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Article Cite This: Inorg. Chem. XXXX, XXX, XXX−XXX

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Unraveling the Structure−Raman Spectra Relationships in V2O5 Polymorphs via a Comprehensive Experimental and DFT Study Mikhail B. Smirnov,*,† Evgenii M. Roginskii,‡ Konstantin S. Smirnov,§ Rita Baddour-Hadjean,∥ and Jean-Pierre Pereira-Ramos∥ †

Department of Physics, St. Petersburg State University, 7/9 Universitetskaya nab., 199034 St. Petersburg, Russia Ioffe Institute, Polytekhnicheskaya 26, 194021 St. Petersburg, Russia § Université de Lille, CNRS, UMR 8516−LASIR−Laboratoire de Spectrochimie Infrarouge et Raman, F-59000 Lille, France ∥ Institut de Chimie et des Matériaux Paris Est, ICMPE/GESMAT, UMR 7182 CNRS−Université Paris Est-Créteil, 2 rue Henri Dunant, 94320 Thiais, France

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‡

S Supporting Information *

ABSTRACT: Vanadium pentoxide polymorphs (α-, β-, γ′-, and ε′-V2O5) have been studied using the Raman spectroscopy and quantum-chemical calculations based on density functional theory. All crystal structures have been optimized by minimizing the total energy with respect to the lattice parameters and the positions of atoms in the unit cell. The structural optimization has been followed by the analysis of the phonon states in the Γ-point of the Brillouin zone, and the analysis has been completed by the computation of the Raman scattering intensities of the vibrational modes of the structures. The optimized structural characteristics compare well with the experimental data, and the calculated Raman spectra match the experimental ones remarkably well. With the good agreement between the spectra, a reliable assignment of the observed Raman peaks to the vibrations of specific structurals units in the V2O5 lattices is proposed. The obtained results support the viewpoint on the layered structure of vanadium pentoxide polymorphs as an ensemble of V2O5 chains held together by weaker interchain and interlayer interactions. Similarities and distinctions in the Raman spectra of the polymorphs have been highlighted, and the analysis of the experimental and computational data allows us, for the first time, to put forward spectrum−structure correlations for the four V2O5 structures. These findings are of the utmost importance for an efficient use of Raman spectroscopy to probe the changes at the atomic scale in the V2O5-based materials under electrochemical operation.

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INTRODUCTION Vanadium pentoxide (V2O5) is a transition metal oxide with several structures and a wide range of applications. Besides its use in heterogeneous catalysis1 and as electrochromic material,2 orthorhombic α-V2O5 has been recognized since the 1970s as a promising cathode material for rechargeable lithium batteries due to its high capacity and a wide voltage range (4− 2.15 V vs Li+/Li).3,4 A monoclinic β-V2O5 is obtained from αV2O5 at high-temperature/high-pressure conditions,5 and other V2O5 polymorphs can be produced by chemical removal of metallic species from vanadium oxide bronzes MxV2O5 through oxidation reactions. Thus, γ′-V2O5 and ε′-V2O5 structures are obtained by complete removal of Li or Cu from the γ-LiV2O56 and ε-Cu0.9V2O57,8 bronzes, respectively, with the structure of the bronze precursors kept upon the cation extraction. The operating principle of a battery function relies on the electron transfer reaction accompanied by the electrochemical intercalation/deintercalation of alkali metal atoms into the oxide lattice. These reactions are responsible for structural © XXXX American Chemical Society

changes in the host material whose nature and amplitude greatly influence the electrochemical performance, and especially the cycle life. The α-, β-, γ′-, and ε′-V2O5 lattices can reversibly accommodate up to 2 lithium ions/mol due to the presence of two V5+ centers reducing into V4+. While lithiated phases involved during the discharge−charge of αV2O5 have been thoroughly described,3,4 only a few papers have addressed the electrochemical lithiation of γ′-V2O5,9,10 βV2O5,11 and ε′-V2O5.7,8 The understanding of the origins and atomistic mechanisms of the structural transformations is essential for improvement of the performance of existing cathode materials and for a rational design of new ones with even better characteristics. For this purpose, one needs an effective, rapid, sensitive, and nondestructive tool for monitoring the structural transformations. Methods of vibrational spectroscopy, and Raman spectroscopy in particular, were shown to be very suitable for Received: May 3, 2018

A

DOI: 10.1021/acs.inorgchem.8b01212 Inorg. Chem. XXXX, XXX, XXX−XXX

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Inorganic Chemistry this purpose.12 However, the efficiency of the spectroscopic monitoring of structural changes heavily depends on the availability of a reliable scheme that relates the observed spectral features to the presence of specific fragments in the structure. Such an assignment scheme can only be derived with the help of quantum-chemical calculations that have nowadays become indispensable to studies of cathode materials.13,14 Numerous computational studies based on atomistic simulations have followed the extensive experimental investigation of V2O5 structures. Among different polymorphs, most of the attention has been paid to α-V2 O5 which is thermodynamically the most stable at ambient conditions. First, computational works using the semiempirical tightbinding scheme and force-field models have been aimed at elucidating the band structure15 and the vibrational dynamics16,17 of α-V2O5. Subsequent investigations employing methods of quantum chemistry have been mainly devoted to the structure and electronic states of this compound,18−25 while much less attention has been given to its vibrational dynamics.26−29 Due to the importance of V2O5 as supported catalysts, some studies considered two-dimensional V2O5 models.21,27 Soon after the discovery of the high-pressure βV2O5 phase,5 Gallardo-Amores and co-workers investigated the transformation of α-V2O5 under pressure,30 and more recent works described the electronic structure and the vibrational states of the β-V2O5 lattice.28,31,32 Recently, an atomistic mechanism of the α−β phase transition has been suggested on the basis of quantum-chemical calculations.33 Regarding other V2O5 polymorphs, computational studies of the γ′-V2O5 phase are fewer in number,20,28,29 whereas, to the best of our knowledge, the ε′-V2O5 polymorph has remained beyond the scope of modeling works. Moreover, to the best of our knowledge, its structure is not solved yet, and the experimental structural data existing on ε′-V2O5 are limited to its X-ray diffraction pattern.7 Despite a large number of modeling works on α-, β-, and γ′V2O5, the comparison of their results is hampered by the fact that the calculations were often carried out at different levels of theory and/or used different approximations. Only a few studies have reported comparative investigations of different V2O5 phases. Thus, Willinger et al.20 compared the geometric and electronic structures of α-V2O5 and γ′-V2O5. DFT calculations of the β- and α-V2O5 structures allowed the interpretation of the Raman spectrum of the high-pressure polymorph and highlighted spectral features related to structural differences of the two V2O5 phases.32 Porsev and co-workers28 discussed the bulk and layer stability, electronic structure, and phonon states of the α-V2O5, β-V2O5, and γ′V2O5 phases. In all these studies, except ref 32, the analysis of vibrational dynamics was limited to the frequencies and symmetries of the vibrational modes, without consideration of spectral intensities. Therefore, the outcome of these works can hardly be used for establishing a reliable structure−spectrum relationship for these materials. The present paper presents results of the first comparative experimental and computational spectroscopic study of four V2O5 polymorphs, namely, α-, β-, γ′-, and ε′-V2O5. The experimental structures and Raman spectra of these materials are compared with the counterpart results obtained with DFT calculations performed at the equal theoretical level. In these calculations, the emphasis is set on the correlation between the structural organization of different V2O5 phases and their Raman-active vibrational states. The first goal of this study is to

provide a reliable description of observed spectral pattern at the atomic level. The second goal is to find how the structural peculiarities of the crystalline lattices manifest themselves in the Raman spectra and, thus, to establish structure−spectrum correlations that can be used for monitoring structural changes in V2O5-based materials. The paper is organized as follows. The next section provides a summary of the experimental procedures used for the sample preparation and characterization, and the section also reports on computational protocol. Then, the structures of the V2O5 polymorphs are discussed with an emphasis on similarities and differences of the crystalline lattices. This discussion is followed by the analysis of the experimental Raman spectra with the help of the results of calculations. This analysis highlights likenesses and distinctions in the spectra of the polymorphs and relates them to specific structural characteristics. Final discussion deals with structure−spectrum correlations that can be inferred from the comparative study of the four structures, and these findings are summarized in Conclusions. The experimental and calculated structural data of the V2O 5 polymorphs are gathered in Supporting Information.

