Electronic Structure of Î²-NaxV2O5 (x â 0.33) Polycrystalline Films

Article pubs.acs.org/JPCC

Electronic Structure of β‑NaxV2O5 (x ≈ 0.33) Polycrystalline Films: Growth, Spectroscopy, and Theory Bo Chen,† Jude Laverock,† Dave Newby, Jr.,† Ting-Yi Su,† Kevin E. Smith,*,†,‡ Wei Wu,§ Linda H. Doerrer,‡ Nicholas F. Quackenbush,∥ Shawn Sallis,⊥ Louis F. J. Piper,∥,⊥ Daniel A. Fischer,# and Joseph C. Woicik# †

Department of Physics, Boston University, 590 Commonwealth Avenue, Boston, Massachusetts 02215, United States Department of Chemistry, Boston University, 590 Commonwealth Avenue, Boston, Massachusetts 02215, United States § Department of Materials, South Kensington Campus, Imperial College London, London SW7 2AZ, United Kingdom ∥ Department of Physics, Applied Physics and Astronomy, Binghamton University, Binghamton, New York 13902, United States ⊥ Materials Science and Engineering, Binghamton University, Binghamton, New York 13902, United States # Materials Science and Engineering Laboratory, National Institute of Standards and Technology, Gaithersburg, Maryland 20899, United States ‡

ABSTRACT: We present a detailed study of the microstructure and electronic structure of β-NaxV2O5 (x ≈ 0.33) polycrystalline films, combining film growth, X-ray spectroscopies, and first-principles calculations. High-quality crystalline and stoichiometric V2O5 and β-Na0.33V2O5 films were grown by a sol−gel process, spin-coating, and rapid thermal annealing. The V2O5 film, which exhibits a rough surface, is preferentially oriented in the (001) direction perpendicular to the surface, whereas the b-axis of β-Na0.33V2O5 is oriented in the substrate plane. The β-Na0.33V2O5 film consists of a nested layered structure composed of single-crystalline rods of a few hundred nanometers in diameter and a few micrometers in length. Photoemission and X-ray absorption measurements of βNa0.33V2O5 confirm the Na incorporation and the presence of mixed V5+ and V4+ species and weakly occupied V 3d states. At the V L-edge, X-ray absorption and resonant inelastic X-ray measurements suggest a larger crystal field for β-Na0.33V2O5 compared with isoelectronic β-Sr0.17V2O5. We observe the lowest local crystal-field dd* transition at an energy of ∼−1.6 ± 0.1 eV for β-Na0.33V2O5, which is substantially larger than β-Sr0.17V2O5; this large difference is interpreted as arising from the stronger distortions to the VO6 octahedra in β-Na0.33V2O5.

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INTRODUCTION The β-phase sodium vanadium bronzes, β-NaxV2O5 (0.2 ≤ x ≤ 0.4),1−3 are well-known as quasi-one-dimensional (1D) conductors with rich magnetic, electric, and structural properties. The excellent electrochemical properties of β-NaxV2O5 also make it of value as a high performance cathode material suitable for secondary lithium batteries.4−6 When x = 0.33, βNa0.33V2O5 undergoes three successive phase transitions upon cooling below room temperature: at ∼230 K the ordering of Na+ cations along the b-direction, a metal−insulator transition (MIT) along the b-axis with the presence of a charge ordering around 136 K, and magnetic ordering at ∼24 K.3,7 The deviation of x from 0.33 drastically decreases the MIT and magnetic transition temperatures and magnitudes. In addition, both the high temperature metallic behavior and the magnetic ordering are lost.3 Finally, pressure-induced superconductivity develops below ∼8 K at pressures greater than ∼8 GPa, after the eventual suppression of the charge-ordered phase.8 The quasi-1D conductivity of β-NaxV2O5 (ρc/ρb ≈ 100 when x = 0.33) is determined by its highly anisotropic crystal structure, which develops in the monoclinic C2/m space group.3 Figure 1 shows the crystal structure of β-NaxV2O5 © 2014 American Chemical Society

projected along the b-axis and the arrangement of vanadium polyhedra within the bc-plane. The vanadium atoms occupy three crystallographically independent sites, usually referred to as V1, V2, and V3, with octahedral coordination for the V1 and V2 atoms and square pyramidal coordination for the V3 atom.2,9 The distortion of these polyhedra leads to a shortening of the bond length between vanadium and one apical oxygen, which allows a multiple vanadium−oxygen covalent (vanadyl) bond with strong delocalization to occur. Additionally, the distortions expand the bond length to a sixth neighboring oxygen, particularly for V3, leading to the common consideration of the polyhedra as distorted square pyramids.10 The zigzag double chains formed by (V1)O6 octahedra and (V3)O5 pyramids and the two-legged ladders formed by (V2)O6 octahedra constitute a V2O5 framework with infinite tunnels along the b-axis, as illustrated in Figure 1. Two specific interstitial sites, usually denoted by A1 and A2 (and which are not simultaneously occupied), are contained in these tunnels, Received: October 16, 2013 Revised: December 30, 2013 Published: January 2, 2014 1081

dx.doi.org/10.1021/jp410277m | J. Phys. Chem. C 2014, 118, 1081−1094

The Journal of Physical Chemistry C

Article

thermal treatment is very important to obtain samples of high crystallinity. Often, the crystallization of β-NaxV2O5 xerogel is achieved at 550 °C with air flow in a conventional furnace.19,20 An alternative method is to use a rapid thermal anneal, which is becoming an increasingly important method in thermal treatment due to the practical advantages of the simplicity of process control for large-area coating, especially on Si wafers, and the reduction of process time at high temperatures.22 The electronic structure of solids can be measured using a variety of X-ray excited electron and photon spectroscopies, such as X-ray absorption spectroscopy (XAS), X-ray emission spectroscopy (XES), resonant inelastic soft X-ray scattering (RIXS), X-ray photoemission spectroscopy (XPS), and angleresolved photoemission spectroscopy (ARPES). Although there has been a significant amount of work on two related vanadium bronzes, V2O523−26 and α′-NaV2O5 ,27,28 the electronic structure of β-NaxV2O5 has not been extensively studied. The reported soft X-ray spectroscopic studies are XAS,29 XPS,17 and ARPES30 measurements of β-Na0.33V2O5 and XAS, XES, and RIXS measurements of β-Sr0.17V2O5.31 The X-ray absorption near-edge structure spectra at the V L-edge and O K-edge were recorded for β-Na0.33V2O5 powders, which present better resolution than the electron energy-loss spectroscopy data.29 The core-level XPS spectra revealed a double-peak structure of the V 2p3/2 level due to the coexistence of V5+ and V4+ in βNa0.33V2O5 nanobelts.17 The valence band (VB) of singlecrystal β-Na0.33V2O5 was found to disperse only along the crystal b-direction, and the V 3d band was observed to present a Gaussian-like broad line shape using ARPES.30 For singlecrystal β-Sr0.17V2O5, strong orbital anisotropy was detected using polarization-dependent XAS, and low-energy excitations were measured by RIXS.31 In this paper, we present a comprehensive investigation of the electronic structure of β-NaxV2O5 (x ≈ 0.33) including thin film growth and characterization, alongside synchrotron-based spectroscopic measurements (XAS, XES, XPS, and RIXS). This combined study provides the unique advantage of addressing the intimate connections among 1D as-grown microstructure, highly distorted crystal structure, and strongly anisotropic electronic structure of β-Na0.33V2O5. Polycrystalline films of βNa0.33V2O5 and V2O5 were synthesized by the sol−gel process, spin-coating, and followed by a rapid thermal anneal. V2O5 is chosen for comparison since its electronic structure is wellcharacterized both theoretically 24,25 and experimentally23,25,26,32−34 including through the soft X-ray spectroscopic tools employed here, and it shares the same basic building blocks to its crystallographic structure as β-NaxV2O5. The purpose of using a novel rapid thermal processor (RTP) instead of a conventional furnace for annealing was to explore the capability of a RTP anneal to achieve high-quality crystalline and stoichiometric vanadium oxide films. The electronic structures of the V2O5 and β-Na0.33V2O5 films were measured using a variety of synchrotron-based X-ray spectroscopies. The computed O 2p partial density of states (PDOS) of βNa0.33V2O5, by means of density-functional theory (DFT), is directly compared to the O K-edge XAS and XES spectra. The orbital anisotropy existing in these preferentially oriented films and the low-energy excitations of β-Na0.33V2O5 were studied in detail. Finally, these results are compared with similar measurements of single-crystal β-Sr0.17V2O531 in order to investigate the effects of the distortion of the VO6 octahedra and the cation valence and concentration on the electronic structure of β-Na0.33V2O5.

