Structure of haloform intercalated C60 and its influence
on superconductive properties
Robert E. Dinnebier1, Olle Gunnarsson1, Holger Brumm1, Erik Koch1,
Peter W. Stephens2, Ashfia Huq2, and Martin Jansen1,*
1
Max-Planck-Institut für Festkörperforschung
Heisenbergstrasse 1, D-70569 Stuttgart, Germany
2
Department of Physics and Astronomy
State University of New York, Stony Brook
New York 11974-3800, U.S.A
* To whom correspondence should be addressed.
E-Mail: [email protected]
CHCl3 and CHBr3 intercalated C60 have attracted particular interest after superconductivity up to
Tc=117 K was discovered. We have determined the structure using synchrotron x-ray powderdiffraction. The expansion due to intercalation mainly takes place in one dimension, leaving
planes of C60 molecules on an approximately hexagonal, slightly expanded lattice. We have
performed tight-binding band structure calculations for the surface layer. In spite of the slight
expansion of the layers, for the range of dopings where a large Tc has been observed, the density
of states at the Fermi energy is smaller for C60·2CHCl3 and C60·2CHBr3 than for C60. This
suggests that the lattice expansion alone cannot explain the increase of Tc.
1
The groundbreaking experiments of Schön et al. have demonstrated that chemical doping is not
the only way to make the Fullerenes metallic and superconducting. Using a field-effect transistor
setup they showed that pristine C60 can be field-doped and becomes superconducting with
transition temperatures Tc up to 11 K for electron doping (1) and 52 K for hole-doping (2). For
the chemically electron doped Fullerenes it is known that Tc increases with the lattice constant,
which is commonly explained by the corresponding increase in the density of states (3-5). This
was the motivation for investigating Fullerene crystals intercalated with inert molecules that act
as spacers to expand the lattice. And, indeed, it was found that Tc increases to spectacularly high
values of about 80 K for C60·2CHCl3 and 117 K for C60·2CHBr3, seemingly confirming the
assumption that in order to increase Tc one simply has to increase the density of states (6).
Here we report structure determinations of the C60·2CHCl3 and C60·2CHBr3 co-crystals and give a
comparison with pristine C60. We find that intercalation of chloroform and bromoform indeed
increases the volume per C60 molecule. That increase is mainly due to an expansion of the lattice
perpendicular to the close-packed planes, which are presumably the free surface on which the
superconducting FET's have been grown; the area per fullerene in these planes is only increased
slightly. In contrast to chemically electron-doped Fullerenes, which are bulk superconductors,
superconductivity in the field doped materials is confined to the immediate neighborhood of the
surface. The prepared surface is not necessarily a simple truncation of bulk; for example there
may be reconstruction, different fullerene orientations, a different concentration of intercalants,
etc. However, it is reasonable to expect that the lattice spacings of the 3D structure should persist
to the surface, and therefore estimates of the density of states (DOS) derived from the 3D
structure will provide a useful insight into the superconductivity. To understand the effect of
intercalation on the DOS at the Fermi energy, we have performed tight-binding calculations. We
find that, in contrast to what one would expect based on the increase in Tc, the DOS for pristine
2
C60 is actually larger than for the co-crystals in the doping range where a large Tc has been
observed. Comparing C60·2CHCl3 and C60·2CHBr3 we find that although the DOS differs
slightly, this is by far not enough to explain the difference in the observed transition
temperatures.
C60·2CHCl3 and C60·2CHBr3 were obtained by dissolving C60 in bromoform/chloroform with
further evaporation. High resolution X-ray powder diffraction data of C60·2CHCl3 and
C60·2CHBr3 were collected at various temperatures in a closed cycle helium cryostat at a
wavelength of 1.15 Å on beamline X3B1 of the Brookhaven National Synchrotron Light Source
in transmission geometry with the samples sealed in 0.7 mm lithiumborate glass capillaries (Fig.
1). The crystal structures of the different phases of C60·2CHCl3 and C60·2CHBr3 were determined
by Rietveld refinements (7) using flexible rigid bodies (8) (Fig.2). Details of the experimental set
up and the method of structure solution are given in Table 1 and in the supplementary material.
