Metastable crystalline and amorphous carbon phases obtained from fullerite C60 by high-pressure-high-temperature treatment

Article abstract of DOI:10.1103/PhysRevB.56.11465

A number of metastable ordered and disordered carbon phases have been prepared from fullerite C₆₀ by heating to different temperatures at 12.5 GPa and subsequent quenching to ambient conditions. We studied the structure, Raman spectra, and hardness of the phases obtained. The increase of synthesis temperature up to 500°C leads to a gradual three-dimensional polymerization and subsequent formation of a disordered network with a high share of sp³ sites. Further increase of the synthesis temperature leads to the formation of graphitelike clusters and then crystallization of graphite and diamond at T～900°C. The structure of the polymer phases was identified as fcc, the lattice parameter value decreasing down to ～11.6 A with increase of synthesis temperature. A model of three-dimensional polymerization explaining the observed structural modification is proposed. The model allows one to calculate the share of covalently bonded molecules and describes the change of mechanical properties of polymeric phases in terms of rigidity percolation. Experimental results obtained for strongly polymerized states which favor a polymerization mechanism, other than [2 + 2] cycloaddition are discussed.

Full text of DOI:10.1103/PhysRevB.56.11465

PHYSICAL REVIEW B
VOLUME 56, NUMBER 18
1 NOVEMBER 1997-II
Metastable crystalline and amorphous carbon phases obtained from fullerite C60
by high-pressure–high-temperature treatment
V. V. Brazhkin, A. G. Lyapin, S. V. Popova, R. N. Voloshin, and Yu. V. Antonov
Institute for High Pressure Physics, Russian Academy of Sciences, Troitsk, Moscow region, 142092, Russia
*
S. G. Lyapin
Clarendon Laboratory, Physics Department, University of Oxford, Parks Road, Oxford OX1 3PU, England
Yu. A. Kluev and A. M. Naletov
Russian Scientific-Research Institute of Diamonds, 119110, Moscow, Russia
N. N. Mel’nik
Lebedev Physics Institute, Russian Academy of Sciences, 117924, Moscow, Russia
͑Received 21 January 1997; revised manuscript received 14 April 1997͒
A number of metastable ordered and disordered carbon phases have been prepared from fullerite C60 by
heating to different temperatures at 12.5 GPa and subsequent quenching to ambient conditions. We studied the
structure, Raman spectra, and hardness of the phases obtained. The increase of synthesis temperature up to
500 °C leads to a gradual three-dimensional polymerization and subsequent formation of a disordered network
with a high share of sp3 sites. Further increase of the synthesis temperature leads to the formation of graphi-
telike clusters and then crystallization of graphite and diamond at Tϳ900 °C. The structure of the polymer
phases was identified as fcc, the lattice parameter value decreasing down to ϳ11.6 Å with increase of syn-
thesis temperature. A model of three-dimensional polymerization explaining the observed structural modifica-
tion is proposed. The model allows one to calculate the share of covalently bonded molecules and describes the
change of mechanical properties of polymeric phases in terms of rigidity percolation. Experimental results
obtained for strongly polymerized states which favor a polymerization mechanism, other than 2ϩ2 cycload-
͓
͔
dition are discussed. ͓S0163-1829͑97͒07141-5͔
I. INTRODUCTION
main classes of metastable carbon phases prepared from C60
under pressure: ͑i͒ polymerized phases with covalently
bonded C60 molecules, ͑ii͒ amorphous states with collapsed
molecules and varied fraction of sp2 or sp3 sites, ͑iii͒ disor-
dered phases with diamond or graphite microcrystals. In this
paper we investigate carbon phases from all the three groups,
which have been prepared upon heating at Pϭ12.5 GPa with
subsequent quenching to ambient conditions. One should
emphasize that the pressure-temperature region under con-
sideration ͑290ϽTр1200 K and Pϭ12.5 GPa͒ is still a
gray area on the ‘‘phase diagram’’ of fullerite. Particular
interest is directed to understanding the structural mechanism
of transformation from C60 crystal to amorphous phase
through 3D polymers, before graphitization of the sample.
We investigated x-ray diffraction, Raman spectra, and hard-
ness of 3D fullerite polymers and amorphous phases.