Figure 1. Crystal structure of β-NaxV2O5 projected along the crystal baxis is displayed on the top. V1, V2, and V3 refer to three crystallographically independent vanadium sites. A represents interstitial sites within the tunnels along the b-axis. At the bottom, the polyhedra arrangement of the (V1)O6 and (V3)O5 zigzag chains and the (V2)O6 ladder in the bc-plane is also demonstrated.

which yields either β- or β′-phase vanadium bronzes (AxV2O5), respectively, as illustrated by ref 7. The Na+ cations are preferably situated on the A1 site in each tunnel and form a pair of chains along the b-axis within the V2O5 framework.3,11 Owing to the high anisotropy in its crystal structure, βNa0.33V2O5 displays quasi-1D conductivity, as demonstrated by resistivity measurements.3,7,12 Owing to the equivalent electron doping and the similar crystal structure, β-Na0.33V2O5 with monovalent A+ cations and β-Sr0.17V2O5 with divalent A2+ cations are isoelectronic and isostructural compounds. On the other hand, the electrostatic potential in these two compounds is substantially different, with the A-sites half-filled in β-Na0.33V2O5 and quarter-filled in βSr0.17V2O5.13 The electronic structures of two crystallographically distinct compounds, β-A0.33V2O5 (1D structural arrangement) and α′-NaV2O5 (2D arrangement), are based on similar units containing a square-pyramid environment of vanadium,10 and their similarities have been illustrated experimentally. 14,15 Optical conductivity studies of βNa0.33V2O516 and β-Sr0.17V2O513 showed that the spectra in the far-infrared region differ at low temperature although the mid-infrared band is very similar in these two compounds. A Raman scattering study demonstrated that the spectra of βCa0.33V2O5, one member of β-AxV2O5 family, and α′-NaV2O5 are very alike at room temperature, which indicates similar charge-phonon dynamics in those two compounds.14 Single-crystal β-NaxV2O5 is usually grown by a self-flux method and the starting powder samples are synthesized by solid state reaction.3,7,12 Polycrystalline β-NaxV2O5 can be synthesized by a variety of techniques, such as sol−gel and hydrothermal processes, or metalorganic chemical vapor deposition, and in the forms of thin films, nanobelt networks, and nanowires, respectively.1,17−19 Generally, the sol−gel process has the advantages of producing high-purity films, simplicity of equipment, and easy scaling for large substrates.20 Moreover, the sol−gel process offers a versatile route for the synthesis of vanadium bronze cathodes with improved electrochemical properties.21 Compared to solid state derived bronzes, the preferred orientation of sol−gel derived βNaxV2O5 layers is reported to enhance the diffusion of Li+ ions into the host lattice.4−6 In the sol−gel process, appropriate 1082



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GROWTH AND CHARACTERIZATION

Pure and sodium-doped V2O5 gels were synthesized by means of the sol−gel method through hydrolysis and condensation of vanadium alkoxides.21,35,36 The precursor chemicals were commercial vanadium(V) oxytriisopropoxide (formula OV(OCH(CH3)2)3, purity 99.71%), 2-propanol ((CH3)2CHOH, 99.7+%), acetyl acetone (CH3C(O)CH2C(O)CH3, 99%), and sodium acetate (NaOOCCH3, 99.997%). Acetyl acetone was added as a complexing reagent to stabilize the reaction because the VO(OPri)3 and PriOH solution tends to be rapidly hydrolyzed.36,37 The synthesis route was to add vanadium oxytriisopropoxide drop by drop into a mixed solution of isopropanol and acetyl acetone in a sealed flask with magnetic stirring. The molar ratio of OV(OCH(CH 3 ) 2 ) 3 : (CH3)2CHOH:CH3C(O)CH2C(O)CH3 was approximately 1:20:1. A red V2O5 gel with ∼0.5 M concentration was then obtained and the sodium doping was achieved by immediately adding sodium acetate to the V2O5 gel at the molecular ratio of x = 0.33. The chemical reaction of the gel solution was fully completed by continuing vigorous stirring for 2 h. Thin film deposition was achieved by spin-coating and rapid thermal annealing. Thin films were fabricated by spin-coating of the gel solution (3000 rpm, 15 s) on substrates ultrasonically cleaned in acetone, isopropanol, and deionized water in sequence.38 A variety of substrates, such as silicon, fused silica, ITO glass, and sapphire, were employed to explore different film structures. The coated films were dried in an oven at 90 °C for 30 min and then annealed in a rapid thermal processor at 500 °C for pure V2O5 and 550 °C for Na-doped V2O5, respectively, under pure O2 gas flow for 30 min. Thicker films were produced by repeating multiple cycles of spin-coating and heat treatment. Our study shows that the multiple coatings significantly increase the signals of X-ray spectroscopic measurements, particularly the V L-edge RIXS, with no appreciable qualitative change in the measured spectra. The V2O5 film was transparent, as reported,38 and had a light green appearance for a single coating, which developed to a light red color for multiple coatings. The coloration of the films, and their evolution with film thickness, is due to interference between light reflected from the surface of the film and from its interface with the substrate. For example, previous V2O5 sol− gel films have been reported to appear orange-yellow.39 In contrast, the β-Na0.33V2O5 film was black with a slightly metallic sheen similar to previous reports.19 The surface microstructure and crystallinity of the resultant V2O5 and NaxV2O5 films were characterized by X-ray diffraction (XRD), optical microscopy, and scanning electron microscopy (SEM). The extent of sodium doping was determined by energy dispersive X-ray spectroscopy (EDS). The electric resistivity of sol−gel films was qualitatively investigated by a two-probe method. The film thickness was measured by ellipsometry. Figure 2a shows XRD patterns of V2O5 (5 coatings) and βNa0.33V2O5 (9 coatings) films grown on Si (100) substrates. The sharp and well-defined peaks with low noise background demonstrate high-quality polycrystallinity of both sol−gel derived films. The XRD patterns of our samples agree very well with the reference patterns of standard powder polycrystalline V2O5 (JCPDS No. 09-0387) and β-Na0.33V2O5 (JCPDS No. 24-1155). The V2O5 film has the typical XRD pattern of V2O5 with a preferable (001) orientation. The β-Na0.33V2O5 film displays the typical pattern of β-Na0.33V2O5, which shows

Figure 2. (a) XRD patterns and (b) EDS spectra of V2O5 (red line) and β-Na0.33V2O5 (blue line) polycrystalline films deposited on Si (100) substrates are plotted on a linear vertical axis. The XRD peak reflections in (a) are assigned according to the reference patterns of standard powder polycrystalline V2O5 and β-Na0.33V2O5. The Si Kα EDS peaks are not included in (b).

