M10350B
Supplementary Information
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Structural peculiarities of TDAE*C60 single crystal at low temperatures.
Bakhyt Narymbetov*, Hayao Kobayashi*, Madoka Tokumoto‡, Ales Omerzu†,
and Dragan Mihailovic†
*Institute for Molecular Science, Okazaki 444, Japan
‡Electrotechnical Laboratory, 1-1-4 Umezono, Tsukuba, Ibaraki 305, Japan
†Institute Josef Stefan, Jamova 39, 1000 Ljubljana, Slovenia
Since the discovery of a ferromagnetic transition in TDAE*C60 compound by Allemand et
al. [1] at about 16 K, a lot of efforts by many research groups have been made to investigate the low
temperature state of these crystals, but, however, the structural features of TDAE*C60 compound at
low temperatures were not still characterized by single crystal diffraction methods. There were
suggestions that orientations of C60 molecules may be important and the magnetism could be
strongly depend on the orientational state of the molecules [2,3]. In fact, high molecular symmetry
of C60s and their weak intermolecular interactions lead to orientational degree of freedom in solids.
It gives raise to order-disorder type phenomena which plays important role in the structural and
physical properties of materials based on C60. It is known that in pure C60 crystal fullerene
molecules rotate rapidly at room temperatures and freeze out below about 260 K, and a low
temperature state of the crystal is characterized to be orientationally disordered [4]. 13C NMR
studies of TDAE*C60 crystals have shown that the rotational motion of C60 molecules in this
compound freezes out below 150 K [5]. On the base of theoretical investigations it was suggested
that the orientational randomness of C60 molecules could be related to the spin-glass-like behavior
[3].
Earlier X-ray powder diffraction studies [6] indicated that TDAE*C60 is a 1:1 charge transfer
complex and that the structure has a C-centered monoclinic unit cell with the c-parameter equal to
9.965 Å and a symmetry of the space group was determined as C2/m. Later, the room temperature
structure of TDAE*C60 has been determined on the single crystal X-ray data and shown that the
space group of symmetry is C2/c with a doubling of the c-parameter: 19.992 Å with four formula
units per unit cell and rapidly rotating C60 molecules [7].
TDAE*C60 exists in two modifications, one ferromagnetic and one paramagnetic. Fresh
single crystals of TDAE*C60 when grown below 10 oC show no ferromagnetic behavior and are
paramagnetic down to 2 K, and upon annealing they transform into the ferromagnetic phase [8].
Recently we have carried out a structural analysis of an unannealed TDAE*C60 single crystal at
11K [9], which confirmed that the structure refined at room temperature by Golic et.al. [7] was
correct, where the TDAE units are located at the two-fold axes with the C=C double bonds parallel
to the c-axis. C60 anions are located at inversion centers and form a chain along the c-axis.
Here we describe low temperature X-ray diffraction studies of both unannealed and
annealed TDAE*C60 single crystals in temperature range 270 – 7 K as well as structure analysis of
annealed sample at 7K. These studies show that: 1) some structural changes occur below 50 K for
both samples and these changes have time-dependent character; 2) in annealed sample, in addition
to the conventional 120 o rotations, we find evidence of additional rotations of C60 molecules by ±60
o
about their threefold molecular axis.
The crystallographic parameters of both samples at elevated temperatures are in good
agreement with that reported earlier [7] and all diffraction reflections observed on X-ray oscillation
patterns are indexed in C2/c space group. The diffraction patterns have not revealed any essential
changes of the structures in temperature range 160 – 70 K, except that with decreasing of
temperature slight decreasing of reflections intensities are occurred. However, the remarkable
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changes of diffraction patterns are found for both samples below 50 K. At about this temperature an
appearance of diffuse lines on X-ray oscillation patterns of both samples is observed, which are
gradually transformed in a period of a few hours. Diffuse lines on the diffraction patterns from
unannealed sample disappear as the sample is kept at low temperatures for 3-4 hours, as can be seen
in Figs.1 (a) and (b), and all reflections observed can be indexed in C2/c space group. In the case of
annealed sample the diffuse lines are transformed into additional diffraction spots (Figs. 1 (c) and
(d)), the positions of which coincide with those for a primitive unit cell. The temperature
dependencies of lattice constants, shown in Fig. 2, testify to the presence of noticeable changes of
the b- and the c- parameters of both crystals with temperature at around 50K. These experimental
data testify to the existence of structural changes in TDAE*C60 crystals at around of this
a) th = 15 minutes
b) th = 4 hours
c) th = 15 minutes
d) th = 8 hours
Figure 1. The fragments of X-Ray oscillation patterns of TDAE*C60 single crystal: a) and b) – an
unannealed sample at 7K; c) and d) – an annealed sample at 20K; th is a time of keeping the sample at these
temperatures before starting the measurements.
