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Solid-state DFT-assisted Raman study of titaniate nanostructures
Spectrochimica Acta Part A: Molecular and Biomolecular Spectroscopy 116 (2013) 646–650
Contents lists available at ScienceDirect
Spectrochimica Acta Part A: Molecular and Biomolecular Spectroscopy journal homepage: www.elsevier.com/locate/saa
Short Communication
Solid-state DFT-assisted Raman study of titaniate nanostructures c,b,⇑ _ Katarzyna Łuczyn´ska-Szymczak a,b, Wojciech Starosta a, Kacper Druzbicki a
Institute of Nuclear Chemistry and Technology, Dorodna 16, 03-195 Warsaw, Poland Joint Institute for Nuclear Research, 141980 Dubna, Russia c Department of Chemical Physics, Faculty of Chemistry, Jagiellonian University, Ingardena 3, 30-063 Cracow, Poland b
h i g h l i g h t s
g r a p h i c a l a b s t r a c t
Titaniate nanostructures were
characterized with Raman spectroscopy. The Raman spectra were simulated with solid-state DFT. The general interpretation of most prominent spectral features is given.
a r t i c l e
i n f o
Article history: Received 5 July 2013 Received in revised form 28 July 2013 Accepted 2 August 2013 Available online 13 August 2013 Keywords: Solid-state DFT Linear-response Titaniate nanostructures Raman spectroscopy
a b s t r a c t The first principle solid-state computations in frame of Density Functional Theory have been employed to analyze the Raman spectra of typical titaniate nanostructures. The Raman scattering studies of the nanotitaniates synthesised hydrothermally at different temperature conditions are reported. Local Density Approximation in combination with linear-response computations have delivered detailed analysis of Raman spectra based on the reference Na2Ti3O7 and NaHTi3O7 structures. The interpretation of the most prominent spectral features commonly reported in the literature have been postulated. Ó 2013 Elsevier B.V. All rights reserved.
Introduction In recent years, the multi-dimensional nanostructures have received considerable attention owing to their small sizes, large surface-to-volume ratios or increased density of surface sites. Titanate nanofibers and nanowires belong to group compound with interesting physicochemical properties with still growing application potential. For this reason they have very wide range applicability in such areas as: photocatalysis, ion-exchange or sorption. Recently, Na2Ti3O7 structures were found to be under interest as ⇑ Corresponding author at: Department of Chemical Physics, Faculty of Chemistry, Jagiellonian University, Ingardena 3, 30-063 Cracow, Poland. Tel.: +48 12 663 22 65. _ E-mail address: [email protected] (K. Druzbicki). 1386-1425/$ - see front matter Ó 2013 Elsevier B.V. All rights reserved. http://dx.doi.org/10.1016/j.saa.2013.08.034
potential non-carbon based, low-voltage anode material for room temperature sodium ion battery applications [1]. The titaniate nanostructures became also important in pollution control as revealing good absorption properties e.g. for radioactive ions Sr2+ [2]. Following the pioneer work by Kasuga et al. [3] many papers have been published, reporting relation between synthetic conditions and resulted resulted morphology (nanowires, nanofibers, nanoribbons). In general, the most convenient synthesis strategies are based on TiO2 and TiOSO4 systems. The most important temperature conditions are the temperature, NaOH concentration as well as solvent selection. Raman spectroscopy has found to be very powerful and well established method for the characterization of titanium oxides. Recently, it has been shown by several authors that Raman
´ ska-Szymczak et al. / Spectrochimica Acta Part A: Molecular and Biomolecular Spectroscopy 116 (2013) 646–650 K. Łuczyn
spectroscopy allows one to obtain valuable information about the structural properties of titaniate nanostructures [4–6]. However, according to the quoted literature, the band assignment is still under debate. The main goal of this paper is hence to propose the assignment based on the first-principle solid-state quantumchemical computations.
Experimental and computational details Synthesis The titante nanofibers with Na2xHxTi3O7 stoichiometry were synthesized using hydrothermal method based on the receipt given by Kasuga et al. [3]. 0.025 mol of titanium (IV) oxysulfate (TiOSO4 H2O), received as purchased from Sigma–Aldrich, was dissolved in 80 cm3 of deionised water and mixed with 24 cm3 NaOH. Each synthesis was carried out for 48 h in Teflon-lined stainless steel Berghoff autoclave at following temperatures: 120, 140, 160, 180 and 200 °C. The system was magnetically stirred during the synthesis. The resulted product was cooled down to room temperature. The resulted reaction was strongly alkaline (pH = 14). In the next step the product was filtered and washed with HCl water solution, reducing the pH down to 7, to obtain Na2xHxTi3O7 nanostructures. The final product was dried in air at about 50 °C for 24 h. Raman Spectroscopy The Raman measurements were performed with Nicolet 6700 NRX Fourier-transform spectrometer using 1064 nm excitation line of Nd:YAG laser. The spectra were collected for the powder samples prepared as described earlier, after accumulation of 128 scans and the resolution of 4 cm1. Theoretical Calculations The ab initio computations in periodic boundary conditions (PBC) were performed for the reference titaniate structures, namely Na2Ti3O7 and NaHTi3O7, by means of Density Functional Theory (DFT). The computations were done with CASTEP 6.01. code [7] using Local Density Approximation (LDA) of the exchange–correlation functional (CA-PZ) based on the Ceperley and Alder [8] data as parameterized by Perdew and Zunger [9]. The initial structures were constructed based on the refined data for Na2Ti3O7, published by Yakubovich and Kireev [10,11]. The studied crystals were of the monoclinic P21/m space group (C2h2) with two formulas per unit cell (Z = 2). The experimental lattice parameters, namely: a = 9.1330, b = 3.8060, c = 8.5660 and angles a = 90.00, b = 101.57, c = 90.00 were kept fixed during the internal coordinates optimization. In the case of the NaHTi3O7, half
647
of the sodium atoms were substituted by hydrogens, preserving the assumed symmetry. The computations of the electronic energy were performed in the reciprocal-space with the 2 4 2 Monkhorst–Pack mesh and the 1.00 1009 eV/atom convergence criterion. The normconserving pseudopotentials of Troulliers–Martin were employed to describe the core electrons, while the valence electrons were described with the 900 eV (66 Ry) plane-wave kinetic energy cut-off quality. The geometry optimization has been performed in terms of delocalised internal coordinates [12], with the 0.10 1004 eV/ atom total energy, 0.50 1002 eV/Å max ionic force and 0.50 1002 eV/Å max ionic displacement convergence tolerance, respectively. The phonon computations were performed for the primitive cells at the C point within the quasi-harmonic approximation. The phonon frequencies were obtained by diagonalization of the dynamical matrices computed using density functional perturbation theory (DFPT) [13]. The analysis of the resulting eigenvectors was used in a tentative assignment of the computed modes character, where the symmetry was labeled according to the IUPAC convention. The Raman activity tensors were calculated using a hybrid finite displacement/DFPT method [14] in the presence of external field. The acoustic sum rule (ASR) has been imposed for the frequency of three acoustic modes and no imaginary frequencies were found in both cases. The calculated Raman activities (Ai) were finally transformed into the Raman intensities (Ii), using the relationship derived from the theory of Raman scattering [15].