distinctive difference from the other phases of sodium vanadium bronzes and provides confirmative evidence for the β-phase structure of our sample. Only β-Na0.33V2O5 (h0l) reflections exist in the XRD pattern of our β-Na0.33V2O5 sample, which suggests that the sol−gel film has the growth preference with the b-axis oriented in the plane parallel to the substrate. This preferable orientation is found to vary little with different substrates and film thickness in our films. Figure 2b displays EDS spectra of V2O5 (3 coatings) and βNa0.33V2O5 (9 coatings) films fabricated on silicon substrates. EDS detects emission lines of certain elements due to radiative decay of electrons from outer subshells to fill vacant holes on an inner shell created by means of high-energy electron bombardment and provides spatially localized chemical analysis. Our EDS spectra were collected with an incident electron energy of 10 keV and a detector resolution of ∼0.13 keV. The observation of the Na Kα peak confirms the presence of sodium in our β-NaxV2O5 sample, in contrast to pure V2O5. The sodium doping content x is determined to be 0.34 ± 0.03, after background removal. Figures 3a and 3b present optical microscope images of V2O5 and β-Na0.33V2O5 surfaces, respectively, of films (3 coatings) deposited on silicon substrates. Distinctive differences in the 1083



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single-crystalline rods dominate the signals during the X-ray spectroscopic measurements, and the influence of the small particles is undetectable. As a comparison, at 20K× magnification, the V2O5 film is clearly observed to be composed of irregular crystallites varying in size from a few ten to a few hundred nanometers. The microstructure of our V2O5 film is in agreement with the fine granular structure of the V2O5 film pyrolyzed on fused silica by Partlow et al.20 but presents more detailed structure. The film thickness of a V2O5 single-coating on silicon is measured to be ∼80 nm. The electric conductivity of the βNa0.33V2O5 layer deposited on fused silica (insulating substrate) is found to be semiconducting at room temperature and insulating at low temperature. However, owing to the nested and layered structure of our β-Na0.33V2O5 polycrystalline film, particularly the unknown contact resistance between singlecrystalline rods, the conventional two-probe method does not accurately measure the electric resistivity of the film. Nevertheless, a resistivity transition is not observed in our sample, most likely due to a combination of the polycrystalline form, disorder, or a slight deviation of x from 0.33.3 It has been reported that β-Na0.33V2O5 exhibits metallic behavior only in defect-free single crystals and that phase transitions do not take place in polycrystalline samples.3

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Figure 3. Optical microscope images of (a) V2O5 and (b) βNa0.33V2O5 surfaces of the films (3 coatings) grown on silicon substrates. SEM images of the β-Na0.33V2 O5 surface at the magnification of (d) 1K× and (f) 20K× are displayed along with the V2O5 images at (c) 2K× and (e) 20K× for comparison. The scales in the measurements are marked in the corresponding images.

SYNCHROTRON-BASED X-RAY MEASUREMENTS The soft X-ray measurements were performed at Beamline X1B, National Synchrotron Light Source (NSLS), Brookhaven National Laboratory. This undulator beamline is equipped with a spherical grating monochromator. The XAS spectra were measured in both total electron yield (TEY) and total fluorescent yield (TFY) detection modes with an energy resolution of approximately 0.2 eV at the O K-edge. The XES spectra were recorded using a Nordgren-type, Rowland circle spherical grating spectrometer set to an instrumental energy resolution of approximately 0.8 eV at the O K-edge.40 For the resonant emission spectra recorded at the V L-edge and O Kedge, the incident photon energy resolution was set to approximately 0.48 eV. The XAS photon energy scale was calibrated using the O K-edge and Ti L-edge absorption peaks of rutile TiO2.41 The XES spectrometer energy scale was calibrated using metal Zn L-shell emission lines in the second order.42 The hard X-ray photoemission measurements were performed at Beamline X24A at the NSLS. This beamline has a bending magnetic source and is equipped with an electron analyzer. The measurements were performed with an incident photon energy of ∼4023 eV and an analyzer pass energy of 500 eV in transmission mode for the valence band region and core levels. The wide scan measurements were employed with a pass energy of 200 eV in angular mode. The sample geometry had a takeoff angle of ∼85° with respect to the analyzer (i.e., enhancing the bulk sensitivity). The XPS binding energy scale was calibrated using both the Au 4f core levels and the Au Fermi edge as measured from a gold foil in electrical contact with the sample. The spectrometer energy resolution is determined to be approximately 0.2 eV from a Sigmoid function fit of the Au Fermi edge. The Au reference was measured both before and after the measurements of the samples in order to account for shifts in the photon energy. All the sol−gel samples studied in the soft X-ray measurements were deposited on silicon substrates. Before loading into the endstation chamber with an ultrahigh vacuum (UHV)

surface structure between the two compounds are clearly observed. The V2O5 sample is a solid film with a rough surface, whereas β-Na0.33V2O5 is a nested layer composed of needle-like pieces. In Figure 3c−f, SEM images of the same β-Na0.33V2O5 surface as above are shown at a magnification of 1K× and 20K× as well as the V2O5 images at 2K× and 20K×. At 1K× magnification, the β-Na0.33V2O5 layer microstructure is clearly observed to be comprised of regular rods with an average diameter of a few hundred nanometers and a few micrometers in length; the average diameter:length ratio was determined to be ∼1:7. This structure is very similar to the reported nanobelt17 and nanowire1 forms of polycrystalline β-NaxV2O5, indicating that polycrystalline β-NaxV2O5 preferentially grows in a one-dimensional-like structure. In contrast, at 2K× magnification, the rough surface of the V2O5 film revealed by the optical microscope is more clearly shown in the SEM. At 20K× magnification, a single rod of β-Na0.33V2O5 clearly displays a well-established single-crystalline shape, in contrast to the amorphous surface of the substrate (possibly SiO2 and organic residue). This is in agreement with the singlecrystallinity of nanobelts and nanowires revealed by transmission electron microscopy and selected area electron diffraction.1,17 Small particles are visible at very high magnification in Figure 3f possibly owing to either small size single-crystalline rods or small irregular particles, which are not well crystallized during the growth. However, thicker films adopted in X-ray spectroscopic measurements are found to have the increased density of the large single-crystalline rods in the film texture and the reduced area of the exposed substrate surface with the small particles. Our study shows that the large 1084



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pressure of 10−10 Torr, sample surfaces were rinsed with ethanol and dried under nitrogen gas flow to remove any macroscopic surface contamination. In situ surface cleaning was then carried out through a degas and mild anneal at a temperature of over 100 °C in UHV. In order to avoid beaminduced damage during the XES measurements, the sample was continuously moved via a raster scanning of the sample. The experimental setup at X1B makes it possible to rotate the sample holder with respect to the polarized synchrotron light, which allows for orbital-resolved measurements under the dipole approximation (see, for example, our previous measurements on β-Sr0.17V2O531 and WO343). In particular, for V2O5, the XAS spectrum measured at grazing incidence (GI) (∼15° grazing angle) primarily reflects the O 2p component along the c-direction, while at normal incidence (NI) the spectrum mainly reflects a combination of the O 2p PDOS projections along both the crystal a- and b-axes. For the β-Na0.33V2O5 film, GI primarily couples to the crystal c- and a-axes and NI to orbitals oriented along the b-axis. For intermediate incident photon angles (referred to as intermediate geometry), the recorded XAS and XES spectra probe a mixture of all three O 2p components (along x, y, and z crystal axes). During the soft X-ray measurements, only the angular XAS spectra were recorded at both GI and NI geometries, and all the other spectra were collected at an intermediate geometry.