At room temperature, C60·2CHCl3 and C60·2CHBr3 are isotypic to magnesiumdiboride (9) (space
group P6/mmm, aluminumdiboride structure type) in which a primitive hexagonal packing is
formed by C60 molecules with the trigonal prismatic voids at (1/3, 2/3, 1/2) and (2/3, 1/3, 1/2)
fully occupied by chloroform or bromoform molecules, respectively. Therefore the structure can
be viewed as a sequence of alternating layers of C60 and intercalated molecules perpendicular to
the c-axis. With a six-fold axis through the center of the bucky ball (molecular symmetry 3m )
and inversion centers in the center of the chloroform and bromoform molecules (molecular
symmetry 3m ), a minimum of two fold disorder is created, whereas Rietveld refinements
confirm almost spherical shell electron density for the C60 molecule and at least threefold
disorder for the chloroform molecules (10-12).
Upon cooling, both materials pass through a monoclinic phase (which will be discussed
elsewhere) into a fully-ordered low temperature triclinic phase (space group P 1 ) at ∼150 K with
3
cell dimensions similar to those of the hexagonal room temperature phase. The crystal structure
of the triclinic low temperature phase may be viewed as an anisotropically distorted hexagonal
room temperature structure. Whereas the dimensions of the hexagonal closed packed layers of
C60 molecules show only small distortions when compared to the room temperature structure, the
distance between the C60 layers (triclinic b-axis) increases considerably (Tab. 1), causing a
decrease in dimensionality. The C60 molecules are oriented such that two hexagons on opposite
sides of the C60 molecule are congruent with the triclinic b-axis (corresponding to the hexagonal
c-axis) running through the centers of the hexagons and one of their three short carbon-carbon
bonds oriented parallel to the c-axis (Fig. 3). This way, eight short bonds of a C60 molecule (two
in ±a- and ±c-direction each) face short bonds of neighbor molecules with twisting angles
between 60 and 90°. The differences in the orientation of the C60 molecules between the low
temperature phases of C60·2CHCl3 and C60·2CHBr3 are only marginal. The shortest carboncarbon distances (Tab.2) occur between the C60 molecules within a layer along the a- and c-axis
(~3.3 Å). In contrast, the shortest carbon-carbon distances between C60 molecules of consecutive
layers is increasing considerably when going from chloroform (~3.6 Å) to bromoform (~3.8 Å)
doped C60, which is in accordance with the observed increase in the lattice parameters. The
orientation of the chloroform and bromoform molecules in the two trigonal prismatic voids are
related by inversion symmetry. Two halogene atoms point towards the middle between two C60
molecules of consecutive layers, whereas the third halogen atom points either up or down.
Consecutive voids along the b-axis show the same orientation. The decrease of disorder from the
hexagonal to the triclinic structures is accompanied by a decrease of the average crystalline
coherence length (domain size) from approximately 7 µm down to 0.2 µm (in case of
C60·2CHCl3) causing severe peak broadening. It should be noted that despite the low quality of
the powder patterns at low temperature, the weighted profile R-value (R-wp) of the triclinic low
4
temperature phase is sensitive enough to determine the orientation of the C60 molecule within
reasonable accuracy: The R-wp of a completely misaligned C60 molecule deviates by more than
3%. Heating-cooling cycles showed pronounced hystereses (up to 40 K) and coexistence of the
different phases over a large temperature range. In general, the transition temperature and the
existence of the different phases of C60·2CHCl3 and C60·2CHBr3 depends strongly on their
thermal history. In the case of C60·2CHCl3, additional intermediate phases of low symmetry
occurred during slow cooling. At the low temperatures where superconductivity is observed
basically all material is transformed into the thermodynamically stable low temperature phase as
described above.
In the C60 compounds, the electron-phonon coupling λ is described as a product of an
intramolecular coupling and the electron density of states (DOS). Since the intramolecular
coupling should be essentially the same for all C60 compounds, the focus has been on the DOS,
since an increase in the DOS should increase λ and the superconductivity transition temperature
Tc. This widely accepted approach was successfully used to interpret the results for A3C60 (A= K,
Rb) (4) and it was the motivation behind the work of Schön et al. (6). Here we therefore compare
the different intercalated C60 compounds at fixed doping, as in A3C60. The main change is then
expected to be the increase in the DOS as the lattice is expanded (6).
To describe the electronic structure of C60·2CHCl3 and C60·2CHBr3 we use a tight-binding
formalism (13,14) that describes the variation of Tc for A3C60 (A= K, Rb) (15). We put one radial
2p orbital on each carbon atom and calculate the molecular orbitals (MO) of a free C60 molecule.
Only the five-fold degenerate hu MO is kept, and the hopping integrals between the hu MOs on
different molecules are calculated. The resulting Hamiltonian matrix is diagonalized. The
coupling to the CHCl3 or CHBr3 molecules is neglected, since their levels are energetically rather
5
well separated from the C60 hu (16) orbital. Since the strong electric field should confine the
charge carriers to the surface layer (2,19), we consider the close packed (010) and (111) surfaces
of the P 1 and Pa 3 (17) structures, respectively.
