C60 Based Materials

Encyclopedia of Nanoscience and Nanotechnology www.aspbs.com/enn

C60-Based Materials

J. G. Hou, A. D. Zhao, Tian Huang, Shan Lu

University of Science and Technology of China, Hefei, Anhui, People’s Republic of China

CONTENTS as high temperature superconductivity in alkali metal intercalated C compounds, ultrahigh hardness even exceeding 1. Introduction 60 diamand in three-dimensional (3D) polymerized C60, and 2. C60 Molecule high temperature organic ferromagnetism in 2D rhombohedral polymerized C . 3.C Crystal 60 60 In this chapter, we summarize the structure and prop- 4. C -Based Materials 60 erties of the single C60 molecule and C60 based materials, 5. Low-Dimensional Structures including metal-intercalated, polymerized, doped, compos- Appendix A ite, and other derivative compounds. Moreover, recent progress in the search for some novel low-dimensional C60 Appendix B derivative structures, such as heterofullerenes, endohedral

Glossary fullerenes, exohedral fullerene complexes, C60 in carbon nanotubes, and (C clusters, is also summarized. References 60 n

2. C MOLECULE 1. INTRODUCTION 60 2.1. Synthesis Since the discovery of Buckminsterfullerene C60 by Kroto et al. [1] in 1985and the discovery of large quantity synthesis Fullerenes can be extracted from the soot made by either by Krätschmer et al. [2] in 1990, this molecular allotrope of combustion [4–7] or pyrolysis of aromatic hydrocarbons carbon has attracted intense interest because of its unique [8–13] or by an arc-discharge process [1]; the latter is now physical and chemical properties. Varied novel materials the most commonly adopted and convenient method. It is based on C60 have been synthesized successfully showing usually achieved by heating resistively and evaporating car- fantastic properties. bon (usually graphite) electrodes with a small gap con-

C60 is a beautiful spherical hollow molecule with a diam- trolled as a constant in a helium or an argon atmosphere by eter of ∼1 nm possessing the highest degree of symmetry passing a high electric arc-discharge current between them of all known molecules. Remarkable potential applications (see Fig. 1). For the carbon arc-discharge method, the best in future nanoscale molecular electronic devices were pro- inert gas atmosphere is high-purity helium with preferred posed [3] for C60 molecules based on their fantastic prop- quenching-gas pressure in the range 100–200 Torr. Rods of erties and structural and chemical stabilities. Moreover, the smaller diameter of about 5mm are most suitable for cur- molecule shows a strong ability to form derivative structures, rents of 100 ampere; larger reactor volumes and high purity such as substituted heterofullerenes, encapsulated endohe- rods give higher yields and lower impurity content soot. drals fullerenes, metal-adsorbed exohedral fullerenes, and Since the fullerene containing soot is better able to diffuse so on. These novel structures broaden the ﬁeld of nano- away from the hot discharging zone and the intense ultra- structured carbon materials and stimulated the research on violet (UV) light of the arc, it is better that the inert gas fullerene-based nanotechnology. is ﬂowed through the arc zone. Either ac or dc discharge

Crystalline C60, as a new third form of crystalline carbon, may be available and the latter results in consumption of the along with diamond and graphite, has also exhibited many anode only which gives facilities for the use of anode rod interesting properties. Solid C60 is a typical molecular crys- autoloaders and continuous operation. The common yield tal, it can be intercalated by metal atoms and molecules, of fullerenes in soot through this method is about 10%, polymerized, or composited to form complex solid-state of which the yields of C60 and higher fullerenes (mainly C70) structures. Many novel properties have been discovered such are about 75and 25%,respectively.

ISBN: 1-58883-057-8/$35.00 Encyclopedia of Nanoscience and Nanotechnology Copyright © 2004 by American Scientiﬁc Publishers Edited by H. S. Nalwa All rights of reproduction in any form reserved. Volume 1: Pages (409–474) 410 C60-Based Materials

Figure 2. (a) Schematic 3D structural diagram for a C60 molecule. (b) Scanning tunneling microscopy images of a C molecular array Figure 1. Schematic view of the generation process of fullerenes. 60 which shows clearly the cage structure and double and single bonds. Inset is a theoretical simulation image. Adapted with permission During the fullerene formation process, insoluble nano- from [20], J. G. Hou et al. Nature 409, 304 (2001). © 2001, Macmillan scale carbon soot is formed together with soluble fullerenes Magazines Ltd. and other soluble impurity molecules. Extraction can now most conveniently be performed with chloroform or toluene. about 7.10 Å [23], or considering the thickness of the elec- The latter is more rapid but risks reaction brought about tron cloud shell the outer and inner diameters are approxi- by the toluene (or xylene, mesitylene, etc.) solvent due to mately 10 and 4 Å, respectively. their susceptibility to electrophilic substantial reaction and The point group of C60 is icosahedral Ih which com- degradation. The efficiency of this solvent method for the prises 120 symmetry operations consist of identity operation, extraction is tied to the solubility of the fullerene molecules 12 fivefold axes through the centers of the 12 pentagons, in solvents. 20 threefold axes through the centers of the 20 pentagons, Liquid column chromatography is the main technique and 30 twofold axes through the centers of the 30 edges used for fullerene purification. Here purification means the joining 2 hexagons combined with their inversion operations. separation of the fullerenes to distinguish C ,C , etc. Ear- 60 70 Thus the C60 molecule has the highest degree of symmetry lier experiments used alumina [14] or mixtures of alumina/ of any known molecule. charcoal with toluene/hexane elution [15, 16]. The simpler The 2D representation of the 3D structure of C60 is shown and less expensive method employs Norit Elorit carbon in Figure 3 [24]. It is created by shrinking the polygons of granules as the stationary phase with toluene elution for C60 the nearest face and expanding those of the far face to fit all and following 1,2-dichlorobenzene for C70, in this way C60 60 carbon atoms within one plane. Obviously the Schlegel can be obtained at a fairly high rate of 10 gram per hour diagrams for C60 may have either a pentagon or hexagon at [17]. It is also necessary to wash the samples after purifi- the center, and a pentagon in Figure 3. cation with acetone to remove traces of hydrocarbons and other impurities.

A recent experiment showed that C60 can be synthesized in 12 steps from commercially available starting materials by rational chemical methods [18]. A molecular polycyclic aromatic precursor bearing chlorine substituents at key posi-

tions forms C60 when subjected to ﬂash vacuum pyrolysis at 1100 C and no other fullerenes are formed as by-products.

2.2. Structure

For C60 there are 1812 possible structures [19], but the most stable isomer and the only one in which all the pentagons are nonadjacent is depicted as a truncated icosahedron cage structure with 90 edges, 60 vertices, and 32 surfaces, 12 of which are pentagonal and 20 are hexagonal (see Fig. 2 [20]). This building principle obeys Euler’s theorem predicting that exactly 12 pentagons and an arbitrary number n of hexagons are required for the closure of a carbon closed cage. Other-

wise C60 is the most stable fullerene because it is the smallest possible to obey the isolated pentagon rule (IPR) [21, 22] Figure 3. 2D Schlegel diagram for a C60 molecule. Adapted with per- which predicts fullerene structures with all the pentagons mission from [24], A. Hirsch, in “Fullerenes and Related Structures, isolated by hexagons to be stabilized against structures with Topics in Current Chemistry” (A. Hirsch, Ed.), Vol. 199, p. 13. Springer- adjacent pentagons. The mean diameter of a C60 molecule is Verlag, Berlin/Heidelberg, (1999). © 1999, Springer-Verlag. C60-Based Materials 411

2.3. Electronic Structure expected. But in the case of neutral C60 with the symmetry lowered from ideal spherical symmetry to icosahedral A neutral C molecule has 240 valence electrons; 180 are 60 symmetry, the l = 5state split into the ( h + t + t irre- involved in -bonding energy levels lying well below the u 1u 2u ducible representations and the fivefold-degenerate h level Fermi level. They brace and stabilize the cage structure. The u (the lowest energy level) is completely filled by the remain- remaining 60 electrons are involved in -bonds, contributing ing 10 electrons (see Fig. 4). This level forms the highest to the conduction. occupied molecular orbital (HOMO) in C . The threefold- Since C forms a near-sphere cage structure, the devia- 60 60 degenerate t level of l = 5state forms the lowest unoccu- tion from planarity leads to an admixture of s orbitals char- 1u pied molecular orbital (LUMO) and this low-lying LUMO acter into the pz orbitals, where z is perpendicular to the suggests that the C60 is a fairly electronegative molecule. (local) surface of the buckyball sphere. An average bond The HOMO–LUMO gap is calculated to be about 1.7 eV. hybridization of sp2 278 with a fractional s (about 9%) character into the pz orbitals was estimated [25–29], compared to 2 graphite with pure bond hybridization of sp . Geometrically 2.4. Properties of Single C60 Molecule the p orbitals extend further outside the cage than inside z 2.4.1. Main Description the cage. The bonds at the junctions of two hexagons ([6,6] bonds) The main properties of C60 molecule are summarized in (∼1.40 Å) are somewhat shorter than the bonds at the junc- Table 1 [23, 30–39]. The comparison of properties of C60 tions of a hexagon and a pentagon ([5,6] bonds) (∼1.45Å); with other fullerenes (from C20,C36 to C106 is listed in thus the [6,6] bonds are usually considered to be double Appendix A [23, 36, 40–55]. bonds and the [5,6] single. The shortening of bonds is caused by the partial localization of the -orbitals into localized 2.4.2. Electronic Transport Properties bonds and thus is directly related to the symmetry of C . 60 Electronic transport properties of individual C60 molecules This ununiformity of bond lengths has been demonstrated have been investigated using a scanning tunneling micro- by a series of theoretical [30, 31] and experimental investi- scope (STM) which enables controlled two-terminal mea- gations [32–34]. As a consequence, the double bonds in C60 surements or a three-terminal transistor configuration which only lie at the junctions of the hexagons ([6,6] double bonds) enables gate-voltage controlled current amplifications. and do not lie in the pentagonal rings. The resistance of a C60 molecule was determined by the Due to the near-spherical shape of the C molecules, the 60 study of electrical contact with an individual C60 introduced fullerene electronic eigenstates can be considerd by spher- between a STM tip and a clean Au(110)-(1 × 2) surface ical harmonics and classified by their angular momentum at 300 K in ultrahigh vacuum [56]. It was revealed that at quantum numbers l (see Fig. 4). Due to the Pauli exclusive low applied bias voltages of ±200 mV this system exhib- principle, 50 -electrons fully occupy the angular momen- ited linear current–voltage (I–V ) characteristics at all fixed tum states up through l = 4, leaving 10 -electrons in the tip displacement, indicating that the system behaves simi- l = 5state which can accommodate 22 electrons in full larly to a metal–vacuum–metal tunnel junction at low bias spherical symmetry, assuming that all the l = 5states are voltage within the C60 HOMO–LUMO gap. In this sense, 10+ filled before any l = 6 level becomes occupied. For C60 the linearity allows us to define the intrinsic electrical resis- with l = 4 filled, no significant bond length alternation is tance of an individual C60 molecule. It was observed in

Table 1. Properties of C60 molecules.

Property Quantity Ref.

IPR isomers 1

Symmetry (point group) Ih Double bond length ∼1.40 Å [30–34] Single bond length ∼1.45Å [30–34] Average C–C distance 1.44 Å [33] Diameter 7.10 Å (mean) [23] Volume per molecule 1 87 × 10−22/cm3 (abc) Number of distinct C sites 1 Number of distinct 2 C–C bonds Figure 4. (a) Schematic diagram of the electronic structure for the 60 Binding energy per atom 7.40 eV [35] -electrons in C by Hückel theory calculation of the molecular energy 60 Electron afﬁnity 2 65 ± 0 05eV [36] spectrum of neutral C . The number l is the orbital angular quantum 60 Cohesive energy 1.4 eV/atom [37] of the spherical harmonic from which a molecular orbital is derived. per C atom (b) Density of states (DOS) for the isolated C molecule calculated 60 Ionization potential 7 95 ± 0 02 eV [38] using the discrete variational local density approximation method. Ver- HOMO–LUMO gap 1.7 eV (Dmol3 cal.) tical lines denote energy levels of the molecule. The DOS is obtained Heat of formation (41 8 ± 0 3 kJ per C atom) [39] by broadening the discrete levels with a Lorentz function for better (at 298 k) comparison with experimental data. 412 C60-Based Materials

the current–distance (I–s) characteristics that the tunneling 2.4.3. Scanning Tunneling Spectroscopy current increases approximately exponentially with tip dis- Scanning Tunneling Spectroscopy of Isolated C60 placement in the tunnel regime, but this behavior changes Molecule The scanning tunneling microscope is a power- signiﬁcantly as contact is established. A theoretical calcu- ful tool for measuring the local density states of surfaces and lation using the elastic scattering quantum chemistry tech- molecules. STS of an isolated C60 molecule can be obtained nique conﬁgured for STM (STM-ESQC) [57] considering in a DBTJ system (see Fig. 5a) where the individual C60 the full atomic structure and valence orbitals of the tip, the molecule is coupled via two tunnel junctions to the metal C60 molecule, and the Au(110) surface agreed very well with substrate and an STM tip of vacuum and insulating layer, the experimental I–s curve. The deformation of C60 was respectively, in order to eliminate the interaction between also included in STM-ESQC using the molecular mechanics the metal substrate and C60 molecule. Figure 5shows a she- (MM2) routine with a standard sp2 carbon parametrization matic view and equivalent circuit of the experimental setup

[58], and the C60 conformation was optimized for each tip and a typical spectroscopy of C60 in this system. displacement s. The current I through the molecule was Zeng et al. [62] measured the STS with such a system then calculated for each conformation. The point of electri- at a low temperature of 78 K by employing a hexanethiol cal contact was found to be s = 12 3 Å, where the van der self-assembled monolayer as the insulating barrier between Waals expansion induced by tip attraction is compensated by C60 and a gold substrate. Their results exhibited a noticeably larger HOMO–LUMO gap of ∼2.8 eV (see Fig. 5), which tip compression, and the C60 molecule may be considered approximately as its original shape. An apparent electrical is about 1 eV larger than the intrinsic HOMO–LUMO gap of ∼1.7 eV. Because the size of a C molecule is about 7 Å, resistance of 54.80 M for the total junction with C60 was 60 determined at this point. In the Landauer formalism [59] of much smaller than other metal or semiconductor quantum 2 −1 dots so far, the charging energy E of such a nanojunction, T = h/2e R , this value corresponds to the C60 electronic C transparence (ease of transmission) of T = 2 3 × 10−4. about 1 eV, is significant enough to be comparable with the molecular HOMO–LUMO bandgap (E of a neutral This experiment of “squeezing” a C60 molecule by apply- g ing a small force in the nanonewton range with a metallic C60 molecule. So they attributed the larger gap width they STM tip also results in a shift of the molecular orbital levels observed to the sum of Eg and EC . It was also noted that [56]. The mechanically induced shift provides a means to their differential tunneling spectra showed clearly fine peaks at the position of HOMO and LUMO energy regions. The modulate tunnelling through a single C60 molecule, even in a nonresonant tunnelling regime, and to change its resistance three peaks in the negative bias region and five peaks in the up to a limiting value approaching the quantum of resis- negative bias region were well attributed to the degenerate splitting of threefold degenerated LUMO (t ) and fivefold tance, h/2e2 (∼12.9 k [56]. The phenomenon, mechan- 1u degenerate HOMO (h level. The reason for the orbital ically modulated virtual-resonant tunnelling, has also been 1u degeneracy was considered to be the strong local electrical used to design an single-molecule electromechanical ampli- field and the Jahn–Teller effect. fier, by making use of the ability to mechanically reduce Porath et al. [61] performed similar experiments at a low molecular level degeneracy [60]. temperature of 4.2 K by using a polymethyl-methacrylate Electronic transport properties of C molecules have also 60 layer (less than 40 Å thick, determined by X-ray measure- been studied in some other systems: The scanning tunneling ments) as the insulating barrier. The tunneling current– spectroscopy (STS) investigation of an isolated C molecule 60 voltage spectra they observed also showed both Comlomb considered as a quantum dot in a double barrier tunnel junc- blockade and Coulomb staircase behavior and rich fine tion (DBTJ) configuration [61] was carried out showing clear structures resulting from the discrete levels of a single C60 discrete molecular-level spectrum and obvious interplay with molecule and the splitting of the degenerate energy levels. single-electron charging effects. But the HOMO–LUMO gap in their specra observed was A novel negative differential resistance (NDR) molecu- about 0.8 eV (generally less than 1.5eV), which is much less lar device is realized involving two C molecules; one is 60 than that of a free neutral C60 molecule. They attributed the adsorbed on a STM tip and the other is on the surface of the hexanethiol self-assembled monolayer [62]. It was demonstrated that it is the narrow local density of states features near the Fermi energy of the C60 molecules that lead to the obvious stable and reproducible NDR effect.

In a single-C60 nanomechanical transistor configuration based on an individual C60 molecule connected to gold electrodes [63], the transport measurements provided obvious evidence for a coupling between the center-of-mass motion of the C60 molecules and a single-electron hopping— a novel conduction mechanism. The coupling is manifest as quantized nanomechanical oscillations of the C60 molecule against the gold surface with a frequency of about 1.2 THz which agreed well with a simple theoretical estimate based Figure 5. Scanning tunneling spectroscopy of a single C60 molecule in on van der Waals and electrostatic interactions between C60 a double barrier tunneling junction system. Dashed line is the dI–dV molecules and gold electrodes [63]. curve; solid line is the I–V characteristic curve. C60-Based Materials 413 origin of the smaller gap mainly to the level space between 2.4.4. 13C Nuclear Magnetic − + LUMO(C60 and HOMO(C60. Resonance Spectroscopy 13 Inelastic Electron Tunneling Spectroscopy of Single By using room temperature C nuclear magnetic resonance (NMR) spectroscopy, Taylor et al. [14] and several research C60 Molecule Inelastic electron tunneling spectroscopy (IETS) is a powerful technique to obtain average vibra- groups [74–76] obtained the first structure data for C60 tional information on condensed molecule species [64]. molecules in solution. In the spectrum, there is only one Combined IETS–STM can provide vibrational information peak, showing extremely simple character, at a chemical resolved on single molecules [65–72]. It has been demon- shift of 143.2 ppm relative to tetramethyl silane (the standard reference molecule for 13C NMR spectroscopy). This strated that when C60 is adsorbed on a surface, the structure of the free molecule remains fairly unaltered [73]. Pascual only-one-peak character confirms that each carbon atom in the C molecule is equivalent in the solution environment. et al. [64] extend the inelastic STS (ISTS) studies to single 60 In comparison with C60, the C70 molecule has five inequiv- C60 molecules adsorbed on Ag(110) surface; they observed peaks at ±54 mV in the d2I/d2V curves in ISTS spectras alent carbon sites out of total atoms in geometry, corresponding to a richer NMR spectrum character of five peaks on those C60 molecules which oriented along one of their symmetry axes upon adsorption (see Fig. 6). In strong coin- at 130.9, 145.4, 147.4, 148.1, and 150.7 ppm in a ratio of 13 cidence, those fullerenes maintain a resonance structure at 10:20:10:20:10. Figure 7 shows typical C NMR spectra for the C and C /C mixture in benzene solution showing the Fermi level that resembles the first unoccupied molec- 60 70 60 ular orbital distribution of a free molecule. The enhanced clear peak features [74]. signal was attributed to the excitation of a fullerene-cage vibrational mode by inelastic tunneling electrons. The vibra- 2.4.5. Optical Properties −1 tion was assigned to the Hg2 mode (431 cm , a fivefold In gas phase or in organic solutions, optically excited denegerated mode of a free C60 molecule corresponding to a fullerene molecules are influenced relatively weakly by their “gerade” breathing of the molecular cage with larger radial environments, thus the photophysical properties can be con- component along the C5 symmetry axis. Only in those cases sidered as those for near free molecules. The molecular where some molecular symmetry survives upon adsorption energy level and photophysical behavior of electronically does some mode degeneracy remain, leading to a detectable energized states for an individual C60 molecule can be contribution in the inelastic signal; for molecules in a non- well described by using a Jablonski diagram, as shown in symmetric orientation, degeneracy splitting, and subsequent Figure 8. In this type of diagram, photoexcited electronic mode mixing, may be so extensive that the observation of states of molecules include spin triplets S = 1 and spin clear vibrational features in the ISTS spectra is suppressed. singlets S = 0. The energy state definitions and transitions They concluded that the nature of the electronic molecu- between these states are interpreted in Table 2. lar resonances around the Fermi level E , which determines F The low-lying electronic transitions in C60 are only weakly the vibrational mode primarily, and the existence of a sur- allowed because of the high degree of symmetry in the viving symmetry on the adsorbed species, which determines the magnitude, were the two principal detection selection rules.

Figure 6. Comparison of ISTS spectra measured consecutively on two neighboring C60 molecules. The dashed plot corresponds to the spec- 13 trum acquired on the bare silver surface. Each spectrum is the aver- Figure 7. C NMR spectra for C60,C70, and C70/C60 mixture in ben- age of six bias voltage scans (25sec/scan). In (a), the peak at 54mV zene solution at 298 K. (a) C60 sample; (b) C60/C70 mixture sample; (−54 mV) represents a normalized change in conductance of 9% (8%). (c) C70 sample, peaks labeled a, b, c, d, and e are assigned to C70 and

(I = 1 6 nA, Vs = 0 5V, Vac = 5mVrmsatfac = 341 Hz.) Adapted correspond to the distinct ﬁve carbon atoms in a C70 molecule in the with permission from [64], J. I. Pascual et al., J. Chem. Phys. 117, 9531 right panel. Adapted with permission from [14], R. Taylor et al., Chem. (2002). © 2002, American Institute of Physics. Commun. 1423 (1990). © 1990, Royal Society of Chemistry. 414 C60-Based Materials

phosphorescence reﬂects a low radiative rate for T1 → S0 emission, which is both spin and orbitally forbidden, plus

comparatively rapid T1 → S0 nonradiative decay of intersystem crossing; see Figure 8. Previous results for the triplet T1 lifetime of C60 in room-temperature solutions range from 37 to 285 s and even longer [77, 96, 98, 99, 101–105]. Recently Weisman [106] concluded that the wide discrepancies among these values likely reﬂect the presence of bimolecular decay channels such as self-quenching or unrecognized triplet– triplet annihilation, the effects of impurities in solution, or

uncertainties in the kinetic data. He obtained an intrinsic T1 triplet lifetime of 143 s by eliminating the self-quenching component of this decay of 0.21%/ M. Fullerenes and their derivatives were found to be excellent optical limiters in room-temperature solution [107–111].

The first report of the optical limiting (OL) of C60 was that C60 in toluene possesses the strongest OL response toward a laser at 532 nm. Optical power limiting occurs when the optical transmission of a material decreases with increas- Figure 8. Diagram of electronic energy levels of C60 molecule. ing laser fluence [112] which is now attributed to strong triplet absorption [112–115]. C is an excellent broadband closed-shell electronic configuration. The absorption band 60 nonlinear absorber for potential optical limiting and optical of C in the visible is very weak, with the molar absorptiv- 60 switching applications [108, 112, 116–119], because of higher ity at the band maximum of only ∼950 M−1 cm−1 [14, 74, triplet–triplet transient absorption cross sections than the 77, 78]. Only a small fraction of the broad visible absorption ground-state absorption cross sections [101, 108, 120]. How- band in the 430–670 nm region is due to the contribution of ever, a recent study suggested that in addition to the strongly the transition to the lowest excited singlet state S [79]. 1 absorptive excited singlet and triplet state, other transient With extensive experimental investigations [79–95], it was species that are most likely associated with photoexcited well known that both C and C are only weakly fluores- 60 70 state bimolecular processes may also be responsible for the cent from the lowest singlet S to the ground state, with C 1 70 observed strong optical limiting responses of fullerene in having a slightly higher fluorescence quantum yield. Due to solution [119, 121]. There have been several mechanisms the weak interaction with each other, fluorescence lifetimes suggested to account for the optical limiting behavior of C , and fluorescence quantum yields of the fullerene molecules 60 including reverse saturable absorption (RSA) [107], nonlin- in solution under ambient conditions are essentially solvent ear scattering [122], thermal blooming [108, 123], and mul- independent. tiphonon absorption [108]. RSA was proved by transient In fact, upon photoexcitation, the excited singlet state S 1 absorption spectra to be the dominant mechanism, whereas decays are mainly dominated by nonradiative intersystem other processes become important at high input influences crossing to the excited triplet state T , with a very large quan- 1 [108, 122]. tum yield of nearly 100% [77, 96–99]. The extremely effi- Photoexcited fullerenes are also excellent electron accep- cient intersystem crossing produces a high population of the tors, exhibiting strong interactions with a variety of electron excited triplet state T . Phosphorescence emission from the 1 donors [89, 124, 125]. The unique properties of fullerenes T state to the ground state S is so weak that it could not be 1 0 with respect to photoinduced electron transfers include the detected initially even in a cryogenic sample [100]. The weak small solvent reorganization energy [126] and the ability of a single fullerene cage to accept multiple electrons [127].

Table 2. Energy states and transitions in a C60 molecule. Photochemical reactions of fullerenes through an electron transfer mechanism often yield products that are differ- Energy states ent from those expected on the basis of known reactions of typical aromatic systems [128, 129], and in these reac- S0 ground (singlet) state S (T ) ﬁrst excited singlet (triplet) state tions fullerenes often behave quite differently from polyaro- 1 1 matic compounds and other electron acceptors such as por- Sn (Tn) higher excited singlet (triplet) state phyrins. The recent development of cage functionalization Transitions or decays methods [118, 130–133] has made it possible to prepare redox active fullerene derivatives for fundamental studies Absorption including ground state absorption S0 → of photoinduced electron transfers and charge separations Sn and excited state absorption Tn →

Tm n m ≥ 1 and for potential technological applications such as solar Fluorescence S1 → S0 (usually) energy conservation. Fullerene molecules and their deriva- Phosphorescence T1 → S0 (usually) tives have also been used as charge generators in photocon- Internal conversion Sn → Sn−1 and Tn → Tn−1, radiationless tran- ductive polymer thin ﬁlms [134–136]. sitions The photophysical quantities for C molecules in solution Intersystem crossing S → T for n>0, or T → S for m>0, 60 n m m n are listed in Table 3, corresponding to the physical proper- (ISC) radiationless transitions ties illustrated in Figure 8. C60-Based Materials 415

Table 3. Photophysical quantities for C60 molecules in solution. Table 4. Room temperature solubility of fullerene C60.

