Neutron diffraction and structural models of RbC60 phases

CHEMICAL

2 February 1996

PHYSICS LETTERS

ELSEVIER

Chemical Physics Letters 249 (1996) 195-200

Neutron diffraction and structural models of RbC 60 phases J.R. Fox a, G.P. Lopinski a, J.S. Lannin a, G.B. Adams b, J.B. Page h, J.E. Fischer c a Department of Physics, Penn State University, University Park, PA 16802, USA b Department of Physics andAstronomy, Arizona State University, Tempe, ZA 85287, USA c Department of Materials Science and Engineering, University of Pennsylvania, Philadelphia, PA 19104, USA Received 9 October 1995

Abstract

Pair distribution functions (PDFs), obtained from powder neutron diffraction measurements have been used to construct structural models for the body centered orthorhombic (bco) and fcc phases of RbC6o. The PDF exhibits small differences, primarily due to the shortened inter-fullerene distance in the bco phase. The bco-RbC6o system is well fit to a model derived from first-principles quantum molecular dynamics in which the C-C interfullerene distance is 1.57 ,~. While the geometry of the interfullerene linkages is similar to a previously proposed model, the present results imply less distortion of the C6o molecules and larger interfullerene distances. The PDF analysis also indicates significant orientational disorder between chains of linked molecules.

The body centered orthorhombic (bco) phase of RbC60 has attracted considerable attention due to the presence of an unusually small interfullerene distance of 9.14 A indicated by X-ray diffraction [1]. The nature of the intermolecular interactions in this phase has been the subject of considerable debate, Based on a Rietveld analysis of powder X-ray diffraction data, Stephens et al. have suggested a picture of strongly linked and distorted fullerene molecules with an interball bond distance of 1.44 A, similar to bond lengths within undistorted C6o molecules [2]. This model also involves a mixture of rather long (1.9 A) and extremely short (1.32 ~,) C - C intramolecular bonds lengths. The proposed mechanism for the creation of interfullerene linkages in this phase is a [2 + 2] cycloaddition [3], invoked previously to account for the formation of intermolecular bonds upon laser irradiation [4]. In contrast, Raman scattering studies of bco-RbC60 have suggested weaker intermolecular interactions based o

on comparisons with the vibrational spectrum of C60 dimers produced by laser modification [5-7]. Raman spectra of bco-RbCt0 did indicate enhanced scattering from several modes not allowed for isolated molecules, indicative of substantial interball coupiing. However, the small frequency shift and polarization dependence of the Ag(2) model suggested weaker perturbations of the molecule than indicated by the Stephens model. In the present work we have employed a real space method employing pair distribution functions, obtained from powder neutron diffraction experiments, to investigate the structure of both orthorhombic and fcc RbCt0. This approach has distinct advantages over Rietveld analysis for structural studies in systems with considerable disorder. The pair distribution function (PDF), once extracted from the scattering measurements, can be compared to models of local atomic arrangements [8,9]. This method has been shown to be valuable in determining the struc-

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ture of pure C60 over short and medium distance scales. Fullerene bond distances have been measured to high accuracy [10], and in the case of the simple cubic phase of C60 it has yielded information on orientationai correlations between the molecules [ 11,12]. In this study, similar use of neutron diffraction data extended to high wavevectors is employed to test structural models of bco-RbC60, including the previously proposed Stephens model and the low energy structures produced in first-principles quanturn molecular dynamics (QMD) simulations of this system. The first-principles models are found to yield the best agreement with experiment. While these models involve identical molecular orientations within a chain as in the Stephens model, the interball C - C distance is somewhat larger and the distortion of the C60 molecules considerably smaller than proposed in that model. The present results also indicate considerable orientational disorder between the chains, A 1.3 g sample of RbC60 was prepared by reacting Hoechst lab grade C60 and Rb metal in evacuated pyrex. In a first step, 250°C for one week, all the Rb was absorbed by the C60. After re-grinding the material and re-sealing in evacuated pyrex, an anneal was performed for 2 weeks at 450°C. The sample was first cooled to 100°C for 1 day to avoid quenching in a small fraction of rocksalt, then furnace-cooled to room temperature. Prior to the neutron diffraction experiments, the material was checked by 13-C NMR, cw ESR and powder X-ray diffraction, all of which yielded the known signatures of the body centered orthorhombic phase of RbC60 (bco-RbC60) and no evidence for other phases. Powder neutron diffraction measurements were performed using the Glass, Liquid, and Amorphous Materials Diffractometer (GLAD) of the Intense Pulse Neutron Source (IPNS) of Argonne National Laboratory. After measuring the diffraction intensities of the orthorhombic phase at room temperature for 16 h, the sample was heated to 180°C to affect the phase transformation to the face-centered cubic phase (fcc-RbC60). Diffraction intensities of the fccRbC60 phase were then measured for a further 8 h. The powder diffraction spectrum was corrected for absorption, multiple scattering, background scattering from the instrument and the vanadium sample container, and the Plazcek