Fig. 4 shows the calculated densities of states. We focus on the doping range where substantial
Tc's have been observed ( p = 2....3.5). We find that the DOS for C60 exceeds that of C60·2CHCl3
− contrary to what was expected from the observed Tc's. This might seem surprising, given that
the surface area per molecule for C60·2CHCl3 (86.5 Å2) is larger than for C60 (85.4 Å2). The
reason is that the hopping mainly takes place via a few ``contact atoms''. The hopping thus
depends on the relative phases of the hu-orbitals at these atoms. These phases are relatively
unfavorable for the Pa 3 structure of pure C60 compared with the P 1 structure of C60·2CHCl3,
making the hopping somewhat weaker for C60.
In C60·2CHCl3 and C60·2CHBr3 the relative orientations of the molecules are similar. The lattice
expansion leads to an overall larger DOS, but over most of the doping range 2 to 3.5 the DOS is
increased by at most 10 %. Solving the isotropic Eliashberg equations using realistic parameters
(18) we find, however, that the DOS of C60·2CHBr3 would have to be about 25 to 35 % larger
than for C60·2CHCl3 in order to explain the change in Tc. Also for electron doping the difference
in Tc between C60·2CHCl3 and C60·2CHBr3 cannot be explained based on the DOS. The above
conclusions persist when the DOS is broadened by 0.2 eV, to simulate the effect of the large
phonon energy.
What might then cause the observed strong enhancement of Tc? What comes to mind first is that
superconductivity may not be limited to the surface layer. However, to obtain a substantial
doping, the levels in the surface layer have to be well separated from those in layers underneath
(19). Therefore their contribution to the DOS can be expected to be small. Also the strong electric
field in the surface layer may play an important role. Our estimates suggest, however, that its
6
effect on the DOS would not change the conclusions (20). There could also be some coupling to
the vibrational modes of CHCl3, which might tend to enhance Tc (21). The fairly large separation
of its levels from the C60 hu-orbital (16) suggests, however, that this coupling may be weak. For
CHBr3 the coupling could be stronger as its levels are closer to the C60 hu level. Finally, as
discussed above, the DOS is quite sensitive to the orientations of the C60 molecules, which could
be different at the surface. For instance, the CHCl3 and CHBr3 molecules, having a dipole
moment, would tend to align with the electric field at the surface, possibly influencing the
orientations of the molecules. The surface of pristine C60 could also be reconstructed in such a
way that its DOS is reduced.
Above we have based our discussion on the DOS at the Fermi energy. This is the accepted
approach for describing the variation of Tc for A3C60 (4), i.e., as a function of the lattice
parameter for fixed doping. However, it does not describe the strong doping dependence of Tc
(22), since the DOS of the merohedrally disordered A3C60 is rather constant (23). In addition, for
the electron-doped systems, field-doping and chemical doping give similar values of Tc (1,6).
This is surprising, since the reduced number of neighbours at the surface should lead to a larger
DOS and a correspondingly higher Tc. These problems raise questions about the conventional
interpretation in terms of the DOS.
7
Table 1:
Crystallographic data for the low temperature phase of C60·2CHCl3 and
C60·2CHBr3. R-p, R-wp, R-F2 refer to the Rietveld criteria of fit for profile and weighted profile
respectively, defined in (24).
Temperature [K]
Formula weight [g/mol]
Space group
Z
a [Å]
b [Å]
c [Å]
α [°]
β [°]
γ [°]
V [Å3]
ρ-calc [g/cm3]
2Θ range [°]
Step size [°2Θ]
Wavelength [Å]
µ [1/cm] (100% packing)
R-p [%]
R-wp [%]
R-F2 [%]
No of reflections
C60·2CHCl3
50
959.42
P1
1
9.8361(3)
10.0906(3)
9.8179(3)
101.363(2)
116.457(2)
79.783(2)
850.82(5)
1.872
5 - 49.76
0.005
1.15015(2)
20.8
7.9
10.0
21.6
756
C60·2CHBr3
80
1226.15
P1
1
9.8982(3)
10.3386(3)
9.8993(3)
100.951(2)
115.920(2)
78.202(3)
886.04(5)
2.298
3 – 44.0
0.003
1.15052(2)
35.4
9.0
11.7
16.3
607
8
Table 2: Selected bond lengths and torsion angles for the low temperature phases of C60·2CHCl3
at T= 50 K and of C60·2CHBr3 at T= 80 K. Realistic standard deviations have been
obtained by multiplication of the Rietveld estimates by a factor of 6 in accordance to
Ref. 25 and are of the order of 0.01 Ǻ for distances and 2° for the torsion angles.
