Fig. 2.4. Graphite Brillouin zone showing several high-symmetry points and a schematic version of the graphite electron and hole Fermi surfaces located along the HKH and H'K'H' axes

C-C spacing is very small. Interestingly, the intramolecular C-C spacing in fullerenes (see §3.1) is also close to ac_c for graphite. Disorder does, however, have a significant effect on the crystallite size in the basal plane and on the interplanar spacing because of the weak interplanar bonding. One consequence of the small value of ac_c is that impurity species are unlikely to enter the in-plane lattice sites substitutional^, but rather occupy some interstitial position between the layer planes. The weak interplanar bonding also allows entire planes of dopant atoms or molecules to be intercalated between the carbon layers, as discussed in more detail in §2.14.

Weak disorder results in stacking faults (meaning departures from the ABAB stacking order) giving rise to a small increase in the interlayer distance until a value of about 3.440 A is reached, at which distance the stacking of the individual carbon layers (called graphene layers) becomes uncorrelated; the resulting two-dimensional (2D) honeycomb structure of uncorrelated graphene layers is called turbostratic graphite [2.12,13], The electronic structure of turbostratic graphite, a zero gap semiconductor, is qualitatively different from that of ideal graphite, a semimetal with a small band overlap (0.04 eV). Likewise, as the stacking disorder is increased, the interplanar spacing also increases, which further modifies the electronic properties.

To describe the electronic and phonon dispersion relations of 3D graphite, the Brillouin zone shown in Fig. 2.4 is used. Since the in-plane nearest-neighbor distance in real space is much larger than the interplanar separation, the Brillouin zone for graphite has a small length in reciprocal space along kz. As the interplanar correlation becomes less and less important, as in the case of turbostratic 2D graphene layers, the Brillouin zone is reduced to a sheet. The special point K at the Brillouin zone corner in 2D graphite is the location of the Fermi level and the symmetry-imposed degeneracy of the conduction and valence bands [2.14]. The band structure model for graphite near EF focuses on the electronic dispersion relations in the vicinity of the HKH and H'K'H' edges of the Brillouin zone. Shown in the figure are electron and hole pockets which form along the zone edges [2.12],

In the following sections, a review of the most important forms of graphite-related materials is given, showing the wide variety of materials that have been prepared and investigated.

2.3. Graphite Materials

Many sources for crystalline graphite are available. For example, natural single-crystal graphite flakes are found in several locations around the world, especially in Madagascar, Russia, and the Ticonderoga area of New York State in the United States. These flakes can sometimes be as large as several millimeters in the basal plane and are typically much less than 0.1 mm in thickness. Natural graphite flakes usually contain defects in the form of twinning planes and screw dislocations and, in addition, contain chemical impurities such as Fe and other transition metals.

A synthetic single-crystal graphite, called "kish" graphite, is commonly used in scientific investigations. Kish graphite crystals form on the surface of high carbon content iron melts and are harvested as crystals from such solutions [2.15]. The kish graphite flakes are often larger than the natural graphite flakes, which makes kish graphite the material of choice when large single-crystal flakes are needed. The most perfect single-crystal flakes presently available are smaller size kish graphite flakes, ~1 mm in diameter.

In materials research laboratories, the most commonly used high-quality graphitic material today is highly oriented pyrolytic graphite (HOPG), which is prepared by the pyrolysis of hydrocarbons at temperatures above 2000°C and is subsequently heat treated to higher temperatures [2.16,17]. When stress annealed above 3300° C, the HOPG exhibits electronic, transport, thermal, and mechanical properties close to those of single-crystal graphite, showing a very high degree of c-axis alignment. For the high temperature, stress-annealed HOPG, the crystalline order extends to about 1 /¿m within the basal plane and to about 0.1 ju,m along the c-direction. The HOPG basal planes are sufficiently parallel and ordered to be useful commercially for neutron and x-ray monochromator crystal applications. For all HOPG material however, there is no long-range in-plane a-axis alignment, and the a-axes of adjacent crystallites are randomly oriented [2.16,17]. The degree of structural order and c-axis alignment of HOPG can be varied by control of the major processing parameters: heat treatment temperature Tm, residence time at Tm, and applied stress during heat treatment [2.16,17]. Turbostratic pyrolytic graphites are obtained for Tm < 2300° C, and higher values (typically above 2800°C) are needed to establish 3D ordering. Thus under normal x-ray diffraction measurements, HOPG appears to be polycrystalline but under selected area electron diffraction, HOPG can show a sharp single-crystal spot pattern. Large-area, ~5 mm thick plates of HOPG are used for x-ray and neutron spectrometers and are available commercially.

Recently, new precursor materials, such as polyimide (PI) and polyoxadi-azole (POD) resins [2.18-22], have been used to synthesize graphite films, and, after suitable pyrolysis steps to drive off non-carbon constituents in the vapor phase and subsequent heat treatment steps, the resulting carbon films show a high degree of 3D structural ordering, especially when heat treated to > 2800°C. The quality of these thin-film graphite materials, especially those based on Kapton and Novax (polyimide) precursors, is rapidly improving and these graphite materials may soon become materials of choice for specific applications.