Phase transformations in C60 fullerite have been actively
studied in a wide pressure range for the last six years. A
majority of recent papers concerning temperature-induced
transformations in fullerite under pressure dealt with pres-
sures Pр9 GPa. One- and two-dimensional ͑1D or 2D͒ po-
lymerization has been observed at pressures Pр8 GPa,1–5
and several polymorphic forms of solid C60 have been syn-
thesized. Polymerization of fullerite is associated with the
formation of covalent sp3 bonds between molecules via the
2ϩ2 cycloaddition mechanism.6–10 The polymer phases
may be reverted to pristine C60 by heating at ambient
pressure,1,3 and hence may be treated as metastable phases of
the molecular fullerite crystal. Three-dimensional ͑3D͒
polymerization,5,11,12 occurring at PϾ8 GPa, is not well
studied now, and the mechanism of such transformations is
practically unclear.
͓
͔
In Sec. III we present the main experimental results. In
Sec. IV we propose the model of 3D polymerization, sup-
ported by a set of experimental data. Some aspects of order-
disorder and sp2-sp3 transformations in fullerite C60 under
pressure-temperature treatment, including experimental evi-
Under high-temperature and high-pressure conditions, ful-
lerite C60 was found to transform into amorphous carbon
phases
of
different
nature,11–19
microcrystalline
graphite,11,18,20 and cubic diamond,15,16,18,21 both in static and
shock compression experiments. All these transformations
are accompanied by irreversible collapse of C60 molecules.
It is well known that atoms in solid carbon phases may
exist in sp2 or sp3 states. A variation of the average atomic
valency during the transformation of fullerite to polymerized
and disordered phases is of great interest from both funda-
mental and applied points of view. One can indicate the three
dence for a polymerization mechanism other than the
2
͓
ϩ2 cycloaddition, will be discussed in Sec. V.
͔
II. EXPERIMENT
The samples were synthesized from fullerite powder pro-
duced at Russian Scientific Center ‘‘Kurchatov Institute,’’
with the C60 content not less than 99.9% and 50-100 ␮m
0163-1829/97/56͑18͒/11465͑7͒/$10.00
56
11 465
© 1997 The American Physical Society

11 466
V. V. BRAZHKIN et al.
56
crystalline grains. The powder of C60 microcrystals was
formed into 2-mm high and 2-mm diameter cylinders. A new
version of the ‘‘toroid’’ chamber22 was used for high-
pressure–high-temperature generation ͑up to 13 GPa in the
temperature range 300–2000 K͒ in a large volume ͑up to
30 mm3͒ The samples were placed into Pd or Pt cells and
heated by passing electric current through the outer graphite
container.
The density of samples was determined by the Arkhimed
method. The structure of samples was investigated by con-
ventional x-ray diffraction ͑Cu K␣͒. Raman measurements
were performed at 300 K using Jobin-Yvon T64000 triple
grating spectrometer with a nitrogen-cooled multichannel
CCD detector. The typical bandpass was less than 2 cmϪ1
.
The 514.5 nm line of Arϩ laser was used for excitation, and
the beam was focused to a spot less than 10 ␮m in diameter.
All Raman spectra presented here were independent of the
excitation intensity, which was typically within the range
0.1–15 mW. The radiation power of the laser was chosen to
prevent the photopolymerization effects.6 The Raman spectra
were taken in the true backscattering configuration with in-
cident and scattered polarizations orthogonal to each other.
The hardness was investigated by means of indenting the
diamond Vickers pyramids under loads 1.96 and 5.5 N.
FIG. 1. X-ray diffraction patterns ͑with subtracted midle lines͒
for the polymerized crystalline phases of fullerite C60 prepared at
12.5 GPa. Numeration of the curves is the same as in Table I. The
similar fcc reflections are marked by identical symbols.
calculations7–9,24 and experiments3 show that in the cases of
polymerized dimer, chain, as well as 1D and 2D fullerene
polymers the intermolecular distance varies in the range 9–
9.2 Å which corresponds to the period aϷ12.7 Å for the fcc
lattice. So it would be reasonable to consider the crystalline
samples 5–8 as the 3D polymers of fullerite. Significant dis-
tortion and/or destruction of the convex C60 molecules in
strongly polymerized samples 9 and 10 (aϽ12 Å) are evi-
dently due to weak compressibility of the covalent bonds that
restrict further mutual uniform approach of the molecules to
each other. The broad amorphous peaks at QϷ3 and
5.5 ÅϪ1 visible in the x-ray-diffraction patterns of the poly-
merized phases correspond to amorphous carbon with sp3
sites,25–27 and may be associated with the appearance of the
covalent sp3 bonds between C60 molecules.
