Exploring T-carbon for energy applications

Guangzhao Qin ^a, Kuan-Rong Hao ^b, Qing-Bo Yan *^c, Ming Hu *^a and Gang Su *^bd
aDepartment of Mechanical Engineering, University of South Carolina, Columbia, SC 29208, USA. E-mail: hu@sc.edu
^bSchool of Physical Sciences, University of Chinese Academy of Sciences, Beijing 100049, China. E-mail: gsu@ucas.ac.cn
^cCollege of Materials Science and Opto-Electronic Technology, University of Chinese Academy of Sciences, Beijing 100049, China. E-mail: yan@ucas.ac.cn
^dKavli Institute for Theoretical Sciences, and CAS Center for Excellence in Topological Quantum Computation, University of Chinese Academy of Sciences, Beijing 100190, China

First published on 19th March 2019

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Guangzhao Qin

Dr Guangzhao Qin received his B.S. degree (2011) from Zhengzhou University, his M.Sc. degree (2015) from the University of Chinese Academy of Sciences, and his Ph.D. degree (2018) from RWTH Aachen University. He is currently working at the Department of Mechanical Engineering at the University of South Carolina as a Post-doctoral Fellow. He was the winner of “National Award for Outstanding Self-financed Chinese Students Abroad 2017” and was honored the RWTH Aachen University Award for Outstanding Graduated Thesis (summa cum laude). His research interests are mainly on micro-/nano-scale energy transport and conversion, together with the mechanical/electronic/magnetic properties of materials (http://qgz.sxl.cn).

Kuan-Rong Hao

Ms Kuanrong Hao received her B.S. degree (2015) from Henan Normal University and her M.Sc. degree (2018) from the College of Materials Science and Opto-Electronic Technology of the University of Chinese Academy of Sciences (UCAS). She is currently a Ph.D. student at the School of Physical Sciences in the UCAS. Her research interests are mainly on condensed matter physics and computational materials physics, focusing on the applications of novel two-dimensional materials.

Qing-Bo Yan

Qing-Bo Yan is an associate professor of the University of Chinese Academy of Sciences (UCAS). His research interest is mainly on the physical properties of two-dimensional materials and energy storage materials through density functional theory based first-principles calculations and other atomistic simulation methods. Dr Yan obtained his Ph.D. degree in the School of Physical Sciences at UCAS in 2009.

Ming Hu

Dr Ming Hu received his B.S. degree from the Department of Mechanical Engineering, University of Science and Technology of China in 2001 and his Ph.D. degree in solid mechanics from the Institute of Mechanics, Chinese Academy of Sciences in 2006. He is currently an Associate Professor at the Department of Mechanical Engineering, the University of South Carolina. His research interests include micro-/nano-scale thermal transport in novel energy systems, particularly low-dimensional materials and nanostructures, interfacial heat transfer for advanced thermal management, multiphysics modeling of complex energy transport process, and novel materials design by high-throughput calculation and machine learning techniques (http://hu-lab.strikingly.com).

Gang Su

Dr Gang Su received his B.S., M.Sc. and Ph.D. degrees from Lanzhou University in 1986, 1989 and 1991, respectively. Then he joined the University of Chinese Academy of Sciences (UCAS) and was promoted as a Professor in 1997. He is currently the Distinguished Professor of Physics and the Vice President of UCAS. His research interests are mainly on frontier research in the field of condensed matter theoretical physics and computational materials physics, including strong correlation systems, low-dimensional quantum magnetism, molecular magnetism, spintronics, superconducting physics, quantum information, nanostructures and material design, new energy materials, etc. (http://tcmp2.ucas.ac.cn).