In addition to highly crystalline graphite, several less-ordered forms of graphite are available and are widely used for specific applications (e.g., high surface area or high strength applications).

2.4. Graphite Whiskers

A graphite whisker is a graphitic material formed by rolling a graphene sheet (an atomic layer of graphite) up into a scroll [2.23]. Except for the early work by Bacon [2.23], there is little literature about graphite whiskers. Graphite whiskers are formed in a dc discharge between carbon electrodes using 75-80 V and 70-76 A. In the arc apparatus, the diameter of the positive electrode is smaller than that of the negative electrode, and the discharge is carried out in an inert gas using a high gas pressure (92 atmospheres). As a result of this discharge, cylindrical boules with a hard shell were reported to form on the negative electrode. When these hard cylindrical boules were cracked open, scroll-like carbon whiskers up to ~3 cm long and 1-5 /j,m in diameter were found protruding from the fracture surfaces. The whiskers exhibited great crystalline perfection, high electrical conductivity, and high elastic modulus. Since their discovery [2.23], graphite whiskers have provided the benchmark against which the performance of carbon fibers is compared. The growth of graphite whiskers has many similarities to the growth of carbon nanotubes (see §19.2.5). It would be useful to verify once again the scroll structure of graphite whiskers.

2.5. Carbon Fibers

Carbon fibers represent an important class of graphite-related materials. Despite the many precursors that can be used to synthesize carbon fibers, each having different cross-sectional morphologies (see Fig. 2.5), the preferred orientation of the graphene planes is parallel to the fiber axis

Fiber axis

Outer, thickened sheath

Initial growth region

Outer, thickened sheath

Initial growth region

Fiber axis

Fig. 2.5. Sketch illustrating the morphology of vapor-grown carbon fibers (VGCF): (a) as-deposited at 1100°C [2.12], (b) after heat treatment to 3000°C [2.12], The morphologies for commercial mesophase-pitch fibers are shown in (c) for a "PAC-man" cross section with a radial arrangement of the straight graphene ribbons and a missing wedge and (d) for a PANAM cross-sectional arrangement of graphene planes. In (e) a PAN fiber is shown, with a circumferential arrangement of ribbons in the sheath region and a random structure in the core.

Fig. 2.5. Sketch illustrating the morphology of vapor-grown carbon fibers (VGCF): (a) as-deposited at 1100°C [2.12], (b) after heat treatment to 3000°C [2.12], The morphologies for commercial mesophase-pitch fibers are shown in (c) for a "PAC-man" cross section with a radial arrangement of the straight graphene ribbons and a missing wedge and (d) for a PANAM cross-sectional arrangement of graphene planes. In (e) a PAN fiber is shown, with a circumferential arrangement of ribbons in the sheath region and a random structure in the core.

for all carbon fibers, thereby accounting for the high mechanical strength of carbon fibers [2.12], Referring to the various morphologies in Fig. 2.5, the as-prepared vapor-grown fibers have an "onion skin" or "tree ring" morphology [Fig. 2.5(a)] and after heat treatment to about 3000°C, form facets [Fig. 2.5(b)], Of all carbon fibers, these faceted fibers are closest to crystalline graphite in both crystal structure and properties. The commercially available mesophase pitch fibers, with either the radial morphology [Fig. 2.5(c)], the PAN-AM cross-sectional arrangement, or other morphologies (not shown), are exploited for their extremely high bulk modulus and high thermal conductivity, while the commercial PAN (polyacrylonitrile) fibers with circumferential texture [Fig. 2.5(e)] are widely used for their

Fig. 2.6. The breaking strength of various types of carbon fibers plotted as a function of Young's modulus. Lines of constant strain are shown and can be used to estimate the breaking strains [2.12,24,25],



Fig. 2.6. The breaking strength of various types of carbon fibers plotted as a function of Young's modulus. Lines of constant strain are shown and can be used to estimate the breaking strains [2.12,24,25], high strength [2.12], The high modulus of the mesophase pitch fibers is related to the high degree of c-axis orientation of adjacent graphene layers, while the high strength of the PAN fibers is related to defects in the structure, which inhibit the slippage of adjacent planes relative to each other. Typical diameters for these individual commercial carbon fibers are ~ 10 /Am, and they can be very long. These fibers are woven into bundles called tows and are then wound up as a continuous yarn on a spool. The remarkable high strength and modulus of carbon fibers (see Fig. 2.6) are responsible for most of the commercial interest in these fibers. The superior mechanical properties of carbon fibers should be compared to steel, for which typical strengths and bulk modulus values are 1.4 and 207 GPa, respectively [2.12],