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RESULTS AND DISCUSSION

I. Hard X-ray Photoelectron Spectroscopy. In the XPS process, both valence and core electrons are ejected by incident X-rays. By measuring the kinetic energy of the photoelectrons, XPS probes the occupied density of states (DOS) of the VB and the binding energies of core levels. Moreover, combined with EDS in this study, XPS provides complementary information about element identification and quantification. Compared to surface-sensitive soft XPS, hard X-ray photoelectron spectroscopy (HAXPES) has the advantage of greater bulk sensitivity. Data were analyzed by fitting peaks with a Voigt function after subtracting a Shirley background. Figure 4 shows the HAXPES spectra of both V2O5 (4 coatings) and β-Na0.33V2O5 (9 coatings) films. Sharp and welldefined core-level peaks are observed in the wide scan, as shown in Figure 4a. Our V2O5 spectrum is in excellent agreement with the wide scan from the (001) plane of singlecrystal V2O5 cleaved in vacuum.33 In contrast to V2O5, and as expected, our β-Na0.33V2O5 spectrum demonstrates the presence of a strong Na 1s peak at 1071.3 eV and a visible Na 2s feature at 63.3 eV. The binding energy of the Na 1s level agrees well with the energy location of 1071.0 eV from βNa0.33V2O5 nanobelts,17 and the presence of the Na 2s level illustrates the high quality of our samples. Owing to the difficulty in reliably estimating the photoionization cross section at 4 keV and the sensitivity factor of the spectrometer, the precise stoichiometry of Na in the β-NaxV2O5 sample is not determined from our data. Rather, the measurements are qualitatively consistent with a Na concentration of 0.33, in agreement with the EDS results. For both compounds, the V 2p core-level spectra are composed of V 2p1/2 and 2p3/2 levels due to the spin−orbit splitting, separated by 7−8 eV, as shown in Figure 4b. The clean O 1s peak is absent of any extra signal on the higher binding energy side that could originate from surface contamination of carbon oxides34 or hydroxide bonding from synthesis.17 In contrast to the single-peak spectral shape of V2O5 with pure V5+ charge state, the V 2p3/2 core-level spectrum of β-Na0.33V2O5 presents a double-peak structure composed of V5+ (main peak) and V4+ (lower energy shoulder) characters. The V 2p3/2 binding energies are determined to be 517.2 eV (the same as our V2O5 sample) and 515.7 eV, respectively, which are in excellent agreement with the energies of 517.2 and 515.8 eV for V5+ and V4+, respectively, reported by Silversmit et al.52 Moreover, our results agree very well with the binding energies of 517.3 eV (V5+) and 516.0 eV (V4+) of the βNa0.33V2O5 nanobelts17 but show a better resolved V4+ feature. The fitted areas of the V5+ and V4+ components of the V 2p3/2 core level suggest a ratio between the two species (V5+:V4+) of 0.78:0.22, in excellent agreement with a mixed valence of 0.83:0.17 expected from stoichiometric β-Na0.33V2O5, particularly given the errors involved in approximating the form of the components and the energy-dependent background. Finally, the slightly broader and more asymmetric line shape of the O 1s core level (and, indeed, the valence band) of βNa0.33V2O5 compared with V2O5 is consistent with the weak contribution from electron shakeup processes (Doniach−Šunjić processes) across the Fermi edge of conducting β-Na0.33V2O5. For example, a similar asymmetric broadening of core levels was observed in the metallic phase of V2O3 compared with insulating TiO2.53

COMPUTATION

The DFT calculation of the electronic structure of βNa0.67V2O5 has been carried out using the hybrid functional PBE044 as implemented in the CRYSTAL09 code.45 The Gaussian-type basis sets designed for Na,46 V,47 and O48 atoms in solid-state compounds are used throughout the calculation. The Monkhorst−Pack sampling49 of reciprocal space was carried out choosing a grid of shrinking factor to be 4 × 20 × 6 to maintain approximate consistency with the ratios between the reciprocal lattice parameters in β-NaxV2O5. The experimental structure,2 in which all Na sites are occupied, is adopted in the calculation, and the experimental stoichiometry (x = 0.33) is approximated by subsequently rigidly shifting the Fermi level. Such a rigid-band approximation, although crude, is considered sufficiently accurate for the purposes employed here. The truncation of the Coulomb and exchange series in direct space is controlled by setting the Gaussian overlap tolerance criteria to 10−6, 10−6, 10−6, 10−6, and 10−12.46 The self-consistent field (SCF) procedure is converged to a tolerance of 10−6 au per unit cell. To accelerate convergence of the SCF process, all calculations have been performed adopting a linear mixing of Fock matrices by 30%. Electronic exchange and correlation are described using the PBE0 hybrid-exchange functional.44 The advantages of hybridexchange functional include a partial elimination of the selfinteraction error and balancing the tendencies to delocalize and localize wave functions by mixing a quarter of Fock exchange with that from a generalized gradient approximation (GGA) exchange functional.44 The performance of the hybrid-exchange functional such as PBE0, implemented in CRYSTAL code,46 has previously been shown to provide an accurate description of the electronic structure and magnetic properties for both inorganic and organic compounds.50,51 1085



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feature, located at ∼0.9 eV below the Fermi level, in the βNa0.33V2O5 spectrum is attributed to weakly occupied pure V 3d states, which is absent in the V2O5 spectrum. The origin of this feature is assigned to dxy orbital by a qualitative analysis of our DFT calculation, in agreement with the dominance of V 3dxy states at the bottom of the conduction band in the two electronically and structurally related vanadium bronzes, V2O5 and β-Sr0.17V2O5.24,31 The line shape of the pure V 3d feature is Gaussian-like, in agreement with ARPES measurements.30 The weak intensity of the pure V 3d states is due to both the low fraction of V4+ character (17%) in β-Na0.33V2O5 and the small ionization cross-section of V 3d subshell at this photon energy. II. Soft X-ray Absorption Spectroscopy. XAS involves the excitation of core electrons into the conduction band (CB) by incident X-rays, governed by the dipole-selection rule. At the O K-edge, XAS approximately measures the O 2p PDOS of the CB (owing to the transition from O 1s core level to unoccupied 2p orbitals) in the presence of a core hole. At the transition metal L-edge, the XAS process is dominated by the interactions between the 2p core hole and the 3d valence wave functions (multiplet effects).54,55 Nevertheless, angle-dependent XAS measurements on V2O5 have illustrated the detailed information on the unoccupied PDOS that is available at the transition metal L-edge under favorable circumstances, despite the dominance of multiplet effects.25 The XAS spectra presented here were recorded in both TEY and TFY modes with sampling depths of ∼10 nm (more surface sensitive) and ∼100 nm (more bulk sensitive), respectively. Figure 5a presents normalized V L3,2-edge XAS spectra of both V2O5 (4 coatings) and β-Na0.33V2O5 (6 coatings) films recorded at an intermediate geometry. The angular XAS spectra of the V2O5 film collected at both GI and NI geometries are displayed in Figure 5b. Two main absorption peaks, at ∼519 and ∼525 eV, correspond to V L3-edge and L2-edge transitions from the spin−orbit split V 2p3/2 and V 2p1/2 core levels to unoccupied V 3d orbitals, respectively. The features of the XAS spectra of the two sol−gel compounds are in excellent quantitative agreement with the reported absorption spectra of V2O525 and β-Na0.33V2O5,29 consistent with good quality samples. Both sol−gel films present the V5+ spectral features of the main peak at 518.8 eV and the notable feature at 515.8 eV. According to atomic multiplet calculations of β-Sr0.17V2O5,31 the energy separation of these two V5+ features varies in proportion to the crystal field parameter 10Dq. The larger separation of V5+ species (3.0 eV) here than that in β-Sr0.17V2O531 (2.4 eV) at the V L3-edge indicates a larger crystal field splitting 10Dq in our Na-doped samples. A pronounced knee, located at ∼−1.6 eV below the L3 main peak, is observed in the β-Na0.33V2O5 spectrum. The absence of this feature in V2O5 is consistent with its origin being of V4+ character. According to atomic multiplet calculations, this feature can be attributed to the presence of occupied V4+ species, which is located at ∼−1.4 eV off the L3 main peak for β-Sr0.17V2O5,31 contrary to the interpretation of the same knee at ∼−1.5 eV in polycrystalline β-Na0.33V2O5 as due to the crystal-field splitting.29 The angular XAS results of our sol−gel V2O5 film agree well with both the angle-dependent XAS measurements of singlecrystal V2O525 and PDOS calculations of bulk V2O5.24 In total, seven spectral features, as reported by Goering et al.,25 are clearly resolved in our V L3-edge spectra. Features located at 515.2 eV (labeled as V7 in ref 25), 515.9 eV (V1), 518.8 eV (V5), and 519.4 eV (V6) are observed in both GI and NI