The heating to 500 °C leads to a complete disorder in the
structure of fullerite ͑see Fig. 3͒. The x-ray diffraction pat-
tern of the corresponding sample ͑11͒ revealed broad lines
around 3 and 5.5 ÅϪ1 associated with sp3 amorphous
carbon.25–27 The sp2-rich forms of amorphous carbon dis-
play broad lines around 2 and 3 ÅϪ1, having approximately
the same intensity.26,28,29 This indicates a considerable share
of sp3 sites in the amorphous sample 11 and agrees well
with the density 3.15 g/cm3 ͑Table I͒ typical for amorphous
films containing ϳ80–90% of sp3 sites.30 The line at
QϷ1.4 ÅϪ1 shows a maintaining of certain ordering, or cor-
relation, which may be connected to the initial molecular
structure, because the corresponding interlayer distance
dϳ4.5 Å is approximately equal to half the intermolecular
distance in strongly polymerized phases.
III. STRUCTURE AND RAMAN SPECTRA
The samples were subject to different temperatures under
pressure 12.5 GPa, and their structure was investigated after
quenching the samples to the ambient conditions. The x-ray
patterns of the samples prepared at relatively low tempera-
tures Tsynр450 °C revealed distinct crystalline reflections
͑Fig. 1͒. The structure of all crystalline phases prepared was
identified as fcc. The lattice parameter a was found to de-
crease with increasing synthesis temperature Tsyn ͑Table I͒,
simultaneously with increase in the degree of disorder. The
calculated crystallographic densities are in good agreement
with the experimental data ͑Table I͒.
The calculated and measured intensities of ͑111͒, ͑200͒,
and ͑220͒ reflections are compared in Fig. 2. The calcula-
tions were based upon the geometry of the experiment,
atomic scattering factors, the number of reflecting atomic
planes, and the molecular factor Fmol in the uniform sphere
approximation, i.e., Fmolϰsin(QR)/QR ͑see, for example,
Ref. 23͒, where Q is the scattering wave vector and R is the
radius of the fullerene molecule ͓RϷ3.5 Å ͑Ref. 23͔͒. The
theoretical and experimental intensities are in satisfactory
agreement for the phases with the lattice parameter
aу12.3 Å. The behavior of the intensities observed sug-
gests that the C60 molecules can be regarded as structure-
forming units in the case of crystalline phases with
aу12.3 Å. The samples heated to higher temperatures
T
synϷ450 °C ͑9 and 10͒ revealed essential distortion and
possibly destruction of the spherelike C60 molecules ͑Fig. 2͒.
A decrease of the lattice parameter in these phases indi-
cates the appearance of stronger interaction between the mol-
ecules due to formation of covalent bonds,6–9 i.e., polymer-
ization. Considering the molecular radius to be RϷ3.5 Å,
the average intermolecular distance for 3D-polymerized
samples ͑5–8͒ must be Ϸ1.6 Å, that is close enough to the
length of covalent bonds in fullerene polymers.3,7–9,24 Both
Further heating under pressure evokes narrowing of the
line around 3 ÅϪ1 and the appearance of the two new peaks
at ϳ2 and ϳ4 ÅϪ1, clearly identified as the ͑002͒ and ͑004͒
reflections from parallel-packed hexagonal planes of graphite
͑Fig. 3͒. Upon strong heating ϳ900 °C the location of the
͑002͒ reflection corresponds to the tabulated value for crys-

56
METASTABLE CRYSTALLINE AND AMORPHOUS CARBON . . .