Vapor-grown carbon fibers can, however, be prepared over a wide range of diameters (from less than 1000 A to more than 100 /¿.m) and these fibers have hollow cores. The preparation of these fibers is based on the growth of a thin hollow tube of about 1000 A diameter from a transition metal catalytic particle (~100 A diameter) which has been supersaturated with carbon from a hydrocarbon gas present during growth at 1050°C. The thickening of the vapor-grown carbon fiber occurs through an epitaxial growth process whereby the hydrocarbon gas is dehydrogenated and sticks to the surface of the growing fiber. Subsequent heat treatment to ~2500°C results in carbon fibers with a tree ring concentric cylinder morphology [2.26]. Vapor-grown carbon fibers with micrometer diameters and lengths

Fig. 2.7. Tangled structure within a grain proposed for many polymer-derived graphitic carbons including glassy carbon. The presence of voids accounts for the low mass density of glassy carbons, and the voids are likely sources of mechanical weaknesses [2.27].

of ~30 cm provide a close analogy to carbon nanotubes with diameters of nanometer dimensions (see Chapter 19).

2.6. Glassy Carbon

Glassy carbon (GC) is another common carbon material which is manufactured as a commercial product by slow, controlled degradation of certain polymers at temperatures typically on the order of 900-1000cC [2.27]. The name glassy carbon is thus given to a family of disordered carbon materials, which are glass-like and can be easily polished to attain a black, shiny appearance. Because they are prepared over a range of conditions, glassy carbons have a range of properties that depend somewhat on the precursor material and significantly on the processing conditions. Glassy carbons are granular, moderately hard, thermally conducting, impermeable, biocompatible, and stable at high temperatures. The apparent density of GC is in the range 1.46-1.50 g/cm3 irrespective of heat treatment temperature, implying the existence of pores in the matrix.

According to one model [2.27], the microstructure of GC consists of a tangle of graphite-like ribbons or microfibrils, about 100 A long and 30 A in cross section (see Fig. 2.7), and resembles the polymer chain configuration from which the GC has been derived. Because of the tangled ribbon microstructure, Jenkins and Kawamura [2.27] have argued that glassy carbon does not fully graphitize, even when heat treated above 3000°C. X-ray diffraction studies of the radial distribution function show that within the graphite-like ribbons the carbon atoms are ordered in the honeycomb inplane structure of the graphene layers, but that the 3D registry between the graphene layers is poor, so that the ribbons form a turbostratic structure, typical of hard carbons; a hard carbon denotes a carbon material

Typical strong

Typical strong

Fig. 2.8. Schematic diagram for the microstructure of the closed pore structure model for glassy carbon and other hard carbons [2.30,31].

which does not fully graphitize, even under high-temperature (~3000°C) heat treatment [2.28,29]. Detailed structural studies have indicated that glassy carbons have a network of closed pore structures, according to a competing structural model for glassy carbon proposed by Shiraishi (see Fig. 2.8) [2.30-32],

The temperature dependence of the electrical conductivity cr{T) for glassy carbons prepared at various heat treatment temperatures i® shown in Fig. 2.9, where Tm in °C is indicated by the number following GC. This general behavior is seen in a variety of other disordered carbons. The temperature dependence of the conductivity of glassy carbon, which is due to hopping, exhibits an exp[—(7"0/7')1/4] dependence, characteristic of 3D variable range hopping for carbon materials with THX < 1000°C. With increasing Tm, it is shown in Fig. 2.9 that <t(T) increases in magnitude and eventually becomes independent of temperature over a very wide temperature range. Glassy carbons have also been extensively characterized by the Raman effect, which is discussed in §2.7 in the context of carbon blacks.

2.7. Carbon Blacks

Classical carbon blacks represent many types of finely divided carbon particles that are produced by hydrocarbon dehydrogenation [2.33,34] and are widely used in industry as a filler to modify the mechanical, electrical, and optical properties of the materials in which they are dispersed [2.34]. The various types of industrial carbon blacks are usually named following the processes by which they are produced. For example, thermal blacks are typically obtained by thermal decomposition of natural gas, channel blacks by

Fig. 2.9. Temperature dependence of the electrical conductivity for glassy carbon samples heat treated to various temperatures (indicated by numerals following GC) [2.31], Note the many orders of magnitude change in <r for GC 800 in (a) as compared to glassy carbon samples with higher heat treatment temperatures shown in (b).


Fig. 2.9. Temperature dependence of the electrical conductivity for glassy carbon samples heat treated to various temperatures (indicated by numerals following GC) [2.31], Note the many orders of magnitude change in <r for GC 800 in (a) as compared to glassy carbon samples with higher heat treatment temperatures shown in (b).

partial combustion of natural gas, acetylene blacks by exothermic decomposition of acetylene, furnace blacks by partial combustion of oil droplets, and plasma blacks by decomposition of ethylene in a plasma arc [2.33]. Other types of carbon blacks are synthesized on a laboratory scale by special processes, such as laser ablation of graphite [2.35]; C02 laser pyrolysis of acetylene (C2H2) [2.36,37] and of ethylene (C2H4), which is catalytically assisted by small amount of Fe(CO)5 [2.38]; and by the heat treatment of coal [2.33]. These synthesis routes have produced various types of carbons with different physical and chemical properties.

