Dynamic origin of the orthorhombic symmetry of C60-n-pentane

~)

Solid State Communications,Vol. 89, No. 5, pp. 417-419, 1994 Copyright © 1994 Elsevier Science Ltd

Pergamon

Printed in Great Britain. All rights reserved 0038-1098/9456.00+.00 0038-1098(93)E0132-H

DYNAMIC

ORIGIN OF THE ORTHORHOMBIC C60-n-PENTANE

SYMMETRY

OF

G. Oszlanyi, G. Bortel, G. Faigel, S. Pekker, M. Tegze Research Institute for Solid State Physics, H-15~5 Budapest, POB. 49. Hungary ( R e c e i v e d 30 S e p t e m b e r 1993 by A. Z a w a d o w s l d ) In t h i s p a p e r we p r e s e n t the r e s u l t s of s i n g l e c r y s t a l x-ray diffraction e x p e r i m e n t s a n d molecu l a r d y n a m i c s s i m u l a t i o n s on C s 0 - n - p e n t a n e . T h i s m a t e r i a l is a t y p i c a l C s 0 - c l a t h r a t e a n d s h o w s o r t h o r h o m b i c s y m m e t r y at r o o m t e m p e r a t u r e . W e c o n c l u d e t h a t the o r t h o r h o m b i c s y m m e t r y can only b e e x p l a i n e d by t h e d y n a m i c s of b o t h C60 and n - p e n t a n e molecules.

on slightly distorted square layers of C60 molecules. The packing of the layers is alternating between close and loose packing and generates two channels per unit cell along the a direction. The composition of the samples has been determined 6. The 1 : 1 = Cs0 : n-pentane ratio and the size of the npentane molecules require that each channel contains two n-pentane molecules in the unit cell. We proposed a zigzag array of the n-pentane molecules which satisfies the experimentally determined composition. Figure 2. shows the y --- 0 and y = 1/2 a c planes of the structure. The direction of the zig-zag chain is along the a axis, the npentane molecules are in between the loosely packed layers but they extend into the neighboring closely packed layers. Although this model is consistent with the composition, further x-ray diffraction work was required to clarify the details of the structure and the origin of the orthorhombic symmetry. Our recent single crystal measurements clearly show t h a t the C60-n-pentane has an A-centred orthorhombie structure (u = 10.101(2) ~, b = 10.t63(2) h, c = 31.706(6) ,~). W i t h i n the 20 range all equivalent (:t:h, :[:k, +l) reflections were measured to check orthorhombic symmetry. Apart from the lattice centring condition the only systematic absence found was k = 2n -t- 1 for (h, k, 0) type reflections. This means that systematic absence conditions do not determine the space group uniquely, three space groups: A21ma, Aroma and Am2a have identical systematic absences. A21ma (equivalent to Cmc21) was chosen over Am2a and Aroma because packing considerations allow only this local symmetry. According to the A21ma symmetry the a-c plane of the structure is a mirror plane. The n-pentane molecules must lie on the mirror plane as shown on Fig. 2, but with this arrangement the van der Waals radii of the closest npentane and C60 molecules penetrate ( ~ 0.3 ~). To avoid this, the n-pentane molecules must turn around their long axis and slightly tilt out from the mirror plane. However, this molecular arrangement does not show orthorhombic symmetry. To solve this contradiction between symmetry and packing considerations both structure refinement and molecular dynamics simulations were performed. Structure refinement was carried out using the CRYSTALS program l°. 142 unique reflections were used in the refinement and using restraints the number of refined parameters were kept at a relatively low value. It was previously known from DSC measurements that C60-n-pentane shows a phase transition at 160 K H which was assumed to be connected to the orientational ordering of the C60 molecules as found in earlier studies on pure C60. Our initial a t t e m p t s focused on deciding if the Cs0 molecules rotate in the room temperature structure. We compared R factors between the model with rotating

