- Email: [email protected]
Classification schemes for carbon phases and nanostructures
NEW CARBON MATERIALS Volume 28, Issue 4, Aug 2013 Online English edition of the Chinese language journal Cite this article as: New Carbon Materials, 2013, 28(4):273–283.
RESEARCH PAPER
Classification schemes for carbon phases and nanostructures Evgeny A Belenkov*, Vladimir A Greshnyakov Chelyabinsk State University, Bratiev Kashirinih 129, Chelyabinsk 454001, Russia
Abstract: New schemes of structural classification for carbon phases and nanostructures have been proposed, which are based on the types of chemical bonds formed and the numbers of the nearest neighbors with which each atom forms covalent bonds. The classification schemes can describe not only the known phases, but also new phases and nanostructures. New phases can be derived by linking, superpositioning or cutting precursor structures. The classification scheme has been used to predict diamond polymorphs, yielding thirty diamond-like phases that consist of atoms in equivalent crystallographic positions and eighteen of which were predicted for the first time. Key Words: Diamond crystal; Diamond-like carbon; Fullerenes; Graphite; Nanotubes
1
Introduction
Phases and nanostructures, consisting only of carbon atoms in spite of the same chemical composition, exhibit a variety of properties [1,2]. The existing classifications of carbon materials facilitate the solution of practical problems of known materials to find desired properties[3]. However, carbon materials with a set of properties that do not correspond to a set of properties of any of the known carbon materials are often required. Therefore, it is necessary to develop a methodology to obtain new materials with the desired set of properties. Before proceeding to the synthesis of new materials, one must decide whether they can be synthesized and what properties they possess. A variety of properties of carbon materials are determined by a variety of structural modifications at a constant chemical composition[1,2], therefore, it is interesting to develop carbon phases and nanostructures based on classification schemes to predict all the possible structural carbon types and to determine the variation range of their properties. A wide range of properties of carbon materials is determined by the possibility of being in different states of hybridized carbon atoms in various compounds. The hybridization of carbon atoms is the basis for the classification scheme of carbon allotropes, which was proposed in Ref. [4]. According to this scheme each of the three main valence states is characterized by a specific and unique allotropic form: sp3 hybridization of the corresponding diamond (3D structure); sp2 hybridization – graphite layers (2D structure); sp hybrid state – linear-chain carbine (1D structure). Under this scheme fullerenes are so-called quasi-zero-dimensional allotropes (0D), and nanotubes are so-called quasi-one-dimensional (1D)
allotropes. Other forms of elemental carbons are in transitional forms. These forms are separated into two large groups: mixed and intermediate forms. The first group includes mixed forms of carbon. The second group consists of carbon phases and nanostructures with intermediate degree of hybridization of carbon atoms (spn, where n is a fractional number: 1 < n < 3, n ≠ 2). This group is divided into two subgroups. The first, with 1 < n < 2, consists of cyclo[N]carbons. The second group of carbon combines various closed-frame structures with 2 < n < 3, such as fullerenes and carbon nanotubes [4]. General scheme for the classification of carbon allotropes can be represented in the form of so-called configuration diagram [4], depending on the electronic spn configurations of carbon atoms. The disadvantage of this classification scheme is that the points on the configuration diagram do not have a definite meaning because they can be interpreted as giving the ratio of carbon atoms in state of sp, sp2, and sp3 hybridization or as information about the average degree of hybridization of all atoms comprising the composition of a carbon material. However, many of the carbon materials contain carbon atoms in several different hybridization states, not only in the sp, sp2, and sp3, but also in the intermediate states spn. For example, the fullerene C70 has five different atomic positions corresponding to different hybridization types, and for similar structures the scheme [4] is not correct.
2 Structural classification of hybrid carbon phases The Ref. [5] reported a modified scheme that divided it into two complementary classification schemes: firstly, scheme describing the structural states of carbon allotropes; secondly, scheme that classifies the possible hybridization
Received date: 19 March 2013; Revised date: 05 July 2013 *Corresponding author. E-mail: [email protected] Copyright©2013, Institute of Coal Chemistry, Chinese Academy of Sciences. Published by Elsevier Limited. All rights reserved. DOI: 10.1016/S1872-5805(13)60081-5
Evgeny A Belenkov et al. / New Carbon Materials, 2013, 28(4): 273–283
states of a single carbon atom in different compounds. For the construction of the first diagram it is necessary to ignore the possibility of the existence of different (not discrete) intermediate hybridization states of carbon atoms, and to assume that there are only three structural states. It is proposed to determine the number of neighboring atoms (2, 3 or 4) by structural state of a single atom, with which the atom forms covalent bonds. Then any point on this diagram for the relevant structural modifications gives unambiguous information on the ratio of carbon atoms that form covalent bonds with two, three or four neighboring atoms (Fig. 1). The second phase diagram should be introduced for the classification of single carbon atom states (Fig. 2). Single carbon atom states differ in the hybridized states that are determined by the mutual spatial arrangement of the four orbitals and their sizes. Therefore, the classification scheme should clearly define this orbital configuration. If we assume, that the orbital sizes are not independent variables and, taking the orientation of one of the orbitals as z-axis, six variables are enough to describe the orientation of the other three orbitals (relatively basic orbital) in spherical coordinates: ϕ(1), θ(1), ϕ(2), θ(2), ϕ(3), θ(3) (Fig. 2). Therefore, it is impossible to use its construction of the traditional pattern [4]. It is possible to simplify the classification in this case, if we consider the carbon atom in a state intermediate between the three main hybridization states. Let’s consider sp→sp2, sp→sp3, sp2→sp3 and backward transitions. In the process of transition angles between the orbitals can take different values and the transition is carried out along different trajectories in the space of six variables. However, if the orbitals take the basis shape, then simplification is possible. Orbitals may be in the shape of symmetric or asymmetric dumbbells, and sp state has the different types of orbitals: two symmetric and two asymmetric; in sp2 state: one is symmetric and three are asymmetric; in sp3 state all orbitals are asymmetric. In transition from sp state to sp2 state one of the symmetric orbitals must become asymmetric, so that all intermediate states of atoms with one symmetric orbital can be attributed to the same class of intermediate states. In transition from sp2 state to sp3 state the last of symmetric orbitals must become asymmetric and, therefore, all intermediate states of atoms, in which all orbitals are asymmetric, can be attributed to another class of intermediate states. Thus, the first class of states is intermediate between sp and sp2 states, the second is between sp2 and sp3 [5]. As a result the classification diagram of the atomic states in a simplified form should be linear (Fig. 2).
body-centered cubic (BCC) carbon phases have been described in which each carbon atom has 12 and 8 nearest neighboring atoms, respectively, while in the scheme of [5] the maximum coordination number is assumed to be 4. The maximum value assumption for the coordination number of carbon atoms equal to four is only fair if the type of chemical bond in the compounds is predominantly covalent. For the same phase, as described in [9, 10], the types of bonds, obviously, are not covalent. Therefore, it is necessary to set the type of chemical bond formed between carbon atoms as the basis for a complete classification scheme of carbon phases and nanostructures.
3 Classification scheme of carbon phases with different types of chemical bonds All of the carbon phases can be divided into two classes. The first class includes phases with ordered crystalline structures. Amorphous phases can be attributed to the second class, a typical representative of which is the amorphous diamond-like carbon from sp3 hybridized atoms[11], as well as carbon phases with a partially ordered structure, for example, turbostratic carbon from sp2 hybridized atoms[12,13]. The structures of the second class can be considered as subsidiaries resulting from violations of the ordered crystalline structure of the first class phases due to defects[11,14,15]. Therefore, it is necessary to develop a common classification scheme for carbon phases of the first class in order to describe all the possible carbon phases. The general classification scheme of carbon phases and nanostructures with ordered structures should consider the chemical bond type which form in one or another structure. Therefore, all the carbon compounds can be divided into two types of phases and nanostructures:
Scheme, proposed in [5], allows classifying well and predicting new hybrid carbon phase consisting of carbon atoms in various states of hybridization. Based on this classification scheme by a number of new phases and nanostructures [6-8] was predicted. The disadvantage of classification scheme of [5] is that the scheme is incomplete and does not allow describing all possible structural varieties of carbon. For example, in [9, 10] experimentally obtained face-centered cubic (FCC) and
Fig. 1 The structural classification scheme of carbon materials by the number of neighboring atoms (2, 3 or 4), with which any atom forms covalent bonds (italics – hypothetical structure).