The microcrystalline structures of several types of carbon blacks (in sizes of 1000 A and higher) in both their as-synthesized and heat-treated (up to 3000°C) forms have been established by study over many years, mainly using x-ray diffraction (XRD) [2.34,39-46], high-resolution transmission electron microscope (TEM) lattice imaging [2.47-51], and Raman scattering techniques [2.38,52,53]. The earliest XRD studies on carbon blacks [2.39,40] indicated that as-synthesized carbon blacks are composed of small graphitelike layers in which carbon atoms have the same relative atomic positions as in graphite. These studies led to a model in which the dimensions of the layers are described by two characteristic lengths, La and Lc, where La is the crystalline size in the plane of the layers and Lc is the size along the c-axis perpendicular to the planes. This simple model was frequently used in later studies to characterize the microcrystalline structures of carbon blacks including thermal blacks, channel blacks, acetylene blacks, plasma blacks, and furnace blacks [2.44],

Another characteristic signature associated with carbon blacks is a concentric organization of the graphite layers in each individual particle. This structural property was mainly established by studies involving high-resolution TEM lattice imaging [2.34,43,47-49], These concentric graphene layers are found to be more pronounced in the region close to the particle surface than in the center. The development of the graphitic layers was also found to be correlated with carbon particle size, synthesis time and temperature, and microporosity of the particles [2.54,55]. Furthermore, subsequent heat treatment of "as-synthesized" carbon blacks in Ar up to 3000°C was found to produce polygonized particles with an empty core and a well-graphitized carbon shell centered around the growth starting point [2.34,38,50,51].

The morphology of carbon black particles changes as three-dimensional (3D) order is established, since 3D correlations can exist only over very short distances for curved concentric graphene layers. This same argument also applies to the nanometer scale carbon spherules (or onions) discussed in §19.10. Hence the transformation from 2D to 3D graphite requires graphene layer flattening through formation of faceted surfaces. Heat-treated carbon blacks do indeed display a high degree of faceting, as observed in transmission electron micrographs [2.56]. An idealized shape for partially graphitized carbon black particles was proposed [2.43] and is shown schematically in Fig. 2.10(a) as a faceted external surface in the shape of a polyhedron. As-prepared carbon blacks generally exhibit short layer segments which are roughly aligned with the particle surface, shown schematically in Fig. 2.10(b). As the particles are heat treated to higher temperatures, the segment lengths of the graphene layers increase and the graphene layers increase their parallelism with respect to the particle surface. The junctions between facets represent high-angle grain boundaries.

Raman scattering was first used by Tuinstra and Koenig [2.52] to characterize several forms of carbons including single-crystal graphite, pyrolytic graphite, activated charcoal, and carbon blacks. In their studies, all disordered graphite samples showed two prominent Raman features with peaks at 1580 and 1355 cm-1. They assigned the dominant peak (1580 cm-1) as due to the in-plane Elg Raman-allowed mode vibration, which has the value of 1582 cm-1 for single crystal graphite, and the second peak (1355 cm-1)

Fig. 2.10. (a) Idealized structure of a partially graphitized carbon black particle, (b) Another schematic view of a carbon black particle showing short graphitic segments [2.43,55,56].

was identified with in-plane disorder-induced scattering from graphitic modes throughout the Brillouin zone, but mostly emphasizing the zone edge, where the phonon density of states has a strong maximum. Of particular importance for characterizing the amount of disorder in the graphitic material is the close correlation between the in-plane crystalline size La as established by x-ray diffraction and the relative integrated intensity of the disorder-induced line (1355 cm-1) to the first-order Raman-allowed line (1580 cm-1) [2.38,53,57]. These two Raman lines are frequently used to monitor the graphitization process of carbon blacks upon annealing at elevated temperatures and for characterizing the internal microcrystalline size of nanoscale carbon black particles.

The synthesis of carbon blacks involving a COa laser was carried out first by Yampolskii et al. [2.36] and later by Maleissye et al. [231]. In their studies, carbon blacks were obtained by decomposing acetylene (C2H2) gas using a C02 laser beam as a heating source. They reported that carbon blacks produced in this way are identical to those obtained by classic thermal pyrolysis of acetylene. However, no detailed studies were performed to characterize the physical properties of these carbon blacks in either the as-synthesized or heat-treated forms. Another approach producing nanoscale carbon blacks using a C02 laser as a heating source involves the pyrolysis of benzene (C6H6) vapor, assisted catalytically by a small amount of Fe(CO)5 [2.38]. In this way, highly disordered and spherical carbon particles, 200-500 A in diameter, have been synthesized. Subsequent heat treatment of these particles in argon gas to temperatures up to ~2800°C produces graphitized polygonal particles with central polygonal cavities. An important advantage of C02 laser pyrolysis for carbon black synthesis is that only carbon blacks are produced in the reaction zone defined by the intersection of the reactant gas stream and the C02 laser beam [2.38,58,59]. Since the reaction zone is away from the chamber wall, which remains at room temperature during the synthesis, no pyrolytic carbons are deposited on the hot chamber walls. The formation of pyrolytic carbons in heated furnaces [2.33] inhibited the development of carbon black formation theory because of the complex reaction products produced on the chamber walls. The C02 laser pyrolysis technique [2.60,61] closely resembles the flame synthesis approach but does not require the presence of oxygen to initiate or sustain the reaction process, in contrast to the conventional flame technique in which oxygen must be used to provide heat to the reaction zone.

