J . Phys. Chem. 1993,97, 10301-10311
10301
6Li and ’Li NMR in High-Temperature Phases of LixV205 Bronzes (0.2 Ix I1) JMme Hirschinger,’ Thierry Mongrelet, Claire Marichal, and Pierre Granger Znstitut de Chimie, UMR 50 CNRS, Bruker Spectrospin, UniversitC Louis Pasteur, BP 2961R8, 67008 Strasbourg Cedex, France
Jean-Michel Savariault, Eric Mramond, and Jean Galy Centre d’Elaboration de MatCriaux et &Etudes Structurales, Laboratoire d’Optique Electronique (CEMES-LOEICNRS UPR S O l l ) , 29 Rue Jeanne Marvig, BP 4347, 31055 Toulouse Cedex, France Received: May 4, 1993; Zn Final Form: July 20, 1993”
A series of high-temperature phases of Li,VzOs bronzes (0.2 I x I 1) has been studied by 6Li and ’Li NMR. Static spin-echo and MAS N M R experiments have been carried out a t two magnetic field strengths (4.7 and 7.1 T). It is shown that the MAS technique permits a very accurate direct determination of the lithium site occupancies in the different phases. The spectra are influenced by interactions from both the quadrupole coupling and the paramagnetic shift due to the dipole interactions of the Li nuclear moment with the paramagnetic vanadium ion moments. Both the magnitudes and relative orientation of the quadrupole (Q)and anisotropic shift (S) tensors have been determined by iterative fitting of the 6Li and 7Li MAS N M R line shapes at the two magnetic field strengths. The large difference between the 6Li and 7Li quadrupole moments is found to be particularly useful for an accurate determination of the N M R interaction parameters. Calculations of the quadrupole and paramagnetic shift coupling parameters have been performed by using a point monopole and point dipole model, respectively. The S tensor is related to the positions of the unpaired electrons in the different crystalline phases: while the electronic localization in the y phase is confirmed, it is shown that the unpaired electrons become increasingly delocalized over the vanadium atoms as the lithium content decreases in the B and 8’ phases. On the other hand, the Q tensor is used to test several atomic electric charge distributions. N M R is found to be a valuable experimental validation test for quantum chemistry computations.
I. introduction
11. Theory
Lithium-inserted vanadium oxide bronzes, Li,V20~(0 Ix I 2), have attracted much scientific and technological interest in relation to their variable composition and the mixed valence of the vanadium atoms.14 In particular, the intercalation process of lithium governing the cathodic reaction in Li/Li+/V205 galvaniccells has been shown to result in the formation of several crystalline LixV2Os phases.sq6 For x > 1, there may also be formation of amorphous material as well as alteration of the V205 grain ~ u r f a c e s . ~These . ~ important structural changes are believed to cause the observed decrease of the reversibility of the electrochemicalreaction. This constitutes a major drawback for using V2O5 cathode material in a secondary battery. Therefore, it is of primary importance to study the local environment and the dynamics of the lithium atoms in the different Li,V205 phases. NMR spectroscopy is a very powerful tool for studying molecular order and dynamics.p-ll Moreover, as opposed to X-ray diffraction, its use can be extended to noncrystalline systems. Lithium has two stable isotopes, 6Li ( Z = 1) and 7Li ( Z = 3/2), which are amenable to the NMR experiment. Since these quadrupolar nuclei strongly differ by their quadrupole moment Q,I2J3they are expected to yield complementary information, especially in the presence of additional spin interactions such as chemical shift or dipolar couplings. In the present paper, we use 6Li and 7Li NMR in order to characterize the structure of the &/3’, and y phases. Although they usually are formed at high temperat~re,3.~ there is renewed interest in these bronzes because the y phase has recently been shown to appear in room temperature Li//V205 batteries when discharged beyond x = 1.14
A. Spin-EcboSetpace for a Static Sample. When the Zeeman interaction HZof nuclear spin Z with the applied magnetic field Bo is predominant, the internal spin Hamiltonians HAwith X # Z may be approximated by their first-order average Z$) over the Larmor period 2 ~ 1 ~ In 0 .the presence of quadrupolar (A = Q) and anisotropic shift (X = S)interactions, the effective Hamiltonian in the Zeeman interaction representation is written899J5J6
*Abstract published in Aduance ACS Absrracrs, September 1, 1993.