Ii ¼
vi
h
f ðv 0 v i Þ4 Ai i vi 1 exp hc kT
ð1Þ
where v0 is the exciting wavenumber (in cm1), vi is the frequency of the ith normal mode; h, c and k are the fundamental constants; and T is the temperature (298 K), f is a suitably chosen common scaling factor for all the peak intensities. Results Structure The equilibrium structures optimized with solid-state DFT have been presented in Fig. 1. The assumed structures differ from the real ones by infinite periodicity. The structures include the edge sharing TiO6 octahedra, forming the zig-zag chainlike structures with the cations built in between, allowing to represent the Na2xHxTi3O7 stoichiometry. The real nanostructures are expected to exhibit more or less amourphous characteristic, with non-uniformly defined Na2xHx
Fig. 1. The bulk structures of Na2Ti3O7 (a) and NaHTi3O7 (b), optimized at the DFT/PBC/CA-PZ/900 eV/NC-pps theory level.
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Table 1 Interatomic distances (Å) of bulk Na2Ti3O7 and NaHTi3O7 as reported in the literature [10] and calculated with CA-PZ/900 eV. Atoms
Na2Ti3O7 [10]
Na2Ti3O7 [DFT]
NaHTi3O7 [DFT]
Coordination polyhedron
O1–Ti21 O2–Ti20 O2–Ti21 O3–Ti20 O4–Ti19 O4–Ti20 O5–Ti19 O5–Ti20 O13–Ti20 O14–Ti19
1.98725 1.98120 1.75517 1.70864 1.80651 2.08930 2.18551 2.24458 1.95836 1.97768
1.93753 1.95316 1.76164 1.71293 1.78327 2.06912 2.16006 2.22452 1.95749 1.97073
1.90273 1.8708 1.81476 1.93248 1.85099 2.02551 2.12291 2.09116 1.95989 1.98793
Octahedron
Na18–O8 Na18–O3 Na18–O4
2.48081 2.57823 2.56240
2.51586 2.5354 2.59825
2.30974 2.37398 2.59859
Seven-vertex polyhedron
Na18–O13 Na17–O1 Na17–O2 Na17–O3 Na17–O13 Na17–O10
2.72484 2.77639 2.50760 2.96068 2.89801 2.23804
2.7376 2.83579 2.49656 2.93436 2.88956 2.27861
2.88996 O–H = 0.96089
Nine-vertex polyhedron
Fig. 2. The FT-RS spectra recorded for the titaniate nanostructures synthesised at the different temperature conditions (120, 140, 160, 180 and 200 °C) along with the theoretical spectra calculated at DFT/PBC/CA-PZ/900 eV/NC-pps theory level for the model Na2Ti3O7 and NaHTi3O7 bulk structures. The theoretical frequencies were multiplied by scaling factor of 0.95. The most prominent bands taken for the discussion were denoted with an asterisk.
stoichiometry relation. The selected model is also consistent with the assumption that the Na2Ti6O13 disodium hexatitanate structures may be found only for the high calcining temperatures, greater than 500 °C[6]. The interatomic distances reported by Yakubovich and Kireev [10,11] are given in Table 1 along with the results delivered by the theoretical computations. The average RMS errors for the Na2Ti3O7 equal 0.019 Å (0.9%) and 0.272 Å (1.17%) for the Ti–O and Na–O distances, respectively. The corresponding errors for the NaHTi3O7 structure, with respect to the quoted reference, equal 0.081 Å (4.2%) and 0.656 Å (5.6%). Raman Spectroscopy The theoretical Raman spectra have been presented in Fig 2. along with the experimental data recorded for the samples prepared at different temperature conditions.