temperature. It should be noted that these changes are reversible, i.e. above 50 K, on warming the
samples from low temperatures, the diffraction patterns of high-temperature state are restored. The
presence of features of crystal properties in TDAE*C60 at around 50K was observed earlier [10-12],
but it was not given of especial attention to these features. As it was mentioned above the C 60
molecules in TDAE*C60 rotate rapidly at room temperature and these rotations freeze out below
150K and suggested that the reorientation of C60 molecules and their orientational ordering occurs
below this freezing out temperature. However, in fact, it seems that freezing of C60 molecules with
orientational randomness takes place at these temperatures, and that the reflections intensities
decrease in temperature range 160-70K can to some extent testify to it. The real process of
molecular reorientations and the tendency to orientational ordering in TDAE*C60 arises below 50K.
The apperance of diffuse lines can be considered as a consequence of occurrence of the short-range
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order in the structure, i.e. short-range orientational correlations of C60 molecules, and further
disappearance of diffuse lines or their transformations to the additional sharp diffraction spots can
be an evidence of the fact that these correlations become long range.
Crystal structure analysis of the samples at low temperature has revealed the
structural peculiarities characteristic to these crystals. We have performed intensity data collection
from unannealed sample at several temperatures: 160, 30, 7 (the data collections were started shortly
after reaching the temperatures), and 11K (data collection was started after keeping the crystal at
this temperature for about 4 hours), and from annealed sample at 7K only. The crystal structure of
unannealed TDAE*C60 sample was solved on data collected at 7K in C2/c space group and shown
that the C60 molecules form linear chains along the c-axis of the crystal, which is the direction of the
shortest center to center distance between near neighbor fullerene molecules (9.915Å at that
temperature) and that there are very short contacts (the shortest one is 3.082Å) between adjacent C60
molecules along the chains. The obtained structural parameters were used as initial values to
analyze the intensity arrays collected at other temperatures. The refinement of the structures in
anisotropic approximation for all non-hydrogen atoms has revealed the features characteristic to this
compound. Figs. 3(a) and 3(b) show the molecular structures of C60 and of TDAE, obtained at 160
and 11K, drawn in the projections
Figure 3. ORTEP
drawings of molecular
structures of C60 and of
TDAE showing 50%
thermal ellipsoids.
Projections are along the
unique threefold axes of
C60 molecules.
a)
160 K
b) 11 K
along the C60's threefold axis. It is clearly seen there that the carbon atoms located close to the
equatorial plane of C60 have elongated thermal ellipsoids while the atoms located close to the
molecular threefold axis have the least values of thermal coefficients. This picture can be considered
as visualization of the rotating or strongly librating C60 molecule with the rotation/libration axis
coinciding with the threefold molecular axis of symmetry of C60.
The results of the structure analyses of unannealed crystal at rest temperatures show that
down to low temperatures relatively high values of thermal coefficients are kept. Table 1 shows the
isotropic-equivalent temperature factor Beqv values averaged over all symmetrically-independent
carbon atoms of C60 molecule, obtained at different temperatures. It is seen there that the least value
of Beqv corresponds to data obtained at 11K after keeping the sample at this temperature for about 4
hours. Nevertheless, the values of thermal coefficients, even at 7 and 11K, are remained high
enough to these temperatures and this fact does not allow us to exclude the possibility of the
orientational degree of freedom about unique threefold axis of C60 molecule in TDAE*C60 crystal
structure, i.e. the rotations by ±120 o.
It should be noted here that the orientation of the unique threefold axis of C60 in this
structure does not coincide with the main crystallographic axes of the crystal and makes angles 81,
24, and 68o with the a, b, and c-axes, respectively. The mutual locations of C60 and of TDAE
molecule are also shown in Figs. 3, where it can be seen that a carbon atom of one of the methyl
group of TDAE unit is located directly upon hexagonal face of C60 and at 160K this atom almost
lays on the threefold axis of C60.
