Lithium di�usion and C60 dynamics by quasielastic and inelasticneutron scattering in Li12C60 fulleride.L. Cristofolini1, P. Facci1;2, M.P. Fontana1, G. Cicognani3, A.J. Dianoux4,1Dipartimento di Fisica and INFM, Universita' di Parma Parco Area delle Scienze 7/A, I-43100 Parma,Italy2 INFM and Universit�a della Tuscia, Viterbo, Italy3INFM and ILL, Avenue des Martyrs, 38042 Grenoble, France4ILL, Avenue des Martyrs, 38042 Grenoble, France(October 20, 1999)AbstractWe have performed inelastic and quasielastic neutron scattering experiments onthe highly lithium doped fulleride Li12C60 covering the T range from 150K to 600K,across a tetragonal to cubic fcc phase transition which was shown to occur aroundT=550K by synchrotron x-ray di�raction. In this work we focus on the dynamicsof the Li ions and C60 molecular units. The QENS data suggest a dynamical modelin which the Li ions di�use in the con�ned environment of the octahedral void ofthe pristine C60 molecule, in agreement with the structural information that we haveobtained on the same compound. These results are discussed together with ourpreviously reported analysis of the changes in the vibrational density of states acrossthe phase transition. The emerging picture is that Li12C60 at high temperature (fccphase) has the same dynamical features as pure C60 with the addition of Li localizeddi�usion within the octahedral void, while the low temperature tetragonal phase ischaracterized by a broadening and disappearance of many dynamical features, i.e. of1

the Li di�usion and of the C60 librations and molecular modes.PACS:78.70.Nx, 63.50.+x, 78.30.Na, 63.20.Dj

Typeset using REVTEX2

I. INTRODUCTIONLithium doping of fullerene has recently attracted special attention1{3 also because of subtlestructural and charge transfer e�ects that take place in alkali metal doped fullerenes AxC60(A=alkalimetal, x=1,3,4,6,...) when the radius of the alkali metal is much smaller than the typical radii r of thetetrahedral and octahedral voids of the pristine C60 pseudo-cubic structure (r=1.12�A and r=2.06�Arespectively). In large radius alkali metal doped fullerenes (A=K, Rb,Cs) the crystal structure can bemodeled (with the only exception of A1C60) as intercalation of the alkali metal ions into the pristineC60 cubic structure. Moreover these compounds show full electronic transfer from the alkali metal ionto the C60 unit, thus the stoichiometric parameter x re ects the charge state of the C60 unit. This classof materials has commanded much interest because of its superconducting and magnetic properties4:for instance A1C60 compounds are cubic at high temperature, while the low temperature equilibriumphase displays unusual 1-D polymeric chains5 con�rmed by the presence of a distinct inter-C60vibrational signature of polymeric bond6;7, moreover A1C60 supports a magnetic spin density wavetransition8;9 below T=50K. A3C60 compounds display superconductivity (Tc=33K in Cs2RbC6010)with a positive correlation between the critical temperature Tc and the lattice parameter a (whichcan be varied by choosing the radius of the dopant alkali metal ion), in agreement with BCS-LDApredictions11. For all these compounds a natural limit in the doping level is reached at x=6 due tothe complete occupancy of the voids of the pristine cubic structure. On the contrary the intercalationwith small radius alkali metals (Li and Na, ionic radii= 0.63, 0.97 �A respectively) may yield phaseswith higher alkali metal content, due to the tendency to form metallic clusters located in the voidsof the pseudo cubic fullerene structure, as is the case of Na11C6012;13. In addition, in the case of Naand Li doping there are indications that the charge transfer from the alkali metals to the C60 unit isonly partial13;1, which might imply co-ordination between the alkali metal and the C60 units.Parrinello and co-workers14, based on Car-Parrinello �rst principles molecular dynamics calcula-tions, proposed that Li12C60 could be a stable, highly symmetric fullerene cluster, a 'superfulleroid',with the 12 Li ions coordinated with the 12 pentagonal faces of C60 thus preserving the icosahedralIh symmetry. Clearly such a system should have an interesting dynamics, in particular due to the3