TABLE I. Parameter of fcc lattice a, calculated ␳calc , and ex-
11 467
perimentally measured ␳exp densities, and hardness HV for polymer-
ized fullerite samples and disordered phases obtained from C60 un-
der pressure Pϭ12.5 GPa at various synthesis temperatures Tsyn
.
Tsyn
͑°C͒
a
͑Å͒
␳
␳
HV
͑GPa͒
calc
exp
Sample
(g/cm3)a (g/cm3)
1
2
3
4
5
6
7
8
9
10
11
12
13
14
20 14.04Ϯ0.01
100 14.03Ϯ0.08
1.73
1.73
1.95
2.20
2.57
2.60
2.59
2.62
2.80
3.05
1.7
1.75
1.9
2.3
2.5
0.15Ϯ0.05
4.2Ϯ0.6
33.6Ϯ2.2
25.7Ϯ0.8
36Ϯ7
26.4Ϯ0.7
44.0Ϯ1.2
52Ϯ6
150
200
300
300
13.5Ϯ0.1
12.95Ϯ0.1
12.3Ϯ0.2
12.25Ϯ0.1
400 12.27Ϯ0.03
450 12.23Ϯ0.03
450 11.95Ϯ0.05
450 11.62Ϯ0.06
2.8
3.0
3.1
3.15
3.0
3.2
3.0
65Ϯ5
500
600
700
900
Disordered
Disordered
Disordered
Disordered
76.4Ϯ0.6
75.4Ϯ1.1
69Ϯ6
FIG. 3. X-ray-diffraction patterns for disordered carbon phases
prepared from fullerite C60 at 12.5 GPa.
87Ϯ10
in this spectrum. These lines are similar to those that become
Raman active in the pristine C60 under pressure PϾ0.4 GPa
͑Ref. 33͒ and in photopolymerized C60 .6 Apart from the nar-
row lines, the broadbands ͑1100–1600 cmϪ1 and
250–600 cmϪ1͒ are seen in the Raman spectrum of sample 3
͑Fig. 4͒. The samples with higher polymerization degree ͑4
and 8͒ have broadbands ͑200–800 and 1200–1700 cmϪ1͒ in
their Raman spectra, which are usual for the amorphous
phases, although x-ray-diffraction patterns of these samples
definitely reveal their crystalline nature ͑Fig. 1͒.
The Raman spectrum of a completely disordered phase
differs from those of strongly polymerized phases and looks
very much like the spectrum of amorphous carbon with a
high degree of sp3 bonding.30 It is well known34 that the
Raman features of sp3 bonding are difficult to observe be-
cause of their much lower cross section (ϳ1/50) than that
for sp2 bonding. So, the spectra obtained reflect the activity
of sp2 sites. The increase of the synthesis temperature
Uncertainty Ϯ10%
Ϯ0.15
aCrystallographic density ␳
lattice parameter a.
was calculated using experimental
calc
talline graphite, whereas at lower synthesis temperatures the
hexagonal layers should be somewhat squeezed. The size of
graphitic clusters along the z axis can be evaluated from the
linewidth of the ͑002͒ and ͑004͒ reflections. The calculation
gives ϳ25 Å for samples with Tsynϳ600–700 °C, that is
equivalent to ϳ8 graphite layers, and ϳ50 Å for higher syn-
thesis temperatures. With the temperature increase crystalli-
zation of sp3 sites into diamond microcrystals occurs since
the ͑111͒ diamond line becomes narrow, and the ͑220͒ and
͑311͒ diamond reflections come into view though weak and
diffused ͑sample 14͒.
The Raman spectra for the pristine C60 and some of the
polymerized phases are presented in Fig. 4. Our spectra for
the pristine C60 and the polarization relationships for the line
intensities are in good agreement with the literature data.31–33
The Raman spectra of the slightly polymerized C60 phase
͑sample 3͒ revealed clearly the narrow lines corresponding to
the fullerene modes. New lines 300 and 527 cmϪ1 are visible
FIG. 2. Calculated dependences and experimental data ͑sym-
bols͒ for intensities of the ͑111͒ ͑solid line and triangles͒, ͑200͒
͑dashed line and circles͒, and ͑220͒ ͑dashed and dotted line and
stars͒ reflections vs lattice parameter.