Although the general agreement is satisfactionary, the experimental spectra do not clearly correspond to the theoretically predicted ones. The few reasons of such effect may be pointed out. The first one is related with the computational limitations. As the linear-response computations are practically limited to the use of norm-conserving pseudopotentials, it may be linked with the errors delivered by the core description. Another limitation is related to the strong electron–correlation within the titanium-oxide fragments, which could not be properly restored with pure LDA approach and would require the use of so-called Hubbard correction. Unfortunately, using LDA + U approach for the linear-response computations is also still practically unavailable. However, we can rate our computational quality by comparing the calculated Raman spectra with the literature result reported for bulk Na2Ti3O7. Very good quality Raman spectra have been published by Viana et al. [16]. By comparing our spectrum calculated at the centre of the Brillouin Zone one may found indeed good agreement, and satisfying computational quality. Hence, on the other hand, the problem may be linked not with the artificial computational source, but with the character of the studied samples. The experimental bands are broad and weakly resolved, what indicates their amourphous nature. Such effect breaks the momentum conservation rule, which limits the observed phonons to the C point, and allows phonons from the interior of the Brillouin zone to contribute to the Raman response, revealing the full vibrational density of states throughout the Brillouin Zone. What is more, the real system is definitely not far-periodic, with poorly defined Na2xHx stoichiometry relation. Hence, it may suggest the competition between the contributions of two considered models (pure Na2 and Na2xHx) which is far away from the idealized structures. Despite of these uncertainties, a general analysis of the theoretical spectra may provide the support for the experimental band assignment (as for typical titaniate nanostructures) and deliver some information about the sample character and its crystallinity. The comparison of the theoretical spectra predicted for both structures with the experimental data, may suggest that in the studied samples the Na2Ti3O7 structure is absent – or at least – very strongly dominated by the structures of general formula: H2(1z)TinO2nm+(1z)(OH)2mxH2O. Hence, we have based our spectral analysis on the NaHTi3O7 computations. Because of the limited periodicity of the real system, periodic boundary computations of 24-atomic conventional unit cell is rather simplified model.
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Table 2 The interpretation of the Raman spectra recorded for the samples synthesised at different temperature conditions based on the theoretical computations at the DFT/PBC/CA-PZ/ 900 eV/NC-pps theory level.
mDFT/LDA*0.95 (cm1)
Synthesis temperature (°C) 120
140
Wavenumber (cm1) – 923 vw 671 m 669 m – – 444 m 453 m – 422 m – 365 w – 310 sh 279 st 277 st 251 sh 246 sh 197 m 193 m 168 w 159 w 124 vw 125 vw
160 912 675 599 461 427 367 312 270 238 194 160 119
180 vw m vw m m w sh st sh st vst vw
880 675 – 473 430 373 311 270 245 192 166 108
200 vw m m m w sh st sh m w w
914 672 603 474 428 373 311 277 241 197 168 113
Tentative assignment DFT-LDA
vw m vw m m w sh st sh vst st vw
876 643 587 489 424 373 282 255 220 205 175 120
[Ag] [Bg] 666 [Ag] /695 [Ag] [Bg]/ 598 [Ag] [Bg] [Ag] [Ag] [Ag] [Ag] [Ag], 225 [Bg] [Ag]; 205 [Bg] [Bg]; 194 [Bg] [Bg]; 123 [Ag]; 126 [Ag]
masTi–O–Ti mTi–O; dOH; sOH, cTi–O-Ti mTi–O; dOH msO–Ti–O masO–Ti–O dOH; dO–Ti–O dTi–O–Ti dTi–O–Ti delocalized c Ti–O–Ti delocalized c lattice c lattice d lattice
vw – very weak; w – weak; m – medium; st – intense; vst – very intense; sh – shoulder; m stretching; d bending; s twisting; c out-of-plane; [mode symmetry].
Fig. 3. The projection of the gamma phonon modes linked with the most prominent bands in the experimental spectra. The results obtained with DFT/PBC/CA-PZ/900 eV/NCpps theory level. The frequencies were given according to Table 1 (mDFT/LDA*0.95). The displacement vectors are coloured in black.
The analysis of the most prominent bands allows one to conclude that the structures synthesised at lower temperatures (below 160 °C), may be described as more amourphous, while the structures synthesised at higher temperatures are more crystalline, since the recorded bands are more structured and much better resolved.
Gajovic´ et al. have also presented the analysis of Raman spectra for the titaniate nanostructures synthesised at various temperature conditions [4]. The spectra of the samples synthesised here at 120 and 140° stay in close agreement with the ones published in the quoted paper. Liu and the co-authors [5] have found the following bands for the probed samples: 104, 197, 245, 279, 309, 373, 413,
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428 and 471 cm1. The samples synthesised here at higher temperatures stay in better agreement with the Liu’s data. The bands recorded in our work have been presented in Table 2, along with the assignment based on the first-principle computations. As the crystal point group is C2h (2/m) the mechanical representation is:
Cred ¼ 24Ag þ 12Au þ 12Bg þ 24Bu Three acoustic modes are: Cacoustic = Au + 2Bu and hence, the remaining optic modes are Coptic = 24Ag + 11Au + 12Bg + 22Bu. Within the optical modes 11Au + 22Bu are infrared active while 24Ag + 12Bg are the Raman active ones. In order to facilitate the discussion, the assigned modes have been illustrated in Fig. 3. Based on the presented computations, the very weak band observed near 900 cm1 is defined as the antisymmetric masTi–O stretching within the oxygen shared Ti– O–Ti groups. The mode is related with very weak change in polarizability, what results in very low band intensity. Gajovic´ et al. [4] have observed the red-shifting, accompanied by the increase of the intensity, in function of growing sodium concentration. Our computations seems to confirm this effect, where the related mode is shifted from 876 down to 812 cm1 if compare with the Na2Ti3O7 results. The band near 670 cm1 does not exhibit any wavenumber shift, being directly related with the presence of the hydrogen atoms. The band has been assigned to the mTi–O modes, mixed with the dOH bending vibrations. The band corresponds to the set of vibrations, predicted theoretically at: 698, 666 and 643 cm1, respectively. The dominating mode at 643 cm1 is related to the out-of-plane deformation of the Ti–O–Ti groups, accompanied by the O–H groups twisting. The experimental band does not exhibit any noticeable shifting, however it goes sharper and stronger with the increase of sample crystallinity. The band near 600 cm1 has been observed incidentally in the case of 160 and 200 °C samples. The band is linked to the modes of similar character as the band near 670 cm1, where the Ti–O stretching are observed toward the c-axis direction. The band around 460 cm1 has been assigned to the symmetric O–Ti–O stretchings. The experimental band visibly evolves up to higher wavenumbers with an increase of the structural ordering and gets sharper. Simultaneously, the growth of the 430 cm1 band, correlated with the antisymmetric O–Ti–O stretching, may be also found. Same doublet has been previously reported by Liu et al. [6], but its nature was not explained. It seems that such modes are related with the increase of the system periodicity and the regularity related with the TiO6 building blocks. The more symmetric TiO6 geometry may results in the extension of the longrange interactions and the oscillators coupling, and hence in the increase of their strength. The absence of the quoted band for the structure synthesized at 120 °C may suggest a large disturbance of the TiO6 building blocks. The similar effect has been found in the case of the 370 cm1, slightly blue-shifted upon increase of the structural order. The band has been treated in the literature as the marker band of the heavy atoms sorption [6]. An influence of the sorbed ions on the observed intensity was found, however the nature of this band had not been clearly assigned. It should be mentioned that the observed influence is not striking, hence the Raman measurements may not give an unambiguous confirmation of the heavy ion sorption phenomenon. However, our computations clearly suggest that the observed band may be assigned to the coupled bending modes in the c-a plane. Another characteristic band, also treated as a sorption marker, is the 310 cm1 one. The band may be clearly assigned to the localized dTi–O–Ti bendings in the c-a plane.
Toward the lower wavenumbers, the modes become more delocalized, engaging translations of the cations within the cell. The mode near 280 cm1 may be described as a delocalized c-a plane bending mode of the zig-zag titaniate layer, coupled with the in-plane translation of the cation. The bands observed below 200 cm1 may be described as a complex bending deformation, strongly delocalized over the cell. Conclusions The Raman measurements have been performed for the titaniate nanostructure samples, prepared at different temperature conditions. The experimental studies have been supported by solidstate density functional theory computations. The results clearly manifest an increasing crystallinity of the prepared samples in function of growing synthesis temperature. The theoretical results do not stay in direct relation with the experiment, however a valuable support for the interpretation has been provided. The computations helped us to understand the experimental data and propose the band assignment, supporting the still actual debate. The most prominent bands in the experimental spectra have been assigned and discussed here. The computations have rather excluded the presence of the Na2Ti3O7domains in the studied samples, synthesised with standard procedure. Acknowledgements We are grateful to Barbara Pałys, D.Sc. from the Faculty of Chemistry, University of Warsaw, for the access to the Raman spectrometer and kind help in the measurements. This work was carried out as part of the Strategic Project ‘Safe Nuclear Power Engineering Development Technologies’ supported by The National Centre for Research and Development, Poland. This research was supported in part by PL-Grid Infrastructure. _ K. Druzbicki acknowledges the financial support of Polish Government Plenipotentiary for JINR in Dubna (Grant No. 61/8 11.02.2013). Appendix A. Supplementary Material Supplementary data associated with this article can be found, in the online version, at http://dx.doi.org/10.1016/j.saa.2013.08.034. References [1] A. Rudola, K. Saravanan, C.W. Mason, P. Balaya, J. Mater. Chem. A 1 (2013) 2653. [2] D.J. Yang, Z.F. Zheng, H.Y. Zhu, H.W. Liu, X.P. Gao, Adv. Mater. 20 (2008) 2777. [3] T. Kasuga, M. Hiramatsu, A. Hoson, T. Sekino, K. Niihara, Langmuir 14 (1998) 3160. [4] A. Gajovic´, I. Frišcˇic´, M. Plodinec, D. Ivekovic´, J. Mol. Struct. 924 (2009) 183. [5] H. Liu, D. Yang, E.R. Waclawik, X. Ke, Z. Zheng, H. Zhu, R.L. Frost, J. Raman Spectrosc. 41 (2010) 1792. [6] H. Liu, D. Yang, Z. Zheng, X. Ke, E. Waclawik, H. Zhu, R.L. Frost, J. Raman Spectrosc. 41 (2010) 1331. [7] S.J. Clark, M.D. Segall, C.J. Pickard, P.J. Hasnip, M.J. Probert, K. Refson, M.C. Payne, Z. Kristallogr. 220 (2005) 567. [8] D.M. Ceperley, B.J. Alder, Phys. Rev. Lett. 45 (1980) 566. [9] J.P. Perdew, A. Zunger, Phys. Rev. B 23 (1981) 5048. [10] O.V. Yakubovich, V.V. Kireev, Crystallogr. Rep. 48 (2003) 24. [11] O.V. Yakubovich, V.V. Kireev, Kristallografiya 48 (2003) 29. [12] J. Andzelm, R.D. King-Smith, G. Fitzgerald, Chem. Phys. Lett. 335 (2001) 321. [13] K. Refson, P.R. Tulip, S.J. Clark, Phys. Rev. B 73 (2006) 155114. [14] V. Milman, A. Perlov, K. Refson, S.J. Clark, J. Gavartin, B. Winkler, J. Phys.: Condens. Matter. 21 (2009) 485404. [15] G. Keresztury, S. Holly, J. Varga, G. Besenyi, A. Wang, J.R. Durig, Spectrochim. Acta 49 (1993) 2007. [16] B.C. Viana, O.P. Ferreira, A.G. Souza Filho, J. Mendes Filho, O.L. Alvesa, J. Braz. Chem. Soc. 20 (2009) 167.