H,,,=
H6)+
) :$
(1)
with
q = 93z2 - Z(Z + l ) ] 6 H y = wszz where the orientation dependent frequencies for a static sample corresponding to the interactions X = Q, S are w A = w’;”
+4-(3
cos’
@A
- 1 - ix sin’ oxcos 2aA) (2)
with Jso
= 0;
wi-
up = woao;
3rQcc/2Z(2Z- 1) bJpO
= O0bs/2
QCC= e2qQ/h is the quadrupole coupling constant. j 3 ~and ah are the spherical polar angles that define the orientation of in the principal axes system (PAS) of the interaction tensor A. Each coupling tensor is completely defined by its isotropic value
0022-3654/93/2097-10301$04.00/00 1993 American Chemical Society
10302 The Journal of Physical Chemistry, Vol. 97,No. 40, 1993 AX (AS = uoand AQ = 0), its anisotropy 6~ which is a measure of the strength of the interaction, and its asymmetry parameter VX, which is a measure of the deviation of the interaction tensor from axial symmetry (0 Ivx I1). These parameters are related to the principal axes components A: (i = 1-3) of the coupling tensor (6Q = A? = eq)8,9
Hirschinger et al. (n/2), pulse. After this second pulse, the density matrix becomeslOJ7 p(t)
= exp(-iHeff(t - T))YI-’~(T)YI exp(i&(t
- T)) (6)
with
93 = exp(i&) exp(iO1,) exp(-icpl,)
+ +Ai)
AX= ‘ / 3 ( A : A t
is given by eq 3. In practice, only two values of the phase shift cp corresponding to in-phase (cp = 0) or quadrature (cp = ~ / 2 pulses ) are relevant. From eqs 1,3, and 6, dropping all the terms that are not refocused at t = 27, Le., are averaged to zero for times t 1 27 due to the presence of all the molecular orientations, the powder averaged spin-echo signal is readily obtained (t’ = t - 27)’’
p(7)
The principal axes 1-3 are labeled according to the following convention
[Ai- AXI 1 IA: - AXl1 bt - AXI Note that the A? are the principal components of the electric field gradient (EFG) tensor (for convenience, we shall refer to the A? as the field gradients, although strictly speaking it is the negative of this). At thermal equilibrium in the strong magnetic field Bo,the density matrix p is assumed to be equal to Iz. After a strong radio frequency (RF) 7r/2 pulse along they axis (HRF = WII, >> I&$),@)), we havep = ZX.l0 At a timet after this short (7r/2), pulse, the density matrix becomes
= exp(-i~elft)Z, exP(iHefft) (3) From eqs 1and 3, it is straightforward toderive the contribution from a single (OX, ax) orientation to the complex amplitude of the free induction decay (FID) for a spin-Z system17 P(t)
~
m
where
- 3[I(Z+ Pm
-
l)-m(m-
l)]
where
A = -3 sin2(O/2) cos4(8/2)
B = -[sin3(O/2) - 2 sin(O/2) ~ o s ~ ( O / 2 ) ] ~ Since the subscript X has been dropped (@A, ax) = (8,a)),eq 7 implicitely assumes that the Q and S tensors are coincident. If this is not the case, one simply has to express, for example, ws in the principal axes system of the Q tensor, as previously de~cribed.l*21.2~Note that, for t ’10, is similar to the FID (Z+) (eq 5 ) . Thus, an undistorted spectrum is obtained by Fourier transformation of (Z+)= starting at the top of the echo (t = 27). The theoretical powder spectrum resulting from both the one- and two-pulse sequences may then be written
cw
S(w) = -JoZrJ;=; 1
-
[2Z(Z+ 1)(2Z+ l)]
is the probability of the m m - 1 transition. m runs over all 21 absorptive single-quantum transitions. For Z = 312, eq (4) reduces to
-
-