FIG. 4. Raman spectra, measured in the perpendicular geometry,
for carbon phases prepared from fullerite C60
.

11 468
V. V. BRAZHKIN et al.
56
intermolecular bonds ͑ 2ϩ2 cycloaddition mechanism͒ is
͓
͔
much more favorable energetically than the alternative poly-
merization mechanisms.7
The main idea of the model proposed is the assumption
that a pair of nearest molecules can in fact be found in two
states being connected by the covalent or van der Waals
forces, while the observable period of the fcc lattice is a
continuous function of the share of covalently bonded ͑poly-
merized͒ molecular pairs and is obtained by means of the
averaging procedure throughout the lattice with varying de-
gree of disorder in the types and lengths of bonds. This sug-
gests the existence of uniform and random ͑or quasirandom͒
distribution of polymerized pairs over the lattice.
The van der Waals lattice of pristine C60 and completely
3D-polymerized phase with a certain lattice parameter ap
would be the extremities for a set of 3D polymeric phases.
The lower limit of the lattice parameter range, in which the
spherical molecular factor approximation holds ͑Fig. 2͒,
would be an appropriate approximation for ap , i.e.,
apϳ12.3 Å. This parameter corresponds to an intermolecu-
lar distance of 8.7 Å which is very close to the sum of the
C60 molecule diameter (Ϸ7 Å) and the length of covalent
sp3 bonds in carbon (ϳ1.54–1.6 Å), and we will use the
estimation apϷ12.3 Å. In our approach the distortion of C60
molecules in the fcc phases with apϽ12 Å is caused by the
strong repulsion between covalently bonded atoms of adja-
cent molecules. So, probably polymerization mechanisms
FIG. 5. Some characteristics of the fcc 3D-polymerized phases:
the lattice parameter vs synthesis temperature ͑a͒ and the FWHM
for the ͑220͒ reflection ͑b͒ and hardness ͑c͒ vs lattice parameter.
The dotted lines are guidance for eyes. The vertical dashed lines
correspond to different rigidity percolation thresholds.
other than the 2ϩ2 cycloaddition, for example, the forma-
͓
͔
tion of four bonds between molecules,7 become prevalent.
The model proposed treats partly polymerized fullerite as
a substitution solid solution, with different types of bonds
instead of different atoms. Analogous to the Vegard’s law for
solid solutions, the lattice parameter of a partially polymer-
ized phase can be linearly approximated as a function of the
share of polymerized molecular pairs np
͑samples 12–14͒ leads to the appearance of a distinct doublet
structure in the Raman spectra with the maxima of the lines
being located within the intervals 1360–1420 and
1580–1600 cmϪ1. Taking into account the results of x-ray-
diffraction study, these two lines can be identified as the
graphite Raman-active G line and the interlayer ‘‘disor-
dered’’ D line observable in microcrystalline graphite.35–37
The change of spectra with increase of synthesis temperature
is qualitatively analogous to that obtained during the crystal-
lite formation in amorphous carbon films.37 The broadening
of Raman lines is connected with the bond-angle disorder in
hexagonal layers. We believe one reason for such disorder to
be the interplanar sp3 linkage, that explains squeezing of the
hexagonal layers observed from structural data.
aϭa0ϩ͑apϪa0͒np ,
͑1͒
which, as in the case of solutions, is connected with the
relaxation of intermolecular stresses.
By analogy with substitution solid solutions, the static
dispersion of atomic positions connected with the disorder of
the bond types must exist in a fcc crystal with two charac-
teristic lengths of the bonds. The highest fluctuations of
atomic locations would be present for npϳ0.5, that means
equal share of both van der Waals and covalent bonds. These
fluctuations must influence the width of crystalline reflec-
tions on the x-ray-diffraction pattern. Figure 5͑b͒ shows the
full width at half maximum ͑FWHM͒ ⌬Q for the ͑220͒ peak
vs lattice parameter. This reflection was chosen due to its
moderately large intensity in the x-ray patterns for all fcc
phases. The largest width was obtained for the phase with
aϷ13 Å, intermediate between the 3D-polymerized and de-
polymerized states. The analogous behavior was revealed by
the ͑111͒ and ͑200͒ reflections.