2.8. Carbon Coated Carbide Particles

Closely related to carbon blacks are graphitic structures (~100 A in diameter) which form around nanoscale carbide particles such as cementite (Fe3C) and are prepared by a C02 laser pyrolysis process [2.59] or by arc discharge methods [2.62]. These carbon-coated particles may have a significant bearing on the synthesis of single-wall carbon nanotubes [2.63-66] discussed in §19.2.2. The synthesis of cementite nanoparticles involves a gas-phase reaction of Fe(CO)5 vapor with ethylene (C2H4) which strongly absorbs the C02 laser energy. A high degree of crystallinity has been observed for the graphitic structure that forms around the cementite particle, based on high-resolution transmission electron microscopy (TEM) measurements [2.59] of the lattice image from a single particle (diameter ~300 A) taken from a batch of similarly prepared particles. X-ray diffrac tion (XRD) studies on these particles indicate that the particles are a nearly pure Fe3C phase. Lattice fringe spacings were observed at d ~ 6.75 A for Fe3C(001) and 3.5 A for C(002) from both Fe3C and the carbon coating material. The carbon coating was found to be thick (~60 A), serving to passivate and stabilize the Fe3C nanocrystalline particles. The carbon coating has also been characterized by Raman spectroscopy, where a broad doublet is observed with peaks centered at 1375 and 1580 cm1, and this doublet is identified with the well-known Raman spectrum for disordered pyrolytic carbons [2.12,52] as discussed in §2.7. The formation mechanism of the carbon coatings has been identified with a catalytic decomposition of C2H4 at the particle surface. This decomposition occurs when the "hot" (~1000°C) carbide particle leaves the reaction zone defined by the intersection of the C02 laser beam and the reactant gas flow. The rapid cooling of the carbide particle at the reaction zone boundary "freezes" the carbons on the particle surface, rather than allowing these carbons to diffuse into the interior of the carbide particle. Furthermore, no carbon fiber growth has been observed on these cementite nanoparticles, presumably because of the rapid transfer of the Fe3C particles to a cooler environment, which prevents carbon filament growth from occurring to any great extent. The same laser pyrolysis technique has also been used to produce nanoscale carbon blacks by pyrolyzing benzene (C6H6) vapor, catalytically assisted by a small amount of Fe(CO)5 [2.38,67] as discussed in §2.7. Transition metals or the transition metal carbides (Fe3C, Ni3C, Co3C) form crystalline particles that are tightly wrapped by a thin layer of carbon. Carbon-encapsulated nanoscale Co particles have been produced similarly using the arc discharge method, in which one of the graphite electrodes was packed with Co powder (see §19.2.2).

The carbon encapsulation of pyrophoric, nanoscale lanthanide carbide single crystals was first observed by Ruoff et al. [2.62] and Saito et al. [2.68,69] in a fullerene-related synthesis process using a dc arc discharge between two graphite electrodes. The positive electrode was impregnated in the center with La203 powder (or some other lanthanide oxide powder) with an La:C molar ratio of 0.02. Roughly 50% of nanoscale carbon particles produced by this method are observed to contain single crystalline LaC2 crystals, and these carbon encapsulated metals are found to be stable in air, indicating that the otherwise pyrophoric LaC2 metals are protected by the surrounding carbon layers. The carbons on the metal particle surface are found to be well graphitized, presumably due to the high temperature (~3000°C) in the arc discharge region. Because of the high temperature in the arc, the solidification starts on the surface, forming polyhedra of carbon with faceted faces inside which the lanthanide carbide forms a crystalline particle with composition La2C. The carbon-coated lanthanide carbide par-

tides have been called nanocapsules [2.68], and differ from the carbon wrapped transition metal carbide particles by having a small vacuum region formed during the cooling process from high temperature, whereas the transition metal carbides formed at lower temperatures are tightly wrapped. In both cases the carbon wrapping pacifies and stabilizes the carbides, which otherwise would be quite reactive [2.68].

2.9. Carbynes

Linear chains of carbon which have sp bonding have been the subject of research for many years [2.70], Nevertheless, the present state of knowledge in this field is still fragmentary.

A polymeric form of carbon consisting of chains [----CsC----]„ for n > 10 has been reported in rapidly quenched carbons and is referred to as "carbynes." This carbon structure is stable at high temperature and pressure as indicated in the phase diagram of Fig. 2.1 as shock-quenched phases. Carbynes are silver-white in color and are found in meteoritic carbon deposits, where the carbynes are mixed with graphite particles. Synthetic carbynes have also been prepared by the sublimation of pyrolytic graphite [2.71,72], It has been reported that carbynes are formed during very rapid solidification of liquid carbon, near the surface of the solidified droplets formed upon solidification [2.73], Some researchers [2.72-76] have reported evidence that these linearly bonded carbon phases are stable at temperatures in the range 2700 < T< 4500 K.