The first term of eq 5 representing 60% of the magnetization corresponds to the -l/2 -3/2 and +3/2 + l / 2 or ‘satellite” transitions (m = -112 and +3/2). The second term is the contribution due to the + l / 2 -l/2 or “central” transition (m = l/2). It is also remarked that this transition is not influenced to first order by the quadrupolar interaction. The NMR spectrum is given by the real part of the Fourier transform of (Z+). A complete determination of the Q and S tensors, as well as the determination of their principal axes systemswith respect to some reference frame, can be achievedby recording the NMR spectrum at different orientations of a single crystal.8JOJ8 In polycrystalline samples, both the magnitudes and relative orientation of the Q and S tensors can also be determined from the analysis of the NMR powder pattern.19-23 However, the presence of all the molecular orientations combined with the large magnitude of both the quadrupole coupling constant and the shift anisotropy renders the FID very rapid (eq 2), so that a significant part of the signal may be lost during the receiver dead time. This results in severe distortions of the NMR s p e c t r ~ m . ~Fortunately, ~.~~ pulsed NMR methods can be used to generate spin echoes.l7,24,26S27 Indeed, suppose that a second pulse of angle 8 is now applied at the time t = 7, with a phase difference cp with respect to the first
-
I
2
-B exp(iost? da sin 0 dB (7) 5
47r
x
m
G[w - ( m -f)wQ-ws]
da sin BdB (8)
where G(o) =
*)
1 exp( A w ( 2 ~ ) ” ~ 2A02
After a (7r/2), pulse, pfm= pm: for I = 3J2, p-112 = p+3/2 = and^+^/^ = 2 / ~ . On the other hand, after the (77/2),-7-(O), or (7r/2),-~-(8)~ spin-echo pulse sequence ( I = 3/2), pL1/2 = pf+3/2= *3A/10 and p’+1/2 = *2B/5. G(w) is a normalized Gaussian broadening function of standard deviation Aw accounting for unresolved dipolar interactions, relaxation effects, inhomogeneous magnetic fields, etc.Equation 7 demonstrates that (I+)= is independent of the sign of 8 and that a change of phase cp from 0 to */2 gives an inverted, but otherwise identical, echo. On the other hand, it has been shownI7that the echo amplitude strongly depends on cp when only the quadrupolarinteraction is present. In this case, for example when 8 = u/2, (I+),is proportional to sin cp; i.e., no signal is present after two in-phase pulses while maximum echo amplitude is obtained after two quadrature pulses (the so-calledquadrupolar ech017927),Note finally that the spin-echo sequence, in addition providing an undistorted NMR spectrum, allows one to change the ratio of satellite to central transition signals simply by varying the pulse angle 8. 3/1~
The Journal of Physical Chemistry, Vol. 97,No. 40, 1993 10303
High-Temperature Phases of Li,V205 Bronzes
B. Magic Angle Spinning (MAS). Under sample spinning with a frequency Y, = 4277, the orientationdependent frequencies (eq 2) become periodic functions of time10J8.29
wpso w F + -5-{KA(3 COS’ 0 - 1) + [cCOS(^ + o,t) + St sin(y + w,f)] sin 2 6 + [C; cos(2(y + wrt)] +
wA(t)=
S; sin[2(y
+.,
+ w,t)]] sin2 0) ( 9 ) exp[i(wp
where
+ No$]
da sin B d/3 (20)
where
S, cos(n@)]}d@ (21) with Ck = (3 + q,, cos(2a)) sin2 0- 2q,, cos(2a) =&a,@
s,X
= 2qA cos B sin(2cu) =&(a,@)
(13)
(14) Hence, the corresponding NMR spectrum is given by
8 is the angle between Bo and the spinner axis, and a,6,y are the Euler angles as defined by Spiess9 giving the orientation of the X tensor in the spinner frame. When the principal axes of the Q and S tensors are noncoincident, the shift interaction is expressed in the PAS of the Q tensor (or vice versa). Equations 10-14 then become
P - 1) + fl($,x) COS r + sin ri sin B cos B + 1 / 2 ~ ( $ , x cos(2r) ) + &Ax) sin(2r)l sin2 B
KA= ‘/&($,~)(3
fi($,x)
L(w - wl;” - Ab,)d a sin
dfl (22)
where
COS’
1 L(w) = -
k / 2
* w2 + 6Wi/,
(15)
is a Lorentzian broadening function of half-width at half-height (hwhh) b01/2. Of course, when Gaussian broadening is more appropriate, L(w) can be replaced by G(w). Equation 22 clearly shows that the MAS spectrum is composed of a set of spinning side bands (ssb’s) of hwhh b w 1 p and separated by w, around the central line (N = 0) at the isotropic shift When w, >> utiso,the ssb intensities IN = FN*FN( N # 0) become very small. Each magnetically non-equivalentnucleus is then characterized to first order by a single sharp line ( l o = l), as in liquids (highresolution NMR).”J
wp.
