Unexpected Huge Dimerization Ratio in One ... - ACS Publications

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Unexpected huge dimerization ratio in one-dimensional carbon atomic chains Yung-Chang Lin, Shigeyuki Morishita, Masanori Koshino, Chao-Hui Yeh, Po-Yuan Teng, Po-Wen Chiu, Hidetaka Sawada, and Kazutomo Suenaga Nano Lett., Just Accepted Manuscript • DOI: 10.1021/acs.nanolett.6b04534 • Publication Date (Web): 22 Dec 2016 Downloaded from http://pubs.acs.org on December 27, 2016

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Unexpected Huge Dimerization Ratio in One-Dimensional Carbon Atomic Chains Yung-Chang Lin1*, Shigeyuki Morishita2, Masanori Koshino1, Chao-Hui Yeh3, Po-Yuan Teng3, Po-Wen Chiu3, Hidetaka Sawada2, Kazutomo Suenaga1,4* 1

National Institute of Advanced Industrial Science and Technology (AIST), Tsukuba 305-8565, Japan 2 3

4

JEOL Ltd., 3-1-2 Musashino, Akishima, Tokyo 196-8558, Japan

Department of Electrical Engineering, National Tsing Hua University, Hsinchu 30013, Taiwan

Department of Mechanical Engineering, The University of Tokyo, 7-3-1 Hongo, Bunkyo-ku, Tokyo 113-8656, Japan

Abstract Peierls theory predicted atomic distortion in one-dimensional (1D) crystal due to its intrinsic instability in 1930. Free-standing carbon atomic chains created in situ in transmission electron microscope (TEM)1–3 is an ideal example to experimentally observe the dimerization behavior of carbon atomic chain within a finite length. We report here a surprisingly huge distortion found in the free-standing carbon atomic chains at 773 K, which is 10 times larger than the value expected in the system. Such an abnormally distorted phase only dominates at the elevated temperatures, while two distinct phases, distorted and undistorted, co-exist at lower or ambient temperatures. Atom-by-atom spectroscopy indeed shows considerable variations in the carbon 1s spectra at each atomic site but commonly observes a slightly downshifted π* peak which proves its sp1 bonding feature. These results suggest that the simple model, relaxed and straight, is not fully adequate to describe the realistic 1D structure, which is extremely sensitive to perturbations such as external force or boundary conditions.

KEYWORDS: graphene, carbon atomic chain, STEM, EELS, carbon dimerizing, Peierls distortion *Corresponding Author: [email protected], [email protected]

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Monoatomic carbon chain is an ideal 1D crystal of carbon and the last missing puzzle of the carbon allotropes. Astonishing properties, such as unusual electrical transport phenomenon4,5, the extremely high stiffness6 and ballistic thermal conductivity7 have been so far predicted in theory. Experimentally, the carbon chains have been synthesized as long molecules by organic chemistry methods8,9 and has been found either within the cavity of carbon nanotube (CNT)10,11 or sculpted from CNT1,12 or graphene2,3,13,14 by using a high energy electron beam in TEM. However, the detailed atomic structure, involving the C-C bond nature, of this new 1D crystal has hardly ever been experimentally investigated at atomic level.

The sp1-hybridized carbon chain with an infinite length is believed to form two possible chemical structures, i.e., cumulene which consists of periodic identical double bonds (=C=C=C=C=), and polyyne which consists of alternating single and triple bonds (‒C≡C‒C≣C‒)15. The π bands in the undistorted cumulene should behave as a metallic 1D free electron system, while the π electrons in the distorted polyyne tend to be localized at the triple bonds and behave as a dielectric with charge density wave (CDW)6,16,17. Two phases are close in energy and can be easily alternated by changing the total number of carbon atoms or boundary conditions16,18–21. A transformation from the metallic cumulene to semiconducting polyyne has been expected in theory to be initiated by applying strain6,18 or different thermal perturbations17,22. Linear and nonlinear electrical conductivities of a carbon chain have been recently reported by two-probe transport method in a TEM23,24. However, the atomic configuration of these carbon chains has never been corroborated so far, neither the direct phase discrimination has been made. The instability and fragility of the carbon 1D crystals indeed disturb the precise detection of atomic position.