IV. MODEL FOR THREE-DIMENSIONAL
POLYMERIZATION OF FULLERITE C60
A. Polymerization of fcc phases
The dependence of the lattice parameter on the synthesis
temperature has a quasicontinuous character for fcc 3D-
polymerized fullerite phases. ͓Fig. 5͑a͔͒ The fcc phases with
relatively large lattice parameters have been obtained
previously.1,12 So it is natural to suppose the possible exis-
tence of the fcc polymers with any lattice parameter within
the range from 14.17 Å ͑pristine C60͒ to ϳ11.6 Å ͑strongly
polymerized phases obtained in the current study͒. This
means the average intermolecular distance can vary from 3
to 1.4 Å.
B. Rigidity percolation in fcc polymers of the fullerite C60
The calculations for different polymer configurations of
C60 molecules give the intermolecular bond length about
ϳ1.6 Å,7–9 comparable with that in diamond 1.54 Å. Theo-
retical analysis also shows that the formation of two covalent
One more advantage of the model considered is the pre-
diction of the mechanical properties of 3D fcc phases. Cova-
lent bonds are much more rigid than van der Waals bonds.
The bulk modulus of the pristine fullerite is ϳ18 GPa,23

56
METASTABLE CRYSTALLINE AND AMORPHOUS CARBON . . .
11 469
which is an order of magnitude less than that of covalent
diamond. If the lattice parameter of a fcc polymer is close to
that of the pristine fullerite, the share of polymerized pairs is
small according to Eq. ͑1͒, so just a few clusters would be
covalently bonded. Such a situation apparently has been ob-
tained for the photopolymerization process.6 The phases with
a→a0 would be as soft as the pristine fullerite itself and
cannot be treated rigorously as 3D-polymerized phases. For
a→ap , we, in fact, deal with a rigid covalent network which
is corroborated by the experimental measurements of hard-
ness ͑See Table I͒.
The elastic rigidity percolation defined by the degree of
covalency between molecules seems to be an appropriate de-
scription of a transition between the two extremities if we
consider the contribution of van der Waals forces to be neg-
ligible. A 3D network of covalently bonded atoms becomes
rigid when the average coordination number reaches or ex-
ceeds the value of Z1cϭ2.4.38 The average coordination
number of covalently bonded pairs of C60 molecules Zp
would be defined by their share np as ZpϭnpZ, where Zϭ12
is the coordination number of a fcc lattice. Considering the
threshold intermolecular coordination number for the appear-
ance of hardness and elasticity in a system of covalently
bonded C60 molecules to be Z1cϭ2.4, we obtain the thresh-
old concentration n1cϭ0.2 and the corresponding lattice pe-
riod a1cϷ13.8 Å ͓see Eq. ͑1͔͒.
Covalent bonds possess the angular rigidity diminishing
the number of freedom degree in the system. In our case the
upper limit for the threshold rigidity value may be obtained
if we consider the bonds without the angular rigidity. Then,
the rigidity percolation appears when three bonds per mol-
ecule correspond to three translational degrees of freedom
for each molecule ͑rotations of rigidly connected molecules
may be excluded͒. The critical coordination number is
Z2cϭ6.39 For the upper limit of rigidity we obtain the critical
concentration of covalently bonded pairs of molecules
n2cϭ0.5 and the lattice period a2cϷ13.2 Å.
lymerization the disorder in the system may be connected to
the presence of different types of intermolecular bonds.
However, the reason for the appearance of the amorphous
carbonlike Raman spectra seems to be somewhat different.
The icosahedral point-symmetry group of an individual C60
molecule (Ih) and the point-symmetry group of fcc lattice
(Oh) have the point-symmetry group of tetrahedron Th as the
common subgroups. This gives a possibility for construction
of the 3D fcc polymer with the Th symmetry. Nevertheless,
the random character of formation of covalent bonds be-
tween the molecules in 3D polymers causes an orientational
disorder. The appearance of covalent sp3 intermolecular
bonds ͑almost tetrahedrally oriented͒ should enforce local
tensions and slight distortions in C60 molecules. As a result,
the Raman spectra of strongly polymerized phases look com-
pletely ‘‘amorphous.’’ Unlike 3D polymers, both 1D- and
2D-polymerized phases reveal clearly crystalline Raman
spectra.1,4,5
The Raman spectrum of some 3D polymer sample ͑e.g.,
3͒ displays both ‘‘crystalline’’ and ‘‘amorphous’’ features.
