9152
J. Phys. Chem. 1996, 100, 9152-9160
Electron Nuclear Double Resonance of Polarons in r-LixV2O5 Brigitte Pecquenard, Didier Gourier,* and Daniel Caurant Laboratoire de Chimie Applique´ e de l’Etat Solide, URA 1466 CNRS, Ecole Nationale Supe´ rieure de Chimie de Paris, 11 rue Pierre et Marie Curie, 75231 Paris Cedex 05, France ReceiVed: January 24, 1996X
A single crystal of R-LixV2O5 (x ) 0.005) is studied by electron nuclear double resonance spectroscopy (ENDOR). It is shown that the ESR spectrum is composed of two overlapping signals. The first one (Acenter) is the well-known 29-line spectrum due to polarons trapped by the Coulomb field of Li+ ions. The second (B-center) is unknown so far and is studied here for the first time. It consists of a broad unresolved line hidden inside the 29-line spectrum. The B-center represents a free polaron localized on a single vanadium site of one [V2O5]n layer and is responsible for the compound’s electronic conductivity. The ENDOR lines of this center are assigned to two nearest neighbor vanadium nuclei, one being located in the same [V2O5]n layer as the polaron while the other belonging to the adjacent layer. ENDOR spectroscopy shows the existence of a significant covalent interaction between layers, in contrast with the usual assumption of Van der Waals interactions. This covalency manifests itself by the transfer of about 10-2 unpaired polaron spin density into 4s and dz2 vanadium orbitals of the closest vanadium ion in the adjacent layer. Bound polarons (A-centers) do not give an ENDOR response. This feature is attributed to an inhomogeneous distribution of Li+ ions in the matrix (in the form of shallow clusters), which provokes a concentration quenching of the ENDOR enhancement.
I. Introduction The Li/V2O5 system has attracted much interest during the last decade because of its potential application in secondary lithium batteries.1,2 The electrochemical insertion of lithium in V2O5 leads to the formation of four successive LixV2O5 phases, namely R, , and δ for 0 < x < 1, and of γ-LixV2O5 for x > 1.3-5 These phases have been essentially characterized by X-ray diffraction methods, electrochemical methods,3-6 susceptibility measurements,7,8 and more recently, electron spin resonance (ESR).9,10 Each LixV2O5 phase produced by electrochemical intercalation shows a characteristic ESR “finger print” with its own g-parameters, line shape, and temperature dependence of intensity. ESR also demonstrated the persistence of the γ-phase after lithium deintercalation in LixV2O5 for x > 1.10 The alteration of the cathodic surface grains during the δ f γ phase transition is also responsible for the liberation of vanadyl complexes VO2+ in the cathodic medium, easily detected by ESR.9,10 7Li and 51V nuclear magnetic resonance (NMR)11,12 have also been performed on LixV2O5 phases. Conductivity measurements of V2O513 and R-LixV2O514 have been interpreted in terms of small polarons (free and bound). Only bound polarons could be characterized by ESR13-16 with the clear evidence that the unpaired electron is delocalized over two or four vanadium sites. The ionic defects responsible for the polaron trapping are oxygen vacancies in V2O5 and extra Li+ ions in R-LixV2O5. These defects are magnetically diluted in V2O5 and R-LixV2O5 because of their small concentration, so their ESR spectrum exhibits a well-resolved hyperfine structure,13-16 which is not the case for -, δ-, and γ-phases10 because of the high unpaired spin concentration. However, even for V2O5 and R-LixV2O5 the resolution of ESR is too low (≈60 MHz) to monitor hyperfine interactions with nuclei other than those at the unpaired electron sites. Electron nuclear double resonance (ENDOR)17,18 provides a considerable increase in ESR resolution (up to ≈0.1 MHz in the present case) * To whom correspondence should be addressed. X Abstract published in AdVance ACS Abstracts, May 1, 1996.
S0022-3654(96)00237-7 CCC: $12.00
so that interactions with nuclei localized at a distance of several angstroms from the unpaired electron spin can be measured. With this technique, very weak 51V or 7Li hyperfine interactions not resolved by ESR can in principle be measured with high accuracy. In the present work, ENDOR experiments were performed on a R-LixV2O5 (R < 0.01) single crystal. The structure of V2O5 is shown in Figure 1. It consists of [V2O5]n layers built from VO5 square pyramids sharing edges and corners. These layers are assumed to be assembled via Van der Waals interactions.19 The structure of R-LixV2O5 (x < 0.1) is identical to that of V2O5, the small amount of lithium residing between layers, in sites with trigonal prismatic geometry.20 The extra electron is delocalized on vanadium sites, giving rise to the semiconducting properties of LixV2O5.21 The strong electronphonon coupling is responsible for the formation of small polarons, which govern the low mobility of charge carriers.14 At low temperatures, polarons are assumed to be trapped in the Coulomb field of Li+ ions, as suggested by the existence of 29 well-resolved hyperfine lines in the ESR spectrum, which indicates that the unpaired electron spin is delocalized on four equivalent vanadium sites surrounding the lithium site16,22 (Acenter in Figure 1). The initial motivation of the present work was to focus on three particular points concerning the structure of bound polarons in R-LixV2O5. (i) The first is the precise measurement of the 7Li hyperfine interaction in the paramagnetic defect. This is expected to locate the position of Li+ with respect to the unpaired electron site.18 (ii) The second is the detection of hyperfine interactions with neighboring 51V nuclei localized at several angstroms away from the electron site. This should give information on the size of the polarons and thus on the magnitude of the electron-phonon interaction. (iii) Finally, the hyperfine interaction with a 51V nucleus belonging to an adjacent [V2O5]n layer should provide information on the nature of interaction between layers. If this interaction is purely of the Van der Waals type, as is generally © 1996 American Chemical Society
Polarons in R-LixV2O5
Figure 1. Structure of R-LixV2O5 showing the two paramagnetic defects. The A-center (bound polaron) is an unpaired electron delocalized over four vanadium atoms around a Li+ ion. The B-center (free polaron) is an unpaired electron trapped on a single vanadium site by the polarization of surrounding ions. The first neighbors of the site V(0) are labelled V(1) to V(3).