Property Quantity Ref. Solvent Solubility (mg ml−1

S1 energy 2.0 eV [77] Nonaromatic hydrocarbons

T1 energy 1.62–1.69 eV [77, 137] Noncyclic: S2 energy 3.4 eV [120] n-pentane 0.005, 0.004 (303 K)

T2 energy 3.3 eV [120] n-hexane 0.043, 0.052, 0.040 (303 K) !T , ISC quantum yield (S1 → T1 0.88–0.98 [77, 96–99] octane 0.025(303 K) (near 100%) isooctane 0.026 (303 K) −4 !F , ﬂuorescence quantum yield 3 2 × 10 [79] n-decane 0.071, 0.070 (303 K) "F , singlet (S1) lifetime 1.2 ns [138, 111] dodecane 0.091 (303 K) (ﬂuorescence lifetime) tetradecane 0.126 (303 K) −4 !F , phosphorescence 8 5 × 10 [77] Cyclic and derivatives: quantum yield cyclopentane 0.002

"F , triplet (T1 lifetime 143 s [106] cyclohexane 0.036, 0.035, 0.051 (303 K) (phosphorescence lifetime) decalin (3:7 cis and trans mixture) 4.60 cis-decalin 2.20 trans-decalin 1.30 1,5,9-cyclododecatrien 7.14 2.4.6. Solubility Properties of C60 cyclopentyl bromide 0.41 cyclohexyl chloride 0.53 Solubility of C60 in Various Solvents The solubility of cyclohexyl bromide 2.20 C60 in various solvents has been measured extensively in the past 10 years [139–153]. These experimental studies were cyclohexyl iodide 8.06 mainly motivated to improve the efficiency of the separa- +−-trans-1,2-dibromocyclohexane 14.28 cyclohexane 1.21 tion process of fullerenes. Studying the organic solvents of 1-methyl-1-cyclohexane 1.03 C60 is important for the separation of fullerenes, investiga- methylcyclohexane 0.17 tion of their chemical properties, and the synthetic reaction 1,2-dimethylcyclohexane 0.13 to functionalize fullerene in organic solvents. Moreover, the (cis and trans mixture) globular molecule provides a near-ideal model for the the- ethylcyclohexane 0.25 oretical studies of solubility. Full coverage of the solubility Halogen-containing alkanes and alkynes: properties of C60 in various solvents from various literature dichloromethane 0.26, 0.23, 0.25(303 K) tetrachloromethane 0.32, 0.45 is given in Table 4. In general, C60 has poor solubility in most chloroform 0.16, 0.17, 0.25 common solvents. These results include: C60 is slightly soluble in alkanes with the solubility increasing with the number carbon tetrachloride 0.32, 0.45(303 K) of carbons; the solubility in halogen-containing alkanes is dichloroethane 0.36 generally higher than in alkanes and it is essentially insol- bromoform 5.64 iodomethane 0.13 uble in polar and H-bonding solvents such as alcohol and bromochloromethane 0.75 water; the solubility in aromatic solvents is generally higher bromoethane 0.07 than in other solvents, so increasing the size of the aromatic iodoethane 0.28 system (benzene to naphthalene) will increase the solubil- freon TF (dichlorodifluoroethane) 0.02 −1 ity. The highest solubilities of C60 of about 50 mg ml are 1,1,2-trichlorotrifluoroethane 0.01 found to be in naphthalene derivatives. 1,1,2,2-tetrachloroethane 5.30 In recent years, there have also been a number of the- 1,2-dichloroethane 0.08 oretical studies focused on the decision of the relationship 1,2-dichloromethane 0.50 between possible influential factors and solubility parame- 1,1,1-trichloroethane 0.15 ters [140, 143, 154–158]. 1-chloropropane 0.02 1-bromopropane 0.05 No single solvent parameter or property can uniformly 1-iodopropane 0.17 predict the solubility. Early studies indicated the compos- 2-chloropropane 0.01 ite picture of solvents with high solubility for C60: large 2-bromopropane 0.03 index of refraction n, dielectric constant # around 4, large 2-iodopropane 0.11 molecular volume, and Hildebrand solubility parameter $ 1,2-dichloropropane 0.10 around 19 MPa−1/2 [140, 143]. Recently, several theoreti- 1,3-dichloropropane 0.12 cal studies were performed in order to develop applicable +− 1,2-dibromopropane 0.35 and suitable influencing factor relationships. Marcus et al. 1,3-dibromopropane 0.40 [154, 155] analyzed a comprehensive set of solubility data 1,3-diiodopropane 2.77 of C in various solvents at 298 and 303 K by multivari- 1,2,3-trichloropropane 0.64 60 1,2,3-tribromopropane 8.31 ate stepwise linear regression applied as the linear sol- 1-chloro-2-methylpropane 0.03 vation energy relationships (LSER) approach. Considering 1-bromo-2-methylpropane 0.09 the formation of crystalline solvates in a few solvents, they 1-iodo-2-methylpropane 0.34 used the calculated “hypothetical solubility” of unsolvated continued C60 instead of the solubility of the solvate in the statisti- cal procedure. Their results showed that increasing molar 416 C60-Based Materials

Table 4. Continued Table 4. Continued

Solvent Solubility (mg ml−1 Solvent Solubility (mg ml−1

2-chloro-2-methylpropane 0.01 Polar solvents: 2-bromo-2-methylpropane 0.06 methanol 0.000, 0.000035 2-iodo-2-methylpropane 0.23 ethanol 0.001, 0.0008 1,2-dibromoethylene 1.84 1-propanol 0.0041 trichloroethylene 1.40 1-butanol 0.094 tetrachloroethylene 1.20 1-pentanol 0.030 1-chloro-2-methylpropane 0.21 1-hexanol 0.042 bromopropin 0.22 1-octanol 0.047 Aromatic hydrocarbons nitromethane 0.000 Benzene and derivatives: nitroethane 0.002 benzene 1.70, 1.50, 0.88, 0.89, acetone 0.001 1.44 (303 K) acetonitrile 0.000 acrylonitrile 0.0040 toluene 2.80, 2.90, 0.54 2.15 (303 K) n-butylamine 3.688 1,2-dimethylbenzene 8.70, 7.35, 9.30 monomethylglycol ether 0.032 1,3-dimethylbenzene 1.40, 2.83 N , N -dimethylformamide 0.027 1,4-dimethylbenzene 5.90, 3.14 dioxane 0.041 (303 K) 1,2,3-trimethylbenzene 4.70 Miscellaneous 1,2,4-trimethylbenzene 17.90 carbon disulfide (CS 7.90, 7.70, 5.16 (303 K) 1,3,5-trimethylbenzene 1.50, 1.70, 1.00 (303 K) 2 tetrahydrofuran 0.00, 0.06 1,2,3,4-tetramethylbenzene 5.80 thiophene 0.40, 0.24 1,2,3,5-tetramethylbenzene 20.80 tetrahydrothiophene 0.03, 0.11 ethylbenzene 2.60, 2.16 2-methylthiophene 6.80 n-propylbenzene 1.50 N -methyl-2-pyrrolidone 0.89 isopropylbenzene 1.20 pyridine 0.89, 0.30 n-butylbenzene 1.90 methithilol 1.5, 1.0 hexabutylbenzene 1.10 quinoline 7.20 tributylbenzene 0.90 Inorganic solvents tetrahydronaphthalene 16.00 water 1 3 × 10−11 fluorobenzene 0.59, 1.20 silicon (IV) chloride 0.09 chlorobenzene 7.00, 5.70 bromobenzene 3.30, 2.80 iodobenzene 2.10 1,2-dichlorobenzene 27.00, 24.60, 7.11 1,2-dibromobenzene 13.80 et al. [156] examined the solubility of C60 in 75organic 1,3-dichlorobenzene 2.40 solvents and succeeded in developing a solubility model 1,3-dibromobenzene 13.80 of quantitative structure–solubility relationships by using 1,2,4-trichlorobenzene 8.50, 10.40, 4.85 the quantitative structure–property relationships (QSPR) o-creosol 0.01 approach. They used topological indices and polarizability benzonitrile 0.41 parameters computed from refractive indexes to form the nitrobenzene 0.80 regression models. Kiss et al. [157] utilized a multiparame- methoxybenzene 5.60 ter artificial neural network (ANN) approach to model the benzaldehyde 0.42 solubility of C in 126 solvents. The trend of nonlinear fit of pentylisooctane 2.44 60 2-nitrotoluene 2.43 the ANN suggested the same results as in the LSER studies: 3-nitrotoluene 2.36 the solubility in a large number of solvents decreases with thiophenol 6.91 increasing molar volumes of the solvent and increases with benzylchloride 2.46 increasing polarizability parameters, saturated surface areas, benzylbromide 4.94 and average polarizability. ',','-trichlorotoluene 4.80 One of the most striking peculiarities of fullerenes in Naphthalene derivatives: solutions is the extraordinary nonmonotonic behavior of the 1-methylnaphthalene 33.00, 33.20 temperature dependence of the solubility of fullerene C . dimethylnaphthalene 36.00 60 Experimental results of temperature dependence of the sol- 1-phenylnaphthalene 50.00 1-chloronaphthalene 51.00 ubility of C60 in hexane, toluene, CS2 [139], and xylene 1-bromo-2-methylnaphthalene 34.80 [153] in the temperature range 200–400 K showed that, whereas the absolute values of the solubility of C60 for dif- continued ferent solvents differ over two orders of magnitude, the nonmonotonic behavior of the temperature dependence of the volume and solvent polarity (as measured by the Dimroth– solubility is almost independent of the type of solvent over

Reichardt “general polarity” parameter, ET [30, 158]) will a wide range of temperature variation. This dependence decrease the solubility of C60, but electron pair donation reaches its maximum magnitude near 280 K and notably ability and polarizability will enhance solubility. Natarajan decreases at further enhancement of temperature. It is of C60-Based Materials 417 interest to note that the nonmonotonic temperature dependence of solubility is inherent only to C60 and is not observed for other fullerenes, such as C70. The temperature dependences of the solubility of fullerene C70 in toluene, xylene, and CS2 [153] are monotonically rising, which is inherent to the majority of solvent–solute pairs. The experimentally found distinctions in the temperature dependence of solubility of different fullerenes may be explained by a cluster mechanism of solubility based on the possibility of formation in solution of clusters consisting of a number of fullerene molecules [159, 160]. This aggregation phenomenon inﬂu- ences the thermodynamic parameters of fullerenes in solutions as well as the solubility; thus the observed lowering in the solubility of C60 with rising temperature can be treated as a result of the thermal decomposition of Figure 9. (a) A model of C60{H2O}80 cluster, obtained from an icosahe- clusters. dral water cluster with a C60 molecule taking the place of its inner water dodecahedron. (b) C60 molecules in aqueous solution form colloidal

C60 in Water Fullerene is not soluble in water. But it can clusters based on 3.4-nm-sized icosahedral arrangements of 13 C60 be dispersed in water with the C60 concentration >2mM molecules, where the C60 molecules are separated by water molecules (1.4 mg/ml) and forms two types of fullerene–water col- [164]. The water network is formed by fully tessellated tetrahedral tri- cyclo decamer (H O) structures. loidal systems: molecular-colloidal C60 solution in water 2 10 (also called C60FWS; here FWS is the abbreviation of “fullerene–water system”) [161–164] and typical monodis- and spherelike H2O molecular shells around the fullerene’s perse C60 hydrosol (also called ChH) [165]. surface. C60FWS can be produced by transferring fullerene from organic solution into the aqueous phase with the help 2.5. C on Surfaces of ultrasonic treatment [162], without using any stabiliz- 60 ers and chemical modiﬁcation. It has been characterized 2.5.1. On Metal Surfaces as an aqueous molecular-colloidal solution having proper- C60 adsorpted on a noble-metal surface usually form strong ties of both true solutions and colloidal systems simulta- ionic bonding via charge transfer [170–179] from the metal neously, which consists of both single hydrated fullerene near-Fermi-level surface states to the fullerene 5t1u-derived molecules, C60@{H2O}n, and their fractal spherical clusters LUMO. Quantities of charge transfer can be estimated indi- [161–164]. Tests of C60FWS biological activity showed that rectly from the following experimental results: (i) the shift of these hydrated fullerenes appeared to be very promising in C60 vibrational energies in high-resolution electron-energy- the context of their biological and therapeutical applications loss spectroscopy (HREELS) (Au(110) [171], Ni(110) [180], [166]. ChH is another monodisperse aqueous colloidal sys- and Cu(111) [181]); (ii) the shift of carbon C1s core- tem with a particle size of 10 nm [165], it can be obtained by level absorption spectra using electron-energy-loss spec- oxidation of the C60 anion with oxygen in “tetrahydrofuran- troscopy (EELS) (Au(110) [171]); (iii) using near-edge water” solutions. Both C60FWS and ChH have the following x-ray-absorption spectroscopy (NEXAFS) (Cu(111) [179]) similar characteristics: (i) high concentration (1 mg/ml and compared to the known shift of alkalidoped compounds more); (ii) high stability, that is, preservation of their prop- [182]; (iv) the anglur dependence in angle-resolved valence- erties within a number of months even more under ambient band photoemission spectroscopy (PES) (Au(111) [183]); conditions; (iii) almost identical color of solutions (from pale and (v) direct comparison of relative photoemission inten- red to dark brown–red) that depends on C60 concentration; sities (Ag(111) [175] and Cu(111) [179]). But for Al [184, (iv) negative charge of colloidal particles; (v) preservation of 185] and Pt(111) [186] surfaces, experimental results by the same properties in the case of dilution or concentration NEXAFS, HREELS, or PES show no charge transfer evi- of both colloidal solutions; (vi) a similar ability to coagulate dence and suggest the interaction of a covalent bonding. under the inorganic cation inﬂuence [166, 167]. At the initial state the individual C60 molecules are read- In contrast to well-known reasons of stabilization of typ- ily mobile on most metal surfaces at room temperature, ical colloidal systems [168], the main mechanism of FWS stabilized at the step edges on Au(110) [172], Au(111) stabilization is the hydration of fullerene molecules with for- [187], Ag(111) [188], and Cu(111) [189], and form two- mation of the supramolecular complex of C60@{H2O}n type dimensional islands on Ag(110) [190]. [164] (see Fig. 9). The C @{H O} clusters are stabilized 60 2 n On many low-index metal surfaces, C60 forms√ commen- by the weak donor–acceptor interactions of unpaired elec- surate monolayers, such as Au(111) (23 × 3) [187, 191], trons of H2O oxygen atoms with fullerene molecule to form Ag(111) [188], Ag(110) [190], Cu(111)-c(1 × 1) [192], and -OH hydrogen bonds (such -OH hydrogen bonds Au (100)-c(5 × 20), with uniaxial stress along the 110 have been found to possess about half the binding energy of direction [193]. But C60 adsorption on Au(110) [172] and -OH O hydrogen bonds with, optimally, the -OH atoms Ni(110) [178] surfaces causes strong substrate reconstruc- centrally and vertically placed and the distances from the tions due to the strong interaction between the substrates oxygen atom to the aromatic centroid of about 3.1–3.7 Å and the C60 adsorbates. In the case of a high anisotropic [169]) and by the formation of the ordered, H-bounded, Au(110)-p(1 × 2) surface, C60 molecules adsorbed on this 418 C60-Based Materials

surface induce the Au surface atoms to form a (1 × 5) missing row reconstruction as a precursor for the p6 × 5 adsorbate structure and form a hexagonal close-packed corrugated layer [172]. Recent in-plane X-ray diffraction data suggested that a large fraction of Au surface atoms are displaced from their original positions producing micro- scopic pits to accommodate the C60 molecules [194]. In the case of Ni(110) surface, strong interaction between C60 and the surface causes a formation of added/missing Ni [001] rows which creates a corrugated structure resulting in for-

mation of (100) microfacets and maximizing the C60–Ni coordination [178]. It is suggested that the small separation

between the LUMO of C60 and Ni Fermi level located in the d band leads to a strong hybridization interaction (i.e., cova-

lent in character). Generally, the interaction between C60 and transition metal surfaces is stronger than that between

C60 and noble metal surfaces [170, 178]. Images of the intramolecular features of adsorbed C60 molecules which are bias dependent have been studied by

STM in C60/Cu(111)-c4 × 4 [195] and C60/Au(110) [196] systems. X-ray photoelectron diffraction has also been used

to determine the molecular orientation of adsorbed C60 molecules [196–200]. For C monolayers on several common metal sur- 60 √ √ faces, the adsorptive structures as well as their interac-√ Figure 10. A model of the 2 3 × 2 3R30 phase. The dashed tions√ are summarized in Table 5, and a typical 2 3 × hexagon encloses an overlayer-induced unit cell, while the solid hexagon 2 3R30 model of the adsorptive structure on M(111) encloses a unit cell of the M(111) surface (M = Au, Ag, Al). Adapted M = Au Ag Al surfaces is shown in Figure 10 [185]. with permission from [185], A. J. Maxwell et al., Phys. Rev. B 57, 7312 (1998). © 1998, American Physical Society. 2.5.2. On Semiconductor Surfaces Si(111)-(7 × 7) The interaction of adsorbed C60 molecules The initial state of adsorption of C60 on most common semi- with the Si surface is still not very clear. The Si(111)-(7 × 7) conductor surfaces shows individual isolated molecules, no surface is (weakly) metallic due to the surface dangling

island or speciﬁc interaction with step edge or defects on the bonds. Initially, it was suggested [205, 206] that the C60– surface. At room temperature the C60 molecules are gener- Si(111) interaction was ionic in character and similar to the ally immobile, showing strong interactions with the surface. C60–noble metal interactions. HREELS data supported this

Table 5. Summary of C60 adsorption structures and interactions for several common metal surfaces.

WF of clean WF with 1 ML

Surface Structure NDD (Å) Interaction CT (eV) DT (K) sample (eV) C60 (eV)

Au (111) 38 × 38 in√ phase’√ ∼10 [188] intermediate 0.8 [183] 770 [188] 5.3 [183] 4.7 [183] R14 2 3 × 2 3 chemisorption, ionic R30 [188, 191] Au (110) p6 × 5 [194, 172] 10.04 [201] 800 [202] 5.37 [185] 4 82 ± 0 05 reconstruction [185] √ √ Ag (111) 2 3 × 2 3 ∼10 [188] intermediate 0.75[175] 770 [188] R30 [188] chemisorption, ionic Ag (110) c4 × 4 [190] 10.07, 10.23 [190] 4.52 [203] 4.9 [203] Cu (111) c4 × 4 [192] 10.2 [192, 179] intermediate 1.6 [183] 4.94 [179] 4.86 [179] chemisorption, ionic 1.5–2.0 [179] 10 0 Cu (110) [178] 9.7–11.1 [178] 730 [178] 4.48 [178] 13 Ni (110) Reconstruction [178] 10.5, 10.0 [178] strong mainly covalent 2 ± 1 [180] 690 [204] 5.04 [203] 5.61 [203] √ √ Al (111) 6 × 6, 2 3 × 2 3 9.91, ∼10 04 [185] intermediate 730 [185] 4.25 [185] 5.15 [185] R30 [185] mainly covalent [185] Al (110) Psedo-c4 × 4 [185] 9.91, 11.44, 12.13 730 [185] 4.35 [185] 5.25 [185] [185] √ √ Pt (111) 13 × 13 10 0 ± 0 3 [186] mainly covalent [186] <0.8 [186] 560 [204] 5.7 [186] R±13 9 [186]

Note: NDD—nearest neighbor distance, WF—work function, CT—charge transfer, DT—decomposition temperature. C60-Based Materials 419 charge-transfer model well with quantitative estimates of the amount of electron transfer to the fullerene LUMO being as high as (3 ± 1) electrons per molecule at the coverage lower than 0.25monolayer (ML) and (0 7 ± 1) electrons at an average of about 1 ML [207]. But photoemission measurements [208–210] showed that the charge transfer to the fullerene LUMO is negligible, suggesting that the bonding is strongly covalent in character with a clear Si–C-related peak observed in both the C1s core level and valence-band photoemission spectra.

Individual isolated C60 molecule adsorption on Si(111)- (7 × 7) surface is strongly site dependent due to the different surface atom arrangements and dangling bond conﬁgura- tions caused by surface (7×7) reconstruction [205, 211, 212].

STM experiment reveals that about 80% C60 molecules are adsorbed on faulted half and unfaulted half sites (sites A and A), about 13% molecules on corner holes (site B), and only 7% on dimer lines (site C) [212]. Figure 11 gives high resolution STM images of single C60 molecules adsorbed on different surface sites showing clear and rich intramolecular features which agree well with the theoretical calculation using the local density approximation with C60SimHl cluster Figure 12. Curves A, B, and C are typical STS results corresponding to models [212]. C60 adsorbed at sites A, B, C (see Fig. x1b), respectively, on a Si(111)- A STS study was also carried out to probe the local (7×7) surface. Curve D is the average STS result on the bare Si surface. These STS results are represented in a graph of (dI/dV )/(I/V )vsV . electronic structure of individual C60 molecules on Si(111)- (7 × 7) surfaces (see Fig. 12). It was found that the HOMO– Adapted with permission from [213], H. Wang et al., Surf. Sci. 442, L1024 (1999). © 1999, Elsevier Science. LUMO gaps of C60 adsorbed at sites A, B, and C are 1.4, 0.8, and 1.3 eV, respectively, much smaller than that of free ¯ C60 molecules (∼1.8 eV). Thus it was conﬁrmed that the two domains exhibit interfacial structures with the C60 [110] ¯ mixing states of the C60 orbitals with the local density of directions ±11 off the [211] axis of a Si substrate [215, 216]. states (LDOS) of Si(111)-(7 × 7) are site dependent due Si(100)-(2 × 1) The interaction of C with Si(100)-(2 × 1) to the strong interaction between the C and the dangling 60 60 surfaces is suggested to be weak and van der Waals force like bonds of the surface and the different surface structures at [217, 218] without charge transfer [207]. Annealing the sur- different sites [213]. face at an elevated temperature will cause a rearrangement As the submonolayer coverage increases to about 1 ML, of surface Si atoms and change the interaction from physical the adsorbate–adsorbate interaction becomes large enough adsorption to a chemical one [90] and cause a hybridization that two kinds of local ordered structural domains regis- of C molecular orbitals with the surface states [219]. tered with those pinned on the substrate corner holes will 60 At room temperature, individual isolated adsorbed C form [214]. After the completion of monolayer C cover- 60 60 molecules on the Si(100)-(2 × 1) surface reside in the val- age, a R-19 double-domain structure forms in which the leys between the (2 ×1) reconstruction dimer rows randomly at the initial state [220]. For monolayers on Si(100)-(2 × 1)

surfaces, C60 form two short-range local order structures of c(4 × 4), and c(4 × 3), with nearest-neighbor distances of 10.9 and 9.6 Å [217], respectively.

In the case of chemical adsorption of C60 on Si(100)- (2 × 1) surfaces after annealing, the scanning tunneling

spectroscopy of individual C60 molecules on two different adsorption sites of the Si(100) surface was investigated [221, 222] (see Fig. 13). It was found that the HOMO–LUMO

gap of C60 molecules at the top of a single dimer (type A molecules) is about 1.8 eV, which is about the same as

that of free C60 molecules; the HOMO–LUMO gap of these molecules which is usually located at a missing dimer defect (type B molecules) is about 2.2 eV, which is close to the Figure 11. High resolution STM images of single C molecule 60 bandgap of SiC [223, 224]. STS results indicated that the recorded with different bias voltages on an faulted half site: (a1) V = s interaction between a type B molecule and the Si surface −1 8 V, (a2) V = 1 5V, (a3) V = 1 8 V, and (a4) V = 2 5V; and s s s is much stronger than that for a type A molecule; type B on corner holes: (b1) Vs =−1 8 V and (b2) Vs = 2 3 V. The tunneling current is 0.15nA for positive bias images and 0.1 nA for negative bias molecules form covalent bonds not only with second layer images. Adapted with permission from [212], J. G. Hou et al., Phys. Rev. Si atoms but also with the surrounding Si atoms in the ﬁrst Lett. 83, 3001 (1999). © 1999, American Physical Society. layer. 420 C60-Based Materials

growth is found to be unique and quite different from other

GaAs(001) phases: C60 ﬁlm takes its (110) crystalline axis which cannot be obtained on other substrate. The C60 overlayer is highly strained with a lattice expansion of ∼13% due

to a charge transfer from the As-dangling bonds to C60 and a site-speciﬁc C60–substrate interaction, and this structure is very stable at least up to 10 ML [233].

