Diamane: design, synthesis, properties, and challenges

Abstract Diamane, the two-dimensional counterpart of diamond, is achieved from bi-layer graphene (BLG) or few-layer graphene (FLG) through surface chemical adsorption or high-pressure technology. Diamane with interlayer sp 3 bonding is found to have excellent heat transfer, ultra-low friction, high natural frequency, and tunable band gap, which shows the potential technological and industrial applications in nano-photonics, ultrasensitive resonator-based sensors, and improved wear resistance. In this review, we summarize the structure character, synthesis strategies, and physical properties of different diamanes, including hydrogenated diamane (HD), fluorinated diamane (FD), and pristine diamane (PD). In addition, we discuss the effect of functional groups, element doping, and stacking order on the physical properties of diamane. Finally, the remaining challenges and future opportunities for the further development of diamane are addressed.


Introduction
Graphene is a two-dimensional (2D) layered material having semi-metallic properties with zero band gap. Extensive investigations have been performed to reveal the interesting physical properties. It is found that the physical properties are strongly influenced by the stacking mode or chemisorption functional group. For example, AB stacking BLG shows high carrier mobility [1] and AA stacking BLG makes the split of linear energy bands intersected with each other [2]. The interlayer interaction of bi-layer graphene (BLG) is critical for the presence of superconducting when the twist angle of the BLG changes to be about 1.1°, that is, the "magic" angle [3]. In addition, the chemical adsorption of various functional groups (such as hydrogen [4,5], fluorine [6][7][8], and oxygen [9]) on the surface of a single-layer graphene (SLG) can modify the chemical bonding and open the band gap. Furthermore, the studies have found that BLG or few-layer graphene (FLG) can generate single C-C bond between layers by the adsorption. It is well known that the free energy difference between graphite and diamond in bulk is 0.03 eV/atom [10], however, the conversion of graphite to diamond usually requires extreme conditions, such as high temperature and high pressure or plasma chemical vapor deposition technology [11][12][13][14], due to the high energy barrier of diamond nucleation. The presence of defects or dangling bonds in the precursors [15][16][17] is found to be able to decrease the energy barrier for diamond nucleation. Intuitively, the 2D graphene functionalized by the heteroatoms (foreign atoms or functional groups) is suggested to be one possible way to decrease the activation energy of the ortho-and para-positions of the hexagonal ring [18] and thus greatly reduce the transition pressure required for carbon atoms from sp 2 to sp 3 bonding state.
The study of functionalized graphene can be traced back to 2007. A structure was proposed by Sofo et al. [5] with hydrogen saturated surfaces of SLG, in which the carbon atoms becomes sp 3 hybridization, and the fully hydrogenated SLG structure was named "graphane. " After that, Elias et al. [4] obtained partially hydrogenated SLG that behaved as an insulator by placing a remarkably conductive graphene sample in hydrogen plasma. Following, the electronic properties of partially hydrogenated SLG were investigated [4,19] and the fully fluorinated SLG [7] were synthesized successfully in experiment. Then in 2009, Chernozatonskii et al. [20] tentatively simulated the C 2 H structure formed by the adsorption of hydrogen atoms on the BLG of AB (Bernal) stacking and AA (Lonsdaleite) stacking and named them "diamane. " In the past decades, numerous investigations on the properties of diamane were performed and its potential applications were found in the fields of nano-photonics [21,22] and ultrasensitive resonator-based sensors [23]. Recently, it is exciting that the fully fluorinated AB-stacked diamane [24] and pristine diamane with (2 -110) orientation [25] were synthesized successfully in experiments. It should be noted that in previous literatures, different names, such as diamane [20,[24][25][26], diamondol [27], diamondene [28], or diamene [29], was adopted for diamane, due to the diversity of surface functional groups on the diamond film surface. Here, for the convenience of discussion, we call them collectively as diamane.
In this review, we outline the structural design of diamane, including the stacking sequence of carbon layers, the number of carbon layers, the types of functional groups, and the surface hydrogenation concentration. The electronic structure, mechanical properties, heat transfer and potential superconductivity, and magnetic properties are also summarized. The stability of diamane is analyzed in thermodynamics, including diamane with different types of functional groups and pristine diamane. We also discuss the current challenges and future opportunities in the research of diamane.