III. Experimental Section A. Samples. A series of vanadium oxide bronzes, LixV2O5 (0.3 Ix I l), was prepared following the equation
+
V205 (x/2)Li,C20,
with r = a + E. As in ref 30, we have chosen first to transform by the Euler angles ($, x, E) the S tensor from its PAS into the PAS of the Q tensor, which is itself related to the rotor frame by the Euler angles (a,8 , ~ )Thus, . wQ(t) and w s ( t ) are readily obtained by substituting eqs 10-14 (A = Q) and eqs 15-19 (A = S) into eq 9, respectively. Note that our expression for ws(t) is much more compact than the one recently derived by Skibsted et ~ 1 . Following Mehring,”Jthe FID after a ( ~ / 2pulse ) ~ is then written
3 ~
-
Li,V205
+K O 2
The reaction is obtained by heating under vacuum at 600 OC the finely ground and mixed reagents during 12 h. According to thevalueofx, different high-temperature phases areobtained.1 We have prepared Li,V205 bronzes with the crystal structures of the 6 phase (x = 0.30),31the 8’ phase ( x = 0.48),32and the y phase (x = 1).32.33 The structure of each sample was checked by X-ray powder diffraction patterns. While both the 6- and y-phase samples appeared as “pure”, some amounts of the y phase were shown to be present in the fl-phase sample. According to the phase diagram of LixV205$ this is believed to result from heating that is too intensive.
Hirschinger et al.
10304 The Journal of Physical Chemistry, Vol. 97,No. 40, 1993
B. NMR Measurements. 6Li and 7Li NMR measurements were carried out on Bruker MSL-300 (BO = 7.1 T, 4 2 = ~ 44.1 50 and 116.598 MHz in 6Li and 7Liresonance, respectively) and CXP-200 (BO= 4.7 T, w 0 / 2 ~ = 77.751 MHzin 7Liresonance) spectrometers. For spin-echo experiments on static samples, a standard broad-band Bruker probe was used. Single-pulse 6Li and 7Li MAS spectra wereobtained by using Bruker MAS probes with cylindrical 7- and 4-mm-0.d. zirconia rotors, respectively. The pulse lengths ranged from 1 to 3.1 ps, RF field strengths ul/2r from 80 to 160 kHz, relaxation delays from 1 to 5 s, and spinning frequencies vr from 0.4 to 15 kHz. Spectral widths between 125 kHz and 1 MHz were used. After left shifting, the spin-echo signal is Fourier transformed with no line broadening starting at the top of the echo to yield an undistorted NMR spectrum. On the other hand, the base line distortions in the MAS spectra resulting from spectrometer dead time (-4 ps) were removed computationally using a polynomial base line correction routine. The isotropic chemical shifts, reported in parts per million, are relative to an external sample of 1.O M LiCl solution in H2O. Static and MAS NMR spectra were simulated directly in the frequency domain according to eqs 8 and 22 of section 11, respectively. The powder average over a and @ is done numerically. In addition, for MAS, the trapezoidal rule is used to approximate the integral over 3 in eq 21. In our case, good results were