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EXPERIMENTAL AND COMPUTATIONAL DETAILS

Experimental Procedure. α-V2O5 is a commercial material (Sigma-Aldrich company, 99.995%). γ′-V2O5 and ε′-V2O5 were obtained by chemical oxidation of γ-LiV2O5 and ε-Cu0.9V2O5, respectively, using NO2BF4 as an oxidizing agent with details of the experimental conditions described elsewhere.34 The electrochemical titration using galvanostatic oxidation and the chemical redox titration have confirmed the 5+ oxidation state of vanadium in as-prepared γ′V2O5 and ε′-V2O5 samples. In addition, a color change from brown to orange and from black to orange was observed for the ε′- and γ′phases samples, respectively, that indicates the loss of metallic properties for the metal-free structures. X-ray diffraction (XRD) patterns were collected using a Panalytical X’Pert Pro diffractometer equipped with a Co Kα X-ray source (λ = 1.7889 Å) and an X’celerator linear detector. The collected data were treated with the Rietveld analysis procedure using the GSAS ExpGUI package.35,36 The Raman spectra were measured with a LaBRAM HR 800 (Jobin-Yvon-Horiba) Raman microspectrometer including Edge filters and equipped for signal detection with a back illuminated charge coupled device detector (Spex CCD) cooled by Peltier effect to 200 K. A He:Ne laser (632.8 nm) was used as the excitation source. The spectra were measured in backscattering geometry. The resolution was about 0.5 cm−1. A 100× objective was used to focus the laser light to a spot of 1 μm2 size on the sample surface. To avoid a local heating of the sample, the power of the laser beam was adjusted to 0.2−0.5 mW with a neutral filter. According to experiments,37,38 the bandgap in α-V2O5 ranges from 2.3 to 2.8 eV, which is larger than the photon energy of the excitation light (1.96 eV). There are no experimental data on the bandgap in other V2O5 polymorphs, but one can reasonably assume that its value is close to that in α-V2O5. Hence, the Raman measurements were carried out in the off-resonance conditions. Computational Procedure. The calculations were carried out with VASP39,40 code using the pseudopotential approach and the plane-wave basis set for valence electronic states. The 3p3d4s electrons of the V atom and the 2s2p electrons of the O atom were considered as valence electrons, and the interactions between the core and valence electrons were described with the projector-augmented wave (PAW) method.41,42 Exchange and correlation were treated within the GGA approximation to DFT with the Perdew−Burke− Ernzerhof (PBE) exchange-correlation functional.43 The dispersion interactions necessary for a proper description of interlayer spacing in layered V2O5 structures24,25 were taken into account via the B

DOI: 10.1021/acs.inorgchem.8b01212 Inorg. Chem. XXXX, XXX, XXX−XXX

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Figure 1. Crystal structure of α-V2O5 in the xz- (a) and xy- (b) projections and an isolated V2O5 chain (c). White and gray circles represent the oxygen and vanadium atoms, respectively; interchain contacts (ladder steps) are shown by dashed lines. The dashed light blue rectangle in part a indicates the unit cell.

Table 1. Space Group (SG), Lattice Parameters (in Å and deg), and Lengths of Intralayer V−O Contacts (in Å) in the V2O5 Structures According to Experimental Data and Calculation Results (in Parentheses) parama

α-V2O5b

β-V2O5c

γ′-V2O5b

ε′-V2O5b

bond

SG a b c β d1

Pmmn (No. 59) 11.513 (11.603) 3.566 (3.606) 4.379 (4.472) 90° 1.575 (1.609)

d2

1.768 (1.803)

d3

1.877 (1.905)

d4

2.012 (2.041)

P21/m (No. 11) 6.2846 (6.3284) 3.5718 (3.6185) 7.1140 (7.1826) 90.069 (90.050) 1.583 (1.598) 1.645 (1.674) 1.881 (1.901) 1.705 (1.755) 1.871 (1.908) 1.872 (1.894) 2.296 (2.342) 2.176 (2.124)

Pnma (No. 62) 9.9439 (10.1346) 3.5835 (3.6163) 10.0376 (10.1931) 90° 1.572 (1.609) 1.568 (1.606) 1.790 (1.801) 1.814 (1.822) 1.897 (1.917) 1.866 (1.906) 1.978 (2.016) 2.068 (2.040)

C2/m (No. 12) 11.70 (11.794) 3.63 (3.663) 8.84 (9.087) 109.60 (109.40) − (1.592) − (1.596) − (1.835) − (1.836) − (1.922) − (1.915) − (2.022) − (2.085)

Va−O1a Vb−O1b Va−O3 Vb−O3 Va−O2a Vb−O2b LS(Va) LS(Vb)

a

See Figure 1 for the notation of V−O contacts. bPresent work, see text for details. cExpt, ref 5.

semiempirical D2 correction.44 The localized character of vanadium 3d states was considered with the DFT+U scheme by Dudarev et al.45 with the value of the Habbard parameter U = 4 eV.22 Optimizations of V2O5 polymorph structures were performed for a series of five volumes of unit cell. In each optimization the atomic positions and cell parameters were allowed to vary, whereas the volume and the symmetry of the lattice were kept fixed. The optimization was considered to be completed when the maximum force on ions was less than 2 × 10−3 eV/Å. The equilibrium cell volume was obtained by fitting the energy vs volume curve with the Murnaghan equation of state.46 This approach permitted us to avoid problems related to the Pulay stress and to changes of the plane-wave basis set size that accompany volume variations while simultaneously optimizing both the volume and atomic positions. The results were tested for the convergence with respect to the k-point sampling and to the plane-wave kinetic energy cutoff. It was found that the convergence of total energy within 2.5 meV/atom was achieved with the energy cutoff of 950 eV and with 2 × 6 × 6, 4 × 6 × 4, 2 × 6 × 2, and 2 × 6 × 4 grids of k-points chosen according to the Monkhorst−Pack scheme47 in the irreducible part of the Brillouin zone of the α-, β-, γ′-, and ε′-V2O5 structures, respectively. The optimized structures were employed in the subsequent calculations of the phonon states that were done with the same calculation parameters and the convergence criterion as in the optimization runs. The vibrational states in the Γ-point of the Brillouin zone were computed using the density functional perturbation theory (DFPT) realized in VASP.39,40 No scaling was applied to the calculated frequencies of vibrational modes.