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In this paper, we directly identified the atomic structures of individual carbon atomic chains at various temperatures ranging from 773 K to cryogenic temperature (97 K) by atomic resolution annular dark field (ADF) imaging in scanning TEM (STEM) as the schematic shown in Fig. 1a. The ADF images were obtained by using JEOL-2100F microscope equipped with delta correctors and a cold-field emission gun operated at 60 kV25. Simultaneous atom-by-atom electron energy-loss spectroscopy (EELS) mappings were performed to confirm the atomic species and perceive the bonding state by using a post-column electron spectrometer (Gatan Image Filter Quantum). Elevated temperature and cryogenic temperature experiments were realized by using JEOL heating holder and Gatan liquid Nitrogen sample holder, respectively. Carbon atomic chains were created in situ from a suspended single-layer graphene by electron beam (e-beam) sculpting as previously reported2,3. The experiment was very well reproducible and the carbon chains thus created were completely free-standing between two graphene edges.

Figure 1b~1f show typical ADF images of carbon chains recorded at 773 K. Suspended carbon chains sculpted from graphene were extremely stable at 773 K and could sustain more than several hundred seconds under the 60kV e-beam continuous irradiation. We believe that the main reason that the carbon chain breaks is due to the beam-induced chemical etching which is largely dependent on the TEM environment. The specimen becomes ultraclean after high temperature annealing. Empirically we know that a better vacuum level and clean specimen helps the carbon chains last longer. We show the raw ADF images (left) and the filtered images (right) in Fig. 1b and 1c. The carbon chains appear one or two strands bridging between two graphene edges with rather shorter length (< 1 nm). The atomic positions were clearly identified with surprisingly large bond length alternation as pairing of two carbon atoms


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(highlighted in Fig. 1d~1f). We have analyzed more than 80 different carbon chains in ADF images (See more examples in Figure S1) to determine the bond length as the longer one (~1.51±0.14 Å) and the shorter one (~1.08±0.11 Å) in the suspended carbon chain at 773 K with careful calibrations and specimen drift corrections. To preclude any possible artefacts in the slow-scan STEM imaging (scan rate of 0.05~0.3 fps), we performed identical experiment to visualize suspended carbon atomic chains by using aberration corrected TEM with a fixed electron beam. The TEM images were obtained by using another JEOL-ARM microscope equipped with double delta correctors and a monochromator after the Schottky field emission electron source operated at 60 kV26 which enables to achieve a point resolution of 1Å and to resolve the carbon atoms in chains. High resolution (HR) TEM imaging was acquired by a Gatan OneView camera with 1~3 fps (4k x 4k resolution).

Figure 2a~2e shows HR-TEM images obtained at 298K where the atomic positions were clearly resolved and the carbon chains exhibit unambiguous dimerization. The atomic pairing exists in short carbon chains (4~6 atoms, Fig. 2a) and also in longer chains (10~12 atoms, Fig. 2b and 2c). Extra HR-TEM images are shown in Figure S2. Some of the measured interatomic distances are surprisingly short. We cannot fully exclude the out-of-plane vibration/movement and/or inclination of chains during the acquisition. The out-of-plane distortion is most probably not visible in our experiments even for the faster TEM imaging not for the sharper defocus depth of employed monochromated TEM (energy width ∆E~160 meV). The chains are indeed often curved and our DFT calculation does not exclude the out-of-plane bending either (Figure S3). Therefore the measured C-C distance might have been slightly underestimated due to its projected images as the reviewer pointed out. However, it gives only a few % error for the measured C-C bond lengths. In our


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experiment, carbon chains consisting of odd number atoms are very rare to find by the slow-scan STEM-ADF imaging. By considering the boundary condition which forms a single bond at the contact of carbon chain and graphene edge, the single-triple bond alternation causes the odd-numbered carbon chain less stable due to a bond number mismatch in the center27,28. Despite of their short lifetime, the odd-numbered carbon chains become visible under the high-speed HR-TEM imaging. Figure 2d and 2e are the consecutive HR-TEM images showing structural transformation from two 4-atom chains to two 5-atom chains with a cross-link between the middle carbon atoms (marked as 3rd) at 298K. The extra 5th atom of the carbon chain was supplied from the connecting pentagon through a bond breaking (highlighted by yellow arrows). Figure S4 shows another example of structure transformation between a pair of 4-atom chains and 5-atom chains as well as longer chains of 9-atom and 11-atom chains (more clearly visible to eye in Movie M1 and M2). The formation energy of two 5-atom chains with a cross-link between the middle carbon atoms was calculated about 26 meV higher than two isolated 5-atom carbon chains12. In our experiment, carbon atoms can gain energy from the high energy electron beams and result in structure transformation. Forming a cross-link between two odd-atom chains can stabilize the alternating single-triple bonding configuration to maintain the huge atomic dimerization. Previously, Jin et al and Chuvilin et al have reported the sp2 bonding configurations existing in the middle of single carbon chains with a bifurcation or a knot-like structure2,3. Here, this is the first experimental visualization of how two carbon chains interact and switch between sp1 and sp2 bonds of specific carbon atoms with unambiguous atomic configurations.

