J. Phys. Chem. 1993,97, 5741-5744
5741
The Structure of C&x L. E. Hall,+D. R. McKenzie,'y+ M. I. Attalla,* A. M. Vassallo,*R. L. Davis,#J. B. Dunlop,l and D. J. H. Cockaynet School of Physics, University of Sydney, N.S.W. 2006 Australia, C.S.I.R.O.Division of Coal and Energy Technology, Delhi Rd., North Ryde, N.S. W. Australia, Australian Institute of Nuclear Science and Engineering, Private Mail Bag Sutherland, Australia, C.S.I.R.O.Division of Applied Physics, Lidfield, N.S.W. Australia, and Electron Microscope Unit, University of Sydney, N.S.W. 2006 Australia Received: January 1 1 , 1993
Electron and X-ray diffraction techniques have been used to study the structure of polycrystalline C6oH36 with 10-1 5% C70H36. X-ray diffraction has shown that the molecular packing is body-centered cubic. Electron diffraction data were converted to a reduced density function by Fourier transformation. Comparison of the reduced density functions for three molecular models shows that C60H36 is best described by a structure having D3d symmetry. These results are consistent with recent solid-state 13Cnuclear magnetic resonance and infrared spectroscopy studies. The D3d structure has an oblate spheroidal shape for which we show body-centered cubic packing to be more efficient than the face-centered cubic packing of C60.
Introduction The molecule C60H36 is a hydrogenated derivative of the fullerene molecule c60 which has recently been prepared using high-pressure hydrogenation.' The aim of this work is to study the molecular structure and molecular packing of in the solid state. The hydrogenation of 36 carbon atoms in the C ~ O sphere will necessarily lower its symmetry because of the local distortion resulting from the higher hybridization of protonated carbons. As is the case with c60 itself, dynamic or static disorder limits the use of conventional X-ray crystallographictechniques for the determination of the internal molecular structure. Accordingly, we have used a method based on evaluationof radial distribution information obtained by Fourier transformation of the scatteredintensity. This method has been used for determining the internal structure of the C70 molecule2from electrondiffraction data and for determining the structure of c 6 0 using neutron diffraction data.3 The molecular packing of both C60 and C70 is ~ , room ~ temperature with a transition, facecentered cubic ( ~ C C ) at in the case of c 6 0 , to simple cubic at temperatures below 249 K.4 The electron diffraction data are supplemented with X-ray powder diffraction data for lattice type and parameter determination. Specimen heparation
The material used in this study was prepared by high-pressure hydrogenation of fullerite containingapproximately 10-1 5%C70. The product was shown to consist predominantly of CsoH36 with approximately 10-15% C70H36, using a combination of mass spectrometry (FABIMS) and solid-state 13CNMR.' For the electron diffraction studies, the powder was dissolved in nitrobenzene, and the resulting solution was allowed to evaporate on the surface of a salt crystal. The salt was subsequently dissolved in distilled water, allowing a free-standing film of CmH36 to be collected on a copper grid.
Electron M r a c t i o n Electron transmission diffraction was carried out using 300keV electronsin a Philips EM430 electron microscope fitted with Author to whom corruipondence should be addressed. University of Sydney. 1 C.S.I.R.O. Division of Coal and Energy. 8 Australian Institute of Nuclear Science and Engineering. C.S.I.R.O. Division of Applied Physics. +
0022-3654/93/2097-5741$04.00/0
a Gatan parallel electron energy loss spectrometer (PEELS)and a Gatan CCD camera. The principal advantage of electrons in determining the internal structure of molecules lies in their relatively short wavelength, enabling data to be collected to large values of s = (2 sin O)/A. The range covered in this study was 0.01 < s < 3.50 A-1, enabling extensive sampling of the diffuse scattering resulting from the orientational disorder to be carried out. In our technique: the diffraction pattern is scanned under computer control and the data are collected into the computer for processing. Two variations of the collection technique were used. The first technique was the same as described previously5 and employed the PEELS spectrometer to remove inelastic scattering. The second technique employed the CCD camera to collect intensity from a range of scattering anglessimultaneously, with the final data set being obtained by merging the data from eight regions. Sufficient overlap was arranged between regions to enable accurate scalingvia least-squaresfits. In each case, the raw intensity I(s) was converted to a reduced intensity function defined by
@(s) = (I(s) - NflS)*)/NflS)*
(1) where N is a scaling factor and f is the atomic scattering factor for carbon? @(s) was then converted to the reduced density function G(r) by Fourier transformation
G(r) = 8 r ~ " " s 4 ( s )sin 2rsr dr
(2)
The function s y s ) is shown in Figure 1. This functionprovides a more convenient way of displayingthe scattered intensity than does the raw intensity I(s), owing to the large dynamic range of I@). Both data collection procedures gave a similar result for G(r), which is shown in Figure 2. Peaks in G(r) correspond to interatomic distances. Since carbon is a much stronger electron scatterer than hydrogen, the peaks in G(r)will represent carboncarbon correlations only. The closed cage shape of the molecule is clearly shown by the termination of interatomic correlations at a definite distance, after which G(r) becomes negative. The orientationaldisorderis shown by the lack of any sharpcorrelations between atom positions in neighboring molecules, although, as we discuss later, there are broad peaks in C(r) corresponding to intermolecular positional correlations. Q 1993 American Chemical Society
Hall et al.