3. C60 CRYSTAL 3.1. Structure 3.1.1. Main Description

At room temperature (RT), solid C60 usually forms black or brownish powder or crystals. C60 single crystal forms a molecular crystal through weak van der Waals force C60– C60 bonding and adopts a closed–packed face-centered cubic (fcc) structure with a lattice constant of 14.17 Å [234, 235]

and a nearest neighbor C60–C60 distance of 10.02 Å [236]. It is chemically active but stable in air or at temperatures

well above RT. A pure C60 single crystal and a schematic view of the fcc structure is shown in Figure 14 [237]. The

more physical constant for crystalline C60 in the solid state is Figure 13. Curves A, B, and C are typical STS results corresponding to shown in Table 6. The comparison of properties of solid C60 with other fullerene solids (C ,C ,C ,C ,C is listed C60 adsorbed at sites A, B (see Fig. x2b), respectively, on an Si(100)- 36 70 76 78 84 (2 ×1) surface. Curve C is the average STS result on the bare Si surface. in Appendix B. These STS results are represented in a graph of (d ln I/d ln V )vsV . Adapted with permission from [221], X. Yao et al., Surf. Sci. 366, L743 3.1.2. Symmetry and Space Group (1996). © 1996, Elsevier Science. The symmetry of the space group for fcc C60 crystal at RT Ge(100)-(2 × 1) and Ge(111)-(2 × 8) The C60 monolayer has been identified by X-ray and neutron diffraction [235, adsopted on Ge(100)-(2 × 1) exhibits uniaxial incommen- 5 ¯ 238, 272, 273] to be Oh or Fm3m, using the Schoenflies and surate near-ordered lattice close to a structure of c(3 × 4) International Crystallographic nomenclature, respectively. in the direction of the dimer rows of the Ge(100)-(2 × 1) Solid state 13C NMR [32, 274–276], quasi-elastic neutron surface [218, 225–227] and preserves the Ge(100)-(2 × 1) scattering [277], and muon spin resonance ( SR) [278, 279] reconstruction [227]. studies showed that the C60 molecules in the crystal are In contrast to Ge(100) and Si(111), the Ge(111) surface rotating rapidly with three degrees of rotational freedom undergoes a structural rearrangement upon the adsorption and reorienting rapidly. The rotational reorientation time of C60 molecules [228]. The C60 monolayer on a Ge(111) at RT is about 9–12 ps which is 50% faster than molecu- system exhibits several ordered structures as a function of lar reorientation in solution (about 15.5 ps) [280], so that the annealing temperature [228]. Two stable surface phases, √ √ √ √ solid C60 may be considered as a nearly ideal close-packed (3 3 × 3 3)R30 and ( 13 × 13)R14, form upon anneal- configuration of spheres at room temperature. The rapid ing at 450–500 and above 500 C, respectively, as well as a reorienting and rotating mechanism is consistent with RT localized√ √ metastable 5 × 5phase by suddenly quenching the NMR results that all carbon atoms are equivalent although (3 3 × 3 3)R30 phase heated at 500 C. The interaction

of C60 with the Ge(111) surface is prevalently covalent and strong [229].

GaAs(110) and GaAs(001) The interaction of C60 molecules on the GaAs(110)-(1 × 1) surface is weak (domi-

nantly via van der Waals force), resulting in well-ordered C60 thin ﬁlm growth and rotating C60 molecules. The C60 layer on GaAs(110)-(1 × 1) is stressed due to the competition between the intermolecular interaction and the adsorbate– substrate interaction and the fact that the lattice parameter of the GaAs(110) substrate does not match with those of

C60 [230, 231]. The interaction of C60 molecules on the GaAs(001) sur- Figure 14. Pure C60 crystal (left) and schematic view of the fcc structure face is weak too and the C60 molecules are mobile at room of the solid (right). Adapted with permission from [110], L. Forró and temperature on the surface [232, 233]. Particularly in the L. Mihaly, Rep. Progr. Phys. 64, 649 (2001). © 2001, Institute of Physics case of C60 on the As-rich 2 × 4 substrate, the epitaxial Publishing. C60-Based Materials 421

Table 6. Physical constant for crystalline C60 in the solid state. scattering introduces additional interference which happens to extinguish just those fcc diffraction peaks [235]. Property Quantity For the RT fcc structure, subsequent studies in very close Fcc lattice constant 14.17 Å [234, 235] detail by X-ray [281, 282] and neutron diffraction [282–285] reveal that the molecular rotation is not, in fact, completely C60–C60 distance 10.02 Å [236] Tetrahedral interstitial site radius 1.12 Å[236] free, and provide evidence for pronounced local orienta- Octahedral interstitial site radius 2.07 Å [236] tional order with a correlation length ∼40 Å [282] which Mass density 1.72 g/cm3 [236] is four times the shortest intermolecular distance and con- Volume thermal-expansion 6 2 × 10−5/K [238] sists of several dozen molecules. The local order seems to coefﬁcient be driven by the same nearest neighbor interaction which Molecular density 1 44 × 1021 cm3 [236] leads to long range order below the phase transition tem- Compressibility −d ln V/dP 6 9 × 10−12 cm2/dyn [239] perature T01 but does not possess the symmetry of the low (compared with: graphite 2.7, temperature structure [282]. diamond 0.18) Bulk Modulus 6.8 GPa [240] ∼12 GPa [241] 3.2. Vibrational Modes Young’s modulus 15.9 GPa [242]

Phase transition temperature (T01 260–261 K [243] 3.2.1. Overview dT /dP ∼11–16K/kbar [244, 245]a 01 The vibrations of C molecules can be very well classed 60 Sublimation temperature ∼434 C [246] into two distinct groups: intermolecular and intramolecu- Heat of sublimation 38 kJ mol−1 [247] lar vibrations. For intermolecular molecular vibrations, C Cohesive energy ∼1 7 eV [248, 249] 60 molecules translate or rotate as nearly rigid entities, and the a The value varies with different pressure medium. highest measured intermolecular phonon frequency at room temperature is only ∼50cm−1, well below that of the lowest the point group I of C molecule is incompatible with any −1 h 60 intramolecular frequency, namely 272 cm for the Hg(1) crystal space group [14]. “squashing” mode [286, 287]. Figure 15shows an X-ray powder-diffraction pattern of The intramolecular vibrations of an isolated C60 molecule crystalline C60 compared to that of gold. In these two kinds involve changes of the bond distances or bond angles of the of materials, both the C molecules and the gold atoms 60 carbon atoms on the C60 molecule. Starting with 60 × 3 = present a close-packed fcc structure, but in the pattern of 180 total degrees for an isolated C60 molecule and subtract- C60 crystals the (200) and (400) diffraction peaks are missing the 6 degrees of freedom corresponding to 3 translations ing. The reason for the missing peaks can be attributed to and 3 rotations results in 174 vibrational degrees of freedom. the unique intrinsic properties of C60 molecules. Because However, there are only 46 distinct mode frequencies corre- C60 molecules are rotating rapidly at room temperature, all sponding to the 174 degrees of freedom due to the high sym- molecules in the fcc lattice can be well approximated by hol- metry of C60 (point group Ih. According to the symmetry low spherical shells ﬁlled by electrons. This “hollow-sphere” of the displacement patterns, the 46 distinct intramolecular vibrations can be classed into several groups as follows:

2Ag + 1Au + 3T1g + 4T1u + 4T2g + 5T2u + 6Gg + 6Gu

+ 8Hg + 7Hu

Here, the subscripts g (gerade or even) and u (ungerade or odd) refer to the symmetry of the eigenvector under the action of the inversion operator. The T -modes are triply, the G-modes are fourfold, and the H-modes are ﬁvefold degenerate. These degeneracies are a consequence of the

high symmetry of the C60 molecule and lead to the fact that the number of distinct modes (46) is much lower than 174 (the vibrational degrees of freedom). Group theory indicates that only 10 of the 46 distinct mode frequencies are Raman-

active (2Ag + 8Hg in ﬁrst order and 4 (T1u are infrared (IR)-active in ﬁrst order. These activated frequencies have been assigned with certainty. The remaining 32 modes

(1Au + 3T1g + 4T2g + 5T2u + 6Gg + 6Gu + 7Hu are optically inactive (“silent”) so that the identiﬁcation of these modes has been difﬁcult. Early calculations of the vibrational fre-

quencies of C60 used mainly classical force constant treat- Figure 15. X-ray powder-diffraction pattern of crystalline C60 compared to that of gold. In both kinds of materials, the molecules (i.e., ments [288–293] or relied on quantum chemistry calcula- atoms in case of gold) crystallize in a face-centered-cubic arrangement, tions [294–300]. However, they did not display the accuracy corresponding to a closest packing of spheres. Notice the absence of required to use them as a reliable guide for a clear iden- the (200) and (400) diffraction peaks in crystalline C60. tiﬁcation of the silent modes. Analysis of the second-order 422 C60-Based Materials

Raman and infrared spectra for C60 provides a good deter- The Raman and IR spectra of the pristine monomeric mination of assignments of the 32 silent mode frequencies fcc phase of C60 are shown in Figures 16 and 17, together [301–303]. The results of density functional theory (DFT) with the spectra of the orthorhombic (O, tetragonal (T,

calculations can provide a more reliable complete assign- and rhombohedral pressure-polymerized (R phase of C60 ment of the C60 modes [304–308]. Since Raman and infrared as well as the pressure-dimerized state for comparation spectra can only provide 14 active mode frequencies, a num- (for comprehensive knowledge on the polymerized C60, ber of other experimental techniques were developed to please refer to Section 4.2). Raman and IR spectra of solid probe silent modes, such as inelastic neutron scattering, C60 remain almost unchanged relative to the isolated C60 EELS, and single oxygen photoluminescence (PL). Table 7 molecule. Raman scattering spectra in Figure 16 for solid gives recommended values for the 46 distinct vibrational fre- C60 show 10 strong Raman lines, including two “breathing” quencies of an isolated C60 molecule and their assignments Ag-modes related to symmetric oscillations of the entire [309]. Several alternative assignments of vibrational frequen- molecule (496 cm−1 and of pentagons (1468 cm−1, and

cies in C60 can be found in the literature [301, 303, 310–315]. eight Hg-modes: 272, 432, 710, 772, 1100, 1248, 1422, and 1574 cm−1 [301, 318–323]. The ﬁrst-order infrared spec-

trum for C60 contains only four strong lines (see Fig. 17) 3.2.2. Raman and Infrared Spectra at 526, 576, 1184, and 1428 cm−1, each identiﬁed with an First-Order Active Raman and Infrared Modes Raman intramolecular T1u mode [303, 318, 324]. and IR spectra provide the most quantitative methods for Isotopic Effects in the Raman Spectra The natural determining the vibrational mode frequencies. Since C60 is very nearly an ideal molecular solid, so the Raman abundance of 13C isotopes is about 1.1%, with the result that approximately half of the molecules in ordinary C sam- and infrared spectra are sensitive for distinguishing C60 60 from higher-molecular-weight fullerenes with lower symme- ples produced from natural graphite contain one or more 13C isotopes. The isotopic distribution within the molecule try (e.g., C70 has D5h symmetry). Because most of the higher molecular weight fullerenes have lower symmetry as well as is random [325]. The truncated icosohedral structure of C60 12 more degrees of freedom, they have many more infrared- molecule belongs to icsohedral point group (Ih. The C60 and Raman-active modes [316, 317]. molecule shows the highest degree of symmetry and most stringent selection rules and there are 4 infrared-active and 10 Raman-active modes for the molecule. The remaining 32 Table 7. Recommended values for the 46 distinct normal mode fre- distinct modes, silent modes, are IR and Raman forbidden. quencies of an isolated C molecule [309]. 13 60 However, the addition of C isotopes lowers the symmetry of the molecule. Since the symmetry restrictions against ﬁrst- Even modes Odd modes order Raman or IR activity for the silent modes have been Frequency Activated Frequency Activated removed, it is expected that all of the previous silent modes (cm−1 Assignment modes (cm−1 Assignment modes become active. The lowering of the icosohedral symmetry by the presence of 13C isotope has been used to investigate 496 Ag (1) R 984 Au (1) 1470 A (2) R the silent modes in the isotopically pure molecule [310, 326– g 329]. 526 T1u (1) IR

568 T1g (1) 575 T1u (2) IR

831 T1g (2) 1182 T1u (3) IR

1289 T1g (3) 1429 T1u (4) IR

553 T2g (1) 342 T2u (1)

756 T2g (2) 753 T2u (2)

796 T2g (3) 973 T2u (3)

1345 T2g (4) 1205 T2u (4) 1525 T2u (5)

485 Gg (1) 567 Gg (2) 353 Gu (1) 736 Gg (3) 764 Gu (2)

1079 Gg (4) 776 Gu (3)

1310 Gg (5) 961 Gu (4) 1482 Gg (6) 1309 Gu (5) 1422 Gu (6)

272 Hg (1) R

433 Hg (2) R 403 Hu (1) 709 Hg (3) R 534 Hu (2) 772 Hg (4) R 668 Hu (3)

1099 Hg (5) R 743 Hu (4) 1252 H (6) R 1223 H (5) g u Figure 16. Raman spectra of the pristine C (a), polymerized DS (b), 1425 H (7) R 1344 H (6) 60 g u and O phase (c), excited by a 1064-nm line; those of the O (d), T (e), 1575 H (8) R 1567 H (7) g u and R (f) phases, excited by a 568.2-nm line. Adapted with permission Note: “R” represents Raman activated mode; “IR” represent infrared activated from [318], V. A. Davydov et al., Phys. Rev. B 61, 11936 (2000). © 2000, mode. American Physical Society. C60-Based Materials 423

Figure 18. Unpolarized Raman spectrum of a frozen solution of C60 in

CS2 at 30 K. The solid line is a 3-Lorentzian ﬁt to the experimental data. The highest frequency peak is assigned to the totally symmetric 12 pentagonal-pinch Ag mode in C60. The other two lines are assigned to the pentagonal-pinch mode in molecules containing one and two 13C isotopes, respectively. The inset shows the evolution of these peaks as the solution is heated. They are no longer resolved as the solution melts above 150 K. Adapted with permission from [330], S. Suha et al., Phys. Rev. Lett. 72, 3359 (1994). © 1994, American Physical Society.

with 13C. Comparison between the Raman and mass spectra shows that the two line shapes have a remarkable correlation [330]. The simple correlation was further confirmed by using a variety of first-principle and phenomenological dynamical models [332]. Within the framework of a first-principle cal-

culation, normal modes of vibration of the C60 isotopomers Figure 17. IR spectra of the pristine C60 (a), and polymerized O (c), 3 12 13 12 T (d), R (e) phases, and DS (b). Adapted with permission from [318], C1 C59 and C2 C58 have been calculated [333]. V. A. Davydov et al., Phys. Rev. B 61, 11936 (2000). © 2000, American Physical Society. 3.2.3. Inelastic Neutron Scattering Spectrum Inelastic neutron scattering (INS) offers the potential to

Besides the symmetry-lowering phenomena due to the detect all 46 intramolecular distinct modes of C60, includ- presence of 13C, the isotopes can also cause the shifts and ing those silent for first-order Raman and infrared spec- splittings of the active modes [330, 331]. This isotope effect troscopies, because the technique is sensitive to modes of on the mode frequencies is due to their dependence on all symmetries. The scattering intensity is proportional to (0/M1/2, where 0 and M are the force constants and atomic the mode degeneracy, which can be used to identify the 13 mass, respectively. Thus in a C60 molecule with n C iso- vibrations. Although, in principle, inelastic neutron scatter- topes, at first order, the vibrational frequency is expected ing allows one to unambiguously assign all the modes, it to be lowered proportional to the mass difference between has so far not been so ideal. In fact this technique has two 12 13 12 C60 and Cn C60−n, which can be simply written as main disadvantages, which make it difficult to individually assign all of the modes. First, the determination of eigenvec- n2 n = 1 − tors is traditionally based on single-crystal samples, but the 2 0 720 available C60 crystals were too small for inelastic neutron- scattering experiments. Second, the poor spectral resolution 12 where (0) is an eigenmode frequency of C60 and 720 a.u. is its atomic mass.

A high-resolution Raman spectrum for a C60 sample with the natural isotopic abundance is shown in Figure 18. To reduce the natural Raman linewidth, the C60 was dissolved in CS2 solution, and the spectrum was taken at 30 K. A fine structure of the high-energy pentagonal-pinch Ag(2) mode near 1470 cm−1 was observed. Three peaks in the fine struc- 12 13 12 ture could be resolved, associated with C60, C1 C59, and 13 12 C2 C58, respectively. The measured separation between the first and second peaks is 0 98 ± 0 01 cm−1, while for −1 the second and third peaks it is 1 02 ± 0 02 cm . Spectra Figure 19. Comparison of the mass spectra and the Raman spectra taken at higher temperatures are shown in the inset [330]. 13 for a C-enriched C60 sample. Adapted with permission from [330], Figure 19 shows Raman and mass spectra for a 13C enriched S. Suha et al., Phys. Rev. Lett. 72, 3359 (1994). © 1994, American Phys- C60 sample, which is produced by enriching the graphite nod ical Society. 424 C60-Based Materials

of INS makes it difﬁcult if not impossible to achieve assign- scattering is by short-range components of the electron–

ments of many of the C60 modes, especially those whose molecule interaction. frequencies are clustered within a narrow range. A num- A few experimental works have performed HREELS

ber of workers have measured the intramolecular mode fre- experiments on C60 films, using a variety of substrates quencies for C60 by INS, and the results are summarized in [343–345]. Depending on the substrate used, the films are Table 8. For more experimental and theoretical details and crystalline or disordered. This has a significant effect on the principal INS technique, one can read several review and the relative intensity of the different spectral features (see original research papers [285, 334–340]. Table 8).

3.2.4. High-Resolution Electron Energy 3.2.5. Optical Spectroscopy Loss Spectrum Some optical spectra, including singlet oxygen PL [346], fluorescence, and phosphorescence spectra, can also be pow- Infrared-active modes can be observed in HREELS mea- erful tools for the identification of intramolecular vibrational surements because the electric dipole associated with modes of C . The applicability of the photoluminescence infrared-active vibrations can scatter the incident mono- 60 technique to probe fundamental vibrational excitations of energetic electrons. An ultrahigh vacuum environment is C is based on the weak vibronic coupling of O molecules necessary for HREELS experiments and the resolution of 60 2 intercalated into the C lattice. Thirty-two of the 46 distinct HREELS experiments can not match that of optical mea- 60 vibrational modes of C can be observed in the PL spec- surements. Although HREELS has no obvious advantage 60 tra, some of which are not Raman and IR first-order active in the determination of the infrared mode frequencies, it modes. Mode energies determined from this technique show is very useful for the assignment of vibrational frequencies good agreement with those determined from INS, IR, and in C . This is because all modes in C can induce inelastic 60 60 Raman spectroscopies. At high energies (>700 cm−1, the scattering of electrons due to the impact scattering mecha- technique has a significant advantage over INS, since the nism [341, 342]. In the impact scattering mode, the electron much sharper peaks can provide very accurate data for mode frequencies [346]. By investigating the vibrational fine structure in the fluorescence [347] and phosphorescence [348] Table 8. Assignment and comparative list of peak positions (in meV) of neutron inelastic scattering, HREELS, and photoluminescence (PL). spectra of C60 molecules isolated in neon and argon matri- ces, the unambiguous identification of several vibrational

Assignment Neutron [336] HREELS [343] PL [346] modes of T3u, Hu, and Gu symmetry were obtained.

H 33 34 33 g 3.3. Phase Transition T2uGu 43,44 43,43 43 H 5050 u 3.3.1. Orientational Phase Transition

Hg 54 54,53 53 On cooling below a temperature of about T01 ∼ 260 K, Gg Ag 60 60 the nearly free rotation of C60 molecules in solid C60 will T 66 66,66 66 1u be frozen by losing two of their three degrees of rota-

T1u 71 72 72 tional freedom; the four neighboring molecules in an fcc 77 unit cell remain in their positions but become orientationally 83 82 inequivalent. Their rotation motions are constrained along H 88 88 g two standard favorite orientations and become hindered, 92 94,94 94 resulting in an orientational ordering [235, 243, 249, 273, H 96 96 g 349], but the random reorientation between the two pos- 104 103 sible standard orientations for each molecule in the solid 109 still lead to a residue disorder (a so-called “merohedral dis- 114 119 119,119 119 order”) [32, 243, 274, 275, 349–352]. The two favorite ori- 124 entations are corresponding to electron-rich double bonds 132 133 134 on one molecule facing the electron deficient centers of hexagons (HF) and pentagons (PF) respectively on its adja- Hg 136 136 136 139 cent molecules, obtained by rotating the molecules around the four 111 axes of the C molecules through about 38 T1u 147 147 146 60 149 150 and 98 (60 jumps) respectively [243, 284, 349, 353–355]. Recently, elastic diffuse neutron-scattering study, consider- Hg 156 156,161 158 168 166 ing the optimization of nearest-neighbor orientations rather H T 176 179,178 177 than long-range orientational order, showed that the actual g 1u angles may be closer to 42 and 102 [356]. The PF struc- Ag 184 H 196 194,192 195 ture has been indicated to be an idealized ordered structure g and the HF structure a “defect structure,” because the HF Note: The HREELS peak positions observed in an ordered C film on 60 structure has a slightly higher energy than the PF structure. GaSe(0001) and a crystalline C film on GeS(001) are italic. The other numbers 60 The lower energy configuration is about only 11.4 meV [352, correspond to the peaks detected in the spectra of an amorphous C60 films on Si(100). 357] below the higher energy configuration, and the two are C60-Based Materials 425 separated by a potential barrier of ∼235–295 meV [243, 274, 280, 284, 349, 352, 357–361] which has been confirmed by various experiments. A schematic 3D model of a close-packed (111) plane of

C60 molecules exhibiting uniaxial reorientation about 111 directions (low temperature phase, 90–260 K) is shown in Figure 20 [243]. The molecules reorientate between a number of different sites but principally perform 60 jumps about [111] residing in the two conﬁgurations corresponding to 38 and 98 (or 42 and 102, using latest data) rotations.

Although the centers of the C60 molecules remain in the same places, the four molecules of the conventional fcc unit cell become orientationally nonequivalent. The incompati- bility of the icosahedral molecular symmetry of the different molecular orientations and the cubic lattice symmetry lowers the crystal symmetry from fcc into a simple cubic (sc) 6 ¯ structure (space group Th or Pa3, which is a subgroup of the space group Fm3¯m of an fcc structure) [235, 273, 362]. Thus Figure 21. Electron diffraction patterns of C crystallite along [001] the C60 crystal undergoes a so-called orientational ordering 60 phase transition. (a, c) and along [011] (b, d) at room temperature (a, b) and at 100 K The orientational ordering transition is first order [111]. (c, d). Note the appearance of extra reflections at low temperature related to a lowering of symmetry due to orientation ordering. Adapted The occurrence of this transition has been confirmed by with permission from [371], G. Van Tendeloo and S. Amelinckx, in various experimental methods such as differential scanning “Electron Microscopy of Fullerenes and Related Materials, Character- calorimetry (DSC) [235, 273, 363], X-ray diffraction [235, ization of Nanophase Materials” (Z. L. Wang, Ed.), Wiley–VCH, 2000. 273], NMR [14, 23, 274–276, 363–366], neutron diffraction © 2000, Wiley–VCH. [243], dielectric spectroscopy [359]; SR [279]; specific heat measurements [352, 361, 367, 368], inelastic neutron scat- 13 Figure 22 shows the C NMR spectra of solid C60 at tering [33, 277, 369, 370], electron diffraction [371], sound temperatures from 295down to 77 K [275].The low- velocity and ultrasonic attenuation [242, 372], and Raman temperature NMR line shape for the C60 solid is quite spectroscopy [326, 373–375]. different from that of C60 in solution. From RT to low tem- Figure 21 shows a comparative electron diffraction pat- perature below Tg, the spectra changes from a single line terns of crystalline C60 at room temperature and at 100 K peak at 298 K to a line shape at 77 K. The symmetry of the [371]. Additional spots appear at positions which are extinct molecule and the equivalence of all C60 carbon atoms in C60 in an fcc lattice on cooling below T01 and correspond to a crystals are broken by two factors: the presence of the crystal primitive cubic lattice. The appearance of these spots reveals lattice and the applied magnetic field. As the temperature the low temperature structure in which the molecules are is reduced, the “motionally narrowed” NMR line at 295K still situated on an fcc lattice but orientationally ordered and (143 ppm from tetramethyl silane) in the 13C NMR spec- ¯ also shows that the space group Pa3 is a subgroup of the trum of C60, which proves that C60 molecules are rotating space group Fm3¯m of the high temperature fcc phase. rapidly with respect to the NMR time scale at RT, is broad-

ened and the C60 molecule’s orientation become static on the NMR time scale. At 77 K there is little evidence of the narrow line at 143 ppm, and a ﬁt to this line shape yields an asymmetric chemical-shift tensor with components of 220, 186, and 25ppm, reﬂecting the chemical-shift anisotropy of the 13C nuclei averaged over the crystallite orientations. The phase transition affects various physical properties; the changes of some of these properties at the transition

temperature T01 are listed in Table 9. It has also been indicated that both the transition temperature and the size and shape of the transition anomalies are strongly inﬂuenced by deformation, impurities, and solvent Figure 20. Close-packed (111) plane of C60 molecules depicting uniaxial reorientation about 111 directions (low temperature phase, 90– [354, 378]. 260 K). The “dimples” correspond to the centers of electron-poor hexagonal/pentagonal faces; the equatorial protrusions depict electron- 3.3.2. Glass Transition ¯ rich 6:6 bonds. The constraints demanded by Pa3 symmetry imply that Below about 90 K the molecules in C crystal are entirely the electron-rich and electron-poor regions have well-deﬁned loci cor- 60 responding to constant latitudes relative to [111]. These electrostatic frozen but never order perfectly; the C60 crystal undergoes a considerations are consistent with the assumption that the preferred so-called glass transition. The glass transition of C60 crystal easy reorientation direction is [111]. Adapted with permission from is second order [243]. [243], W. I. F. David et al., Europhys. Lett. 18, 219 (1992). © 1992, EDP The fraction of molecules in the more stable PF ori- Science. entation is only about 60% near 260 K but increases to 426 C60-Based Materials

Table 9. Physical properties at orientational phase transition tempera-

ture T01.