Contents lists available at ScienceDirect
Spectrochimica Acta Part A: Molecular and Biomolecular Spectroscopy journal homepage: www.elsevier.com/locate/saa
Short Communication
Solid-state DFT-assisted Raman study of titaniate nanostructures c,b,⇑ _ Katarzyna Łuczyn´ska-Szymczak a,b, Wojciech Starosta a, Kacper Druzbicki a
Institute of Nuclear Chemistry and Technology, Dorodna 16, 03-195 Warsaw, Poland Joint Institute for Nuclear Research, 141980 Dubna, Russia c Department of Chemical Physics, Faculty of Chemistry, Jagiellonian University, Ingardena 3, 30-063 Cracow, Poland b
h i g h l i g h t s
g r a p h i c a l a b s t r a c t
Titaniate nanostructures were
characterized with Raman spectroscopy. The Raman spectra were simulated with solid-state DFT. The general interpretation of most prominent spectral features is given.
a r t i c l e
i n f o
Article history: Received 5 July 2013 Received in revised form 28 July 2013 Accepted 2 August 2013 Available online 13 August 2013 Keywords: Solid-state DFT Linear-response Titaniate nanostructures Raman spectroscopy
a b s t r a c t The first principle solid-state computations in frame of Density Functional Theory have been employed to analyze the Raman spectra of typical titaniate nanostructures. The Raman scattering studies of the nanotitaniates synthesised hydrothermally at different temperature conditions are reported. Local Density Approximation in combination with linear-response computations have delivered detailed analysis of Raman spectra based on the reference Na2Ti3O7 and NaHTi3O7 structures. The interpretation of the most prominent spectral features commonly reported in the literature have been postulated. Ó 2013 Elsevier B.V. All rights reserved.
Introduction In recent years, the multi-dimensional nanostructures have received considerable attention owing to their small sizes, large surface-to-volume ratios or increased density of surface sites. Titanate nanofibers and nanowires belong to group compound with interesting physicochemical properties with still growing application potential. For this reason they have very wide range applicability in such areas as: photocatalysis, ion-exchange or sorption. Recently, Na2Ti3O7 structures were found to be under interest as ⇑ Corresponding author at: Department of Chemical Physics, Faculty of Chemistry, Jagiellonian University, Ingardena 3, 30-063 Cracow, Poland. Tel.: +48 12 663 22 65. _ E-mail address: [email protected] (K. Druzbicki). 1386-1425/$ - see front matter Ó 2013 Elsevier B.V. All rights reserved. http://dx.doi.org/10.1016/j.saa.2013.08.034
potential non-carbon based, low-voltage anode material for room temperature sodium ion battery applications [1]. The titaniate nanostructures became also important in pollution control as revealing good absorption properties e.g. for radioactive ions Sr2+ [2]. Following the pioneer work by Kasuga et al. [3] many papers have been published, reporting relation between synthetic conditions and resulted resulted morphology (nanowires, nanofibers, nanoribbons). In general, the most convenient synthesis strategies are based on TiO2 and TiOSO4 systems. The most important temperature conditions are the temperature, NaOH concentration as well as solvent selection. Raman spectroscopy has found to be very powerful and well established method for the characterization of titanium oxides. Recently, it has been shown by several authors that Raman
´ ska-Szymczak et al. / Spectrochimica Acta Part A: Molecular and Biomolecular Spectroscopy 116 (2013) 646–650 K. Łuczyn
spectroscopy allows one to obtain valuable information about the structural properties of titaniate nanostructures [4–6]. However, according to the quoted literature, the band assignment is still under debate. The main goal of this paper is hence to propose the assignment based on the first-principle solid-state quantumchemical computations.
Experimental and computational details Synthesis The titante nanofibers with Na2xHxTi3O7 stoichiometry were synthesized using hydrothermal method based on the receipt given by Kasuga et al. [3]. 0.025 mol of titanium (IV) oxysulfate (TiOSO4 H2O), received as purchased from Sigma–Aldrich, was dissolved in 80 cm3 of deionised water and mixed with 24 cm3 NaOH. Each synthesis was carried out for 48 h in Teflon-lined stainless steel Berghoff autoclave at following temperatures: 120, 140, 160, 180 and 200 °C. The system was magnetically stirred during the synthesis. The resulted product was cooled down to room temperature. The resulted reaction was strongly alkaline (pH = 14). In the next step the product was filtered and washed with HCl water solution, reducing the pH down to 7, to obtain Na2xHxTi3O7 nanostructures. The final product was dried in air at about 50 °C for 24 h. Raman Spectroscopy The Raman measurements were performed with Nicolet 6700 NRX Fourier-transform spectrometer using 1064 nm excitation line of Nd:YAG laser. The spectra were collected for the powder samples prepared as described earlier, after accumulation of 128 scans and the resolution of 4 cm1. Theoretical Calculations The ab initio computations in periodic boundary conditions (PBC) were performed for the reference titaniate structures, namely Na2Ti3O7 and NaHTi3O7, by means of Density Functional Theory (DFT). The computations were done with CASTEP 6.01. code [7] using Local Density Approximation (LDA) of the exchange–correlation functional (CA-PZ) based on the Ceperley and Alder [8] data as parameterized by Perdew and Zunger [9]. The initial structures were constructed based on the refined data for Na2Ti3O7, published by Yakubovich and Kireev [10,11]. The studied crystals were of the monoclinic P21/m space group (C2h2) with two formulas per unit cell (Z = 2). The experimental lattice parameters, namely: a = 9.1330, b = 3.8060, c = 8.5660 and angles a = 90.00, b = 101.57, c = 90.00 were kept fixed during the internal coordinates optimization. In the case of the NaHTi3O7, half
647
of the sodium atoms were substituted by hydrogens, preserving the assumed symmetry. The computations of the electronic energy were performed in the reciprocal-space with the 2 4 2 Monkhorst–Pack mesh and the 1.00 1009 eV/atom convergence criterion. The normconserving pseudopotentials of Troulliers–Martin were employed to describe the core electrons, while the valence electrons were described with the 900 eV (66 Ry) plane-wave kinetic energy cut-off quality. The geometry optimization has been performed in terms of delocalised internal coordinates [12], with the 0.10 1004 eV/ atom total energy, 0.50 1002 eV/Å max ionic force and 0.50 1002 eV/Å max ionic displacement convergence tolerance, respectively. The phonon computations were performed for the primitive cells at the C point within the quasi-harmonic approximation. The phonon frequencies were obtained by diagonalization of the dynamical matrices computed using density functional perturbation theory (DFPT) [13]. The analysis of the resulting eigenvectors was used in a tentative assignment of the computed modes character, where the symmetry was labeled according to the IUPAC convention. The Raman activity tensors were calculated using a hybrid finite displacement/DFPT method [14] in the presence of external field. The acoustic sum rule (ASR) has been imposed for the frequency of three acoustic modes and no imaginary frequencies were found in both cases. The calculated Raman activities (Ai) were finally transformed into the Raman intensities (Ii), using the relationship derived from the theory of Raman scattering [15].