shift. T h e c o r r e c t i o n s

were performed via a GLAD modified version of the ATLAS suite of analysis programs. The powder structure factor S(Q) is then transformed to the pair distribution function, p(r), using the expression

f~Q[ S(Q) -

p ( r ) = P0 +

1] sin(Qr)

"0

dQ,

( 1) where P0, the microscopic number density, is obtained from X-ray diffraction experiments [1,2]. To avoid spurious oscillations in the PDF the S(Q) data was terminated by a Lorsch function at 35 ~,-J. A plot of the p(r) data for both fcc and bco-RbC60 is shown in Figs. la and lb as open circles. The PDF of the fcc and bco data sets both exhibit low-r peaks at 1.44, 2.45, 2.87, 3.62, and 4.13 ,~. These distances are within 0.02 ,~ of previously established peak positions for pristine fullerenes by PDF analysis [10]. At r > 7 ,~ the PDF loses structure quickly in both phases indicating significant disorder. This is in contrast to PDFs obtained for C60 and Rb3C6o in which orientational correlations between the molecules give rise to structure out to higher distances [10,13]. Both pair distributions of Fig. 1 exhibit a systematic error at low r, most noticeably between the first and second peak in the PDF where p(r) is expected to fall to zero in the fcc phase. The source of these small errors is most likely from the afore-mentioned complex data reduction scheme. Since these regions

0.6 06 0.4 x 0.3 a) 6.2 ' o.1 0.¢

1

2

b) 3

4

5

6

rcA)

7

8

9

10

Fig. I. (a) Measured PDF of fcc-RbC6o (open circles) with the best-fit PDF generated by model FCC (solid) of Table 1. (b) Measured PDF of bco-RbCeo (open circles) with the best fit model of this phase, model BCO-E (solid) of Table 1.

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J.R. Fox et al. / Chemical Physics Letters 249 (1996) 195-200

of synthetic non-zero amplitude appear nearly identically in both data sets, they are not a result of the phase transition, The PDFs for the fcc and bco phases are rather similar, exhibiting only small differences associated with the structural transition. A plot of the difference A p ( r ) = pbco(r) -- Pfcc(r), as shown in Fig. 2 (open circles), emphasizes these small changes in the local atomic arrangements. Note that the amplitude of these differences is on the order of 0.01 ,&-3 in contrast to the amplitude of the first peak with a maximum of --0.5 ,&-3. Although the measured A p ( r ) suffers from high frequency oscillations due to low amplitude Fourier noise exaggerated by the small scale, several broad features are prominent above the noise, especially those at = 2.5, 3.8 and 4.9 ,&. Producing a model PDF for comparison to an experimentally determined PDF is straightforward, complicated only by the large number of interatomic distances which must be calculated, sorted, and broadened. As the scattering from Rb atoms is greatly overwhelmed by the large proportion of C scatterers, the Rb contributions were neglected in all PDF models. A set of distance pairs, rij, between the ith and jth elements of a set of N atomic coordinates for a particular model is calculated. The model p(r) is thus defined by the expression