5742 The Journal of Physical Chemistry, Vol. 97, No. 21, 1993
b 0.8
0.7 0.6 0.5
0.4
0.3 0.2
0.1
d
0
.0.1 .0.2 0
1.5
1
0.5
2
2.5
3
3.5
s (d') Figure 1. Reduced intensity function of C60H36 as a function of s = ( 2 sin @)/A obtained using energy-filtered electron diffraction.
0
4 S 6 7 8 9 10 R (Angstroms) G(r) from two different data collection Figure 2. Comparison of techniques: (A) PEELS collection and (B) CCD collection.
1
3
2
Figure 3. Three possible structures Of CmH36: (a) Th, looking down one c3 axis; (b) 4 view perpendicular to c3 axis; (c) 9 1 , looking down one c3 axis; (d) D3d view perpendicular to c3 axis; and (e) D3d, looking down one c3 axis.
Molecular Modeling The experimentally determined G(r) was compared with the calculated G(r) from three different molecular structures. The first of these was based on the structure obtained by Dunlap et al.' having a Th symmetry. Dunlap et al. obtained coordinates using local density functional (LDF) calculations with a PerdewZunger (PZ)* fit to the free electron gas results of Ceperley and Alder.9 We have investigated two other isomers, one having C,, symmetry and the other having D j d symmetry. We used a calculation in which initial coordinates of these three models were relaxed using semiempirical techniques (MNDO carried out on a CRAY computer using the UniChem package), repeating the procedure until no further adjustments were made. The coordinates of the Th structure did not change significantly from those given by Dunlap et a1.2 whereas the other two models relaxed from the initial hypothetical structure into lower energy configurations. The three resulting molecules are shown in Figure 3. In all calculations,we placed the hydrogen atoms on the outside of the molecule. The common feature of the hydrogenation pattern of the Th and D3d structures is the "double Y"pattern in which hydrogen atoms are attached to the set of six neighboring carbon atoms lying in pentagons bonded at their vertices. The coordinates were used to calculate G(r)by using the Debye formula to calculate the diffracted intensity: sin 2rsrm,, ~ ( 8 )=
FJ-'fm(s)Jn(s) m
n
Zusr,,,,,
(3)
I
.8
"
0
'
~
"
2
"
"
'
4
~
"
I "
6
'
~
8
10
R (Angstroms) Figure 4. Comparison of predicted with experimental G(r) of C60H36.
where r,,,. is the distance between atom m and atom n in the molecule and$ is the atomic scattering factor for atom i obtained from tables of Doyle and Turner.6 The Debye formula (eq 3) gives the intensity which would result from a specimen consisting of molecules randomly oriented with respect to the incident electron beam and without spatial correlation, as in a gas. The G(r) function was then calculated by treating the calculated intensityin thesame wayas themeasured intensity. Theresulting values of G(r) were then compared to the measured G(r) over a range of r corresponding to intramolecular distances, as shown in Figure 4. In order to rank the proposed structures in order of their agreement with experiment, the mean-square deviation of each calculated G(r) from the experimental G(r) was evaluated using intervals of 0.02 A between 0.9 and 10.0 A. The results are shown in Table I. The model providing the best fit is clearly
Structure of CmHj6
The Journal of Physical Chemistry, Vol. 97, No.21, 1993 5743