Structural design of diamane
The chemical adsorption of functional groups on the carbon rings in graphene, similar to aromatics, usually leads to a disturbance of properties. As shown in Figure 1, different from the flat honeycomb pattern in graphene, the basic unit of graphane (Figure 1(a)) and diamane ( Figure 1(b,c)) with the chair-like C 6 rings forms slightly puckered carbon sheets due to the pyramidalization of hydrogenated (fluorinated) carbon atoms. Meanwhile, the presence of heteroatom increases the thickness of the material due to the addition of extra atomic layers. The studies of hydrogenated (fluorinated) diamane [20,26,30,31] indicate that the structure of hydrogenated carbon atoms is similar to diamond, and the presence of hydrogen on the surface makes the crystal lattice distorted slightly. The movement of adjacent carbon atoms in hydrogenated BLG is much smaller than that in hydrogenated SLG, because the coupling between layers drives the graphene flatter.

Different stacking and electronic structures
Unlike graphane, the stacking sequence of BLG also plays an important role in the structure and properties of diamane. When the rotation angle of the BLG is 60°, AB stacking becomes the most preferred coherent stacking sequence in energy. Without rotations, BLG is simply stacked together with AA stacking. When the different stacked graphenes meet with the surface functional groups, the cubic diamane (c-D) and hexagonal diamane (h-D) are formed, corresponding to the (111) crystal plane of cubic diamond and the (0001) crystal plane of hexagonal diamond [20], respectively. Theoretical calculations showed that the two types of diamanes with the complete hydrogenation were insulated with a narrower band gap, but harder and more brittle than graphane [20]. In addition, three-layer graphene showed the multiple stacking sequence (ABC, AAA, and AAC types) [26] accompanying with different formation energy band gap. The theoretical calculation results are shown in Figure 2. Among all the stacking types, the diamane with Bernal stacking has the lowest formation energy and the widest band gap within the same number of layers. The difference in formation energy of HD with different stacked structures in the same number of layers is less than 0.02 eV/atom. Considering the smaller difference in energy, the existence of every kind of stacked diamane cannot be ruled out. Moreover, it was found that the band gap energy of diamane with a larger number of carbon layers was smaller than that of graphane (3.5 eV), and as the number of carbon layers increases, the band gap decreases gradually. The quantum confinement effect similar to the above situation could appear in even 5-layer HD [32]. This situation is completely different from several members of diamondoid family in that the band gap is close to diamond as the number of layers increases [33].

Different conformations and multiple functional groups of diamane
In addition to the stacking sequence, the different conformations of the C 6 skeleton can also lead to varied polymorphs of diamane. In previous studies, graphane with C 6 skeleton was confirmed to have multiple conformations [35][36][37][38]. Due to the similarity of skeleton structure, the conformation of diamane could be constructed by following the conformations of cyclohexane and graphane [37,39,40]. Generally, the basic units of the C 6 skeleton can be classed into four different conformations, that is, "chair1," "chair2," "boat1," and "boat2" [41] (as shown in Figure 3

Influence of metal substrate and hydrogenation concentration
Substrate materials are vital for the preparation of the atomic-thick diamane films in experiments. Growth, transfer [1,44], and functionalization [24,43] of graphene always needs the substrate materials, which makes it necessary to study the interaction between single-sided hydrogenation (fluorination) of graphene and the substrate materials. The adsorption of graphene on metal surfaces can be classified into two categories, a strong interaction by chemical adsorption on the surface of cobalt or nickel and a weak interaction by physical adsorption on the surface of copper or platinum. the first group is a methane molecule. the next group is composed of several members of diamondoid family (adamantane, diamantine, and triamantane [34]). the last group consists of graphane and diamanes, where D (ij) stands for diamane with different stacking sequences. Reprinted from [26]. copyright 2011 american chemical Society.
The properties of these two different types of substrates were theoretically predicted during graphene hydrogenation [31]. It was found that, when there was no metal substrate, the one-side hydrogenation/fluorination of BLG was not energetically favorable to form sp 3 bonds between neighboring carbon layers. When the AB-stacked BLG was hydrogenated on a metal substrate, the "chair-like" carbon layer could not only be stabilized at the more reactive interface, such as cobalt (0001) and nickel (111), but also could form stable covalent bonds with less reactive interface, such as copper (111). The main driving force for this transformation comes from the hybridization between sp 3 orbitals and dz 2 orbitals on the metal surface. The induced electronic gap states and spin moment in the carbon layers are confined to the area within 0.5 nm of the metal surface. This metal/sp 3 carbon interface was predicted to have superconducting properties [31]. In addition, studies on the hydrogen coverage and the number of graphene layers on the metal substrate showed that when the hydrogen concentration was more than half (C 2 H) of the full coverage (C 4 H), it is beneficial to generate the interlayer sp 3 hybridization (Figure 4(a)). The stability of HD and hydrogen concentration (increase of the number of carbon layers) showed a positive correlation. Different stacks of HD can form a stable structure thermodynamically with a thickness of seven carbon layers [31] (Figure 4(b)). Graphene with low hydrogenation concentration was also predicted to be magnetic because of the localization of unhydrogenated carbon atoms and unpaired electrons [31].