Quantity Under T01 Above T01 Jump Structure sc fcc — ¯ 6 ¯ 5 Space group Pa3 Th Fm3m (Oh — Lattice constant 14.11 Å 14.15Å 0.04 Å [238, 243] Reorientational 2 × 10−9 s9 2 × 10−12 s ∼200 times [274] correlation

time of C60 molecules Volume small large ∼1% [243] Thermal 0.5 W/m K 0.4 W/m K 25% [352] conductivity Enthalpy change low high 9000 J/kg (6500 J/mol) [368] 12,500 J/kg (9000 J/mol) [376] Young’s modulus high low 8% [242] Magnetic small large 1.2% [377] susceptibility ∼4 56 10−9 ∼4 61 10−9 in cgs) in cgs)

studies [242, 372], specific heat measurements [361, 379], thermal conductivity [352, 380], elasticity [242, 358, 372], high resolution capacitance dilatometry [357], dielectric relaxation studies [359], electron microscopy observations [381], and neutron scattering measurements [243, 349]. It has been demonstrated that the measured values of transi- Figure 22. 13C NMR spectra of solid C obtained at ambient tem- 60 tion temperature T varying in a wide range (∼90–165K) peratures of 123, 100, and 77 K. The 13C NMR spectrum of C is g 60 rely strongly on the time scale of the measurements [358]. expected to be a broad “powder pattern” resonance (width greater than ∼200 ppm) reflecting the chemical-shift anisotropy of the 13C nuclei The temperature dependence of the relaxation time may be averaged over the crystallite orientations. The “motionally narrowed” described by the relation "t = "t0 expEAt/kBT, where EAt is the activation energy for the transition and " is a charac- NMR line at 295K (143 ppm from tetramethyl silane) proves that C 60 t0 −14 molecules are rotating rapidly with respect to the NMR time scale, teristic relaxation time with values of "t0 = 4±2×10 s and −4 which is defined by the inverse of the spectral spread (∼10 s). As the EAt = 300 ± 10 meV [358]. For high-frequency measurement temperature is reduced, the powder pattern is recovered as the molecu- probes, the molecules cannot reorient quickly enough to fol- lar motion decreases. At 77 K there is little evidence of the narrow line low the probe frequency, so that the molecules seem to be at 143 ppm, and a fit to this line shape yields an asymmetric chemical- frozen at a higher transition temperature and a lower tran- shift tensor with components of 220, 186, and 25ppm. Adapted with sition temperature for low-frequency measurement probes. permission from [275], C. S. Yannoni et al., J. Phys. Chem. 95, 9 (1991). It is concluded that below T a quenched disorder occurs © 1991, American Chemical Society. g rather than an equilibrium glass phase [358].

about 84% near T ∼ 90 K, the glass transition temperature g 3.3.3. Phase Transition [243]. Below Tg, the thermal energy becomes too small compared with the energy barrier between the two states for fur- in Low-Dimensional Structures ther reorientation to occur; therefore the C60 molecules are At room temperature, the molecules on C60 (111) surfaces frozen in their orientation and the fraction of PF orienta- are hexagonal close-packed and rotating and reorientating tion (∼84%) or HF orientation (∼16%) becomes invariable. freely corresponding to a 1×1 structure. Below a tempera- The remaining orientational disorder causes an orientational ture of surface orientational ordering transition temperature

glass phase. Because the nearest-neighbor distance of HF Ts01 about 230 K [382–386] (about 30 K lower than that of oriented C60 molecules is slightly smaller than that of the C60 bulk), the C60 (111) surface exhibits a (2 × 2) reconstruc- PF oriented molecules, there is an anomalous increase of tion [382, 387] due to the four inequivalent frozen molecules volume thermal expansion coefﬁcient in the transition tem- ina(2×2) unit cell holding four different orientations. STM perature [243]. study clearly revealed the surface structure and indicated

Evidence for this glass transition at low temperature has that the orientational conﬁgurations of the C60 molecules been provided by a number of experimental techniques, on the surface are similar to those in the bulk, except for including velocity of sound and ultrasonic attenuation some complex details. This similarity indicates that it is the C60-Based Materials 427

interaction of the neighboring C60 molecules that drives the molecules to an orientational ordered state [387]. Recently, a two-stage rotational disordering mechanism, with a new intermediate regime between a low-temperature ordered (2 × 2) state and a high-temperature (1 × 1) disordered phase, has been proposed for this surface phase transition based on Monte Carlo simulations [388].

C60 submonolayers adsorbed on a self-assembled monolayer of an alkylthiol can be considered as ideal two- dimensional hexagonal arrays with a nearest-neighbor distance of ∼10 Å [20] due to the weak van der Waals force between C60 and the organic monolayer surface. At room temperature the C60 molecules at this surface are mobile and rotating freely. At 77 K, the C60 molecule appears as a hemi- sphere, a tilted doughnut, or an asymmetric dumb-bell, each being consistent with a rotating pattern around a ﬁxed axis.

That is, unlike in the case of bulk C60, the two-dimensional rotationally ordered phase persists down to 77 K (already 13 K below the bulk freezing temperature) [20].

Unlike the orientation-related glass phase in bulk C60 and the bulk C60 (111) surface, the two-dimensional C60 array forms orientationally ordered domains at 5K although the Figure 23. Phase diagram of C drawn on a logarithmic pressure scale C60 molecules are not commensurate with alkylthiol mono- 60 layer [20]. The molecular rotation is frozen and the internal to show the low pressure range: ( ), data from experiment; (- - -), ﬁne pattern of C with a well-known native cage struc- theoretical curves or extrapolations from experiment. Adapted with per- 60 mission from [389], D. M. Poirier et al., Phys. Rev. B 51, 1830 (1995). ture can be clearly revealed by STM, because of the fairly © 1995, American Physical Society. weak interaction between C60 and the organic monolayer surface with a negligible inﬂuence on the C60 molecule by the substrate. 3.4. Crystal Growth 3.4.1. Single Crystal

3.3.4. Phase Diagram Solvent grown C60 crystals may form various structures due to the intercalation of solvent molecules or small atmo- Figure 23 gives an equilibrium phase diagram of C crystal 60 spheric molecules into C crystal lattices [392–395], such as covering a wide range of temperatures and pressures, drawn 60 hexagonal close packed (hcp) structure [2, 396], fcc struc- on logarithmic scales to bring out clearly the low-pressure ture [397], orthorhombic or monoclinic structure [398, 399], behavior [389]. and so on, and various shapes, even decagonal crystals with The solid lines are derived from experiment, and dashed pseudo tenfold symmetry, can formed [392, 400, 401]. lines are theoretical or reflect extrapolations from exper- C60 has an extraordinarily high vapor pressure of strong iment. The solid–vapor coexistence line PT is given by temperature dependence [246] (at 500 C, the vapor pres- plotting the equilibrium vapor pressure against temperature. sure of C is about 1035 times greater than that of the The thermal gravimetric analysis data (shown by solid cir- 60 graphite [247]) and solid C60 sublimes at relatively low tem- cles) [247] are fitted to PT= P0 exp−5H/kT , which can perature (see Table 4) [247]. A vapor transport method is be derived from the Clausius–Clapeyron equation assuming used to grow pure C60 single crystal free of solvent or gas in ideal gas behavior [390]; the low pressure experimental data a large quantity and a perfect quality conveniently by slow (shown by a bar and a open diamand) [389, 391] are in good condensation or deposition of the molecules from vapor agreement with extrapolation of the solid–vapor coexistence [402]. See Table 10. line using the ideal gas relationship. It can be indicated from The vapor growth technique for synthesizing single-crystal the diagram that solid fcc C60 sublimes on heating without fullerenes usually uses a carefully cleaned, dynamically forming a liquid phase at normal pressures. The fcc–sc coexistence line at the left of the phase diagram defines the pressure-dependent temperature of the Table 10. Available rate of weight loss and vapor pressure of C60 at solid-state orientational ordering phase transition; the data selected temperatures [247]. shown by filled squares are measured using DSC [244]. Temperature (C) dw/dt ( g/s) Vapor pressure (mTorr) At high temperature or under ultrahigh pressure, the

C60 molecules will collapse into amorphous carbon. Under 400 0 004 0 019 higher pressure (>1 GPa) and high temperature, which is 450 0 014 0 069 500 0 0850 446 not shown in the phase diagram, crystal C60 will polymerize, induced by pressure. The pressure-induced polymerization 550 0 43 2 32 600 1 759 67 will be introduced in Section 4.2. 428 C60-Based Materials

pumped, horizontal quartz tube (usually about 50 cm long by 1 cm in diameter) placed in a furnace with a tempera-

ture gradient [403–405] (see Fig. 24). The initial C60 powder is filled in a gold boat and heated in the vacuum furnace at about 250 C under dynamic vacuum for 6–72 hours in order to remove the solvent intercalated in the powder. Sub- sequently the Au boat is heated above the C60 sublimation temperature to about 590–620 C, and high-purity, dry helium flow kept at a flow rate below 5cc/min is employed

to carry the C60 vapor to the colder part of the quartz tube. Crystallization starts at the part where the temperature is Figure 25. A sketch of diffusion oven composed of three independently below 520 C. The growth rate in this method is expected to temperature-controlled zones; T1T2, and T3 are the temperatures of

be about 15mg per day. The vapor transport procedure is the C60 source: “hot wall” and substrate, respectively. Adapted with permission from [426], J. G. Hou et al., Thin Solid Films 320, 179 (1998). always kept for several days to yield larger C60 crystals. Several modified techniques based on the vapor trans- © 1998, Elsevier Science. port growth method have been developed to grow larger and more perfect C60 crystals such as the vibrating tempera- set to T1 = 420 C and T2 = 440 C, respectively [426]. The ture method [406], the double temperature gradient method substrate temperature (T3 is usually set from 100 to 200 C. [407], optimization of temperature distribution [408], use of Most of well-ordered C60 thin films or multilayers were a vectical furnace with a pulling technique [409], the Piz- grown on substrates including layered substrates, alkali zarello method [410, 411], very small temperature gradient halides surfaces, semiconductor surfaces, and metal surfaces. control [412], and so on. But studies showed that crystalline films can grown relatively easily on layered substrates like mica [417, 427–439], 3.4.2. Thin Films graphite [386, 440, 441], MoS2 [437–439, 442, 443], fluo- rophlogopite [444], and lamellar substrates such as GeS(001) High-quality crystalline C thin films have been grown suc- 60 [445–448], GaSe(0001) [341, 343], and Sb [449]. Because cessfully on many substrates and studied extensively for of the natural passivation of these substrate surfaces, the the understanding of growth mechanisms and properties. C –substrate interactions are dominated by van der Waals The potential applications of C thin films in electronic 60 60 force which can relax the stringent lattice match condition devices have been explored, such as rectifying electronic and result in the formation of fcc (111) oriented C60 crystal diodes [413], photodiodes and solar cells [413], and thin-film grains. field-effect transistors [414–416]. The results showed those Well-ordered crystal C60 monolayers and thin films can fullerene electronic devices have stable, reproducible perfor- also be grown on alkali halides and other ion crystals such as mances and excellent device characteristics. NaCl [417, 418, 437, 438, 450, 451], KCl [418, 438, 450, 451], Most of the C60 thin films are grown under ultrahigh KBr [418, 438, 450–453], KI [245, 246], and CaF2 [247, 248], vacuum (UHV) environment using a sublimation-deposition due to the very weak surface bonding dominated by the elec- method, such as a simple or enhanced vapor deposition tech- trostatic force that restricts the diffusion of C ad-species. nique [417–419], organic molecular beam epitaxy [420], the 60 But C60 thin films grown on metal substrates are much hot-wall diffusion method, or the ionized cluster beam depo- different from the weak-bonding substrates mentioned. It sition technique [421–425]. A schematic sketch of a univer- has been shown that there exist very strong interfacial inter- sal hot-wall diffusion method setup is shown in Figure 25. actions and charge transfer from the metal substrate to the The diffusion oven (lower part of Fig. 25) employed is com- LUMO of C60 [172, 191]. Compared with the nonmetal sub- posed of three parts. The temperature of each part can be strates, the metal substrates are usually less smooth and con- controlled independently to get three different temperature tain much higher densities of steps, so it is more difficult zones (upper part of Fig. 25). The source C60 powder and to grow high-quality single crystal films on metal surfaces. substrate are placed in zone I and zone III in a quartz tube, There have been reported high-quality C60 (111) oriented respectively. The C60 molecules are evaporated from zone I, films successfully grown on Au [191, 419, 458], Ag [191, 419, through zone II, then deposited on the substrate in zone III. 459, 460], Cu(111) [191, 461, 462], as well as Ni Fe(111), The temperature of zone II (hot wall) is higher than the 3 Ni3Co(111), and Ni3Fe(110) [426, 463] using a hot-wall dif- other two zones, which can generate a very low growth rate. fusion method. As an example, the temperatures of zone I and zone II are Several techniques have been attempted to improve

the crystallization and quality of C60 thin ﬁlms. Using a self-mediated process [451] or using Sb as the surfac- tant or buffer layer [464, 465] and the multistep growth

method [418], higher quality and larger grain-sized C60 can be obtained. Figure 26 shows a transmission electron microscopy (TEM) image as well as diffraction pattern of a

high-quality single crystal C60 fcc (111) oriented ﬁlm with a thickness of about 60 nm prepared by using Sb as the sur- Figure 24. Schematic view of a horizontal quartz tube furnace appara- factant on a freshly cleaved (001) NaCl single crystal surface

tus for the vapor transport growth of C60 single crystals. [465]. C60-Based Materials 429

By properly treating the electron excitations with an ab initio quasiparticle approach, a GW (G represents Green’s function and W is a dynamically screened Coulomb interaction) approach was developed. In the GW approach, the Dyson equation is solved within a Green’s function formalism using a dynamically screened Coulomb interaction W to obtain the quasiparticle energy spectrum. Because the method includes a treatment of the electron self-energy (in terms of a dynamically screened Coulomb interaction), it predicted a larger value of 2.15eV [469] for the HOMO– LUMO gap, with bandwidths of 0.9, 0.7, and 0.8 eV for the HOMO-, LUMO-, and (LUMO + 1)-derived bands, respec- Figure 26. TEM image and diffraction pattern of a C ﬁlm with nom- 60 tively. This result is very close to the gap value of ∼2.3 eV inal thickness of 60 nm. Large (111) orientated C60 grains with average size of about a few micrometers were formed. Adapted with permission given by high-energy spectroscopy experiments like PES from [465], J. G. Hou et al., J. Appl. Phys. 84, 2906 (1998). © 1998, and inverse photoemission spectroscopy (IPES) [470–472]. American Institute of Physics. There are also many other experiments carried out by different methods showing different results [473]. A scheme in 3.5. Properties Figure 28 shows the difference of the gap values given by different methods.

3.5.1. Electronic Structure A detailed electronic structure of C60 thin ﬁlms was studied by surface photovoltage spectroscopy [474, 483, 484]. C60 solid is a semiconductor with a minimum of the energy gap at the X point of the Brillouin zone. The value of It is illustrated in Figure 29, which includes a mobility gap the energy gap is still under debate, which is in the range of 2.25eV and exponential Urbach tails of states determin- of 1.43–2.35eV. In early studies, a typical and widely ref- ing the optical gap of 1.65eV [481, 485].In addition, there exist two deep gap states: one donor and one acceptor. The erenced band calculation for solid C60 is based upon the local density approximation (LDA) in density functional acceptor level lies 0.8 eV below the conduction band tail, theory, in which all many-body effects are collected into and the donor level is 1.25eV higher than the valence band the exchange-correlation energy, which is evaluated within tail. The exponential Urbach tails in the density of gap states a free-electron model. The LDA calculations obtained a may be due to thermal disorder rather than from static structure, topological, or compositional disorder. The donor level bandgap of ∼1.5eV for fcc C 60 crystals [466] and a value of 1.18 eV for the bandgap at the X point [467]. The arises from the unbound intercalated oxygen and the accep- band structure of C crystals is derivated from the energy tor level is considered to be the result of chemical reaction 60 of oxygen with fullerene. This detailed electronic structure level distribution of an isolated C60 molecule. Figure 27 shows the electronic structure of the HOMO- and LUMO- shows that the optical absorption edge [481] is not simply connected to the HOMO–LUMO gap. derived bands of C60 in the solid state obtained from LDA calculations.

Figure 27. Left-hand panel; a schematic diagram of the C60 Figure 28. Energy gap of C60 fullerene, obtained in various stud-

-molecular orbit energy scheme. The HOMO (h1u and LUMO (t1u ies, including: surface photovoltage spectroscopy [474], photoemission are shown in the expanded region. Central panel; the band structure of [471], EELS [475], microwave conductivity [476], ac photoconductivity the HOMO- and LUMO-derived bands of C60 in the solid state. Right- [477], real part of complex conductivity [478], photoconductivity [479], hand panel; the density of states of the HOMO- and LUMO-derived optical absorption [480] (the upper one), optical absorption [481] (the bands of solid C60 predicted from LDA calculations [466]. Adapted with lower one), quasiparticle approach [482], and LDA calculations [466]. permission from [468], M. Knupfer, Surf. Sci. Rep. 42, 1 (2001). © 2001, Adapted with permission from [473], T. L. Makarova, Semiconductors Elsevier Science. 35, 243 (2001). © 2001, MAIK Nauka/Interperiodika. 430 C60-Based Materials

written as = 0 exp−Ea/kT), and the prefactor 0 correlates with the activation energy Ea as 0 = 00 exp−Ea/kT), where 00 and T0 are the Meyer–Neldel parameters. For example, the relationship between the conductivity prefac-

tor 0 and activation energy Ea in C60 ﬁlms under different O2 exposure can be described by the MN rule. The obtained −1 00 and kT0 are 15.6 ( cm) and 0.11 eV, respectively [493]. The relationship between the conductivity prefactor

and activation energy in C60 films at different stages of the growth process also obeys the MN rule with the MN param- −19 −1 eters of 00 = 7 7 × 10 ( cm) and kT0 = 0 012 eV [493]. High pressure has a strong effect on the conductivity, Figure 29. Electronic structure of C thin films, from which we can 60 as well as the width of the gap between LUMO- and see exponential tails of states between conduction mobility edge and HOMO-derived bands of C solids [504, 505]. The elec- conduction band bottom, as well as tails between valence band top and 60 tric conductivity changes four orders of magnitude from 2 × valence mobility edge. Adapted with permission from [474], B. Mishori −6 −1 −2 −1 et al., Solid State Commun. 102, 489 (1997). © 1997, Elsevier Science. 10 cm) (below 8 GPa) to 3 × 10 ( cm) (around 20 GPa). The bandgap is as follows: 1 6 ± 0 1eVat3and 6 GPa, and 1 2 ± 0 1 eV at 10 GPa. Exposed to air, upon the To get a complete description of the electronic struc- interaction with oxygen, the conductivity of C single crys- ture of C solids, a number of many-body calculations have 60 60 tals [506] and films falls [493, 507] by 3–6 orders of magni- focused on calculations of quantities of electron correlation tude. Such an effect may be caused by trap levels for carriers effects. Direct in-situ comparison of C 1s absorption spec- and neutralizes defects forming localized electronic states, tra taken in the gas phase with those from solid C reveals 60 which are created by the intercalated oxygen. a close similarity [486]. It can be concluded that solid-state The conduction mechanism at different temperatures interactions are not important in this new material, and has been studied by measuring the ac (1

MN rule describes an exponential relation between the acti- troscopies The optical properties of solid C60 in the vation energy Ea and the pre-exponential factor 0. The visible-UV range were investigated by a variable angle expression of the MN rule for the dc conductivity can be spectroscopic ellipsometry (VASE) technique [513–515] and C60-Based Materials 431

near-normal-incidence reflection and transmission experi- Table 11. Spectral features for solid C60 and C60 molecules. All energies ments [516]. UV data above ∼7 eV were obtained using are given in eV [480]. EELS [475] by Kramers–Kronig analysis of the EELS loss Band code Solid C C molecules Transition assignment function. The observed optical properties of C60 solids are 60 60 usually expressed in terms of the complex optical dielectric = 1 918 1 995 h → t + T , H , G function # = # + i# . Figure 30 shows the results 0 u 1u u u u 1 2 =1 2 035( +Hg , Ag ) for #1 and #2, obtained from VASE and transmission- =2 1 992 2 070 FTIR (Fourier transform infrared) studies on thin solid films =3 2 028 2 105 = 2 097 2 180 of C60 on KBr substrate at T = 300 K [316]. The strong, 5 sharp structure at low energy (below 0.5eV) is identified A2 41 hu → t1g with infrared-active optic phonons. The imaginary part of B2 70 the dielectric constants of C60 begins to rise at 1.7 eV, which C3 2 can be considered the absorption edge. At higher energies D1 3 489 3 58 h , g → t in the visible and UV ranges, the spectrum structure is due g g 1u to allowed optical transitions at 3.5–5.6 eV and to excitons D2 3 541 3 732 at energies below 3 eV. There are four prominent absorp- E3 99 4 21 hu → hg tion peaks at ∼2.7, 3.6, 4.7, and 5.6 eV for the pristine C60 F1 4 36 with dipole-allowed electronic transition [480, 481, 517–519]. F2 4 546 4 6 Optical transitions between the HOMO and LUMO bands G1 5 500 5 437 hg , gg → t2u are forbidden by symmetry [520]. G2 5 77 5 73 Luminescence spectra appear to be more sensitive to sample quality and to show wider sample to sample variation respectively [480, 513]. The oscillator strengths of these than absorption spectra [521] The temperature dependence dipole-allowed transitions are in reasonable agreement with of the photoluminescence spectra is given in [522]. At a tem- the calculations of [525]. The D band assigned to h g → perature of 7 K, the absorption curve intersects the photo- g g t transitions is strongly reduced in doped films due to the luminescence curve at the point 1.8 eV, which may be the 1u filling of the lowest state in the conduction band derived optical gap at this temperature [523]. from the t1u molecular states [527]. The molecular F1 2 Transition Assignment An accurate study of optical band, which originates from the hu → hg transition, split transition in C60 was carried out by comparing the optical into F 1 and F 2 bands in the solid due to the splitting spectra of C60 films on mica with the transmission of toluene, of the fivefold-degenerate huhg levels to the threefold- hexane, and heptane solutions [480]. Experimental spectra and twofold-degenerate tutg and eueg levels, respectively were fitted with Gauss–Lorentz (GL) line shapes to deter- [467]. The weak E band possibly also originates from the mine the energy positions of individual transitions. hu → hg transition. The assignment of the electronic transitions given in The assignment of the two lowest transitions, hu → t1u −1 Table 11 is based on the calculated transition energies of and hu → t1g, is more delicate. The t1ghu molecular state [524–526]. The best agreement of the calculated gap posi- consists of electron–hole excited states with T1uT2uHu, and tions with experimental results is provided by the tight- Gu symmetry [528]. According to several calculations, the binding models [525, 526]. An overview of the energy levels lowest allowed transition hu → t1g to the T1u excited state and optical transitions discussed is shown in Figure 31. should be located near 3 eV with an oscillator strength The three leading GL bands D E +F , and G are assigned of about 3% of that of the hggg → t1u band at 3.5eV to the transitions hggg → t1uhu → hg, and hggg → t2u,

Figure 30. Real and imaginary parts of the dielectric function #) determined from VASE and FTIR measurements for C60. Adapted with Figure 31. Electronic energy levels in solid C60 and in C60 solution in permission from [520], M. S. Dresselhaus et al., Synthetic Metals 78, 313 n-hexane. Adapted with permission from [480], J. Hora et al., Phys. Rev. (1996). © 1996, Elsevier Science. B 54, 5106 (1996). © 1996, American Physical Society. 432 C60-Based Materials

[524, 525, 529]; the very small oscillator strength has been value of the real #1 part at 1.5eV is 4.1. The whole attributed to plasmon screening [525]. In addition to this trend of the optical dielectric function of C60 is as below. allowed transition, phononinduced transitions of compara- Where there is a loss process represented by a peak in the

ble strengths [529] to the T2uHu, and Gu excited states [528] #2 dielectric loss spectrum, there is a rise or a resonant should appear in the same energy region. The comparison of oscillation in the #1 spectrum. This result is consistent the energies and oscillator strengths of the B and D bands with Kramers–Kronig relations. With frequency decreasing 13 is essential for the following assignment of =BB , and D to 10 Hz, #1 is approaching its dc value. The small dif- 13 5 subbands to the electronic transitions (see Table 11). ference between #1 (10 Hz) ≈ 3 9 [517] and #1 (10 Hz) ≈ −1 The A-group is attributed to the t1ghu electron–hole state 4 4 [391] might be due to the losses associated with C60 parity forbidden in an isolated molecule, but becoming par- molecules rapidly rotating (at the rate of ∼109 Hz) at room

tially allowed because of level splitting. temperature (T>T01, T01 = 260 K is the structure transition The =-group results from the forbidden molecular tran- temperature). 5 sition hu → t1u. These transitions gain nonzero strength In the low frequency regime (below 10 Hz), polarization through the excitation of an appropriate odd-parity vibra- mechanisms come into play. The dielectric properties in this tional mode [530] (Hertzberg–Teller coupling) and their regime were investigated by ac impedance measurements, upper electronic states can be inﬂuenced by Jahn–Teller which are usually performed on a sample between closely

dynamic distortions [518]. spaced parallel conducting plates. These M–C60–M (M = metal) “sandwich” structures consist of 200- m-wide alu- Photoconductivity Experiments conﬁrmed the existence minum down stripes as base electrodes, a known thickness of the photoconductivity in fullerene solids [531, 532]. Pho- of C , and 200- m-wide aluminum cross stripes as coun- toconductivity spectra of C are, on the whole, similar to the 60 60 terelectrode [535]. The ac equivalent capacitance C and absorption spectra, apart from the conduction dip at about the dissipation factor D of the resulting capacitor can 350 nm of wavelength. Such a photoconduction dip appears be obtained. The real part of the relative dielectric func- frequently in intense absorption regions in many photo- tion # can be calculated since the relation between the conductors. The photoconduction edge is at about 730 nm 1 capacitance and # is known to be C = # # A/d. (1.7 eV) [523]. The main spectra features are related to 1 1 0 Here, A is the cross-sectional area of the capacitor, d excitons rather than to interband transitions. The photocon- is the separation distance between the plates, and # is duction spectra measured at various light-intensity modula- 0 the absolute permittivity of free space (8 85 × 10−12 F/m). tion frequencies, light intensities, and applied voltages shows The imaginary part of the dielectric function # can that the photocurrent is proportional to light intensity and 2 be extracted from measurement of the dissipation factor applied voltage. Moreover, the photocurrent increases with D = # /# . To ascertain the intrinsic dc # (0) of decreasing light-intensity modulation frequency, which may 2 1 1 C , the dielectric measurement needs to be performed at arise from some deep carrier traps in the energy gap. 60 frequencies low enough to include the intrinsic relaxation processes of the material, but high enough to escape the 3.5.4. Dielectric Properties effects of impurities (e.g., molecular oxygen). The effects of

Solid C60 is a soft dielectric material [533]. The complex oxygen and other impurities occupying the interstitial sites dielectric function # = #1 + i#2 of solid C60 was of solid C60 on the dielectric relaxation of C60 ﬁlms can be studied over a broad frequency range using a wide variety ignored only above ∼5kHz. So the intrinsic dielectric con- of techniques including ac impedance measurements at low stant was obtained by performing a series of capacitance frequencies and optical measurements at high frequencies measurements at 100 kHz. By this method, a value of 4 4 ±