Based on the Peierls theorem at a nonzero vibrational or a strained condition, atoms in a 1D carbon chain tend to dimerize in pair15,17. The dimerization ratio (∆) in


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a monoatomic carbon chain can be derived by ∆=

ߜܴ ܴ

where the bond length alternation value δR = |r1 - r2| is described as the difference between two adjacent bonds; R = (r1 + r2)/2 is the mean bond length of the two adjacent bonds. The dimerization in the carbon chains can be attributed to several parameters such as contact geometry, even number of atoms, shorter chain length, higher temperature, charging state, or larger strain. We carried out a density functional theory (DFT) calculation to find an optimized structure of 4~6 atom carbon chains under a strain with different contact geometries. Short carbon chains consisting of 4 and 6 carbon atoms show similar behavior in dimerization level under a strain in this calculation (Fig. 2f). The dimerization level in a 4-atom carbon chain spanning between armchair graphene edges is more sensitive to a strain than that spanning between zigzag graphene edges. In addition, we found that the local negative charging, a reasonable situation for a thin specimen under e-beam irradiation, can slightly increase the dimerization level as shown in Fig. 2g.

In our STEM and TEM experiments, the dimerization ratio obtained statistically is shown in Fig. 3. At 773K, the distortion degree was distributed at a maximum value at ∆= 0.33±0.04 (Fig. 3a) which is more than 10 times larger than the theoretical value (∆= 0.03) of an ideal infinite polyyne18 and 2 times larger than short polyyne molecules8,9 and that under a

highest possible strain of 12~40% (∆=

0.13~0.24)6,15,17,23,29,30. At 298K, the statistical dimerization ratio histogram therefore shows roughly a monotonous decrease from the undistorted value as shown in Fig. 3b. Such distribution suggests that the carbon chains are also dimerized at room temperature but less than that at higher temperature. Looking back to the dimerized


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4-atom carbon chain shown in Fig. 2d, we found that the two ends of the carbon chains were pulled out 10.6% by analyzing the distance between two graphene contact edges (See Figure S5). Based on the DFT calculation, 10.6% strain can only contribute ∆DFT = 0.7~0.13 dimerization ratio which is about 2~3 times smaller than our experimental value (∆ = 0.21±0.12). When the graphene sample was cooled down to cryogenic temperature (97 K), defects and/or large holes were very rapidly generated in a suspended graphene layer under the e-beam irradiation at the cryogenic temperature due to the ice/water mediated chemical etching. The length of carbon chains created by e-beam was relatively longer (2~3 nm, about 8~16 atoms) as shown in Figure S6. The bond length distribution between carbon atoms in the carbon chains was found a peak in equal distance with the minimum dimerization ratio as one can see in Fig. 3c. This suggests the carbon chains at low temperature are mostly cumulene with the symmetric bonds. In some cases, however, carbon atomic pairs are also found occasionally and the distorted polyyne phase appears to coexist even with a lower possibility (Figure S6a and S6e). Some other theoretical studies also dealt with the distorted chains and predicted higher dimerization ratio in shorter carbon chain under the same strain17. A most reasonable explanation for our experiment would therefore be an unintentional strain applies to the carbon chain and a possible charging. Although no intentional tensile/compressive force was applied to the carbon chains during our experiments, one can easily expect that a free-standing carbon atomic chain bridging two macroscopic graphene edges could feel an external force due to the elastic constant of the graphene layer during being thinned by e-beam. Interestingly, the length of the single bonds is similar as in fullerenes where the underlying graphene lattice is also heavily strained. The present existing DFT model does not fully support the experimental value. Many-body perturbation theory could provide more accurate approximation than DFT for the determination of excited


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states31. New atomic model with stronger bonding force to form carbon dimers will be needed in future study.