Complete Raman spectra of the V2O5 polymorphs were obtained by computing the Raman scattering intensities of Raman-active vibrational modes. The intensity Ik of the mode k in the spectrum of a powder sample was calculated as Ik =

(ω0 − ωk )4 Rk ωk (1 − exp(−ℏωk /kBT ))

(1)

where ω0 is the frequency of the incident radiation, T is the temperature, and ℏ and kB have their conventional meaning. The quantity Rk in eq 1 is the Raman activity of the mode k

R k = A̅ k2 + (7/45)Bk2

(2)

where A̅ k and Bk are the trace and the anisotropy of the Raman tensor Ak. The latter was calculated by numerical differentiation of the macroscopic dielectric tensor ϵ

Ak =

Ω ∂ϵ 4π ∂Q k

(3)

with Ω being the unit cell volume and Qk being the k-th vibrational mode. The intensities Ik were computed for T = 300 K and for the frequency of the incident radiation ω0 corresponding to the wavelength λ0 = 633 nm of the helium−neon laser. The so-obtained bar spectrum was convoluted with a Lorentzian function with fwhm = 8 cm−1. C

DOI: 10.1021/acs.inorgchem.8b01212 Inorg. Chem. XXXX, XXX, XXX−XXX

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CRYSTAL STRUCTURE OF V2O5 POLYMORPHS Four crystalline polymorphs of pure vanadium pentoxide have been reported; these are α-, β-, γ′-, and ε′-V2O5. The primary member of this family is α-V2O5 whose structure is presented in Figure 1. The orthorhombic crystal lattice of the α-phase consists of layers stacked along the z-axis.48 The layers are built of infinite V2O5 chains running in the y-direction (Figure 1c). Each vanadium atom in the chains forms four valence bonds: vanadyl VO1 double bond (d1), VO3 bond (d2) in V O3V bridge lying in the xz-plane, and two VO2 bonds (d3) resulting in the VO2V bridges oriented along the yaxis. The chains in the layers are linked to each other by interchain VO2 contacts (d4) named hereafter “ladder steps” (LS) and shown by dashed lines in Figure 1. Finally, the layers are held together by weak van-der-Waals-type interlayer interactions. The structure of α-V2O5 has all features typical of other members of the family, namely, the V2O5 chains running in the y-direction and connected in layers via ladder steps and the layers then stacked in the third dimension and held together by weak interlayer interactions. Relatively weak interchain and interlayer interactions in V2O5 lead to the ability to form a number of polymorph structures and to a high structural flexibility playing an important role in the electrochemical applications of V2O5.34,49 The space groups and lattice parameters of the vanadium pentoxide polymorphs are gathered in the upper part of Table 1, whereas the complete experimental and computed data on the structures are given in Supporting Information. Upon a high-pressure/high-temperature impact, α-V2O5 undergoes a phase transition and the monoclinic β-V2O5 phase appears;5 its structure is presented in Figure 2. In the

Figure 3. Crystal structure of γ′-V2O5 in the xz-projection. See caption to Figure 1 for notations.

While the VO1 vanadyl bonds in a chain of the α-structure are parallel to each other, they are antiparallel in the γ′structure (cf., Figure 1a and Figure 3). In addition, the neighboring layers in the γ′-V2O5 lattice are not related by translation but by gliding mirror-plane transformation. This results in the c-parameter of the γ′-V2O5 unit cell that is approximately 2 times larger than that of the α-V2O5 cell. ε′-V2O5 is obtained by extraction of copper atoms from εCu0.9/0.95V2O5 bronzes. In contrast to other V2O5 polymorphs, the structure of the ε′-phase has not been solved yet. Sharp diffraction lines present in the X-ray diffraction pattern measured for the ε′-V2O5 sample (Figure S1 in Supporting Information) can be fully indexed with that of the parent εCu0.9V2O5 precursor, which indicates that copper extraction does not significantly alter the host lattice. The resulting lattice parameters are given in Table 1. The XRD pattern exhibits very pronounced (00l) refections which have been ascribed to the existence of both a strong preferential orientation along the c-axis and a long-range disorder in the ab-plane promoted by copper removal.7 However, the diffractogram does not have enough well-defined peaks to allow a high-quality Rietveld refinement. Consequently, by presenting the structure of this polymorph, we rely on that of ε-Cu0.95V2O5 bronze that has been accurately solved in ref 50. Like in other polymorphs, the layered structure of the ε′phase is built of infinite V2O5 chains lying in the ab crystallographic plane, Figure 4. The unit cell of the ε′-V2O5 structure has two types of such chains, noted hereafter as W and M, that are related to each other by the inversion

Figure 2. Crystal structure of β-V2O5 in the xz-projection. See caption to Figure 1 for notations. Dotted lines indicate Va−O1b contacts, see text for details.

course of concerted displacement of V2O5 chains of the αphase,33 the V atoms switch oxygens in ladder steps and bring about new Va−O2b and Vb−O2a LS contacts, which are depicted by dashed lines in Figure 2. This transformation results in doubling the layer thickness in the β-V2O5 structure compared to the α-V2O5 one (Table 1). Furthermore, a half of the vanadyl d1 bonds lose their terminal character and form highly asymmetric Va−O1b−Vb bridges. The new Va−O1b contacts of ca. 2.06 Å length, shown in Figure 2 by dotted lines, connect the chains in the x-direction. Finally, the Va− O3−Vb bridges become asymmetric in the β-V2O5 lattice. The γ′-V2O5 structure (Figure 3) retains the memory of the parent γ-LiV2O5 bronze lattice,6 and its structure also consists of layers formed by V2O5 chains. However, the shape of the chains in the layers differs from that in the α-V2O5 lattice.

Figure 4. Crystal structure of ε′-V2O5 in the ac-projection. See caption to Figure 1 for notations. Letters W and M denote two types of V2O5 chains in the structure. D

DOI: 10.1021/acs.inorgchem.8b01212 Inorg. Chem. XXXX, XXX, XXX−XXX

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Inorganic Chemistry transformation (see Figure 4). Along the a-direction, the W (and M) chains are linked via ladder steps, thus yielding WW and MM layers. In the c-direction, the layers are connected by weak Vb−O3′ and Va−O2′ interactions (the prime denotes atoms of neighboring layer) shown by dotted lines in Figure 4. Thus, one can consider ε′-V2O5 as a layered structure built of the WM bilayers. It should be noted that a more traditional viewpoint on the structure of V2O5 polymorphs is to consider them as an arrangement of VOx polyhedra or V2O4 chains in which V−O contacts longer than 2 Å are viewed as ”real” chemical bonds. The above presented approach to the organization of V2O5 structures as ensembles of [V2O5]∞ chains linked in threedimensional lattices via weaker interchain and interlayer interactions is more consistent with the crystal chemistry viewpoint and follows the V−O bond multiplicities.17 The analysis of V−O bond lengths in the structures of the polymorphs is also in line with the approach. The experimental and calculated values of the bond lengths are gathered in the lower part of Table 1, and one can see that the LS contacts d4 are longer than the intrachain V−O bonds d1, d2, and d3 in all the V2O5 polymorph structures. (The absence of corresponding entries for the ε′-V2O5 structure in Table 1 is due to the lack of data on the atom positions.) It is noteworthy that Kubas et al.51 analyzed the V−O bond length distribution in various VOx compounds and pointed out that the V−O bonds longer than 2 Å are always found in the structures containing V atoms in the hypervalence state. Finally, the presented viewpoint is supported by results of calculations in which the energy gain upon the formation of layer of α-V2O5 from isolated [V2O5]∞ chains was estimated.52 The gain was computed to be equal to ca. 15 kJ/mol per V−O ladder-step contact that is at least by 1 order of magnitude smaller than a typical energy of metal−oxygen bond. Figure 5 compares the lengths of the V−O bonds in the experimental and optimized structures of α-V2O5, β-V2O5, γ′-

With the information on the structure of the V 2O 5 polymorphs in hand, we now turn to the consideration of their vibrational dynamics with a particular emphasis on the Raman-active phonon states.