accepted,19,23-25
the magnetic interaction should not be influenced by the covalent transfer of spin density through interlayer spacing. However, it was also argued that the failure to incorporate under mild conditions ions larger than Na+ also indicates that V2O5 behaves as a three-dimensional framework rather than a Van der Waals host.7,26 In that case weak covalent effects should be easily detected by the observation of unpaired spin density transfer from the polaron site to the adjacent layer. II. Experimental Section Single crystals of composition R-Li0.005V2O5 were obtained by slow cooling of the melt.27 The silica crucible containing the mixture of V2O5 and LiCO3 was placed in a device consisting of two reversed alumina crucibles covered by alumina powder in order to preserve a homogeneous temperature. The mixture was heated at 800 °C and maintained at this temperature for 2 h to ensure a perfect homogeneity of the melt. Slow cooling from 750 to 600 °C at a rate of 2 °C/h made crystals grow as needles of size 5 × 2 × 0.5 mm3. The lithium composition x ) 0.005 corresponds to an unpaired electron spin concentration of ≈3 × 1019 cm-3. It is high enough to give a good signal-to-noise ratio of the ESR spectra and sufficiently low to avoid spin-spin interactions between unpaired electrons, which should decrease or suppress the ENDOR response.18 Increasing the concentration of lithium (and thus the concentration of unpaired electron spins) would produce excitation transfer between electron spins, which provokes in turn a quenching of the ENDOR signal. For this reason ENDOR cannot be used for magnetically concentrated -, δ-, and γ-LixV2O5 phases. ENDOR spectra were recorded at the X-band with a modified Bruker 220 D ESR spectrometer equipped with the Bruker ENDOR cavity working in the TM110 mode and a 100 W ENI broad-band power amplifier. ENDOR spectra were detected using a 12.5 kHz frequency modulation of the radio-frequency carrier (noted rf1) without magnetic field modulation (only used for the ESR detection). With this modulation scheme, the ENDOR signal takes the form of the first derivative of the ENDOR enhancement. Some ENDOR-induced ESR spectra (EI-ESR) were also recorded. They correspond to the variation of the intensity of an ENDOR line under a magnetic field sweep. Electron-nuclear-nuclear triple resonance, referred to as double-ENDOR,18 were obtained by saturating an ENDOR transition with a radio-frequency field rf2 while sweeping the other (modulated) field rf1.
J. Phys. Chem., Vol. 100, No. 21, 1996 9153
Figure 2. X-band ESR spectra at 10 K of R-LixV2O5 (x ) 0.005) for two different orientations of the magnetic field: (a) B0 || c, where the dotted line represents the calculated component, which must be added to the 29-line spectrum to simulate the experimental spectrum; (b) B0 ⊥ c.
All the ESR, ENDOR, EI-ESR, and double-ENDOR spectra were recorded at 10 K by using an Oxford Instrument ESR 9 continuous flow helium cryostat. This low temperature ensures complete electron trapping and sufficiently long electron and nuclear spin-lattice relaxation times to allow an easy saturation by both ESR and NMR transitions. Most of the spectra were obtained at a microwave power of 63 mW, a radio-frequency power of 100 W, and a modulation depth of 100 kHz. III. ENDOR Spectra A. General Features. Figure 2 shows two selected X-band ESR spectra of a R-LixV2O5 single crystal recorded with the magnetic field B0 parallel and perpendicular to the c-axis. In the former case, the partially resolved 29-line spectrum reflects the delocalization of the unpaired electron spin over four equivalent 51V nuclei, as found previously.14,16,22 The hyperfine interaction is not resolved for the other field orientation B0 ⊥ c, implying a smaller vanadium hyperfine interaction. The spin Hamilontian parameters of the paramagnetic defect are14 g|| ) 1.912 ( 0.002, g⊥ ) 1.981 ( 0.002, |A||| ) (44.4 ( 0.5) G, and |A⊥| e 17 G. Despite the fact that the parallel spectrum was previously interpreted in terms of a single paramagnetic center,14 the spectrum of Figure 2a can be simulated as the sum of a 29-line spectrum and a single broad line in a 1/9 ratio. The two spectra possess the same g˜ tensors and are thus superimposed, giving a single line for the field orientation B0 ⊥ c (Figure 2b). We shall see below that this interpretation of ESR spectra agrees with the ENDOR results, so to start with, we suppose that we are dealing with two paramagnetic centers: (i) the 29line ESR spectrum, which corresponds to a single electron delocalized over four equivalent vanadium sites (hereafter referred to as A-center) and (ii) the broad line corresponding to another center hereafter referred to as B-center. Each ESR line is composed of a multitude of unresolved hyperfine lines due to interactions with neighboring nuclei. It is possible to resolve these small hyperfine interactions by ENDOR, which consists of partially saturating an ESR line at a fixed value Bobs (the observing field) of the magnetic field while sweeping the radio-frequency field rf1 over nuclear resonance transitions.17
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In order to give the general features of ENDOR spectra in R-LixV2O5, let us consider an unpaired electron spin S at a vanadium site weakly interacting with a neighboring nucleus of spin I and nuclear g-factor gn, this nucleus being either 7Li (I ) 3/2, gn ) 2.170 961, Q ) -0.040 × 10-24 cm2, 92.5% natural abundance) or 51V (I ) 7/2, gn ) 1.468 36, Q ) -0.0515 × 10-24 cm2, 99.75% natural abundance). The spin Hamiltonian of this simple pair system contains four terms:
H ) gβB0Sz - gnβnB0Iz + ASzIz + 0.5P{Iz2 - I(I + 1)/3} (1) which represent, respectively, the electron and the nuclear Zeeman interactions and the magnetic hyperfine and quadrupolar interactions. The g-factor in expression 1 is given by g ) (g||2 cos2 θ + g⊥2 sin2 θ)1/2. A is the hyperfine parameter, which we suppose is nearly isotropic for the sake of clarity, and P is the quadrupole parameter. A and P are much smaller than the electron Zeeman interaction gβB0 so that a first-order treatment is sufficient to derive the expression for the energy of the spin states:
Figure 3. General view of the ENDOR spectrum for B0 || c in the frequency range 1-100 MHz. All the lines above 20 MHz are ghost lines. Only the lines below 20 MHz correspond to ENDOR transitions.