Apparently, the reason for this is the different degree of in-
termolecular covalent connectivity for different molecules.
About 30% of molecular pairs in sample 3 (aϭ13.5 Å)
must be covalently bonded, according to Eq. ͑1͒. This value
exceeds substantially both the rigidity threshold in the sys-
tem (n1cϭ0.2) and the percolation threshold for the forma-
tion of three-dimensional infinite cluster ͑ncZϷ1.43 or
ncϷ0.12͒ in the fcc lattice.40
To analyze the mechanism of order-disorder transition the
knowledge of the sp3 sites share is of great importance. A
natural assumption arises that the initial stage of 3D poly-
merization is due to the 2ϩ2 cycloaddition mechanism,
͓
͔
which is much more favorable energetically.7 This means
that four sp3 atoms correspond to each covalently bonded
pair of C60 molecules. The share of sp3 atoms in 3D polymer
can be defined by the share of bonded molecular pairs np
from the equation
Figure 5͑c͒ shows the dependence of the hardness for the
fcc phases of fullerite vs the lattice parameter, which com-
pletely supports the picture described above. The hardness
continuously increases with the average coordination number
for molecules similar to the increase of elastic constant in the
models mentioned.38,39 Linear interpolation with the least-
squares fitting gives the threshold parameter close to the first
one, a1cϷ13.7 Å. The growth of hardness for the phases
with aϽap , when polymerization is considered complete in
the framework of this model, is probably connected to the
further increase of the number of covalent bonds between
molecules due to their deformation and partial destruction.
2npZ
Nsp3ϭ
,
͑2͒
60
where Zϭ12 is the fcc-lattice coordination number. A maxi-
mum value of Nsp3ϭ0.4 is reached at aϭap for the com-
pletely 3D-polymerized fullerite.
Using Eqs. ͑1͒ and ͑2͒ one can obtain the dependence of
Nsp3 vs the crystallographic density ␳ ͑Fig. 6͒, if we choose
the value of ap from the realistic domain 12.2–12.6 Å. One
should note that the density values for the completely poly-
merized phases with aϳap are rather close to those for the
corresponding amorphous carbon films30 with ϳ40% of
fourfold atomic sites ͑Fig. 6͒, thus supporting the consider-
ation of the 3D-polymerized phases as sp2-sp3 networks.
The partially polymerized fullerene fcc phases (aϾap) are
less dense than the corresponding amorphous samples. Fur-
ther decrease of the lattice parameter (aϽap) and density
increase should apparently be accompanied by a further fast
increase of the share of sp3 sites, according to the data for
amorphous films. In the framework of the views on the po-
lymerization of C60 molecules the mechanism of this in-
crease can be connected to the formation of four covalent
bonds between molecules instead of two bonds ͑see Ref. 7͒.
V. DISCUSSION
The sequence of carbon phases synthesized under pres-
sure corresponds to the successive structural transformations
taking place on heating at 12.5 GPa. The structural and Ra-
man data show that the increase of the synthesis temperature
evokes both disordering of the location of C60 molecules and
their destruction with the formation of the amorphous
sp2-sp3 network.
The first evidence for disordering may be seen from the
Raman spectra ͑Fig. 4͒. At the intermediate stage of 3D po-

11 470
V. V. BRAZHKIN et al.
56
FIG. 7. Relative intensity of the wide x-ray-diffraction peak
around 3 ÅϪ1 as a function of density. The summarized intensity I⌺
was obtained by summation of areas under all peaks in the range
Qр3.5 ÅϪ1. The dashed lines are guides for the eyes.
FIG. 6. Concentration of sp3 atomic sites vs density depen-
dences for the amorphous carbon films from Ref. 30 ͑dashed and
dotted line͒ and 3D-polymerized phases of fullerite C60 ͑shaded
area͒. The last is calculated using Eqs. ͑1͒ and ͑2͒, where
2.2рapр2.6 Å. The horizontal dashed line correspond to the
maximum concentration of sp3 cites, when 3D polymerization oc-
(ϳ900 °C) treatment of C60 evokes a transformation to a
microcrystalline graphite-diamond mixture. The transforma-
tion occurs through
a number of intermediate 3D-
curs via the 2ϩ2 cycloaddition mechanism.
