www.sciencemag.org/cgi/content/full/337/6096/825/DC1
Supplementary Materials for
Long-Range Ordered Carbon Clusters: A Crystalline Material with
Amorphous Building Blocks
Lin Wang,* Bingbing Liu, Hui Li, Wenge Yang, Yang Ding, Stanislav V. Sinogeikin,
Yue Meng, Zhenxian Liu, Xiao Cheng Zeng, Wendy L. Mao
*To whom correspondence should be addressed. E-mail: lwang@ciw.edu
Published 17 August 2012, Science 337, 825 (2012)
DOI: 10.1126/science.1220522
This PDF file includes:
Materials and Methods
SupplementaryText
Figs. S1 to S11
References
Materials and Methods
The starting material was synthesized by a simple evaporation method (18). The in
situ high-pressure XRD was conducted at the High Pressure Collaborative Access Team
(HPCAT) and GSECARS sectors of the Advanced Photon Source (APS), Argonne
National Laboratory (ANL). Focused monochromatic X-rays with beam sizes of 7 µm
FWHM were utilized for angle-dispersive XRD experiments. The wavelengths of the Xrays are 0.4151 and 0.5166 Ǻ for in-situ high pressure measurements and recovered
samples, respectively. The diffraction patterns were collected on an MAR345 image
plate. Pressure was determined from the equation of state of Au which was added as an
internal standard. Samples recovered from different pressures were also characterized
using a Raman spectrometer (Renishaw inVia, UK) with 514.5 nm excitation laser.
The inelastic X-ray scattering (IXS) experiments were performed at station 16ID-D
of the HPCAT at APS of ANL. Incident monochromatic X-rays were focused to 10 μm
by 40 μm (vertical by horizontal) (FWHM) at the sample location. A 50 μm pinhole was
used to cut the tail of the X-ray beam at 50 mm upstream from the focus point. A
panoramic type diamond anvil cell with a culet size of 300 μm was used to generate high
pressure for the sample. A composite c-BN gasket assembly was used for the IXS
measurements to increase the gap size between two diamond anvils and isolate the
sample from the surface of the diamonds. A drilled Be gasket served as the outer part of
the gasket to hold the c-BN insert. The gap size is ~80 μm at 42 GPa. The X-ray beam
was directed into the gasket and was aligned parallel to the gap between the diamond
anvils. The beam was at least 20 μm away from the surface of each anvil. The IXS signal
was collected by scanning the incident x-ray energy relative to the fixed energy of 9.885
keV which was set for each of the 17 spherically bent Si (555) analyzers, which were
mounted vertically in a Rowland circle to refocus the IXS signal to the Si detector
(Amptek R®) in a back scattering geometry. The resolution for the measurements was 1
eV.
The infrared absorption spectrum for recovered sample was performed at station
U2A at National Synchrotron Light Source (NSLS) of Brookhaven National Laboratory
(BNL). Type II diamond anvils were used for the measurement. The background was
carefully subtracted by taking a background at the area without sample.
Supplementary Text
Detailed Information of Simulations
1.Comparison of Lattice Constants from Experiment and Quantum Molecular Dynamics
Simulation for the Purpose of Calibration.
First, we used a classic molecular dynamics (MD) simulation to produce a
thermally equilibrated hexagonal-closed packing (hcp) crystalline system of mixed C60
and m-xylene (C8H10) (based on atomic coordination published in ref. 23) for subsequent
quantum MD simulations. The ratio of C60 to m-xylene molecules is 1:1. A unit cell of
the hcp crystal contains six C60 molecules and six m-xylene molecules. The m-xylene
molecules are filled in the cavity region among the close-packed C60 molecules. The
supercell of the simulation system has 8 unit cells, which contains 3264 C atoms and 480
H atoms. The consistent valence force field (CVFF) implemented in the Material Studio
2
4.4 package is employed. The MD is performed in an isothermal-isobaric (NPT)
ensemble simulation (using the Discover program in Material Studio 4.4). The simulation
time is 2 ns with a time step of 1.0 fs.
Next, the equilibrium structure (as shown in Fig. S4) is used as the initial crystalline
structure for the Born-Oppenheim molecular dynamics (BOMD) simulation. The initial
pressure of the system is computed from BOMD simulation in the constant-volume and
constant-temperature ensemble (NVT). The density function theory (DFT) in the PerdewBurke-Ernzerhof (25) scheme is chosen with unrestricted wave-function for the BOMD
simulation. The core electrons of carbon are described by the Goedecker-Teter-Hutter
(26) norm-conserving pseudopotential. The basis sets are a combination of the polarized
double-ζ quality Gaussian basis and a plane-wave basis set (with an energy cutoff of 280
Ry). The total simulation time for equilibration is 2.0 ps with the time step of 1.0 fs. All
the BOMD simulations are performed using the QUICKSTEP program in CP2K software
package (27,28).