[259, 391, 475, 516, 517, 534]. 0 2 was obtained for the relative permittivity #1(0) [391]. The complex optical dielectric function # = #1 + The plate spacing d of the C60 capacitor may change due i#2 can be expressed in the terms of the complex refrac- to the thermal expansion or to phase transition at T01 ≈ tive index N = 9n + ik:. Here, n is the refrac- 260 K. The interaction of oxygen or other species into the tive index and k is the extinction coefficient. Both n and interstitial spaces of C60 solid can also lead to such problems. k are frequency-dependent optical constants. The expres- To avoid these problems, a microdielectrometry technique sion is # = 9N:2 = 9n + ik:2. The optical [536, 537] has been employed at low frequencies (from 10−2 5 dielectric function # of C60 was studied over a wide to 10 Hz). In this technique, a coplanar electrode configu- frequency range of 1013–1016 Hz (corresponding to 0.05– ration was used as an alternative to the “sandwich” configu- 40 eV, 1 eV = 8066 cm−1. Below 7 eV, it was studied using ration. Both electrodes in the microdielectric measurement infrared (between 0.05and 0.5eV) [534]and visible-UV are placed on the same surface of an integrated circuit, and

(1.5–5.5 eV) [516, 525] spectroscopies. UV data above 7 eV C60 ﬁlm is placed over the electrodes by thermal sublima- were obtained using EELS by Kramers–Kronig analysis of tion in vacuum [391]. In comparison with the “sandwich” the EELS loss function [475]. The features of the #2 geometry, this geometry has the advantages as follows. First, dielectric loss spectrum in the infrared range include four the comb electrodes of a coplanar sensor, in contrast to par- strong lines at 526, 576, 1182, and 1428 cm−1 due to molec- allel plates, ensure proper calibration of the device even if ular vibrations. At higher energies in the visible and UV the material being measured undergoes structure transfor- ranges, the imaginary #2 part of the dielectric constants mations. Moreover, the open-face layout facilitates studies begins to rise at 1.65eV and there are four prominent peaks of diffusion of foreign species into the bulk of the material. at ∼2.75, 3.55, 4.50, and 5.50 eV in the #2 spectrum, By means of capacitance and dissipation factor measure- corresponding to four absorption peaks [269]. An absolute ments discussed previously, the temperature dependence of C60-Based Materials 433

the dielectric properties of C60 single crystals, polycrystalline The measurement performed on a C60 powder sample C60, and microcrystalline C60 films were studied [359, 538, shows the temperature dependence of the magnetic suscep- 539]. On cooling below the first-order structural phase tran- tibility [544]. At temperatures greater than 180 K the sus- sition at 260 K, a Debye-like relaxational contribution to ceptibility is temperature independent with a mass value of −6 the dielectric response was observed. From the Debye-like >g =−0 35 × 10 emu/g, where the subscript g refers to the relaxation, the presence of permanent electric dipoles was susceptibility per gram of sample. At low temperatures, due found, which are unexpected in the centrosymmetric struc- to a relatively small number of electron spins, >g increases ture of the pure ordered cubic phase C60. It is suggested that and becomes paramagnetic, yielding a molar Curie constant the high degree of frozen orientational disorder of the C −4 60 CM = >M T = 0 75 × 10 (>M is a molar susceptibility), molecules is responsible for the existence of electric dipo- which gives an electron spin value of 1 5 × 10−4 per carbon lar activity. In addition to the structure phase transition at atom. It is believed that the Curie constant here is caused 260 K, a signature of the glass transition was detected at by a foreign paramagnetic impurity in the C60 sample. ∼90 K. Studies on the dielectric properties of C films in 60 Magnetization of a large single C60 crystal was measured the high-temperature region discovered that both the capac- as functions of applied field and temperature [377]. The itance and dissipation factor curves as a function of temper- sample was carefully prepared and handled to avoid oxygen ature have a pronounced feature at 435K, which confirms contamination. The result shows no low-temperature Curie the fact that above 400 K a phase transition does occur in term, from which it is concluded that the low-temperature the crystal [539]. Curie contribution is likely due to oxygen contamination. A small charge transfer between the C60 and O2 In addition, near T01 = 260 K, a discontinuity with a 1.2% molecules, which occupy interstitial space of solid C60 − change in susceptibility was observed, with >T01 more neg- exposed to oxygen (or ambient air), creates large electrical ative than >T + for the susceptibility at either side of dipole moments due to the large size of the C molecules 01 60 the phase transition. The discontinuity is attributed to the [535]. The dipole moments can be coupled to the applied change in the intramolecular geometry at the orientational ac electric field via a diffusion-controlled relaxation mecha- order–disorder transition. The susceptibility can be consid- nism. This leads to a significant increase in the permittivity ered to be independent of the temperature below and above # accompanied by a broad dielectric loss peak # at ∼10– 1 2 the structural transition temperature, T = 260 K. The 100 Hz. For instance, the dielectric function # increases 01 1 experiment demonstrated that the cooperative phase transi- dramatically from 4.4 at 105 Hz to 18.4 at 100 Hz due to tion affects the magnetic susceptibility of a single molecule. the polarization caused by the interstitial oxygen [535]. With Whereas the unpolymerized C is diamagnetic, a increasing oxygenation, the interstitial sites are nearly fully 60 few fullerene-based materials were found to be ferro- occupied. As a result, interstitial hopping is inhibited, and magnetic. Ferromagnetism has previously been observed the loss peaks disappear. in [TDAE]C60 [TDAE = tetrakis(dimethylamino)ethylene] below 17 K [552]. It has been reported that hydrogenated 3.5.5. Magnetic Properties fullerene [553], C60H24, and some palladium fullerides [554], Pristine C solids are diamagnetic materials due to the pres- 60 C60Pdn, may be ferromagnetic. Recently, the finding of ference of ring currents in the C molecule [1]. In compar- 60 romagnetism in pure Rh-C60 (rhombohedral phase 2D C60 ison with other carbon-based materials [540–543], such as polymer) samples by Makarova et al. [555] appears to be the graphite and diamond, C60 has an unusually small diamag- first report on magnetic ordering in a pure molecular car- netic susceptibility of about −0 35 × 10−6 emu/g [544, 545]. bon material up to temperatures above 300 K (see Section This is because there is an unusual cancellation of ring cur- 4.2.4). rents in the C60 molecule. There are two kinds of rings in the C60 molecule: the aromatic rings and the pentagonal rings. The aromatic rings in C60 set up shielding screening 3.5.6. Thermal Properties currents in a magnetic field [546, 547] which contribute a Specific Heat Measurement of the temperature depen- diamagnetic term to susceptibility >, while the pentagonal dence of the heat capacity at constant pressure CpT rings contribute a paramagnetic term of almost equal mag- provides the most direct method for the study of the temper- nitude. Table 12 presents the diamagnetic susceptibility for ature evolution of the degrees of freedom, phase transitions, C60 and related materials. and the enthalpy change.

The temperature dependence of the specific heat of C60 solids is studied mainly by DSC. The overall shape of the C Table 12. The diamagnetic susceptibility for C60 and related materials 60 at T = 300 K. specific-heat curve in the temperature range of 0.2–400 K is as follows. At very low temperature (below 1 K), the specific Material >10−6 emu/g) Ref. 3 3 heat shows a CpT = C1T + C3T behavior. The T depen- C −0 35 [544, 545] dence component of CpT yields a Debye temperature 60 ? = 80 K [556–558]. The linear T contribution arises from C70 −0 59 [544, 545] D Graphite −21 1(c-axis)a [548] the tunneling modes in the glassy systems [559]. The contri- Carbon nanotubes −10 2 [549, 550] bution saturates above ∼5K and contributes little at high Diamond −0 49 [551] temperatures. In the temperature range 2 ≤ T ≤ 80 K, there is an initial rise in the specific heat, followed by a plateau a The value refers to c-axis susceptibility of graphite. The H in-plane suscep- −6 tibility of graphite is 0 4 × 10 emu/g. near 80 K [560]. The intermolecular modes of C60 contribute 434 C60-Based Materials

signiﬁcantly in this range. The plateau is due to the satu- surprising that measurements of ' taken to high tempera- ration of these low-energy excitations. The low-energy exci- ture (1180 K) show a lower value of 4 7 × 10−5/K than for tations in this range consist of both acoustic (translational) the lower temperature range [563]. The thermal expansion

modes and rotations (also called librations) involving the coefficient of C60 films with thickness t were investigated. As entire C60 cage. Because the bonds between cages are weak t decreases ' increases and is described well by the relation van der Waals bonds, these low-energy modes saturate below ' = 17 × 10−6 K−1 + 8 3 × 10−5 nm K−1t−1 [564]. 80 K. With six modes (three translational and three libra- tional) and a molecular number density (N /60), the Dulong– Thermal Conductivity Because C60 is a van der Waals– bonded molecular solid, its Debye temperature A due to Petit limit for the C60 molecules is 6(N /60)kB = 69 3 mJ/g K, D which matches the level of the plateau. Here, N is the num- the intermolecular phonon modes is low with a value of ber density (per unit mass) of carbon atoms. about 70–80 K [350, 556]. Above the Debye temperature the specific heat due to propagating modes is independent Above 100 K, there is a nearly linear rise in CpT curve, and this rise in Cp is caused by the higher energy intramolec- of temperature. Consequently, the thermal conductivity 0 is ular excitations on the ball, which start to be activated and an ideal probe of the phonon mean free path through the

contribute to the speciﬁc heat. The Dulong–Petit limit for kinetic expression 0 = CsB/3, where C is the speciﬁc heat, the carbon atoms is equal to 3NkB = 2 08 J/g K. Based on s is the sound velocity, and B is the phonon mean free path. the highest energy on-ball mode (196 meV), the saturation Experiments showed that 0 ∼ 0 4 W/mK at room temper- temperature is expected to be above 2500 K. Since C60 sub- ature and is approximately temperature independent down limes around 300 C, it could not be observed anyway. It is to 260 K [380, 352]. At 260 K, 0 takes a sharp jump from the large difference in bond strength between the covalent 0.4 to 0.5W/mK with a transition width of ∼2 K. Because bonds on the cage and the molecular bonds between the the heat capacity due to intermolecular modes is constant at cages that leads to the energy separation between the intra- 260 K, the 25% jump in 0 must be due to a sudden increase and intermolecular modes [560]. in the phonon mean free path. Upon further cooling, the A remarkable feature in the temperature dependence of thermal conductivity increases. At about 85K, the thermal

the specific heat for C60 is the large specific heat anomaly conductivity shows a shoulderlike structure. The tempera- near T01 = 261 K orientational order–disorder transition ture and time dependence of the thermal conductivity below [368, 561]. The structure of the CpT curve near the phase 260 K can be described by a phenomenological model that transition temperature T01 is strongly impurity concentra- involves thermally activated jumping motion between two tion dependent. Moreover, the specific heat of C60 depends nearly degenerate orientations, separated by an energy bar- dramatically on the cooling or heating rate. Extremely slow rier of ∼260 meV. heating and cooling runs (at rates of the order of 100 mK/h) showed that even at such low scanning rates the results are 3.5.7. Mechanical Properties rate dependent [368]. The material is not in a thermodynamic equilibrium state and behaves as a system with a very Primary C60 is fcc molecular crystal formed by Van der Waals long internal relaxation time (order of 10 h) in complet- interaction between rigid C60 molecules. It is a soft and fri- ing the first-order transition. The lower the scanning rate, able material showing low strength and high-elastic compli- the more the ordering transition temperature shifts to lower ance. Information on the temperature dependence of the (higher) temperatures for the heating (cooling) runs. Mea- elastic moduli is incomplete and partially contradictory [242, 358, 372, 565–567]. The elastic constants of single-crystal surements [368] on high-purity sublimed C60 show that for the orientational transformation occurring at 262.4 K during C60 at room temperature have been established [568, 569]. Since solid C at room temperature is cubic, the matrix the heating run, the associated CpT peak is remarkably 60 sharp and attains a value of 12,360 J/kg K. The correspond- of the elastic constants has three independent components: ing heat of transition is about 9000 J/kg (6500 J/mol), a C11, C12, and C44. The elastic moduli C11, C12, and C44 were value considerably smaller than reported for single crystal obtained experimentally on the basis of sound velocity and of 12,500 J/kg (9000 J/mol) [376]. For the slow cooling run the density C by using the well-known relations between the 2 an even larger peak value of 16,730 J/kg K at a transition elastic moduli and sound velocity in cubic crystal: C;T = C44, temperature of 260.6 K is observed. where ;T is the velocity of transverse ultrasonic waves in the 2 If the specific heat anomalies associated with phase tran- [100]-direction, C;T = C11 − C12 + C44/3, where ;T is the sitions are removed from the experimental CpT data for velocity of transverse ultrasonic waves in the [111]-direction, 2 C60, then the temperature dependence of the residual spe- and C;L = C11, where ;L is the velocity of longitudinal waves cific heat contribution for C60 is in good agreement with that in the [100]-direction. These values of the elastic moduli of graphite [367, 562] for T ≥ T01 (261 K). determined by the experiments are presented in Table 13. Thermal Expansion The temperature dependence of the

lattice constant a0 for C60 shows a large discontinuity at the Table 13. Experimental and theoretical values of the elastic moduli Cij structure phase transition temperature T01 = 261 K, where (GPa) of the fcc phase of solid C60 (300 K). the lattice parameter a0 jumps by +0 044 ± 0 004 Å on heating [238]. The fractional jump of the unit cell volume of C11 C12 C44 C11–C12 Ref. 5v = 5V /V is (9 3 ± 0 8 × 10−3. The average isobaric volume coefﬁcient of thermal expansion ' both above and 14 9 ± 0 98 8 ± 1 06 6 ± 0 18 6 1 ± 0 45Experiment [571] 13.8 6.6 7.0 7.2 Theory [570] below the transition is (6 2 ± 0 2 × 10−5 K−1 [238, 349]. It is C60-Based Materials 435

For comparison, the theoretical values of the elastic stiff- appear to be completely absorbed by the C60. After that, the ness constants obtained in terms of the model intermolecu- sample tube is held at 200–300 C for a period between 24 lar interaction are also given in Table 7 [570]. In the theory and 72 hours to ensure complete diffusion of the metal into approach, the interatomic Buckingham potential was used the C60 sample. for calculating the intermolecular interaction and the elec- For preparing single-crystalline samples, the intercalation trostatic interaction was taken into account. process can be controlled by measuring the conductivity of

To compare the previous results of a single crystal with the the samples in-situ. Electrical contacts to the pristine C60 measurements of the elastic properties performed on com- samples are made prior. Then the conductivity apparatus is pact samples and polycrystalline films of C60, the isotropic sealed together with fresh alkali metal in a Pyrex glass appa- moduli of polycrystalline C60 were estimated by averaging ratus under high vacuum. Uniform doping is accomplished the elastic constants Cij of a single crystal. By regarding the using a repeating high-temperature dope–anneal cycle. Both anisotropy in polycrystalline C60 as a result of the disordered the sample and dopant are heated uniformly from room orientation of individual single-crystal grains, the bulk mod- temperature to ∼200 C in a furnace first while the sam- ulus K is determined from the equation K = C11 + 2C12/3 ple resistance is continuously monitored. At the point where and the shear modulus G from the relation G = 9C11 − the resistance of the sample reaches a minimum, the alkali- 2/5 C12/2C44: . All other elastic constants of the polycrystal metal end of the tube is cooled to room temperature and the material (Young’s modulus E, the longitudinal modulus CL, sample alone is annealed for several hours. Then the metal and the Poisson ratio ;) can be estimated from G and K end is reheated and the sample was further doped until a using the well-known relations between the elastic moduli of new resistivity minimum point is reached. The sample alone an isotropic medium. Isotropic moduli obtained from single- is then again annealed for several hours. This doping and crystal, compacted samples and polycrystal films are pre- annealing process is repeated until the resistance reaches an sented in Table 14. equilibrium state. A method similar to this is also applied to

obtain thin film M3C60 samples [575]. In order to obtain M3C60 samples with more certain chem- 4. C60-BASED MATERIALS ical compositions, two methods based on vapor transport 4.1. Intercalated Compounds are used. One is the azide technique, in which the metal azides (i.e., MN ,M= K, Rb) are used as the metal sources 4.1.1. Alkali Metal Doped C 3 60 [580–582]. A mixture of C60 powders and stoichiometric amounts of azides is loaded into a quartz tube and heated M3C60 (M = K, Rb, and Cs) When the alkali metals (M = slowly under dynamical vacuum. At 550 C for a couple K, Rb, and Cs) are doped in C60, stable crystalline phases of hours, the azide of any alkali metal decomposed into M1C60,M3C60,M4C60, and M6C60 are formed. The M3C60 free alkali metal and N , during which C is doped. After system is the most widely studied of the doped C60 com- 2 60 pounds because of the discovery of superconductivity [574]. completion of the reaction, the sample is cooled to room temperature and sealed to avoid exposure to air. In the K3C60 and Rb3C60 other method, stoichiometric control is markedly improved (i) Synthesis The usual way to produce M3C60 com- by reacting pristine C with the saturation-doped product pounds is the vapor transport technique which is most suit- 60 [577]. Two aliquots of C60 are weighed outside the drybox able for intercalation of heavy alkali metals into C60 lattice. first. A weighed amount of C60 is treated with a large excess A wide variety of methods based on this technique have of alkali metal at 225 C under vacuum to produce M C . been employed to prepare the samples with different crys- 6 60 The air-sensitive product is then diluted with the C60 in the talline forms (thin film [575], powder [576, 577], and single dry box. After heating and annealing under vacuum, the crystal [578, 579]). single-phase K C and Rb C are prepared. For preparing powder samples, the alkali metals are mea- 3 60 3 60 Metal fullerides can also be prepared in solution at low sured out using precision inner-diameter capillary tubes. The temperatures [583]. The solvents usually used are THF, liq- quantity of the metal is controlled by cutting an alkali metal- uid ammonia, or CS . The compounds are obtained by dis- filled capillary tube to the required length in a dry box. The 2 solving proportional molar amounts of the metal and the capillary tube is then placed in a 5–10 mm Pyrex (or quartz) C powder in the solvent and then heating at ∼300 Cto tube along with the C powders. Then the Pyrex (or quartz) 60 60 remove the solvents. tube is sealed under high vacuum and heated to a temper- (ii) Crystal structure In K C and Rb C compounds, ature of 200 to 450 C for several days. The alkali metals 3 60 3 60 the structure of K3C60 and Rb3C60 is still fcc although the lattice constants become larger than that of pristine C60. Table 14. Isotropic moduli obtained from different samples. Table 15summarizes some of the structural parameters of K3C60 and Rb3C60. K (GPa) G (GPa) E (GPa) CL (GPa) ; Sample M3C60 have a merohedral disorder which means the individual C molecules have two different possible orienta- 10 8 ± 0 754 85 ± 0 18 12 6 ± 0 4517 2 ± 0 450 306 ± 0 012 a 60 8 4 ± 0 53 75 ± 0 19 8 ± 0 413 4 ± 0 40 305 ± 0 02 b tions in the fcc lattice. Except this disorder, the symmetry 6 4 ± 0 54 1 ± 0 212± 113 3 ± 0 80 18 ± 0 04 c of the C60 molecule is not further reduced by the doping from C60 to M3C60. Vibrational properties have been studied Note: Sample a—Isotropic moduli of polycrystalline C , calculated from the 60 by Raman scattering [586–590] and IR spectroscopy in the values of the moduli Cij of a single crystal [568]; b—compacted samples powder [572]; c—polycrystalline films [573]. mid-IR and the far-IR spectral range [324, 591]. 436 C60-Based Materials

Table 15. Crystal structure and lattice constants of M3C60. effect of the intermolecular binding on the molecular geometry itself can be represented reasonably within LDA at any

Compounds K3C60 Rb3C60 level, the band structure depends more signiﬁcantly on the Cation position occupy all the available tetrahedral level of accuracy of the calculations. The band dispersion is and octahedral interstitial sites of also determined by the weak interaction between the chains, the host lattice which cannot be expected to be correctly described within Lattice constant (Å) 14 24 14 43 the LDA. PES and EELS were widely used to investigate the elec- Distance of C60–C60 (Å) 10 06 10 20 Distance of C–M (Å) 3 27 3 33 tronic structure of the C60 compounds [382, 607–618]. The 3 C (g/cm )1 93 2 16 metallic nature of M3C60 has been reported from PES stud- Ref. [236] [584, 585] ies [182, 610, 611, 619] as well as from conductivity measurements [620, 621]. The PES result indicated the metallic

(iii) Normal state properties ground state for K3C60 through a considerable density of states at the Fermi level and a clear Fermi cutoff in the spec- Electronic structure In M3C60, the alkali metal is tra [608, 609]. The C excitation spectrum results of K C expected to donate its electron to the t1u-derived conduction 1s 3 60 and C implied the half-filling of the t -derived band [622, band. Hence M3C60 is expected to be a metal, with a half- 60 1u 623]. The bandwidth observed for the half-filled t -derived filled t1u band. In the solid, molecular orbitals on neighbor- 1u ing molecular sites mix to form bands. The band structure conduction band is about 1.2 eV and is much larger than the band structure calculations [624]. A clue to the explana- and density of states for K3C60 using the LDA in DFT are tion of this observation can be gained from high resolution shown in Figure 32 [592, 593]; the electronic structure of C60 is also shown in the figure for comparison. PES studies of Rb3C60 and K3C60 [609, 610] at low temperature. PES profiles of M C calculated within a model [609, In the M3C60 solids (M = K, Rb), the C60 molecules have 3 60 binary (merohedral) orientational disorder, and the statisti- 625] showed that good agreement can be obtained by taking cal occupancy of the two molecular orientations remains dis- into account relatively strong coupling of the electronic sys- ordered even at low temperatures [236]. This disorder was tem to the molecular Ag and Hg vibrational modes, together predicted to have significant effects on the band structure of with an additional coupling to the charge carrier plasmon the materials [594], with a smearing out of the fine structure observed at about 0.5eV in the loss function. Electrical resistivity The electrical resistivity (C)of in the tlu-derived conduction band density of states (DOS), whose width remains unaffected by the disorder [595]. How- M3C60 was measured on various samples using different methods such as dc four-point measurement [578, 579, 626– ever, despite the disorder, the electronic states near EF are best described using an effective Bloch wave vector, and the 632] and other contactless techniques [627, 633–635]. Tem- states localizcd due to disorder lie only at the bottom or top perature dependences of the CT of single crystal K3C60 of the band [596]. and Rb3C60 have been measured under conditions of constant sample pressure [578, 579]. The measurement results The calculated t1u-derived bandwidth is ∼0.5eV for K 3C60 [597]. The LDA-DOS clearly supports a rigid-band picture. are typically metallic as the sharp drop of resistivity at Tc and CT varies as (a + bT 2. Results on pellets (pressed In this rigid band model, the band structure of MxC60 (M = from polycrystalline powders and subsequently annealed) alkali) remains roughly the same as that of pure C60, expect that the Fermi level is shifted due to the filling of elec- obtained with a contactless technique such as optical exci- trons donated by the alkali atoms [598]. Many other calcula- tation spectrum and microwave techniques also showed that CT varies as (a+bT 2 [627, 635]. Early CT measurement tions of the electronic properties of M3C60 were performed at different levels of accuracy [594, 599–606]. Whereas the for underdoped granular film showed that CT increases with decreasing temperature [626]. However, it has been confirmed with new measurements on crystalline films that

the transport properties of both K3C60 and Rb3C60 exhibit metallic behavior up to 500 K and a T 2-like dependence at temperatures from 50 to 250 K [631]. The granularity of the thin films is most probably the reason for the dis- crepancy. Although the electron–phonon (el–ph) scattering mechanism is expected to result in a linear temperature dependence of the resistivity, however, the T 2-like dependence behavior cannot be the evidence for other scattering mechanism because the volume of sample varies along with the temperature during the constant pressure measurements and this change will affect the temperature dependence of C significantly. The measurement of C vs T under conditions of constant sample volume can help to find the real scatter- Figure 32. Left: Hückel theory calculation of the molecular energy ing mechanism. A linear temperature dependence CT ∼ T on Rb3C60 was reported [630] and this linearity is consis- spectrum of neutral C60. Right: Band structure and density of states using the LDA formalism [592]. Adapted with permission from [593], tent with the picture that the scattering mechanism is simply C. H. Pennington and V. A. Stenger, Rev. Mod. Phys. 68, 855 (1996). of the electron–phonon type with a coupling constant Btr ∼ © 1996, American Physical Society. 0 65–0.80. Table 16 lists some values of C. C60-Based Materials 437

Table 16. Electrical resistivity of M3C60. Table 17. Tc and reduction gap of M3C60.

Property K3C60 Rb3C60 Ref. Property K3C60 Rb3C60 Ref.