͓
͔
polymerized crystalline and disordered phases.
The structure of 3D-polymerized modifications was iden-
tified as fcc. The analysis of the intensity of x-ray crystalline
peaks shows that the pristine C60 units retain their spherical
symmetry in the range of lattice parameters 12.3–14.17 Å,
while the distortion of C60 molecules occurs at lower lattice
parameter values. A model of 3D polymerization is proposed
for the first stage of polymerization (aу12.3 Å), which re-
lates the fcc lattice parameter to the share of covalently
bonded molecular pairs. The model explains a set of struc-
tural anomalies and the changes of mechanical properties of
3D-polymerized phases in terms of rigidity percolation. The
approach given is strictly supported by experimental data.
The Raman spectra of strongly polymerized phases look
analogous to those of amorphous carbon, that may be ex-
plained by the incompatibility of point-symmetry groups for
single C60 molecule and fcc lattice. Careful analysis of ex-
perimental data allowed us to suppose the importance of a
This is in good agreement with the strong deformation of
initially spherical pristine C60 units in the fcc phases with
aϽap ͑Fig. 2͒. For the new mechanism of polymerization
the maximum share of sp3 sites in a fcc polymer may be
equal to 4Z/60ϭ0.8. It is interesting to note that the atomic
network of the collapsed C60 sample simulated under pres-
sure by the tight-binding molecular-dynamics calculation41
gave the value of share of sp3 sites to be 79%. The Nsp3(␳)
dependence for the fullerite compressed in this simulation
consists of intervals of slow and fast increase of Nsp3, which
is in good accordance with the analysis shown above. The
mechanical characteristics and densities of both the strong
polymerized phase and ‘‘diamondlike’’ amorphous carbon
͑sample 11͒ are rather adequate to such a high share of four-
fold atoms.
Other evidence of the growing disorder in the system is
the appearance of the amorphous peak around 3 ÅϪ1 in the
structure factor ͑Fig. 1͒. It can be assumed that the intensity
of this peak is defined by scattering from sp3 sites ͑including
four nearest-neighbors forming a tetrahedron for each such
site͒ and is proportional to the share of sp3 sites. The relative
intensity of this peak vs lattice parameter is presented in Fig.
7. The intensity change is relatively small in the interval
apϽaϽa0 , where apϷ12.3 Å, whereas a much more rapid
increase of the intensity takes place for aϽap or
␳Ͼ2.5 g/cm3. The experimental pattern agrees well with the
above analysis based on Fig. 6.
polymerization mechanism other than 2ϩ2 cycloaddition
͓
͔
at the second stage of 3D polymerization (aр12.3 Å), pre-
ceding the formation of the amorphous network with a high
degree of sp3 bonding. Further heating leads to an increase
of heterogeneity in disordered phases and induces the ap-
pearance of graphitelike sp2 clusters.
ACKNOWLEDGMENTS
The work was financially supported by the Russian Fund
for Fundamental Research ͑Grant Nos. 95-02-03677 and 96-
02-17328a͒. The authors are grateful to Professor S. M.
Stishov and Yu. A. Osipyan for useful discussions, to N. V.
Kalyaevea, N. I. Epishina, and T. I. Bulygina for assistance
with measurements of mechanical properties, to Dr. M.
Grimsditch for preliminary Raman measurements of some
samples, and to Dr. R. A. Sadykov for assistance in x-ray
experiments.
VI. CONCLUSION
A set of metastable carbon phases obtained by heating C60
fullerite under the pressure 12.5 GPa were investigated in
this paper by x-ray diffraction, Raman spectroscopy, and
hardness measurements. High-pressure–high-temperature
*
On leave from Institute for High Pressure Physics, Russian Acad-
emy of Sciences, Troitsk, Moscow region, 142092, Russia; elec-
tronic address: s.lyapin@physics.ox.ac.uk
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