new aspects in the interpretation of the t′ and t 87rb nmr lines in rb3c60

*Corresponding author. Tel.: #49-30-838-3719; fax: #49-30-831-1355.

E-mail address: [email protected] (K. LuK ders)

Physica B 271 (1999) 7}14

New aspects in the interpretation of the T@ and T 87Rb NMRlines in Rb

3C

60M. Kraus!, O. Klein!, G. Buntkowsky", K. LuK ders!,*!Fachbereich Physik, Freie Universita( t Berlin, Arnimallee 14, D-14195 Berlin, Germany

"Fachbereich Chemie, Freie Universita( t Berlin, Takustr. 3, D-14195 Berlin, Germany

Received 13 April 1999; accepted 3 August 1999

Abstract

It is shown that the intensity ratio of the T@/T 87Rb NMR lines can be in#uenced by a variation of the cooling rate fromthe preparation temperature to ambient temperatures. We discuss the origin of the appearance of the T@ line in Rb

3C

60and the changes in the intensity ratio of the T@ and T 87Rb NMR lines with respect to magnetically di!erent surroundingsof the Rb` ions caused by the two standard orientations of the C3~

60ions. This interpretation of the T lines in 87Rb NMR

is consistent with the structural results of X-ray analyses. Additionally, the sample's superconducting volume fraction isin#uenced by the cooling rate after the annealing process. ( 1999 Elsevier Science B.V. All rights reserved.

PACS: 61.48.#c; 74.70.Wz; 76.60.!k

Keywords: Fullerenes (C60

); Rb3C

60; Nuclear magnetic resonance; Superconductivity

1. Introduction

Particularly the exciting discovery of supercon-ductivity in fullerene intercalation compounds(A

3C

60with A"K, Rb, Cs or a combination of

di!erent alkali metals) [1] has stimulated intenseresearch activities to investigate this new material.Nuclear magnetic resonance (NMR) experimentscontributed detailed information to the dynamicsand the structure (for a review see e.g. [2,3]) offullerenes and their compounds. In A

3C

60with an

ideal face-centered cubic array of C60

ions, one

octahedral (O) and two equivalent tetrahedral (T)interstitial sites per C

60molecule exist. Accord-

ingly, one should expect two di!erent NMR lines(O and T) for the intercalated alkali}metal ionswith an O : T intensity ratio of 1 : 2. In Rb

3C

60this

is indeed the case for temperatures above 370 K[4]. However, at room temperature a third 87Rbline clearly separated from the two others is indicat-ing three locally di!erent interstitial sites ratherthan two. This unexpected result was "rst pub-lished by Walstedt et al. [4]. They showed that thisthird line corresponds to a magnetically inequi-valent tetrahedrally coordinated site labeled [email protected] experimental results were con"rmed by sev-eral research groups for tetrahedrally coordinatedpotassium [5,6], rubidium [7,8] and cesium ions[2]. But yet the origin of the T lines is still under

0921-4526/99/$ - see front matter ( 1999 Elsevier Science B.V. All rights reserved.PII: S 0 9 2 1 - 4 5 2 6 ( 9 9 ) 0 0 2 3 9 - 2

Table 1Intensity ratios of the 87Rb or 39K NMR lines attributed to the tetrahedrally coordinated interstitial sites (T@ and T, with T consisting ofT! and T") of Rb

3C

60and K

3C

60. The T@/T intensity of Ref. [10] listed here is a value obtained by scanning and evaluating the NMR

spectra shown in this reference on page 9269, Fig. 3. The T@/T intensity of Ref. [8] listed here is obtained by evaluating the NMRspectrum published in this reference (this spectrum and the evaluation is also shown in Fig. 1 of this work). The error of the values for theT@/T intensity ratios published in this work is less than 5%. Using the interpretation proposed in this work, one obtains the last valuelisted in this table for the case that the fullerene molecules are randomly distributed between the two possible standard orientations

Sample T@/TT@ : (T!#T")

Source

Rb3C

600.18 Walstedt et al. [4]

Rb3C

60&0.2 Bu$nger et al. [10]

K3C

60&0.17 Yoshinary et al. [1]