obtained with integration increments smaller than 5O-15O. The number of simulated ssb's was chosen according to the considered experimental spectrum (from 16 to 32). No finite pulse length ~ o r r e c t i o nwas ~ ~ tincluded ~~ in the simulation. The two quadrupolar (Qm, VQ), the three shift (UO, as, 7s) parameters,the line broadening (Auor 6w1/2), and, when needed, the Euler angles x, and [ are determined by nonlinear leastsquares (six to nine parameters) fitting of the experimental line shapeusing our computer programs combined with the subroutine VA02A of the Harwell subroutine library.34 Actually, because the quadrupolar interaction symmetrically affects the satellite transitions, only the absolutevalue of QCC can be determined. In the case of a mirror plane symmetry at the lithium site, $ and [ must be equal to Oo, 180°, or &9O0so that only the Euler angle x has to be adjusted. In practice, the Euler angles and [ have been set to zero but 7s and VQ were allowed to take negative values (-1 I7 I+l). Indeed, a change of the sign of 7s and VQ is equivalent to a change of and [ from Oo, 180° to *90°, respectively. For the spin-echo experiment,the fraction of central transitionsignalj+ =p'+112/(pC112+p'+l/~ +p'+3/2)wasincluded in the fit (seven- to ten-parameter fit). For the MAS experiment, it is also possible to fit the calculated to the experimental ssb intensities. In this case, the isotropic shift and the line broadening need not be optimized (four- to seven-parameter fit). Moreover, in the presence of non-equivalent nuclei, a particular set of ssb's may then be fitted (see below). We also included the possibility of fitting several line shapes at different magnetic fields, isotopes (6Li and 7Li), and (or) spinning speeds.
+,
+
+
IV. Results and Discussion A. y-LiV20~.This phase has an homogeneity range of 0.88 Ix I1. The crystal structure (orthorhombic,space group Pnma,
cell parameters for x = 1, a = 9.702(5), b = 3.607(2), c = 10.644(6) A) exhibits puckered [V~OS],, layers held together by lithium atoms in octahedral coordination.32s3 Within the layers, an electronic localization has been established for the first time by crystallographic ~tudies,3~ the square pyramids [V4+05] and [VS+Os]being attributed to the nonequivalent crystallographic V 1and V2 sites, respectively. A projection of the LiV205 structure ontothe(010) planeisgivenin Figure 1,togetherwith thelithium coordination octahedron. Figure 2 shows the experimental spectrum in 7Li resonance (BO = 7.1 T) resulting from the
n'l
Figure 1. Projection onto the (010) plane of the idealized structure of yLiV205 together with a view of the lithium coordination polyhedron. Light and dark motives stand for y = 0 and y = I/*, respectively.
1
I
I
80
40
I
I
0 kHz
-40
I
-80
I
-120
Figure 2. Room temperature experimental and fitted 'Li static solidecho line shapes (Table I) for the 7 phase at BO = 7.1 T (T = 40 @).