In recent years extensive theoretical and experimental work has been done on Cs0 and related compounds. The understanding of the physical properties of these new materials requires the detailed investigation of the structures. However, the high symmetry of the C60 molecule poses unusual structural problems in these new materials. Even the simplest pure C60 shows interesting structural characteristics. At room temperature diffraction methods revealed a face centred cubic structure, which is not compatible with the icosahedral symmetry of the C60 molecule. This contradiction can only be resolved by the quasi free rotation of the Cs0 molecules as it was experimentally verified by NMR and diffraction methods L2. However, the charge distribution of the C60 molecule deviates from spherical s y m m e t r y 3,4. The full understanding of the microscopic picture behind the data is not yet complete. C60 compounds can show even more complicated structural behaviour. An interesting class of C60 compounds is C60 clathrates, where weak van der Waals forces stabilize the structure s. A representative member of these clathrates is the C60-n-pentane. This material is chemically well characterized and stable up to 400 K s . Previous structural studies have determined the C60 layer sequence of this material and suggested a zig-zag network for the n-pentane molecules 6, but a detailed structural study was still required. In this paper we present room temperature structural studies and molecular dynamics simulation on C60-npentane. We show that the orthorhombic symmetry of this material can not be understood by merely supposing the quasi free rotation of the C60 molecules. The dynamics of the n-pentane molecules plays an important role. C60 powder has been prepared and purified by the conventional method 7'8. The Cs0-n-pentane crystals were grown from saturated toluene solution of Cs0 due to the slow diffusion of petroleum ether as described in Ref. 6. The best single crystals were selected for single crystal diffraction experiments. These crystal diffraction measurements were performed on a four circle Huber diffractometer using graphite monochromatized CuK~ radiation. Reflections were collected in the 20 ~ 50 - 500 range. No radiation damage or aging of samples was observed. Several crystallites were measured in order to find good quality (not twinned) single crystals. The results described below were obtained from the measurements on a single crystal with a size of ~ 200 x 300 × 80/~m 3. In the first x-ray diffraction work on a multiply twinned Cs0-n-pentane crystal a monoclinie unit cell was found 9. This cell can be transformed to an A-centred orthorhombic cell, but the orthorhombic s y m m e t r y was not proved. Figure l. shows the "skeleton" of the structure based

417

C60_N_PENTANE

418

Vol. 89, No. 5

TABLE I. Refined positional parameters of the n-pentane carbon atoms and the center of the C60 molecule x 0.000 0.024 - 0.058 0.067 0.033 0.158

Cs0 CI C2 C3 C4 C5

y 0.000 0.000 0.000 0.000 0.000 0.000

z - 0.362 - 0.150 0.103 0.075 - 0.028 0.000

Since the resolution of our d a t a was severely limited by the small q range ( 0 - 3 . 4 / ~ - l ) covered in the experiment we did not expect to solve the s t r u c t u r e in a direct way. However, the i n f o r m a t i o n in the experimental d a t a was sufficient to o b t a i n the best orientation of the n-pentane molecules while keeping the o r t h o r h o m b i e s y m m e t r y . We used the above refined coordinates a n d tried to t u r n the n - p e n t a n e molecule a r o u n d its main axis. The mirror s y m m e t r y required by the space g r o u p was taken into account as two s y m m e t r y related molecules each with half occupancy. T h e results show t h a t the n-pentane molecule c a n n o t t u r n more t h a n 90 o away from the position on Fig. 2., w i t h o u t the R factor increasing significantly (R = 1 6 - 1 8 % ) . T h e orientation o f g 0 ° is unstable a n d it is driven t o w a r d s the 45 o position, which is the ideal configuration if the stretched n - p e n t a n e configuration is used. However, a n y position "close" to this ideal position (20 - 70") does not change during refinement, due to the low resolution, there is not enough driving force in the fit. We would like to emphasize t h a t the conformation of the n - p e n t a n e molecule is not rigid in the crystal, the molecule has more internal degrees of freedom (molecular f r a g m e n t s can t u r n a r o u n d the bonds) t h a n the above model suggests. This is well shown by the fact t h a t once the t h e r m a l p a r a m e t e r s of the n-pentane molecule are refined they increase considerably (Uc~ - Uc4 = 0.07 / ~ , Uc5 = 0.12 ~2). While the inclusion of two mirror related orientations with balf occupancies decreases the t h e r m a l p a r a m e t e r s of C 1 - C 4 atoms, the thermal par a m e t e r of the C5 carbon remains u n r e a s o n a b l y high (0.1O ]~2). T h i s is the end carbon a t o m of the n-pentane molecule which has a s y m m e t r y related (x + 1 / 2 , - y , z)