Rb3C

600.17 Zimmer et al. [9]

Rb3C

600.19 Kanowski et al. [8]1.3 : (3.7#3)

Rb3C

60as prepared 0.22 This work; Fig. 2a

Rb3C

60after fast cooling 0.15 This work; Fig. 2b

Rb3C

60after slow cooling 0.34 This work; Fig. 2c

Rb3C

60after renewed fast cooling 0.28 This work

Rb3C

60(assuming a random distribution of orientations) 0.143 See text

1 : (4#3)

Fig. 1. Analysis of the 87Rb NMR spectrum of the fullerenecompound Rb

3C

60previously published in Ref. [8].

discussion. Also the resonance line of the octahed-rally coordinated rubidium ions is not a single line[8,9].

The T@/T intensity ratios reported agree ratherwell with each other (Table 1). Di!erent methods ofsample preparation, sample impurities, lattice con-stants or even underdoped samples (Rb

2.75C

60) [8]

seem to have almost no in#uence on the T@/T inten-sity ratio [8,10,11]. Since up to now no systematicin#uence on this intensity ratio is observed (e.g. bydi!erent preparation methods), the appearance ofthe T@ line is regarded as an intrinsic e!ect of A

3C

60fullerides.

In several NMR spectra published the T lineitself seems to consist of two lines (T! and T"). Thisis observable by a clear shoulder ([8] and Fig. 1)and more pronounced in MAS NMR spectroscopy[9]. Yet the origin of the T! and T" lines has notbeen discussed.

Another striking feature reported in some of thepublications is the temperature dependence of theNMR spectra: For Rb

3C

60above 370 K [4], and

for K3C

60above 210 K [5] and 100 K [6], respec-

tively, the T@ and T lines collapse into a single line.Moreover, the 13C NMR line is motionally nar-rowed roughly over a similar temperature range

[11] as the collapse of the T@ and T peaks. Theappearance of magnetically di!erent tetrahedralsurroundings therefore could be correlated with theorientation of the C3~

60ions [9].

The idea of this work is to in#uence the localstructure (orientation of the C3~

60ions with respect

8 M. Kraus et al. / Physica B 271 (1999) 7}14

Fig. 2. Comparison of the 87Rb NMR spectra of the fullerenecompound Rb

3C

60(120 000 scans, repetition time 0.5 s) after

di!erent cooling rates from 3803C, the temperature originallyused for the intercalation process, to room temperature: (a) asprepared (b) after rapid cooling (within 2}3 min), and (c) afterslow cooling (within 3 weeks).

to each other) of a Rb3C

60sample by shorter or

longer cooling times from the preparation temper-ature (3803C) to ambient temperatures. We showby 87Rb NMR that the intensity ratio of the T@ andthe T NMR line can be in#uenced by these di!erentcooling rates. We discuss the origin of the change inthe intensity ratio of the T@ and T NMR lines withrespect to the orientation of the C3~

60ions. The

existence of three T lines will be part of our inter-pretation to explain di!erent magnetically sur-roundings for Rb ions on tetrahedrally coordinatedinterstices.

Since there is a correlation between the degree ofthe fullerene compound's structural order and theirsuperconducting volume fraction [12] we addition-ally examined the sample with respect to supercon-ductivity after the respective annealing processes bysusceptibility measurements.

2. Sample preparation and characterization

The Rb3C

60sample was prepared earlier [12]

and sealed in a glass tube since then. A detaileddescription of the puri"cation process of the pris-tine C

60is given in Ref. [12]. By this procedure

highly crystalline powder samples are obtainedshowing #at, shiny faces. The increasing reductionof lattice defects (TEM) leads to a decreasing latticeconstant as observed by X-ray di!raction. After the"nal sublimation, phase pure C

60samples with

a lattice constant of a0"14.152$0.001 As (room

temperature value) are obtained. This lattice con-stant is even smaller than that of single crystals(14.17$0.01 As [13] and 14.192(4) As }14.195(6) As[14]).