application of a spin-echo sequenceof two 3.1-ps ?r/2 pulses (01/ 2~ = 80 kHz) to the 7 phase of LiV2Os at 293 K. As expected, it consists of a rather narrow central transition line superimposed at the bottom by large satellite transition line shapes broadened by first-order quadrupolar interaction, as already noted by Cocciantelli et ~ 1 . 3We ~ checked that the spectrum does not change when increasing the delay 7 between the two RF pulses. This demonstrates that we effectively observe only the desired spin-echosignal. Moreover, only the sign (not the amplitude) of the spin echo appears to be changed by the relative phase of the two RF pulses (in-phase or quadrature). This fact is the first evidence for the presence of a strong shift anisotropy interaction in addition to the quadrupolar interaction (seesectionII).17Thus, the 16-step phase cycling proposed by Rance and Byrd24 was employed. The second evidence comes from the line shape analysis. Indeed, if only quadrupolar (and nuclear dipolar) interaction is present, the spectrum must be symmetric about its isotropic value.8-'0 This is clearly not the case since, as can be seen in Figure 2, four satellite transition shoulders of frequencies -65, -50, +45, and +70 kHz areobserved. In fact, close inspection also shows the asymmetry of the central transition line. This result is confirmed by the line shape fit of Figure 2, leading to the interaction parameters listed in Table I. Good agreement between the experimental and calculated line shapes is obtained (the slight intensity losses near the outer edges of the experimental line shape can be attributed to finite pulse length distortionsand, possibly, a small error in the estimation of the top of the echo). No significant improvement of the fit was obtained when noncoincident Q and S tensors were considered. The interaction parameters remain essentiallyunchanged,and x converges toward 8' (Table I). The Euler angles and [ have been set to zero (eight-parameter fit) because there is a mirror plane forcing one axis of each tensor to lie perpendicular to it, i.e., along the crystallographic Oy axis.32 Thus, in this case, considering coincident Q and S tensors is a good approximation. The shift
+
High-Temperature Phases of Li,V205 Bronzes
The Journal of Physical Chemistry, Vol. 97, No. 40, 1993 10305
TABLE I: Fitted Interaction Parameters for the Series of LixV20s Bronzes
interacn param
static -
7Li at 7.1 T
coinc
noncoinc
-9 97 0.65
-10 97
121 0.80 4100 0.18
121 0.79 4065
-
0.18 8d
'Li, 4.7 T
MAS
6Li,7.1T
7Li,7.1T 0.4
7Li,4.7 T 7Li,7.1T -33.0 f 0.4
MAS
MAS
6Li,7.1T
6Li,7.1T
-7.8 f 98 f 3 0.70 f 0.10
0.70
-
B phase
8' phase
y phase
1504
68 f 5 0.40 f 0.12 504 9@/14oC
0.75 f 0.15
-
25@/3W -
-
9f
-
anisotropy is found to be close to 100 ppm. Note also thatfip is in excellent agreement with the theoretical value for ?r/2pulses 2B/(3A + 2B) = 2/11 (see section 11). In a recent study25 the asymmetry of the spin-echo'Li NMR spectrum was qualitatively observed for BO= 4.7 T. On the other hand, no anisotropic shift interaction was previously detected by wide-line NMR in low magnetic field (BO= 0.49 T),36as expected. Indeed, the observed central transition line shape (Aw = 2 kHz) then appears to be dominated by the 7Li-51V and 7Li-7Li nuclear dipoldipole interactions (Table I). Figure 3 shows experimental 6Li and 7Li MAS spectra of the y phase at 293 K for BO= 4.7 and 7.1 T. In this case, the short pulse length (1 bs) and large RF field strength (160 kHz) prevent any finite pulse length distortions.29 It is seen that a good fit of the ssb intensities is obtained for the two isotopes and magnetic field strengths with the same anisotropic interaction parameters consideringcoincident S and Q tensors (four-parameter fit of the three MAS spectra). The quadrupole moment ratio Q(7Li)/ Q(6Li) = 56.25 was taken from literature.12J3 For convenience, in the following, we shall refer to QCCas the quadrupole coupling constant for the 7Li isotope. UO,vr, and 6 w 1 p which only affect, respectively, the positions and line width of the ssb's are subsequently adjusted by visual comparison of the simulation with the experiment. These results clearly confirm the analysis of the static spin-echo experiment (Table I). Moreover, note that they likewise confirm the ratio of the quadrupole moments. Since the MAS spectrum breaks up into sharp ssb's, it gives a more reliable value for uo than the broad static spectrum. As expected, MAS strongly reduces the homogeneous line broadening accountingmainly for unresolved nuclear dipolar interactions.36.37 Also, note that 6 w 1 p in 6Li resonance is much smaller than in 7Li resonance. This comes from a decrease of both the dipole4ipole interactions (y(6Li) < T ( ~ L ~and ) ) quadrupolar relaxation effects (IQ(6Li)l