Figure 4. Hard XPS spectra of both V2O5 (red solid and dash lines) and β-Na0.33V2O5 (blue solid lines) films are plotted on a binding energy scale showing (a) wide scan, (b) O 1s and V 2p core levels, and (c) valence band. The inset in (a) demonstrates the appearance of the Na 2s feature of β-Na0.33V2O5 in the enlarged region between 0 and 80 eV. The weakly occupied V 3d states of β-Na0.33V2O5 in (c) are magnified and fit by a Gaussian function (black solid line).

The broad structure of the valence band developing between 2.5 and 9 eV in binding energy, as shown in Figure 4c, comes predominantly from the contribution of the O 2p band.30 No surface contamination signal, which usually appears around 9− 10 eV for transition-metal oxides, is observed. The weak 1086



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latter case. In particular, for V2O5, features V1−V3 and V7 arise from t2g orbitals and peaks V4−V6 are dominated by eg character, as interpreted by the direct comparison between the angle-dependent XAS spectra25 and the V 3d PDOS calculations.24 Figure 6 shows angular XAS spectra at the O K-edge of V2O5 (4 coatings) and β-Na0.33V2O5 (6 coatings) films recorded at both GI and NI geometries and the orbital-resolved PDOS of the O 2p CB of β-Na0.33V2O5 calculated from DFT. The spectral intensities of the O K-edge XAS are normalized to the corresponding XAS spectra at the V L-edge. The O 2p PDOS of the CB has been convoluted with a Lorentzian function with half width at half-maximum (HWHM) of 0.22 eV and then a Gaussian function with full width at half-maximum (FWHM) of 0.20 eV, in order to account for the O 1s lifetime broadening57 and the absorption energy resolution, respectively. Two main features visible in the O K-edge XAS spectra are attributed to the hybridization of O 2p states with V t2g* and eg* states from our calculations, which is consistent with the V L3-edge XAS spectra. The photon energies of these two features are determined to be 529.6 and 531.3 eV for V2O5 and 529.4 and 531.2 eV for β-Na0.33V2O5, respectively, which indicates a similar energy separation between t2g* and eg* states for both compounds. As the eg* feature is very broad at its higher energy shoulder, the energy splitting at the O K-edge is determined to be at least ∼1.8 eV for β-Na0.33V2O5, which agrees well with a measured splitting of ∼1.7 eV for β-Sr0.17V2O531 and our DFT calculations (∼2.0 eV). In our V2O5 spectra, an additional feature appears on the high-energy shoulder of the eg* states, located at ∼1.1 eV above the main σ* peak. This second eg* feature appears more discernible and the orbital anisotropy becomes more prominent in the TEY spectrum (the blue dashed line in Figure 5a) of the thinner V2O5 film (1 coating) measured at GI geometry. This can be explained by the better growth quality in the thinner film, such as surface smoothness and preferential c orientation. The observation of these double eg* features, which become more notable at GI geometry in our sample, is consistent with the presence of a second σ* peak (∼1.2 eV above the main peak) in the single-crystal V2O5 XAS spectra at E||z geometry.25 This observed eg* manifold splitting also agrees well with the separation of ∼1.2 eV between the top (due to dz2 orbitals) and the bottom (due to dx2−y2 orbitals) of the manifold from band calculations of bulk V2O5.24 Again, the double-peak structure of eg* states was also observed in the O K-edge NEXAFS spectra of (001) oriented V2O5 nanowires,56 which presented very alike polarization dependence as the results of our (001) oriented film. A second σ* peak at ∼0.8 eV above the main peak was reported to also exist in single-crystal β-Sr0.17V2O5.31 The splitting of eg* states in our polycrystalline β-Na0.33V2O5 spectrum is weaker but still discernible. For both compounds, the XAS spectra show pronounced anisotropy with the experimental geometry. The intensity of eg* states is substantially suppressed in the spectrum at NI geometry, and the spectral weight is shifted to higher photon energy in the spectrum at GI. This can be explained by orbital specificity under the dipole approximation. As discussed above, for V2O5 (β-Na0.33V2O5) the XAS spectrum at GI has mostly O 2pz (2pz and 2px) character, whereas the spectrum at NI has largely O 2px and 2py (2py) character. For V2O5, the dominant contribution to the eg* hybridization states comes from the O 2pz orbitals of the vanadyl bond as suggested by ab initio band structure calculations.24 This result was confirmed by angle-

Figure 5. Normalized V L3,2-edge XAS spectra detected in both TEY (solid lines) and TFY (open symbols) modes of (a) both V2O5 (red color) and β-Na0.33V2O5 (blue color) films recorded at an intermediate geometry and of (b) V2O5 film collected at NI (olive color) and GI (black color) geometries are displayed on a photon energy scale. The photon energies of the L3-edge spectral features are indicated by vertical short dashed lines.

spectra. Features at 517.1 eV (V2) and 518.2 eV (V4) (both of which are much better resolved in the TFY) are only discernible in the NI spectra, whereas the peak at 517.6 eV (V3) is notable only in the GI spectra. The intensity variation of features V2, V3, and V4 with the experimental geometry in our measurements is in excellent agreement with ref 25 and can be attributed to the similar sample orientation (crystal c-axis) with respect to the photon polarization (E vector). Furthermore, the strong anisotropy that is present in these polycrystalline films is consistent with and directly illustrates the preferred growth direction of V2O5. The GI (or NI) geometry of our (001) oriented film corresponds to the orientation of the polarization vector E nearly parallel (or perpendicular) to the crystal c-axis, i.e. Φ = 75° (or 0°), respectively. Similar spectral features (V1−V6) were also found in the near-edge X-ray absorption fine structure (NEXAFS) spectra at the V L3-edge of (001) oriented single-crystalline V2O5 nanowires,56 and their polarization dependence resembles the results of our (001) oriented film. According to dipoleselection and k-selection rules, transitions from V 2p to the V 3dxz, 3dyz, and 3d3z2−r2 states are allowed in the former geometry, whereas transitions to all five V 3d states occur in the 1087