TABLE I: Mean-SquareDeviation of Predicted C d x C(r) Fuactioas from the ExperimentPl C(r)Function model symmetry mean-square deviation A, proposed D3d 0.7816 B, Attalla et a1.l C, Dunlap et aL6
0.8889 1.253
9 1
Th
TABLE Ik Coordinates of tbe Relaxed Dj,,Isomer of C6OHu X
Y
X
Y
1
-1.300 -2.714 -2.744 -3.278 -3.701 -2.962 -2.583 -2.022 -0.876 0.421 0.745 1.829 1.464 2.005 1.258 -0.178 -1.220 -2.527 -3.310 -2.182 -2.693 -1.824 -0.423 0.088 -0.703 -0.767 0.755 1.188 2.871 2.925
2.710 2.295 0.981 -0.032 0.511 -0.307 -1.586 -2.219 -3.135 -2.434 -1.605 -0.660 0.672 1.686 2.964 2.610 3.370 2.541 2.016 1.572 0.142 -1.017 -0,700 0.763 1.649 3.713 3.791 3.401 2.368 1.364
-1.129 -1.121 -1.864 -1.052 0.288 1.273 1.066 2.284 1.946 2.114 3.297 2.843 3.054 2.265 1.941 1.978 1.241 1.489 0.284 2.612 2.662 3.282 3.187 3.658 2.773 -0,164 -0.523 0.549 0.125 1.253
1.228 -1.326 2.067 4.353 -2.263 -2.870 3.084 4.891 2.894 -4.762 -4.344 -3.757 -3.314 -0.391 3.999 -1.271 1.319 -2.088
4.687 4.220 3.607 1.785 4.141 2.739 -1.631 -0.699 -0.020 0.429 -0.754 -2.677 -1.930 -0.505 -2.692 4.659 4.235 -3.621
2
3.0Id
2.5
Id
2.0
Id
,
,
,
,
,
,
,
,
,
,
,
,
,
,
,
,
,
,
1.5 Id
1.0
Id
Carbon 0.707 2.198 2.710 1.850 0.427 -0.075 -1.45 1 -1.830 -0.737 -0,403 0.879 2.035 2.541 2.910 3.682 3.292 2.533 1.216 0.178 -1.250 -1.996 -2.9 18 -2.892 -1.790 -0.771 0.775 1.306 2.711 2.738 3.286
-1.589 -1.589 -0,151 1.019 0.694 -0.779 -0.674 0.662 1.614 2.399 3.136 2.245 1.590 0.305 -0.501 -2.001 -2.563 -3.378 -2.564 -2.945 -1.681 -1.359 -2.369 -3.392 -3.805 -3.750 -2.753 -2.300 -0.982 0.035
-2.686 -2.686 -2.686 -3.301 -3.191 -3.659 -3.055 -2.861 -3.304 -2.086 -1.966 -2.322 -1.087 -1.283 -0.304 -0.281 -1.486 -1.231 -1.918 -1.926 -2.266 -1.265 -0.147 -0.539 0.520 0.182 1.149 1.122 1.842 1.045
-4.288 -0,480 -3.673 -3.240 1.467 -0.907 4.807 -1.209 2.357 3.354 -0.979 -3.874 1.330 4.283 2.854 -1.062 0.472 3.701
2.587 -0.885 0.124 3.292 3.774 -3.989 0.408 4.720 4.360 -3.067 -4.899 -2.897 4.345 -2.547 2.884 2.299 0.874 -0.136
0.313 4.906 3.231 1.958 2.700 2.688 0.462 -0.421 0.752 1.637 0.704 -0.018 -1.799 -0.295 -2.756 -4.126 -4.905 -3.216
Hydrogen 0.136 -2.381 -2.598 -1.372 1.087 -2.828 -3.332 0.951 3.852 1.198 -2.366 -1.423 3.247 4.779 0.863 -0.077 2.402 2.565
the proposed Djd structure. The coordinates of the relaxed structure are given in Table 11. This structure is of lower symmetry than that studied by Dunlap et al.' The NMR spectrum of the sample used in this work has recently been measured.I Of the three proposed structures discussed here, the D3dstructureprovides the best fit with experiment, as it has six different kinds of carbon atoms to match the six observed peaks in the NMR spectrum.
X-ray Diffraction For X-ray studies, a pressed powder sample 20 mm in diameter and 2 mm thick was prepared. Intensity data using Cu Ka radiation were collected over the range 0.022 < s < 1.175 A-I, where s = (2 sin O)/X = l/d. The raw diffracted intensity is shown in Figure 5. The peak
5.0 I @
0.0 108 0
0.4
0.2
S
1
0.8
0.6
(k')
Figure 5. X-ray diffraction pattern of C6OH36 showing indices for some reflections of a bcc lattice with a lattice constant of 11.785 A. 40
-10 -20 "
-30 0
"
I
10
'
"
'
I
'
'
"
20
I
30
'
"
'
I
40
'
so
R (Angstroms)
Figure 6. Comparison of the intermolecular packing G(r)of an ideal bcc lattice with the experimental C ( r ) .