C (transport, crystalline 0.12 m cm 0.23 m cm [579] Tc 19.5K 29.5K [636]

paraconductivity) 25/kB Tc (tunneling) 5 3 ± 0 25 2 ± 0 3 [647, 652] C (optical) 0.77 m cm 0.8 m cm [633, 634] 25/kB Tc (tunneling) — 2.0–4.0 [653]

C (microwave) 0.41 m cm — [627] 25/kB Tc (NMR) 3.0 4.1 [654] C (room-temperature, — 2.5m cm [630] 25/kB Tc (optical) 3.44 3.45[634]

ambient pressure) 25/kB Tc (tunneling and optical) — 4 2 ± 0 2 [650] 25/kB Tc ( SR) — 3 6 ± 0 3 [649] 25/kB Tc (photoemission) — 4.1 [651] (iv) Superconductivity T and superconductivity gap It is widely believed c ac susceptibility [660, 661], transport [626, 663], and radio that M C (M = K, Rb) are s-wave BCS-like supercon- 3 60 frequency (rf) absorption [662]. ductors, driven by the coupling to the intramolecular H g Early measurements were usually carried on powder sam- phonons and probably with some strong-coupling effects ples. Field-cooled curves from dc magnetization are first [636]. Transition temperature (T as a function of the lat- c used to obtain the temperature dependence of the upper tice constant a has been widely studied for M3C60 supercon- critical field [Hc2T ]. Measurements on powder K3C60 [659] ductors [272, 637–639]. In these studies the constant a was and Rb C [642] samples in this way both showed that the changed either by chemical substitution or by applied pres- 3 60 temperature dependence of Hc2 is linear at temperatures sure. It was found that Tc is increased by substituting Rb not far below Tc. Due to the experimental limitations of for K and the authors speculated that an elastic response of the magnetic field window (5–8 T in superconductivity quan- the lattice to the large ionic size of Rb would lead to a nar- tum interference device (SQUID) magnetometers), mea- rowing of the conduction band and a subsequent increase in surements of Hc2 by this method are usually performed at NEF which has the general effect of raising Tc [640]. temperatures close to the transition temperature. Therefore A linear relationship between Tc and pressure P was a large uncertainty will occur in the extrapolations of H T −1 c2 observed with dTc/dP =−6 3 ± 0 8KGPa performed up to T = 0 K which depend on the fitting scheme signifi- −1 to 0.6 GPa [641] and with dTc/dP = 7 8KGPa performed cantly. Using the standard theory of Werthamer–Helfand– up to 2 GPa respectively for K3C60 [637]. A similar result has Hohenberg (WHH) [664], the critical field extrapolated to −1 also been obtained in Rb3C60 with dTc/dP =−9 7 K GPa T = 0KisH 0 = 49 T for K C [659] and H 0 = 78 K [642]. The authors considered that applied pressure causes c2 3 60 c2 for Rb3C60 [642], respectively. band broadening, which leads to both a smaller NEF and Ac susceptibility [660, 661] and rf absorption [662] tech- a smaller Tc. nique measurements also show linear temperature depen- In the BCS theory for a system with only one type of dence of Hc2 near Tc. These two measurements can obtain ion with mass M, the transition temperature behaves as the data under high fields (the ac susceptibility technique − 12 Tc ∼ M , where = 0 5. The isotope effect when Cis can be performed up to 30 T [660, 661] and the rf absorp- 13 substituted by CinM3C60 has been investigated in order to tion technique can be performed up to 60 T [662]). There- establish the mechanism of superconductivity. Various val- fore the Hc2T curves can extend near 0 K and this will ues of were obtained by different groups [643–646] and reduce the uncertainty in the extrapolations of Hc2T to it was indicated that = 0 3 should be the best available 0 K. More accurate values of Hc2(0) are obtained in these experimental result [645, 646]. experiments (28 T for K3C60 and 40 T for Rb3C60 [660], 30– The superconductivity energy gap (5) was first measured 38 T for K3C60 [661], 38 T for K3C60, and 76 T for Rb3C60 by point-contact tunneling spectroscopy using a scanning [662]). Good agreements of the experimental Hc2T curves tunneling microscope [647], which gave a reduced energy with the WHH predictions are obtained [660, 662], demon- gap 25/kBTc = 5 3 for Rb3C60. NMR measurements were strating that this theory is successful in describing fullerene also performed to obtain 25/kBTc and were found to be superconductors. However, a result of an enhancement of in good agreement with the BCS value of 3.53 for the gap Hc2T compared to theory has also been found [661]. [648]. Moreover, the data has been obtained using other A likely mechanism proposed by the authors is the dirty- methods such as muon spin relaxation [649], optical meth- limit effect which showed that the high upper critical fields ods, [634, 650], and photoemission [651]. It is noted that the might partly result from a reduction of the mean free path by data obtained from different experiments show substantial different types of defects and the limitation of the mean free variation ranging from the BCS value of 3.53 up to about path could be the reason for the strong scatter of the exper-

4.2 (see Table 17). The value of the reduced gap that is imental data for Hc2(0) [661]. The magnetoresistance of substantially larger than the BCS value indicates that strong K3C60 samples with different granularity has been measured coupling effects are important. in fields up to 7.5T and showed that Hc2T is dependent Upper critical field and coherence length A large on the grain size of the K3C60 regions within the sample. number of experiments was performed to determine the dHc2T /dT varies from −2 18 to −2 8 T/K near the super- upper critical field for crystal [184, 578, 651, 655–657], pow- conducting transition temperature [663]. der [642, 658–663], and thin film [626] samples of M3C60 Upper critical fields in single-crystalline samples have using different techniques such as magnetication [642, 659], been obtained using various methods. All of these results 438 C60-Based Materials

showed a linear temperature dependence of Hc2 near Tc In the second method based on direct measurements of [655, 656, 665, 666]. The Hc2(0) has ﬁrst been estimated the reversible magnetization, the quantitative calculation is from transport measurements, with the results 17.5T for uncertain, especially in case of powder sample with a large

K3C60 [655] and 62 T for Rb3C60 [656], and later from dc distribution of grain sizes. Therefore a method based on magnetization measurements, with the results 28.5T for measurement of the trapped magnetization was used to eval-

K3C60 [665] and 43 T for Rb3C60 [666]. uate Hc1 [668]. This measurement was performed on powder A upturn of Hc2T at temperatures very close to Tc has and single crystalline K3C60 and Rb3C60 samples [665, 668]. been observed in almost all experiments on all supercon- Much smaller values of Hc1, which are about 1 mT at zero ducting compounds. Different authors suggested different temperature, were obtained in these studies. It is consid- 3− explanations for this effect and the best possible explanation ered that wave functions between adjacent C60 ions overlap [657] is that the upturn is a consequence of the anisotropy relatively weakly leading to the smallness of Hc1 [668]. of the Fermi surface of fullerene superconductors [599]. Using Ginzburg–Landau relations, the penetration depth B has been calculated and the value of the coherence length From Hc2(0), the coherence length H can be calculated using Ginzburg–Landau relations. Despite a large scatter used in the calculations was obtained from independent measurements. These values of B are listed in Table 19. (see Table 18) arising from the large scatter of Hc2(0), it is Moreover, the penetration depth has also been estimated clearly seen that the coherence length of M3C60 is very small (a few tens of nanometers) and comparable to the short H from muon spin resonance, with the results 480 nm for K C and 420 nm for Rb C [672, 673], from optical con- of high-Tc superconductors. 3 60 3 60 Lower critical field and penetration depth A large ductivity, with the result 800 nm for both K3C60 and Rb3C60 number of experiments were performed to determine the [674], and from NMR data, which give 600 nm for K3C60 lower critical field using various methods [642, 659, 665, and 460 nm for Rb3C60 [654]. 667–671]. Critical current density The critical current density (J in the M C system has been obtained from magne- Results on Hc1 for powder K3C60 [659] and Rb3C60 c 3 60 [642] samples were first obtained from a dc magnetization tization measurements by using Bean’s critical state model [675]. Based on this model, J is determined simply from method. In this method Hc1 was defined as the field at c which a deviation from linearity in MH first appeared. the dc magnetization curve by the equation Jc = AM+ − M /R. In the equation, A is a coefficient which is depen- The result show that the values of Hc1(0) lies in the range − dent on the sample geometry, M+ and M− denote the 10–16 mT and Hc1T follows the simple empirical formula 2 magnetization measured in increasing and decreasing fields Hc1T /Hc10 = 1 − T /Tc [642, 659]. However, different from the ideal superconductor, the at a certain magnetic field, and R is the sample radius [675, 676]. measurements of MH in K3C60 and Rb3C60 usually do not exhibit ideal linearity and only have a smooth posi- In the case of powders which can be approximated as a tive (even a negative) curvature. The deviation is so small collection of spheres, R is set by the average grain size which that it is very hard to get the point of first deviation from can be measured in various ways. Different values of Jc for such a curve. Therefore this method may not provide the M3C60 powders are obtained from magnetization measurements which showed substantial hysteresis up to high enough “intrinsic” values of the Hc1. Politis et al. [667] measured the reversible magnetization at high external fields and cal- fields (higher than 5T) [642, 659,677–679]. However, the values of J in the order of 1010 Am−2 indicate substantial culated H from Ginzburg–Landau relations. The value of c c1 flux pinning and high values of the critical current density. Hc1 obtained by this method is slightly smaller (9–11.4 mT at zero temperature) than the data obtained by the first For single crystalline samples, certain assumptions about the internal microstructure must be made to obtain R. J of method. c single crystal K3C60 and Rb3C60 obtained from magnetization measurements by using Bean’s critical state model [670] 7 −2 Table 18. Experimentally obtained Hc2(0) and H of M3C60. was of the order of 10 Am , that is, much smaller than 10 −2 the value of Jc for powdered samples (∼10 Am . K3C60 Rb3C60 The qualitative character of the temperature and mag- Samples Measurements H 0H(nm) H (0) H (nm) Ref. netic field dependence of Jc has been acquired. Jc shows a c2 c2 near logarithmic dependence on H and does not correspond Powder dc magnetization 49 T 2.6 — [659] Powder dc magnetization — 78 T 2 [642] Powder ac susceptibility 28 T 3.4 40 T 3 [660] Table 19. Experimentally obtained Hc1(0) and B of M3C60. Powder ac susceptibility 30–38 T 2.9–3.3 — [661] Powder rf absorption 38 T 3.1 76 T 2 4 [662] K3C60 Rb3C60 Single transport 17.5 T 4.5 — [655] Samples H 0B(nm) H (0) B (nm) Ref. crystal c2 c2 Single dc magnetization 28.5T 3.40 — [665] Powder 13.2 mT 240 — [659] crystal Powder — 12 ± 3 mT 247 [642] Single transport — 62 T 2 4 [656] Powder — 16.2 mT 215[669] crystal Powder — 9–11.4 mT 240–280 [667] Single dc magnetization — 43.0 T 2 77 [666] Single crystal 4.2 mT — 3.2 mT — [670] crystal Single crystal 1.2 mT 890 1.3 mT 850 [665, 668] Film transport 47 T — — [626] and powder C60-Based Materials 439

to a simple analytic functional form [670] in single crystalline (i) High temperature MC60 Above 400 K the XRD pat- K3C60 and Rb3C60 samples. The temperature dependence tern showed that MC60 has a fcc rocksalt structure in which of Jc was first found to follow the empirical equation Jc ∼ C60 molecules are orientationally disordered [690]. M ion 2 n Jc091 − T /Tc : , with n = 3–5[680] in Rb 3C60 pow- occupies an octahedral site in the fcc lattice (shown in ders. Subsequently, similar results for K3C60 [681, 682] and Fig. 33). This phase is nonmetallic. The lattice parameters Rb3C60 powders [681] were obtained with n = 1 3–5. This of MC60 are listed in Table 21. This phase is nonmetallic. temperature dependence was confirmed by measurements (ii) (MC60)n When the fcc MC60 is gradually cooled, new on single-crystalline K3C60 [657] and Rb3C60 [670]. The metallic polymeric phase forms [692–694]. Covalent bonding higher the magnetic field, the more rapidly Jc decreases with is formed between neighboring C60 ions and results in the increasing temperature. short interfullerene distance along the distorted orthorhom- Cs C Cs C cannot be synthesized by vapor transport bic a-axis (also shown in Fig. 33). The linkage is through a 3 60 3 60 92 + 2: cycloaddition [695]. Therefore MC phase exhibits reaction because of its thermodynamic instability above 60 ∼200 C which will cause the phase to segregate into the a quasi-one-dimensional polymer character as in the case in pristine C60 [693–697]. The (MC60n is used to denote this more stable CsC60 and Cs4C60. Stable Cs3C60 was synthesized in solution using liquid ammonia as solvent [683]. Raman phase. These polymer phases are stable in air, in contrast to the vast majority of fulleride salts which are extremely sen- measurement showed the Cs3C60 has a single sharp Ag mode centered at 1447 cm−1 with a linewidth of 11 cm−1 [683]. sitive in air [696]. Polymerization is reversible; heating the This indicated that all the fullerene molecules are in the 3− sample recovers the monomer fcc phase. XRD studies indi- state. X-ray diffraction data showed that the compound con- cated that (MC60n phase has a body-centred orthorhombic (bco) lattice with space group Pnnm. The lattice parameters sists of two phases: a body-center tetragonal (bct) Cs3C60 and an A15cubic Cs C . The lattice parameters are a = of (MC60n are listed in Table 21. 3 60 13 12 057 and c = 11 432 Å for the bct phase, and a = 11 77 Å C NMR spectroscopy gave the direct evidence for the 3 presence of sp hybridized carbon atoms in (MC60n [698, for the A15phase. It was reported that the Cs 3C60 had a Tc of 40 K under high pressure [683], but this result has not yet 699]. Another piece of direct spectroscopic identification of been reproduced. the intermolecular bridging C–C modes in (MC60n (M = Rb, Cs) has been achieved by neutron inelastic scattering M3−x Mx C60 Structures (M, M = K, Rb, Cs) A series measurements [700, 701]. A first-principles quantum molec- of ternary alkali doped C60 have been synthesized with ular dynamics model was developed [702] to describe the the general formulae of M3−xMxC60 [272, 684, 685]. All vibrational properties of polymerized fullerenes. Rigid ball– of these compounds are fcc structures. Most of these ball chain modes are predicted to occur in the energy range M3−xMxC60 compounds are superconductors. Table 20 lists 10–20 meV in good agreement with the measured low- some of these compounds as well as their structural param- temperature neutron spectra. eters and Tc’s. Only few DFT-based calculations have been performed M3−xMxC60 has merohedreal orientational disorder like on the (MC to obtain the band structures [703, 704]. M C . The relations of T and lattice constants in these 60 n 3 60 c (iii) Metastable structure MC60 Moreover, depending on compounds are similar to M3C60 (see Fig. 34). The overall the cooling rate from the high temperature rocksalt fcc trend is an increase in Tc with increasing lattice constant, phase, a variety of other metastable phases are encountered. which is interpreted in terms of a decrease in the LUMO- A medium quenching rate to just below room tempera- derived bandwidth and hence an enhancement of the Fermi ture leads to the stabilization of a low-symmetry insulating energy density of states NEF at constant band filling [272, structure which has been characterized by synchrotron XRD 639, 684–687]. − studies to comprise (C602 dimers, bridged by single C–C bonds [705, 706]. The RbC dimer phase crystallizes in Mx C60 (M = K, Rb, and Cs, x = 1, 4, 6) 60 the monoclinic space group P2 /a with lattice parameters MC MC can be synthesized by reacting an appropriate 1 60 60 a = 17 141 Å, b = 9 929 Å, c = 19 277 Å, and K = 124 4 at amount of pristine C with the saturation-doped product 60 220 K [706] and transforms back to the polymer phase on (M6C60 using the vapor transport technique [688–690]. The heating. Another metastable conducting phase of RbC60 and existence of a crystal phase with stoichiometric MC60 was CsC60 was reported with very rapid quenching by immers- first indicated by Raman [688], photoemission [691, 692], ing the high-T sample in liquid nitrogen [707]. In this case, and X-ray diffraction (XRD) [690] studies.

Table 20. Structural parameters and Tc of M3−xMxC60.

a M3−xMxC60 Dopant location a (Å) Tc (K) Ref.

KRb2C60 K(t)Rb(t)Rb(o) 14.243 23.0 [686] K1 5Rb1 5C60 K(t)K(o)Rb(t)Rb(o) 14.253 22.2 [272]

K2RbC60 K(t)K(t)Rb(o) 14.243 23.0 [686] K2CsC60 K(t)K(t)Cs(o) 14.292 24.0 RbCs2C60 Rb(t)Cs(t)Cs(o) 14.555 33.0

Rb2KC60 Rb(t)K(t)Rb(o) 14.323 27.0 Figure 33. The left: high-T fcc phase of MC ; the middle: bco polymer Rb2CsC60 Rb(t)Rb(t)Cs(o) 14.431 31.3 [272] 60 phase stabilized by slow cooling from the fcc phase. The thick lines a (o) = Octahedral site, (t) = tetrahedral site. represent polymer chains; right: the linkage of C60 in (MC60n. 440 C60-Based Materials

Table 21. Crystal structure and parameters for MxC60 x = 1, 4, 6). correlation and Jahn–Teller effects which may lead to a Mott insulator without a magnetic ground state. M C Crystal structure Lattice constants (Å) Ref. x 60 No superconductivity has been observed in M4C60 down to2K. KC60 fcc (rock salt) a = 14 07 [690] RbC fcc (rock salt) a = 14 08 60 M C The alkali metal-saturated compounds M C were CsC fcc (rock salt) a = 14 12 6 60 6 60 60 synthesized by a vapor transport technique [709]. Syn- (KC60n bco a = 9 11b = 9 95, [693, 694] chrotron XRD data indicated that the M6C60 compound has c = 14 32 a bcc structure and corresponds to the space group T 5 or (RbC bco a = 9 11b = 10 10, h 60 n Im3¯ [722]. In the M C structure, the alkali metal ions all c = 14 21 6 60 occupy equivalent distorted tetrahedral sites, which are sur- (CsC60n bco a = 9 10b = 10 21, c = 14 17 rounded by four C60 anions, two with adjacent pentagonal faces and two with adjacent hexagonal faces. NMR spectra K4C60 bct a = 11 867, [711] c = 10 765 of M6C60 are quite similar and in good agreement with the X-ray studies [723]. From the result it is apparent that the Rb4C60 bct a = 11 969, c = 11 017 C60 molecules are ordered at all temperatures. The structural parameters for M C are given in Table 21. Cs4C60 bct (orthorhom- a = 12 15b= 11 90, [710] 6 60 bic distorted) c = 11 45 M6C60 has completely filled electronic levels which results K6C60 bcc a = 11 38 [724, 725] in its observed insulating nature. No superconductivity was Rb C bcc a = 11 54 6 60 observed in M6C60. Cs6C60 bcc a = 11 79 Na and Li Doped C60 the 3D isotropic character of the structure is retained while Na Doped C60 orientational ordering of the C− ions leads to a simple cubic 60 (i) Nax C60 The NaxC60 compounds were synthesized by structure with a = 13 9671 Å at 4.5K. Upon heating, it a vapor transport technique [684]. All of the NaxC60 phases returns to the most stable polymer phase. except Na4C60 have intercalated fcc structures. In Na2C60, M C K C and Rb C were synthesized by a vapor the dopants fill the tetrahedral sites, leaving the octahedral 4 60 4 60 4 60 sites unoccupied [726]. In Na C , two Na ions occupy tetra- transport technique [584, 585, 708, 709]. XRD results 6 60 showed that they have a bct structure with a space group hedral sites and four Na atoms (not ions) go into octahedral sites [684]. It was reported that Na3C60 tends to phase sep- I4/mmm [709]. The early experiments suggested that Cs4C60 arate (disproportionate) into Na2C60 and Na6C60 [684, 727, is isostructural with K4C60 [584, 708]. Single phase Cs4C60, which has an orthorhombic distortion of the ideal bct struc- 728]. The small size of the Na atom also allows the inter- ture, was later synthesized by the low-temperature liquid calation of Na to high concentrations. The saturated phase is Na C in which Na atoms are located at the tetrahe- ammonia route [710]. Cs C is not as well studied as K C 10 60 4 60 4 60 dral and octahedral sites, and at the general point with frac- and Rb4C60 due to problems in stabilizing single phase tional occupancies [728]. Later a new Na4C60 polymer phase samples. The structure parameters for M4C60 are listed in Table 21. which has a body-centered monoclinic unit cell was identi- M C compounds have an insulating, nonmagnetic fied [729, 730]. Superconductivity has not been observed in 4 60 any Na–C binary compounds. The structural parameters ground state [620, 712] although their t -derived bands are 60 1u for Na C are listed in Table 22. only partly (2/3) filled, which would lead one to expect a x 60 (ii) Na MC M = Alkali, Cs Rb ,Hg The vacant metallic behavior within a one-electron description. Detailed 2 60 1−x x x octahedral site in Na2C60 allows this unique phase to act LDA calculations predict that M4C60 is a metal [713]; this indicated that the insulativity does not come from the gap as a host lattice for further intercalation of dopants into created by tetragonal symmetry split of the conduction band. the vacant octahedral site. The crystal structure and lattice Furthermore, electron paramagnetic resonance (EPR) [714], parameters of Na2MC60 are list in Table 23. NMR [715] and EELS [716] measurements imply that ori- Superconductivity was observed in Na2MC60 with M = K, entational disorder is not a key ingredient in the insulating Rb, Cs and Cs1−xRbx. The Tc-lattice parameter correlation behavior of the M4C60 phases. The scenarios proposed to explain this insulativity have included the suggestion of a Table 22. Crystal structure and parameters of NaxC60.

Mott–Hubbard ground state for M4C60 [471, 717, 718] and a description of these compounds as Jahn–Teller insulators Compound Lattice constant Group Ref. [719, 720]. ¯ Na2C60 a = 14 19 Å Pa3 [726] A systematic study of the optical conductivities of M4C60 ¯ Na3C60 T ≥ 250 K, a = 14 183 Å Fm3m [684] has provided strong evidence for a Mott–Hubbard ground T<250 K, unknown state of these compounds [716]. Low-temperature NMR low-symmetry structure showed the development of a Koringa-like term under Na4C60 T<500 K, a = 11 235Å, b = 11 719 Å, I2/m [729] pressure, indicating that a metal–insulator transition occurs c = 10 276 Å, K = 96 16 above 8 kPa [721]. Either a Mott insulator or a Jahn–Teller T>500 K, a = 11 731 Å, c = 11 438 Å I4/mmm [730] distortion is consistent with this NMR observation. It seems ¯ Na6C60 a = 14 38 Å Fm3m [684] that a complete understanding of the electronic properties ¯ Na10C60 a = 14 59Å Fm3m [728] of M4C60 requires a unique combination of both electron C60-Based Materials 441

Table 23. Structural properties and Tc ’s of Na2MC60. Table 24. Structural parameters of LixC60.

Na2MC60 Structural properties Ref. Compound Structural parameters Ref. ¯ Na2KC60 Pa3a= 14 025Å, Tc = 2 K [731] Li3C60 hexagonal, a = 9 840 Å, c = 16 10 Å [737] ¯ Li C hexagonal, a = 9 835Å, c = 16 16 Å Na2RbC60 fast cooling → Pa3a= 14 095Å, [732] 4 60 Li C hexagonal, a = 9 918 Å, c = 16 26 Å Tc = 3 5K 6 60 ¯ slow cooling → P21/a a = 13 711 Å, [733] Li12C60 Fm3m (T>553 K), a = 14 09 Å, no Tc [738] b = 14 544 Å, c = 9 373 Å, I4/mmm (T<553 K), a = 14 21 Å, c = 13 98 Å (at T = 293 K) K = 133 53 ,noTc ¯ Na2CsC60 Pa3a= 14 19 Å, Tc = 12 K [726] ¯ Na2RbxCs1−xC60 Pa3 for 0

Calcium intercalation into single-crystal C60 thin ﬁlms was studied with scanning tunneling microscopy and their real-

space images were obtained [757]. A model of the Ca5C60 structure was deduced in which octahedral sites of the fcc lattice are occupied by four Ca ions while one of the tetrahedral sites is filled. The other tetrahedral site is filled at higher concentration, but these later-filled sites are arranged in rectangular or triangular lattices so that their distances are maximized. Measurements of microwave loss, magnetic susceptibil-

ity, and Meissner effect ﬁrst showed that Ca5C60 becomes superconducting below 8.4 K [234]. The Tc for Ca5C60 follows the same relation between Tc and the C60–C60 separation found in the alkali–metal compounds. However, the

Table 25. Structural properties and Tc ’s of LixMC60.

¯ LixMC60 Structural and electronic properties Ref. Figure 34. Tc as a function of the lattice parameter a for the Fm3m ¯ (triangles, circles, and open squares) and Pa3 (ﬁlled squares) super- Li RbC Li(t)Li(t)Rb(o), a = 13 896 Å, no T [739] conductors. For K C and Rb C the lattice parameter was varied by 2 60 c 3 60 3 60 Li CsC Li(t)Li(t)Cs(o), a = 14 120 Å, T = 12 K [685, 740] changing the pressure, while for M M C (with M, M = K, Rb, Cs) 2 60 c x 3−x 60 Li CsC X-ray, no T for x<2 5and x>4 5 [741] the lattice parameter was varied by changing the composition. Adapted x 60 c x = 3 → Fm3mT = 10 5K with permission from [735], T. Yildirim et al., Solid State Commun. 93, c x = 4 → Fm3mT = 8 0K 269 (1995). © 1995, Elsevier Science. c 442 C60-Based Materials

Table 26. Structural parameters and Tc of ammoniated MxC60.

Synthesization Lattice

Compounds method Structure parameter (Å) Tc (K) Ref.

(NH3)K3C60 fco 14 971 × 14 895No Tc [742, 743] vapor ×13 687

(NH3)8K3C60 bct 12 15 × 15 7 [743]

NH3NaK2C60 fcc 4.36 8

NH3NaRb2C60 fcc 14.52 8.5

(NH3)xNaK2C60 x = 0 55 fcc 14.500 17 x= 0.60 liquid NH3 14.520 12 [744] x= 1.01 14.531 8.5

(NH3)xNaRb2C60 x = 0.67 14.350 13 x = 0.71 14.369 11 x = 1.06 14.400 8

(NH3)4Na2CsC60 vapor fcc 14.473 29.6 [745]

Note: Although (NH3)K3C60 exhibits no superconductivity at ambient pressure, superconductivity can be induced by hydrostatic pressure with an onset at 28 K.

pressure dependence of Tc of Ca5C60 is quite different. AEx C60 (AE = Ba, Sr) In contrast to calcium fullerides Schirber et al. [758] found that opposite to that observed in which are fcc at all compositions, BaxC60 and SxC60 only the alkali fullerides, the Tc of Ca5C60 increases with increas- exist in bcc-based structures at x = 3x= 4, and x = 6 [746– ing pressure. 749]. All of these compounds have been synthesized by solid Band calculations using the local density approximation phase reaction [746]. Their crystal structure and lattice con-

[752–754] showed that the t1u level is totally filled, while the stant are listed in Table 27. t1g level of C60 is half-filled. These half-filled t1g-hybridized No superconducting transition is observed down to 1.5K levels are the ones responsible for the conductivity and in Ba3C60 and Sr3C60 [763, 762]. Early investigations show superconductivity in Ca5C60. Experimental evidence for the that both of the Ba6C60 and Sr6C60 are superconductors, with transition temperatures of 7 and 4 K, respectively [746, 762]. partial filling of the t1g level comes from both photoemission spectra [755] and transport measurements [759, 760]. However, later studies indicate that AE4C60AE = Ba, Sr) is Electron energy loss [761] and inverse photoemission [755] the actual superconducting phase rather than AE6C60AE = Ba, Sr) as originally proposed [747–749]. In contrast to studies showed that the completely filled t1u band for x<3 Ca C , T of Ba C decreased with increasing pres- is below EF , giving nonmetallic character. 5 60 c 4 60 sure. High magnetic susceptibility measurements show that Ca C Studies by Ozdas et al. showed that Ca C is 275 60 2 75 60 AE6C60 phases are metallic, even though they are not super- the only stable phase for 1 8

The Ca2 75C60 phase is not superconducting down to 2 K differences in vapor pressures. This can be avoided by using under ambient pressure. Electron energy loss [761] and azides BaN6 and MN3 (M = alkali metal) as metal source. inverse photoemission [755] studies showed that the com- Direct reactions with BaN6 and MN3 yielded complicated pletely ﬁlled t1uband for x<3 is below EF , giving nometallic mixed phases [763]. Stable compounds were eventually syn- character. thesized by reacting BaN6 powder with the fcc M1C60 phase

Table 27. Structural parameters of AExC60 (AE = Ba and Sr, x = 3, 4, 6).

