287 δaO5‐Ti2‐O6 76 10.9 Bu 110 αNa2 369 25.1 Bu 308 σO2‐Ti2‐O3 87 13.0 Au 114 αNa1 388 22.0 Bu 313 δaO5‐Ti1‐O7 105 16.2 Au 115 αNa2 421 43.2 Bu 362 δaO5‐Ti1‐O7

122 16.2 Bu 146 ρO2‐Ti2‐O3 446 30.0 Bu 387 δaO5‐Ti2‐O4 140 19.0 Au 151 αNa2,O3 475 34.0 Au 400 δaO5‐Ti1‐O7 156 18.2 Bu 181 αNa2 502 26.4 Bu 444 υaO1‐Ti3‐O6 176 19.0 Au 187 τTi2‐O2‐Ti3 538 38.2 Bu 465 υTi1‐O5

192 18.4 Bu 189 αNa1ρO2‐Ti2‐O3 565 46.0 Au 479 υaTi1‐O7 209 17.3 Bu 210 αNa2 587 40.4 Bu 523 σO1‐Ti1‐O4 221 16.4 Au 219 ωO1‐Ti3‐O2 617 51.0 Bu 538 δsO6‐Ti3‐O7 233 16.3 Bu 246 ρO1Ti3‐O6 676 76.4 Au 585 υaTi2‐O6

249 16.8 Au 255 τO1‐Ti3‐O2 711 43.6 Bu 640 υaO1‐Ti1‐O4 264 17.0 Bu 266 αNa1‐O3 743 48.7 Bu 695 υsO1‐Ti1‐O4 279 18.2 Bu 273 ρTi2‐O2‐Ti3 858 39.6 Bu 783 υaO2‐Ti2‐O3 301 27.6 Au 273 ωO3‐Ti2‐O4 930 32.8 Bu 874 υsO2‐Ti2‐O3

317 14.4 Au 284 ωO2‐Ti2‐O3 — — — — —

Note. The full width at half maximum (FWHM) of the experimental curves is also listed.

so, they are related to displacements along the [010] direc-tion, whereas the Bu modes, which are symmetric with respect the mirrors planes, are due movements parallel to the (010) planes. Some examples of Au and Bu vibra-tional modes are presented in Figure 7. The first two schemes in Figure 7 refer to the main Au IR bands at 301 cm−1 (due to the rocking motion involving the

Ti2‐O2‐Ti3 atoms) and 475 cm−1 (antisymmetric

defor-mation involving the O5‐Ti1‐O7 atoms). Schemes in Figure 7c,d show two Bu vibrational modes with wavenumbers 858 and 930 cm−1, respectively. Both are

related to stretching movements of the short Ti–O bonds in distorted TiO6octahedra, (O2‐Ti2‐O3 atoms), the first

one being antisymmetric and the second one symmetric. The results obtained in this work, with a comprehensive description of the optical vibrational characteristics of sodium trititanate, improve our knowledge about the structural and dynamical behavior of the system and contribute for designing new optical applications (for instance, photocatalysis) of the material.

4

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C O N C L U S I O N S

In this work, a sodium trititanate sample was synthesized by solid‐state reaction and characterized through electron microscopy (SEM, TEM, and HRTEM), XRD, and Raman and infrared spectroscopies. Structural measurements confirm the formation of the monoclinic phase belonging to the C2_2h(P21/m) space group. Electron microscopy

techniques reveal that the sample has an elongated morphology with several microns in length and some hundreds of nanometers in width, with good crystallinity. The zone axis and crystal grown direction of the particles were determined by selected area electron diffraction, which supported the determination of the Ag and Bg phonon modes in the polarized Raman measurements. A detailed analysis of the vibrational modes of the Na2Ti3O7

has been performed by comparing the experimental Raman and IR results with first‐principles calculations within the framework of density functional theory. In particular, all the vibrational modes predicted by group theory could be discerned in the Raman and infrared spec-tra altogether. The experimental and theoretical results are in very good agreement, allowing a sound assignment of all the vibrational modes of Na2Ti3O7crystalline sample.

A C K N O W L E D G E M E N T S

This work was financially supported by the Brazilian agencies CNPq, CAPES, FAPEMIG, FINEP, and Vale S.A. Company. The TEM images were performed in the Microscopy Center of UFMG. E. W. S. C. received finan-cial support from CNPq project 304781/2016‐9.

O R C I D

Fábio Lacerda Resende e Silva

http://orcid.org/0000-0001-9719-4734

Ariete Righi http://orcid.org/0000-0001-8752-9609 FIGURE 7 Infrared normal modes corresponding to the experimental lines at (a) 301, (b) 475, (c) 858, and (d) 930 cm−1. The atomic

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S U P P O R T I N G I N F O R M A T I O N

Additional Supporting Information may be found online in the supporting information tab for this article.

How to cite this article: Silva FLR e, Filho AAA, da Silva MB, et al. Polarized Raman, FTIR, and DFT study of Na2Ti3O7microcrystals.J Raman Spectrosc. 2018;49:538–548.https://doi.org/10.1002/