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1 Introduction

With the rapid development of human society and the global economy, the expense of resources has increased progressively, especially since the first industrial revolution.¹ The existing fossil fuels such as coal, oil and natural gas, which were accumulated in the past billions of years, would be probably exhausted in a time scale of hundreds of years due to the huge energy demand. Such approaching to resource exhaustion and the accompanying production of environmentally harmful by-products push us to find possible solutions for future energy. This could be remedied in two ways. One is to promote current utilization efficiency of energy, and to develop novel technologies to reduce the waste of energy, and to collect waste heat for reuse. The other is to find sustainable energy, renewable sources, clean fuels, etc.

It is known that a large amount of energy is wasted in factories, home cooking and vehicle driving because of the low efficiency of energy conversion. As just one example, the efficiency of engines is about 25–50%, where the remaining part of energy is dispersed in the form of waste heat, which leads to serious environmental pollution and the waste of valuable resources. If the waste heat can be recycled, we would improve fundamentally the efficiency of energy utilization and solve, to some extent, the current energy and environmental problems. On the other hand, carbon dioxide and carbon monoxide, as well as dust particles such as PM 2.5, are harmful by-products when consuming fossil fuels, which are responsible for global warming due to the greenhouse effect, and are very harmful to human health in addition to the environmental pollution. Thus, it is imperative to solve these challenges by seeking next-generation energy sources that should be economic, sustainable (renewable), clean (environment-friendly), and earth-abundant.

There have been numerous studies exploring the possible utilization of carbon-based materials for next-generation energy applications due to their promising physical and chemical properties.^2–5 However, large-scale fabrication of carbon materials or carbon-based nanostructures is a formidable challenge.⁶ Extensive efforts have been dedicated to a variety of synthesis processes, such as bottom-up approaches from designed carbon molecules,⁷ pseudo-topotactic conversion of carbon nanotubes by picosecond pulsed-laser irradiation,⁸etc. Benefiting from the progress and emergence of new synthetic technology, the synthesis of novel carbon materials becomes feasible. Recently, T-carbon, which was a previously predicted carbon allotrope by theoretical study,⁹ was experimentally synthesized (Fig. 2G and H).⁸

Herein, we would like to introduce T-carbon and discuss its promising applications for next-generation energy technologies (Fig. 1 and 2). It is shown that T-carbon can be potentially used in thermoelectrics, hydrogen storage, lithium ion batteries (Fig. 3), etc. The challenges, opportunities, and possible directions for future studies of energy applications of T-carbon are also addressed.

2 T-carbon

Carbon is one of the most abundant elements on the Earth and is essential for life. Carbon atoms possess a unique ability to form bonds with other carbon atoms and nonmetallic elements in diverse hybridization states (sp, sp², sp³).^4,13 Countless carbon-based organic compounds in the form of a wide range of structures from small molecules to long chains can be generated, which have great diversity in their chemical and biological properties, and thus result in our complex living world.² Carbon exists as three natural allotropes, namely graphite, diamond and amorphous carbon (Fig. 2A–C).¹⁴ Despite the same and exclusive component of only carbon atoms, their properties are drastically different from each other, which is a strong hint of the diversity in the properties of carbon materials with different structures and orbital hybridizations. Over the last several decades, several new carbon allotropes have been synthesized with novel properties and potential applications in technology. The three most typical examples include zero-dimensional (0D) fullerenes discovered in 1985 (Fig. 2D), one-dimensional (1D) carbon nanotubes identified in 1991 (Fig. 2E), and two-dimensional (2D) graphene isolated in 2004 (Fig. 2F).¹⁵ The outstanding properties of these carbon allotropes and their highly anticipated engineering probabilities have attracted intensive attention from both academia and industry.⁵