Evgeny A Belenkov et al. / New Carbon Materials, 2013, 28(4): 273–283
multi-wall nanotubes[29], nanotubes bundles[30], peapods[31], onions[32], etc.). Carbon nanostructures and phases with covalent chemical bonds differ, firstly, by the number of covalent bonds formed by an individual atom; and secondly, by the dimension of the formed crystalline structure (crystallographic dimensions, denoted as nDc) and the dimension of the atomic structure (denoted as mDa). Under the crystallographic nDc dimension it is implied that the number (n = 0, 1, 2, 3) of the crystallographic axes along which the structure has translational symmetry. The dimension of the atomic structure mDa means that the Cartesian coordinate axes are required to describe the relative positions of the atoms in the nanostructure or phase. In terms of the number of formed covalent bonds all the carbon phases and nanostructures can be divided into two subtypes: the first subtype has the structures in which all atoms form an equal number of covalent bonds with neighboring atoms; the second subtype has all hybrid structures in which atoms are covalently bound to different numbers of neighboring atoms (between 2 to 4). The classification scheme of hybrid carbon phases and nanostructures is a scheme described above in [5]. The classification scheme for the first subtype phases and nanostructures has not previously been described and is for the first time set out below.
Fig. 2 Classification scheme of hybridized states of carbon atom various compounds.
(1) with one type of chemical bonds: covalent (cubic diamond, diamond-like phases[16,17], carbyne chains[18], fullerenes[19], single wall nanotubes[20,21], graphene[22], graphene-like layers[23], 3D-graphites[24-26], etc.), metal (carbon fcc and bcc phases[9,10]) and van der Waals (monatomic carbon vapor); (2) with a combination of different types of chemical bonds, for example, covalently-van der Waals (graphite, carbyne[18], steam of carbon clusters[27], fullerites [28],
Phases and nanostructures of the first subtype can be divided into the structures in which all atoms are in crystallographically equivalent positions, and structures are composed of atoms at crystallographically non-equivalent states. Structures of the atoms in non-equivalent positions may be of unlimited quantity – they can be obtained as various combinations of structures’ fragments consisting of atoms with the identical degree of hybridization. So, first of all, it is necessary to develop a classification scheme of carbon nanostructures and phases consisting of atoms in the crystallographically equivalent states (the number of such structures must be finite and all of them can be described). Attempts to develop such a scheme have been made earlier in [16, 17]. The scheme proposed in these papers was applied to the classification and mechanism of model formation of diamond-like phase structures only. Complete classification scheme should describe all the carbon phases and nanostructures with covalent bonds. This classification scheme has the form as shown in Table 1. A unique group of carbon nanostructures and phases corresponds to the individual table cell. The table strings correspond to the phases and nanostructures with different crystallographic dimensions: 0Dc (quasi-zero-dimensional), 1Dc (quasi-one-dimensional), 2Dc (quasi-two-dimensional), and 3Dc (three-dimensional). The table columns determine the number of the nearest atoms (Na) with which each atom forms covalent bonds in the corresponding phase or nanostructure. The parameter Na can range from 0 (when the atoms do not form covalent bonds) to 4 (all four electrons of the outer
Evgeny A Belenkov et al. / New Carbon Materials, 2013, 28(4): 273–283
Table 1 Classification of carbon phases and nanostructures with covalent bonds Na
nDc 0
1
2
pair of bonded
nanorings
atoms 1Da
2Da and 3Da
0Dс
single atom 0Da
1Dс
-
-
2Dс
-
3Dс
-
3
4 frame clusters
fullerene-like clusters 3Da
chains
nanotubes 3Da
1Da -3Da
ribbon 3Da
-
-
graphene-like layers 2Da
-
-
nanotubes and 3Da ribbons 2Da и 3Da spirals and 3Da
three-dimensional graphites 3Da
3Da
layers 2Da и 3Da
diamond-like phases 3Da
Note: The positions of all atoms in each structure are equivalent; Na is the number of nearest neighbors with which each atom forms covalent bonds.
electronic shell of the carbon atoms are involved in the formation of covalent bonds). Also the parameter Na can be seen as a quasi-coordination number, i.e. the number of atoms in the first coordination sphere. The number is a quasi-coordination as lengths of covalent bonds in some carbon compounds are different and the distances to the nearest-neighbor atoms are slightly different (considering the structure in rough approximation: at an equality of lengths of all covalent bonds the parameter Na is a quasi-coordination number). There are 20 cells in Table 1, each of which corresponds to a particular group of carbon phases or nanostructures. However, not all the cells in the table correspond to the allowable carbon structures. So, it is impossible to obtain covalently-bonded quasi-one-dimensional, quasi-two-and three-dimensional structure from the carbon atoms which are not forming covalent bonds and the atoms forming covalent bonds with only one neighboring atom. Also you can’t obtain 2Dc and 3Dc structures of carbon atoms that form covalent bonds with two neighboring atoms. Thus, there may be only 12 groups of carbon phases and nanostructures with covalent type of bonds. In the cells of Table 1 the geometrically optimized structures (basic structures), which can stably exist under normal conditions, being isolated in space are shown. Except for these structures, it is required to consider phases and nanostructures in the deformed states (deformed structures), derived from the basic structures by a deformation in such a way that all the atomic positions in them are equivalent. The need for consideration of deformed structures is connected with the fact that with their introduction the model mechanism of obtaining of the phases and nanostructures as a result of the cross-linking and superpositioning of atoms or cutting of bonds is simplified. In addition, the deformed structures can stably exist as structural elements in carbon phases with a mixed covalent-van der Waals type of bonds. The first five groups are quasi-zero-dimensional. There is only one nanostructure in the [0Dc,0] and [0Dc,1] groups that
correspond to a single carbon atom (with the 0Da dimension of the atomic structure) and a pair of bonded atoms (1Da), respectively. The [0Dc,2] group contains flat carbon nanorings with the 2Da atomic structure dimension (Fig. 3a). Besides, into this group two more structural species should be considered, that are curved zigzag (Fig. 3b) and armchair (Fig. 3c) rings with an even number of atoms (3Da dimension), related to the deformed structures. The [0Dc,3] group is presented by fullerene clusters that have 3Da atomic dimensions. Such clusters have the regular and semiregular polyhedral structures (Fig. 4) and prisms (Fig. 5). The number of fullerene-like clusters of the regular and semiregular polyhedral forms is limited, there are only 10 of them while no limit is set for the number of prismatic clusters. The last of the quasi-zero-dimensional groups ([0Dc,4]) contains frame clusters: 5 semi-regular polyhedra (octahedron, cuboctahedron, rombicuboctahedron,icosidodecahedron,and rhombicosidodecahedron) and an unlimited number of antiprisms. Such clusters, apparently, are only a result of modeling abstraction. The following three groups of phases and nanostructures are quasi-one-dimensional. The [1Dc,2] group contains a linear carbyne chain (1Da) (Fig. 6a). Also this structural group includes various deformed nanostructures: planar zigzag and armchair chains (2Da) (Fig. 6b, 6c), curved in space chains (3Da) (Fig. 6d) and different spirals (3Da) (Fig. 6e, 6f), whose number is unlimited. The [1Dc,3] group includes armchair, zigzag and chiral single wall nanotubes (3Da) as indicated in Fig. 7a, 7b and 7c, respectively, whose number is unlimited, an unlimited number
Fig. 3 Different nanoring structures of eight carbon atoms: (a) flat; (b) zigzag; (c) armchair.
Evgeny A Belenkov et al. / New Carbon Materials, 2013, 28(4): 273–283
Fig. 4 Structures of fullerene-like clusters.
Fig. 5 Structures of fullerene-like trigonal, hexagonal and octagonal prisms.
Fig. 7 Carbon nanotubes of the structure group [1Dc,3]: (a) armchair (3,3); (b) zigzag (6,0); (c) chiral (4,1) and (d) nanotube with a surface of 4- and 8-gons. Fig. 6 The quasi-one-dimensional nanostructures of the group [1Dc,2]: (a) linear chain; (b) planar zigzag(c) armchair chains; (d) chain curved in space and (e,f) spirals.