AExC60 (AE = Ba and Sr) Synthesis Crystal structure Lattice constant Ref.

AE3C60 Ba3C60 solid phase reaction simple cubic A1511.34 Å [763]

Sr3C60 fcc and A15coexis- 14.144 Å (fcc) [762] tence 11.140 Å (A15)

AE6C60 Ba6C60 body-centered cubic 11.171 Å [746]

Sr6C60 10.975Å [762]

AE4C60 Ba4C60 orthorbombic (bco) 11 25 × 11 69 × 10 90 Å [747, 748]

Sr4C60 — [749] C60-Based Materials 443 prepared by the azide decomposition method [582, 624,765– c = 27 87 Å [771]. Near-edge X-ray absorption measure- 767]. This process worked well for all MBa2C60 with M = K, ments show that all of the Yb cations are divalent, meaning Rb, or Cs. But the M BaC cannot be obtained following 2 60 that the average negative charge of the C60 anions is 5.5 the same process. However, starting from CsC60 ensuring [772, 773]. EXAFS and Raman measurements also reveal octahedral Cs and then adding BaN and AN together in 6 3 that the C60 anions are distorted in shape, despite their the second step yielded single-phase products MBaCsC60 for well-ordered local structure around the Yb cations [773]. M = Na or K, while phase separation occurred for M = Rb Yb2 75C60 becomes superconducting below 6 K. or Cs. X-ray diffraction and Raman scattering showed that these compounds are fcc with pentavalent and quadrivalent Sm Doped C60 The SmxC60 compounds have been synthesized by solid phase reactions [774]. The unit cell structure C60’s, respectively [768]. Table 28 lists the structural parameters of these compounds. of the nominal Sm3C60 phase is identified as orthorhombic No superconductivity was observed in these compounds (a = 28 17 Å, b = 28 07 Å, and c = 28 27 Å) derived from down to 0.5K [624]. Electron spin resonance (ESR) indi- the fcc M3C60 (M = Alkali metal) cell by doubling the cell 13 cated weakly metallic behavior [769]. C NMR indicated dimension in each direction, analogous to that of Yb2 75C60 strong dynamical disorder above room temperature, which [774]. However, the exact structure of the Sm3C60 phase is may be related to the anisotropic crystal field induced by still an open question. The quality of the diffraction data has cations of different valence [624, 770]. prevented a full structure determination. Sm3C60 is superconducting at Tc = 8 K [774]. M3−y My Ba3C60 M, M = K, Rb, Cs Samples of Temperature dependent resistivity measurements of M M Ba C were typically synthesized by intercalation 3−y y 3 60 SmxC60 samples have been reported. The results show that of alkali metals into preformed Ba3C60 [765–767]. XRD the resistivity decreases with increasing Sm concentration x for the samples show single phase bcc patterns with space [775, 776]. The temperature coefficient of resistivity is neg- group Im-3. Simulation of diffraction patterns indicates the ative for all compositions and the absolute value decreases random occupation of the interstitial sites by M and Ba. The with increasing x. lattice parameter in M3Ba3C60 is controllable by changing linearly with the alkali ionic radii. Moreover, by changing Eu Doped C60 EuxC60 compounds can be synthesized by either high-temperature solid state reaction [777, 778] or the y in KyRb3−yBa3C60, the lattice parameter can be tuned through the liquid ammonia route [779]. quasi-continuously between K3Ba3C60 and Rb3Ba3C60 [765]. The structural parameters of these compounds are listed in The EuxC60 prepared by ammonia route was found to be Table 29. amorphous by XRD [779]. Crystalline phases prepared by solid state reaction with the compositions of x ∼ 3 and 6 M3Ba3C60is a half-filled metal in which the Fermi energy exists at the center of the next lowest unoccupied molec- are stabilized [777, 778]. The structure of the x ∼ 3 phase is complicated. Experimental data show the coexistence of ular orbital with the t1g symmetry [767]. Superconductiv- a minor A15phase and a majority phase that has the same ity was observed in all compounds except for Cs3Ba3C60 in which superconductivity was absent down to 0.5K [765]. structure as Yb2 75C60. The Eu C phase has the same bcc structure of the satu- Tc decreased with increasing lattice parameter in M3Ba3C60 6 60 ration M C (M = alkali metal) compounds [777, 778]. The [765]. This Tc–lattice parameter correlation is in striking 6 60 experiments reveal the presence of both Eu2+ and Eu3+ ions. contrast with the positive correlation between Tc and the fcc Furthermore, it is found that at T = 65K ferromagnetic Eu cell parameter in M3C60 superconductors. pairs form through a superexchange mechanism via the C60 4.1.3. Rare-Earth and Lanthanide molecules [777].

Metal Doped C60 4.1.4. Halogen Intercalated C60 Yb275C60 Yb2 75C60 was successfully synthesized by solid phase reaction [771]. X-ray diffraction studies showed that I2 Intercalated C60 Iodine-doped C60 C60I4 was synthesized by vapor phase reaction of iodine with pure C under Yb2 75C60 has an orthorhombic unit cell with Pcab symme- 60 try and lattice constants of a = 27 87 Å, b = 27 98 Å, and helium gas of 10 Torr at 250 C for several days in evac- uated Pyrex tubes [780]. XRD results show than C60I4 has a simple hexagonal cell with a = 9 962 and c = 9 984 Å.

Table 28. Structural parameters and Tc of M3−xBaxC60 (0

Crystal Lattice

M3−xBaxC60 structure constant Atom position Tc Ref. Table 29. Structural parameters and Tc of M3−y My Ba3C60 (M, M = K, Rb, Cs) compounds. KBa2C60 fcc 14.173 Å K(o)Ba(t) no Tc [624] RbBa C fcc 14.185Å Rb(o)Ba(t) 2 60 Crystal Lattice Atom CsBa2C60 fcc 14.206 Å Cs(o)Ba(t) M3−y My Ba3C60 structure constant position Tc Ref. KbaCsC60 fcc 14.215Å Cs(o),K and Ba

randomly K3Ba3C60 bcc 11.24 Å Randomly 5.6 K [765] occupy (t) Rb3Ba3C60 bcc 11.34 Å occupy 1.9 K Cs Ba C bcc 11.47 Å no T Note: (o) = Octahedral site, (t) = tetrahedral site. 3 3 60 c 444 C60-Based Materials

between the host layers, as in a graphite intercalation com- Table 30. Synthesis and structural properties of gas intercalated C60. pound. The {111} planes of the fcc C60 become the {001} planes in the compound by relative shear motions which Structural transform the layer stacking sequence from ABCABC Compound Synthesis properties Ref. in fcc C60 to A/A/A/ in C60I4, where “/” denotes an (N C Powder and pellets sam- 0

I–I (in-plane) distance is 2.53 Å, which is close to the (O2)xC60 separately subjected to 0

interpreted in terms of a C-centered orthorhombic cell with C60 were separately gas at T ∼ [795] a = 17 33b = 9 99c = 9 97 Å, containing two formula subjected to hydrogen 260 K, nearly units. Iodine atoms were placed in sites slightly shifted from gas, at 750 atm for 5 h free quantum the centers of the trigonal prisms, with near-neighbor and at 323 K and soon was rotor at all T next-near-neighbor distances of 3.9 and 7.21 Å, respectively cooled below 150 K, thereby “freezing” the [781, 782]. interstitial H2 inside the Iodine intercalated C60 is nonmetallic and has a resistivity C lattice. at300Kof109 cm. In addition, no superconductivity is 60 (CH C The powdered C was 0

The species C60F36 have been reported by several groups [786, 787]. Complete ﬂuorination of C (C F has also 60 60 60 form triangular planes as in the case of graphite sheets and been reported [788]. A very high chlorine content has been the intercalants go between them. This is the case in sim- found in a photochlorinated fullerene sample which was ple systems such as C (P ,C (S . Larger organic and found to ﬁt the average formula C Cl [789]. Bromination 60 4 2 60 8 2 60 40 organometallic molecules, like benzene and ferrocene, can of C has also been observed in chemical reactions carried 60 also be intercalated to give C (C H and C (ferrocene) , out in the 25–55 C range. X-ray crystallographic evidence 60 6 6 4 60 2 respectively. In addition, reacting C60 with protonic acids, indicates the existence of C60Br6,C60Br8, and C60Br24 [790, Lewis acids SbCl5, AsF5, InCl3 [797–799] also produce dif- 791]. These X-ray studies showed that the attachment of Br ferent compounds. Table 31 lists some of these compounds is accomplished by placing Br at symmetrically bonding ver- and their structural parameters. tices of the C60 molecule. These Halogenated fullerenes can be used in substitution reactions to attach aromatic groups sequentially to the fullerene shell. Table 31. Structural parameters of larger species intercalated C60.

4.1.5. Molecules Intercalated C60 Compound Structural properties Ref. Intercalation of Gases into Solid C Various gases such 60 C60(P42 hexagonal, a = 10 084 Å, [800, 801] as H2,N2,H2O, CH4, CO, and O2 can be intercalated into c = 10 105Å solid C60. These neutral gas molecules can be intercalated C60(S82 monoclinic, a = 20 867 Å, [802] into the interstitial sites of the C60 lattice without drastically b = 21 062 Å, c = 10 508 Å, altering the host structure. The intercalants occupy octahe- K = 111 25, four formula per cell. dral sites of the C60 lattice and depress the C60’s fcc–sc tran- C (ferrocene) triclinic, a = 9 899 Å, [803] sition temperature (Tm. These compounds have possible 60 2 potential applications such as gas separation, sensors, hydro- b = 10 366 Å, c = 11 342 Å, gen storage, etc. Table 30 lists some of these compounds ' = 90 96 , K = 90 96 , = = 118 33 (at 143 K) along with a few structural properties. C60(AsF5)1 88 tetragonal (bct), a = 12 794 Å, c = [797, 798] 12 426 Å Intercalation of Larger Species into Solid C60 When C (C6H6) triclinic, a = 9 938 Å, [804, 805] the guest species are larger than the voids in the C60 solids, a 60 4 change in stacking of the fullerene molecules from cubic to b = 15 031 Å, c = 17 425Å, hexagonal usually occurs. Structures of these compounds are ' = 65 38 , K = 88 30 , = = 74 83 (at 104 K) different from C60. In most of these phases, C60 molecules C60-Based Materials 445

The TDAE intercalated C60 organic molecular system polymers has been observed [826]. But high purity 3D poly- raised much interest owing to its ferromagnetic-like phase mers with uniform structure have not been synthesized effi- transition at Tc = 16 K [552]. Furthermore, the TDAE- ciently. C material has the highest T of any molecular organic 60 c Other Polymerization Methods Polymerization of C ferromagnet [552]. An X-ray diffraction study first estab- 60 lished that TDAE-C is a stoichiometric material with a can also be accomplished by plasma treatments [827, 828], 60 ion bombardments at a low does [829], a low-energy elec- TDAE:C60 ratio of 1:1 [806]. The diffraction data were interpreted in terms of a centered monoclinic unit cell, a = tron injection from STM probe tips to C60 films [830], or 15 807 Å, b = 12 785Å, c = 9 859 Å, and K = 94 02 [806]. electron-beam bombardments from an electron gun [560]. The latter process has been successfully used for chlorine- based reactive ion beam etchng in electron beam lithography 4.2. Polymerized C 60 where a C60 film acts as a negative-type electon beam resist 4.2.1. Synthesis and Preparation mask [831]. Photopolymerization of C First evidence for polymer- 60 4.2.2. Structures and Phase Diagram ization [534] showed that oxygen-free thin films of C60 can be polymerized by the irradiation of intense visible or ultra- Structures voilet light with photon energies greater than the optical 1D Orthorhombic Phase The orthorhombic phase forms a absorbtion edge (∼1.7 eV) [534, 807]. Because of the strong one-dimensional linear molecular-chain structure along the light absorption of C , only films thinner than 0.1 m can be 60 110 direction of the original fcc phase (see Fig. 16a) [813, photopolymerized efficiently. The photopolymerized C no 60 833]. The smaller value (∼9.1–9.2 Å, compared to the value longer dissolves in many common organic solvents compared of 10.02 Å of prinstine C ) of the nearest-neighbor distance to pristine C . Dioxygen diffused into C films seem to be 60 60 60 observed by XRD experiment provides the evidence for a inhibitors during the photopolymerization process [534, 808] covalent bonding between the C cages. The space group and CCl can promote the process [809]. The photopoly- 60 4 has been identified as Pmnn, corrected from the earlier pro- merization process found to occur only in the fcc phase posed Immm space group [818, 834]. above 260 K, the orientational transition temperature of pristine C60 crystals [808], goes by the [2 + 2] cycloaddition 2D Tetragonal Phase The tetragonal phase forms a two- mechanism [534] with the double intramolecular bonds bro- dimensional tetragonal molecular-network layered structure ken and a four-atom ring formed by covalent C–C bonds via [2+2] cycloaddition in the (001) plane of the original fcc (i.e., accompanied with rehybridizations from sp2 to sp3). phase (see Fig. 16b) [813, 833]. The most recent study identi- Direct evidence for the covalent intermolecular bonds con- fied the “tetragonal” phase representing a pseudo-tetragonal firms the photopolymerization from laser desorption mass packing model with an orthorhombic space group Immm spectroscopy measurements [534, 810]. On heating above [823] although with a very small higher energy (4 kJ mol−1 ∼400 K polymerized C60 reverts to normal monomeric C60 [835] than another possible packing model with a truly by breaking up the intermolecular bonds and reforming the tetragonal space group P42/mmc. intramolecular bonds. Recent Raman [811] and atomic force microscopy studies [812] also suggested that two different 2D Rhombohedral Phase The rhombohedral phase forms photopolymerized states might exist. Photopolymerization at a two-dimensional hexagonal molecular-network layered temperatures above 350 K seems to produce mainly dimers, structure via 92 + 2: cycloaddition in the (111) plane of the while material polymerized at 320 K and below contains original fcc phase (see Fig. 16c) [813, 833]. The hexagonal layers are proposed to be stacked in a close-packed arrange- larger oligomers. The photopolymerization of C60 usually forms one-dimensional linear-chain structured polymers. ment of the type ABCABC with space group R3¯m [816]. There are three possible packing modes of the hexagonal Pressure-Induced Polymerization of C60 Pressure- layers proposed [835]; recent XRD studies confirmed most induced polymerization has been studied extensively under stable modes, which suggest a trigonal symmetry in individ- various temperatures and pressures in recent years [813]. ual layers but not a hexagonal one [818, 825]. Several polymerized fullerites have been synthesized from the fcc C60 by applying moderate pressures at elevated 3D Polymers and Superhard Phase The structure of 3D temperatures [814–816]. Three different phases possessing C60 polymers is still ambiguous due to the complex structure one- or two-dimensional C60–C60 networks have been identi- and bonding mechanism. There are several theoretically and fied: one-dimensional orthorhombic phase (O-phase) [816], experimentally suggested structures under nonhydrostatic or two-dimensional tetragonal phase (T-phase) [816], and two- hydrostatic compression and high temperature treatment dimensional rhombohedral phases (3R-phase, also called [836–839]. Recently one surperhard phase of 3D polymer

Rh-C60 [814–816]. Recently single crystals of these three treated under 13 GPa, 820 K has been characterized to structures have been successfully synthesized (O-phase [817, be a body-centered orthorhombic structure (space group 818], T-phase [819–823], and 3R-phase [824, 825]). The one- Immm), with 93 + 3: cycloaddition bonding between the 92 + dimensional and two-dimensional pressure-induced poly- 2: cycloaddition bonded tetragonal layers from a 2D polymerization of C60 goes by the same cycloaddition mechanism mer [826, 840]. of the photopolymerization. Figure 35gives the geometric structural diagrams of C 60 Under ultrahigh pressure and a higher temperature polymers. The crystallographic data from different authors

(∼13 GPa, 820 K), evidence for the existence of 3D for the 1D and 2D C60 polymers are listed in Table 32. 446 C60-Based Materials

of the icosahedral C60 due to its distortion and the formation of intermolecular bonds. The electronic structures of

1D and 2D C60 polymers have been studied theoretically using tight-binding calculation and LDA in the framework of the DFT.

From tight-binding calculation, a linear C60 chain has been found to be semiconductive with a ﬁnite band gap of 1.148 eV and almost pure s-type intermolecular bonding [843]. Assuming the weak van der Waals interlayer interaction in the rhombohedral and tetragonal polymers, a theoretical prediction on stability and conducting properties has been made according to the tight-binding calculation of a single layer [844]. Different numbers of intermolecular covalent bonds in the tetragonal and rhombohedral structures

Figure 35. Geometric structures of C60 polymers: (a) 1D C60 polymer were found to cause the distinction of bandgap values, which (orthorhombic phase), (b) 2D C60 polymer (tetragonal phase), (c) 2D were estimated to be 1.2 and 1.0 eV, respectively. The inves- C polymer (rhombohedral phase). 60 tigation of the electronic structure of the rhombohedral and tetragonal 2D C polymers has been carried out using the Phase Diagram There have been several tentative phase 60 LDA [845, 846]. These phases were found to be elemen- diagrams under pressure–temperature treatments of C60 presented in some of the literature [318, 813]. Since the tal semiconductors having indirect gaps of 0.35and 0.72 eV and three-dimensional electronic structures due to the short phase formation and purity of polymerized C60 depend strongly on the temperature and pressure as well as the time interlayer distance. Although the LDA generally underesti- of the treatment, those phase diagrams are still under dis- mates the energy gap, its value is consecutively reduced from the C to the rhombohedral phase, which correlates well cussion. The typical detailed conditions for the formation of 60 with the result of tight-binding calculations [844]. pressure-polymerized C60 have been reported as follows: 1D orthorhombic phase 1–1 2 GPa, 550–585 K, about 5 hours Recently, empirical tight-binding calculations showed that [318, 818]; 2D tetragonal phase: 2–2.5GPa, 700–873 K 0.5– all 1D and 2D polymers are semiconductors with the small- 4 hours [318, 822, 823]; 2D rhombohedral phase 5–6 GPa, est energy gap for the rhombohedral phase, and the greatest 773–873 K, 0.5–1 hours [318, 825]. It has also been reported energy stability for the 1D polymer [847]. that after a 1000 s treatment under conditions of temper- Energetics and Stabilities DSC study [848] showed that ature of ∼1.5GPa and pressure of ∼423 K, most of the all polymers are more stable than monomers because the pristine C will form dimer phase with a (C content of 60 60 2 stabilization energy decreases with increasing number of about 80 mol% [318] (to learn more about C donors. See 60 intermolecular bonds per molecule. Formation of polymer Section 5.2). bonds lowers the total energy [844]. The stability sequence of a distinct polymerized phase of C is dimer (C ) > 4.2.3. Electronic Structures and Energetics 60 120 1D polymer > 2D polymer > Pristine C60 (monomer). All Electronic Structures Polymerization of fullerene C60 polymers depolymerize into pristine C60 on heating to 300 C results in the narrowing of the HOMO–LUMO gap that is and the depolymerization reaction is endothermic, indicat- caused by the splitting of the degenerated molecular orbitals ing that the monomer form is the least stable phase [848].

Table 32. Crystallographic data for C60 polymers.

Polymer phase Space group a (Å) b (Å) c (Å) V (Å3,Z d (g/cm3 Ref.

Orthorhombic phase Immm 9.26 9.88 14.22 650 [816] Immm 9.29 9.81 14.08 641 [841] Pmnn 9.098 9.831 14.72 658 [834, 841, 842] Pmnn 9.14 9.90 14.66 663 [818] Tetragonal phase Immm 9.09 9.09 14.95618, 1 [816]

P42/mmc 9.097 9.097 15.04 1245, 2 1.92 (cal.) [819] 1.88 (exp.)

P42/mmc 9.097 9.097 15.02 622, 1 [834] P42/mmc 9.02 9.02 14.93 [822] Immm 9.026 9.083 15.077 1236, 2 1.936 (calcd.) [823] Rhombohedral phase R3¯m 9.19 — 24.50 597 [816] R3¯m (60) 9.204 — 24.61 602 [834] R3¯m (60) 9.175 — 24.568 1791.1,3 2.004 [825] 3D polymer Immm 8.67 8.81 12.60 2.48 (X-ray) [840] 2.5(exp.) Immm 8.69 8.74 12.71 2.43 (X-ray) 2.5(exp.) C60-Based Materials 447

Compared to the most stable phase, graphite, the energies decrease in intensity after being annealed at different high of diamond and C60, reckoned from the graphite level, are, temperatures [856]. respectively, 0.020 and 0.42 eV per carbon atom. The total The inverse transmission spectra for 1D and 2D polymers energy of distinct phases of C60 occur within a very narrow indicate that raising the polymerization temperature shifts energy range of about 0.01 eV per carbon atom and the the absorption edge to lower energies [857], showing that difference between the polymer and monomer forms of C60 the polymers are semiconductors with energy gaps Eg ∼ 1 4 is rather small [848]. and 1.1 eV which agree well with the theoretical calculations

for the orthorhombic and rhombohedral phases (Eg ∼ 1 2 4.2.4. Physical Properties and 1.0 eV, respectively) [844]. The Raman and infrared spectroscopies of polymerized Electrical Properties Generally, the conductivity of poly- has also been studied; the spectra are given as comparisons merized C increases with the polymerization degree and 60 with those of pristine C60 crystals in Section 2.2.2. depends on their structure and the ratio of the number of sp2 to sp3. Magnetic Properties Among all the 1D and 2D C60 poly- Field effect transistor investigations indicate that the 1D mers, the 2D rhombohedral polymer is the only phase known that shows ferromagnetic features such as saturation plasma-polymerized C60 acts as a p-type semiconductor in contradiction to the n-type semiconductor behavior of pris- magnetization, large hysteresis, and attachment to a small tine C [849]. The gas and photosensitivity of transport samarium–cobalt magnet at room temperature (shown in 60 Figure 36) [555]. The temperature dependences of the sat- properties of a C60 polymer thin ﬁlm are promising for a sensing device [849]. In addition, it is known that the alkali- uration and remanent magnetization indicate a remarkably high Curie temperature about 500 K higher than that of the metal doped (AC60n 1D polymer will formed spontaneously below 400 K from the monomer AC salts. It was found that other known organic ferromagnets [555, 858]. The discovery 60 of ferromagnetism in Rh-C has opened up the possibility (KC has metallic conductivity; (RbC and (CsC 60 60 n 60 n 60 n of a whole new family of magnetic fullerenes. are also conducting at high temperatures but have a metal– insulator transition at 50 and 40 K, respectively [850]. Elastic Properties Ultrasonic measurements have

2D C60 high-oriented C60 polymer shows a gigantic con- revealed that the elastic module of C60 polymer increases ductivity anisotropy. Conductivity in the polymerized planes with the polymerization degree which depends on the exhibits a metallic-like behavior and the out-of-plane one polymerization pressure and temperature [859]. Table 33 is semiconductor-like [851]. The anisotropy is temperature gives the elastic properties of C60 polymers compared to 3 6 dependent and lies in the range of 10 –10 . A randomly ori- pristine C60 and polycrystalline diamond [859]. Remarkably, ented polymer shows a semiconductor behavior and obeys the disordered 3D polymer and amorphous C60 synthesized the Arrhenius law [852]. The observed in-plane conductiv- at a temperature higher than the collapse temperature of ity has been explained by a theoretical calculation which C60 cages shows comparable and exceeding bulk moduli considered the formation of distinguishable intermolecular with diamond, respectively. bondings of 66/66, 56/66, and 56/65 models. The calculated It has been shown that amorphous C60 synthesized at results indicated that the occurrence of regions containing very high pressure and temperature (∼13 GPa, 1850 K) can 65/56 bonded molecules within a 66/66 connected hexago- scratch the diamond surface easily [860, 861], with hardness nal layer may cause variations of in-plane conductivity from exceeding that of diamond making the ultrahard C60 among a semiconducting behavior to a metallic behavior [853]. the hardest known materials. If a 2D polymer is formed at a temperature above the collapse temperature of the C molecular cages (about 60 4.3. Metal/C60 Composites 800 C), the conductivity increases intensively by four orders of magnitude [824]. For metals other than alkali or alkali earth ones, which have Both semimetallic, variable range hopping (VRH) and much higher cohesive energy, it is energetically unfavor- semiconducting behaviors have been observed in the elec- able for them to diffuse into the interstitial sites of the C60 trical resistivity measurement on samples with disordered structures synthesized from pure C60 at pressures in the range 8–12.5 GPa and temperatures of 900–1500 K [854]. Particularly, the temperature dependence of resistivity in a disordered crystalline 3D-polymerized C60 obtained after 9.5GPa and 900 K treatment ﬁts Mott’s VRH law C = 0 079exp1/T 1/4 − 1:cm in the range 270 K down to 5K for hopping conductivity [854].