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As was mentioned above, the diffraction pattern from annealed sample of TDAE*C60 have
shown the presence of additional diffraction spots and that there is a tendency of crystal structure to
transform from C-centered type of lattice to primitive one. Our attempts to solve the structure of
annealed crystal have failed to be satisfactory. The using of the structural parameters of unannealed
crystal, converted to the primitive set, as an original model of structure and refinement of the
parameters were not successful and resulted in high values of R-factors and unreasonable thermal
coefficients (some of them were negative) of individual atoms. Statistical analysis of the results of
this refinement showed that there is a large divergence between calculated and observed intensities
of reflections with hkl indexes satisfactoring to condition h+k=2n+1, i.e. for reflections responsible
for breaking of C-centricity of crystal lattice. The refinement of the structure in C2/c space group
with using the model of unannealed crystal structure also resulted in high value of R-factor, but the
temperature factors were all positive. The refinement in anisotropic approximation of thermal
coefficients resulted in the picture of molecular structure of C60 analogous to that for hightemperature structure of unannealed sample. The molecular structure of C60 obtained at this point is
shown in Fig. 4(a). Further we had tried to analyse schematically the obtained molecular structure of
C60 and found that the same schematic picture can be drawn by combining of two C60 molecules
rotated by ± 60o relatively to each other about their threefold axes of symmetry. The resulted picture
is shown in Fig.4(b), where painted areas mean the regions of molecule where carbon atoms are
located close to each other and the electron density is smeared because of it. The final schematic
picture is practically analogous to that observed experimentally in averaged structure with Ccentered unit cell. Taking into account of this fact we have tried in further refine the structure in the
approximation of this model, i.e. with taking two molecules with equal probability
Figure 4. Molecular structures of C60
in the crystal of annealed
TDAE*C60: a) in C2/c space group;
b) schematic representation of
averaged structure of C60 with two
orientations of molecule related to
each other by rotating on 60o
around the 3-fold axis. Filled figures
represent the overlap regions of
carbon atoms of the two molecules
in the resulted structure.
b)
a)
Table 2. The refinement data for an annealed sample of TDAE*C60
No. Observations
No.Variables
R
Max. peak in Final Diff.Map e-/Å3
Min. peak in Final Diff.Map e-/Å3
*)
C2/c
3361
334
0.22
1.44
-0.81
P2/c
5666
667
0.16
0.44
-0.41
C2/c *
3361
604 (313)**
0.059
0.23
-0.19
refinement with account of two orientations of C60 molecule;
in parentheses the number of restraints is given.
**)
at the same positions. As result the R-factor was essentially improved in spite of the fact that there
were restrictions to bond lengths and the temperature factors of individual carbon atoms were
refined in rigid-body approximation. 6:6 and 6:5 type bond lengths were restricted to 1.41 and 1.45
Å, respectively, within the standard deviation 0.01 Å. The individual atoms of TDAE molecule
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were not restricted and all non-hydrogen atoms refined in anisotropic approximation. The final Rfactor was 0.066 and Table 2 shows these refinement data in compare with the data on refinements
in primitive and C-centered sets without taking into account the orientational
Orientation I
Orientation II
Figure 5. Molecular structures of
C60 in two orientations (I and II,
ORTEPIII, 50% probability) in
the crystal of annealed
TDAE*C60, obtained on 7K data
by the refinement with taking
into account half-occupied
molecules rotated by 60o. The
bold (red) lines denote relative
orientations of C60.
differences. Thus, the obtained data testify that the low temperature state of annealed TDAE*C60
crystal is characterized by the presence of high degree orientational disorder, where besides the
conventional rotation of C60 molecule by 120o along the threefold axis, there is an additional
rotation along the same axis by ±60o. The orientation of the threefold axis of the molecule relatively
to the main crystallographic axes is not changed after annealing procedures, but the orientation of
the molecule I differs from that for C60 in unannealed sample by turn on about 15o along the unique
molecular axis.
It is known that the spherical C60 molecule undergoes Jahn-Teller distortions with
the anionization of the molecule and the symmetry of the molecule has to change from Ih to D5d, D3d
and/or D2h [13,14]. And to nowadays the orientational disorder in TDAE*C60 is also considered as
conversion between these almost degenerated states of molecule. But our data testify that in low
temperature state of TDAE*C60 crystal fullerene molecules have only unique threefold axis and at
idealization of the molecular shapes C60 has to have the D3d symmetry.
Also, at elevated temperatures above 150K, there are fast jumps of C60 molecules along the
threefold unique axis by 60o rather than they rotate rapidly as it was suggested earlier.
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