Ii ¼
vi
h
f ðv 0 v i Þ4 Ai i vi 1 exp hc kT
ð1Þ
where v0 is the exciting wavenumber (in cm1), vi is the frequency of the ith normal mode; h, c and k are the fundamental constants; and T is the temperature (298 K), f is a suitably chosen common scaling factor for all the peak intensities. Results Structure The equilibrium structures optimized with solid-state DFT have been presented in Fig. 1. The assumed structures differ from the real ones by infinite periodicity. The structures include the edge sharing TiO6 octahedra, forming the zig-zag chainlike structures with the cations built in between, allowing to represent the Na2xHxTi3O7 stoichiometry. The real nanostructures are expected to exhibit more or less amourphous characteristic, with non-uniformly defined Na2xHx
Fig. 1. The bulk structures of Na2Ti3O7 (a) and NaHTi3O7 (b), optimized at the DFT/PBC/CA-PZ/900 eV/NC-pps theory level.
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Table 1 Interatomic distances (Å) of bulk Na2Ti3O7 and NaHTi3O7 as reported in the literature [10] and calculated with CA-PZ/900 eV. Atoms
Na2Ti3O7 [10]
Na2Ti3O7 [DFT]
NaHTi3O7 [DFT]
Coordination polyhedron
O1–Ti21 O2–Ti20 O2–Ti21 O3–Ti20 O4–Ti19 O4–Ti20 O5–Ti19 O5–Ti20 O13–Ti20 O14–Ti19
1.98725 1.98120 1.75517 1.70864 1.80651 2.08930 2.18551 2.24458 1.95836 1.97768
1.93753 1.95316 1.76164 1.71293 1.78327 2.06912 2.16006 2.22452 1.95749 1.97073
1.90273 1.8708 1.81476 1.93248 1.85099 2.02551 2.12291 2.09116 1.95989 1.98793
Octahedron
Na18–O8 Na18–O3 Na18–O4
2.48081 2.57823 2.56240
2.51586 2.5354 2.59825
2.30974 2.37398 2.59859
Seven-vertex polyhedron
Na18–O13 Na17–O1 Na17–O2 Na17–O3 Na17–O13 Na17–O10
2.72484 2.77639 2.50760 2.96068 2.89801 2.23804
2.7376 2.83579 2.49656 2.93436 2.88956 2.27861
2.88996 O–H = 0.96089
Nine-vertex polyhedron
Fig. 2. The FT-RS spectra recorded for the titaniate nanostructures synthesised at the different temperature conditions (120, 140, 160, 180 and 200 °C) along with the theoretical spectra calculated at DFT/PBC/CA-PZ/900 eV/NC-pps theory level for the model Na2Ti3O7 and NaHTi3O7 bulk structures. The theoretical frequencies were multiplied by scaling factor of 0.95. The most prominent bands taken for the discussion were denoted with an asterisk.
stoichiometry relation. The selected model is also consistent with the assumption that the Na2Ti6O13 disodium hexatitanate structures may be found only for the high calcining temperatures, greater than 500 °C[6]. The interatomic distances reported by Yakubovich and Kireev [10,11] are given in Table 1 along with the results delivered by the theoretical computations. The average RMS errors for the Na2Ti3O7 equal 0.019 Å (0.9%) and 0.272 Å (1.17%) for the Ti–O and Na–O distances, respectively. The corresponding errors for the NaHTi3O7 structure, with respect to the quoted reference, equal 0.081 Å (4.2%) and 0.656 Å (5.6%). Raman Spectroscopy The theoretical Raman spectra have been presented in Fig 2. along with the experimental data recorded for the samples prepared at different temperature conditions.