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RAMAN SPECTRA OF V2O5 POLYMORPHS

α-V2O5. The α-V2O5 structure (Z = 2, point symmetry D2h) has 21 Raman-active vibrational modes distributed over the irreducible symmetry representations as follows: Γ(R) = 7Ag + 7B2g + 3B1g + 4B3g

(4)

A peculiarity of the α-V2O5 lattice is that all atoms are situated in mirror planes perpendicular to the y-axis (see Figure 1b). Consequently, modes of Ag and B2g symmetry can involve only atomic displacements in the xz-plane, i.e., symmetric with respect to the σy mirror plane, while only displacements along the y-axis, antisymmetric with respect to the σy-plane, can contribute to the B1g and B3g modes. Frequencies of bands in the experimental Raman spectrum of α-V2O5 and the calculated frequencies and Raman activities Rk (eq 2) of the Raman-active vibrational modes of the structure are listed in Table 2. One can see that the calculated frequencies agree well with the experimental values and with results of previous computational studies.27−29 The simulated Raman spectrum obtained with the procedure described above is compared with the experimental spectrum of a powder sample in Figure 6. Owing to a very good agreement between the two spectra, one can reliably establish a one-to-one correspondence between the spectral features and the vibrational modes. Analysis of the atomic displacements (eigenvectors of the dynamical matrix) allows relating the observed bands to specific atomic motions. The assignment is presented in Table 2, and it is in line with previously proposed attributions based on either force-field16,17,53 or quantumchemical21,26−29 calculations. In Figure 6 it stands out that the number of peaks in the Raman spectrum of α-V2O5 is much less than the number of Raman-active vibrational modes. This particularity is explained by two reasons: (i) Some modes have a very low scattering intensity. (ii) There are modes of different symmetry with close frequencies. Both reasons are related to a relatively high symmetry of the α-lattice that constrains all vanadium atoms to be equivalent and the V−O3−V bridges to be symmetric. The first reason accounts for the absence of peaks corresponding to B2g modes with calculated frequencies of 1001, 947, 489, and 138 cm−1 (Table 2). While these modes are formally allowed in the Raman spectrum, they are asymmetric with respect to the mirror plane bisecting the V−O3−V bridges, and the mode intensities are low because of a cancellation effect. The closeness of frequencies of modes of different symmetries (reason ii) is due to a weak kinematic and energy coupling between y-displacements of atoms in the neighboring ladders. Owing to this factor, the B1g and B3g modes, which correspond to the in-phase and antiphase combinations of y-displacements, respectively, are almost degenerate. This concerns the B1g/B3g couples with calculated frequencies of 694, 287, and 160 cm−1. From the mode assignment presented in Table 2, one can see that all modes above 480 cm−1 can be described as bondstretching vibrations. The highest-frequency mode can be characterized as a V−O1 bond-stretching vibration, and its high frequency is due to a double character of the bond.

Figure 5. Correlation of the V−O bond lengths in the experimental and optimized V2O5 structures. The dashed line is the identity line.

V2O5, and ε′-V2O5, and one can see a very good correlation between the computed and measured values. Most of the points in Figure 5 lie above the identity line, thus, indicating that the calculations slightly overestimate the bond lengths. This outcome is typical of the GGA level calculations. E

DOI: 10.1021/acs.inorgchem.8b01212 Inorg. Chem. XXXX, XXX, XXX−XXX

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Table 2. Frequencies ω (in cm−1) and Raman Activities Rk (Equation 2, in 10−6 au) of the Raman-Active Phonons of the αV2O5 Structure expt

calcd, this work ω

ω

Rk

symm

1

995

3

702

4

528

6 7

483 404

1005 1001 947 694 695 519 489 482 393 352 299 296 287 280 229 200 194 160 160 138 103

4562 0 0 393 878 281 35 266 46 97 63 70 321 135 49 25 31 6 149 0 8

Ag B2g B2g B1g B3g Ag B2g Ag Ag B2g B2g Ag B3g B1g B3g B2g Ag B3g B1g B2g Ag

peaka

306 A1

285

198

A2

146 107

assignmente ν(VO1) νas(VO3V) νas(VO2V) νs(VO3V) ν(LS) δ (VO3V) LM(a) LM(b − c) LM(d) y(O3) LM(b + c) LM(e) LM(f) LM(g)

calcdb ω

calcdc ω

calcdd ω

1031 1031 929 693 693 518 482 467 396 352 309 303 285 285 230 192 186 148 147 145 104

1105 1102 1008 728 727 560 522 505 431 378 323 316 303 301 243 211 205 163 160 150 109

1051 1047 968 742 742 535 516 508 382 357 289 282 276 273 217 187 175 160 156 138 100

Figure 6. bRef 27. cRef 28. dRef 29. eν, bond-stretching vibration; δ, angle-bending vibration; LM(X), ladder mode, X = type of the distortion, Figure 7; y(O3), mode with maximal amplitude of the O3 atoms in the y-direction. a

the polarizability variations due to the V−O3 bond-stretchings cancel each other. Peak 3 at 702 cm−1 (Figure 6) is related to the couple of B1g/B3g modes corresponding to the νas(V−O2−V) vibrations. This is a prominent example of quasidegeneracy of the B1g/B3g congeneric modes due to weak interchain interactions. The vibrational mode at the origin of peak 4 at about 528 cm−1 can be characterized as a symmetric stretching νs(V− O3−V) vibration. This vibration is partly mixed with the ladder step stretching vibration ν(LS) that has a major contribution to the mode corresponding to the peak 6 at 483 cm−1. Such a low-frequency value of the ν(LS) mode is due to the fact that the V−O2 LS bonds are not real valence bonds but interchain quasi-intermolecular contacts. As it was first noted by Abello and co-workers,16 the frequency sequence ν(d1) > ν(d2) > ν(d3) > ν(d4) is in line with the relationship d1 < d2 < d3 < d4. The Raman bands below 400 cm−1 correspond to modes involving angle-bending vibrations. The highest-frequency band 7 in this region is attributed to a mode consisting of a δ(V−O3−V) angle-bending vibration coupled with ν(LS). Atomic displacements in modes below 350 cm−1 are mostly localized within the ladder steps, and thus, we refer to these modes as ladder modes (LM). Their patterns are schematically shown in Figure 7. The analysis of atomic displacements sheds some light on the origin of the intense Raman peaks A1 and A2 in this region. Thus, peak A1 is due to the B3g mode that involves a shear-like distortion of the ladders accompanied by wagging oscillations of the vanadyl bonds (Figure 7d). Peak A2 is related to the B1g mode that can be described as a pure shear-like distortion of the ladders (Figure 7e). β-V2O5. The phonon spectrum of the β-V2O5 lattice (Z = 2, point symmetry C2h) contains the same number of Raman-

Figure 6. Comparison of experimental and calculated Raman spectra of α-V2O5. Raman scattering intensities are in arbitrary units, and the intensity in the calculated spectrum was negated for the sake of clarity. Color bars denote positions of vibrational modes of different symmetry species shown on the left side.

Next in frequency is the νas(V−O3−V) mode that is formally allowed in a Raman spectrum with a crossed xz polarization but can hardly be detected experimentally. The calculated frequency value of 947 cm−1 is close to the values of 954 and 963 cm−1 reported in the only experimental works mentioning this vibrational mode.17,54 The low intensity of this mode is caused by the fact that the V−O3−V bridge is symmetric with respect to the bisecting mirror plane, and thus, F

DOI: 10.1021/acs.inorgchem.8b01212 Inorg. Chem. XXXX, XXX, XXX−XXX

Article

Inorganic Chemistry

Figure 7. Atomic displacements in ladder modes below 400 cm−1. Displacements of atoms in the plane of the figure are denoted by arrows, and displacements perpendicular to the plane are denoted by plus and minus signs: (a) breathing, (b) puckering, (c) VO1 wagging, (d, e) shear-like distortions, and (f, g) rotations of ladders as a whole in the xz-plane.