FIG. 1. Skeleton structure of C~o-n-pent~ne based on slightly distorted square layers of C~o molecules

C60 as a single " a t o m "~2 a n d several other models with different orientations of the rigid Cs0 molecule (compatible with the space group). While the rotating model yielded an R factor of 13%, fixed C~0 models were in the R = 25 - 30% range proving t h a t the Cs0 molecules do rotate at r o o m t e m p e r a t u r e . Once the largely correct description of C~0 was determined, we chose a rigid model for the n-pentane molecule in i t s stretched c o n f o r m a t i o n ( C 1 - C 5 a t o m s are coplanar, C - C bonds: 1.54 ~ , C H bonds: 1.09 /~, C C - C angles: 112 o , H - C H angles: 109 °, C1 C 3 = C 2 C 4 = C 3 - C 5 = 2 . 5 5 /~). Only the positional parameters of this model were refined constraining the carbon a t o m s of the n - p e n t a n e molecule on the a e mirror plane. The isotropic t h e r m a l p a r a m e t e r s of all a t o m s were fixed at ph~csically reasonable values (Uc = 0.04 .~2, Ucc,o = 0 A2). Table 1. s u m m a r i z e s the refined positional par a m e t e r s of the carbon a t o m s a n d the center of the C60 moLecule.

f~ o o

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l

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l

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-1 1

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\ FIG. 2. y = 0 and y = 1/2 planes of the (~s0-mpentane structure

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i

i

i

I 1 [ 1 1 1 1

i

59

o

_1

©

i

.<

t

t

t

i

i

,

i

i

,

i

t

t

~o z

-1

,

0 o t

I

i

~

i

I

i

i

-1

i

0 4000 8000 NUMBER OF STEPS

o

0 NUMBER

4000 OF

8000 STEPS

FI(-;. 3. Four quaternions describing the orientation of selected C60 and n-pentane molecules

Vol. 89, No. 5

C60-N-PENTANE

C5 n e i g h b o u r . T h e correlated motion of the two end f r a g m e n t s can a p p e a r in our fit as an u n r e a s o n a b l y high thermal parameter. A filrther c o m p l i c a t i o n already encountered in the case of pure fee Cs0 is the charge distribution of the Cs0 molecules. While in fcc C60 there were no positional par a m e t e r s to be refined, in the case of C60-n-pentane the s i t u a t i o n is m o r e complicated: positional p a r a m e t e r s a n d the charge d i s t r i b u t i o n should be refined simultaneously. Tiffs requires h i g h - q s y n c h r o t r o n d a t a on single crystals. In conclusion, the above results of the x-ray refinement s u p p o r t the s t r u c t u r e proposed for Cs0-n-pentane s. However on the basis of these results, we can not decide if the a - e mirror plane imposed is the consequence of d y n a m i c processes or static disorder. Molecular d y n a m i c s calculations based on a P a r r i n e l l o - R a h m a n type a p p r o a c h a3'14 is an ideal tool to solve this problem. Considering the weak van der Waais forces between molecules a n d neglecting i n t r a m o l e c u l a r degrees of freedora the use of classical equations of motion can be justiffed. T h e m a i n features of the model used are the following: - energy, pressure a n d n u m b e r of molecules are constant - f l u c t u a t i n g t e m p e r a t u r e , unit cell volume a n d s h a p e - periodic b o u n d a r y conditions - rigid Cs0 a n d n - p e n t a n e molecules - a t o m a t o m additive L e n n a r d - J o n e s potential At first the m e t h o d was applied to pure Cs0 a n d all i m p o r t a n t physical p a r a m e t e r s deduced from the model calculations agree well with e x p e r i m e n t a l d a t a 15. This makes us confident t h a t the model describes the system adequately. T h e n the m e t h o d was applied for C~0-np e n t a n e using a 2 × 2 × 2 unit cell containing 64 molecules (32 f o r m u l a units). T h e time evolution of the system was followed with a typical 0.01 psec step size for 1 0 - 3 0 thous a n d steps. T h e results of the calculations as an effect of cooling are presented elsewhere Is, here we consider only the r o o m t e m p e r a t u r e b e h a v i o u r of the system. In order to visualize the results of the vast a n m u n t of d a t a supplied by molecular d y n a m i c s calculations we m a d e a "movie" of the molecular motion in real space. T h e C60 molecules r o t a t e freely as in the pure fcc Cs0. T h i s is well shown by the four quaternions 17 describing the orientation of a single Cs0 molecule (see Fig. 3.). (:60 q u a t e r n i o n s take up all allowed values in the range [ - l , + l ] . In c o n t r a s t tim quaternions of np e n t a n e molecules change much m o r e rapidly (see Fig. 3.) a n d two of t h e m take up only two distinct values. This corresponds to a flip flop motion a r o u n d their long axis