Carbynes were first identified in samples found in the Ries crater in Bavaria [2.77] and were later synthesized by the dehydrogenation of acetylene [2.72,78]. The carbynes have been characterized by x-ray diffraction, scanning electron microscopy (SEM), ion micromass analysis, and spectroscopic measurements which show some characteristic features that identify carbynes in general and specific carbyne polymorphs in particular. Since several different types of carbynes have been reported, and carbynes are often found mixed with other carbon species, it is often difficult to identify specific carbynes in actual samples. Carbynes have a characteristic negative ion mass spectrum with constituents up to C17. This mass spectrum is different from that of graphite, which has negative ion emissions only up to C4, with C3 and C4 being very weak. Thus ion micromass analysis has provided a sensitive characterization tool for carbynes.

The crystal structure of carbynes has been studied by x-ray diffraction through identification of the Bragg peaks with those of synthetic carbynes produced from sublimation of pyrolytic graphite [2.74,78], In fact, two polymorphs of carbynes (labeled a and 0) have been identified, both be ing hexagonal and with lattice constants aa = 8.94 A, ca = 15.36 A; dp = 8.24 A, Cp = 7.68 A [2.72]. Application of pressure converts the a phase into the ¡3 phase. The numbers of atoms per unit cell and the densities are, respectively, 144 and 2.68 g/cm3 for the a phase and 72 and 3.13 g/cm3 for the /3 phase [2.79]. These densities determined from x-ray data [2.72] are in rough agreement with prior estimates [2.80,81]. It is expected that other less prevalent carbyne polymorphs should also exist.

In the solid form, these carbynes have a hardness intermediate between diamond and graphite. Because of the difficulty in isolating carbynes in general, and specific carbyne polymorphs in particular, little is known about their detailed physical properties, and some have even questioned the existence of carbynes.

2.10. Carbolites

In an effort to prepare larger quantities of carbynes for detailed measurements, a new crystalline form of carbon was synthesized. Because of its relatively low mass density (pm = 1.46 g/cm3) it was called carbolite [2.82], The carbolite material was synthesized using a carbon arc powered by two automobile batteries (/ ~ 600 A) to generate carbon vapor which was rapidly quenched onto a copper plate in an argon or argon-hydrogen atmosphere [2.82]. The carbolite material is a slightly orange-colored transparent crystal, suggesting nonconducting transport properties. Depending on whether or not hydrogen is contained with argon as the ambient gas, two crystal structures are obtained by analysis of x-ray diffraction patterns. For carbolites (type I) synthesized in argon gas, the crystal structure is hexagonal with a0 = 11.928 A, c0 = 10.62 A, and for carbolites (type II) formed using an argon-hydrogen gas mixture, the lattice constants are aQ = 11.66 A, c0 = 15.68 A, which could also be indexed to a rhombohedral structure with a unit cell length of 8.52 A and a rhombohedral angle of 86.34°. From the structural analysis, the crystal model described in Fig. 2.11 was proposed, showing the stacking of four-atom carbon chains with a nearest-neighbor distance of 1.328 A and 1.307 A in a hexagonal lattice with 3.443 A and 3.366 A separation between the chains. In the type I structure, the four-atom chains have an AB stacking, while the type II structure shows ABC stacking. Infrared spectra suggest that the interchain bonding is of the -C=C-C=C- polyyne type. Evidence for modification of the electrical properties of carbolites by intercalation with K, Na, and I2 was also reported [2.82]. Further structure/properties measurements on carbolites can be expected.

^ 0.3443 nm J ^0.3366 nm

Fig. 2.11. Proposed structural model for the two forms of hexagonal carbolite.

Hexagonal face of unit cell showing

Hexagonal face of unit cell showing b a > A i B

C alignment of the chains for (a) type I carbolite and (c) for type II carbolite. View of the four-atom carbon chains

A (b) with AB stacking for type I, and (d) with ABC stacking for type II [2.82],

2.11. Amorphous Carbon

Amorphous carbon (a-C) refers to a highly disordered network of carbon atoms that have predominantly sp2 bonding, with perhaps 10% sp3 bonds and almost no sp1 bonds (see Fig. 2.3) [2.9], Although amorphous carbon has no long-range order, some short-range order is present. Since the nature of the short-range order varies significantly from one preparation method to another, the properties of amorphous carbon films likewise vary according to preparation methods [2.83]. Two parameters, the carbon bonding (expressed in terms of the ratio of sp2/sp3 bonds) and the hydrogen content, are most sensitive for characterizing the short-range order, which may exist on a length scale of ~10 A. Thus the s/72-bonded carbons of a-C may cluster into tiny warped layered regions, and likewise the sp3-bonded carbons may also cluster and segregate, as may the hydrogen impurities, which are very effective in passivating the dangling bonds. Amorphous carbon is also commonly formed by neutron, electron, or ion beam irradiation of carbon-based materials which had greater structural order prior to irradiation [2.84].