Distances [Ǻ]
C―C (C60) intramol.
C═C (C60) intramol.
C―C (C60) intermol (along a, c)
C―C (C60) intermol (along a+c)
C―C (C60) intermol (along b)
C60-C60
C-Cl/Br intramol.
C-H intramol.
C-H intermol.
C-Cl/Br intermol.
C60·2CHCl3
C60·2CHBr3
1.45
1.39
3.26, 3.28
3.42
3.63
9.8361(3)
1.78
1.05 (fixed)
2.67
3.33
1.46
1.40
3.28, 3.30
3.51
3.81
9.8982(3)
1.97
1.05 (fixed)
2.78
3.33
Torsion angles [°]
C═C (C60) intramol.
76. 93
58. 59
9
Figure Captions:
Figure 1. Scattered X-ray (λ = 1.15015(2) Å) intensity for C60·2CHCl3 as a function of diffraction
angle 2Θ and temperature T. The temperature range of each scan is on the order of 10 K (cooling
on the fly).
Figure 2. Scattered X-ray intensity for C60·2CHCl3 at T= 295 (top), T= 170 (middle), and T= 50
K (bottom) as a function of diffraction angle 2Θ. Shown are the observed patterns (diamonds),
the best Rietveld-fit profiles (line) and the difference curves between observed and calculated
profiles in an additional window below. The high angle parts of the room temperature and the
low temperature phases are enlarged for clarity.
Figure 3. Crystal structure of the low temperature phase of C60·2CHCl3 at T= 50 K (isotypic to
C60·2CHBr3) in a view along b-axis showing the close relationship to the hexagonal room
temperature phase.
Figure 4. Density of states (DOS) for the (010) surface of C60·2CHCl3, C60·2CHBr3 and the (111)
surface of pure C60. Panel a) shows the DOS as a function of energy ε. We have introduced a 0.02
eV full width half maximum Lorentzian broadening. Panel b) shows the DOS as a function of the
hole doping p. For p from 2 to 3.5 a substantial Tc is observed.
10
1. J. H. Schön, C. Kloc, R. C. Haddon, B. Batlogg, Science 288, 656 (2000).
2. J. H. Schön, C. Kloc, B. Batlogg, Nature 408, 549 (2000).
3. M. J. Rosseinsky et al., Phys. Rev. Lett. 66, 2830 (1991).
4. R. M. Fleming et al., Nature 352, 787 (1991).
5. O. Gunnarsson, Rev. Mod. Phys. 69, 575 (1997).
6. J. H. Schön, C. Kloc, B. Batlogg, Science 293, 2432 (2001).
7. H. M. Rietveld, J. Appl. Crystallogr. 2, 65 (1969).
8. R. E. Dinnebier, Powder Diffr. 14, 84 (1999).
9. M. E. Jones, R. E. Marsh, J. Am. Chem. Soc. 76, 1434 (1954).
10. M. Jansen, G. Waidmann, Z. Anorg. Allg. Chem. 621, 14 (1995).
11. G. Waidmann, Dissertation, (1996).
12. L. A. Solovyov, N. V. Bulina, G. N. Churilov, Russ. Chem. Bull 50, 78 (2001).
13. O. Gunnarsson, S. Satpathy, O. Jepsen, O. K. Andersen, Phys. Rev. Lett. 67, 3002 (1991).
14. N. Laouini, O. K. Andersen, O. Gunnarsson, Phys. Rev. B 51, 17446 (1995).
15. The intermolecular parameters are υσ = 0.296d exp(-(d-3.1)/L) eV, υπ = - υσ / 4 and L =
0.91Å, where d is the atomic separation. L was adjusted to obtain a variation of N(0) (26,27)
needed to describe the Tc of A3C60 (A = K, Rb). The intramolecular hopping integrals are 3.17 and -3.40 eV for the single and double bonds, respectively.
16. Density functional calculations put the highest occupied and lowest unoccupied MOs of a free
CHCl3 molecule 1.7 eV below and 3.5 eV above the hu-orbital of the free C60 molecule,
respectively. The corresponding numbers for CHBr3 are 1.1 and 2.7 eV.
17. To make the calculations for the P 1 and the Pa 3 structures as comparable as possible, the
C60 coordinates determined for C60·2CHCl3 were used also for the Pa 3 structure, instead of
the slightly different coordinates found by David et al. (28)
11
18. Guided by estimates from photoemision (26), we have, e.g. , used a single Einstein phonon
with the energy 1000 K, the Coulomb pseudopotential µ = 0.4 and the band width 0.5 eV, as
well as variations around this parameter set.