Thermodynamics of pristine diamane
The transformation to diamane of FLG with clean surface is very attractive. In order to distinguish the functionalized diamane, we refer to diamane with a pristine surface as pristine diamane (PD). Kvashnin et al. [42] studied the thermodynamic phase diagram of the conversion of 2-8 layers of graphene with (111) surface to PD. It is found that when the number of layers was two, the diamond could not be nucleated due to the graphitization effect. This graphitization effect is the conversion of diamond to graphite due to the surface effects in the diamond nanostructure [35,45], which indicates that the diamond film formed by low-layer graphene requires the stability of heteroatom. At greater thicknesses, the nucleation of diamond would not be affected by surface effects. When the number of layers was greater than 5, the pristine diamane become metastable. As the number of layers increases, a semi-metal to semi conductor transition took place. Paradoxically, molecular dynamics simulation suggested that the conversion of pristine graphene to diamane was reversible [21]. In terms of phase transition pressure, theoretical results support that the formation of PD requires high-pressure conditions and as the number of layers decreases, the phase transition pressure of PD increases accordingly [21,42].

Synthesis and characterization of diamane
Experimentally, the studies on diamane are limited to HD, FD, and PD. Due to the unpaired electrons of surface carbon atoms, the synthesis of PD requires extreme higher pressure and the products cannot be maintained at ambient pressure. In addition, even though HD and FD have similar structures, the functional group atoms have a significant influence on their properties. So far, it is still difficult to synthesize fully hydrogenated diamane in experiment. The difference in stability also requires the precise control of temperature for HD preparation. Furthermore, the hydrogen and carbon atoms are difficult to characterize their content and valence properties [24]. Here, we have discussed the current experimental investigations of diamane and summarized the available synthesis method of diamane.

Hydrogenated and hydroxylated diamane
SLG hydrogenation shows that graphene with only one side exposed to hydrogen has a non-stoichiometric composition [4,46] and graphene hydrogenated from one or both sides would also easily lose hydrogen rapidly at moderate temperatures [4]. Furthermore, theoretical results prove that BLG is more difficult to be hydrogenated than SLG [32,46]. Therefore, the preparation of fully hydrogenated diamane remains difficult and requires specific temperature control. In a previous experiment, pressure was applied on the bi-layer and multi-layer graphene samples covered by the water layer through the tip of the scanning probe microscopy (SPM), and it was observed that the electric force microscopy (EFM) response was reduced significantly. However, this phenomenon was not observed in a dry environment [47]. Through simulation, it was believed that the hydroxyl group provided by the water layer on the top promoted the diamondization of graphene under the pressure but the proposed structure could not maintain at the ambient pressure. Hydroxylated diamane was predicted to be a 2D ferromagnetic insulator.
Martins et al. [28] performed the high-pressure experiments in a diamond anvil cell (DAC) to functionalize the top of BLG. Water acted as both a pressure transmission medium (PTM) and a provider of hydroxyl or hydrogen atoms in the experiment. The BLG prepared by the chemical vapor deposition is transferred to Teflon substrate. The substrate did not react with the precursor graphene and could prevent the bottom carbon atoms from being functionalized. As a result, chemical adsorption only occurred on top of graphene. Through the measurement of Raman spectroscopy during the pressurization process ( Figure 5), it was found that, as the pressure increases, the sp 3 hybridization occurred in the carbon layer, forming a mixed sp 2 and sp 3 and G band broadening. Calculations within density functional theory showed that diamane was formed at 4-5 GPa. Nevertheless, Raman spectroscopy is an indirect method to detect sp 3 carbon bonds, and the single-point measurements cannot determine hydrogen position bounded either to the surface of the layer or only to the edge. To prove that graphene forms the interlayer sp 3 bonds, more direct evidence is needed in future [48]. Hydrogenation of graphene could be also achieved by the hot filament process at nearly ambient conditions. The hot filament process can effectively generate hydrogen atoms [43,48,49] and avoid ion acceleration damage to the graphene sample. Experimentally, FLG can be grown on Pt(111) by chemical vapor deposition, and then, HD can be prepared by chemical adsorption of carbon atoms on the graphene surface with deuterium atoms produced by the hot wire process [43]. Using synchrotron spectroscopic techniques, it was confirmed that 76% of the carbon atoms in the fourlayer graphene formed interlayer sp 3 hybridization. Theoretical calculations argued that the surface adsorption of hydrogen caused the sp 3 hybridization to propagate from the surface to the carbon layers and the bottom carbon atoms interacted with the substrate and were stabilized eventually. The hot filament process can also realize the double-sided hydrogenation of graphene. However, due to the difference in the number of layers and stacking patterns during the preparation of graphene, the hydrogenated products were found to be a variety of mixtures of diamane checked by Raman spectroscopy and Fourier transform infrared (FTIR) microscopy [48].