active modes as that of the α-V2O5 structure. The modes are distributed by symmetry representations as follows: Γ(R) = 14Ag + 7Bg

significantly better agreement with the experimental data than the previously reported results.32 The comparison of Figure 8 with Figure 6 reveals spectral features in the Raman spectrum that distinguish β-V2O5 from α-V2O5. Below we try to relate the observed distinctions between the spectra with the structural differences between the two V2O5 polymorphs. Two intense peaks at 942 and 1021 cm−1 dominate in the high-frequency part of the spectrum of the β-V2O5 structure instead of one at 992 cm−1 in the spectrum of α-V2O5. These peaks are related to the bond-stretching vibrations of the V− O1 vanadyl bonds. There are two types of such bonds in the βV2O5 lattice with the lengths 1.583 and 1.645 Å for the Va− O1a and Vb−O1b bonds, respectively. This structural peculiarity of the β-phase becomes apparent in the Raman spectra as the appearance of the two peaks 1a and 1b, and the frequency difference between the peaks correlates with an empirical relation between the V−O bond length and the corresponding bond-stretching frequency.16 In the frequency interval 500−800 cm−1, there are three Raman peaks (2, 3, and 4) in the spectrum of β-V2O5, whereas two peaks (3 and 4) are observed in the spectrum of the αphase. The reason for the appearance of the new peak in the spectrum of the β-phase is a strong asymmetry of the V−O3− V bridge in the structure (see values of d2 contacts in Table 1). This difference in the bond lengths results in a large difference of the corresponding V−O bond-stretching force constants, and consequently, the νas(V−O3−V) and νs(V−O3−V) modes of the bridge transform into the ν(Va−O3) and ν(Vb−O3) modes with relatively high Raman activities. The eigenvector analysis allows us to ascribe peaks 2 and 4 to the vibrational modes corresponding to the ν(Vb−O3) and ν(Va− O3) vibrations, respectively. Peak 3 in the Raman spectra of both the polymorphs results from modes that can be characterized as an asymmetric stretching vibration of the V−O2 bonds, νas(V−O2−V). Each structure has two such Raman-active modes whose corresponding eigenvectors are schematically shown in Figure 9. One can see that the main difference between the modes of the α-V2O5 and β-V2O5 lattices consists of the phase ratios between y-displacements of the O2 atoms in the ladders. The oxygen atoms of the same ladder oscillate in antiphase in the B1g and B3g modes of the α-structure, whereas they are both inphase and antiphase in the two Bg modes of the β-structure (see Figure 9b). These in-phase and antiphase oscillations of the O2 atoms are depicted in a different projection in Figure 10, and in what follows we refer to these modes as Bg-Low and Bg-High modes, respectively. Since the B1g and B3g modes in α-V2O5 and the Bg-High mode in β-V2O5 involve similar antiphase oscillations of the O2 atoms, these modes have close frequencies of ca. 690 cm−1

(5)

The Ag modes involve atomic oscillations in the xz-plane, and the displacements of atoms in the Bg modes occur along the yaxis (see Figure 2). In a comparison of the decompositions eqs 4 and 5, one can see that the Ag and B2g species of α-V2O5 merge into the Ag species of β-V2O5, and the Bg species of the latter structure take in the B1g and B3g species of the α-lattice. However, this relation is rather approximate because the linkage of V2O5 chains is different in the unit cells of the αV2O5 and β-V2O5 structures (cf., Figures 1 and 2). Owing to stronger interladder interactions and to the asymmetry of the Va−O3−Vb bridges in the β-V2O5-structure, the quasidegeneracy of Ag/B2g and B1g/B3g modes inherent to the α-structure is removed. As a result, the spectrum of β-V2O5 contains most of the Raman-active modes. The experimental and calculated Raman spectra of a powder β-V2O5 sample are compared in Figure 8.

Figure 8. Comparison of experimental and calculated Raman spectra of β-V2O5. See caption to Figure 6.

Due to a very good agreement of peak positions in the experimental and simulated Raman spectra, one can unambiguously ascribe the observed spectral features to the calculated Raman-active phonons, and the eigenvectors give the displacements of atoms in the vibrational modes. The frequencies of Raman-active modes of the β-V2O5-structure, their Raman activities Rk, and the mode assignments are presented in Table 3. The frequency and Rk values are in G

DOI: 10.1021/acs.inorgchem.8b01212 Inorg. Chem. XXXX, XXX, XXX−XXX

Article

Inorganic Chemistry

Table 3. Frequencies ω (in cm−1) and Raman Activities Rk (Equation 2, in 10−6 au) of the Raman-Active Phonons of the βV2O5 Structure expt

calcd, this work

peaka

ω

ω

Rk

symm

assignmentc

calcdb ω

1a 1b 2 3 4

1021 942 736 686 574

6a 6b

476 434 357 340 301 285 271 244 230

1038 918 722 668 558 524 452 417 349 319 290 284 269 252 231 226 207 181 171 114 101

1827 1378 89 326 127 58 113 109 132 234 0 192 15 49 29 10 109 6 44 8 221

Ag Ag Ag Bg Ag Bg Ag Ag Ag Ag Bg Bg Ag Ag Ag Bg Ag Ag Bg Bg Ag

ν(Va−O1a) ν(Vb−O1b) ν(Vb−O3) νas(V−O2−V)-high ν(Va−O3) νas(V−O2−V)-low ν(Vb−O2a)LS ν(Vb−O2b)LS LM(b)−O2a ν(Va−O2b)LS + Ry LM(d) − y(O1b) y(O3) LM(a) − LM(c) LM(a) + LM(c) Tz LM(d) − y(O1a) LM(c) + Ry Ry LM(e) + y(O3) LM(e) Tx

1093 957 741 695 581 564 473 428 350 320 291 272 275 253 228 220 206 175 165 109 104

211 B1

176

B2

96

Figure 8. bRef 32. cSee footnote to Table 2. Tα denotes relative translations of chains in the α-direction, and Ry stands for rotations of chains around the y-axis.

a

Figure 9. Eigenvectors of V−O2−V modes in the α-phase (a) and β-phase (b) structures. Positive and negative y-displacements of O2 atoms are shown by filled and open red circles. See text for details.

antiphase displacements must strongly affect an effective force constant of the mode, while the in-phase displacements leave the corresponding force constant virtually unchanged. Summarizing, because of a weak interchain interaction, the B1g and B3g modes of the α-structure appears as one peak 3 in the Raman spectrum (Figure 6). The counterpart feature at about the same frequency in the spectrum of the β-phase (Figure 8) corresponds to the Bg-High mode, whereas a peak corresponding to the Bg-Low can be expected in the spectrum at ca. 520 cm−1, but this signal has not been detected experimentally due to a low Raman activity of the mode. Peak 6 in the spectrum of the α-phase at 483 cm−1 originates from the ν(LS) modes (see Figure 6). The unit cell of α-phase has two such ladders that transform to each other by the screw axis rotation. The corresponding Ag and B2g ν(LS) modes have very close frequencies due to the weakness of the interladder interactions. The β-V2O5 lattice also has two ladders related to each other by the same symmetry operation. However, the lengths of steps in the ladders are different: 2.176 and 2.296 Å for the Vb−O2a and Va−O2b ladders, respectively. Correspondingly,

Figure 10. Displacements of O2 atoms in the in-phase Bg-Low (a) and antiphase Bg-High (b) modes of β-V2O5, see also Figure 9b. The interchain O2−O2 contacts are shown by dotted lines.

in both the structures. On the other hand, the Bg mode of the β-structure with the in-phase displacements of the O2 atoms (Bg-Low mode) has a smaller frequency of 524 cm−1 in our calculations. Such a large difference between the Bg-High and Bg-Low frequencies is caused by the O2···O2 interchain interactions in the ladders. Indeed, the length of the O2···O2 contacts (see dotted lines in Figure 10) is extremely short (less than 2.5 Å), and the variation of O2···O2 distance upon the H

DOI: 10.1021/acs.inorgchem.8b01212 Inorg. Chem. XXXX, XXX, XXX−XXX

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Inorganic Chemistry there are two ν(LS) modes at 476 and 340 cm−1 in the spectrum of the β-phase. The latter mode is essentially mixed with LM, and therefore, only the Ag mode observed at 476 cm−1 (see peak 6a in Figure 8) can unambiguously be identified as a ν(LS) mode. A thorough analysis of the β-V2O5 structure reveals the presence of one more ladder type formed by Vb−O2b contacts; these are shown in Figure 11 by dotted lines. The

anisotropy of the Raman tensor that, together with a large Bosé−Einstein prefactor in eq 1, accounts for very high Raman scattering intensity of this mode. The existence of such a mode is a particular property of double-layer structures, and this mode plays the role of the soft mode in the α → β phase transition.33 γ′-V2O5. The number of Raman-active modes in γ′-V2O5 (Z = 4, D2h point symmetry) is twice as large as that in the α- and β-phase structures. The modes are distributed by symmetry representations as follows: Γ(R) = 14Ag + 14B2g + 7B1g + 7B3g