E(ms,mI) ) gβB0ms - gnβnB0mI + AmsmI + 0.5P{mI2 - I(I + 1)/3} (2) where the quantum numbers ms ) (1/2 and mI ) I, I - I, ..., -I are the components of the electron and nuclear spin states along the external field B0. The ESR transitions are characterized by the selection rules ∆ms ) (1, ∆mI ) 0, giving 2I + 1 unresolved ESR lines at frequencies ν(mI) ) (gβB0 + AmI)/h. ENDOR spectroscopy is governed by the NMR selection rules ∆mI ) (1, ∆ms ) 0, which give transitions in the rf range. Their number depends on the relative magnitude of A, P, and the ENDOR line width ∆ν. If the inequality P < ∆ν , A holds, the ENDOR spectrum consists of two lines at frequencies
1 ν(ms) ) |msA - gnβnB0| h
(3)
The shape of the spectrum depends on the relative magnitudes of A and νn ) gnβnB0. For |msA| > νn, the two lines are centered on |A|/2 and separated by 2νn. For |msA| < νn, the two lines are centered on νn and separated by A. The quadrupolar interactions is resolved if ∆ν < |P| , |A|, which leads to ENDOR lines at frequencies
1 ν(ms,mI) ) |Ams - gnβnB0 + P(mI ( 1/2)| h
(4)
If the hyperfine interaction A is much smaller than the ESR line width, several unresolved hyperfine lines (characterized by different quantum numbers mI) are saturated simultaneously at a single observing field Bobs. In this case we expect a maximum of 4 × I ENDOR lines (2 × I for each ms state). Since expressions 3 and 4 depend on gn, it is possible to identify the nucleus by monitoring the B0 dependence of ENDOR frequencies.18 Figure 3 shows a typical ENDOR spectrum recorded for B0||c by setting Bobs at the center of the ESR spectrum of Figure 2a. It exhibits a number of lines in the frequency range 1-100 MHz. The lines at high frequencies (>20 MHz) are not due to NMR transitions. This has been checked by setting the observing field outside the field range of the ESR spectrum, showing that all the lines at frequencies larger than 20 MHz are still present and are independent of the field setting, while the lines at frequencies below 20 MHz are no longer present. This proves
Figure 4. ENDOR spectrum for B0 ⊥ c. The observing field Bobs is set at the center of the ESR line of Figure 2b.
TABLE 1: Distances and Angles in V2O5 distances (Å) V(0)-V(1) V(0)-V(2) V(0)-V(3)
2.95 3.56 4.35
angles (degree) V(1)-V(0)-V(1) V(2)-V(0)-V(2) V(2)-V(0)-V(3)
78 90 90
that only the latter are real ENDOR transitions. The parasite lines could be due to a capacitance effect between the cavity wall and the coil.28 The ENDOR lines in the 1-20 MHz range are composed of two sets: (i) a low-frequency set in the range of 1 to ≈5 MHz, characterized by weak ENDOR lines whose positions are only slightly dependent on the orientation of B0 and that are not observed for B0 ⊥ c and (ii) a high-frequency set in the range of ≈5 to 20 MHz characterized by intense lines whose positions vary significantly with the field orientation. For B0 ⊥ c, this “high-frequency” component extends from 2 to 16 MHz. It corresponds to ENDOR of the nearest neighbor nuclei, while the “low-frequency” component corresponds to nuclei at larger distances from the paramagnetic center. In what follows we shall distinguish the different vanadium nuclei by labels V(i) (i ) 0, 1, 2, 3, ..., n) as shown in Figure 1. For an unpaired electron spin trapped in site V(0), the two first neighbors in the [V2O5]n layer are labelled V(1) and V(2). The vanadium site V(3) lies in the adjacent layer. The distances and angles between V(0) and the other sites are given in Table 1. Two typical ENDOR spectra are shown in Figures 4 and 5a corresponding to the orientations B0 ⊥ c and B0 || c, respectively. For B0 ⊥ c (Figure 4) the spectrum is composed of three pairs of lines labelled R-β, R′-β′, and γ-δ respectively. All these pairs are split by twice the nuclear frequency of vanadium. This fact and the lack of quadrupolar splitting indicate that we are dealing with the situation where |P| e ∆ν , |A| and |A|/2 > νn, characterized by the ENDOR frequencies ν(ms) ) 1/h((|A|/ 2) ( gnβnB0). For the orientation B0 || c (Figure 5a) the two pairs R-β and R′-β′ collapse, which indicates that they belong to a single vanadium neighbor, while the other pair γ-δ,
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J. Phys. Chem., Vol. 100, No. 21, 1996 9155
Figure 6. EI-ESR spectrum for the field orientation B0 || c, obtained by observing the ENDOR line β of Figure 5a.