19. S. Wehrli, D. Poiblac, T. M. Rice, Eur. Phys. J. B 23, 345 (2001).
20. Applying an electric field of 0.2 V/Ǻ in a nonself consistent calculation left the relative
magnitudes of the DOS for C60 and C60·2CHCl3 largely uncharged in the doping range from 2
to 3.5.
21. A. K. Bill, V. Z. Kresin, (unpublished).
22. T. Yildirim et al., Phys. Rev. Lett. 77, 167 (1996).
23. M. P. Gelfand, J. P. Lu, Phys. Rev. Lett. 68, 1050 (1992).
24. J. I. Langford, D. Louer, Rep. Prog. Phys. 59, 131 (1996).
25. R. J. Hill, L. M. D. Cranswick, J. Appl. Crystallogr. 27, 802 (1994
26. O. Gunnarsson et al., Phys. Rev. Lett. 74, 1875 (1995).
27. M. Schluter, M. Lannoo, M. Needels, G. A. Baraff, D. Tomanek, J. Phys. Chem. Solids 53,
1473 (1992).
28. W. I. F. David et al., Nature 353, 147 (1991).
29. Acknowlegments: O.G. thanks the Max-Planck-Forschungspreis for support. Research carried
out in part at the National Synchrotron Light Source at Brookhaven National Laboratory, which
is supported by the US Department of Energy, Division of Materials Sciences and Division of
Chemical Sciences. The SUNY X3 beamline at NSLS is supported by the Division of Basic
Energy Sciences of the US Department of Energy under Grant No. DE-FG02-86ER45231.
12
Te
mp
era
t
ure
[
K]
288
260
228
203
195
169
145
123
93
74
56
41
34
14.00
14.50
15.00
15.50
16.00
16.50
17.00
2Θ[°]
13
14
b
a
c
15
16
Supplementary data
X-RAY DIFFRACTION EXPERIMENTS:
X-ray powder diffraction data of C60·2CHCl3 and C60·2CHBr3 were collected at various
temperatures in a closed cycle helium cryostat on beamline X3B1 of the Brookhaven National
Synchrotron Light Source in transmission geometry with the samples sealed in 0.7 mm
lithiumborate glass (No. 50) capillaries (Fig. 1 and Fig. 1 in the paper). X-rays of wavelength
1.15 Å were selected by a double Si(111) monochromator. Wavelengths and the zero point have
been determined from eight well defined reflections of the NBS1976 flat plate alumina standard.
The diffracted beam was analyzed with a Ge(111) crystal and detected with a Na(Tl)I
scintillation counter with a pulse height discriminator in the counting chain. The incoming beam
was monitored by an ion-chamber for normalization for the decay of the primary beam. In this
parallel beam configuration, the resolution is determined by the analyzer crystal instead of by
slits (1). Data of the low temperature phases were collected at T= 50 K in steps of 0.005°2Θ for
3 seconds from 3° to 51.265° at each 2Θ for C60·2CHCl3 and at T= 80 K in steps of 0.003°2Θ for
5.1 seconds from 6° to 20.316° and in steps of 0.005°2Θ for 3.3 seconds from 14.0° to 44.0° at
each 2Θ for C60·2CHBr3. The samples were rocked by 10°Θ for C60·2CHBr3 and 3°Θ for
C60·2CHCl3 during measurement for better particle statistics. Further experimental details are
given in Tab. 1. Data reduction was performed using the GUFI (2) program. Indexing of powder
patterns at low temperature with ITO (3) led to primitive triclinic unit cells with similar volumes
as compared to the hexagonal room temperature phases with lattice parameters given in Tab. 1.
The number of formula units per unit cell could be determined to Z = 1 from packing
considerations, indicating P 1 as the most probable space group, which could later be confirmed
17
by Rietveld refinements (4). The peak profiles and precise lattice parameters were determined by
LeBail-type fits (5) using the programs GSAS (6) and FULLPROF (7). The background was
modeled manually using GUFI. The peak-profile was described by a pseudo-Voigt function in
combination with a special function that accounts for the asymmetry due to axial divergence (8,
9). Low angle diffraction peaks of the triclinic low temperature phases had a FWHM of 0.04°2Θ
for both compounds, compared to 0.01°2Θ for the disordered room temperature phases, which is
close to the resolution of the spectrometer.