According to the experiment presented above, the carbon chains exhibit unambiguous dimerization at high temperature, which suggests the more preferable polyyne-like carbon chain. On the other hand, the carbon chains can be a mixture with less distorted and undistorted phases, closer to cumulene, at cryogenic temperature. The near-edge fine structure accessible by EELS is a method to perceive single atom bonding-state32–37. EEL spectra of carbon chains at different temperatures (773K, 298K and 97K) are shown in Fig. 3d, 3e and 3f. The energy-loss near-edge structure of the carbon chain at 773K shows a pronounced sharp π* peak at 284.4±0.2 eV with a reduced intensity of σ* peak. An additional noticeable resonance peak near 289±0.4 eV (labeled with asterisk) is also found for the carbon chain. This resonance peak is often referred to the bonding with hydrogen or oxygen38, which is not validated in our experiment because no oxygen signal was detected along the chain, though we cannot rule out the existence of hydrogen. Alternatively the asterisk-labeled peak can be a second π* resonance resulting from the interaction of the triple bonds as already found in the known carbon molecules, such as 2,4-Hexadiyne39. This asterisk-labeled peak signifies the existence of triple bonds between the dimerized atomic pair in the suspended carbon chain. The π* peak at 773K is found 0.2 eV higher in its position than that at 97K. This suggests that the π* peak of polyyne-like chain is considerably higher than the cumulene-like chain even though both share the sp1 feature. The energy difference between π* and σ* peaks at 97K is 2 eV larger than that at 773K, while the intensity ratio of π*/σ* is definitely higher in the less distorted phase at lower temperatures. Furthermore, an additional resonance peak at 287±0.1 eV (labeled †) was often visible at the cryogenic temperature, which may be attributed to


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a characteristic resonance from the carbon double bonds.

To realize the single atom spectroscopy along the 1D carbon chain, a high beam current (~30 pA) was employed with the convergence semi-angle of 48 mrad and the inner acquisition semi-angle of 53 mrad through a 9 mm EELS aperture to obtain sufficient S/N ratio. Figure 4 shows an atom-by-atom EELS mapping of the hugely distorted polyyne-type double carbon chains at the specimen temperature of 773 K. Unambiguous bond length alternation along the carbon chain can be seen in the simultaneously recorded ADF image in Fig. 4a. Figure 4c shows the distinct EEL spectra of the carbon chain (red), graphene (green), and graphene edges (blue) extracted from the EELS colored maps (13 x 10 pixels) shown in Fig. 4b (an atomic model is overlaid). The carbon chain shows a pronounced sharp π* peak at 284.5 eV (labeled π*-C) with a reduced intensity of σ* peak (extracted from the red colored pixels in Fig. 4b). The standard sp2-graphene spectrum shows a sharp π* peak at 285 eV (labeled π*-G) and the exciton σ* peak at 291 eV extracted from the green colored pixels in the same set of spectrum-image in Fig. 4b. At the graphene edges, an extra π* peak around 282.7 eV (labeled π*-E) shown in the spectrum (extracted from the blue colored pixels in Fig. 4b) is fully consistent with the armchair edges previously reported33,40. The π* peak intensity of carbon chain is 2 times stronger than the graphene π* peak. The prominent π* excitation peak of carbon K-edge is unique for the sp1 hybridized hydrocarbon molecules38,41–45, which clearly indicates the existence of unsaturated carbon bonds in the suspended carbon chain. Figure 4d lists the EEL spectra of each single carbon atom corresponding to the numbered atomic position in Fig. 4b. Each carbon atom exhibits a sharp π* peak for the sp1-hybridization K-excitation feature which fits well with the EELS simulation based on CASTEP code (purple dashed line). Note that the intensity ratio of π*, asterisk, and σ* peaks


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can vary at each atomic site. Even though the inevitable noise level for each atomic spectrum, we infer that these states can be affected by the finite length carbon chain due to the different boundary conditions.