Evgeny A Belenkov et al. / New Carbon Materials, 2013, 28(4): 273–283
Fig. 8 The quasi-one-dimensional nano-objects of the structure group
There are two groups of three-dimensional carbon phases. To indicate the phases of the first of these groups [3Dc,3] the term three-dimensional graphites (3D-graphites) [26] is used in the literature. One of the first theoretically studied phases of this group is a metallic carbon [24] with a crystal structure similar to the network of 3-coordinated nodes [33, 34]. The review [25] describes a group of three-dimensional graphites, which were obtained by modeling cross-linking right- and left-symmetry spirals. The structures of some of these phases refer to the following types of uninodal 3D-nets: srs [33-35], utp [33] and etb [36]. The remaining sp2 phases can have crystal lattices like three-dimensional nbo-a [35] and etc [36] networks. Examples of images of 3D-graphite structures are shown in
[1Dc,3]: (a) zigzag ribbon; (b) flat ribbon; (c) armchair ribbon and (d,e) curved ribbons.
Fig. 9 Helical ribbons of the structure group [1Dc,3].
of armchair nanotubes with surfaces of the 4- and 8-gons (Fig. 7d) and a zigzag ribbon (Fig. 8a). A number of deformed structures can be derived from the basic structures of this group that should be considered for the model construction of other carbon phases. The deformed structures in the [1Dc,3] group are a flat ribbon (2Da) (Fig. 8b), three curved ribbons (3Da) (Fig. 8c, 8d) and an unlimited number of spiral ribbons (3Da) (Fig. 9).
Fig. 10 The quasi-one-dimensional nano-objects of the structure group [1Dc,4]: (a) flat ribbon; (b) curved ribbon; (c) spiral and (d,e) nanotubes.
The last of the quasi-one-dimensional groups [1Dc,4] contains ribbons (2Da and 3Da) (Fig. 10a, 10b) and spirals (3Da) (Fig. 10c) of the triangles and nanotubes (3Da), whose surfaces are composed of tetragons (Fig. 10d, 10e). The number of different nanotubes and spirals in this group is not limited. Just as in case of quasi-zero-dimensional group [0Dc,4] nanostructures, the group [1Dc,4] are probably only model abstractions. There are only two quasi-two-dimensional groups. The first of these groups ([2Dc,3]) consists of four flat graphene-like layers L6, L4-8, L3-12, L4-6-12 (2Da) (Fig. 11). Several corrugated layers of different structural types can be generated on the basis of these layers: 5 layers of L6 type, 7 – L4-8 type, one – L3-12 type, 3 – L4-6-12 type (3Da) (Fig. 12). The second of the quasi-two-dimensional groups ([2Dc,4]) consists of three flat monatomic (at thickness) layers (2Da) (Fig. 13), several corrugated layers, and flat diatomic layers (3Da) (Fig. 14). All structures of the [2Dc,4] group are only model abstractions.
Fig. 11 Structure fragments of graphene-like layers of the group [2Dc,3].
Evgeny A Belenkov et al. / New Carbon Materials, 2013, 28(4): 273–283
The phases of the second three-dimensional group [3Dc,4] in literature are called diamond-like. Fragments of the crystal lattices of some diamond-like phases are shown in Fig. 16. The number of these phases is also limited, and by present time the existence possibility is established for 30 diamond-like phases (excluding the cubic diamond), 25 of which are described in [16, 17].
Fig. 12 Examples of corrugated layers of the group [2Dc,3].
Fig. 13 Fragments of flat monoatomic layers of the structure group [2Dc,4].
The classification scheme of carbon phases with covalent type of bonds is the basis of a model process for generating any structures with crystallographically equivalent positions of the atoms. For obtaining any carbon structure it is necessary to take the nanostructures or phases-precursors, in which the parameter Na is not equal to similar parameter of the required structure. If the required structure is obtained by cross-linking or superpositioning, then the exponent n in the nDc parameter of precursor structure must be less or equal to the corresponding exponent of the final structures. The number of structure obtained by the operation of cutting the exponent value (n) of precursor should be greater than that in obtained nanostructure by cross-linking or superpositioning. Further, we find the initial configuration of the atomic nets from the selected precursors by the operations of cross-linking, superpositioning or cutting. The required phases and nanostructures are obtained in the process of geometric optimization of initial configurations, during which relative arrangement of atoms, corresponding to the minimum of the free energy, is found. Let’s consider the examples of how the described classification scheme can be used to predict new carbon phases and nanostructures. Any of the carbon structures can be derived by the geometric optimization of the atomic nets resulting from cross-linking or superpositioning of phases and nanostructures, pertaining to the groups of corresponding cells of the classification in Table 1, located to the left and below of the table cell for that structure we want to get. For example, graphene-like layers belonging to the [2Dc,3] group can be derived from basic and/or deformed nanostructures of the [0Dc,2] and [1Dc,2] groups (i.e. from nanorings, chains or
Fig. 14 Examples of flat diatomic layers of the group [2Dc,4].
Fig. 15. Possible number of such phases should be limited, however, how many of them can exist and what their structures are has not been established yet.
Fig. 15 Fragments of the crystal lattices of sp2 carbon phases belonging to the group [3Dc,3]: (a) metallic carbon and (b) C1 (31) (notation from [25]).
Evgeny A Belenkov et al. / New Carbon Materials, 2013, 28(4): 273–283
Table 2 Classification of carbon phases and nanostructures with mixed covalently-van-der-Waals bond types Na
nDc
0Dс
0
1 chain,
chain*, plane* and
chain and plane of
condensate of pairs of
condensate* of
fullerene-like clusters,
bonded atoms
nanorings
fullerite
planes and bundles of 1Dс
-
-
3Dс
-
-
-
-
planes
chains planes* and bundles* of spirals
2Dс
4
steam
individual atoms
and
3
chain, plane and of
plane
2
-
-
and
bundles
chain, plane and pairs of frame clusters of
planes
and
bundles
of
nanotubes, ribbons* and
nanotubes, ribbons* and
spirals*
spirals*
graphite-like phases,
graphite-like and
auto-intercalated
auto-intercalated phases of
graphite-like layers
graphane layers
auto-intercalated
auto-intercalated
three-dimentional graphites
diamond-like phases
Note: Na : the number of nearest neighbors with which each atom forms covalent bonds; *: there are two possible structural varieties: regular and auto-intercalated.
equivalent. The fragments of these phases and nanostructures, having more than one type of crystallographic positions, and different crystallographic and atomic dimensions of the structures, are shown in Fig. 17. The classification scheme for structures with covalent bonds can be used as the basis for classification of carbon phases with a combination of covalent and van der Waals types of chemical bonds (Table 2). The structure of these phases can be obtained by a geometrical optimization of the relative positions of structural elements, in which all atoms form covalent bonds, and the bonds between the structural units are carried out by van der Waals forces. The initial structural units with covalent bonds are the phases and nanostructures of the structural groups of cells in Table 1.
Fig. 16 The crystal lattices of diamond-like phases: (a) graphane-A5 (LA5); (b) tubulane-A5 (TA5) and (c) fullerane-A6 (CA6) [16, 17].
spirals) by the process of cross-linking or combining and subsequent geometric optimization. Graphene-like layers can also be obtained by geometric optimization of deformed layers found after cutting of bonds in the diamond-like phases [3Dc,4] or layers of [2Dc,4]. The general model scheme to obtain a structure has an exception for the described rules: one can not get a frame 3Da clusters of the [0Dc,4] structure group from the fullerene-like clusters of the [0Dc,3] group. Note also, that from 12 groups of carbon phases and nanostructures featured in the classification scheme, only 9 groups feature the structures, which can stably exist in nature, the three groups [0Dc,4], [1Dc,4] and [2Dc,4] correspond to fully model structures. The scheme, illustrated in the form of Table 1, can also be used for classification of carbon phases and nanostuctures, in which not all the atomic positions are crystallographically
Fig. 17 The structures with nonequivalent crystallographic atomic positions: (a) fullerene C28 ([0Dc,3]); (b) ribbon ([1Dc,3]); (c) graphene sheet ([2Dc,3]) and (d) diamond-like phase ([3Dc,4]).