Figure 5. (a) ENDOR spectrum for B0 || c, where the observing field Bobs is set at the center of the ESR line of Figure 2a; (b) double-ENDOR spectrum obtained by saturating the β-line by the field rf2 during the sweeping of rf1.
corresponding to another vanadium neighbor, is shifted toward higher frequencies. It can be seen that the quadrupolar interaction of R- and β-lines is partially resolved for the orientation B0 || c. B. Origin of the ENDOR Lines. Let us consider the different possibilities for the interpretation of these ENDOR lines. The two sets R-β and γ-δ may belong to the same paramagnetic center (A or B), or one set may belong to the A-center and the other set to the B-center. The combination of double-ENDOR and EI-ESR techniques and also some features of the ENDOR spectrum allow us to choose between these four possible interpretations. Double-ENDOR, which consists of inducing an ENDOR transition of a given paramagnetic center by a saturating field rf2 (the pump) while sweeping the field rf1, results in a modification of the intensities of all the ENDOR lines corresponding to this center. In particular, the lines characterized by the same value of ms as that of the pumped ENDOR line are weakened, while the ENDOR lines corresponding to the other ms values are enhanced. Two kinds of information can thus be obtained from a double-ENDOR experiment.18 (i) Only the ENDOR lines corresponding to the same paramagnetic center are affected by the pumping field rf2. ENDOR lines of other centers are not modified. It is thus possible to separate ENDOR spectra originating from different types of paramagnetic centers in overlapping ESR spectra. (ii) It is also possible to determine the relative sign of the hyperfine interactions of two different neighbor nuclei.29 In a single pair of ENDOR lines, the exact assignment of each transition to a particular ms value depends on the sign of the hyperfine interaction. If the hyperfine interactions with two different neighbor nuclei have the same sign, the modification of the ENDOR intensities by the pump will be identical for the two pairs of lines. On the other hand if the signs of the hyperfine interactions of the two nuclei are different, the two pairs of lines will exhibit opposite modifications of their intensities.29 Figure 5b shows the double-ENDOR response for the orientation B0 || c when the transition β is pumped by the field rf2. One observes a decrease of β and an enhancement of its low-frequency partner R. It can be seen that lines δ and γ are also modified, showing that they belong to the same paramagnetic center as the R and β lines. Moreover, the intensity modification of the γ-δ pair is opposite to that of the R-β pair, since in the former case pumping reduces the intensity of the low-frequency line γ. Thus, the hyperfine interactions with
Figure 7. Angular variation of ENDOR lines for rotation of B0 in the ab-plane. Full and discontinuous lines represent the calculated variations for δ-γ and R-β pairs, respectively.
the two vanadium neighbors are of opposite signs. It is, however, not possible to determine the absolute signs on the basis of the present experiments. It should be noticed that the double-ENDOR effect also increases the resolution of some ENDOR lines, since the δ-line exhibits a well-resolved quadrupolar splitting under the action of the pumping field rf2 (Figure 5b). This splitting is not so well resolved in the ENDOR spectrum (Figure 5a). In addition, the pumping field rf2 produces new lines that are not easily observed in the ENDOR spectrum of Figure 5a. These lines are marked by asterisks in Figure 5b. They belong to the same paramagnetic center as the R-β and γ-δ lines and represent also ENDOR transitions of 51V nuclei as shown by partially resolved quadrupolar splitting and by Zeeman splitting equal to twice the vanadium nuclear frequency. The ENDOR-induced ESR (EI-ESR) technique was used to determine the paramagnetic center at the origin of the ENDOR lines. Its principle is to monitor the intensity of a single ENDOR line under a magnetic field sweep. This gives the ESR spectrum at the origin of the observed ENDOR line. Figure 6 shows an example of an EI-ESR spectrum for the orientation B0 || c recorded by observing the intensity of the β-line in Figure 5a. It consists of a single symmetrical line without resolved hyperfine structure, suggesting that the B-center is most probably at the origin of the ENDOR lines. The width of the EI-ESR is, however, smaller than that of the broad unresolved component of the true ESR spectrum (Figure 2a). This is a common feature of EI-ESR because some ESR transitions are lacking for nuclei with I > 1/2.30 The attribution of all the ENDOR lines to the B-center is confirmed by their angular variation in the ab-plane (Figure 7). In particular, the lines R and β exhibit a pronounced anisotropy, showing that there is no motional averaging effect. Consequently, these lines do not belong to center A, since in that case the electron hopping around four equivalent vanadium sites would average to zero the anisotropy of the hyperfine interaction in the ab-plane, which is not observed.
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Figure 9. Expanded view of the ENDOR line γ for the field orientation B0 || c showing the quadrupole splitting. Figure 8. Angular variation of ENDOR lines for rotation of B0 from the c-axis to the ab-plane. Full and discontinuous lines represent the calculated variations for δ-γ and R-β pairs, respectively.