coupling of the large C60 molecules to the intercalated Li ions: vibrational, librational and di�usionalmotions of both components could mix and in uence each other yielding quite complex behavior.In a previous work15 we reported the successful synthesis of bulk quantities of di�erent LixC60compositions, and we have shown that Li12C60 in the solid state is a single phase compound. With ahigh resolution x-ray di�raction (XRD) experiment16 we were able to identify its crystalline structure,that is of an intercalation compound, face centered cubic fcc Fm�3m at high temperature (T=553K)with the Li ions concentrated in the octahedral void of the contracted (lattice parameter a = 14:089�1�A) fullerene pseudo-cubic structure. The structure distorts to tetragonal upon cooling below 553Kand stays tetragonal down to 4.2K. In the high temperature cubic phase we have obtained strongevidence of co-ordination between the carbon density on the C60 unit and the nearest Li ions. Wefound also that the Li ions are all grouped in a cluster located at the octahedral void, while thetetrahedral site re�nes to zero Li occupancy. As it is shown in Fig. 1, the re�ned Li sites are: 4b(1/2, 1/2, 1/2) at the centers of the octahedral void; 32f (x; x; x), x=0.662(1), located at the cornersof a cube centered in the octahedral voids; and 24e (1/2, 1/2, y), y=0.690(1), located at the centersof the faces of the above mentioned cube. While the sites 4b and 32f re�ne to full occupancy, thesites 24e re�ne to partial occupancy N � 12 , which is compatible with di�usion of Li ions betweenthe various 24e sites.The emerging picture for Li12C60 is that of an hybrid between the super-fulleroid cluster werethe Li atoms are attached to the C60 unit and therefore show dynamical features similar to thoseof pristine C6017 (e.g. librations or rotational di�usion) and a conventional intercalation compoundsuch as K3C60 were the C60 units may have some kind of dynamics18 (typically free rotations orlibrations) which is, at least in �rst approximation, decoupled from the alkali metal vibrational ordi�usional processes. In the lower temperature tetragonal phase the lattice parameters contractionsuggests the possibility of formation of inter-C60 polymeric bonds.In this context we want now to focus on the dynamics of the Li ions in conjunction with that ofthe C60 units, as a function of the temperature. In particular we are interested in the changes of Lidi�usion across the tetragonal-cubic phase transition, and how such changes a�ect the vibrational4

and librational dynamics of the C60 molecules. For this in principle IQENS (inelastic and quasielastic neutron scattering) should be an eminently suited technique. There are however di�culties,as it is common with fullerides, due to the overall weakness of the signal, the combination of thecoherent signal from the carbons of C60 and the incoherent contribution arising from the 7Li nuclei,and �nally the interference of Bragg peaks from the C60 crystalline structure, which creates holes inthe usable Q-space.In a preliminary work19 nevertheless we have presented data on the changes in the C60-originatedvibrational density of states across the phase transition. Here we correlate such behavior with changesin quasi elastic scattering (QENS), which we were able to model quantitatively; all this leads to amore detailed and speci�c interpretation of the dynamical changes across the phase transition in thisparticular fulleride.

5

FIGURES

ba

c

FIG. 1. Li sites in the octahedral void of Li12C60 at T=553 K from high resolution x-ray di�raction.The surrounding C60 units are indicated as large meshed spheres (whose radius is reduced by 12 for clarity).The C60's located at the corners of the unit cell are omitted for clarity. The fully occupied (4b and 32f) Lisites are indicated by gray balls, and the half-occupied sites (24e) by black balls respectively. The outer wireframe is the fcc unit cell, the inner frame marks the octahedral site.II. EXPERIMENTALThe samples were prepared using the azide decomposition technique20. In particular, stoichiomet-ric quantities of puri�ed C60 and 99.9% isotopically pure 7Li azide LiN3 were mixed and pellettized inan Ar glove box (� 5ppm H2O, O2). 7Li purity is required to avoid problems of neutron absorptionfrom the natural fraction of 6Li. More details about the sample preparation can be found in ref.15.6