Approximate positions of the C60 and chloroform respectively bromoform molecules could be
directly derived from the metric of the unit cells with respect to the corresponding room
temperature phase. Therefore, the next step consisted in Rietveld-refinements of the crystal
structures of the three phases for C60·2CHCl3 and for C60·2CHBr3 using the GSAS Rietveld
refinement package.
Since the shape of the C60 ball is known in very narrow limits this
additional information was used to stabilize the refinement by setting up flexible rigid bodies
(10). It is unnecessary to determine this molecular moiety which has a well established structure.
At the beginning of the refinement, the lengths of the C-C single and double bonds were
constrained to 1.4526 and 1.3925 Å respectively (10) leading to a radius of the bucky ball of
3.5459 Å, which was defined as a refinable parameter.
In all yet investigated phases of
C60·2CHCl3 and for C60·2CHBr3, the position of the bucky ball is also fixed by symmetry at the
origin of the unit cells. At room temperature, the spherical shell electron density of the C60 ball
caused by rotational disorder was sufficiently modeled by simply applying the space group
symmetry to the rigid body, thus creating a highly disordered molecule, allowing the rotational
parameters of the rigid body to be fixed. This important step reduced the number of refinable
parameters for the C60 molecule to 1 (radius) for the hexagonal phase, and 4 (3 rotations and
radius) for the monoclinic intermediate temperature and the triclinic low temperature phase. An
18
overall temperature factor was used for the entire C60 molecule. The non-centrosymmetric
chloroform and bromoform molecules have also been set up as rigid bodies with the carbonhalogen bond lengths as the internal degree of freedom, thus refining 7 parameters (3 translations,
3 rotations and 1 bond length). For the disordered high temperature phase, the bond lengths were
fixed at literature values. Lowering the space group symmetry of the low temperature phase to
P1 and refining additional degrees of freedom, did not result in an improvement of the
refinement. The final difference electron density map was featureless (< 1.0 electrons/Å3). It
should further be noted that the quality of the powder patterns of the low temperature phases is
quite low with a peak to background ratio of <= 7:1 for C60·2CHCl3 <= 14:1 and C60·2CHBr3
(high temperature phases >40:1 for C<0·2CHCl3 and C60·2CHBr3) and a FWHM of the sharpest
peaks of 0.04°2Θ for both compounds (high temperature phase 0.01°2Θ) with many closely
overlapping Bragg reflections, which explains the relatively low R-factors of the Rietveld
refinements. The size of the domains for coherent scattering was estimated according to the
Scherrer equation. Whereas the background of the powder patterns of the high temperature
phases of C60·2CHCl3 and C60·2CHBr3 is almost featureless, the low temperature phases exhibit a
strongly featured background which is indicative for local disorder which has not been
investigated any further.
EFFECTS OF ELECTRIC FIELD:
To test the effects of the electric field at the surface, we have applied a field with the strength 0.2
V/Å, and performed nonselfconsistent tight-binding calculations. This leads to an increase of the
square root of the second moment from 0.28 to 0.31 eV for C60·2CHCl3 and from 0.25 to 0.28 eV
for C60. This increase is due to a splitting of the hu level by about 0.13 eV and, to a smaller extent,
19
to a modification of the hopping matrix elements. Fig. 2 compares the DOS for the (010) surface
of C60·2CHCl3 and the (111) surface of pure C60. The figure illustrates that the DOS of C60
remains larger than for C60·2CHCl3 in almost the whole range of interest (dopings from 2 to 3.5).
The use of a nonselfconsistent calculation should overestimate the effects of the field. For
instance, applying the same field to a free C60 molecule in a selfconsistent calculation, the
splitting of the hu-level is reduced by a factor of seven.
EFFECTS OF FINITE PHONON FREQUENCIES:
The phonon frequencies extend up to 0.2 eV, and the average phonon frequency should be a
substantial fraction of the band width of about 0.6 eV. It is therefore interesting to consider an
average of the DOS around the Fermi energy. For this reason we have broadened the DOS by a
Lorentzian with the full width at half maximum (FWHM) of 0.2 eV, as shown in Fig. 3. The
figure illustrates that the DOS remains larger for C60 than for C60·2CHCl3 in the interesting
doping range.
EFFECTS OF CHANGING THE MOLECULAR ORIENTATIONS:
To illustrate the sensitivity of the hopping between the C60 molecules to the molecular
orientations, we rotated the C60 molecule in C60·2CHCl3 by just 5° around the b-axis. This
increases the second moment ε 2
of the DOS by 15 %. Rotating the molecules around the three
crystallographic axes we find that ε 2 changes by factors in the range 0.7-1.9. Since the DOS
behaves roughly as 1
ε 2 , this suggests that a change in the C60 orientation is likely to decrease
20
the DOS and a possible increase should be at most 15 % for C60·2CHCl3, still leaving it smaller
than for C60 for the doping range 2 to 3.5.