In this work, we found the two distinct phases existing in truly atomic 1D carbon crystals. A huge atomic dimerization much greater than the Peierls transition was clearly discovered in the short suspended carbon chain. Recently, investigation of 2D materials and 1D nanowires becomes urgently important since the miniaturation of silicon electronics have approached to the atomic scale. Also several low-dimensional materials are demonstrated as promising candidates for next generation electronic devices, and their 1D transformations often exhibit unique electronic properties rather than their bulk crystals46,47. As demonstrated here, quantifying the atomic distortion in low-D materials which is known in textbook to govern the long-range order through the BKT transition such as the CDW, superfluid or superconductivity phenomena is now directly accessible for any 2D materials and their 1D derivatives.

Method Sample preparation. Single domain graphene monolayers were synthesized on Cu foil by chemical vapor deposition of methane at 1323 K. Graphene films were transferred onto SiO2/Si substrate and applied with an O3 plasma for 10 sec at a substrate temperature of 373 K. The graphene films were then transferred to SiN (50nm) microporous TEM window grids using clean transfer technique48,49.

TEM, STEM and EELS experiment condition. TEM images were taken by a double corrected JEOL-ARM microscope equipped with a Schottky field emission


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gun operating at 60kV and a double Wien filter monochromater. Gatan GIF camera was used for image recoding with an exposure time of 1sec, while a new Gatan OneView camera was used for high speed acquisition with the exposure time of 0.32~1 sec. STEM-ADF images were taken by JEOL-2100F microscope equipped with DELTA correctors and a low operating voltage (60keV) cold-field emission gun. A probe current of about 28-36 pA was employed with the convergence semi-angle of 48 mrad and the inner acquisition semi-angle of 53 mrad. The scanning dwell time per pixel was set 40~128 µs. All the ADF images presented in the main text were filtered by Gaussian blur by using ImageJ software, while the raw (unfiltered) ADF images were shown in the Extended Data with detail explanation of experimental condition. High temperature experiment was realized by using JEOL heating holder. Cryogenic temperature experiment was performed by using Gata liquid Nitrogen sample holder. The EELS 2D maps and line scans were performed by using a post-column electron spectrometer (Gatan Image Filter Quantum) with a 9 mm EELS aperture.

EELS simulation. The energy loss near edge structures (ELNES) of carbon K-edge from each atomic site are simulated by the “core spectroscopy” function in CASTEP after self-consistent field (SCF) iterations for the final state (core-hole) electron configurations. The SCF iterations were converged based on GGA – PBE functions47 with ultra-fine quality regarding 5.0×10-7 eV/atom as convergence similar to the geometry optimization. Typical parameters applied in the simulation are, for example, a (1×1×1) K-point set, 440 eV of cut-off energy in plane wave basis set and 48×48×48 FFT grid density with 1.5 of an augmentation density scaling factor. A core-hole is introduced to a carbon atom by removing an electron from core level at the atom of interest in order to simulate carbon K-edge spectra. The obtained spectra are mainly originated from 2p component of unoccupied bands smeared with 0.3 eV of energy


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broadening (FWHM) with a consideration of lifetime effect, 0.3 +0.18×(εk -εthreshold) eV, where the FWHM increases with increasing energy differential between the threshold energy, εthreshold, and the energy above the threshold, εk. For carbon K-edge, we assign a bulk carbon (far enough from vacancies or nitrogen) as a reference, having a π* peak at 285.0 eV.

Geometry optimization. The initial hexagonal structure of graphite, having parameters of a=b=246.4 pm, c=1.0 nm, α=β=90.0°, and γ=120.0° with P-6M2 symmetry, was converted into orthorhombic structure with a= 246.4 pm, b=426.7 pm, c=1.0 nm, α=β=γ=90.0° and P1 symmetry. Chain structures spanning over zigzag edge and armchair edge are created based on the orthorhombic graphite structure in a supercell with 4×6×1 and 8×3×1 unit cells. We performed the geometry optimization of carbon chains spanning over graphene edges, by using the density functional theory (DFT) implemented in the CASTEP module of the Materials Studio ver. 7.0 (Accelrys Co.). We generally obtained the structures by generalized gradient approximation (GGA) – PBE functionals50 with ultra-fine quality although we examined the differences in bond length by localized density approximation (LDA). The GGA tends to result in shorter C-C bond length than LDA and the estimated Δ=δR/R of GGA is 2% larger than that of LDA. The calculation parameters for ultra-fine quality were: the convergence threshold for the maximum energy change, maximum force, maximum stress and maximum displacement set to 5.0×10-7 eV/atom, 0.01 eV/Å, 0.02 GPa, and 5.0×10-4 Å, respectively. An SCF tolerance smaller than 5.0×10-7 eV/atom was regarded as convergence. The BFGS line search was adopted. We also set 390.0 eV of Energy cutoff, 90×72×135 FFT grid density, and a 1×1×1 K-point set. Either ultrasoft or norm conserving Pseudopotentials represented in a reciprocal space were selected as an “on the fly” option. Density mixing of 0.5 charge was used for