The samples were then characterized by NMR, XRD, SQUID and Raman spectrometry. Here wejust recall that up to 373K the 13C NMR spectrum shows the full chemical shift anisotropy (about180 ppm) typical of static fullerides, indicating that the C60 rotational dynamics is frozen on theNMR time-scale.Neutron inelastic scattering measurements were performed at the Institut Laue Langevin, Greno-ble using the IN6 time-of- ight (tof) spectrometer, operating in neutron-energy-gain with incidentneutron wavelength of 5.12 �A (Ei= 3.12 meV). The 450 mg sample was hosted in a at, air-tight(sealed with lead wire) aluminum sample holder placed inside the cryoloop. Data were collected at150, 300, 450 and 600 K. Given the weakness of the signal, in order to obtain an acceptable signal-to-noise ratio we had to use a typical accumulation time of 12h. The tof spectra were collected over thefull range of scattering angles (10.3o- 114.2o). Corrections were made for the aluminum can contri-bution by running an empty sample can. Vanadium was used as calibrant, allowing determination ofthe relative e�ciencies of the counters. The measured instrumental resolution at the elastic line wason average FWHM=0.10 meV . In order to avoid contamination by elastic (i.e. Bragg peaks) andinelastic (C60 lattice phonons) contributions , only six groups, comprising 173 out of a total of 235 tofspectra, were used in the subsequent analysis, as shown in Fig. 2. The average exchanged momentaQ were 0.39, 0.60, 0.89, 1.10, 1.69 and 1.93 �A�1 for the 6 selected regions. From the modeling ofthe scattering function S(Q,!) we could extract the weak quasi-elastic scattering from the data. Theresulting quasi-elastic scattering function can be then �tted with an appropriate model. In our casewe chose a jump di�usion model for the motions of the Li ions in the octahedral symmetry of thevoids between the C60 molecules.

7

10 20 30 40 50 60 70 80 90 100 1100

1

2

3

4

5

6

7x 10

5

2θ (deg)

Cou

nts

1 2 3 4 5 6

FIG. 2. The di�raction pro�le of Li12C60 measured on IN6 as a function of the scattering angle 2�at 300 K. The pro�le is divided into 8 di�erent regions, only 6 of which are not contaminated by elasticcontributions and were used in the present study.The neutron-weighted vibrational DOS G(E) was obtained summing up the inelastic data fromthe 6 regions. Within the framework of the incoherent approximation, the spectral distributionfunction P (�; �) is given by P (�; �) = 2�sinh��2 ��S(Q; !)� � (1)where S(Q; !) is the uncorrected symmetrised scattering law and the dimensionless variables � and� are related to momentum and energy transfer through � = �h2Q22MkT ; � = �h!kT where M is an average8

atomic mass. The spectral distribution function P (�; �) was corrected for instrumental background,Debye-Waller and multiphonon contributions to yield the neutron-weighted vibrational density ofstates G(E) using the ILL suite of programs. Particular care was used in modeling the theoreticalG(E) for the multi-phonon corrections at the higher temperatures.

0 50 100 150 200Energy (meV)

0

0.003

0.006

0.009

G(E

)

FIG. 3. Neutron-weighted v-DOS measured at T=600K after normalization, background and elastic peaksubtraction and multi-phonon correction. Vertical bars mark the modes of pure C60.9

0 10 20 30 40 Energy (meV)

0

0.003

0.006

0.009G

(E)

720, 7, 720, 72, 12 amu

150 K300 K450 K600 K

FIG. 4. Low energy part of the v-DOS as a function of the temperature after normalization, backgroundand elastic peak subtraction and multi-phonon correction.III. RESULTSA. Vibrational DOSThe C60-originated molecular modes, together with the Li ion excitations are the main featuresof the vibrational density of states (v-DOS), which is shown in Fig. 3 for Li12C60 at T=600 K. Thevertical bars in the �gure mark the positions of the vibrational modes in pure C60 as obtained by a10

variety of techniques: neutron scattering, Raman and IR spectroscopy21;22. As it is usual in this kindof experiments, due to the limited experimental resolution in the neutron-energy-gain setup of IN6and the multi-phonon e�ects (only partly taken into account by the data correction procedure) theC60-originated modes are broadened and overlap resulting in a rather unstructured couple of buncheslaying between 30 and 110 meV and between 130 and 200 meV respectively.The same v-DOS is detailed in Fig. 4 for the lower energy transfer region as a function of thetemperature. Note that the mode originated by the C60 'squashing' Hg(1) (33 meV), is distinguishablein the 600K data set as a shoulder emerging from the broader bunch. The same mode disappearscompletely in the v-DOS measured in the lower temperature tetragonal phase.This may indicate that the Li ions clusters act as a "viscous" dampener of the vibrational modeof the C60 units, which appear to be freer only at 600K. In the same �gure the broad peak between10 and 20meV could be identi�ed with the overlap of Li ion excitations and possibly with vibrationsof polymerized C60.In Fig. 5 we show the scattering law S(Q,!) as measured in the �rst region ( �Q=0.39�A�1) asa function of the temperature. In the 600K data a we observe a well de�ned excitation peak atE=2.8�0.2 meV with half width HWHM=1.0�0.2 meV, its intensity is much reduced in the T=450Kdata, while the scattering law is essentially featureless at the lowest temperatures (150K, 300K). Weidentify this feature with the C60 librational peak, which is found e.g. at E=2.6 meV in pure C60at 80K. Its reduction and �nal disappearance upon cooling implies that the librational motion isdampened at the lowest temperatures in the more compact tetragonal phase, while it is restored inthe high T cubic phase. This is a remarkable result since at 600K, the data show also a restorationof the intra-molecular excitation of C60 Hg(1) peak at 33meV. Survival of C60 librational peak in thehigh T phase was already encountered23 in the case of Na2CsC60. Here the case seems to be similar,even if in the lower temperature phase the librational peak vanishes.11