Evgeny A Belenkov et al. / New Carbon Materials, 2013, 28(4): 273–283
Each group of covalent phases and nanostructures will correspond to the group of phases with a mixed covalent-van der Waals type of bonds. The phases, forming structure groups [nDc,Na]CV in each cell of Table 2, are obtained from the initial structures [nDc,Na] (basic and/or deformed) in cells of Table 1. For example, atomic chains, atomic planes or volume filled with atoms, linked together by van der Waals forces ([0Dc,0]CV) (Table 2), can be obtained from separated carbon atoms (structure group [0Dc,0]). Fullerites [0Dc,3]CV are obtained from the fullerene clusters [0Dc,3]. Graphite crystals [2Dc,3]CV are composed from the graphene layers [2Dc,3]. Nanotubes bundles [1Dc,3]CV are derived from the single wall nanotubes [1Dc,3], etc. Except for the usual phases with a mixed type of bonds auto-intercalated carbon phases can also be obtained. Auto-intercalated phases are phases in which the crystal structures of covalent precursors interpenetrate into each other, so that the covalently-linked structure of the initial precursors isn’t violated. Examples of such phases are phases with “chain armours” structure [0Dc,2]CV from carbyne nanorings [0Dc,2] as described in [37], auto-intercalated graphites [2Dc,3]CV and auto-intercalated diamonds [3Dc,4]CV. The above described classification scheme of carbon phases with mixed covalent-van der Waals type of chemical bonds concerns only those phases that are composed of identical structural elements with covalent bonds. Obviously, there may be a much greater variety of phases, where structural elements are the different precursors with covalent bonds. Examples of such carbon phases are multi wall nanotubes, onions and peapodes[29, 31, 32].
4
Conclusions The main innovation of the proposed classification
scheme of carbon phases and nanostructures is the consideration of the types of chemical bonds in carbon phases
[3]
Systematization of data on the physical and chemical properties[J]. High Temp, 2010, 48(6): 830-836. [4]
hybridization[J]. Carbon, 1997, 35(10-11): 1654-1658. [5]
nanomaterials"[J]. May 7-10, Sudak, Crimea, Ukraine 2003, 730-733. [6]
atoms[J]. J Struct Chem, 2005, 46(6): 961-967. [7]
crystalline phases and is a concretization of the developed crystal nets theories[33-36,38-40].
Univ Phys, 2009, 25(163): 22-33. [8]
Pierson H O. Handbook of carbon, graphite, diamond, and
53(11): 2385-2392. [9]
Cowley J M, Mani R C, Sunkara M K, et al. Structures of
[10]
Konyashin I, Khvostov V, Babaev V, el al. A new hard
carbon nanocrystals[J]. Chem. Mater., 2004, 16: 4905-4911. allotropic form of carbon: dream or reality[J]. Int J Refract Met Hard Mater, 2006, 24(1-2): 17-23. [11]
[2]
Dresselhaus M S, Dresselhaus G, Avouris Ph. Carbon nanotubes: synthesis, structure, properties, and applications[J]. Topics Appl Phys 80, Berlin: Springer-Verlag, 2001: 453.
Robertson J. Hard amorphous (diamond-like) carbons[J]. Prog. Solid St. Chem., 1991, 21: 199-333.
[12]
Franklin R E. The interpretation of diffuse X-ray diagrams of carbon[J]. Acta Cryst, 1950, 3(2): 107-121.
[13]
Franklin R E. The structure of graphitic carbon[J]. Acta Cryst., 1951, 4(3): 253-261.
[14]
Maire J, Mering J. Graphitization of soft carbon[J]. Chem Phys Carbon (New York: Dekker), 1970, 6: 125-190.
[15]
Lachter J, Bragg R H. Interstitial in graphite and disorder
[16]
Greshnyakov V A, Belenkov E A. Structures of diamond-like
carbons[J]. Phys Rev B, 1986, 33(12): 8903-8905. phases[J]. J Exp Theor Phys, 2011, 113(1): 86-95. [17]
Greshnyakov V A, Belenkov E A, Berezin V M. Crystal structure and properties of carbon diamond-like phases[J]. Chelyabinsk: South Ural State University, 2012: 150.
[18]
Kudryavtsev Yu P. The discovery of carbyne[J]. Phys Chem Mater Low-Dimens Struct, 1998, 21: 1-6.
[19]
Kroto H W, Heath J R, O'Brien S C, et al. C60: buckmimsterfullerene[J]. Nature, 1985, 318(6042): 162-163.
[20]
Iijima S, Ichihashi T. Single-shell carbon nanotubes of 1-nm diameter[J]. Nature, 1993, 363(6430): 603-605.
[21]
Bethune D S, Klang C H, de Vries M S, et al. Cobalt-catalysed
growth
single-atomic-layer
of
walls[J].
carbon Nature,
nanotubes 1993,
with
363(6430):
605-607. [22]
Novoselov K S, Geim A K, Morozov S V, et al. Electric field effect in atomically thin carbon films[J]. Science, 2004,
fullerenes: properties, processing and applications[J]. Park Ridge: Noyes, 1993: 402.
Belenkov E A, Shakhova I V. Structure of carbynoid nanotubes and carbynofullerenes[J]. Phys Solid State, 2011,
References [1]
Belenkov E A, Greshnyakov V A, Mavrinsky V V. Structure of sp+sp3 hybrid carbon phases. Bull[J]. Chelyabinsk State
may be a part of a more general classification scheme, which can describe the model that yields all possible structures of the
Belenkov E A, Ivanovskii A L, Ulianov S N, et al. New nanostructures of from sp2 and sp3 hybridized carbon
carbon phases in which all atoms are in crystallographically equivalent positions[16,17]. The proposed classification scheme
Belenkov E A. Classification of carbon structures. VIII Int'l Conf. "Hydrogen materials science & chemistry of carbon
of the predictive power of the proposed classification scheme is a description of the 25 possible structures of diamond-like
Heimann R B, Evsyukov S E, Koga Y. Carbon allotropes: a suggested classification scheme based on valence orbital
and nanostructures. This scheme allows not only to classify the known phases, but also to predict new ones. An example
Erkimbaev A O, Zitserman V Yu, Kobzev G A.
306(5696): 666-669. [23]
Balaban A T, Rentea C C, Ciupitu E. Chemical graphs. VI. Estimation of the relative stability of several planar and
Evgeny A Belenkov et al. / New Carbon Materials, 2013, 28(4): 273–283
tridimensional lattices for elementary carbon[J]. Rev Roum
[31]
Chim, 1968, 13(2): 231-247. [24]
[25]
[26]
Hoffmann R, Hughbanks T, Kertesz M. A hypothetical
carbon nanotubes[J]. Nature, 1998, 396(6709): 323-324. [32]
electron-beam
4831-4832.
707-709.
Stankevich I V, Nikerov M V, Bochvar D A. The structural
[33]
1992,
359(6397):
Blatov V A, Carlucci L, Ciani G, et al. Interpenetrating metal-organic and inorganic 3D networks: a computer-aided systematic investigation. Part I. Analysis of the Cambridge
640-655.
structural database[J]. Cryst Eng Comm, 2004, 6(65):
Belenkov E A, Ali-Pasha V A. 3D-graphite structure[J]. Cryst
377-395. [34]
Rohlfing E A, Cox D M, Kaldor A. Production and
structure prediction[J]. Weinheim: Wiley-VCH, 2011, 1-28. [35]
Kratschmer W, Lamb L D, Fostiropoulos K, et al. Solid C60: A Iijima S. Helical microtubules of graphitic carbon[J]. Nature,
2005, 178: 2533-2554. [36]
Deng Y, Liu H, Yu B, et al. Supramolecular coordination assemblies constructed from multifunctional azole-containing carboxylic acids[J]. Molecules, 2010, 15: 3478-3506.
Thess A, Lee R, Nikolaev P, et al. Crystalline ropes of 483-487.
Delgado-Friedrichs O, Foster M D, O'Keeffe M, et al. What do we know about three-periodic nets[J]. J Solid State Chem,
1991, 354(6348): 56-64. metallic carbon nanotubes[J]. Science, 1996, 273(5274):
Blatov V A, Proserpio D M, Periodic-graph approaches in crystal structure prediction. In: Modern methods of crystal
new form of carbon[J]. Nature, 1990, 347(6291): 354-358.
[30]
Nature,
electronic spectrum[J]. Russ Chem Rev, 1984, 53(7):
Chem Phys, 1984, 81(7): 3322-3330.
[29]
irradiation[J].
chemistry of crystalline carbon: geometry, stability, and
characterization of supersonic carbon cluster beams[J]. J [28]
Ugarte D. Curling and closure of graphitic networks under
metallic allotrope of carbon[J]. J Am Chem Soc, 1983, 105:
Rep, 2011, 56(1): 101-106. [27]
Smith B W, Monthioux M, Luzzi D E. Encapsulated C60 in
[37]
Belenkov E A, Shabiev F K. Structure of new carbon phases from carbyne nanorings[J]. Cryst Rep, 2007, 52(2): 343-348.