DOS FOR ELECTRON DOPED C60.
Fig. 4 shows the DOS for electron doped C60 as a function of the doping n. Over a substantial
doping range, the DOS is appreciably larger for C60·2CHCl3 and C60·2CHBr3 than for C60. This
may be in agreement with the larger Tc for these compounds, if one takes into account the finite
phonon frequencies and a corresponding averaging of the DOS. However, the DOS is comparable
for C60·2CHCl3 and C60·2CHBr3, and, as in the hole doped case, for these two systems, the
difference in Tc cannot be explained by the DOS.
21
Table 1:
Positional parameters and Ui/Å2 x 102 for the low temperature phases of
C60·2CHCl3 at T= 50 K, and C60·2CHBr3 at T= 80 K. The values of the
temperature factor are constrained to be equal for the C60 and for the chloroform
respectively bromoform molecules.
C60·2CHCl3
Atom
C60·2CHBr3
x/a
y/b
z/c
Ui
x/a
y/b
z/c
Ui
C1
C2
C3
C4
C5
C6
C7
C8
C9
C10
C11
C12
C13
C14
C15
C16
C17
C18
C19
C20
C21
C22
C23
C24
C25
C26
C27
C28
C29
C30
0.151(1)
0.270(1)
0.245(1)
0.011(1)
-0.015(1)
0.157(2)
-0.129(1)
0.099(1)
0.022(2)
-0.123(2)
0.184(2)
0.297(1)
0.373(1)
0.152(2)
0.231(1)
0.062(2)
-0.005(2)
0.339(1)
-0.089(2)
-0.122(2)
0.383(1)
0.400(1)
0.349(1)
0.315(1)
0.263(1)
0.345(1)
0.208(1)
0.279(1)
0.242(1)
0.172(1)
0.317(1)
0.228(1)
0.172(1)
0.347(1)
0.289(1)
0.290(1)
0.350(1)
0.203(1)
0.293(1)
0.324(1)
-0.025(1)
0.031(1)
-0.048(1)
-0.158(1)
-0.240(1)
0.081(1)
-0.190(1)
-0.187(1)
0.050(1)
-0.089(1)
-0.092(1)
0.010(1)
0.145(1)
-0.056(1)
0.085(1)
-0.214(1)
-0.139(1)
0.184(1)
-0.294(1)
-0.256(1)
0.149(1)
0.249(1)
0.353(1)
0.157(1)
0.265(1)
0.001(2)
0.017(1)
0.361(1)
-0.133(1)
-0.124(1)
0.397(1)
0.375(1)
0.293(1)
0.336(1)
0.250(1)
0.389(1)
0.264(1)
0.229(1)
0.319(1)
0.255(1)
0.053(2)
0.184(2)
0.163(2)
-0.094(2)
-0.116(2)
0.081(1)
-0.219(1)
0.010(2)
-0.040(1)
-0.193(1)
0.64(3)
0.64(3)
0.64(3)
0.64(3)
0.64(3)
0.64(3)
0.64(3)
0.64(3)
0.64(3)
0.64(3)
0.64(3)
0.64(3)
0.64(3)
0.64(3)
0.64(3)
0.64(3)
0.64(3)
0.64(3)
0.64(3)
0.64(3)
0.64(3)
0.64(3)
0.64(3)
0.64(3)
0.64(3)
0.64(3)
0.64(3)
0.64(3)
0.64(3)
0.64(3)
0.131(2)
0.254(2)
0.230(2)
-0.011(2)
-0.036(2)
0.140(2)
-0.150(2)
0.083(2)
0.007(2)
-0.141(2)
0.181(2)
0.291(2)
0.373(1)
0.157(2)
0.242(2)
0.052(2)
0.003(2)
0.348(1)
-0.095(2)
-0.120(2)
0.388(1)
0.397(1)
0.339(1)
0.320(2)
0.259(2)
0.357(1)
0.219(2)
0.269(2)
0.260(2)
0.189(2)
0.316(1)
0.230(2)
0.174(1)
0.343(1)
0.285(1)
0.289(1)
0.344(1)
0.202(2)
0.291(1)
0.319(1)
-0.022(2)
0.035(2)
-0.041(2)
-0.154(2)
-0.234(2)
0.081(2)
-0.189(2)
-0.179(2)
0.048(2)
-0.090(2)
-0.085(2)
0.017(2)
0.150(2)
-0.050(2)
0.089(2)
-0.206(2)
-0.134(2)
0.186(2)
-0.287(1)
-0.250(2)
0.139(2)
0.242(2)
0.347(1)
0.146(2)
0.256(2)
-0.007(3)
0.006(2)
0.354(1)
-0.141(2)
-0.134(2)
0.397(1)
0.374(1)
0.294(2)