The intercalation of Rb into these C60

crystals isalso described in Ref. [12]. As known for graphiteintercalation compounds, the structure of graphitecrystals can easily be destroyed due to the mechan-ical stress during the intercalation process. In orderto reduce lattice defects induced by intercalation ofRb lowest reaction temperatures possible (3803C)and suitably long annealing times (5 days) wereapplied. The intercalation process was controlledby X-ray di!raction. The lattice constant ofRb

3C

60investigated here is 14.432(2) As (room tem-

perature value). The resulting crystals also showed

#at, shiny faces. The size of the mosaic blocks(average length of coherent X-ray scattering) foundin intercalated crystals was larger than 150 nm (res-olution of the X-ray di!ractometer). The size of theparticles ranged from one to a few millimeters. Thereaction steps were done without pressing the sam-ples. AC and DC susceptibility measurements yielda transition temperature to superconductivity of¹

#(onset)"30.6 K.First 87Rb NMR results of the sample prepared

in the described way were published previously [8](cf. Fig. 1 in this work). Now, we reexamined thissample by 87Rb NMR (Fig. 2a). Afterwards weheated the sample to the temperature used for theintercalation (3803C) for about 1 h and cooled it

M. Kraus et al. / Physica B 271 (1999) 7}14 9

Fig. 3. Comparison of the magnetic moment (real part of the ACsusceptibility) of a Rb

3C

60compound after the slow cooling

process and after the following rapid cooling procedure.

very fast to room temperature (within 2}3 min).Hereafter we warmed the sample again to 3803Cand slowly cooled it down to room temperaturewithin 3 weeks. After characterization by NMRand by susceptibility measurements we heated thesample to 3803C and cooled it rapidly (within2}3 min) for a second time.

3. Experimental

The 87Rb NMR measurements were performedin a 7.049 T magnetic "eld with a Bruker MSL 300spectrometer. For the data acquisition a standardHahn-echo pulse sequence was used. Frequencyshifts of the 87Rb NMR spectra are referenced toRbCl (aq. solution). All NMR investigations re-ported here were performed at ambient temper-atures. The intensities (areas) of the lines weredetermined with a base line correction using theaverage values of the noise on both sides of thespectra.

A commercially available AC magnetometer wasused for "eld dependant (2 mT}7 T) and temperaturedependant (300}2 K) susceptibility measurements.

4. Results

The 87Rb NMR spectra show three clearly dis-tinct lines: T@, T, and O (Fig. 2a}c). The intensityratio T@ : T after a &normal' cooling rate (within theoven) is 0.22 (1 : 4.5) at room temperature as isshown in Fig. 2a (cf. Table 1).

As observed before [8], the T line is not a singleline but consists of two lines labeled T! and T" (Fig.1). Analysing this static 87Rb NMR spectrum re-veals an intensity ratio of T@ : T! : T" of 1.3 : 3.7 : 3.Since in static NMR, the T" intensity and positioncannot be de"ned with reasonable accuracy, in thefollowing we will not determine the intensities ofT! and T" separately, but as a sum of both lines(T!#T")"T.

The reexamination of the Rb3C

60sample (Fig.

2a) yielded a T@/T intensity slightly higher than thatobserved before (Table 1). This di!erence might bedue to ordering processes having taken place dur-

ing the long time between the measurements (seeDiscussion).

After the "rst warming and rapid cooling proced-ure the intensity ratio of the three easily resolvable87Rb NMR lines (O, T@ and T) was changed (Fig.2b). We now observed a decreased T@ intensity rela-tive to the intensity of the T line. The T@/T intensityratio was now 0.15 instead of 0.22 as observed be-fore (Table 1).

After the following slow cooling rate (from 3803Cto room temperature within three weeks) the T@intensity increased to a T@/T ratio of 0.34 (Fig. 2cand Table 1). This is the highest relative T@ intensitypublished until now.

Finally, after a renewed warming (1 h at 3803C)and a rapid cooling procedure the T@/T intensityratio was reduced again to 0.28 but it was not at thesame low level as after the "rst rapid cooling pro-cedure (T@/T intensity of 0.15).

AC susceptibility measurements after the slowcooling procedure and after the renewed rapid cool-ing process show clear di!erences in the sample'sdiamagnetic signal below the transition temper-ature to superconductivity (¹

#). After the slow

cooling process the diamagnetic signal below¹

#which is proportional to the sample's supercon-

ducting volume, is up to 30% larger than after therapid cooling procedure (Fig. 3). Above ¹

#, the

sample shows a small paramagnetic signal.