RESEARCH PAPER
Classification schemes for carbon phases and nanostructures Evgeny A Belenkov*, Vladimir A Greshnyakov Chelyabinsk State University, Bratiev Kashirinih 129, Chelyabinsk 454001, Russia
Abstract: New schemes of structural classification for carbon phases and nanostructures have been proposed, which are based on the types of chemical bonds formed and the numbers of the nearest neighbors with which each atom forms covalent bonds. The classification schemes can describe not only the known phases, but also new phases and nanostructures. New phases can be derived by linking, superpositioning or cutting precursor structures. The classification scheme has been used to predict diamond polymorphs, yielding thirty diamond-like phases that consist of atoms in equivalent crystallographic positions and eighteen of which were predicted for the first time. Key Words: Diamond crystal; Diamond-like carbon; Fullerenes; Graphite; Nanotubes
1
Introduction
Phases and nanostructures, consisting only of carbon atoms in spite of the same chemical composition, exhibit a variety of properties [1,2]. The existing classifications of carbon materials facilitate the solution of practical problems of known materials to find desired properties[3]. However, carbon materials with a set of properties that do not correspond to a set of properties of any of the known carbon materials are often required. Therefore, it is necessary to develop a methodology to obtain new materials with the desired set of properties. Before proceeding to the synthesis of new materials, one must decide whether they can be synthesized and what properties they possess. A variety of properties of carbon materials are determined by a variety of structural modifications at a constant chemical composition[1,2], therefore, it is interesting to develop carbon phases and nanostructures based on classification schemes to predict all the possible structural carbon types and to determine the variation range of their properties. A wide range of properties of carbon materials is determined by the possibility of being in different states of hybridized carbon atoms in various compounds. The hybridization of carbon atoms is the basis for the classification scheme of carbon allotropes, which was proposed in Ref. [4]. According to this scheme each of the three main valence states is characterized by a specific and unique allotropic form: sp3 hybridization of the corresponding diamond (3D structure); sp2 hybridization – graphite layers (2D structure); sp hybrid state – linear-chain carbine (1D structure). Under this scheme fullerenes are so-called quasi-zero-dimensional allotropes (0D), and nanotubes are so-called quasi-one-dimensional (1D)
allotropes. Other forms of elemental carbons are in transitional forms. These forms are separated into two large groups: mixed and intermediate forms. The first group includes mixed forms of carbon. The second group consists of carbon phases and nanostructures with intermediate degree of hybridization of carbon atoms (spn, where n is a fractional number: 1 < n < 3, n ≠ 2). This group is divided into two subgroups. The first, with 1 < n < 2, consists of cyclo[N]carbons. The second group of carbon combines various closed-frame structures with 2 < n < 3, such as fullerenes and carbon nanotubes [4]. General scheme for the classification of carbon allotropes can be represented in the form of so-called configuration diagram [4], depending on the electronic spn configurations of carbon atoms. The disadvantage of this classification scheme is that the points on the configuration diagram do not have a definite meaning because they can be interpreted as giving the ratio of carbon atoms in state of sp, sp2, and sp3 hybridization or as information about the average degree of hybridization of all atoms comprising the composition of a carbon material. However, many of the carbon materials contain carbon atoms in several different hybridization states, not only in the sp, sp2, and sp3, but also in the intermediate states spn. For example, the fullerene C70 has five different atomic positions corresponding to different hybridization types, and for similar structures the scheme [4] is not correct.
2 Structural classification of hybrid carbon phases The Ref. [5] reported a modified scheme that divided it into two complementary classification schemes: firstly, scheme describing the structural states of carbon allotropes; secondly, scheme that classifies the possible hybridization
Received date: 19 March 2013; Revised date: 05 July 2013 *Corresponding author. E-mail: [email protected] Copyright©2013, Institute of Coal Chemistry, Chinese Academy of Sciences. Published by Elsevier Limited. All rights reserved. DOI: 10.1016/S1872-5805(13)60081-5
Evgeny A Belenkov et al. / New Carbon Materials, 2013, 28(4): 273–283
states of a single carbon atom in different compounds. For the construction of the first diagram it is necessary to ignore the possibility of the existence of different (not discrete) intermediate hybridization states of carbon atoms, and to assume that there are only three structural states. It is proposed to determine the number of neighboring atoms (2, 3 or 4) by structural state of a single atom, with which the atom forms covalent bonds. Then any point on this diagram for the relevant structural modifications gives unambiguous information on the ratio of carbon atoms that form covalent bonds with two, three or four neighboring atoms (Fig. 1). The second phase diagram should be introduced for the classification of single carbon atom states (Fig. 2). Single carbon atom states differ in the hybridized states that are determined by the mutual spatial arrangement of the four orbitals and their sizes. Therefore, the classification scheme should clearly define this orbital configuration. If we assume, that the orbital sizes are not independent variables and, taking the orientation of one of the orbitals as z-axis, six variables are enough to describe the orientation of the other three orbitals (relatively basic orbital) in spherical coordinates: ϕ(1), θ(1), ϕ(2), θ(2), ϕ(3), θ(3) (Fig. 2). Therefore, it is impossible to use its construction of the traditional pattern [4]. It is possible to simplify the classification in this case, if we consider the carbon atom in a state intermediate between the three main hybridization states. Let’s consider sp→sp2, sp→sp3, sp2→sp3 and backward transitions. In the process of transition angles between the orbitals can take different values and the transition is carried out along different trajectories in the space of six variables. However, if the orbitals take the basis shape, then simplification is possible. Orbitals may be in the shape of symmetric or asymmetric dumbbells, and sp state has the different types of orbitals: two symmetric and two asymmetric; in sp2 state: one is symmetric and three are asymmetric; in sp3 state all orbitals are asymmetric. In transition from sp state to sp2 state one of the symmetric orbitals must become asymmetric, so that all intermediate states of atoms with one symmetric orbital can be attributed to the same class of intermediate states. In transition from sp2 state to sp3 state the last of symmetric orbitals must become asymmetric and, therefore, all intermediate states of atoms, in which all orbitals are asymmetric, can be attributed to another class of intermediate states. Thus, the first class of states is intermediate between sp and sp2 states, the second is between sp2 and sp3 [5]. As a result the classification diagram of the atomic states in a simplified form should be linear (Fig. 2).
body-centered cubic (BCC) carbon phases have been described in which each carbon atom has 12 and 8 nearest neighboring atoms, respectively, while in the scheme of [5] the maximum coordination number is assumed to be 4. The maximum value assumption for the coordination number of carbon atoms equal to four is only fair if the type of chemical bond in the compounds is predominantly covalent. For the same phase, as described in [9, 10], the types of bonds, obviously, are not covalent. Therefore, it is necessary to set the type of chemical bond formed between carbon atoms as the basis for a complete classification scheme of carbon phases and nanostructures.
3 Classification scheme of carbon phases with different types of chemical bonds All of the carbon phases can be divided into two classes. The first class includes phases with ordered crystalline structures. Amorphous phases can be attributed to the second class, a typical representative of which is the amorphous diamond-like carbon from sp3 hybridized atoms[11], as well as carbon phases with a partially ordered structure, for example, turbostratic carbon from sp2 hybridized atoms[12,13]. The structures of the second class can be considered as subsidiaries resulting from violations of the ordered crystalline structure of the first class phases due to defects[11,14,15]. Therefore, it is necessary to develop a common classification scheme for carbon phases of the first class in order to describe all the possible carbon phases. The general classification scheme of carbon phases and nanostructures with ordered structures should consider the chemical bond type which form in one or another structure. Therefore, all the carbon compounds can be divided into two types of phases and nanostructures:
Scheme, proposed in [5], allows classifying well and predicting new hybrid carbon phase consisting of carbon atoms in various states of hybridization. Based on this classification scheme by a number of new phases and nanostructures [6-8] was predicted. The disadvantage of classification scheme of [5] is that the scheme is incomplete and does not allow describing all possible structural varieties of carbon. For example, in [9, 10] experimentally obtained face-centered cubic (FCC) and
Fig. 1 The structural classification scheme of carbon materials by the number of neighboring atoms (2, 3 or 4), with which any atom forms covalent bonds (italics – hypothetical structure).