which is clearly shown by the "movie". The n-pentane molecules s p e n d a p p r o x i m a t e l y equal times in the two positions which are related by an a - c mirror plane. This suggests t h a t the origin of the o r t h o r h o m b i c s y m m e t r y is d y n a m i c a l , only the time average of the s t r u c t u r e possesses o r t h o r h o m b i c s y m m e t r y . At this p o i n t we m u s t consider the possibility of a coupling between the rotation of the C60 molecules and the flip-flop m o t i o n of the n - p e n t a n e molecules. No correlation can be seen in the results of molecular d y n a m i c s calculations. This is s u p p o r t e d by the large difference between the characteristic time of the rotation of C60 a n d the characteristic time of the flip-flop motion of npentane. However, it is not trivial t h a t these motions r e m a i n i n d e p e n d e n t at lower temperatures. The s t u d y of this problem is u n d e r way. Finally, we m u s t make a r e m a r k on the space g r o u p s y m m e t r y of the structure. T h e other possible space groups ( A m m a a n d A m 2 a ) were excluded on the basis of local s y m m e t r y considerations. However, if n-pentane vacancies are existent in the s t r u c t u r e we can envisage a m e c h a n i s m leading to an average s t r u c t u r e which shows the A m m a s y m m e t r y . The e n a n t i o m o r p h of the structure can be g e n e r a t e d by a p p l y i n g a mirror s y m m e t r y on the b - c plane (see Fig. 2.). This t r a n s f o r m a t i o n resuits in a s t r u c t u r e whicl~ gives identical s t r u c t u r e factor a m p l i t u d e s to the original structure, only the phases differ slightly. T h e two s t r u c t u r e s can not be distinguished by x - r a y diffraction. If there is an n-pentane vacancy in the s t r u c t u r e , t h r o u g h a one-by-one slip m e c h a n i s m of n - p e n t a n e molecules, the original structure can transf o r m into its e n a n t i o m o r p h . If the t r a n s f o r m a t i o n is not cmnplete it can result in an average s t r u c t u r e which possesses A r o m a s y m m e t r y . As the phases of the two enant i o m o r p h s differ only slightly, the s t r u c t u r e factors for the average s t r u c t u r e will differ from the original even less. T h e quality of our present x-ray d a t a is not sufficient to decide this problem. However, this has no effect on the above discussed d y n a m i c s of n-pentane molecules which is required for o r t h o r h o m b i c s y m m e t r y in any case. In this p a p e r we have reported joint results of struct u r a l refinement a n d molecular d y n a m i c s simulation on Cs0-n-pentane. We have concluded t h a t the experimentally observed o r t h o r h o m b i c s y m m e t r y of this material can only be explained by t a k i n g into account the d y n a m ics of n - p e n t a n e molecules, a n d only the time averaged s t r u c t u r e shows o r t h o r h o m b i c s y m m e t r y . A c k n o w l e d g e m e n t - - This work has been supported by O T K A g r a n t s u n d e r c o n t r a c t numbers 2943, T4222 and T4474.

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