0.340(1)
0.257(2)
0.385(1)
0.268(2)
0.235(2)
0.316(2)
0.256(2)
0.057(3)
0.185(2)
0.159(3)
-0.090(3)
-0.117(3)
0.088(2)
-0.213(2)
0.005(3)
-0.030(2)
-0.184(2)
3.26(3)
3.26(3)
3.26(3)
3.26(3)
3.26(3)
3.26(3)
3.26(3)
3.26(3)
3.26(3)
3.26(3)
3.26(3)
3.26(3)
3.26(3)
3.26(3)
3.26(3)
3.26(3)
3.26(3)
3.26(3)
3.26(3)
3.26(3)
3.26(3)
3.26(3)
3.26(3)
3.26(3)
3.26(3)
3.26(3)
3.26(3)
3.26(3)
3.26(3)
3.26(3)
Cl/Br1
Cl/Br2
Cl/Br3
C31
H1
0.5216(7)
0.2612(9)
0.279(1)
0.3866(6)
0.444(1)
0.5499(9)
0.5492(8)
0.3808(8)
0.4479(5)
0.368(1)
0.8103(9)
0.5119(7)
0.7290(9)
0.6577(6)
0.6117(9)
4.18(2)
4.18(2)
4.18(2)
4.18(2)
4.18(2)
0.5104(4)
0.1977(4)
0.2773(5)
0.3195(3)
0.3928(5)
0.5582(4)
0.5566(5)
0.3803(4)
0.4481(3)
0.3679(3)
0.7461(5)
0.4710(4)
0.7424(5)
0.6163(4)
0.5573(5)
5.19(1)
5.19(1)
5.19(1)
5.19(1)
5.19(1)
22
Figure Captions:
Figure 1.Scattered X-ray (λ = 1.15052(2) Å.) intensity for C60·2CHBr3 at T= 200 , and
C60·2CHBr3 at T= 80 K as a function of diffraction angle 2Θ. Shown are the observed patterns
(diamonds), the best Rietveld-fit profiles (line) and the difference curves between observed and
calculated profiles in an additional window below.
Figure 2. Density of states N(p) at the Fermi energy as a function of the doping p in the presence
of a field 0.2 V/Å. The figure compares results for the (010) surface of C60·2CHCl3 and the (111)
surface of pure C60. The figure illustrates that the DOS of C60 is larger than for C60·2CHCl3 in
almost the whole range of interest (dopings from 2 to 3.5).
Figure 3. Broadened density of states N(p) at the Fermi energy as a function of the doping p. The
DOS has been broadened by a Lorentzian with a FWHM of 0.2 eV to simulate the effect of the
finite phonon frequencies.
Figure 4.Density of states N(n) at the Fermi energy as a function of the electron doping n.
23
24
25
26
27
1. D. E. Cox, Handbook of Synchrotron Radiation, Vol.3, Ch. 5 Powder Diffraction, (Elsevier,
Amsterdam), (1991).
2. R. E. Dinnebier, L., 6. Jahrestagung der Deutschen Gesellschaft für Kristallographie (DGK),
Karlsruhe, collected abstract, 148 (1998).
3. J. W. Visser, J. Appl. Crystallogr. 2, 89 (1969).
4. H. M. Rietveld, J. Appl. Crystallogr. 2, 65 (1969).
5. A. LeBail, H. Duroy, J. L. Fourquet, Mater. Res. Bull. 23, 447 (1988).
6. A. C. V. D. Larson, R. B., GSAS, Los Alamos National Laboratory Report LAUR (Used
version: August 1997), 86 (1994).
7. J. Rodriguez-Carvajal, Abstracts of the Satellite Meeting on Powder Diffraction of the XV
Congress of the IUCr, (Toulouse, France), 127 (1990).
8. P. Thompson, D. E. Cox, J. B. Hastings, J. Appl. Crystallogr. 20, 79 (1987).
9. L. W. Finger, D. E. Cox, A. P. Jephcoat, J. Appl. Crystallogr. 27, 892 (1994).
10. R. E. Dinnebier, Powder Diffr. 14, 84 (1999).
28