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For β-AxV2O5, the vanadyl bonds of the V1, V2, and V3 polyhedra are approximately arranged along the crystallographic c + a, c, and a directions, respectively, and the crystallographic b-axis uniquely does not pick up a contribution from these vanadyl bonds,31 which will be shown later in Figure 10. Polarization-dependent XAS measurements of β-Sr0.17V2O5 (an isoelectronic analogue of β-Na0.33V2O5) show similar pronounced anisotropy in the spectrum recorded with E||b, in contrast to spectra collected with polarizations parallel to the aand c-axes.31 The strong anisotropy of the unoccupied O 2p PDOS of β-Na0.33V2O5 predicted by our calculations (Figure 6c) is in excellent agreement with the experimental spectra (Figure 6b). The O 2py PDOS of the eg* hybridized states is clearly much weaker than that of t2g* states in our DFT calculations, which is consistent with the XAS spectrum measured at NI geometry. In contrast, the intensities of the σ* and π* states are comparable in both the O 2pz and 2px PDOS, resembling the XAS spectrum collected at GI geometry. Overall, the XAS measurements of our sol−gel samples are in excellent agreement with the previous measurements and calculations on both single-crystalline and polycrystalline V2O5 and β-Na0.33V2O5. The prominent anisotropy of the angular spectra confirms the preferable orientation existing in these sol−gel films, in accordance with the XRD data. All these data strongly support the high-quality crystallinity and stoichiometry of our samples. We notice some small differences in the intensities of some TEY (surface sensitive) and TFY (bulk sensitive) features, e.g., the V L-edge and O K-edge spectra of V2O5 at NI geometry in Figures 5 and 6. We attribute these differences to the enhanced crystalline orientation deeper in the V2O5 film, which leads to more anisotropic electronic structure at deeper probing depths and is also suggested by the SEM image. However, both XAS detection methods employed here essentially measure similar electronic structure, resembling the XAS spectra of β-Sr0.17V2O5.31 III. Soft X-ray Emission Spectroscopy. XES involves the excitation of a core electron in a process similar to the XAS process, followed by the subsequent decay of a valence electron to fill the core hole and accompanied by the emission of a photon, and is a bulk-sensitive technique (with a sampling depth of ∼100 nm). The normal XES process involves all available occupied states in the VB and corresponds to the local partial density of states (LPDOS).58 Nonresonant XES at the O K-edge measures the O 2p PDOS of the VB, owing to the transition from occupied O 2p orbitals to the O 1s core level. Resonant X-ray emission spectroscopy (RXES) involves coupled XAS and XES processes, which can be viewed as a transition similar to an absorption process in the first step and a decay similar to an emission process in the second step. By tuning the incident photon energy to a feature of the absorption spectrum, the system is resonantly excited according to that particular transition, and thereby the decay of VB electrons associated with that particular state is greatly enhanced in the RXES. Figure 7 presents normalized resonant and nonresonant XES spectra at the O K-edge of β-Na0.33V2O5 film (9 coatings), along with the normalized O 2p PDOS of the VB of βNa0.33V2O5 calculated through DFT. The RXES spectra are recorded with excitation energies located at XAS spectral features, which are close to the absorption onset (hν = 528.1 eV) and resonant with the t2g* (hν = 528.8 and 529.5 eV) and eg* (hν = 531.2 eV) states, respectively. The nonresonant XES spectrum is collected with incident photon energy well-above

Figure 6. Angular XAS spectra at the O K-edge detected in both TEY (solid lines) and TFY (open symbols) modes of thick (a) V2O5 (4 coatings) and (b) β-Na0.33V2O5 (6 coatings) films, recorded at both GI (blue color) and NI (red color) geometries, are plotted on a photon energy scale. (c) The unoccupied PDOS of the O 2py (red solid line) and O 2pzx (blue solid line) orbitals of β-Na0.33V2O5 is displayed on a binding energy scale. The blue dashed line in (a) represents the TEY spectrum of a thinner V2O5 film (1 coating) measured at GI geometry. The energy positions of the spectral features are marked by vertical short dashed lines.

dependent XAS measurements,25 which reveal a substantial growth in the intensity of σ* peak as the polarization vector is rotated from perpendicular to collinear to the vanadyl bond. 1088



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incoherent contribution from π hybridization and nonbonding states. Therefore, those bonding states between 523.7 and 525.3 eV in the nonresonant XES spectrum come from π hybridization, with σ hybridization toward the lower bound and nonbonding states near the upper end. Theoretically, our DFT calculations suggest similar energy locations of the O 2p VB states of β-Na0.33V2O5, in agreement with the qualitative V 3d− O 2p orbital interaction in vanadium bronzes, β-A0.33V2O5.10 The well-resolved RXES spectra demonstrate the wellestablished VB structure of our β-Na0.33V2O5 film. The spectral shape and energy dependence of the O K-edge RXES spectra of our V2O5 film (not shown here) is close to β-Na0.33V2O5, indicating a similar oxygen bonding environment in both compounds. The stronger elastic peaks observed for V2O5 reflect the more localized electronic structure of insulating V2O5. IV. Resonant Inelastic Soft X-ray Spectroscopy. The resonant inelastic X-ray spectroscopy (RIXS) process is similar to that of RXES. However, in RIXS, when the incident photon energy is tuned close to the absorption threshold, typically near the transition metal L-edge, the system is left with an electron− hole pair around the Fermi level in the final state. Therefore, RIXS is able to probe low-energy excitations, such as local crystal-field excitations (intrasite d−d* transitions) and O 2p− V 3d charge-transfer (CT) excitations. The RIXS features (of constant loss energy) can be separated from the PDOS features (of constant emission energy) by inspecting their dependence on the incident photon energy. Figure 8 displays normalized (to the maximum intensity) RIXS spectra excited at the V L-edge and the off-resonant XES

Figure 7. Normalized resonant and nonresonant XES spectra (black solid lines) at the O K-edge of β-Na0.33V2O5 are displayed on a common photon energy scale (top axis). The normalized PDOS of the O 2p VB (red solid line) of β-Na0.33V2O5 is displayed on a binding energy scale (bottom axis). The RXES excitation energies are varied across the absorption spectral features. The vertical short dashed lines refer to the lower and upper bounds of the π hybridization states extracted from the XES spectra.

the absorption threshold (hν ≈ 580 eV). Elastic spectral features, which are due to the elastic scattering of X-rays, are visible in the resonant spectra, and the energy positions of the elastic peaks coincide with the excitation energies. The theoretical VB structure of the O 2p states has been broadened with a Lorentzian function (HWHM = 0.22 eV) followed by a Gaussian function (FWHM = 0.8 eV) to take account of the O 1s lifetime broadening57 and the emission instrumental resolution, respectively. To allow a direct comparison, the experimental spectra and the broadened O 2p PDOS in our DFT calculations have been aligned to match up the energy locations of the respective O 2p nonbonding and bonding states. The measured O 2p states of the VB span the energy range from ∼522 to ∼528 eV in the normal XES (above threshold) spectrum with a spectral width of ∼6 eV. This is in excellent agreement with the energy range from ∼−9 to ∼−3 eV in our DFT calculations, as well as previous band structure calculations,11 when the experimental resolution broadening (∼0.8 eV) is taken into account. The origin of these occupied O 2p states can be determined experimentally by comparing nonresonant XES with RXES. When excited close to the absorption onset, the RXES spectrum is resonant with pure t2g* states at the bottom of the CB and provides the lower bound of the π hybridization states in the VB. As the incident energy gradually increases to the π * peak, the spectrum is resonant with the majority of t2g* states and gives the upper end of the π hybridization. When the excitation energy is increased to the σ* peak, the spectrum is composed of the coherent part that is resonant with the majority of eg* states as well as the

Figure 8. Normalized RIXS spectra at the V L-edge and the offresonant XES spectra excited above the V L-edge (solid lines) of (a) V2O5 and (b) β-Na0.33V2O5 films, along with their respective XAS (TFY) spectra (open circles), are plotted on a common photon energy scale. The RIXS excitation energies located at the TFY spectral features are marked with black triangles. The dispersions of the CT excitations along with the elastic peaks are traced by the short dashed lines.