Beyond that, a number of three-dimensional (3D) carbon allotropes have also been predicted theoretically, including M-carbon,¹⁶ bct-C₄,¹⁷ BCO-C₁₆,¹⁸etc., while T-carbon, predicted in 2011⁹ is the most impactful form (Fig. 2G). T-carbon can be simply derived by substituting each carbon atom in cubic diamond with a C₄ unit of a carbon tetrahedron (Fig. 2C and G), which is the origin of the name of ‘T-carbon’. The space group of T-carbon is Fdm, the same as cubic diamond. There exist two tetrahedra (eight carbon atoms in total) in the unit cell. Such a geometric configuration of carbon atoms that forms 3D T-carbon is thermodynamically stable, which is confirmed by Sheng et al. with the non-imaginary frequency of the phonon dispersion.⁹ The lattice constant of the fully optimized T-carbon is about 7.52 Å, which is more than twice that of diamond (3.566 Å). As compared to the bond length in diamond (1.544 Å), the bonds in T-carbon are of two types with bond lengths of 1.502 and 1.417 Å for intratetrahedral and intertetrahedral bonds, respectively.¹⁹ Besides, different from the bond angle in diamond (109.5°), the bond angles in T-carbon are 60 and 144.74° for the bonds in tetrahedra and the two inequivalent bonds, respectively, implying the existence of strain. Because of the large interspaces between atoms in T-carbon, the density is 1.50 g cm⁻³, which is much lower compared to that of diamond, graphite, M-carbon and bct-C₄.⁹ In addition to the low density, the Vickers hardness of T-carbon is calculated to be 61.1 GPa, which is around 1/3 softer than diamond (96 GPa).^9,20 The low density with large interspaces between atoms and the soft nature promise broad applications of T-carbon.

T-carbon has recently been synthesized experimentally (Fig. 2H) from a pseudo-topotactic conversion of multi-walled carbon nanotubes (MWCNTs) suspended in methanol under picosecond pulsed-laser irradiation.⁸ First, MWCNTs (length: 100–200 nm; diameter: ∼10–20 nm) are prepared by chemical vapor deposition (CVD) and subsequent processing. After being dispersed in absolute methanol, the suspension containing individual MWCNTs is irradiated with a laser, while stirring with a magnetic stirring bar under a nitrogen atmosphere. In the fast and far-from-equilibrium process, the metastable structure is captured with a successful transformation from sp² to sp³ chemical bonds (Fig. 2H) and the suspension becomes transparent after the laser reaction. Hollow carbon nanotubes are transformed into solid carbon nanorods, where the connections between carbon atoms are exactly the same as the theoretically predicted T-carbon, demonstrating the synthesis of this structure. During the transformation process, the time scale of energy transfer from the laser to the MWCNTs and the subsequent ultrafast quenching play a key role in the formation and stabilization of T-carbon. The cubic crystal system of the generated T-carbon NWs is confirmed by the fast Fourier transform (FFT) pattern at different tilting angles from high-resolution transmission electron microscopy (HRTEM) images. The successful synthesis of T-carbon provides an additional member in the carbon family, as another achievable 3D carbon allotrope, in addition to graphite, diamond, and amorphous carbon (Fig. 2).

The proposition of T-carbon and its subsequent experimental realization is a breakthrough in carbon science.^21,22 Compared with other allotropes of carbon, T-carbon has many unique and intriguing properties (Fig. 1), suggesting that it could have a wide variety of potential applications in photocatalysis, solar cells, adsorption, energy storage, supercapacitors, aerospace materials, electronic devices, etc. For example, T-carbon is predicted to be a semiconductor with a direct band gap of ∼3.0 eV at the Γ-point (GGA: 2.25 eV; HSE06: 2.273 eV; B3LYP: 2.968 eV).^9,23 The orbitals in T-carbon hybridize with each other and form anisotropic sp³ hybridized bonds. As for the two types of bonds in T-carbon, the charge density is found to be much larger for the intertetrahedron bonds compared to the intratetrahedron bonds, indicating relatively stronger intertetrahedron bond strength with more accumulated electrons. The bond strengths are consistent with the bond lengths, which stabilize the structure by balancing the strain from the carbon tetrahedron cage. Moreover, the band gap could be effectively adjusted by doping elements or strain engineering, so as to be suitable for photocatalysis and solar cells.^23–25 Particularly, the band gap can be tuned in the range of 1.62–3.63 eV with group IVA single-atom substitution, where the doped structures show retained stability.²⁵ Quite recently, it was shown that T-carbon nanowires exhibit better ductility and larger failure strain than other carbon materials such as diamond and diamond-like carbon.²⁶ It was also reported that the transport properties of T-carbon can be effectively modulated by imposing strain.²³ With the specific characteristics of the electronic band structures, such as the efficient electron transport,²³ T-carbon has the potential to be used as a thermoelectric material for energy recovery and conversion,²⁷ especially after doping or strain engineering. Besides, owing to its ‘fluffy’ crystal structure, T-carbon is also a possible candidate for the storage of hydrogen, lithium, and other small molecules for energy purposes. In the following, the specific applications of T-carbon in thermoelectrics, hydrogen storage, and lithium ion batteries will be discussed in detail, to illustrate its potential applications in future energy fields.