A perfectly sp2-ordered graphene sheet is a zero gap semiconductor. The introduction of disorder and sp3 defects creates a semiconductor with localized states near the Fermi level and an effective band gap between mobile filled valence band states and empty conduction states. The greater the disorder and the greater the concentration of sp3 bonds, the larger is the band gap. Amorphous carbon prepared by evaporation tends to have a higher room temperature conductivity aKI ~ 103 fl ^cm 1 and smaller band gap (Eg -0.4-0.7 eV) [2.83,85-87] compared with a-C prepared by ion-beam deposition for which <xRX ~ 102 il_1cm_1 and Eg ~ 0.4 - 3.0eV [2.88-90], Increasing the sp3 content of the films also tends to enhance the mechanical hardness of the films, to decrease crRX, and to increase Eg.

Since amorphous carbon has no long range order, it is customary to characterize a-C samples in terms of their radial distribution functions as measured in a diffraction experiment (electron, x-ray, or neutron). Amorphous carbon samples are also characterized in terms of their densities in comparison to graphite (pm = 2.26 g/cm3) to specify the packing density of the films. The ratio of the sp2/sp3 bonding in a-C samples is usually determined spectroscopically, for example by nuclear magnetic resonance (NMR), x-ray near-edge structure, and electron energy loss spectroscopy [2.9].

2.12. Porous Carbons

There are a number of carbons which form highly porous media, with very high surface areas and pores of nanometer dimensions similar to the dimensions of fullerenes. In this category of porous and high surface area carbons are included activated carbons, exfoliated graphite, and carbon aerogels. The nanopores may be in the form of cages or tunnels. Whereas the surfaces of the nanopores contain a high density of dangling bonds and surface states, the surfaces of fullerene molecules, which may be considered as nanoparticles, have no dangling bonds.

In preparing activated carbons (see Fig. 2.12), isotropic pitch and phenol are commonly used as precursor materials. Of the various activated carbon materials, activated carbon fibers have the narrowest distribution of pore sizes and nanopores. The dominance of the carbon nanopores in the properties of activated carbon fibers makes this fibrous material attractive for various applications [2.91] and of particular interest as a comparison material to fullerene carbon nanoparticles because of the similarity of the sizes of the pores and fullerenes. In the activation process, the precursor fiber is heated in 02, H20, C02, or other oxidizing atmospheres in the temperature range 800-1200°C for pitch-based fibers and 1100-1400°C for phenolic-derived fibers. The main parameter that has been used to characterize activated carbon fibers is the specific surface area (SSA). High values for SSA are achieved (1000-3000 m2/g) in activated carbon fibers by controlling the temperature and the time for activation, and the precursor materials. The SSA is usually measured using adsorption isotherms of N2 gas at 78 K and C02 gas at 195 K, though the highest accuracy is achieved with helium gas near 4 K. Most of the surface area arises from a high density of nanopores with diameters < 1 nm. In the literature on porous carbon,

high surface area fiber where the basic structural units are randomly arranged, (b) for a fiber after some heat treatment, showing partial alignment of the basic structural units [2.91].

the term macropore is used to describe pores with diameters greater than 100 nm, mesopores for diameters in the 2 to 100 nm range and micropores for diameters less than 2 nm [2.92].

Exfoliated graphite is another high surface area form of graphite which is prepared by heating a graphite intercalation compound (see §2.14) above some critical temperature above which a gigantic irreversible c-axis expansion occurs, with sample elongations of as much as a factor of 300 [2.93]. This gigantic elongation, called exfoliation, gives rise to spongy, foamy, low density, high surface area material (e.g., 85 m2/g [2.94]). The commercial version of the exfoliated "wormy" material is called vermicular graphite and is used for high surface area applications. When pressed into sheets, the exfoliated graphite material is called grafoil and is widely used as a high temperature gasket or packing material because of its flexibility, chemical inertness, low transverse thermal conductivity, and ability to withstand high temperatures [2.95].

Carbon aerogels are a disordered form of sp1-bonded carbon with an especially low bulk density and are made by a supercooling process. These materials are examples of a class of cluster-assembled low-density porous materials, consisting of interconnected carbon particles with diameters typically near 12 nm [2.57,96]. Within each particle, a glassy carbon-like nanostructure is observed, consisting of an intertwined network of narrow graphitic ribbons of width ~2.5 nm. The morphology is illustrated schematically in Fig. 2.13. This structure leads to high surface areas (600-800 m2/g) with a significant fraction of the atoms covering the surfaces of the interconnected particles. For a given specific surface area, carbon aerogels tend to have larger size pores than the activated carbon fibers discussed above. Because of their large surface areas and consequently high density of dangling bonds, porous carbons tend to have