spectra excited above the V L-edge of V2O5 (4 coatings) and βNa0.33V2O5 (9 coatings) films, along with their respective XAS (TFY) spectra. The RIXS excitation energy increases from the absorption onset to the main V L3 and L2 absorption peaks. The RIXS intensity of the elastic peak is very strong in insulating V2O5 and weak in semiconducting β-NaxV2O5, in agreement with the O K-edge RXES. 1089



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The broad spectral feature around ∼510 eV, which stays constant on the emission energy scale, originates from the V 3d−O 2p hybridization owing to the L3-edge emission. The weak features centered at ∼515 and ∼518 eV for both compounds in the XES spectrum excited above the V L-edge represent a combination of V 3d−O 2p fluorescence due to L2edge emission and CT features. The presence of O 2p states in the off-resonant XES spectra is due to the overlapping excitation with the O K-edge. When excited close to the absorption threshold, the contribution of the fluorescence features to the RIXS spectra becomes weak and the loss features are relatively prominent, which provides the possibility of directly measuring low-energy excitations. As shown in Figure 8, when excited at 514.3 eV (the absorption onset), a broad feature disperses in energy (in addition to the elastic peak) in both compounds, as indicated by short dashed lines. This feature cannot be interpreted as a fluorescence feature and is assigned to CT excitations, which have been observed in both V2O5 powder26 and α′-NaV2O5 single crystals.27 Following this interpretation, the existence of RIXS loss features can be revealed and their energy locations can be determined, when plotted on a loss energy scale (subtracting the emission photon energy by the incident photon energy). Figure 9 shows normalized V L3-edge RIXS spectra when excited (a) at the absorption threshold (514.3 eV) and (b) close to the absorption onset (514.3−517.2 eV) on a loss energy scale. In addition to the raw spectra, noise-filtered V L3edge RIXS spectra are also shown (employing maximum entropy [MaxEnt] deconvolution as a noise filter).42,59 The elastic peak stays at zero energy on the loss energy scale. The CT excitation is centered at ∼−6 eV on the loss energy scale for both compounds, as shown in Figure 9a. This energy location is in good agreement with the position of the CT band at ∼−6 eV in β-Sr0.17V2O5 single crystals31 and at ∼−7 eV in V2O5 powders,26 α′-NaV2O5 single crystals,27 and V6O13 single crystals.60 In Figure 9b, a feature constant on the loss energy scale is found at ∼−1.6 ± 0.1 eV and can be attributed to a dd* transition. In the V4+ d1 system, the excitation process is 2p63d1 → 2p53d2 → 2p63d1*, where the asterisk in the final state represents an excited configuration of the d1 ion. On the other hand, dd* transitions are naturally very weak in the d0 system, V2O5,26 and are not visible in our data. The presence of the dd* transition in our β-Na0.33V2O5 film indicates the finite bandfilling of the V 3d orbitals, in agreement with the double-peak structure of the V 2p3/2 core level and the weakly occupied pure V 3d states in the VB shown in Figure 4. In α′-NaV2O5, dd* excitations were observed in the V L-edge RIXS spectra at ∼−1.6 eV.27 For isoelectronic β-Sr0.17V2O5, dd* excitations have been observed to be centered at ∼−1.1 eV and are due to on-site transitions from the partially filled dxy magnetic orbital into the unoccupied dyz, zx orbitals.31 The intensity variation of the observed dd* transition with incident photon energy in our β-Na0.33V2O5 film is similar to β-Sr0.17V2O5 and is strongest when excited at ∼−3 eV below the V L3-edge absorption main peak. However, its energy location in β-Na0.33V2O5 is found to be very close to α′-NaV2O5 and significantly larger than βSr0.17V2O5. Since the energy location of the dd* transition is determined by the tetragonal (D4h) distortion, i.e. Dt and Ds crystal field parameters, these results reflect that the splitting of V 3d t2g orbital is very similar in β-Na0.33V2O5 and α′-NaV2O5 and much weaker in β-Sr0.17V2O5. This is in agreement with the

Figure 9. Normalized V L3-edge RIXS spectra are displayed on a loss energy scale. (a) The RIXS spectra excited at the absorption threshold (normalized to the pre-edge of CT states) are compared between V2O5 (red dashed line) and β-Na0.33V2O5 (blue solid line). (b) RIXS spectra excited close to the absorption onset (blue filled circles) together with the noise-filtered spectra (black solid lines) reveal the location of the dd* transitions in β-Na0.33V2O5. The energy locations of the CT excitations, the dd* transitions, and elastic peaks are marked by vertical lines.

larger energy separation between V 3d t2g and eg orbitals (10 Dq) in β-Na0.33V2O5 than that in β-Sr0.17V2O5, revealed by the V L3-edge XAS. This is a topic to which we return in more detail below. Finally, we note that the dimer-type intersite dd transition (0.8 eV) within the V1−O−V2 ladder of β-Sr0.17V2O5 and β-Na0.33V2O5 observed in the optical reflectivity measurements15 is expected to be weak in the RIXS process.

V. DISCUSSION The explanation of orbital splitting in transition metal oxides is well developed by crystal field theory. The orbital levels of transition metal cations, usually d or f levels, are split due to a static electric field (crystal field) resulting from the surrounding 1090



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oxygen anions (ligands). Particularly, in a VO6 octahedron with a cubic crystal field, the 5-fold V 3d orbitals are split into three degenerate t2g levels and two degenerate eg levels separated by 10Dq. A picture of the V 3d orbital splitting due to the VO6 octahedral distortion in β-AxV2O5 is shown in Figure 10. As the

Table 1. Average Bond Lengths (Å) and Bond Angles (deg) Reflecting the Strength of the Crystal Field Distortion of VO6 Octahedra for β-Na0.33V2O5, β-Sr0.33V2O5, and βSr0.17V2O5a av bond length and bond angle ⟨V−O⟩ (Å) ⟨(V−Oap)long − (V−Oap)short⟩ (Å) ⟨α⟩small (deg) ⟨α⟩large (deg)

βNa0.33V2O52

βSr0.33V2O561

βSr0.17V2O513,61

1.951 0.883

1.950 0.764

1.943 0.767

76.9 103.3

78.7 101.7

78.7 101.6

a ⟨(V−Oap)long − (V−Oap)short⟩ represents the average difference between long and short V−Oapical bond lengths. ⟨α⟩small and ⟨α⟩large refer to the average small and large Oapical−V−Obasal bond angles (see Figure 10).