3 Thermoelectrics

In the sense of ‘turning waste into treasure’, thermoelectric power generation has received extensive attention in recent years due to its low cost of operation. By achieving an output voltage through a temperature gradient based on the Seebeck effect, thermoelectrics shows a strong capability of first-hand solid-state conversion to electrical power from thermal energy, especially from the reuse of waste heat,²⁸ thereby revealing a valuable application in reuse of resources and of aid in the saving of energy. Generally, the thermoelectric efficiency and performance can be characterized by a dimensionless figure of merit ZT = S²σT/κ,²⁹ where S, σ, T and κ represent the thermopower (Seebeck coefficient), electrical conductivity, absolute temperature and total thermal conductivity, respectively. To approach the Carnot coefficient, a high energy generation efficiency is necessary, which corresponds to a large ZT. The continuous improvement of thermoelectric performance and the drive to increase the power output under the same heat source are the key focus in thermoelectric technology, which requires the in-depth study of thermoelectric conversion materials and the development of new materials.

Based on electronic structures and previously studied thermal transport properties of T-carbon,²⁷ we examined the thermoelectric performance of T-carbon by combining first-principles calculations with semi-classical Boltzmann transport theory.^29,30 The thermopower of T-carbon shown in Fig. 3A (∼2000 μV K⁻¹) is comparable with, or even larger than some excellent thermoelectric materials, such as SnSe (∼550 μV K⁻¹)³¹ that was reported to have an unprecedentedly high ZT value. The huge thermopower of T-carbon indicates its strong potential to serve as a thermoelectric material for energy recovery and conversion.

The overall view of the evaluated ZT values of T-carbon shows that it is a high-temperature n-type thermoelectric material (Fig. 3B). However, the thermoelectric performance of T-carbon is not good enough when compared with other existing thermoelectric materials.²⁸ For instance, SnSe possesses a ZT value of 2.6 at 930 K along a specific lattice direction.³¹ The reasons could result from two aspects. First, the electronic energy band gap of T-carbon is relatively large, and the conduction band minimum (CBM) and valence band maximum (VBM) are relatively flat, which may lead to a large effective mass of the carriers and thus lower the electrical conductivity. Second, the thermal conductivity of T-carbon at room temperature is 33 W m⁻¹ K⁻¹,²⁷ which is much higher when considering thermoelectric applications relative to SnSe (0.46–0.68 W m⁻¹ K⁻¹).³¹

Nevertheless, there exists large room for further improving the thermoelectric performance of T-carbon in view of its excellent thermopower through, e.g. applying strain,²⁹ doping appropriate elements,³² or cutting into lower dimensional structures to modify the transport properties.³³ We then examined possible approaches for the improvement of the thermoelectric performance of T-carbon. As shown in Fig. 3C, by either applying compressive strain of 2% or doping calcium (Ca) and magnesium (Mg) atoms into the fluffy structure of T-carbon, the power factor can be effectively improved. We focus on n-type doping, since T-carbon is a n-type thermoelectric material as discussed above. The reason for the doping enhanced power factor lies in two aspects. On the one hand, with Ca/Mg atoms doping, the characteristics of the conduction band are retained, promising a large thermopower after doping. On the other hand, the electronic band gap changes from direct to indirect and is largely decreased, leading to a large electrical conductivity. Note that the thermal conductivity commonly decreases with foreign atom doping, thus the thermoelectric performance of T-carbon would be largely improved owing to the simultaneously improved electrical transport properties and reduced thermal transport properties.