Fig. 2.13. Schematic diagram of the carbon aerogel microstructure. Each shaded circle represents an amorphous carbon particle. The microstructure is shown for (A) low (~0.1 g/cm3) and (B) high (~0.6 g/cm3) bulk density forms. The microstructure shows (a) mesopores that span the distance between chains of interconnected particles, (b) micropores sandwiched between particles, (c) individual particles (~12 nm diameter), (d) micropores within the particles, and (e) micropores between contiguous particles [2.57],

Fig. 2.13. Schematic diagram of the carbon aerogel microstructure. Each shaded circle represents an amorphous carbon particle. The microstructure is shown for (A) low (~0.1 g/cm3) and (B) high (~0.6 g/cm3) bulk density forms. The microstructure shows (a) mesopores that span the distance between chains of interconnected particles, (b) micropores sandwiched between particles, (c) individual particles (~12 nm diameter), (d) micropores within the particles, and (e) micropores between contiguous particles [2.57], somewhat different electronic properties from those of other disordered carbons.

2.13. Liquid Carbon

Liquid carbon refers to the liquid phase of carbon resulting from the melting of pure carbon in a solid phase (graphite, diamond, or materials related to these pure carbon solids via disorder). Referring to the phase diagram for carbon (Fig. 2.1), we see that liquid carbon is stable at atmospheric pressure only at very high temperatures (the melting point of graphite Tm ~4450 K) [2.2], Since carbon has the highest melting point of any elemental solid, to avoid contamination of the melt, the crucible in which the carbon is melted must itself be made of carbon, and sufficient heat must be focused on the sample volume to produce the necessary temperature rise to achieve melting [2.7,97]. Liquid carbon has been produced in the laboratory by the laser melting of graphite, exploiting the poor interplanar thermal conductivity of the graphite [2.98], and by resistive heating [2.99], the technique used to establish the metallic nature of liquid carbon.

Although diamond and graphite may have different melting temperatures, it is believed that the same liquid carbon is obtained upon melting either solid phase. It is believed that liquid carbon is a monatomic form of carbon in contrast to a liquid crystal phase. It is also believed that the solidification of the melt under nonequilibrium conditions may yield some novel forms of carbon upon crystallization, as discussed above (see §2.9). Since the vaporization temperature for carbon (~4700 K) is only slightly higher than the melting point (~4450 K), the vapor pressure over liquid carbon is high. The high vapor pressure and the large carbon-carbon bonding energy make it energetically favorable for carbon clusters rather than independent atoms to be emitted from a molten carbon surface [2.6,100]. Energetic considerations suggest that some of the species emitted from a molten carbon surface have masses comparable to those of fullerenes [2.97]. The emission of fullerenes from liquid carbon is consistent with the graphite laser ablation studies of Kroto, Smalley, and co-workers [2.101].

In considering the melting of fullerenes, several types of phase transitions must be taken into account. First the melting of the solid fullerene lattice into a liquid phase of freely moving fullerene molecules would be expected to occur, provided that the fullerene molecules do not evaporate into the gas phase or disintegrate before reaching this melting point. Even if a fullerene liquid were stable, it is unlikely that these molecules would be stable up to the temperature where finally the total dissociation of the fullerene occurs and liquid carbon forms (4450 K).

2.14. Graphite Intercalation Compounds

Because of the weak van der Waals interlayer forces associated with the sp2 bonding in graphite, graphite intercalation compounds (GICs) may be formed by the insertion of layers of guest species between the layers of the graphite host material [2.102,103], as shown schematically in Fig. 2.14. The guest species may be either atomic or molecular. In diamond, on the other hand, the isotropic and very strong sp3 bonding (see Fig. 2.3) does not permit insertion of layers of guest species and therefore does not support intercalation. In the so-called donor GICs, electrons are transferred from the donor intercalate species (such as a layer of the alkali metal potassium) into the graphite layers, thereby raising the Fermi level EF in the graphitic electronic states, and increasing the mobile electron concentration by two or three orders of magnitude, while leaving the intercalate layer positively charged with low mobility carriers. Conversely, for acceptor GICs, electrons are transferred to the intercalate species (which is usually molecular) from the graphite layers, thereby lowering the Fermi level EF in the graphitic electronic states and creating an equal number of positively charged hole states in the graphitic 7r-band. Thus, electrical conduction in GICs (whether they are donors or acceptors) occurs predominantly in the graphene layers and as a result of the charge transfer between the intercalate and host layers. The electrical conductivity between adjacent graphene layers is very poor (especially in the acceptor compounds, where

Fig. 2.14. Schematic model for a graphite intercalation compound showing the stacking of graphite layers (networks of hexagons on a sheet) and of intercalate (e.g., potassium) layers (networks of large hollow balls). For this stage 1 compound, each carbon layer is separated by an intercalate layer [2.104],

Fig. 2.14. Schematic model for a graphite intercalation compound showing the stacking of graphite layers (networks of hexagons on a sheet) and of intercalate (e.g., potassium) layers (networks of large hollow balls). For this stage 1 compound, each carbon layer is separated by an intercalate layer [2.104],

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