(6)

Similar to the α-phase, the Ag and B2g modes involve atomic oscillations in the xz-plane, and the B1g and B3g modes involve displacements of atoms along the y-axis. The comparison of the γ′- and α-phase structures shows that the unit cell of the former contains two layers instead of one layer in the unit cell of α-V2O5 (cf., Figures 1 and 3). Thus, assuming a weakness of interlayer interactions, one can suppose that the phonon states in the γ′-structure must be nearly 2 times degenerate. This is a basic assumption of the twin-mode scheme proposed in ref 29. According to the scheme, phonon states of γ′-V2O5 can be divided into pairs of closely related modes (twin modes) which correspond to the in-phase and antiphase combinations of oscillations localized on atoms of neighboring layers. The layers in the γ′-structure transform one into another by the C2x and C2z screw rotations. Thus, twin modes of the Ag and B2g symmetry species correspond to in-phase and antiphase atomic oscillations in the xz-plane, respectively, while pair modes of the B1g and B3g symmetry consist of inphase and antiphase atomic oscillations in the y-direction, respectively. Furthermore, the antiphase B2g and B3g combinations are expected to have lower Raman intensities than the inphase ones because of a cancellation effect. Due to the mode pairing, the number of peaks in the Raman spectrum of the γ′phase is about the same as that in the spectra of the α- and βphases. The experimental and calculated Raman spectra of γ′-phase are compared in Figure 13. The corresponding frequency and the calculated Raman activities Rk of the modes are presented in Table 4 with the twin modes given in the same lines. One can see that for the majority of the twin modes, their calculated frequencies differ by less than 10 cm−1. The only exception concerns the Ag/B2g pair giving peak 2 (Figure 13). An explanation of this exception is provided below. One can also see that the Raman activity of the Ag twin is notably larger in all the Ag/B2g couples (except that corresponding to peak 1a). On the other hand, the Raman activity of modes in the B1g/B3g couples does not have such a systematic behavior. The remarkably good agreement between calculated and measured spectra in Figure 13 allows the establishment of the unambiguous correspondence between the Raman features in the spectra above 280 cm−1, and the analysis of the calculated eigenvectors provides the basis for the peak assignment. Owing to the similar lattice constitution (the V2O5 chains linked in layers by ladder), the mode assignment of the γ′-structure resembles that of the α-phase even if the chains in γ′-V2O5 are not completely symmetric and the coordination polyhedra around Va and Vb atoms are slightly different (see Table 1 and Figure 3). The highest-frequency peaks in the zone 990−1050 cm−1 correspond the ν(VO1) bond-stretching modes. There are

Figure 11. Three ladders in the β-phase structure. The Vb−O2b LS contacts are shown by the dotted lines.

length of steps in the ladder is 2.308 Å which is comparable with the Va−O2b distance. Thus, one can expect the appearance of one more ν(LS) mode localized within Vb− O2b ladders. The eigenvector analysis points to this mode at 434 cm−1 with the corresponding Raman peak 6b (Figure 8). The mode has a notably larger frequency than the ν(Va− O2b)LS mode because the latter has a large contribution of the rotation of V2O5 chains around the y-axis. In short, the LS stretching modes ν(LS) manifest themselves peak as 6 in the spectrum of α-V2O5, and the analogous modes of the β-phase yield two peaks 6a and 6b in the Raman spectrum. There are a dozen well-resolved bands below 300 cm−1 in both the experimental and calculated Raman spectra of β-V2O5 (Figure 8). By virtue of the high density of phonon states in this spectral region, it is not easy to establish an unambiguous relationship between the experimental and calculated Raman patterns. The eigenvector analysis shows that these modes involve various combinations of LM localized within the three ladders. The very intense peak B2 observed at 96 cm−1 is worth of a special attention. According to our calculations, the peak must be assigned to a relative translation-like oscillation of the V2O5 chains in the (101) direction, Figure 12. One can see that the chains execute a glide-like motion which produces LS stretching deformations and the rotation of the ladders as a whole. The rotation results in significant variations of the

Figure 12. Eigenvector of the lowest-frequency Raman-active mode in the β-phase. Red arrows show displacements of the V2O5 chains. I

DOI: 10.1021/acs.inorgchem.8b01212 Inorg. Chem. XXXX, XXX, XXX−XXX

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Inorganic Chemistry

difference between the twin modes was discussed in ref 29 in detail. In short, the proposed explanation suggests a significant role of the direct interactions between the O3 atoms of neighboring layers and the influence of the V−O1/V−O3 bond−bond interactions. Bands 3a and 3b are related to the νas(Va−O2a−Va) and νas(Vb−O2b−Vb) modes. A slight frequency difference between their positions is caused by the difference of the Va−O2a−Va and Vb−O2b−Vb chains. Peak 4 at 602 cm−1 originates from the νs(Va−O3−Vb) mode. Recall that the analogous mode in the α-phase has a markedly lower frequency of 528 cm−1. This fact can be explained as a manifestation of the interlayer interactions which are stronger in the γ′-phase structure. The peaks below 400 cm−1 correspond to modes which involve various combinations of the LM shown in Figure 7. It is not easy to describe these modes in detail. However, it is worth paying attention to the mode that gives the most intense feature G2. According to the eigenvector analysis, this peak can be ascribed to the B1g mode corresponding to shear-like distortions of the ladders shown in Figure 7e. ε′-V2O5. Let us now turn to the Raman spectrum of ε′-V2O5 (Z = 2, C2h). Due to the same symmetry group and the equal number of atoms in the unit cell, the distribution of the Raman-active modes in the ε′-structure over the symmetry representations is the same as in the β-V2O5 one:

Figure 13. Comparison of experimental and calculated Raman spectra of powder γ′-V2O5. Color bars denote positions of vibrational modes of different symmetry species, and braces group species of twinmodes.

eight vanadyl bonds in the unit cell of the γ′-structure, and thus, there are eight ν(VO1) modes from which four are Raman-active. One of them involves the in-phase oscillations of all vanadyl bonds, and this mode is the Ag mode with very high Raman activity giving peak 1b (Figure 13). Next in frequency, there is peak 2 at 753 cm−1 that we assign to the νas(Va−O3−Vb) Ag mode calculated at 764 cm−1. The calculated frequency of the corresponding B2g twin mode is about 74 cm−1 higher. Such an unusually large frequency

Γ(R) = 14Ag + 7Bg

(7)

Similar to the β-phase, the Ag modes involve the atomic oscillations in the xz-plane (ac crystallographic plane), while the Bg modes involve the atomic oscillations along the y-axis (perpendicular to the ac-plane).