The supercell contains six C60 and six m-xylene molecules (408 C atoms and 60 H
atoms). The BOMD simulation shows that the initial system (a = 23.8 Å) is in slight
compression state with a compression pressure of 1.85 GPa. The lattice constant (a = 23.8
Å) of the hcp C60*m-xylene system is slightly larger than experimental lattice constant a
= 23.06 Å at the low pressure 1.7 GPa. The computed lattice constant is slightly larger
due to the neglect of dispersion interaction in the BOMD simulation. However, we expect
that at high-pressure (strong compression) states, the dispersion interaction becomes
negligible. To prove this point, we performed two additional BOMD simulations (~1 ps
each) to examine the hcp crystalline structure of C60*m-xylene system at ~5 and ~10
GPa, respectively (NPT simulations; see Fig. S5). The computed average lattice constant
of a is 23.25 and 22.54 Å, respectively, whereas the experimental values of a = 22.60 and
22.20 Å at 5.6 and 10.8 GPa, respectively. Hence, with increasing the pressure, the
computed lattice constant from BOMD simulation becomes closer to the experimental
lattice constant. This benchmark calibration suggests that the simulated compression in
the pressure range of 20 – 40 GPa is expected to mimic, semi-quantitatively, the
experimental compression over the same pressure range.
2. Simulation of Compression and Decompression using a Similar Close-Packed System
To demonstrate that the experimentally observed long-range ordered amorphous
carbon cluster is a generic phenomenon, we performed independent BOMD simulations
using the similar close-packed (face-centered cubic, fcc) system as a test model system.
Note that both hcp and fcc systems are close-packed whereas the a fcc unit-cell demands
a much smaller number of atoms (see below), which is feasible with our computational
resources. Our BOMD simulations indicate that many physical/chemical behaviors
observed in the experiment can be qualitatively captured (or even semi-quantitatively
reproduced in terms of transition pressure; see below), thereby suggesting the appearance
of long-range ordered amorphous carbon cluster is indeed a general phenomenon for the
compressed C60*m-xylene system.
Specifically, the spin-unrestricted DFT method is used in the BOMD simulation to
account for the bond breaking and forming process under high pressures. Here, the
supercell contains four C60 and four m-xylene molecules (272 C atoms and 40 H atoms).
3
900,000 CPU hours granted by DOE Oak Ridge National Laboratory Computing Facility
were spent on this series of simulations.
(2.1) Initial Crystalline Structure
Again, we use the classical MD to acquire a thermally equilibrated fcc system in the
NPT ensemble (290 K, 1 atm). Based on the final configuration obtained from the
classical MD simulation, a BOMD simulation in the NVT ensemble is performed to
compute the initial pressure at 290 K, which is about 0.4 GPa. Thus, the fcc system is
also in the slight compression state as in the case of hcp system.
(2.2) BOMD Simulation of Instant Compression and Decompression (Fig. S6, Fig.
S7)
(2.3) Temperature Profile in the Course of Compression and Decompression
Simulations
As shown in Fig. S8, in the BOMD simulations of instant compression, the
temperature of the system increases typically very fast within the initial 0.5 ps, especially
at high pressures. As a result, some chemical bonds of m-xylene molecules appear to be
broken (see Fig. S6). This bond-breaking is not observed in the cold-compression
experiment because in experiments the pressure is normally increased in a step-by-step
fashion (a few GPa per step).
(2.4) Vibrational Spectra of the System after Decompression
Fourier transformation of the velocity auto-correlation functions obtained from the
BOMD simulation gives rise to the vibration spectra at zero-pressure state after
decompression from the six high-pressure states, as shown in Fig. S9. It can be seen that
the characteristic peaks of C60 molecule in the range of 1200-1600 cm-1 of the vibration
spectra are quite high if decompressed from high-pressure state at 20 or 30 GPa. These
peaks become much weaker if decompressed from high-pressure state at or greater than
32 GPa. This behavior is consistent with that shown in the experimental Raman spectra,
in that C60 molecules are still severely broken even after decompressed to zero-pressure
state from the high-pressure states (with pressure > 32 GPa).
(2.5) Pair Distribution Functions
The pair distribution functions (PDFs) of carbon atoms at six high-pressure states
are computed from the BOMD simulations (Fig. S10(A)). As shown in Fig. S10(A), the
first peak (1.4 Å) and the second peak (2.5 Å) correspond to C-C bond length and C-C-C
length with a bent angle of 120º, respectively, indicating that the 6-member rings are well
retained even at very high pressures. The third and fourth peaks are not significant in
PDFs at pressure higher than 32 GPa, implying that the C60 molecules are crushed.
Moreover, the PDFs at zero-pressure states (decompressed from the six high-pressure
states) are computed (Fig. S10(B)). By comparing Figure S10(A) and (B), it can be seen
that the compressed C60 system is fairly elastic when compressed to a pressure lower than
30 GPa. However, when the system is compressed beyond 32 GPa, the deformation of
C60 molecules is irreversible, evidenced by high similarity between PDFs corresponding
to the same high-pressure state. From the enlarged plots of PDFs from 1.0 to 2.0 Å (Fig.