1 N i~j 1 p(r) = -~ j~l= i=l ~" N4--~r2b( r -

rij),

(2)

where the function b(r) is a Gaussian of area unity and width chosen to match the thermal broadening seen experimentally. Three regimes of Gaussian broadenings were chosen, since [ow-r distance pairs tend to be correlated due to bonding and thus require lower broadening factors [8]. To quantitatively evaluate model PDFs we make use of a real space agreement factor. The agreement, A, between a model PDF, pmoo(r), and an experimentally determined, Pexp(r), can be defined by

f[ Pmod(r)A2=

Pexp(r)] 2 d r

p~f dr

(3)

where the range of integration can be chosen for any r-region of interest [8]. To avoid the systematic

errors in the low r region the range of integration of Eq. (3) has been limited to the region above 3.4 ~, and below 7 ,&. This range includes both inter- and intra-fullerene pair distances. To model the experimental PDF of fcc-RbC60, the fcc unit cell determined by X-ray diffraction [1,14] was employed together with random orientations of the C60 molecules. The lack of orientational order is consistent with NMR experiments which indicate rapid molecular rotations in this phase [15]. Many PDFs for different randomly generated configurations were calculated and average until the mean PDF converged. Atomic coordinates within the molecules were based on QMD simulations of C60 [19], expanding the fullerene diameter by = 1% (bond lengths become 1.41 and 1.46 ,&) to match the position of the peaks in p ( r ) at low r. The broadening parameters were also adjusted to match the peak widths with those seen in experiment. After these adjustments, excellent agreement with the experimental fcc data was obtained as indicated in Fig. I a. Upon comparison of the model and measured PDF (see Fig. 1), only small discrepancies are noted: the above-mentioned synthetic low-r contributions, a lower intensity of the 4.13 A peak, and an underestimation of intensity in the valleys near 5.0 and 6.4 ,&. An agreement factor of A = 0.04647 was obtained which compares favorably with a similar analysis for Rb3C60 [13] and serves as a benchmark to judge the success of models of the orthorhombic phase discussed below. For the bco phase, we first tested the model proposed by Stephens et al. based on a Rietveld analysis of X-ray diffraction (BCO-A) [2]. In that study orientational correlations between chains were not determined. In the present case, introducing merohedral disorder between chains significantly improved the agreement with the measured PDF. In fact the best agreement was obtained for completely random orientations of the polymer chains about the a axis. While this orientational disorder improved the agreement, particularly at higher r values, the BCOA model still did not adequately describe the experimental PDF. As can be seen in Fig. 2a, a model difference function exhibits significantly larger amplitude variations than observed in the data. In particul~, the model indicates valleys at 2.3, 3.0 and 4.2 A which are not seen. Furthermore, none of the o

198

J.R. Fox et al./ Chemical Physics Letters 249 (1996) 195-200

o . o 2 ~ ' - ~ ' ' " ' ' ~ ' '_" o.ool /~t~/ ( ~ ~, 0.00~ " -o.ol -0.02 0.02

~

~/~4

''::"":::

'

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' :::"::::"::

~/ ~ D,/ ~

b

)

v v'~ ~

:: ":~ ::

.

b)

~.. o.oo f : . ~ t / ' / ] " \ ^ . / , , ~ . ~ l ~ x ^ ~ t (

e °.°° -0.01 -o.02 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3

4

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6

7

8

Fig. 2. Measured (circles) and calculated(solid) differencefunction Ap(r)= p~co(r)- pfc¢(r) for (a) models FCC and BCO-A and (b)models FCC and BCO-E. peaks in the experimental A p ( r ) are well reproduced. The poor agreement of the BCO-A model with experiment is reflected in the agreement factor of 0.07628, considerably higher than that obtained for the fcc phase. Models in which the fullerene molecules were placed in the orthorhombic unit cell but remained undistorted also failed to give reasonable agreement with the data. Several different orientations between nearest neighbor fullerenes were considered, including parallel hexagon-hexagon bonds as in BCO-A [2], merohedral disorder as in K3C60 [16], and the orientations observed in the simple cubic phase of pristine C60 [11,12]. All of these models (BCO-B, C, D, respectively) gave results inferior to the agreement of the fcc model as summarized in Table 1. The failure of both model BCO-A as well as models with undistorted fullerenes motivated the development of new structural models for bco-RbC60