Fig. 4. Structure and orientation of the Rb3C

60compound as

derived from X-ray di!raction (adopted from Ref. [17]). Thelower left fullerene and the fullerene in the middle are orientedin one of the two standard orientations, while the other threefullerenes shown here are oriented in the other standard orienta-tion.

The imaginary part of the AC susceptibility (re-sults not shown) di!ers only slightly with respect todi!erent cooling procedures. In static magnetic"elds up to 7 T, we observe a tendency to smallerdissipation signals after the rapid cooling process.In all measurements there exists one sharp dissipa-tion peak near ¹

#and a broad signal at lower

temperatures.There are slight in#uences of the cooling rate on

¹#

and the upper critical "eld B#2

. For example, ata temperature of 28.3 K after the fast cooling rateB#2

is 3.5 T while after slow cooling B#2

is 5 T. Inthe same external magnetic "elds the transitiontemperature ¹

#tends to higher values after slow

cooling compared to measurements after fast cool-ing (0.5 K at 5 T). Consequences of these "ndingswill be discussed elsewhere [15].

5. Discussion

Numerous structural and/or electronic struc-tural distortions that could account for the exist-ence of two magnetically inequivalent tetrahedralsites have been discussed in the literature [2,4,6,7,9]. The possible origins of the T@ line proposedare a local deviation of the ideal FCC structurederived from X-ray re"nements like displacementof the Rb` or the C3~

60ions [4], Jahn}Teller distor-

tions on C3~60

[4], carrier density modulation (dis-proportionation of C3~

60ions) [4], Rb` clustering

[4], o!-center positions of the metal ions [16], orvacancies at neighboring tetrahedral or octahedralsites [4]. In this work we concentrate on the ori-entational order of the C3~

60ions in fullerene com-

pounds as an explanation for the formation ofmagnetically di!erent T sites.

In principle, a well-de"ned splitting as is ob-served for the T resonance line necessarily requiresa de"nite origin. The existence of two standardorientations of the fullerene ions (without inter-mediate orientations, cf. Fig. 4) could be such awell-de"ned origin. Additionally, the correlationbetween the motional narrowing of the 13C NMRline and the collapse of the T@ and T lines at highertemperatures suggests that the orientation of theC3~

60ions causes magnetically di!erent tetrahedral

surroundings for the intercalated ions.

In the K3C

60structure, as derived from X-ray

re"nements, the C3~60

ions adopt one of two di!er-ent orientations at room temperature. The orienta-tions are energetically identical and the moleculesappear to be randomly distributed between thesetwo standard orientations (cf. Fig. 4) [17]. Fre-quently, this is called the merohedral disorder ofthe fullerene molecules and this structure is widelyaccepted for other A

3C

60compounds [18].

In either of the two standard orientations anelectron-rich carbon hexagon (one of the C

60's 20

hexagons) is placed adjacent to a tetrahedrallycoordinated Rb` ion. So, each tetrahedrally coor-dinated Rb` ion is surrounded by four C hexagons.The angle between two hexagons facing T sites (Thexagons) of neighboring fullerene ions is 70.63referring to an angle of 109.43 between the Rb`}

C3~60

axes (Fig. 5). Considering the merohedraldisordered C

603~ ions three di!erent surroundings

of the Rb ion can be distinguished: First case: all ofthe four fullerene ions forming the tetrahedral sur-rounding are oriented in the same direction. In the


Fig. 5. Schematic draw of two hexagons facing tetrahedrallycoordinated Rb` ions. Only two of the all in all four surround-ing C hexagons are shown. The directions towards the other twohexagons are shown by straight lines. Right: double bonds arefacing double bonds, single bonds are facing single bonds(eclipsed orientation). Left: single bonds are facing double bondsand vice versa (staggered orientation). The angle between twohexagons facing T sites is 70.63 referring to an angle of 109.43between the Rb`}C3~

60axes.