Considering the huge computational costs, instead we can empirically estimate the thermoelectric performance based on the estimated thermal conductivity with atom doping. Assuming a one order of magnitude decrease of the thermal conductivity with Ca/Mg atoms doping, the ZT value of T-carbon is estimated to be largely enhanced with a two-fold increase. Moreover, by cutting T-carbon into two-dimensional structures along the (111) direction, the power factor can also be improved, especially at low temperatures (Fig. 3C). The large power factor at low temperature makes T-carbon at the nanoscale level change from a high-temperature thermoelectric material to a low-temperature thermoelectric material, suggesting its wider applications for energy conversion, such as waste heat recovery under ambient conditions.

4 Hydrogen storage

The search for sustainable, renewable, and clean fuels on demand, is important as we are facing the challenges of an energy crisis and climate change. Since the 1970s, hydrogen has been regarded as one of the most promising alternatives to fossil fuels due to its clean combustion. Water (H₂O) is the only by-product for hydrogen combustion, which has great advantages compared with the combustion of fossil fuels producing greenhouse gases and harmful pollutants. Moreover, hydrogen is lightweight, providing a higher energy density and making hydrogen-powered engines more efficient than internal combustion engines. The reason hampering the popularization of hydrogen economy lies in that it is difficult to store large amounts of hydrogen safely, densely, rapidly, and then access it easily. Extensive efforts have been dedicated to discovering new materials as next generation hydrogen storage materials, including extremely porous metal–organic framework (MOF) compounds.³⁴

Benefiting from the high surface area and lightweight nature of carbon materials, there have been many efforts in designing novel porous carbon materials for hydrogen storage applications.^3,13,35,36 Since T-carbon itself is a fluffy carbon material, there are large interspaces between atoms compared with other forms of carbon materials, which could make it potentially useful for hydrogen storage (Fig. 1 and 3D). In fact, T-carbon possesses a low density (∼1.50 g cm⁻³) as mentioned above, which is approximately two-thirds that of graphite and half that of diamond.⁹ By absorbing hydrogen into the fluffy structure of T-carbon, the hydrogen storage value can be estimated based on the number of adsorbed hydrogen molecules (H₂), which is a maximum of 16 for one unit cell in a stable structure. The adsorption energy for hydrogen in T-carbon is defined as³⁶

Eadsorption = [ET-carbon + nEH2 − Etotal]/n,	(1)

where E_T-carbon is the total energy of T-carbon, E_H2 is the total energy of hydrogen molecules, n is the number of hydrogen molecules adsorbed, and E_total is the total energy of T-carbon with hydrogen absorbed. E_adsorption is 0.173 and −0.216 eV for 8 and 16 H₂ absorbed, respectively. Considering the strong C–C bonding in T-carbon, the system is stable despite the weak repulsive interactions among the absorbed H₂, like in fullerenes with hydrogen absorbed. Under the condition of maximum H₂ adsorption, the hydrogen storage capacity of T-carbon is estimated to be ∼7.7 wt%, which makes it quite competitive for high-capacity hydrogen storage.⁹

5 Lithium ion batteries

Rechargeable energy storage devices such as lithium ion batteries (LIB) are playing a critical role as portable power sources in electronic devices, biomedicine, aviation space and electric vehicles.³⁷ Various carbon-based materials have been widely used in LIB, among which graphite is the most commonly used anode material. Due to its layered structure with high specific surface area and large interlayer space to accommodate lithium atoms, graphite has a high specific energy capacity (372 mA h g⁻¹).³⁸