Table 4. Frequencies ω (in cm−1) and Raman Activities Rk (Equation 2, in 10−6 au) of the Raman-Active Phonons of the γ′V2O5 Structure calculation expt

twin 1

twin 2

ω

ω

Rk

symm

ω

Rk

symm

G1

1037 1002 753 721 692 602 530 498 391 348 298 280

G2

268 237 188 170 151 138

1032 1015 764 706 692 600 518 487 390 343 291 285 278 263 237 191 169 161 153 132 88

4 1195 13 7 136 46 41 22 46 28 10 34 9 1 10 10 8 2 17 3 3

Ag Ag Ag B1g B1g Ag Ag Ag Ag Ag Ag B1g Ag B1g B1g Ag Ag B1g B1g Ag Ag

1052 1023 838 706 691 609 518 488 394 328 292 280 272 265 242 205 168 160 154 153 99

38 143 4 68 7 4 5 2 2 4 0 24 3 58 5 2 1 1 1 2 0

B2g B2g B2g B3g B3g B2g B2g B2g B2g B2g B2g B3g B2g B3g B3g B2g B2g B3g B3g B2g B2g

peak 1a 1b 2 3a 3b 4 6a 6b

a

93

assignmentb ν(VO1) νas(Va−O3−Vb) νas(Va−O2a−Va) νas(Vb−O2b−Vb) νs(Va−O3−Vb) ν(Va−O2a)LS ν(Vb−O2b)LS

LM(e)(Va) LM(e)(Vb)

a

Figure 13 bSee footnote to Table 2. J

DOI: 10.1021/acs.inorgchem.8b01212 Inorg. Chem. XXXX, XXX, XXX−XXX

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Table 5. Frequencies ω (in cm−1) and Raman Activities Rk (Equation 2, in 10−6 au) of the Raman-Active Phonons of the ε′-V2O5 Structure

The experimental and calculated Raman spectra of powder ε′-V2O5 are compared in Figure 14. One can see that only half

expt

calcd ω

peak

ω

Rk

symm

1a

1044

1a

1073

1351

Ag

1b

1010

1b

1024

37

Ag

3 4 5

705 532 481

6

434 379

2 3 4 5 6a 6b

739 690 527 491 461 436 391 383 314 271 261 254 228 164 157 149 102 94 64

81 155 96 90 63 41 75 19 20 51 41 57 42 0 19 1 1 1 0

Ag Bg Ag Bg Ag Ag Ag Ag Ag Bg Bg Ag Bg Ag Bg Ag Ag Ag Bg

peak

a

304

Figure 14. Comparison of experimental and calculated Raman spectra of powder ε′-V2O5. Color bars denote positions of vibrational modes of different symmetry species.

E1

269 240

E2

157 108

of the 21 Raman-active modes can be discerned in the experimental spectrum. This may be due to merging peaks with close frequencies into one feature or to a low Raman activity of some modes. The calculated Raman spectrum satisfactorily reproduces the experimental one (Figure 14). There are two peaks in the highfrequency region in both the spectra, although with a different intensity ratio. An intense peak 3 observed at 705 cm−1 can be related to the Bg mode calculated at 690 cm−1. The complex spectral feature observed between 350−550 cm−1 has a counterpart in the calculated Raman spectrum which, however, better distinguishes peaks due to individual modes. The same can be said about the intense peaks E1 and E2. The observed and calculated peak positions are compared in Table 5 that also reports the computed Raman activities of the modes. The differences between the experimental and calculated Raman spectra of the ε′-V2O5 structure, especially between the intensities of Ag peaks, which are more intense in the calculated spectrum, can be explained as follows. Figure S1 shows that the ε′-V2O5 sample has strong 00l reflections indicating that the sample is a collection of large platelets in the (ab) plane stacked along the c-direction. To our mind, this particular morphology of the sample leads to the observed discrepancies because the scattering from such a sample is different from the isotropic scattering that has been assumed while deriving eq 2. It is noteworthy that samples of other V2O5 phases did not reveal such preferential reflections in the XRD pattern. Before proceeding to the mode description, it is appropriate to recall that the unit cell of the ε′-V2O5 structure contains only two V2O5 chains which are symmetry equivalent and they transform each to the other by inversion operation. These chains are labeled W and M in Figure 4. Thus, the atomic displacements in the W chain and in the M chain in any phonon mode are related by the inversion with +1 and −1 multipliers for the g- and u-modes, respectively. Hence, in order to specify any phonon mode, one can determine only the atomic displacements in one chain.

a

E2

assignmentb ν(Va−O1a) + ν(Vb−O1b) ν(Va−O1a) − ν(Vb−O1b) νas(V−O3−V) νas(V−O2−V)-high νs(V−O3−V) νas(V−O2−V)-low ν(LS) ν(LS) LM(z) LM(c) + δ(V−O3−V) LM(b) LM(d) + y(O3) LM(d) LM(f) y(O3) LM(c) + δ(V−O3−V) LM(e) Ry Tz Tx Ty

Figure 14. bSee footnote to Tables 2 and 3.

The mode assignment derived from the eigenvector analysis is presented in the last column of Table 5. The VO bondstretching modes of the ε′-V2O5 lattice obey the general trend found for other V2O5 structures: in decreasing order of frequency, the ν(VO1) modes are followed by νas(VO3 V) modes, then the νas(VO2V) mode, the νs(VO3 V) mode, and the ν(LS) modes. The ladders in the ε′-V2O5 structure are asymmetric, which is a common feature of the β- and ε′-phases distinguishing them from the α- and γ′-phases. Consequently, the Raman spectra of both the β- and ε′-V2O5 structures have peaks corresponding to the νas(V−O2−V)-High and νas(V−O2−V)Low modes in contrast to only the νas(V−O2−V)-High mode peak in the Raman spectra of the α- and γ′-phases. Another consequence of the ladder asymmetry is that the LM scheme shown in Figure 7 for the α-phase is incomplete for ladders in the ε′-structure. The ladders in the α-phase are invariant with respect to inversion, and therefore, only modes with displacements of atoms invariant to the operation are allowed in the Raman spectra. These modes are shown in Figure 7. On the other hand, the absence of the inversion invariance of ladder in the ε′-lattice allows all LM to be Raman-active. Particularly, in order to describe atomic displacements in the Ag modes calculated at 436 and 391 cm−1 one should extend the LM scheme by two new modes LM(z) and LM(x) shown in Figure 15. The low-frequency part of the Raman spectrum in Figure 14 shows modes involving rotations and translations of the V2O5 chains as rigid bodies. According to our calculations the most intense peak E2 can be attributed to a superposition of the translational oscillations of the chains in the y-direction. K

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structure because of the disparity in the lengths of the Va−O3 and Vb−O3 bonds. Here, one should rather consider the ν(Va−O3) and ν(Vb−O3) bond-stretching vibrations. Therefore, peak 2 is assigned to the νas(O3) mode for the α-, γ′-, and ε′-phases, whereas it can be ascribed to the ν(Vb−O3) mode for the β structure. The modes corresponding to the symmetric stretching vibration νs(O3) or to the stretching vibration of the Va−O3 bond appear as peak 4 in the spectral region 520−600 cm−1. It is noteworthy that the νas(O3) modes fall into the frequency window, where no other modes are present. The appearance of a band in this region of the spectrum can then be indicative of the presence of symmetric V−O3−V bridges in the structure. Unfortunately, the Raman scattering intensity of these modes is relatively small. The νas(O2)-High modes of the V−O2−V ladders lie in a much narrower frequency interval around 700 cm−1. The presence of the peak 3 is a common feature of all the spectra in Figure 16. The peak splitting in the Raman spectrum of the γ′phase indicates the presence of two nonequivalent V−O ladders. The νas(V−O2)-Low modes are Raman-active only in the β- and ε′-phases, and corresponding peak 5 cannot be reliably identified because of its overlap with peaks 4 and 6. Raman bands 6 are related to the modes that can be described as the ladder-step stretching vibrations ν(LS). The corresponding bands appear below the spectral features due to other V−O bond-stretching and above bands due to bending modes, and hence, they are well-distinguishable in the spectra of all polymorphs. Frequencies of the ν(LS) modes correlate with lengths of the ladder steps, and the magnitude of splitting is indicative of nonequivalency of ladders in the structures. The Raman peaks below 400 cm−1 are related to vibrational modes which consist of combinations of the ladder vibrations shown in Figure 7. It is nearly impossible to describe each of these modes in detail. In line with the paper we discuss below the assignment of the two most intense peaks observed in all four spectra in this spectral region. These peaks are labeled (A1, A2), (B1, B2), (G1, G2), and (E1, E2) in the Raman spectra of α-V2O5 (Figure 6), β-V2O5 (Figure 8), γ′-V2O5 (Figure 13), and ε′-V2O5 (Figure 14), respectively. Among these features, the A2, G2, and E2 peaks have a common origin and can be ascribed to the shear-like distortion of ladders depicted in Figure 7e. The A1 peak is related to a delocalized mode that involves wagging oscillations of the V O1 bonds, the out-of-plane vibrations of the O2 atoms, and a considerable contribution of the δ(VO3V) vibration. The mode responsible for the B1 peak consists of shear-like LM(e)

Figure 15. Atomic displacements in LM(x) and LM(z) modes of the ε′-V2O5, see Figure 7 for notations.