C. Assignment of ENDOR Lines γ-δ. In order to determine the localization of the corresponding nucleus with respect to the paramagnetic site, and also to identify the nature of the B-center, let us now consider the ENDOR pair γ-δ. Stack plot representations of the angular variations for rotations of B0 in the layer ab-plane and from the c-axis to the ab-plane are shown in Figures 7 and 8, respectively. They show that the γ and δ lines exhibit only a weak angular variation of frequencies for rotations in the ab-plane, without evidence of any splitting (Figure 7). This angular variation is more pronounced for the rotation from the ab-plane to the c-axis (Figure 8), which shows that the corresponding hyperfine interaction is nearly axial with the Az direction parallel to the c-axis. The consequence for the location of the vanadium neighbor is that the line connecting the paramagnetic center to the vanadium nucleus is parallel to the c-axis. This feature confirms that the B-center should be considered as a single VIV species instead of an unpaired electron delocalized over four vanadium sites as imposed by the 29-line ESR spectrum (Acenter). In the latter case the site of the paramagnetic defect should be at the center of gravity of the spin density distribution, i.e., the center of the square formed by the four equivalent vanadium sites (Figure 1). There is no vanadium neighbor connected to the center of gravity of the A-center by a line parallel to the c-axis. Consequently, the paramagnetic center B is necessarily a single VIV localized at a single site labelled V(0) in Figure 1, and only the vanadium nucleus at the V(3) site is aligned along the c-axis with respect to V(0). For a general orientation of B0 with respect to the principal axes of the coaxial g˜ and A ˜ tensors, the first-order ENDOR frequencies are given by the following expression:
ν(ms) ) msK(θ,φ) - gnβnB0/h
(5)
with
K2(θ,φ)g2(θ,φ) ) Ax2gx2l2 + Ay2gy2m2 + Az2gz2n2 and
g2(θ,φ) ) gx2l2 + gy2m2 + gz2n2 where Aj and gj (j ) x, y, z) are the principal values of A ˜ and g˜ tensors. The direction cosines l, m, and n are given by l ) sin θ cos φ, m ) sin θ sin φ and n ) cos θ. The terms K and Aj are given in frequency units. The g˜ tensor is characterized by gz ) g|| ) 1.912 and gx ) gy ) g⊥ ) 1.981. The hyperfine components Ax and Ay are obtained from the angular variation in the ab plane, characterized by θ ) π/2.
A fit of the experimental frequencies of γ-δ lines to expression 5 (full lines in Figure 7) gives |Ax| ) 9.7(2) MHz and |Ay| ) 13.6(0) MHz for the V(3) site. The component |Az| ) 30.8(0) MHz is obtained directly from the orientation B0 || c (Figure 5a), characterized by θ ) 0, with the two following ENDOR frequencies for the V(3) site:
ν||(ms) ) msAz - gnβnB0/h
(6)
All the Aj parameters have the same (unknown) sign. The angular variation of Figure 8 shows that the quadrupolar splitting is partially resolved for the V(3) site. This figure also shows that weak lines are adjacent to the γ- and δ-lines with the same angular variations. These additional lines could belong to several “perturbed” variants of the paramagnetic defect, exhibiting slightly different hyperfine interactions with the V(3) site and no resolved quadrupolar splitting. This seems to be confirmed by double-ENDOR measurements, since the pumping field rf2 does not affect the intensity of these lines. Figure 9 shows an expanded view of the γ-line for B0||c. It is composed of several narrow lines with line width ∆ν ≈ 110 kHz. Theoretically, one expects a maximum of 2 × I ) 7 quadrupolar lines for each ms state, with frequencies given by expression 4. It was impossible to monitor the angular dependence of these quadrupolar splittings. However, it seems that these are maximum for B0 || c, with Pmax ≈ 0.13 MHz. The angular variation shown in Figure 8 corresponds to a rotation from θ ) 0 to θ ) π/2, φ ≈ π/4. If we neglect the quadrupolar splitting, the theoretical angular variation is obtained from expression 5 and is represented by full lines in Figure 8. D. Assignment of ENDOR Lines r-β. For rotation of B0 in the ab-plane (Figure 7), the variation of ENDOR lines R and β exhibits a relatively simple pattern with identical variations for R-β and R′-β′, except that their extrema are shifted by 90°. This indicates that the corresponding hyperfine interactions are due to two crystallographically equivalent vanadium nuclei making an angle of 90° with the paramagnetic site V(0). The V(2)-V(0)-V(2) and V(1)-V(0)-V(1) angles being respectively equal to 90° and 78° (Table 1), this implies that R-β lines are due to the V(2) site. In contrast with the angular variation in the ab-plane, the angular variation from the c-axis to the abplane exhibits a rather complex pattern, with a splitting of lines into several components, as shown in Figure 8. In particular it appears that the c-axis does not correspond to an extremum of the hyperfine interaction, as would be expected from the localization of the V(0)-V(2) axis in the ab-plane. The extrema of A occur at about 12° and 78° from the c-axis, respectively. This feature can be interpreted in terms of a site distortion resulting from the polaronic nature of the defect. The observed deviation indicates that the paramagnetic V(0) site is slightly shifted from the ab-plane. By neglect of this distorsion, approximate angular variations of the R-β lines were calculated
Polarons in R-LixV2O5
J. Phys. Chem., Vol. 100, No. 21, 1996 9157 We shall not try to interpret these low-frequency ENDOR transitions. They most probably correspond to further vanadium neighbors V(n) of the B-center. This hypothesis is supported by the fact that some of these lines are enhanced by the pumping field rf2 (Figure 5b), which indicates that they belong to the same paramagnetic center as the β-line. Since these lines are only weakly angular dependent, the corresponding hyperfine interactions are mainly isotropic. IV. Discussion
Figure 10. Low-frequency ENDOR lines in the frequency range 1-5 MHz corresponding to the field orientation B0 || c. The most prominent lines are labeled κ, η, φ, and .
with |Az| ≈ 24.(2) MHz and |Ax| ≈ 18.(2) MHz (Figure 7) and |Ay| ≈ 19.(7) MHz (Figure 8). This site distortion does not affect the angular variation in the ab-plane, since we did not observe any splitting of the R-β lines. However, it is clear that the calculated angular variation from the c-axis to the abplane (represented by dotted lines) is only a rough approximation of the real angular variation (Figure 8). E. Other ENDOR Lines. The spectra recorded with the field orientation B0 || c exhibit a series of weak ENDOR lines in the range 1-5 MHz, which are not due to transitions of first neighbor nuclei at V(2) and V(3) sites. Figure 10 shows a stack plot representation of these ENDOR transitions for different values of the observing field taken across the ESR spectrum of Figure 2a. Their behavior is rather complex, especially for the very weak lines below 1.7 MHz. The most prominent lines are labelled , φ, κ, and η. Figure 11 represents the magnetic field dependence of these lines. Since in the most general cases ENDOR frequencies are given by expression 3, their field dependence is linear with a slope equal to gnβn/h, which in principle allows the identification of the nuclei via their nuclear factor gn. The theoretical B0 dependence of ENDOR frequencies of 51V, 7Li, and 6Li nuclei are also represented in Figure 11. Despite an important dispersion of the experimental points, it appears that the four transitions are due to vanadium.