0 1 2 3 4 5 6 7 8 9 10Energy (meV)

0

0.01

0.02

0.03

S(Q

,w)

(A.U

.)

T=600K

T=450K

T=300K

T=150K

FIG. 5. Scattering law S(Q,!) at the lowest exchanged momentum Q=0.39�A�1 at the di�erent temper-atures marked on the graph. Note the appearance of a well de�ned excitation at T=600K peaked at 2.8meV.B. Quasi-elastic scatteringThe elastic and quasi-elastic (QE) neutron scattering intensity was �tted with a two componentmodel, the elastic intensity being represented by a delta function convoluted with the experimentalresolution function (given by the vanadium scan) and the QE intensity by a Lorentzian functionconvoluted with the same resolution function, as it is shown in Fig. 6. The intensity of the QEsignal decreases on cooling from 600K to 450K but does not completely disappear even at the lowesttemperatures studied. This will be discussed in the following.

12

−1 0 1 2Energy (meV)

0

0.05

0.1

0.15

S(Q

,w)

FIG. 6. Scattering law S(Q,!) measured at T=600K and �Q=0.89�A�1. The heavier continuous line isthe �t model comprising of one Lorentzian QE (light line) and the elastic (dashed line) contributions eachconvoluted with the instrumental resolution.

0 1 2 3Q

2(A

−2)

−1.2

−1

−0.8

−0.6

log(

I 600/I

450)

FIG. 7. Q dependence of the ratio of the elastic intensities measured at 600K versus that at 450K. Notethe logarithmic vertical scale and the quadratic (Q2) abscissae. The continuous line represents the best �tto the Debye-Waller law, from which we estimate with �u2=0.084�0.014�A2The increase of QE intensity at the tetragonal to fcc phase transition, where the C60 units exhibitstrongly increased librational motion, indicates that the increased motional freedom of the Li ions issomehow connected with it. However, the librational mode of the C60 unit indicates also that the Li13

ions are not totally free to di�use between di�erent voids of the C60 structure, which would result ina smearing of the re-orientational potential felt by the C60 units. This is con�rmed by our analysisof the scattering law in the quasi-elastic range. The �rst qualitative result we wish to point out isthe independence of Q of the width of the QE signal (which is about 0.29 meV, see Fig. 8). Atthe same time the elastic intensity follows the normal Debye-Waller behavior. In Fig. 7 we reportthe Q dependence of the ratio of the elastic intensities measured at 600K versus that at 450K. Thisratio is related to the Debye-Waller factor I = I0 exp(�Q2�u2) associated to Li di�usion, from thiswe could estimate for the mean square displacement of the Li ions the value of �u2=0.084 �0:014�A2,in good agreement with the value of �u2=0.083 �0:015�A2 obtained from our Rietveld re�nement ofthe high resolution x-ray di�raction data16. We used the same Debye-Waller factor to correct theQE intensity, which could then be �tted to a theoretical di�usion model for the the motion of theLi ions. From the Q independence of the QE half-widths (HWHM) we deduce that the di�usionalmotion must be localized at least when studied on the space scale of the IN6 experiment, that isbetween 3 and 16 �A from the posed limits on the Q-space.

14

0

0.5

1

1.5

2

I el

150K300K450K600K

0

0.05

0.1

I qe

450K600K

0 0.5 1 1.5 2Q(A

−1)

0

0.25

0.5

HW

HM

(m

eV)