Sr0.33V2O5 and β-Sr0.17V2O5. First of all, the ⟨V−O⟩ bond lengths are similar for all three compounds, meaning that the VO6 octahedra are approximately the same size and the V 3d− O 2p hybridization is similar for the different compounds. However, the difference between the long and short ⟨V−Oap⟩ of β-Na0.33V2O5 is significantly larger than those of β-Sr0.33V2O5 and β-Sr0.17V2O5 by ∼0.12 Å (∼15%), reflecting that the compression of short V−Oapical bonds and the elongation of long V−Oapical bonds are greatly enhanced in β-Na0.33V2O5. Moreover, the small or large ⟨α⟩, which defines the extent of basal-plane oxygen anions being either attracted or repelled out of plane by apical oxygen anions, is substantially exaggerated by almost 2° in β-Na0.33V2O5 than in either β-Sr0.33V2O5 and βSr0.17V2O5. In summary, the VO6 octahedra of β-AxV2O5 become significantly more distorted with the A-site cation varying from Sr2+ to Na+, as demonstrated by the evolution of average bond lengths and bond angles. Compared to β-Sr0.17V2O5, the increased distortion of the VO6 octahedra in β-Na0.33V2O5 explains the larger V 3d crystalfield splitting of β-Na0.33V2O5 revealed by our measurements. The larger energy separation between V5+ species in the V L3edge XAS of β-Na0.33V2O5 (∼3.0 eV) than that in β-Sr0.17V2O5 (∼2.4 eV)31 reflects the larger crystal-field splitting 10Dq (>2.1 eV) in β-Na0.33V2O5, which pulls the weighted centers of V 3d t2g and eg orbitals further apart. For β-AxV2O5, the dd* transitions observed in the V L3-edge RIXS experimentally provide a direct measurement of the energy separation between the split dxy level and two nearly degenerate dyz, zx levels, i.e., 3Ds − 5Dt. These are found to be much larger for β-Na0.33V2O5 (∼−1.6 eV) than β-Sr0.17V2O5 (∼−1.1 eV) in agreement with the larger VO6 distortion in β-Na0.33V2O5 than β-Sr0.17V2O5, which pushes the dxy level and dyz,zx levels of t2g orbitals further apart. Equivalent to Sr2+ in β-Sr0.17V2O5, the Na+ cation in βNa0.33V2O5 donates ∼0.17 electrons per vanadium cation. Recent nuclear magnetic resonance,62,63 electron-spin resonance,64 and optical15 measurements revealed that these 3d electrons preferentially occupy V1 sites in both compounds instead of being distributed equally on all vanadium sites. In the above discussion, we take the average of all three VO6 octahedra in order to discuss more generally the enhancement of the VO6 distortion; however, similar arguments hold for a single V1O6 octahedron.

Figure 10. Orientations of V1O6, V2O6, and V3O6 octahedra of βAxV2O5, projected along the crystal b-axis and with the vanadyl bond (V−Oap) aligned with the paper vertical, are drawn on the top. The average bond lengths and bond angles defining the octahedral distortion are marked in a representative VO6 octahedron. Schematic energy-level diagram of V 3d orbital splitting due to the VO6 octahedral crystal field is sketched at the bottom. The red arrows illustrate the electron occupation of a V d1 system.

basic units of zigzag chains and ladders in β-AxV2O5, the VO6 octahedra are highly distorted with one V−Oapical bond compressed, the other elongated, and the basal-plane oxygen anions displaced out of plane, as shown in Figure 10. On one hand, due to this corner-shared neighboring interaction, these VO6 octahedra are deformed with a tetragonal symmetry, which further splits the formerly degenerate t2g (dxy, dyz, and dzx) and eg (dx2−y2 and dz2) orbitals. For the V d1 system, the electron preferentially occupies the lower-energy dxy orbital and the other two almost degenerate orbitals, dyz and dzx, remain unoccupied, as shown in Figure 10. The energy splitting between the upper and lower t2g levels is given by 5Dt − 3Ds. On the other hand, this electron occupation determined from Hund’s rule favors and strengthens the tetragonal deformation of t2g orbitals. The VO6 octahedral distortion is characterized by the average difference between the long and short V−Oapical bond lengths (⟨V−Oap⟩long − ⟨V−Oap⟩short) and the average small and large Oapical−V−Obasal bond angles (⟨α⟩small, ⟨α⟩large), as shown in Figure 10. Their respective values for β-Na0.33V2O5, βSr0.33V2O5, and β-Sr0.17V2O5 are shown in Table 1 along with the corresponding average V−O bond lengths. All the V−O bond lengths and the O−V−O bond angles were averaged over all three octahedra, V1O6, V2O6, and V3O6. The unit-cell structural parameters of β-Na0.33V2O5 and β-Sr0.33V2O5 were taken from refs 2 and 61, respectively. For β-Sr0.17V2O5, the lattice constants were taken from ref 13, and the internal atomic positions were considered to be the same as those of βSr0.33V2O5. A direct comparison of the average bond lengths and bond angles among the different compounds leads to the conclusion that the mean distortion of the VO6 octahedron distortion is much larger in β-Na0.33V2O5 and very similar between β-

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CONCLUSION We have presented a detailed X-ray spectroscopic study of the quasi-one-dimensional electronic structure of polycrystalline β1091



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film thickness measurement as well as Professor Richard Averitt for useful discussions. The authors also thank Paul Mak and Anlee Krupp for the training and maintenance of equipments in the Photonics Center.

Na 0.33 V 2O 5 films. Preferentially oriented V2 O5 and βNa0.33V2O5 polycrystalline films of high crystallinity and stoichiometry have been obtained through the sol−gel process with an RTP anneal and have been characterized by combined photon and electron techniques. The absorption and emission spectra at the O K-edge of β-Na0.33V2O5 are very similar to those from β-Sr0.17V2O5, which can be explained by the very close mean ⟨V−O⟩ bond lengths of these two compounds. The energy separation between t2g* and eg* states in the O K-edge XAS spectrum (at least ∼−1.8 eV) provides a measured energy splitting of O 2p hybridized orbitals owing to the crystal field in our β-Na0.33V2O5 film, in good agreement with β-Sr0.17V2O5. The measured O 2p PDOS of the CB from the angular XAS at the O K-edge displays strong orbital anisotropy of βNa0.33V2O5, which is consistent with the preferable orientation of our sol−gel derived films and is well predicted by our DFT calculations. The O K-edge RXES spectra of β-Na0.33V2O5 demonstrate that the measured O 2p PDOS of the VB is composed of the main peak near the upper end attributed to nonbonding states and the evident shoulders owing to π hybridization and σ hybridization states toward the lower range, which is also suggested by our theoretical results. The XAS and RIXS spectra at the V L-edge demonstrate a stronger crystal field applied on the V 3d orbitals by the surrounding oxygen ligands in β-Na0.33V2O5 than that in β-Sr0.17V2O5, which is interpreted as the increased distortion of the VO6 octahedra due to the substitution of the Sr2+ cation with Na+. The larger energy separation between the V5+ features in the V L3-edge XAS spectra (3.0 eV) indicates a larger V 3d crystal-field splitting in β-Na0.33V2O5 than is found in β-Sr0.17V2O5. The energy location of the local crystal-field excitation (dd* transition) at ∼−1.6 ± 0.1 eV indicates that the V 3d t2g orbital splitting in β-Na0.33V2O5 is very close to that of α′NaV2O5 and much larger than that of β-Sr0.17V2O5. Additionally, the weakly occupied dxy orbital of β-Na0.33V2O5 is observed at a binding energy of ∼−0.9 eV and presents a Gaussian-like line shape from HAXPES. While β-Na0.33V2O5 and β-Sr0.17V2O5 are often considered isoelectronic and quasi-isostructural, these results illustrate the nontrivial effects of the A-site ionic size and covalency on the electronic structure.

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REFERENCES

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AUTHOR INFORMATION

Corresponding Author

*E-mail [email protected] (K.E.S.). Notes

The authors declare no competing financial interest.

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ACKNOWLEDGMENTS The Boston University (BU) program is supported by the Department of Energy, Basic Energy Sciences, under Grant DEFG02-98ER45680. The NSLS is supported by the Department of Energy under Contract DE-AC02-98CH10886. Acknowledgment is also made to the Donors of the American Chemical Society Petroleum Research Fund for support (or partial support) of this research (Binghamton University). Beamline X24A at the NSLS is supported by the National Institute of Standards and Technology. The authors thank Anny Hierro and Stefanie Cantalupo for help during sol−gel synthesis, Stephen Topping, Jiapeng Xu, and Professor Vinod K. Sarin for help with XRD characterization, and Professor George Zimmerman for help during electric-resistivity measurement. We also thank Dongdong Peng and Professor Ophelia Tsui for 1092



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Electronic Structure of Î²-NaxV2O5 (x â 0.33) Polycrystalline Films

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