A. Polarons in r-LixV2O5. It has been shown in previous investigations that the conductivity of R-LixV2O5 is due to two kinds of charge carriers:14 (i) bound polarons trapped on four vanadium sites around the Li+ ions and (ii) free polarons that are not associated with Li+ ions. Only bound polarons were detected by ESR and characterized by their 29 well-resolved lines14,16,22 (A-center). The existence of free polarons was only deduced from conductivity measurements.14 The present work adds new information to these previous studies, and the following points are particularly worth noticing. (a) The bound polarons (A-centers) do not give an ENDOR response in our crystals, despite the existence of a well-resolved hyperfine structure in the ESR spectrum. This lack of ENDOR enhancement could be due to an inhomogeneous distribution of Li+ ions in the matrix, resulting in the formation of shallow aggregates of A-centers. In that case the mean distances between centers could be much smaller than those expected for a purely statistical distribution of lithium ions. This high local concentration of A-centers is, however, sufficiently small to preserve the hyperfine structure of the ESR spectrum but sufficiently large to quench the ENDOR response. It is well known that a zero ENDOR enhancement is generally found in concentrated systems because the Heisenberg exchange time Tss between paramagnetic centers becomes much smaller than the spin-lattice relaxation time Tle of each isolated center. In that case the saturation of the ESR transition of a single spin system is transferred to the unsaturated levels of other systems and no ENDOR is possible.31 This tendency for lithium to form aggregates in R-LixV2O5 is not surprising, since the same
Figure 11. Magnetic field dependence of ENDOR lines , φ, η, and κ. Theoretical variations are represented by solid lines (51V), dashed lines (7Li), and dotted lines (6Li). Circles represent experimental values.
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behavior has been observed for electrochemical and chemical intercalation of lithium in V2O5.10,32 (b) All the observed ENDOR lines are attributed to free polarons localized on a single vanadium site (B-center). This interpretation is based on the following observations: (i) There is no motional averaging of the vanadium hyperfine interaction in the ab-plane as would be expected for the A- center; (ii) there is no evidence of lithium ENDOR transitions; (iii) the EI-ESR spectrum exhibits no resolved hyperfine structure characteristic of the A-center, in agreement with the existence of a broad unresolved component superimposed on the 29-line ESR spectrum of the A-center. The high ENDOR enhancement observed for these free polarons indicates that the latter are magnetically diluted and well separated from bound polarons. It was previously assumed that all polarons are bound to lithium at low temperature and that free polarons appear only upon increasing the temperature.14 However, it was also found that polarons are much less bound to extra positive charge in R-LixV2O5 than in V2O5,13,14 with activation energies equal to 0.07 and 0.12 eV, respectively. It thus appears likely that a significant fraction of polarons remains unbound even at low temperature. Let us now return briefly to the absence of 7Li ENDOR lines, which is an important argument in the interpretation of our results. The two possible limits for the lithium hyperfine interaction of the A-center can be estimated as follows. From the VIV-Li+ distance of 3.28 Å expected from the defect model (Figure 1), a lower limit of the hyperfine interaction equal to the point dipole-dipole value bdip ≈ +0.87 MHz is obtained (see expression 11). In that case the lithium ENDOR spectrum should consist of a pair of lines centered at the nuclear frequency νn ≈ 5.8 MHz of 7Li and split by 2|bdip| for B0 || c and |bdip| for B0 ⊥ c. The other limit can be obtained from the smallest ESR line width ∆B ≈ 3.2 mT for the hyperfine components of the A-center (Figure 5a). This gives an upper limit of about ∆B/3 ≈ 30 MHz for the 7Li hyperfine interaction, with an ENDOR spectrum centered at about ∆B/6 ≈ 15 MHz. Consequently, if a Li+ ion is close to the unpaired electron, we should expect 7Li ENDOR lines in a 5-30 MHz rf range, which was not observed in the present work. B. Vanadium Hyperfine Interaction. It is now well established that the hyperfine interaction with neighbor nuclei of a paramagnetic center is strongly influenced by the nature of the chemical bond. In the present case the cation-cation hyperfine interactions for the B-center arise both within the [V2O5]n layers and between two adjacent layers, which makes the B-center a possible probe of intralayer and interlayer interactions. The fact that the hyperfine interactions with V(2) and V(3) cation sites are of opposite sign reflects the difference in the nature of the two cation-cation interactions. In particular, intralayer interactions in V2O5 are covalent,24 whereas it is generally assumed that the [V2O5]n layers are weakly bound via van der Waals interactions.19,24,25 The principal argument in favor of this assumption is the unusually large interlayer V-O distance19 (2.791 Å). The hyperfine interaction tensor for a single nucleus is usually written as18
A ˜ ) a‚1˜ + B ˜
(7)
where the scalar term a is the isotropic hyperfine interaction
1 a ) (Ax + Ay + Az) 3
(8)
TABLE 2: Vanadium Hyperfine Interaction Parameters (in MHz) for the B-Center site
|Az|
|Ax|
|Ay|
|a|
|b|
|b′|
V(3) V(2)
30.8(0) 24.(2)
9.7(2) 18.(2)
13.6(0) 19.(7)
18.0(4) 20.(7)
6.3(8) 1.(7)
1.9(4) 0.8
The traceless anisotropic tensor B ˜ is decomposed into an axial term b and a term b′, which describes the deviation from axiality
[
-b + b′
B ˜)
-b - b′
]