As a new member of the carbon materials family, T-carbon could be also a promising electrode material for LIB and other rechargeable energy storage devices due to its fluffy structure. The possibilities of T-carbon acting as an electrode material for alkali metals (Li, Na, K) and alkaline-earth metal (Mg) ion batteries were investigated based on first-principles calculations. The specific capacity of metal atoms is defined as C = nF/M_CX,³⁷ where n represents the number of electrons involved in the electrochemical process (n = 1 for Li, Na, K; n = 2 for Mg), F is the Faraday constant with a value of 26.801 A h mol⁻¹, M_CX is the mass of C_X (C = carbon atoms, X = number of carbon atoms, which is 8 for T-carbon). Our results reveal that T-carbon is a good anode material for LIB with a specific energy capacity of 588 mA h g⁻¹, which is 58% higher than that of graphite (372 mA h g⁻¹).³⁸ In the Li intercalated compound, the corresponding formula is Li₂C₈, indicating that two Li ions can be intercalated in each T-carbon unit cell. The results for Na, K and Mg are also similar, except that the specific energy capacity for Mg is higher, at 1176 mA h g⁻¹, due to its doubled number of valence electrons.

As shown in Fig. 3E, the most stable adsorption site of metallic ions was calculated to be the center of the vacancy of T-carbon, which is indicated as the T₁ site. The migration process of M (= Li/Na/K/Mg) ions in T-carbon was simulated by means of the climbing image nudged elastic band method (CI-NEB)³⁹ in a 2 × 2 × 2 supercell. As indicated in Fig. 3E, the minimum migration path is between neighboring T₁ sites. The middle point (T₂ site) corresponds to the saddle point on the potential energy surface. Fig. 3F shows the energy evolution for the migration process, where the migration barriers are 0.075, 0.233, 0.528 and 0.688 eV for Li, Na, K and Mg, respectively. The lowest barrier for ion moving from a T₁ site to a neighboring T₁ site in T-carbon is observed for Li ion.

It should be noted that the Li migration barrier in T-carbon is about one-quarter of that in graphite (0.327 eV),³⁸ which implies that the diffusion constant of Li ion in T-carbon should be 1.7 × 10⁴ times larger than that of Li ion in graphite following the Arrhenius law (D ∼ exp(−E/k_BT), where E, k_B and T are barrier energy, Boltzmann constants and temperature, respectively).⁴⁰ Thus, T-carbon should be a very good material for the diffusion of Li ions, revealing that it might be useful for the ultrafast charge and discharge of future rechargeable energy storage devices.

6 Opportunities and challenges

Both opportunities and challenges exist for the applications of T-carbon in next-generation energy technologies (Fig. 1). To achieve better thermoelectric performance of T-carbon, doping other elements can be performed by following what researchers have performed previously for clathrates and skutterudites,⁴¹ which are hot thermoelectric materials with hollow cage-like structures. In terms of the fluffy structure with low density and hollow features (Fig. 1), the characteristics of ‘phonon glass & electron crystals’ could be realized in T-carbon by filling the holes with different kinds of atoms and different filling rates, thus reducing its thermal conductivity and simultaneously improving its electrical transport properties, which would make T-carbon a better thermoelectric material. In addition to the filling doping, one can also introduce nanotwin structures into T-carbon, which could have a similar effect.⁴² Based on previous works, possible interstitial atoms to improve the thermoelectric performance of T-carbon could be lanthanides, alkali metals, alkaline-earth metals, and rare-earth metals. Other approaches in addition to applying external fields³³ and bond nanodesigning,^43,44 such as strain engineering and nanostructuring, would also be possible (Fig. 3C). Further detailed and comprehensive studies for examining possible improvement of thermoelectric performance, especially from experimental aspects, are expected to occur.