Although the general agreement is satisfactionary, the experimental spectra do not clearly correspond to the theoretically predicted ones. The few reasons of such effect may be pointed out. The first one is related with the computational limitations. As the linear-response computations are practically limited to the use of norm-conserving pseudopotentials, it may be linked with the errors delivered by the core description. Another limitation is related to the strong electron–correlation within the titanium-oxide fragments, which could not be properly restored with pure LDA approach and would require the use of so-called Hubbard correction. Unfortunately, using LDA + U approach for the linear-response computations is also still practically unavailable. However, we can rate our computational quality by comparing the calculated Raman spectra with the literature result reported for bulk Na2Ti3O7. Very good quality Raman spectra have been published by Viana et al. [16]. By comparing our spectrum calculated at the centre of the Brillouin Zone one may found indeed good agreement, and satisfying computational quality. Hence, on the other hand, the problem may be linked not with the artificial computational source, but with the character of the studied samples. The experimental bands are broad and weakly resolved, what indicates their amourphous nature. Such effect breaks the momentum conservation rule, which limits the observed phonons to the C point, and allows phonons from the interior of the Brillouin zone to contribute to the Raman response, revealing the full vibrational density of states throughout the Brillouin Zone. What is more, the real system is definitely not far-periodic, with poorly defined Na2xHx stoichiometry relation. Hence, it may suggest the competition between the contributions of two considered models (pure Na2 and Na2xHx) which is far away from the idealized structures. Despite of these uncertainties, a general analysis of the theoretical spectra may provide the support for the experimental band assignment (as for typical titaniate nanostructures) and deliver some information about the sample character and its crystallinity. The comparison of the theoretical spectra predicted for both structures with the experimental data, may suggest that in the studied samples the Na2Ti3O7 structure is absent – or at least – very strongly dominated by the structures of general formula: H2(1z)TinO2nm+(1z)(OH)2mxH2O. Hence, we have based our spectral analysis on the NaHTi3O7 computations. Because of the limited periodicity of the real system, periodic boundary computations of 24-atomic conventional unit cell is rather simplified model.
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Table 2 The interpretation of the Raman spectra recorded for the samples synthesised at different temperature conditions based on the theoretical computations at the DFT/PBC/CA-PZ/ 900 eV/NC-pps theory level.
mDFT/LDA*0.95 (cm1)
Synthesis temperature (°C) 120
140
Wavenumber (cm1) – 923 vw 671 m 669 m – – 444 m 453 m – 422 m – 365 w – 310 sh 279 st 277 st 251 sh 246 sh 197 m 193 m 168 w 159 w 124 vw 125 vw
160 912 675 599 461 427 367 312 270 238 194 160 119
180 vw m vw m m w sh st sh st vst vw
880 675 – 473 430 373 311 270 245 192 166 108
200 vw m m m w sh st sh m w w
914 672 603 474 428 373 311 277 241 197 168 113
Tentative assignment DFT-LDA
vw m vw m m w sh st sh vst st vw
876 643 587 489 424 373 282 255 220 205 175 120
[Ag] [Bg] 666 [Ag] /695 [Ag] [Bg]/ 598 [Ag] [Bg] [Ag] [Ag] [Ag] [Ag] [Ag], 225 [Bg] [Ag]; 205 [Bg] [Bg]; 194 [Bg] [Bg]; 123 [Ag]; 126 [Ag]
masTi–O–Ti mTi–O; dOH; sOH, cTi–O-Ti mTi–O; dOH msO–Ti–O masO–Ti–O dOH; dO–Ti–O dTi–O–Ti dTi–O–Ti delocalized c Ti–O–Ti delocalized c lattice c lattice d lattice
vw – very weak; w – weak; m – medium; st – intense; vst – very intense; sh – shoulder; m stretching; d bending; s twisting; c out-of-plane; [mode symmetry].
Fig. 3. The projection of the gamma phonon modes linked with the most prominent bands in the experimental spectra. The results obtained with DFT/PBC/CA-PZ/900 eV/NCpps theory level. The frequencies were given according to Table 1 (mDFT/LDA*0.95). The displacement vectors are coloured in black.
The analysis of the most prominent bands allows one to conclude that the structures synthesised at lower temperatures (below 160 °C), may be described as more amourphous, while the structures synthesised at higher temperatures are more crystalline, since the recorded bands are more structured and much better resolved.
Gajovic´ et al. have also presented the analysis of Raman spectra for the titaniate nanostructures synthesised at various temperature conditions [4]. The spectra of the samples synthesised here at 120 and 140° stay in close agreement with the ones published in the quoted paper. Liu and the co-authors [5] have found the following bands for the probed samples: 104, 197, 245, 279, 309, 373, 413,
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428 and 471 cm1. The samples synthesised here at higher temperatures stay in better agreement with the Liu’s data. The bands recorded in our work have been presented in Table 2, along with the assignment based on the first-principle computations. As the crystal point group is C2h (2/m) the mechanical representation is:
Cred ¼ 24Ag þ 12Au þ 12Bg þ 24Bu Three acoustic modes are: Cacoustic = Au + 2Bu and hence, the remaining optic modes are Coptic = 24Ag + 11Au + 12Bg + 22Bu. Within the optical modes 11Au + 22Bu are infrared active while 24Ag + 12Bg are the Raman active ones. In order to facilitate the discussion, the assigned modes have been illustrated in Fig. 3. Based on the presented computations, the very weak band observed near 900 cm1 is defined as the antisymmetric masTi–O stretching within the oxygen shared Ti– O–Ti groups. The mode is related with very weak change in polarizability, what results in very low band intensity. Gajovic´ et al. [4] have observed the red-shifting, accompanied by the increase of the intensity, in function of growing sodium concentration. Our computations seems to confirm this effect, where the related mode is shifted from 876 down to 812 cm1 if compare with the Na2Ti3O7 results. The band near 670 cm1 does not exhibit any wavenumber shift, being directly related with the presence of the hydrogen atoms. The band has been assigned to the mTi–O modes, mixed with the dOH bending vibrations. The band corresponds to the set of vibrations, predicted theoretically at: 698, 666 and 643 cm1, respectively. The dominating mode at 643 cm1 is related to the out-of-plane deformation of the Ti–O–Ti groups, accompanied by the O–H groups twisting. The experimental band does not exhibit any noticeable shifting, however it goes sharper and stronger with the increase of sample crystallinity. The band near 600 cm1 has been observed incidentally in the case of 160 and 200 °C samples. The band is linked to the modes of similar character as the band near 670 cm1, where the Ti–O stretching are observed toward the c-axis direction. The band around 460 cm1 has been assigned to the symmetric O–Ti–O stretchings. The experimental band visibly evolves up to higher wavenumbers with an increase of the structural ordering and gets sharper. Simultaneously, the growth of the 430 cm1 band, correlated with the antisymmetric O–Ti–O stretching, may be also found. Same doublet has been previously reported by Liu et al. [6], but its nature was not explained. It seems that such modes are related with the increase of the system periodicity and the regularity related with the TiO6 building blocks. The more symmetric TiO6 geometry may results in the extension of the longrange interactions and the oscillators coupling, and hence in the increase of their strength. The absence of the quoted band for the structure synthesized at 120 °C may suggest a large disturbance of the TiO6 building blocks. The similar effect has been found in the case of the 370 cm1, slightly blue-shifted upon increase of the structural order. The band has been treated in the literature as the marker band of the heavy atoms sorption [6]. An influence of the sorbed ions on the observed intensity was found, however the nature of this band had not been clearly assigned. It should be mentioned that the observed influence is not striking, hence the Raman measurements may not give an unambiguous confirmation of the heavy ion sorption phenomenon. However, our computations clearly suggest that the observed band may be assigned to the coupled bending modes in the c-a plane. Another characteristic band, also treated as a sorption marker, is the 310 cm1 one. The band may be clearly assigned to the localized dTi–O–Ti bendings in the c-a plane.