Fluorinated diamane
When the surface of BLG or FLG is functionalized with fluorine atoms, a diamond-like structure can be obtained, namely fluorinated diamane (FD). Compared with the hydrogenation reaction of graphene, the formation for fluorination of graphene is relatively feasible in experiments. Generally, FD can be obtained at a lower temperature [6,24,36,50] and the thermal stability of FD is significantly better than that of HD [4,51]. FD can be stabilized at 400 °C even in air [6,27], and fully fluorinated diamane is more feasible to be prepared experimentally than fully hydrogenated diamane [6,24]. Some reports also described different carbon/fluorine ratios in fluorinated diamane, that is, the new incomplete fluorination of graphene, such as 4:1 [7,52,53], and 2:1 [53]. FD can usually be prepared by "top-down" and "bottom-up" methods: a) Fluorine radical fluorinated graphite to form intercalation compound of graphene [36,54] and other separation techniques [8,27,36,53,55] to obtain FD, as shown in Figure 6. b) To fluoride pre-prepared graphene layer with CF 4 plasma or SF 6 plasma [56] or XeF 2 [6,24,50]. Recently, Bakharev et al. [24] used XeF 2 to fluoride AB stacking graphene on CuNi alloy (111) at ambient pressure and successfully synthesized stable FD over a relatively large area. Through the characterization of samples with different fluorination duration, it is proved that the carbon-carbon interlayer bond is formed by the fluorination of BLG, leading to the formation of FD. The photomicrographs and diffraction patterns of fluorinated and non-fluorinated BLGs match with the corresponding simulation data of FD and AB-stacked BLG, respectively. The K edge and low electron energy loss (EEL) spectra of fluorinated and pristine AB-BLG indicated that AB-BLG fluorination formed a FD that was substantially close to the C 2 F stoichiometry. This diamane is a wide band-gap semiconductor, which can be reduced to AB-BLG by electron beam irradiation [24].