Fig. 6. Projections of the C60

tetrahedron. Open or full circlesrepresent C

60molecules oriented in one or the other (mirror

symmetric) standard orientation, respectively. Straight and dot-ted lines represent staggered and eclipsed positions of neighbor-ing T hexagons, respectively.

following we will call this constellation &A' (cf.Fig. 6A). Second case: three fullerenes are orientedin the same direction, while the fourth C3~

60is in the

other standard orientation (constellation B, cf.Fig. 6B), and the third case possible: two of the fourC3~

60ions are in the same orientation, respectively

(constellation C, Fig. 6C).

On a "rst view, there should be no di!erenceconcerning the surrounding of Rb nuclei placed atthese di!erent T sites since all Rb ions face fourcarbon hexagons as nearest neighbors. But, in fact,there is a di!erence between constellations A, B andC, and especially between A and the other twoconstellations: In contrast to benzene or graphite,where no di!erences in the C}C bond lengths, i.e.,no localized single or double bonds exist, the C}Cbond lengths within the fullerenes' hexagons ex-hibit two di!erent bond lengths (1.45$0.015 and1.40$0.015 As for the undoped C

60[3]). Thus it

follows that C60

hexagons have } at least partially} localized double and single bonds. While there areonly single bonds in the C

60's pentagons, the hexa-

gons consist of alternating single and double bonds.As a consequence of these di!erences in the bondlengths, the hexagons have only a threefold rota-tional symmetry (C3) and not the sixfold symmetryof a benzene ring. From this it follows that each ofthe four fullerene ions which form the tetrahedralinterstice, can be placed in two mirror symmetricorientations. If two adjacent C3~

60ions are oriented

in the same direction, their T hexagons are posi-tioned in a way that every double bond of one C

60's

T hexagon is opposite to a single bond of a neigh-boring C

60's T hexagon (cf. Fig. 5 left). Double and

single bonds are staggered towards each other. Thisis the case in constellation A: all four T hexagonsare opposite to a respective staggered hexagon andthe con"guration has the full tetrahedral pointsymmetry T.

If one of the four C60

ions is placed in the mirrorsymmetric orientation (constellation B), this tet-rahedral symmetry is broken, resulting in a reduc-tion of the interstice to C3 point symmetry. In thiscon"guration, the T hexagons are positioned in away that every double bond of one C

60's T hexagon

faces a double bond of a neighboring C60's T hexa-

gon (Fig. 5 right). The two hexagons are in aneclipsed position. Here, three T hexagon pairs arestaggered towards each other and three are in aneclipsed orientation.

The second possibility to break the full tetrahed-ral symmetry is if two of the four fullerene ions areplaced in the mirrored orientation, resulting in a re-duction of the interstice to C2 point symmetry,constellation C (cf. Fig. 6C). Here, the four T


hexagons are positioned in a way that there areonly two staggered T hexagon pairs and foureclipsed T hexagon pairs.

There are several di!erent NMR interactions,which can account for the isotropic shifts of the Rblines, namely chemical shielding, Knight shift andparamagnetic shifts. Since the splitting exhibitspractically no temperature dependence, we can ex-clude paramagnetic shifts. From NMR studies ofRb in the graphite intercalation compound RbC

8[19] it is evident, that the isotropic Rb Knight shiftspans a range of at least 2000 ppm, while conforma-tional e!ects on chemical shieldings are typicallytwo orders of magnitude smaller. Thus we attributethe major part of the total shift to Knight shiftinteraction. The splitting of the Rb T line into thethree di!erent lines T@, T!, and T" is then due to thedi!erent point symmetries of the tetrahedral inter-stices (constellations A, B and C), as discussedabove } similar to the splitting of an optical trans-ition in a crystal "eld when the symmetry of the"eld is lowered [20].

The question which arises now is how to attri-bute the observed lines to the di!erent constella-tions A, B and C. We therefore exposed the sampleto the warming and cooling experiments describedin the foregoing chapter. As long as there is a ran-dom distribution of the two standard orientations,the relative frequencies of occurrence for the threedi!erent constellations A, B, and C should be1 : 4 : 3 (Table 1). The experimentally observedintensity ratio of T@ : T! : T" is 1.3 : 3.67 : 3 (Fig. 1) isclose to this ratio. The respective T@/T ratio of 0.19found by evaluating the NMR measurements pre-viously published (Table 1) is somewhat largerthan, but rather close to the value expected for theA : (B#C) intensity ratio expected for the com-pletely random distributed case between the twostandard orientations (1 : 7 or 0.14). However, thesmall T@/T ratio of 0.14 would only be measured, ifno further interaction between the C3~

60molecules

would be present. But there are weak orientationalforces between neighboring C3~

60ions tending to

orient them towards the same orientation [21].Therefore, di!erent cooling rates should in#uencethe relative frequency of occurrence of constella-tions A, B and C and herewith the relative inten-sities of the NMR T lines.