Evgeny A Belenkov et al. / New Carbon Materials, 2013, 28(4): 273–283
multi-wall nanotubes[29], nanotubes bundles[30], peapods[31], onions[32], etc.). Carbon nanostructures and phases with covalent chemical bonds differ, firstly, by the number of covalent bonds formed by an individual atom; and secondly, by the dimension of the formed crystalline structure (crystallographic dimensions, denoted as nDc) and the dimension of the atomic structure (denoted as mDa). Under the crystallographic nDc dimension it is implied that the number (n = 0, 1, 2, 3) of the crystallographic axes along which the structure has translational symmetry. The dimension of the atomic structure mDa means that the Cartesian coordinate axes are required to describe the relative positions of the atoms in the nanostructure or phase. In terms of the number of formed covalent bonds all the carbon phases and nanostructures can be divided into two subtypes: the first subtype has the structures in which all atoms form an equal number of covalent bonds with neighboring atoms; the second subtype has all hybrid structures in which atoms are covalently bound to different numbers of neighboring atoms (between 2 to 4). The classification scheme of hybrid carbon phases and nanostructures is a scheme described above in [5]. The classification scheme for the first subtype phases and nanostructures has not previously been described and is for the first time set out below.
Fig. 2 Classification scheme of hybridized states of carbon atom various compounds.
(1) with one type of chemical bonds: covalent (cubic diamond, diamond-like phases[16,17], carbyne chains[18], fullerenes[19], single wall nanotubes[20,21], graphene[22], graphene-like layers[23], 3D-graphites[24-26], etc.), metal (carbon fcc and bcc phases[9,10]) and van der Waals (monatomic carbon vapor); (2) with a combination of different types of chemical bonds, for example, covalently-van der Waals (graphite, carbyne[18], steam of carbon clusters[27], fullerites [28],
Phases and nanostructures of the first subtype can be divided into the structures in which all atoms are in crystallographically equivalent positions, and structures are composed of atoms at crystallographically non-equivalent states. Structures of the atoms in non-equivalent positions may be of unlimited quantity – they can be obtained as various combinations of structures’ fragments consisting of atoms with the identical degree of hybridization. So, first of all, it is necessary to develop a classification scheme of carbon nanostructures and phases consisting of atoms in the crystallographically equivalent states (the number of such structures must be finite and all of them can be described). Attempts to develop such a scheme have been made earlier in [16, 17]. The scheme proposed in these papers was applied to the classification and mechanism of model formation of diamond-like phase structures only. Complete classification scheme should describe all the carbon phases and nanostructures with covalent bonds. This classification scheme has the form as shown in Table 1. A unique group of carbon nanostructures and phases corresponds to the individual table cell. The table strings correspond to the phases and nanostructures with different crystallographic dimensions: 0Dc (quasi-zero-dimensional), 1Dc (quasi-one-dimensional), 2Dc (quasi-two-dimensional), and 3Dc (three-dimensional). The table columns determine the number of the nearest atoms (Na) with which each atom forms covalent bonds in the corresponding phase or nanostructure. The parameter Na can range from 0 (when the atoms do not form covalent bonds) to 4 (all four electrons of the outer
Evgeny A Belenkov et al. / New Carbon Materials, 2013, 28(4): 273–283
Table 1 Classification of carbon phases and nanostructures with covalent bonds Na
nDc 0
1
2
pair of bonded
nanorings
atoms 1Da
2Da and 3Da
0Dс
single atom 0Da
1Dс
-
-
2Dс
-
3Dс
-
3
4 frame clusters
fullerene-like clusters 3Da
chains
nanotubes 3Da
1Da -3Da
ribbon 3Da
-
-
graphene-like layers 2Da
-
-
nanotubes and 3Da ribbons 2Da и 3Da spirals and 3Da
three-dimensional graphites 3Da
3Da
layers 2Da и 3Da
diamond-like phases 3Da
Note: The positions of all atoms in each structure are equivalent; Na is the number of nearest neighbors with which each atom forms covalent bonds.
electronic shell of the carbon atoms are involved in the formation of covalent bonds). Also the parameter Na can be seen as a quasi-coordination number, i.e. the number of atoms in the first coordination sphere. The number is a quasi-coordination as lengths of covalent bonds in some carbon compounds are different and the distances to the nearest-neighbor atoms are slightly different (considering the structure in rough approximation: at an equality of lengths of all covalent bonds the parameter Na is a quasi-coordination number). There are 20 cells in Table 1, each of which corresponds to a particular group of carbon phases or nanostructures. However, not all the cells in the table correspond to the allowable carbon structures. So, it is impossible to obtain covalently-bonded quasi-one-dimensional, quasi-two-and three-dimensional structure from the carbon atoms which are not forming covalent bonds and the atoms forming covalent bonds with only one neighboring atom. Also you can’t obtain 2Dc and 3Dc structures of carbon atoms that form covalent bonds with two neighboring atoms. Thus, there may be only 12 groups of carbon phases and nanostructures with covalent type of bonds. In the cells of Table 1 the geometrically optimized structures (basic structures), which can stably exist under normal conditions, being isolated in space are shown. Except for these structures, it is required to consider phases and nanostructures in the deformed states (deformed structures), derived from the basic structures by a deformation in such a way that all the atomic positions in them are equivalent. The need for consideration of deformed structures is connected with the fact that with their introduction the model mechanism of obtaining of the phases and nanostructures as a result of the cross-linking and superpositioning of atoms or cutting of bonds is simplified. In addition, the deformed structures can stably exist as structural elements in carbon phases with a mixed covalent-van der Waals type of bonds. The first five groups are quasi-zero-dimensional. There is only one nanostructure in the [0Dc,0] and [0Dc,1] groups that
correspond to a single carbon atom (with the 0Da dimension of the atomic structure) and a pair of bonded atoms (1Da), respectively. The [0Dc,2] group contains flat carbon nanorings with the 2Da atomic structure dimension (Fig. 3a). Besides, into this group two more structural species should be considered, that are curved zigzag (Fig. 3b) and armchair (Fig. 3c) rings with an even number of atoms (3Da dimension), related to the deformed structures. The [0Dc,3] group is presented by fullerene clusters that have 3Da atomic dimensions. Such clusters have the regular and semiregular polyhedral structures (Fig. 4) and prisms (Fig. 5). The number of fullerene-like clusters of the regular and semiregular polyhedral forms is limited, there are only 10 of them while no limit is set for the number of prismatic clusters. The last of the quasi-zero-dimensional groups ([0Dc,4]) contains frame clusters: 5 semi-regular polyhedra (octahedron, cuboctahedron, rombicuboctahedron,icosidodecahedron,and rhombicosidodecahedron) and an unlimited number of antiprisms. Such clusters, apparently, are only a result of modeling abstraction. The following three groups of phases and nanostructures are quasi-one-dimensional. The [1Dc,2] group contains a linear carbyne chain (1Da) (Fig. 6a). Also this structural group includes various deformed nanostructures: planar zigzag and armchair chains (2Da) (Fig. 6b, 6c), curved in space chains (3Da) (Fig. 6d) and different spirals (3Da) (Fig. 6e, 6f), whose number is unlimited. The [1Dc,3] group includes armchair, zigzag and chiral single wall nanotubes (3Da) as indicated in Fig. 7a, 7b and 7c, respectively, whose number is unlimited, an unlimited number
Fig. 3 Different nanoring structures of eight carbon atoms: (a) flat; (b) zigzag; (c) armchair.
Evgeny A Belenkov et al. / New Carbon Materials, 2013, 28(4): 273–283
Fig. 4 Structures of fullerene-like clusters.
Fig. 5 Structures of fullerene-like trigonal, hexagonal and octagonal prisms.
Fig. 7 Carbon nanotubes of the structure group [1Dc,3]: (a) armchair (3,3); (b) zigzag (6,0); (c) chiral (4,1) and (d) nanotube with a surface of 4- and 8-gons. Fig. 6 The quasi-one-dimensional nanostructures of the group [1Dc,2]: (a) linear chain; (b) planar zigzag(c) armchair chains; (d) chain curved in space and (e,f) spirals.