Pristine diamane
In a recent experiment, Gao et al. [29] in situ investigated the effect of pressure on the BLG sample (using SiO 2 as the substrate) through the tip of the atomic force microscopy (AFM) probe at room temperature. It is observed that the hardness of obtained sample was almost equivalent to that  (c) show the evolution of the G band with increasing pressure. the date are obtained in two distinct measurement runs (first and second, respectively), performed in two distinct samples. two spectra are shown for each pressure level, one obtained with an excitation laser energy El = 2.33 eV (green symbols), and the other with El = 2.54 eV (blue symbols). the solid lines are Voigt fit to the experimental data. Reprinted from [28].
of diamond and the electrical conductivity showed a reversible drop upon indentation. It was believed that a diamond-like carbon film was formed in this experiment. However, its ability was hindered as the appearance of unfavorable layered stacking structure (AB stacking), when the thickness of graphene increased (3-5 layers) [29]. Previously, the high-pressure phase transition behavior of the pristine FLG was also studied under hydrostatic and non-hydrostatic conditions in a DAC. The results showed that interlayer sp 3 C-C bonds were formed in seven-layered graphene at 16 GPa with partial sp 2 bonds [6]. Unfortunately, the graphene structure maintained after the pressure was released. Recently, the phase transition pressure of pristine graphene was estimated by the measurement of resistance [25]. Sheet resistance of samples with different layers as a function of pressure is shown in Figure  7. Combining XRD and theoretical simulation, the hexagonal PD is found to be formed with three-layer or thicker graphene during the compression. In consistent with previous theoretical studies [21,42], the phase transition pressure gradually decreased with the increase of the number of graphene layer. However, the hexagonal PD formed under high pressure could be retained to 1 GPa, contrary to previous theoretical reports [21,42].
The varied stacking order and layers of graphene make diamane can produce the diversified conformations and functional groups with versatile properties of diamane. Here, we summarize several typical preparation methods for producing diamane, as shown in Table 1. As we can see that PD formed under high pressure is Figure 7. Sheet resistance of mechanically exfoliated 12-, hexa-, tetra-, and bi-layer graphene as a function of pressure. (a) crosssectional schematic of the designed four-terminal nanodevices. ti/au film electrodes were patterned onto the diamond culet and extended with platinum foils. (b) the function of sheet resistance and pressure for 12-, hexa-, tetra-, tri-, and bi-layer graphene measured at room temperature. the inset is pressure dependence of the resistance of graphite. Reprinted from [25]. copyright 2020 american chemical Society. unable to be retained under ambient pressure, HD obtained under pressure is reversibly converted to graphene as the pressure is released, which supports the relatively poor stability of HD. FD is the most stable diamane as observed in experiments.

Properties of diamane
Diamane has a narrower band gap than diamond [20], and the band gap is also tunable by the thickness, functional group type, and conformation of diamane [22]. The presence of dopants or defects also manipulates the electronic states to reduce the band gap of diamane [57]. Electron beam irradiation can selectively revert FD to graphene [24,58]. These properties of diamane bring it potential applications in the field of nano-optoelectronics. In addition, due to the low coefficient of friction of hydrogenated surfaces, diamane can also be used to improve the wear resistance of coated mechanical parts [26]. Recent theoretical research on diamane shows that the stacking sequence and functional groups have the significant effect on the thermal conductivity. As shown in Figure 8, compared with FD, HD exhibits superior thermal conductivity. It is worth noting that thermal conductivity of the AA stacking sequence is higher than that of the AB stacking sequence [59,60]. The main contribution of thermal  conductivity comes from out-of-plane acoustic phonon modes in HD to optical modes in FD. Diamane also exhibits great stiffness and it would make diamane very attractive for ultrathin protective coatings, for example, used for aerospace equipment as ultrahigh-strength components in composite materials [48]. In addition, recent studies on the vibrational properties of diamane nanoribbon (DNR) showed that DNR resonator possesses a high natural frequency and a large quality factor (Q-factor) [23]. Different from thermal conductivity, the stacking sequence of diamane has negligible influence on its vibration properties. High frequency in diamane is expected to be used for the ultrasensitive resonator-based sensors.

Challenges
Although great progress has been made on diamane both theoretically and experimentally, the complete understanding of diamane remains elusive. First, the synthesis of fully hydrogenated diamane remains difficult due to the varied hydrogenation environment, the hydrogen concentration in HD is not well-controlled and determined, and the hydrogenation mechanism of graphene is uncertain [8,28,43]. Second, the rich structure configurations of diamane may present due to the varied stacking, conformation, layers, and functional groups of graphene [24,28,36,43,47,48,50,51] the available products do not allow a clear understanding of the structure features in the present stage, due to the precursors for the synthesis of diamane with the different stacking sequence of graphene. In addition, the hydrogenation and fluorination methods also make the chemical bonding complicated, not favorable for the characterizations of properties. Last but not the end, the diversified physical properties have been predicted for the diamine with different functional groups, many of them needs to be validated in experiments, since only a few of them were synthesized with the functional hydrogen, fluorine, and hydroxyl in experiments.

Conclusion
In summary, we overviewed the design, synthesis, and physical properties of diamane together with the current experimental and theoretical results on HD, FD, and PD. We discussed the influence of the concentration and type of functional groups, carbon layer thickness, temperature, and pressure on the preparation of diamane. Further investigations on synthesis and formation mechanism of diamane are highly needed to understand the new type 2D diamond for superlative properties.

Disclosure statement
No potential conflict of interest was reported by the authors.

Notes on Contributors
Guowen Qin is a graduate student in the College of Material Science and Engineering at Yanshan University in China. His research interests are diamond-related superhard materials.