In addition, with the potentially high capacity of hydrogen storage in T-carbon, the effects of different surface areas, pore volumes, and pore shapes on hydrogen storage parameters should be examined. New methods to enhance the storage capacity are necessary, such as the addition of metal catalysts, which has been previously reported to considerably improve the capacity of hydrogen storage. With the fluffy structure, it is also possible for T-carbon to be used for storing or filtering of other small molecules for energy purposes beyond applications in LIBs. Beyond the applications of T-carbon in thermoelectrics, hydrogen storage, and lithium ion batteries as discussed above, T-carbon, especially T-carbon based heterostructures,^4,7,45 could have a wide variety of potential applications in further energy fields (Fig. 1), such as electrochemical, photocatalysis, solar cells, adsorption, energy storage, supercapacitors, aerospace, electronics, etc., which are clearly worth further investigation in the future.

To further explore potential applications of T-carbon in energy fields, much effort on fabrication methods and large-scale production of T-carbon should be made (Fig. 1).⁶ Apart from the synthesis method reported in ref. 8, plasma enhanced chemical vapor deposition at an appropriate environmental pressure is also a possible route to generate T-carbon. Particularly, T-carbon is found to be more stable and more easily formed in negative pressure circumstances since it possesses a relatively smaller enthalpy than diamond beyond −22.5 GPa. In addition, T-carbon could be grown from seed microparticles in a chemical vapor transport process, where the seed quality and distribution should be optimized to obtain high-quality T-carbon samples. With the development of more environment-friendly technologies, the potential applications of T-carbon in energy fields would not only produce a scientifically significant impact in related fields, but also lead to a number of industrial and technical applications.

Beyond the applications in energy fields, T-carbon may also contribute to solving the observed carbon level in interstellar dust,⁴⁶ which has remained an unsolved question for decades. Observations reveal that the apparent abundance of carbon in the interstellar medium is only ∼60% of its solar value, leading to a difficulty in explaining the interstellar extinction curve with the traditional interstellar dust models.⁴⁶ Due to the fluffy structure of T-carbon, its density is approximately two-thirds that of graphite while the optical absorption of T-carbon has a sharp peak around 225 nm, which is very close to the broad ‘bump’ centered at 217.5 nm in the interstellar extinction curve.^8,46 Moreover, the negative pressure circumstance in the universe is beneficial for the formation of T-carbon. Thus, it would be very meaningful to explore whether T-carbon already exists in the universe beyond the artificial synthesis regime.

7 Computation details

All calculations involved in this paper (Fig. 3) were carried out by means of first-principles calculations in the framework of density functional theory (DFT) as implemented in the Vienna ab initio simulation package (VASP).⁴⁷ The projector augmented wave (PAW) method⁴⁸ was employed for interactions between ion cores and valence electrons. The electron exchange–correlation interactions were described by the generalized gradient approximation (GGA) in the form proposed by Perdew–Burke–Ernzerhof (PBE).⁴⁹ The cutoff energy was set as 1000 eV for plane-wave expansion of valence electron wave functions. The structure relaxation considering both atomic positions and lattice vectors was performed until the total energy was converged to 10^–8 eV per atom and the maximum force on each atom was less than 0.001 eV Å⁻¹. The Monkhorst–Pack scheme⁵⁰ was used to sample the Brillouin zone (BZ) with a 11 × 11 × 11 k-point mesh.

Conflicts of interest

There are no conflicts to declare.

Acknowledgements

G. Q. gratefully acknowledges Dr Zhenzhen Qin (Zhengzhou University) for the literature review and Dr Huimin Wang (Nanjing University) for plotting Fig. 1. G. Q. also thanks Dr Xianlei Sheng (Beihang University) and Mr Jingyang You (University of Chinese Academy of Sciences) for their fruitful discussions. This work was supported in part by the National Key R&D Program of China (Grant No. 2018YFA0305800), the NSFC (Grant No. 11834014, 14474279), and the Strategic Priority Research Program of the Chinese Academy of Sciences (Grant No. XDB28000000, XDPB08).

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