based on first-principles calculations. These structures were created by simulating an infinite line of C6o molecules using the first-principles quantum molecular dynamics (QMD) of Sankey and Niklewski [17]. This simplified first-principles molecular dynamics method utilizes three major approximations: (1) the local density approximation(LDA), (2) the Harris energy functional, and (3) expansion of the wavefunction in a minimal basis of four confined pseudoatomic local orbitals per atom. This QMD method has been used in successful simulations of fullerene molecules [18,19], and carbon solids [20], including a simulation of Jahn-Teller (JT) distortions in both charged and neutral fullerene-related carbon structures [21]. The afore-mentioned orbital confinement is achieved by creating the local orbitals with the boundary condition that they vanish at a selected confinement radius r c. In the present work r c is 4.1 Bohr radii, with one exception. Coulomb integrals were calculated in the electron double counting correction U~ (see Ref. [17]) using, for the charge density only, local orbitals confined within 3.95 Bohr radii. For neutral I h C60 use of this local orbital confinement scheme results in bond lengths of 1.400 and 1.449 A, in excellent agreement with experiment [10,11]. The QMD simulation began with an infinite line of relaxed, JT-distorted C60 molecules [21]. The aligned C~0 are initially oriented so that a line drawn through their centers-of-mass bisects parallel double bonds on each of the molecules with the centers-ofmass of the aligned C60 are separated by 8.728 ,~. In this configuration, the roughly parallel double bonds on adjacent C6o are separated by about 1.8 ~,. Our QMD relaxation of the initial configuration (the lattice vectors do not relax) results in polymerization of the aligned C7,o-balls. We then expand the lattice

Table 1 Various models considered,and the agreementfactor A, between3.4 and 7.0 ~k Model Description FCC randomlyrotatedC~o on fcc lauicepoints BCO-A model of Ref. [2] as determinedby Rietveldof X-ray data BCO-B BCO-A orientationswith no fullerenedistortions BCO-C merohedralorientations BCO-D simple cubic pristineorientations BCO-E calculation - inf'miteline of C~o BCO-E' best interpolatedmodelof Fig. 3

o

A(3.4, 7) 0.04647 0.07628 0.07023 0.07769 0.07076 0.05549 0.05410

J.R. Fox et al. / Chemical Physics Letters 249 (1996) 195-200

vector in 0.5% intervals at each step extending the QMD relaxation until the minimum energy for that lattice vector has been attained. By this method, we find a final, lowest-energy lattice vector of 9.121 A, in good agreement with the X-ray data on the orthorhombic phase [1 ]. The minimum-energy configuration for the charged infinite line is similar to that previously obtained for a neutral linear polymer chain [19o]. The interfullerene bond length is found to be 1.60 A, and the intrafullerene bond in the conr].ecting four-ring is found to be of length of 1.58 A. For undistorted molecules in the bco unit cell the interfullerene C - C o

distance

is 2.1

A;

/~

the

reduced

distance

of

1.60

indicates significant distortions of the molecule, These distortions are largely confined to the carbon atoms of the connecting four-rings and their nearest neighbors. To construct the model PDF we first expanded the QMD derived atomic positions by 1% (as in the fcc case) and then used the experimental lattice vector of 9.14 ~, to separate the molecular centers of mass. This results in an interfullerene C - C distance of 1.54 ,~, and an intrafullerene fourring bond lengthy of 1.60 ,~. The resulting model PDF, model BCO-E, yields considerable improvement in matching peak positions and intensities, giving an agreement factor of 0.05549. To investigate the sensitivity of the agreement factor to modifications of this model, a set of different model PDFs was generated by interpolating between the atomic positions in a line of unconnected C60 and the connected balls of model BCO-E. A suitable measure of the distortions in such a set is the C - C interfullerene distance which varies from 1.54 ,~ in BCO-E to 2.1 ,~ in the unconnected C~0 model, The resulting plot of agreement factor versus interball distance of Fig. 3 shows a minimum at 1.57 ,~ (BCO-E' of Table 1), within 0.03 ,~ of the lowest energy model. This analysis indicates that the best agreement with the experimental PDF is achieved for interfullerene C - C distances in the range from 1.54 to 1.60 ,g,. Allowing variations in the agreement factor of 10% due to experimental uncertainties sugogests that a interball distance as large as 1.65 A might also be possible. These distances are substantially larger than reported in Ref. [2], in which the most probable C - C bond distance is a short 1.44 ,~, although they do fall within the upper limit of the