(9) 2b with b ) Bz/2 and b′ ) (Bx - By)/2. The parameters a, b, and b′ for vanadium neighbors at V(2) and V(3) sites are given in Table 2. It is known from double-ENDOR measurements that the signs of the hyperfine interactions are different for the two vanadium neighbors. These differ also by the anisotropy of their hyperfine interactions, with a ratio b/a, which amounts to 0.35 and 0.08 for the V(3) and V(2) sites, respectively. These interactions are dominated by Fermi contact terms a of opposite signs, which imply different mechanisms for the hyperfine interactions. The isotropic hyperfine terms a arise from unpaired s-electron density transferred on VV ions localized in V(2) and V(3) sites, while the terms b originate from unpaired spin density in dσ (dz2 and dx2-y2) and dπ (dxy, dxz, dyz) orbitals of VV together with the dipole-dipole interaction bdip between VIV ions at V(0) sites and vanadium nuclei at V(2) and V(3) sites. Thus, the anisotropic interaction b is written as the sum of three contributions: b ) bdip + bσ - bπ
(10)
In the point dipole-dipole approximation, bdip is given by
bdip ) gβgnβnR-3
(11)
where R corresponds to the V(0)-V(2) and V(0)-V(3) distances, which are equal to 3.56 and 4.25 Å, respectively. The corresponding values of bdip are +0.46 and +0.27 MHz, which are much smaller than the experimental values of b. Thus, the covalent contributions largely dominate the cation-cation hyperfine interactions. Furthermore, we have to determine the sign of these interactions. This is possible by recalling that the unpaired electron spin occupies a vanadium orbital of almost purely dxy character. Since this orbital has lobes pointing between V-O bonds in the ab-plane, a direct (positive) V(0)V(3) interaction perpendicular to the plane is forbidden by symmetry, while direct in-plane interactions are possible. We thus assume that the V(0)-V(2) interactions are positive, implying from the double-ENDOR experiment that the V(0)-V(3) interactions are negative. Having the signs of bdip and |Ai| (i ) x, y, z), we can deduce from expressions 7-11 the values of a and bσ - bπ given in Table 3. The isotropic hyperfine interaction a is related to the fractional unpaired spin density fs transferred in the 4s vanadium orbital of neighboring cations
a ) fs aiso
(12)
where
8π gβgnβn|Ψs(0)|2 3 ) 2610.4 MHz
aiso )
(13)
is the theoretical value for a single electron in a 4s vanadium orbital.33 Similarly, the anisotropic interaction b is related to
Polarons in R-LixV2O5
J. Phys. Chem., Vol. 100, No. 21, 1996 9159
TABLE 3: Unpaired Spin Densities Transferred in V(3) and V(2) Sites site
a (MHz)
b (MHz)
bdip (MHz)
bσ - bπ (MHz)
fs
fσ - fπ
V(3) V(2)
(-)18.0(4) (+)20.(7)
(-)6.3(8) (+)1.(7)
+0.27 +0.46
(-)6.6(5) (+)1.24
(-)6.9 × 10-3 (+)8 × 10-3
(-)2 × 10-2 (+)4 × 10-3
the fractional unpaired spin densities fσ and fπ in dσ and dπ vanadium orbitals at V(3) and V(2) sites, in addition to the point dipole-dipole interaction, so that expression 10 becomes
b ) gβgnβnR-3 + (fσ - fπ)bd
(14)
The term bd is the hyperfine interaction for an unpaired electron in a vanadium 3d orbital:
bd ) gβgnβn〈r-3〉d|〈3 cos2 R - 1〉| ) +515.4|〈3 cos R - 1〉| MHz 2
(15)
for a VIV ion.34 The term 〈r-3〉d in expression 15 is the average value of r-3, with r being the electron spin-nucleus distance within the metallic orbital. The term 〈3 cos2 R - 1〉 ) +4/7 for dz2 and -4/7 for dx2-y2 and dxy orbitals, is the average direction of the electron spin vector within the orbital. Let us first consider the V(0)-V(2) interaction, which is dominated by a strong positive Fermi contact term a. This feature can be accounted for by assuming a small admixture of vanadium 4s orbital in the dxy ground state. Such an admixture is allowed in symmetry lower than C3, which is compatible with the Cs symmetry of vanadium sites in V2O5, and implies a direct (positive) transfer of a spin density fs at the V(2) site. The experimental value amounts to fs ≈ +8 × 10-3 from expressions 12 and 13. The case of the V(0)-V(3) hyperfine interaction is particularly interesting, since it reflects the nature of the interlayer interaction. If we consider an unpaired electron trapped at a V(0) site in the form of a VIV ion, the only possible mechanism of hyperfine interaction with a vanadium nucleus at a V(3) site is the point dipole-dipole interaction bdip in the case of an interlayer van der Waals interaction. Since bdip depends only on the V(0)-V(3) distance R, the theoretical hyperfine interaction is estimated to be Az ) 2bdip ≈ +0.54 MHz and Ax ) Ay ) -bdip ≈ -0.27 MHz.35 There is no isotropic interaction in that case, so we expect a ) 0. The experimental results summarized in Table 3 disagree with these expectations, since the hyperfine interaction with the V(3) site is characterized by a strong (negative) isotropic contribution a ) (-)18.0 MHz and an anisotropic contribution b ) (-)6.4 MHz, which is much larger than bdip and of opposite sign. This deviation from a purely point dipole-dipole interaction shows that the interlayer hyperfine interaction is dominated by covalent interactions, with fractions fs ≈ (-)6.9 × 10-3 and fσ - fπ ≈ (-)2 × 10-2 of unpaired spin density being transferred in 4s and 3d orbitals of the VV ion at the V(3) site (Table 3). A qualitative explanation of this important covalent contribution in the interlayer hyperfine interaction can be treated within the framework of an independent bonding model36 in which one-electron functions are taken to be molecular orbitals of isolated vanadyl VOII and VOIII ions aligned along the c-axis in two adjacent [V2O5]n layers (Figure 12). This description is relevant, since the V2O5 structure exhibits very short VO bonds (1.577 Å) characteristic of vanadyl complexes.19 In addition, ESR and ENDOR show that the unpaired electron is localized on a single vanadium site with principal values of the g˜ -tensor close to those found in vanadyl complexes.37 The molecular orbital scheme of VOII has been determined by Ballhausen and Gray,38 but we retain only those molecular orbitals that are
Figure 12. Schematic diagram showing the interaction between the energy levels of a1 symmetry of two adjacent vanadyls along the c-axis, separated by the interlayer spacing.