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electronic minimizer. A proper electronic minimization parameters (20 % of empty bands and 0.1 eV of smearing), instead of assigning fixed occupancy, were required for SCF convergence. Strain in both expanding and shrinking the length of vacuum along b-axis for zigzag edge and along a-axis for armchair edge was introduced with a step of 25 to 100 pm. At each step, the geometry optimized structures of carbon chains are obtained and the C-C bond lengths of individual carbon atoms were used to estimate the dimerization value.

Acknowledgements The authors from AIST acknowledge the support from JST Research Acceleration Programme. PWC appreciates the project support of National Tsing Hua University and

of

Taiwan

Ministry

of

Science

and

Technology:

MOST

103-2119-M-007-008-MY3 and MOST 103-2628-M-007-004-MY3(P.W.C.). MK acknowledges financial support by JSPS KAKENHI (grant number 26390004).

Supporting Information Available. The supporting information shows additional STEM and HR-TEM experiment results obtained at 773K, 298K and 97K.

Note: The authors declare no competing financial interest.

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Figure Legends Figure 1. (a) A schematic of a suspended carbon chain been created and studied by electron beam. (b) (c) Raw ADF images single and double carbon chain at 773K (left) and their filtered images (right) by Gaussian blurring. (d-f) More experimental evidences of largely dimerized carbon chains at 773K by ADF imaging. Scale bars are 2Å.

Figure 2. (a-c) HR-TEM images of carbon chain at 298K. (d,e) The consecutive HR-TEM images of two “4-atom” carbon chains transformed to two “5-atom” chains with a cross-link between the middle carbon atoms (marked as 3rd). (f) The dimerization ratio of carbon chains with different chain lengths and boundary conditions as a function of strain. The carbon chain spanning between AC edges shows more dimerized than which spanning between ZZ edges under a strain. With the same boundary condition, the 4-atom and 6-atom carbon chains show equivalent


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dimerization level. (g) The dimerization level of 4-atom carbon chain as a function of strain under different charge states. Inset shows the atomic model and the electron density map of 4-atom carbon chain under a negative (-1e-) charging. Scale bars are 2 Å.

Figure 3. (a-c) The statistical dimerization ratio of carbon chain at 773 K, 298 K, and 97 K. Purple vertical dotted line indicates the theoretical value of an ideal infinite polyyne (∆= 0.03). (d-f) The EEL spectra of carbon chain at 773 K (red curve), 298 K (green curve), and 97 K (blue curve). The π*-peak of carbon chain obtained at 97 K is highlighted by gray dashed line. Two atomic structures of the sp1-hybridized carbon chain, polyyne and cumulene-like chains. Cumulene consists of identical C-C bond length (r1 ≈ r2), while polyyne consists of alternating longer single bond and shorter triple bonds (r1 > r2) as predicted in Peierls theory. ρ(t) represents the distribution of electron charge density.

Figure 4. (a) An ADF image of two parallel carbon chains. Scale bar is 2 Å. (b) The corresponding EELS color mapping overlapped with the extracted atomic model. The 2D spectrum imaging contains 13 x 10 pixels in EELS map and simultaneous the ADF image consists of sub-pixel scan (16x16). Three color indexes in the EELS color integrated with different energy widths correspond to sp1-chain (red, 283.4‒284.5 eV), sp2-graphene (green, 284.6‒299.6 eV), and graphene edges (blue, 281.4‒282.9 eV). The acquisition time for each spectrum is 0.2 s/pixel. (c) Spectra shown are extracted from the sum of 10 pixels from the EELS map shown in (b). The simulated EEL spectra of graphene and edge are presented by green and blue dashed lines, respectively. (d) Atom-by-atom EEL spectra corresponding to each atom in the carbon chain.


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Unexpected Huge Dimerization Ratio in One ... - ACS Publications

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