199

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, .... , .... •

o.o~o

~ ~

0.065

~

0.060

S~ / /

0.0s~

0.05(3

ce0-

•

. . . .

1.5

i . . . .

1.6

, . . . .

1.7

i .... ~. . . . , . . . . ~ . . . . 1.8 1.9 2.0 2.1 2.2

interballdistance(A)

Fig. 3. Variation of the agreement factor with interball distance for interpolation between C~o and model BCO-E. values permitted by the 0.15 ,~ error bars of that study. The largest intraball distance, between the frontier C atoms involved in the formation of the two C - C interball bonds, is only 1.59 ,~ in the best fit model as compared with 1.9 + 0.15 ,~ in the Stephens model [2]. The remaining two nearest neighbors of each of these frontier atoms are found at a distance of 1.53 ,~ as compared to 1.46 ,~ in undistorted molecules. All othero bond lengths are distributed between 1.40-1.47 A, in contrast to the model of Ref. [2] which includes some very short (1.3 ,~,) C - C bonds. The 1.57 ,~, intermolecular distance of the best fit model is somewhat larger than the fourfold coordinated bonds in diamond (1.54 ,~,), although smaller than the largest known C - C bond length in organic molecules of 1.59 A (in C 3 - C - C - C 3 systems) [22]. This intermolecular distance is suggestive of moderately strong interfullerene coupling consistent with the proposal of covalent bonding along the chain direction. While the structural results presented here support the proposal of polymer formation in the bco phase, previous Raman scattering studies indicated considerably weaker interactions. In particular, the small frequency shift of Ag(2) mode by only 4 cmthrough the fcc to bco phase transition [6] is considerably smaller than obtained in theoretical calculations for the first-principles model used to fit the PDF data [23]. This is in contrast to observations for C60 dimers produced upon laser irradiation for which

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J.R. Fox et al. / Chemical Physics Letters 249 (1996) 195-200

good agreement between theory and experiment was achieved [24]. The origin of this discrepancy is unclear and still must be resolved, Although the model BCO-E' gives adequate agreement with the observed PDF, we have achieved significantly better agreement with another model, a model derived from a QMD simulation using two C60 balls per unit cell. With two balls per cell, the system is able to lower its energy through a two-ball J a h n - T e l l e r distortion, placing the two excess elec-

of Pennsylvania was supported by USDOE Grant DE-FC02-86ER45254. JBP acknowledges support from NSF grants D M R 9014729 and DMR 9510182. We thank Hoechst A G for the gift of C60, Pierre Petit for the ESR and Ferid Rachdi for the NMR measurement.

trons per unit cell together in a single state, which is found to reside on a single ball. As opposed to the