■

GENERAL DISCUSSION In this section we summarize the results presented above and try to highlight similarities and distinctions in the Raman spectra of different V2O5 polymorphs. First, we discuss the V− O bond-stretching modes corresponding to peaks 1−6 whose positions in the spectra are gathered in Table 6. The experimental and computed Raman spectra of all considered structures in the region above 400 cm−1 are presented in Figure 16. The ν(O1) modes due to the V−O1 bond-stretching vibrations have the highest frequencies of ca. 1000 cm−1. In all the spectra, these modes give two Raman peaks with positions spread across a large interval. In the spectrum of the α-phase, the peaks merge onto a single feature because of the closeness of the mode frequencies, whereas two distinct peaks are easily discernible in the spectra of other V2O5 polymorphs. The presence of two peaks in this spectral region reflects the existence of two nonequivalent vanadyl bonds in these structures. The correlation between the mode frequency and the V−O1 bond length agrees well with the empirical relation found in ref 55. The vibrational modes corresponding to the asymmetric stretching vibration νas(O3) of the V−O3−V bridges fall into a large frequency interval 720−950 cm−1. Such a difference in the mode frequencies is due to a significant variation of the V− O3 bond lengths in different polymorphs (see Table 1). Another factor affecting the frequency is the symmetry of the V−O3−V bridges. They are symmetric in the α-phase and are almost symmetric in the γ′ and, according to our calculations, ε′ structures (Table 1). Thus, strictly speaking, one can classify V−O3 stretching vibrations of the bridges as the asymmetric νas and symmetric νs in these three structures. On the other hand, the concept is no more valid in the case of the β-V2O5

Table 6. Frequencies (in cm−1) of V−O Bond-Stretching Modesa experiment mode

calculation

α

β

γ′

ε′

α

β

γ′

ε′

995(1)

1021(1a) 942(1b)

1037(1a) 1002(1b)

1044(1a) 1010(1b)

1005(1) 1001 947

1038(1a) 918(1b)

1073(1a) 1024(1b)

736(2)

1052(1a) 1015(1b) 838 764(2) 706(3a) 692(3b) 600(4)

ν(O1) νas(O3)

702(3) 528(4)

686(3) 574(4)

753(2) 721(3a) 692(3b) 602(4)

483(6)

476(6a) 434(6b)

530(6a) 498(6b)

νas(O2)-High νs(O3) νas(O2)-Low ν(LS)

722(2) 705(3) 532(4) 481(5) 434(6)

694(3) 695(3) 519(4) 489(6) 482(6)

668(3) 558(4) 524 452(6a) 417(6b)

518(6a) 487(6b)

739(2) 690(3) 527(4) 491(5) 461(6a) 436(6b)

a

Peak labels are shown in parentheses, see Figure16. L

DOI: 10.1021/acs.inorgchem.8b01212 Inorg. Chem. XXXX, XXX, XXX−XXX

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Inorganic Chemistry

Figure 16. Experimental (a) and calculated (b) Raman spectra of V2O5 polymorphs in the region of the V−O bond-stretching modes.

statistical population of the corresponding vibrational state, see eq 1.

displacements (Figure 7e) localized on the Vb atoms plus inphase oscillations of the O3 atoms in the y-direction. The very intense B2 feature is attributed to a mode consisting of the antiphase translations of layers in a bilayer of the β-V2O5 lattice (see Figure 12). Although this mode is characteristic of a double-layer lattice, analogous modes in the γ′ and ε′ structures do not have such a high Raman intensity. Thus, Tx (ω = 52 cm−1) and Tz (ω = 68 cm−1) modes in the γ′-phase are not Raman-active, whereas the Tx mode of the ε′-V2O5 lattice has a very low Raman activity (see Table 5). The G1 peak originates from the VO1 wagging oscillations, Figure 7d. Finally, the intense E1 peak can be assigned to a mode which consists of the antiphase VO1 wagging oscillations and the antiphase translations of layers along the a crystallographic direction within a bilayer of the ε′-V2O5 structure (Figure 17). It is noteworthy that the high Raman scattering intensity of these low-frequency modes is also explained by their large

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CONCLUSIONS This paper presents results of extensive combined experimental and computational study on the structure and the vibrational dynamics of vanadium pentoxide polymorphs α-, β-, γ′-V2O5, and, for the first time, ε′-V2O5. Data of spectroscopic Raman measurements have been compared with results of quantumchemical calculations based on density functional theory. In these calculations carried out at the equal level of theory for all four V2O5 phases, the crystal structures have been optimized by minimizing the total energy with respect to the lattice parameters and the positions of atoms in the unit cell. The structural optimization has been followed by the analysis of the phonon states in the Γ-point of the Brillouin zone, and the analysis has been completed by the computation of the Raman scattering intensities of the vibrational modes. The optimized structural characteristics agree well with the experimental data, and the calculated Raman spectra match the experimental ones remarkably well. The very good agreement between the experimental and simulated Raman spectra allows us to establish a reliable assignment of the observed spectral peaks to displacements of atoms in the vibrational modes. Modes corresponding to the V−O bond-stretching vibrations appear above 400 cm−1, and the peak positions correlate with the V−O bond lengths. The highest-frequency peaks at 1000 cm−1 are due to vibrations of V−O vanadyl bonds with the number of peaks pointing to the number of nonequivalent vanadyl bonds in the structure. Raman peaks in the region 500−900 cm−1 were found to

Figure 17. Displacements of atoms in the E1 mode of ε′-V2O5 lattice with the calculated frequency 254 cm−1. Light blue dashed line indicates the unit cell. M

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correspond to stretching vibrations in the V−O−V bridges in the structures. The number and intensity of peaks are related to the bridge’s asymmetry. Spectral features in the region 400− 500 cm−1 are attributed to stretching vibrations of V−O interchain ladder-step contacts, and the presence of several peaks in this region indicates the existence of nonequivalent ladders in the structure. Raman bands in the region below 400 cm−1 are due to ladder modes consisting of different deformations of the interchain contacts. This study has also allowed us for the first time to assign low-frequency peaks observed in the Raman spectra for all the V2O5 polymorphs. The most intense peaks in this spectral region are found to be due to shear-like displacements of V2O5 chains or layers. The obtained results endorse the approach to the structural organization of the V2O5 polymorphs as ensembles of V2O5 chains with strong intrachain interatomic interactions that make of the chains common building units in all the structures. The chains are then combined in layers to further form threedimensional lattices by interchain and interlayer interactions whose relative weakness accounts for the polymorphism of vanadium pentoxide. Such a structural organization manifests itself in the Raman spectra. The results of this study are of the utmost importance for understanding structural changes in V2O5-based materials under electrochemical operation.

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ASSOCIATED CONTENT

S Supporting Information *

The Supporting Information is available free of charge on the ACS Publications website at DOI: 10.1021/acs.inorgchem.8b01212.

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Tables with structural characteristics of α-, β-, γ′-, and ε′-V2O5 polymorphs, and X-ray diffraction pattern of ε′V2O5 sample (PDF)

AUTHOR INFORMATION

Corresponding Author

*E-mail: [email protected]. ORCID

Mikhail B. Smirnov: 0000-0002-4292-1989 Evgenii M. Roginskii: 0000-0002-5627-5877 Konstantin S. Smirnov: 0000-0002-8370-8797 Notes

The authors declare no competing financial interest.

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