Toward the lower wavenumbers, the modes become more delocalized, engaging translations of the cations within the cell. The mode near 280 cm1 may be described as a delocalized c-a plane bending mode of the zig-zag titaniate layer, coupled with the in-plane translation of the cation. The bands observed below 200 cm1 may be described as a complex bending deformation, strongly delocalized over the cell. Conclusions The Raman measurements have been performed for the titaniate nanostructure samples, prepared at different temperature conditions. The experimental studies have been supported by solidstate density functional theory computations. The results clearly manifest an increasing crystallinity of the prepared samples in function of growing synthesis temperature. The theoretical results do not stay in direct relation with the experiment, however a valuable support for the interpretation has been provided. The computations helped us to understand the experimental data and propose the band assignment, supporting the still actual debate. The most prominent bands in the experimental spectra have been assigned and discussed here. The computations have rather excluded the presence of the Na2Ti3O7domains in the studied samples, synthesised with standard procedure. Acknowledgements We are grateful to Barbara Pałys, D.Sc. from the Faculty of Chemistry, University of Warsaw, for the access to the Raman spectrometer and kind help in the measurements. This work was carried out as part of the Strategic Project ‘Safe Nuclear Power Engineering Development Technologies’ supported by The National Centre for Research and Development, Poland. This research was supported in part by PL-Grid Infrastructure. _ K. Druzbicki acknowledges the financial support of Polish Government Plenipotentiary for JINR in Dubna (Grant No. 61/8 11.02.2013). Appendix A. Supplementary Material Supplementary data associated with this article can be found, in the online version, at http://dx.doi.org/10.1016/j.saa.2013.08.034. References [1] A. Rudola, K. Saravanan, C.W. Mason, P. Balaya, J. Mater. Chem. A 1 (2013) 2653. [2] D.J. Yang, Z.F. Zheng, H.Y. Zhu, H.W. Liu, X.P. Gao, Adv. Mater. 20 (2008) 2777. [3] T. Kasuga, M. Hiramatsu, A. Hoson, T. Sekino, K. Niihara, Langmuir 14 (1998) 3160. [4] A. Gajovic´, I. Frišcˇic´, M. Plodinec, D. Ivekovic´, J. Mol. Struct. 924 (2009) 183. [5] H. Liu, D. Yang, E.R. Waclawik, X. Ke, Z. Zheng, H. Zhu, R.L. Frost, J. Raman Spectrosc. 41 (2010) 1792. [6] H. Liu, D. Yang, Z. Zheng, X. Ke, E. Waclawik, H. Zhu, R.L. Frost, J. Raman Spectrosc. 41 (2010) 1331. [7] S.J. Clark, M.D. Segall, C.J. Pickard, P.J. Hasnip, M.J. Probert, K. Refson, M.C. Payne, Z. Kristallogr. 220 (2005) 567. [8] D.M. Ceperley, B.J. Alder, Phys. Rev. Lett. 45 (1980) 566. [9] J.P. Perdew, A. Zunger, Phys. Rev. B 23 (1981) 5048. [10] O.V. Yakubovich, V.V. Kireev, Crystallogr. Rep. 48 (2003) 24. [11] O.V. Yakubovich, V.V. Kireev, Kristallografiya 48 (2003) 29. [12] J. Andzelm, R.D. King-Smith, G. Fitzgerald, Chem. Phys. Lett. 335 (2001) 321. [13] K. Refson, P.R. Tulip, S.J. Clark, Phys. Rev. B 73 (2006) 155114. [14] V. Milman, A. Perlov, K. Refson, S.J. Clark, J. Gavartin, B. Winkler, J. Phys.: Condens. Matter. 21 (2009) 485404. [15] G. Keresztury, S. Holly, J. Varga, G. Besenyi, A. Wang, J.R. Durig, Spectrochim. Acta 49 (1993) 2007. [16] B.C. Viana, O.P. Ferreira, A.G. Souza Filho, J. Mendes Filho, O.L. Alvesa, J. Braz. Chem. Soc. 20 (2009) 167.