Evgeny A Belenkov et al. / New Carbon Materials, 2013, 28(4): 273–283
Fig. 8 The quasi-one-dimensional nano-objects of the structure group
There are two groups of three-dimensional carbon phases. To indicate the phases of the first of these groups [3Dc,3] the term three-dimensional graphites (3D-graphites) [26] is used in the literature. One of the first theoretically studied phases of this group is a metallic carbon [24] with a crystal structure similar to the network of 3-coordinated nodes [33, 34]. The review [25] describes a group of three-dimensional graphites, which were obtained by modeling cross-linking right- and left-symmetry spirals. The structures of some of these phases refer to the following types of uninodal 3D-nets: srs [33-35], utp [33] and etb [36]. The remaining sp2 phases can have crystal lattices like three-dimensional nbo-a [35] and etc [36] networks. Examples of images of 3D-graphite structures are shown in
[1Dc,3]: (a) zigzag ribbon; (b) flat ribbon; (c) armchair ribbon and (d,e) curved ribbons.
Fig. 9 Helical ribbons of the structure group [1Dc,3].
of armchair nanotubes with surfaces of the 4- and 8-gons (Fig. 7d) and a zigzag ribbon (Fig. 8a). A number of deformed structures can be derived from the basic structures of this group that should be considered for the model construction of other carbon phases. The deformed structures in the [1Dc,3] group are a flat ribbon (2Da) (Fig. 8b), three curved ribbons (3Da) (Fig. 8c, 8d) and an unlimited number of spiral ribbons (3Da) (Fig. 9).
Fig. 10 The quasi-one-dimensional nano-objects of the structure group [1Dc,4]: (a) flat ribbon; (b) curved ribbon; (c) spiral and (d,e) nanotubes.
The last of the quasi-one-dimensional groups [1Dc,4] contains ribbons (2Da and 3Da) (Fig. 10a, 10b) and spirals (3Da) (Fig. 10c) of the triangles and nanotubes (3Da), whose surfaces are composed of tetragons (Fig. 10d, 10e). The number of different nanotubes and spirals in this group is not limited. Just as in case of quasi-zero-dimensional group [0Dc,4] nanostructures, the group [1Dc,4] are probably only model abstractions. There are only two quasi-two-dimensional groups. The first of these groups ([2Dc,3]) consists of four flat graphene-like layers L6, L4-8, L3-12, L4-6-12 (2Da) (Fig. 11). Several corrugated layers of different structural types can be generated on the basis of these layers: 5 layers of L6 type, 7 – L4-8 type, one – L3-12 type, 3 – L4-6-12 type (3Da) (Fig. 12). The second of the quasi-two-dimensional groups ([2Dc,4]) consists of three flat monatomic (at thickness) layers (2Da) (Fig. 13), several corrugated layers, and flat diatomic layers (3Da) (Fig. 14). All structures of the [2Dc,4] group are only model abstractions.
Fig. 11 Structure fragments of graphene-like layers of the group [2Dc,3].
Evgeny A Belenkov et al. / New Carbon Materials, 2013, 28(4): 273–283
The phases of the second three-dimensional group [3Dc,4] in literature are called diamond-like. Fragments of the crystal lattices of some diamond-like phases are shown in Fig. 16. The number of these phases is also limited, and by present time the existence possibility is established for 30 diamond-like phases (excluding the cubic diamond), 25 of which are described in [16, 17].
Fig. 12 Examples of corrugated layers of the group [2Dc,3].
Fig. 13 Fragments of flat monoatomic layers of the structure group [2Dc,4].
The classification scheme of carbon phases with covalent type of bonds is the basis of a model process for generating any structures with crystallographically equivalent positions of the atoms. For obtaining any carbon structure it is necessary to take the nanostructures or phases-precursors, in which the parameter Na is not equal to similar parameter of the required structure. If the required structure is obtained by cross-linking or superpositioning, then the exponent n in the nDc parameter of precursor structure must be less or equal to the corresponding exponent of the final structures. The number of structure obtained by the operation of cutting the exponent value (n) of precursor should be greater than that in obtained nanostructure by cross-linking or superpositioning. Further, we find the initial configuration of the atomic nets from the selected precursors by the operations of cross-linking, superpositioning or cutting. The required phases and nanostructures are obtained in the process of geometric optimization of initial configurations, during which relative arrangement of atoms, corresponding to the minimum of the free energy, is found. Let’s consider the examples of how the described classification scheme can be used to predict new carbon phases and nanostructures. Any of the carbon structures can be derived by the geometric optimization of the atomic nets resulting from cross-linking or superpositioning of phases and nanostructures, pertaining to the groups of corresponding cells of the classification in Table 1, located to the left and below of the table cell for that structure we want to get. For example, graphene-like layers belonging to the [2Dc,3] group can be derived from basic and/or deformed nanostructures of the [0Dc,2] and [1Dc,2] groups (i.e. from nanorings, chains or
Fig. 14 Examples of flat diatomic layers of the group [2Dc,4].
Fig. 15. Possible number of such phases should be limited, however, how many of them can exist and what their structures are has not been established yet.
Fig. 15 Fragments of the crystal lattices of sp2 carbon phases belonging to the group [3Dc,3]: (a) metallic carbon and (b) C1 (31) (notation from [25]).
Evgeny A Belenkov et al. / New Carbon Materials, 2013, 28(4): 273–283
Table 2 Classification of carbon phases and nanostructures with mixed covalently-van-der-Waals bond types Na
nDc
0Dс
0
1 chain,
chain*, plane* and
chain and plane of
condensate of pairs of
condensate* of
fullerene-like clusters,
bonded atoms
nanorings
fullerite
planes and bundles of 1Dс
-
-
3Dс
-
-
-
-
planes
chains planes* and bundles* of spirals
2Dс
4
steam
individual atoms
and
3
chain, plane and of
plane
2
-
-
and
bundles
chain, plane and pairs of frame clusters of
planes
and
bundles
of
nanotubes, ribbons* and
nanotubes, ribbons* and
spirals*
spirals*
graphite-like phases,
graphite-like and
auto-intercalated
auto-intercalated phases of
graphite-like layers
graphane layers
auto-intercalated
auto-intercalated
three-dimentional graphites
diamond-like phases
Note: Na : the number of nearest neighbors with which each atom forms covalent bonds; *: there are two possible structural varieties: regular and auto-intercalated.
equivalent. The fragments of these phases and nanostructures, having more than one type of crystallographic positions, and different crystallographic and atomic dimensions of the structures, are shown in Fig. 17. The classification scheme for structures with covalent bonds can be used as the basis for classification of carbon phases with a combination of covalent and van der Waals types of chemical bonds (Table 2). The structure of these phases can be obtained by a geometrical optimization of the relative positions of structural elements, in which all atoms form covalent bonds, and the bonds between the structural units are carried out by van der Waals forces. The initial structural units with covalent bonds are the phases and nanostructures of the structural groups of cells in Table 1.
Fig. 16 The crystal lattices of diamond-like phases: (a) graphane-A5 (LA5); (b) tubulane-A5 (TA5) and (c) fullerane-A6 (CA6) [16, 17].
spirals) by the process of cross-linking or combining and subsequent geometric optimization. Graphene-like layers can also be obtained by geometric optimization of deformed layers found after cutting of bonds in the diamond-like phases [3Dc,4] or layers of [2Dc,4]. The general model scheme to obtain a structure has an exception for the described rules: one can not get a frame 3Da clusters of the [0Dc,4] structure group from the fullerene-like clusters of the [0Dc,3] group. Note also, that from 12 groups of carbon phases and nanostructures featured in the classification scheme, only 9 groups feature the structures, which can stably exist in nature, the three groups [0Dc,4], [1Dc,4] and [2Dc,4] correspond to fully model structures. The scheme, illustrated in the form of Table 1, can also be used for classification of carbon phases and nanostuctures, in which not all the atomic positions are crystallographically
Fig. 17 The structures with nonequivalent crystallographic atomic positions: (a) fullerene C28 ([0Dc,3]); (b) ribbon ([1Dc,3]); (c) graphene sheet ([2Dc,3]) and (d) diamond-like phase ([3Dc,4]).