A very slow cooling process therefore shouldfavor the thermodynamically most stable constella-tion. After a slow cooling procedure there should bemore perfectly ordered T surroundings (constella-tion A) than after rapid cooling. The latter shouldresult in an enhancement of the constellationsB and C. Experimentally, we observe a stronglyincreased T@ intensity after the slow cooling processof three weeks: the intensity ratio of 0.34 (Table 1) isthe highest value yet published. We therefore at-tribute the T@ line to the constellation A where thereexists a perfectly oriented T surrounding, while theT line intensities (the sum of T! and T") result fromthe sum of the constellations B and C. Indeed, theT@/T ratio of 0.15 obtained after the "rst rapidcooling process (Table 1) is very close to the valueexpected for a sample where the C

60ions are com-

pletely random disordered between the two stan-dard orientations.

The intermediate value of the T@/T ratio obtainedafter &normal' cooling within the oven of 0.22 (Table1) can be interpreted consistently with the situationthat fewer Rb surroundings are perfectly orderedthan after very slow cooling. The observation of theslightly enhanced T@/T ratio after the long periodbetween the measurement reported here and thoseof Ref. [8] is also consistent with the picture ofincreasing ordering during this time.

After we heated and rapidly cooled the sampleagain, we observed a clear reduction but not a&complete' reduction of the relative T@ NMR lineintensity (T@/T"0.28, cf. Table 1). This might bedue to the fact that there was not enough time (onlyabout half an hour) to let the sample warm up anddestroy the order achieved in the foregoing experi-ment by the slow cooling process.

It should be mentioned that the local symmetryof the octahedrally coordinated Rb` ion is alsoa!ected by di!erent orientations of the neighboringfullerene molecules. Here, the Rb` ion is sur-rounded by six C"C double bonds. Starting witha constellation where all neighboring fullerenes arein the same standard orientation, and turning oneanion into the other orientation will also lower thesymmetry of the O site. Since the distance betweenthe octahedrally coordinated Rb` ion and the sur-rounding fullerene anions is larger than at T inter-stices, the O-line splittings caused by di!erent


symmetries are expected to be much smaller andtherefore might not be resolvable by static NMR.At room temperature the 87Rb NMR spectrumindeed shows a very broad O line for the compoundRb

3C

60. This resonance line is much broader than

the 87Rb O line in K2RbC

60[8]. This can be

interpreted as follows: in K2RbC

60, the Rb ion

tends to occupy the octahedral interstices leavingthe T sites to the smaller K` ion. Because of thesmaller radius, the latter has a smaller orientationale!ect on the fullerenes than the Rb ion would haveon T sites. Therefore, at room temperature the ful-lerene ions in K

2RbC

60are still rotating fast and

a narrow 87Rb O line is observed.

6. Conclusions

In summary, the results show that the coolingprocedure after intercalation can in#uence the T@/Tintensity ratio and also e!ects the superconductingvolume. The origin of the T@ line, the T@/T ratio andtheir changes observed after di!erent cooling pro-cedures can be interpreted consistently with thefullerene ions' two standard orientations existing inRb

3C

60. These di!erent orientations lead to di!er-

ent symmtetries of the tetrahedrally (and also theoctahedrally) coordinated Rb` ion's surrounding.Therefore, with the picture proposed here, the ap-pearance of all in all three T lines are no longer incontrast to the structural X-ray results. Ab initocalculations to quantify the strength of the pro-posed symmetry breaking e!ect on the Rb T linesplitting are currently in progress.

Acknowledgements

We would like to thank Prof. Dr. H.-H. Limbachand H. Breitzke for helpful discussions.

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new aspects in the interpretation of the t′ and t 87rb nmr lines in rb3c60

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