positions were well fitted by a body-centered cubic (bcc) lattice model with a cubic cell dimension of 11.785 f 0.015 A. Data collected at liquid nitrogen temperature revealed no new peaks and gave a lattice parameter of 1 1.715 f 0.015 A. The lattice parameter results gave a thermal expansion coefficient of (2.7f 0.8) x 10-5 K-1. The body-centered cubic structure represents a remarkable departure from the face-centered cubic structure shown by C ~ O and C70. The X-ray data were processed to a G(r) following the same procedures as used for the electron diffraction data except that the X-ray atomic scattering factor for carbon was used in place of the electron atomic scattering factor. The resulting G(r) is shown in Figure 6 and is well fitted by the expected G(r) for a bcc array of atoms. The small discrepancies in peak positions for the first four peaks are probably due to the fact that the molecule is best modeled by a hollow sphere of electron density rather than an atomlike distribution, as assumed in the calculation. The eight nearest-neighbor distancts between molecular centers along the body diagonals in the bcc structure of CsOH36, namely, 10.206 A, are only slightly larger than the 12 nearest-neighbor distances, 10.04A, along face diagonals in c60.'0 On the other hand, the six next-nearest-neighbor distances, 11.785 A, are significantly larger than the nearest-neighbor distance in fcc Cm. This allows the bcc packing to accommodate the nonspherical C60Hj6 molecule more effectively than would a fcc structure. The distortionof the molecule brought about by the hydrogenation, together with the presence of hydrogen atoms around the equator, gives the molecule a strongly oblate character. The bcc structure allows effective packing of oblate spheroids if the polar axes of the molecules are aligned. The longer second-nearest-neighbor distance then prevents close approachesof the equatorial hydrogen atoms. If this alignment does occur, then there should be a
Hall et al.
5744 The Journal of Physical Chemistry, Vol. 97, No. 21, 1993
tendency to form a tetragonal structure with a cla ratio of less than 1. Such a tetragonal distortion is not observed at the temperaturesat which our data were collected;however, a possible reason for this is that the tetragonal axes of small domains are on average distributed equally among the three cubic axes, giving a cubic structure overall. If this structural model is correct, at very low temperatures the axes should align throughout the specimen, giving a tetragonal distortion.
Discussion and Conclusion The structure which provides the best agreement with experimental data for C60H36 as produced under high-pressure hydrogenation conditions is the relatively low-symmetry D3d structure. The packing of the molecules in the crystalline state is found to be bcc,as compared with fcc for CSO.On the basis of a structural model in which the polar axes of the D3d molecule are aligned locally, we predict that the bcc crystal structure will transform to a body-centered tetragonal structure at sufficiently low temperatures.
Acknowledgnmt. L. Hall thanks the Science Foundation for Physics, University of Sydney, for their financial assistance, without which this work could not have been completed.
References and Notes (I) Attalla, M. I.; Vassallo, A. M.; Hanna, J. V.; Finnic, K. S.;Pang, L. S.K.; Tattum, B. J. Phys. Chem., submitted for publication. (2) McKenzie, D. R.; Davis, C. A.; Cockayne, D. J. H.; Muller, D. A,; Vassallo, A. M. Nature 1992, 355, 622. (3) Li, F.; Ramage, D.; Lannin, J. K.; Conceicao, J. Phys. Rev. B 1991, 44, 13167. (4) Heiney, P. A.; Fischer, J. E.;McGhie, A. R.; Romanow, W. J. A,; Denenstein, M.; McCauley, J. P.; Smith, A. B. Phys. Rev. Lett. 1991, 66, 2911. (5) Cockayne, D. J. H.; McKenzie, D. R.; Mulier, D. A. Microsc. Microanal. Microstruct. 1991, 2, 359. (6) Doyle, P. A.; Turner, P. S.Acta Crystallogr. 1968, A24(3), 390. (7) Dunlap, B. I.; Brenner, D. W.; Mintmire, J. W.; Mowrey, R. C.; White, C. T. J. Phys. Chem. 1991, 95, 5763. (8) Perdew, J. P.; Zunger, A. Phys. Rev. B 1981, 23, 5948. (9) Ceperley, D. M.; Alder, B. J. Phys. Rev. k t r . 1980, 45, 566. (10) Fleming, R. M.; Siegrist, T.; Marsh, P.; Hessen, B.; Kortan, A. R.; Murphy, D. W.; Haddon, R. C.; Tycko, R.; Cabbagh, G.; Mujsce, A. M.; Kapian, M. L.; Zahurak, S . M. Mater. Res. SOC.Symp. Proc. (MRC Conference, Pittsburgh, 1991) 1991, 206, 691.