relevant for the description of covalent contribution to hyperfine interaction. The unpaired electron at the V(0) site lies in a nonbonding b2 orbital of almost purely dxy character. For symmetry considerations and because of the large vanadiumvanadium distance, this orbital cannot contribute to the transfer of unpaired s electron density in the adjacent VOIII species. The latter may arise only via molecular orbitals of a1 symmetry, which contain contributions of 4s and dz2 vanadium orbitals. There are three bonding and three antibonding orbitals of a1 symmetry.38 However, we shall consider only the highest bonding and the lowest antibonding orbitals (labeled a1 and a*1 in Figure 12), since the hyperfine interaction is inversely proportional to the splitting ∆E between a1 and a*1 levels. A general expression for these two orbitals is38
|a1〉 ) R1|dz2〉 + R2|4s〉 + β|L〉
(16)
and
|a*1〉 ) R* 1|dz2〉 + R* 2|4s〉 + β*|L〉 where L indicates the symmetry-adapted linear combination of oxygen 2p and 2s orbitals. Interlayer covalency effects could arise from overlap and electron transfer between the a1 and a*1 orbitals of the two adjacent vanadyl at the V(0) and V(3) sites. A possible mechanism of transfer of unpaired spin density in 4s and dz2 vanadium orbitals at the V(3) site is a spin-polarized electron transfer39-41 between a1 and a*1 molecular orbitals of adjacent vanadyls as shown in Figure 12. Such polarized transfer has already been invoked to explain the cation-cation hyperfine interaction in LaAlO3:CrIII.42 This mechanism should result in a transfer of negative spin densities on neighboring cations. A simple calculation by using a configuration interaction method41 adapted to the present situation gives the following expressions for the spin-polarized transfers in the V(3) site:
fs ) -
2τ 2 2 γ R* 2 ∆E
fσ ) -
2τ 2 2 γ R* 1 ∆E
fπ ) 0
(17)
where γ is the covalent parameter, ∆E is the splitting between a1 and a* 1 molecular orbitals, and τ is the exchange integral between unpaired electrons in b2 and a1 orbitals. It is not possible to estimate the values of fs and fσ, since the parameters τ, ∆E, γ, R*1, and R*2 in expression 17 are unknown. However,
9160 J. Phys. Chem., Vol. 100, No. 21, 1996 this mechanism predicts negative spin densities in 4s and dz2 vanadium orbitals at the V(3) site, which should be of the same order of magnitude, in agreement with the experimental results (Table 3), assuming fπ ) 0. It should be pointed out that this interlayer covalent interaction could be significant only at the polaron site, since it is usually admitted that the unusually large interlayer V-O distance of 2.790 Å is only compatible with a van der Waals interaction.19,23-25 The covalent interaction between vanadyl ions in adjacent layers could be enhanced by the polaron distorsion, i.e., the displacement of neighboring ions induced by the electron-phonon interaction. Since strong covalent interactions are only observed with V(2) and V(3) neighbors, the polaron radius can be roughly estimated to 4 Å, which agrees with the model of small polarons. A consequence of the spin-polarized transfer between a1 and a* 1 vanadyl orbitals should be a slight increase in the vanadyl bond lengths VO at the polaron site V(0) and its neighbor V(3). This agrees with the shift of the V(0) site from the ab-plane observed in the angular variation of ENDOR lines (cf. part III.C). Thus, the net result of this interlayer covalent interaction should be a symmetrization of the coordination polyedra at the V(0) and V(3) sites. Finally, it is noteworthy that such site symmetrization has already been observed by EXAFS for electrochemical lithium intercalation in V2O5.43 However, it cannot be excluded that these covalent interlayer interactions could already exist in pure V2O5. They would explain the observation that V2O5 behaves as a 3D network rather than a van der Waals host.7,26 V. Conclusion The main conclusion of this study is that the presence of two kinds of charge carriers in R-LixV2O5 is confirmed by combining ESR and ENDOR spectroscopies. (i) The first ones are free polarons localized at single vanadium sites. Up to now these polarons were only known from conductivity measurements. Strong hyperfine interaction is observed between the unpaired electron spin of the polaron and two vanadium neighbors located in the same [V2O5]n layer and in the adjacent [V2O5]n layer. This indicates the existence of a covalent bond between adjacent layers. (ii) The second kind of charge carrier corresponds to bound polarons delocalized over four vanadium sites around a Li+ ion. This defect, which is known for more than two decades by ESR, does not give an ENDOR response despite the very small lithium concentration. This absence of an ENDOR effect is attributed to the formation of shallow aggregates of lithium ions in the matrix, which results in high local concentrations of bound polarons producing concentration quenching of the ENDOR enhancement. References and Notes (1) Whittingham, M. S. Prog. Solid State Chem. 1978, 12, 41. (2) Walk, C. R. In Lithium Batteries; Gabano, J. P., Ed.; Academic Press: london, 1983; p 265.
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