[I] o. Chanvet et al., Phys. Rev. Letters 72 (1.994) 2721. [2] P.W. Stephens et al., Nature 370 (1994) 636. [3] S. Pekker, L. Forr6, L. Mih,'ilyand A. JAnossy, Solid State Comm. 90 (1994) 349. [41 P. Zhou, Z. H. Dong, A. M. Rao and P. C. Eklund, Chem. Phys. Letters 211 (1993) 337. [51 G.P. Lopinski, M.G. Miteh, J.R. Fox and J.S. Lannin, Phys. Rev. B RapidComm. 50(1994)16098. [6] G.P. Lopinski, J.R. Fox, J.S. Lannin, in: Physics and chemistry of fuUerenesand derivatives,eds. H. Kuzmany,J. Fink, M. Mehrig and S. Roth (World Scientific, Singapore, 1995) p. 335. [7] G.P. Lopinski, M.G. Mitch, J.R. Fox and J.S. Lannin, in: Materials Research Society Symposium Proceedings, Vol. 359, eds. P. Bemier et al. (Materials Research Society, Pittsburgh, 1995)p. 307. [8] B.H. Toby and T. Egarni, Acta. Cryst. A 48 (1992) 336. [9] S.J.L. Billingeand T. Egami, Phys. Rev. B 47 (1993) 14386. [1o] F. Li, D. Ramage, J.S. Lannin and J. Conceicao, Phys. Rev. B44(1991) 13167. [11] R. Hu, T. Egami, F. Li and J.S. Lannin, Phys. Rev. B 45 (1992) 9517. [12] W.I.F. David et al., Nature 353 (1991)147. [13] S. Teslic, T. Egami and J.E. Fischer, Phys. Rev. Letters 51 (1995) 5973. [14] Q. Zhu et al., Phys. Rev. B 47 (1993) 13948. [15] R. Tycho, G. Dabbagh, D.W. Murphy, Q. Zhu and J.E. Fischer, Phys. Rev. B 48 (1993) 9097. [16] P.W. Stephens et al., Nature 351 (1991) 632. [17] O.F. Sankey and D.J. Niklewski, Phys. Rev. B 40 (1989) 3979. [18] G.B. Adams, J.B. Page, M. O'Keeffe and O.F. Sankey, Chem. Phys. Letters 228 (1994)485; G.B. Adams, J.B. Page, O.F. Sankey, K. Sinha, J. Menendez and D.R. Huffman,Phys. Rev. B 44 (1991) 4052. [19] G.B. Adams, J.B. Page, O.F. Sankeyand M. O'Keeffe, Phys. Rev. B 50 (1994) 17471. [20] G.B. Adams, M. O'Keeffe, A.A. Demkov, O.F. Sankey and Y.M. Huang, Phys. Rev. B 49 (1994) 8048. [21] G.B. Adams, O.F. Sankey, J.B. Page and M. O'Keeffe, Chem. Phys. 176 (1993) 61. [22] F.H. Allen et al., J. Chem. Soc. Perkin Trans. II SI (1987). [23]G.B. Adams and J.B. Page, unpublished.. [24] G.P. Lopinski,J.R. Fox and J.S. Lannin,Chem. Phys. Letters 239 (1995) 107.

conducting nature of the one-ball-per-cell electronic structure, which has a single electron in a half-filled state at the top of the valence band, the two-ball-

per-cell electronic structure is insulating, and the two-ball-per-cell QMD solution may, in fact, be related to the insulating phase of RbC60 observed to occur below 50 K [ 1]. However, in case of such

massive charge transfer, the non-self-consistent Harris energy functional approximation is expected to considerably exaggerate the magnitude of that charge transfer, as well as the resulting energy gain and distortions (we calculate an energy gain of 0.048 eV/ball). As a result, our two-bail-per-unit-cell

model must be regarded as only qualitative, even at low temperatures. Still, it is interesting that our calculated agreement factor for this model is 0.04473, about 20% better than the agreement for BCO-E'.

In summary, a model based on first-principles quantum molecular dynamics simulations gives good agreement with the measured pair distribution function for bco-RbC60. The present analysis indicates linkages of the fullerene molecules along the short direction in the orthorhombic unit cell with the C - C interfullerene bond distance estimated in the range 1.54-1.6 ,~. Conservatively estimating experimental errors would allow for values as high as 1.65 A.

Although the interfullerene linkages are similar to those proposed previously and suggest the formation of covalent intermolecular bonds, the present results involve considerably less distortion of the C60 molecules than reported by Stephens et al. [2]. The PDF analysis also indicates orientational disorder

between the polymer chains. Work at Penn State was supported by USDOE Grant DE-FG02-84ER45095. Work at the University

References