Evgeny A Belenkov et al. / New Carbon Materials, 2013, 28(4): 273–283
Each group of covalent phases and nanostructures will correspond to the group of phases with a mixed covalent-van der Waals type of bonds. The phases, forming structure groups [nDc,Na]CV in each cell of Table 2, are obtained from the initial structures [nDc,Na] (basic and/or deformed) in cells of Table 1. For example, atomic chains, atomic planes or volume filled with atoms, linked together by van der Waals forces ([0Dc,0]CV) (Table 2), can be obtained from separated carbon atoms (structure group [0Dc,0]). Fullerites [0Dc,3]CV are obtained from the fullerene clusters [0Dc,3]. Graphite crystals [2Dc,3]CV are composed from the graphene layers [2Dc,3]. Nanotubes bundles [1Dc,3]CV are derived from the single wall nanotubes [1Dc,3], etc. Except for the usual phases with a mixed type of bonds auto-intercalated carbon phases can also be obtained. Auto-intercalated phases are phases in which the crystal structures of covalent precursors interpenetrate into each other, so that the covalently-linked structure of the initial precursors isn’t violated. Examples of such phases are phases with “chain armours” structure [0Dc,2]CV from carbyne nanorings [0Dc,2] as described in [37], auto-intercalated graphites [2Dc,3]CV and auto-intercalated diamonds [3Dc,4]CV. The above described classification scheme of carbon phases with mixed covalent-van der Waals type of chemical bonds concerns only those phases that are composed of identical structural elements with covalent bonds. Obviously, there may be a much greater variety of phases, where structural elements are the different precursors with covalent bonds. Examples of such carbon phases are multi wall nanotubes, onions and peapodes[29, 31, 32].
4
Conclusions The main innovation of the proposed classification
scheme of carbon phases and nanostructures is the consideration of the types of chemical bonds in carbon phases
[3]
Systematization of data on the physical and chemical properties[J]. High Temp, 2010, 48(6): 830-836. [4]
hybridization[J]. Carbon, 1997, 35(10-11): 1654-1658. [5]
nanomaterials"[J]. May 7-10, Sudak, Crimea, Ukraine 2003, 730-733. [6]
atoms[J]. J Struct Chem, 2005, 46(6): 961-967. [7]
crystalline phases and is a concretization of the developed crystal nets theories[33-36,38-40].
Univ Phys, 2009, 25(163): 22-33. [8]
Pierson H O. Handbook of carbon, graphite, diamond, and
53(11): 2385-2392. [9]
Cowley J M, Mani R C, Sunkara M K, et al. Structures of
[10]
Konyashin I, Khvostov V, Babaev V, el al. A new hard
carbon nanocrystals[J]. Chem. Mater., 2004, 16: 4905-4911. allotropic form of carbon: dream or reality[J]. Int J Refract Met Hard Mater, 2006, 24(1-2): 17-23. [11]
[2]
Dresselhaus M S, Dresselhaus G, Avouris Ph. Carbon nanotubes: synthesis, structure, properties, and applications[J]. Topics Appl Phys 80, Berlin: Springer-Verlag, 2001: 453.
Robertson J. Hard amorphous (diamond-like) carbons[J]. Prog. Solid St. Chem., 1991, 21: 199-333.
[12]
Franklin R E. The interpretation of diffuse X-ray diagrams of carbon[J]. Acta Cryst, 1950, 3(2): 107-121.
[13]
Franklin R E. The structure of graphitic carbon[J]. Acta Cryst., 1951, 4(3): 253-261.
[14]
Maire J, Mering J. Graphitization of soft carbon[J]. Chem Phys Carbon (New York: Dekker), 1970, 6: 125-190.
[15]
Lachter J, Bragg R H. Interstitial in graphite and disorder
[16]
Greshnyakov V A, Belenkov E A. Structures of diamond-like
carbons[J]. Phys Rev B, 1986, 33(12): 8903-8905. phases[J]. J Exp Theor Phys, 2011, 113(1): 86-95. [17]
Greshnyakov V A, Belenkov E A, Berezin V M. Crystal structure and properties of carbon diamond-like phases[J]. Chelyabinsk: South Ural State University, 2012: 150.
[18]
Kudryavtsev Yu P. The discovery of carbyne[J]. Phys Chem Mater Low-Dimens Struct, 1998, 21: 1-6.
[19]
Kroto H W, Heath J R, O'Brien S C, et al. C60: buckmimsterfullerene[J]. Nature, 1985, 318(6042): 162-163.
[20]
Iijima S, Ichihashi T. Single-shell carbon nanotubes of 1-nm diameter[J]. Nature, 1993, 363(6430): 603-605.
[21]
Bethune D S, Klang C H, de Vries M S, et al. Cobalt-catalysed
growth
single-atomic-layer
of
walls[J].
carbon Nature,
nanotubes 1993,
with
363(6430):
605-607. [22]
Novoselov K S, Geim A K, Morozov S V, et al. Electric field effect in atomically thin carbon films[J]. Science, 2004,
fullerenes: properties, processing and applications[J]. Park Ridge: Noyes, 1993: 402.
Belenkov E A, Shakhova I V. Structure of carbynoid nanotubes and carbynofullerenes[J]. Phys Solid State, 2011,
References [1]
Belenkov E A, Greshnyakov V A, Mavrinsky V V. Structure of sp+sp3 hybrid carbon phases. Bull[J]. Chelyabinsk State
may be a part of a more general classification scheme, which can describe the model that yields all possible structures of the
Belenkov E A, Ivanovskii A L, Ulianov S N, et al. New nanostructures of from sp2 and sp3 hybridized carbon
carbon phases in which all atoms are in crystallographically equivalent positions[16,17]. The proposed classification scheme
Belenkov E A. Classification of carbon structures. VIII Int'l Conf. "Hydrogen materials science & chemistry of carbon
of the predictive power of the proposed classification scheme is a description of the 25 possible structures of diamond-like
Heimann R B, Evsyukov S E, Koga Y. Carbon allotropes: a suggested classification scheme based on valence orbital
and nanostructures. This scheme allows not only to classify the known phases, but also to predict new ones. An example
Erkimbaev A O, Zitserman V Yu, Kobzev G A.
306(5696): 666-669. [23]
Balaban A T, Rentea C C, Ciupitu E. Chemical graphs. VI. Estimation of the relative stability of several planar and
Evgeny A Belenkov et al. / New Carbon Materials, 2013, 28(4): 273–283
tridimensional lattices for elementary carbon[J]. Rev Roum
[31]
Chim, 1968, 13(2): 231-247. [24]
[25]
[26]
Hoffmann R, Hughbanks T, Kertesz M. A hypothetical
carbon nanotubes[J]. Nature, 1998, 396(6709): 323-324. [32]
electron-beam
4831-4832.
707-709.
Stankevich I V, Nikerov M V, Bochvar D A. The structural
[33]
1992,
359(6397):
Blatov V A, Carlucci L, Ciani G, et al. Interpenetrating metal-organic and inorganic 3D networks: a computer-aided systematic investigation. Part I. Analysis of the Cambridge
640-655.
structural database[J]. Cryst Eng Comm, 2004, 6(65):
Belenkov E A, Ali-Pasha V A. 3D-graphite structure[J]. Cryst
377-395. [34]
Rohlfing E A, Cox D M, Kaldor A. Production and
structure prediction[J]. Weinheim: Wiley-VCH, 2011, 1-28. [35]
Kratschmer W, Lamb L D, Fostiropoulos K, et al. Solid C60: A Iijima S. Helical microtubules of graphitic carbon[J]. Nature,
2005, 178: 2533-2554. [36]
Deng Y, Liu H, Yu B, et al. Supramolecular coordination assemblies constructed from multifunctional azole-containing carboxylic acids[J]. Molecules, 2010, 15: 3478-3506.
Thess A, Lee R, Nikolaev P, et al. Crystalline ropes of 483-487.
Delgado-Friedrichs O, Foster M D, O'Keeffe M, et al. What do we know about three-periodic nets[J]. J Solid State Chem,
1991, 354(6348): 56-64. metallic carbon nanotubes[J]. Science, 1996, 273(5274):
Blatov V A, Proserpio D M, Periodic-graph approaches in crystal structure prediction. In: Modern methods of crystal
new form of carbon[J]. Nature, 1990, 347(6291): 354-358.
[30]
Nature,
electronic spectrum[J]. Russ Chem Rev, 1984, 53(7):
Chem Phys, 1984, 81(7): 3322-3330.
[29]
irradiation[J].
chemistry of crystalline carbon: geometry, stability, and
characterization of supersonic carbon cluster beams[J]. J [28]
Ugarte D. Curling and closure of graphitic networks under
metallic allotrope of carbon[J]. J Am Chem Soc, 1983, 105:
Rep, 2011, 56(1): 101-106. [27]
Smith B W, Monthioux M, Luzzi D E. Encapsulated C60 in
[37]
Belenkov E A, Shabiev F K. Structure of new carbon phases from carbyne nanorings[J]. Cryst Rep, 2007, 52(2): 343-348.