S10(C) and (D)), it can be seen that the C-C length shifts slightly to the right with
increasing the pressure, suggesting a transition of sp2 carbon to sp3 carbon at higher
pressures.
In addition, the radial distribution functions (RDFs) with respective to the center of
C60 molecules are shown in Fig. S10(E) and (F). The single sharp peak in C60-centered
4
RDFs (at compression state) further proves the compression up to 30 GPa is quite
reversible. The position is exactly the same as the radius of fullerene (3.6Å). Significant
deformation of C60 molecules can be seen at the pressure higher than 32 GPa, as sharp
peaks corresponding to the C60 shell in the RDFs become more broad and lower. The
RDFs corresponding to 40 GPa exhibits very different features from the others, indicating
that the symmetric structure of C60 molecules is largely destroyed due to the high
pressure, forming the amorphous carbon.
5
Fig. S1. IXS spectra of the solvated C60 sample at high pressure. The π* and σ* peaks
correspond to 1s – π* and 1s – σ* transitions respectively. The resolution for the
measurements was 1 eV. The X-ray beam was directed into the gasket and was aligned
parallel to the gap between the diamond anvils. The beam was at least 20 μm away from
the surface of each anvil, which ensures no signal from diamond anvils could be counted.
The IXS signal was collected by scanning the incident x-ray energy relative to the fixed
energy of 9.885 keV.
6
Fig. S2. IR spectrum of the OACC recovered from 32.8 GPa. The absorption peaks from
the solvent are labled. No absorption from C60 is observed in the whole spectrum. This
suggests that C60 cages are collapsed, but the solvent molecules are well preserved.
7
Fig. S3. XRD pattern of the decompressed material from 42 GPa after a mild heat
treatment at 107°C for 8 h. The heat treatment was taken place in air. No sharp diffraction
peaks were found in the pattern which suggests that OACC loses its long-range
periodicity and transforms into an amorphous structure after the solvent is removed.
8
Fig. S4. A snapshot of the hexagonal close-packed (hcp) structure of C60*m-xylene
crystal (with the ratio of C60 to m-xylene molecules being 1:1), obtained from the
classical MD simulation at the ambient condition (298 K and 1atm). The green lines refer
to the hexagonal symmetry of the system. The supercell has 8 unit cells, which contains
3264 C atoms and 480 H atoms. After 2 ns MD run, the system reaches thermal
equilibrium, and the calculated lattice constant is a ~ 23.8 Å, compared to the
experimental value (a = 23.63 Å) at 1 atm. Color code: C of C60 (pink), C of m-xylene
(blue), and H (white).
9
Fig. S5. Snapshots of unit cell of the hcp crystal from BOMD simulation (after 1 ps) at
the pressures of (A) 1.85, (B) 5, and (C) 10 GPa. The computed average lattice constant a
= (A) 23.8, (B) 23.25 and (C) 22.54 Å. As a comparison, the experimental values of a are
23.06, 22.60, and 22.20 Å at 1.7, 5.6 and 10.8 GPa, respectively. At 10 GPa, the
computed and measured lattice constants are very close to each other.
10
Fig. S6. BOMD simulations of instant compression processes of the (initial) fcc system from the initial pressure (0.4 GPa) to six different pressures: 20, 30, 32, 33, 35 and 40
GPa, respectively. The pressure-induced crystal-to-amorphous transition appears to occur
in the pressure range of 32 to 35 GPa. The simulation time is 4 ps for each compression
simulation. Polymerization of fullerene molecules can be observed for pressure 33 GPa
or higher, due to the ultrahigh temperature of the system within the 1.5 ps of instant
compression (see Fig. S8 below).
11
Fig. S7. BOMD simulations of instant decompression processes, from states of the
system at six different high pressures to either the zero-pressure or 0.4 GPa-pressure
state, respectively. The simulation time is 1or 2 ps for each decompression simulation.
12
Fig. S8. Temperature evolution in the BOMD simulations during the instant compression
and decompression, respectively.
13
Fig. S9. Computed vibration spectra at zero-pressure state after decompressed from six
different high-pressure states. The vibration spectra are computed form the Fourier
transform of the velocity auto-correction functions of C atoms in the BOMD simulation.
14
Fig. S10. The pair distribution functions of the system at (A) compression states and (B)
zero-pressure states after decompression; the enlarged plots of PDFs from 1.0 to 2.0 Å
are shown in (C) and (D). The C60-centered radial distribution functions at (E)
compression states and (F) decompression states.
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Fig. S11. The relative shift of the strongest XRD peak (100) of the high pressure phase as
a function of pressure. The peak shift of XRD of diamond (B=442GPa and B’=3.5) is
also shown in the figure. From the comparison, OACC has a compressibility slightly
lower than (or comparable to) which of diamond.
16
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