450K600K

FIG. 8. Elastic (top panel) and quasi-elastic (middle panel) intensities and quasi-elastic HWHM as afunction of Q for di�erent temperatures in Li12C60.We recall here that in our structural study16 of the high temperature Fm�3m phase of Li12C60we found three di�erent sites for the Li ions, all of them within the octahedral void of the pristinefullerenic structure: 4b and 32f that have full occupancy, and 24e (fractional coordinates (1/2,1/2, y), y=0.690(1) ) which has fractional occupancy N=12 . It is therefore reasonable to assumea model in which the Li ions di�use among the di�erent 24e sites (due to their loose occupancy)of a single octahedral void. Within such model of octahedral jumps in a con�ned geometry24 thequasielastic intensity consists of two Lorentzian terms A1(Q) = 13 [1 � 2j0(p2Qr) + j0(2Qr)] andA2(Q) = 12 [1 � j0(p2Qr)] where j0 is the spherical Bessel function of order 0, and r is the radius15

of the sphere containing the sites. The two QE widths are !1 = 1:5=� and !2 = 1=� respectively, �being the residence time of the particle on each site. Even if the two QE terms display di�erent Qdependence, in the Q range of interest to our IN6 experiment, the complete QE scattering functioncan be approximated- with an accuracy of �5%- to a single Lorentzian of average width �! = 1:19=� .

0 0.5 1 1.5 2Q(A

−1 )

0

0.05

0.1

0.15Q

E In

tens

ity450K600KOctahedral jumps, r=2.06A

FIG. 9. Q dependence of the QE intensity, after Debye-Waller correction, at T=600K and T=450K.The continuous lines represent the theoretical �t to octahedral jumps as described in the text.

16

0

0.05

0.1

0 100 200 300 400 500 600Temperature (K)

QE

Inte

nsi

ty

-0.005

0

0.005

0.01

0.015

0.02

Tet

rag

on

al d

ist.

FIG. 10. Temperature dependence of the intensity of the QE signal normalized to the elastic intensityat �Q=1.10�A�1 (�lled circles, left scale) plotted together with the amplitude of the tetragonal distortion ofthe cubic lattice de�ned as (p2a� c)=c (empty diamonds, right scale). The latter is plotted in a descendingscale. Note that the increase of the QE signal follows the same T dependence as the decrease of the tetragonaldistortion.In Fig. 9 we show the behavior of the QE intensity, after Debye-Waller correction, for two di�erenttemperatures, respectively below and above the phase transition, and the corresponding theoretical�t, with r= 2.06 �A, which coincides nicely with the radius of the octahedral void. From the widthof the QE intensity the value of the residence time �=2.7�0.5ps can be estimated at T=600K. Herewe wish to note that the measured residence time is, within the experimental accuracy, independentof temperature across the phase transition. This indicates that the temperature acts only on thenumber of ions which di�use according to the rotational di�usion model we propose; once the Li17

ions are freed to move, they move with the given mobility determined by the local environment,which changes very little across the phase transition. From the ratio of the quasielastic intensitiesto the corresponding elastic intensity at 600K and 300K we �nd that the number of di�using Li ionsat 600K is almost 5 times bigger than at 300K. In Fig. 10 we overplot the T dependence of theincrease of the intensity of the QE signal at �Q=1.10�A�1 (normalized to the corresponding elasticintensity) with the decrease of the tetragonal distortion of the cubic lattice ((p2a� c)=c) as derivedfrom our XRD study. The two quantities show the same dependence on T. Since the QE intensityis a direct measure of the fraction of Li ions which are free to di�use, this supports the idea thatin the more compact tetragonal phase the Li ions are blocked, while as T is raised the crystal cellexpands and more and more Li ions are free to di�use and therefore contribute to the QE signal.Clearly such mobility should increase at temperatures higher than 600K, and therefore one shouldbegin to observe some T dependence of the QE width; however to probe this issue further, highertemperature measurements are necessary.IV. CONCLUSIONSThe complex dynamics of the highly lithium doped fulleride Li12C60 has been studied by IQENS.In spite of di�culties connected with the simultaneous presence of crystalline and disordered systemscattering and the weakness of the incoherent scattering signal, we were able to isolate and modelquantitatively the di�usional motion of the Li ions across the fcc to tetragonal structural phasetransition �rst detected by synchrotron x-ray di�raction. In particular we propose a localized jumpdi�usion of the Li ions in the octahedral voids of the Li12C60 structure. Such motion seems to beresponsible for the previously reported changes in the Li12C60 vibrational density of states at thephase transition; in particular it explains the observed approach of G(E) to that of pure C60, e.g. therestoration of the Hg(1) mode at 33 meV. Higher temperatures studies of QENS may be necessaryto probe more quantitatively the di�usional dynamics of the Li ions in Li12C60.18

V. ACKNOWLEDGEMENTSWe thank M. Ricc�o and W. Andreoni for initial discussions on Li12C60 and superfulleroids.

19

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