Optical Properties Optical absorption and PL spectra of polymerized fullerenes have noticeably broader bands than those in pristine C60 [855], and the optical absorption ranges and PL peaks are shifted to the lower energies [522]. Oxygen-containing polymerized fullerene ﬁlms show strong photoluminescence in the near-IR and visible ranges (1.50– Figure 36. 2D rhombohedral polymerized C60 attached to a small 2.36 eV) at room temperature, and the photoluminescence samarium–cobalt magnet at room temperature. 448 C60-Based Materials

Table 33. Measured values of sound velocities and elastic moduli in 1D and 2D polymerized C60 samples.

p(GPa)/TC cL cT KG Structure Material (K) (g/cm3 (km/s) (km/s) (GPa) (GPa) (X-ray results)

Pristine C60 1 68 10 84 850 31 polycrystalline 1D polymer 8/500 1 756 03 70 30 24 0 19 orthorhombic 7 44 842400 14 2D polymer 8/900 1 96 84 1 4530 0 20 rhombohedral 7 44 25040 3D polymer 9.5/970 2 62 18 511 4 450 340 0 20 disordered (fcc + bcc)

Amorphous C60 13/1770 3 30 18 48 7 790 250 0 29 one halo Diamond 3 74 490 350 polycrystalline

Note: cL and cT are longitudinal and transverse sound velocities. K and G are bulk and shear elastic moduli; is Poisson ratio. Accuracy of ultrasonic measurements is ∼5% [859].

lattice and form a MxC60 compound similar to MxC60 alkali suggest that covalent bonding may play a major role in the fullerides [170, 862]. Therefore M/C60 composites (phase- interaction between Al/C60 as that reported by Maxwell et al. separated solids of M/C60) were obtained and investigated to [184]. study the metal–C interaction. The most common compos- 60 Cu/C Hebard et al. found that C covered on the sur- ites are multilayer films [863–865] and the nanodispersion 60 60 face of a Cu layer showed a metallic characteristic [863] films [865–871]. Both of them can be easily obtained by the and a similar result was also observed by STM research co-deposition method using metals and pure C60 (>99.9%) onaC60 layer covered upon the surface of a Cu substrate under high vacuum [865, 869]. [14]. Moreover, it was reported that the cover of C on In the M/C nanodispersion films, metal nanocrystallites 60 60 a layer of metal can effectively affect the conductivity of are well dispersed in the C60 polycrystalline matrix and the metal films [3, 15]. Cu/C60 nanodispersion films grown by a grains of M are very small [866–869]. The volume fraction co-deposition method were obtained and the structures were of the metal and the grain size of the metal particles can observed by TEM [869, 870, 874, 875]. The uniformly granu- be controlled by adjusting the deposition rates of C60 and lar microstructure and the small clusters or grains in Cu–C60 the metal, and the temperature of the substrate, respectively films might form a kind of doped fullerene nanostructure so [869]. that electrons could be transferred from metal atoms to the

surface layers of C60 at the interface [869]. 4.3.1. Al, Cu, Ag/C60 Composites The temperature dependence of the conductivities has been measured in-situ [874]. The linear relationship Al/C60 Al–C60 interaction was first studied in mutilayers [863]. In-situ resistivity measurements showed that the pres- ln/RT ∝ 1/T was observed when the temperature was lower than 250 K, and the relation ln/ ∝ 1/T 1/4 was ence of underlying layers of C60 reduced the critical thick- RT ness at which Al became conducting from ∼35to ∼20 Å observed for temperatures higher than 260 K. The values of −2 and there was a sudden increase in resistance that occurs conductivity of these films (typically in the range of 10 – 2 −1 when each Al layer was covered by a monolayer of C . 10 Scm are much higher than that of the pristine C60 60 −7 −1 A downward shift of 40 cm−1 in frequency of a considerably solid (∼10 Scm . The conduction of Cu/C60 interface compounds is dominated by the electrons hopping between broadened Raman-active Ag(2) pentagonal-pinch mode was observed. A charge transfer model in which up to six elec- the localized states [874]. A Raman backscattering spectra method was performed trons per C60 were transferred from the Al to the C60 layer on Cu/C60 as-grown films [869, 875]. The peak width of the across the planar Al–C60 interface was proposed to explain these experimental results [863]. pentagon-pinch mode [Ag(2)] becomes wider and the peak However, the PES and C 1s X-ray-absorption spectra of position shifts to the lower frequency as the atomic ratio C monolayers on Al(111) surfaces indicated that Al–C of Cu/C60 increases. The vibrational frequencies of the soft- 60 60 −1 bonding is covalent [184]. Therefore Raman spectra were ened modes are about 6 cm lower than that of the pristine mode so it can be inferred that about one electron is trans- measured on Al/C60 nanodispersion films in order to get ferred to C60. some insight into the Al–C60 interfacial interactions [868, 872]. The A (2) pentagon-pinch mode of C splits into two g 60 Ag/C60 Ag/C60 nanodispersion films have been prepared peaks, one pristine mode which still remains at 1468 cm−1, by the co-deposition method [866]. Linear relationships of and one softened mode with a shift of ∼6to9cm−1. The ln versus 1/T were observed in electrical conductivity presence of the pristine mode of C60 demonstrates that Al– measurement from ∼200 to ∼300 C and the conductivities C60 interaction is a localized interface effect. In addition, are in a range similar to those in Cu/C60 films [869]. The the shifts of the softened Ag(2) mode depend weakly on the shift of the soft Ag(2) mode in Raman spectra indicated that Al/C60 ratio and the microstructures of the films. The dis- about 1–1.5electrons are transferred from Ag to C 60. More- tinct relative increase in intensity of the Hg(7) and Hg(8) over, Although the peak positions of the Hg(7) and Hg(8) modes compared to Ag(2) mode has also been observed. modes are about the same as that of C60, the relative inten- This result as well as the local effect of Al–C60 interaction sities of them increase significantly in the Ag–C60 film and C60-Based Materials 449 this increase is difficult to interpret with the charge transfer graphite phase; the carbon interfacial phase is mainly com- model. A plausible explanation is that Ag atoms may dif- posed of fullerenes. fuse into the C60 lattice to form a limited dilute interstitial Out-of-plane hysteresis loops for the Co162C60 films show solid solution under high temperatures similar to the result that both the remanence and the coercivity increase sig- observed in the Al–C60 system [863]. The conductance of nificantly in the films. These values are comparable to discontinuous granular Ag films covered by C60 was mea- the promising perpendicular recording media, Co–Cr and sured in-situ during C60 covering [876]. An anomalous peak Co–CrTa [882]. These C60 comprising media have the poten- of conductivity was observed when the thickness of the C60 tial to achieve ultrahigh storage density because the C60 overlayer was around 1.6 nm. This result indicates that 1– molecules limit grain growth, reside at grain boundaries,

2 monolayer(s) of C60 covered upon the granular Ag films and reduce the magnetic coupling between grains which can are “metallic,” which is attributed to the charge transfer lower media noise [883]. between Ag and C60 [876]. The in-plane major hysteresis loops and the virgin mag- Charge transfer has also been observed in Ag deposited netization curve of the Fe73C60 film display a fast switching C60 films grown on the Si(111)-(7 × 7) surface by using scan- property, which suggests this material had the potential to ning tunneling microscopy [877]. It is found that for individ- be used in magnetic memory, magnetic switches, spin valves, ual Ag atoms and very small Ag clusters, the charge transfer magnetic springs, and other magnetic devices. The unifor- is inhibited or less effective, and there is no chemical bond- mity of the grains and distribution of C60 may contribute to ing between Ag and C60. Only after the Ag atoms aggregated this fast switching ability. to form Ag clusters larger than a critical size will the charge transfer will become effective. From the lateral size distribution of the Ag/C60 clusters, the critical size is concluded 5. LOW-DIMENSIONAL STRUCTURES to be no more than 4 nm. Furthermore, the results indicate 5.1. Heterofullerenes that the growth of the Ag/C60 clusters should be limited to sizes smaller than 10 nm. This self-limiting growth process 5.1.1. Introduction and the critical size effects provide a possible method to con- Heterofullerenes (“dopeyballs,” “heterohedral” fullerenes) trol the growth of metal clusters with a narrow distribution are fullerenes in which one or more carbon atoms in the size. cage structure are substituted by a noncarbon atom (i.e., a heteroatom). In this case, heterofullerene formation is 4.3.2. Magnetic-Metal/C Composites a kind of “on-ball” or “in-cage” doping of the fullerene 60 cage. First spectronscopic evidence for heterofullerenes was Ni/C60 Ni/C60 granular films were also prepared by the observed in gas phase of heterofullerene ions produced co-deposition method [878]. High-resolution transmission by laser vaporization of a graphite pellet containing boron electron microscopy (HRTEM) results show that Ni nano- nitride powder [884]. particles are well isolated and embedded in an amor- Through modification of the cage structure of hetero- phous C60 matrix in the films. Raman spectra indicated fullerene, significant modification of geometry, chemical that the charge transferred to each C60 molecule in functionality, and electronic character of the fullerenes an N(Ni):N(C60 = 30 film is ∼4 electrons, and that in would occur. So it was anticipated that these hetero- N(Ni):N(C60 = 1 5and 6 films are ∼2 electrons. The fullerenes should exhibit a variety of properties and lead to charges transferred from Ni to C60 reduce when the Ni nano- formations of various derivatives due to the in-cage intro- particles become smaller (the average sizes of Ni particles in duction of guest atoms. N(Ni):N(C60 = 1 5, 6, and 30 films are 2.6, 3.3, and 6.6 nm, respectively). This is attributed to the quantum size effects 5.1.2. C N/(C N) of Ni nanoparticles [878]. 59 59 2 Measurements of the surface magneto-optical Kerr effect The aza[60]fullerene C59N is formed by substituting a nitrogen atom for a carbon atom in the C cage structure. Neu- show that the coercivities (HC of Ni/C60 films are enhanced 60 significantly. In other words, the critical size of superpara- tral C59N is an open shell molecule due to the trivalency of magnetic transition (3.3 nm) is much smaller compared to nitrogen leaving a “dangling bond” on an adjacent carbon Ni nanoparticles embedded in graphite (13.6 nm) [879] or atom in the cage (see Fig. 37a). Aza[60]fullerene in the first oxidized state is sometimes called aza[60]fulleronium, for SiO2 matrix [880]. It was suggested that the enhancement of which one resonance structure is shown in Figure 37b. C N HC may be attributed to surface spin disorder of Ni parti- 59 cles induced by the strong interfacial interaction between Ni radical is highly reactive and it easily bonds to form (C59N)2 dimer, the most stable form of azafullerene (see Figure 38), and C60. or is hydrogenized to form hydroazafullerene C59NH. Fe, Co/C60 Unlike the C60 based materials we discussed, Synthesis Up to now, the azafullerenes are the only Fe, Co/C60 composite films obtained by adding C60 as a minor component into Fe, Co matrix have also been investigated known heterofullerenes which can be isolated as pure [881]. The concentrations of the as-deposited thin films were substances. Nitrogen-doped fullerenes can be synthesized basically by expressed in a formula of BxC60 (M = Fe, Co). TEM images showed that the grains are extremely uniform in the film. vaporization of graphite in nitrogen containing atmosphere Raman spectroscopy shows that most of the fullerenes are [885, 886] or by laser ablation of fullerene derivatives which stable in the films and the electronic diffraction shows no possess organic ligands bound to the carbon cage through 450 C60-Based Materials

− unusually low g value of C60 can be explained in terms of Jahn–Teller distortion that splits the triply degenerate t1u states, thus leading to quenching of angular momentum. Electronic Properties Based upon the extended SSH

model for C59N, the calculated results are very consistent with those from the SCF-MO method. The lattice structure

of C59N is different from that of pure C60 due to effects of the dopant ion, but the deformations of the substituted

fullerene cage for the C59N are mainly limited in the vicinity Figure 37. Important resonance structures of (a) aza[60]fullerene radi- of the dopant ions [895]. As one electon is doped into the cal and (b) aza[60]fulleronium. LUMO of C60 in C59N, it was changed so significantly that the energy level near the Fermi level and the correspond- a nitrogen atom [887], or by condensed-phase organic syn- ing smaller bandgap between HOMO and LUMO was about thesis. But the latter which yields aza[60]fullerene dimer is 0.3 eV [895, 896]. The calculated gap was much smaller proved to be the only efficient method leading to the isola- than that for C60. The HOMO states are mainly localized tion of macroscopic quantities of azafullerenes so far. There on the N–C double bonds and the excessive electron density are two different methods succeeding organic synthesis. is concentrated on the impurity sites. The excessive electron In 1995it was found to occur by the effective forma- density of the N atom is 0.27, which implies that electronic tion of azafulleronium C59N+ in the gas phase during charge accumulates on the doped N site and the N atom fast atom bombardment mass spectrometry of a cluster exists as an acceptor [895]. opened N -methoxyethoxy methyl ketolactam, so Humme- The electronic properties of (C59N)2 in thin films have len et al. applied this process in solution in the presence been studied by using PES and EELS [897, 898]. It was found that the HOMO of (C N) is located mainly on N of strong acid and isolated C59N as its dimer (C59N)2 [888]. 59 2 In 1996, Grösser et al. succeeded in converting a bisaza- atoms and the intermolecular C–C bond. In contrast, the LUMO has mainly a C-character. The optical gap of the homofullerene [889] to the aza[60]fullerene dimer (C59N)2 in a different way [890]. By both these methods high-purity dimer is ∼1.4 eV, some 0.4 eV smaller than that of C60 (1.7– 1.8 eV). It was obtained from the energy-loss functions that (C59N)2 samples can be obtained after high performance liquid chromatography (HPLC) purification. the static dielectric constant #1(0) of (C59N)2 is about 5.6, which is larger than that of C60 [#10 ∼ 4], reflecting the Properties smaller energy gap of the heterofullerene dimer. Structure Properties It was found that the C dimer is 59 Properties of (C59N)2 Solid Solid structural investiga- formed by linking two cages in a trans-configuration by one tion of (C59N)2 using X-ray powder diffraction techniques single bond to minimize the repulsion of the nitrogen atoms showed that samples of (C59N)2 obtained by recrystalliza- and to optimize the whole structure (see Fig. 38). The link tion from CS2 exhibit a hexagonal structure (space group is made by the two carbon atoms (C, C) each of which P63/mmc or a subgroup). The hexagonal phase remains joins two hexagons together with the N atom in a C59N stable under hydrostatic compression to 22 GPa, signify- molecule. The molecule has C symmetry. The C–C dimer 2h ing it is somewhat less compressible than pristine C60 [899]. bond was calculated to be 1.609 Å, (i.e., 0.05Å longer than The diffraction patterns point to a CS2 content of about 3 that between two average sp cabon atoms) [891]. The bind- 1/2 molecule per formula unit. The CS2 can be removed by ing energy was calculated to be ∼18 kcal mol−1 [891]. sublimation of the material in vacuo at temperatures of 500– The bonding energy is relatively low and the dimer can be 600 C. This leads to a monoclinic structure with the space

cleaved both thermally and photochemically into two C59N group of at most probably C2/m, where the C59N dimers sit radicals [892]. Light-induced ESR measurement of a solu- on the sites of a monoclinic c-centered Bravais lattice with

tion of (C59N)2 in 1-chloronaphthalene, using 532 nm laser lattice parameters a = 17 25Å, b = 9 96 Å, c = 19 45Å, pulses, yielded a spectrum with three equidistant lines of and K = 124 32 , T = 295K [900]. (C 59N)2 are observed to equal intensity, indicative of 14N hyperfine interaction [893]. be unstable at temperatures higher than 200 C in UHV. The hyperfine coupling constant is 3.73 G. The reported values for the g factor of C59N are 2.0011(1) and 2.0013(2), 5.1.3. Other Heterofullerenes higher than that of C radical anion, 1.9991 [894]. This 60 Borafullerenes Borafullerenes were the first reported heterofullerenes observed in 1991 [884]. In 1996, the macroscopic preparation of borafullerenes was realized by using the arc-evaporation method on graphite rods doped with either boron nitride, boron carbide, or boron [901]. Extrac- tion and enrichment were used for the heterofullerene content of the soot, involving pyridine extraction and subse-

quent treatments of the extract with CS2 and pyridine. XPS spectra of the extract showed a peak at 188.8 eV that was

assigned to boron (1s level) in borafullerene (C59B mainly). The extracted materials appeared to be moisture sensitive,

Figure 38. Schematic 3D structure for a (C59N)2 molecule. leading to the formation of boron oxide or boric acid [901]. C60-Based Materials 451

+ −1 There is another method to synthesize borafullerene by C59O ions in gas-phase experiments [914] or C59O anions high-temperature laser ablation of a B4C-graphite compos- produced via collision-induced dissociation of oxy-fullerene − ite rod under an argon atmosphere. The product was ana- anions C60O2−4 [915]. lyzed with a laser desorption/ionization mass spectrometer, Evidence for the existence of C59P has been identified in revealing that C59B(m/z = 719) was formed together with mass spectroscopy. The formation of these heterofullerenes the C60 molecule [902]. was achieved by evaporating phosphorus and carbon simul- Azafullerenes with Multinitrogen Atoms The synthe- taneously but at different positions in a radio frequency fur- sis of C N is possibly complicated if the formations of nace (i.e., at different temperatures) [916]. 58 2 Existence of substitutionally doped fullerenes C M has the two N sites are not simultaneous, which may cause an 59 also been identified by mass-spectrometric evidence, where open shell intermediate as found in the synthesis of (C59N)2, giving rise to an undesired reaction route. Synthetic route M represents the atom of the transition metals such as Fe, Co, Ni, Rh, and Ir. These in-cage doped fullerenes were toward C58N2 starting from C60 [903] has been proposed; recently, (1,3,5)pyridinophanes having [4.3.2]propellatriene produced by the photofragmentation of precursor metal– units were synthesized as precursors to macrocyclic polyyne fullerene clusters C60Mx [917] − C58H4N2 and diazafullerene anion C58N2 was detected in the laser desorption mass spectrum of the pyridinophanes 5.2. C120 (C60 Dimer) [904]. Since the discovery of the photopolymerization of C via A new fullerene-like material, consisting of cross-linked 60 nano-onions of C and N, was reported [905]. Growth of the 92 + 2: cycloaddition [534, 807], there have been a lot of theoretical studies [918–924] on the smallest subunit of a C onion shells takes place atom by atom on a substrate surface 60 polymer: C (C dimer), a dumb-bell-shaped all-carbon and yields thin solid films during magnetron sputter deposi- 120 60 molecule polymerized from two individual C molecules tion. The N content in the onions, up to 20%, is the highest 60 (see Fig. 39). The most stable isomer of C is confirmed measured for an azafullerene in the solid phase. Total energy 120 to be polymerized via the same 92 + 2: cycloaddition mecha- calculations of C60−2nN2n molecules suggest the existence of a novel C N molecule. nism of C60 polymers (i.e., the double intramolecular bonds 48 12 broken and a four-atom ring formed by covalent C–C bonds, 2 3 Azaborafullerenes Recently, it was reported that C58BN accompanied with rehybridizations from sp to sp ). can be produced by a BN substitution reaction of fullerene C upon irradiation by a KrF excimer laser at room temper- 60 5.2.1. Synthesis ature [906] and isolated by HPLC. Mass spectra and X-ray photoelectron spectroscopy analysis confirmed the substi- C120 can be synthesized by many methods, such as pho- tuted formation of C BN (m/z = 721). topolymerization [534, 808], solid-state mechanochemical 58 reaction [925–927], quasihydrostatic compression of C Heterofullerenes with Heteroatoms Other than N, B 60 [928], and squeezing of a C60 compound [929]. Early theoretical calculation of Si in-cage doped hetero- The photopolymerization method gave the first evidence fullerenes (C59Si, 1,2-, 1,6-, and 1,60-C58Si2 predicted that for the existences of C dimer and polymer [534, 808]. It was these structures are stable and show a steady decrease of 60 observed that solid C60 exposed to visible or ultraviolet light the bandgaps with an increasing number of Si atoms [907]. forms a polymerized phase which is no longer soluble in First evidence for the possible existence of silicon het- toluene. erofullerenes is provided by analyzing the products from The solid state mechanochemical reaction of C60 with pulsed-laser vaporization of silicon–carbon composite rods KCN by the use of a high-speed vibration milling (HSVM) by time-of-flight mass spectrometry (TOF-MS) [908], which technique is the first efficient method to synthesize bulk + showed small peaks that would match the masses of SiCn C120 [925, 926]. In a standard procedure, a mixture of C60 clusters (61 ≥ n ≥ 56). Recently, silicon heterofullerenes and 20 molar equivalents is placed in a capsule and vig- have been synthesized in a laser vaporization source from orously vibrated under HSVM conditions for 30 min in a targets processed as mixtures of graphite and silicon pow- glovebox filled with nitrogen. Separation of the reaction ders [909] or SixC1−x mixed composition targets [910, 911]. mixture by flash chromatography on silica gel, eluted with Another method to generate silicon in-cage doped fullerenes hexane/toluene and then with toluene/o-dichlorobenzene is laser-induced photofragmentation of parent clusters of (ODCB), gives 70% of recovered C and 18% of C [925, composition C Si which are produced in a low pressure 60 120 60 x 926]. It was found that this reaction can take place effi- condensation cell, through the mixing of silicon vapor with ciently also by the use of potassium salts such as K2CO3 a vapor containing C60 molecules [912]. It was indicated from the analysis of photofragmentation mass spectra that at least three Si atoms can be incorporated in fullerenes, the Si atoms are located close to each other in fullerenes, and Si doping was also predicted to increase the fullerene chemical reactivity [911]. Ab initio calculation of optimized geometrical structures of C59Si and C58Si2 isomers showed that the geometrical modifications of the heterofullerenes occur in the vicinity of the Si dopant atom [913]. In the case of oxygen, there is some possible evidence for the existence of O heterofullerenes in the form of Figure 39. Schematic 3D structure for a C120 (C60 dimer) molecule. 452 C60-Based Materials

and CH3CO2K which contain nucleophilic anions, metals 5.2.4. Properties such as Li, Na, K, Mg, Al, and Zn (while Ni and Cu are Far-infrared vibrational property investigation of the C not effective), and organic bases such as 4-(dimethylamino)- 60 dimer showed that all the modes are nondegenerate. Hg(1)- and 4-aminopyridine [925, 927]. Single crystals of C120 can derived modes are allowed in the dimer and appear as a grown in an ODCB solution since it is hardly soluble in most −1 weak quadruplet near 250 cm [933]. The number of T3u(1)- common organic solvents but has a reasonable solubility in derived modes is three, in agreement with group-theory pre- ODCB [925, 926]. dictions for the D2h symmetry of the dimer. The quasihydrostatic compression method for the dimer- In room-temperature solution, a systematic study of the ization of C60 is achieved under a high-pressure, high- photophysical properties and nonlinear absorptive optical temperature treatment [928, 930, 931]. It was shown that the limiting responses of the C60 dimer was given [934]. It was dimerization occurs even at room temperature in the entire found that the absorption, fluorescence (spectrum, quantum pressure range above ∼1.0 GPa. However, the formation of yield, lifetime), and photoinduced electron-transfer proper- a dimer phase as a stable modification is at least at temper- ties of the C60 dimer are somewhat different from those of atures above 400 K. No condition was found that may yield C60 but qualitatively similar to those of other C60 derivatives, pure C60 dimers so far. A typical condition with the pres- indicating that the dimer may be considered as a pair of sure, temperature, and treatment time of 1.5GPa, 423 K, 1,2-functionalized C60 derivatives. The triplet–triplet absorp- and 1000 s yields about 80% C dimers [930]. 60 tion of the C60 dimer is noticeably weaker than those of Squeezing of a C compound was reported to be a high 60 C60 and other C60 derivatives, corresponding to lower opti- yield selective synthesis method of C dimers [929]. Squeez- 60 cal limiting responses of the C60 dimer at 532 nm. It was ing the organic molecular compound crystal (ET) C [ET = 2 60 also concluded that the C60 dimer is photochemically sta- bis(ethylenedithio)tetrathiafulvalene] at 5GPa and 200 C ble since there is no meaningful change in both absorption followed by removing unreacted ET molecules by sonication and fluorescence spectra of the dimer solution after 10 h of in CH2Cl2 produces C60 dimers, with a yield of about 80%. continuous photoirradiation. Most of the product is soluble in o-dichlorobenzene, while The thermal behavior of the C60 dimer was investigated there remains a small amount of insoluble material, which in the range 80–220 C at a rate of 1 C min−1 using dif- may be one-dimensional oligomers or ladder polymers. ferential scanning calorimetry [925]. An endothermic peak from 150 to 175 C and centered at 162 C was found in the heating process, while no such peak was observed in the 5.2.2. Structure cooling scan. It was also found that the C60 dimer could dis- The isolated C forms a dark brown powder. The 13C NMR 120 sociate quantitatively into C60 by heating its ODCB solution spectrum exhibited 15signals (including one overlapped sig- at 175 C for 15min. C 120 should have equal chemical reac- nal) in the sp2 region and one signal at 76.22 ppm in the sp3 tivity to C60 considering their close reduction potentials. region, which are fully consistent with the assigned structure

with D2h symmetry [925]. It was also indicated that C120 is indeed the essential subunit of these polymers by comparing 5.3. Endohedral C60 the data with the 13C NMR spectra of C polymers. 60 Endohedral fullerenes are novel forms of fullerene-based The single crystal structure was determined by X-ray crys- materials in which the fullerenes are encapsulated by tallography; it was found that there is no obvious difference atom(s) (even some small molecules) in their inner hol- in the length of the four bonds in the 92 + 2: cycloaddition low space (see Fig. 40). These new fullerene derivatives are four-atom ring. The intracage bond length was determined usually described using the symbol “@” conventionally and to be 1.575(7) Å, and intercage bond length was found to be conveniently with the encaged atom(s) listed to the left of 1.581(7) Å [925]. In single crystals grown in an ODCB solu- the “@” symbol. For example, a C60-encaged metal species tion, the C120 molecules are arrayed in highly order layers, (M) is written as M@C60 [935]. In recent years endohedral which is different from the face-centered cubic structure of fullerenes have attracted a lot of interest due to their fasci- C [925]. 60 nating properties and novel electronic structures.

5.2.3. Electronic Structure

The lowered symmetry of the C120 as a consequence of dimerization molecule will result in an increased splitting of energy levels and a narrowing of the optical bandgap [920]. The presence of sp3 intermolecular bonds and the caused distortion of the C120 molecule also change its electronic structure. The electronic DOS conﬁrms universal expectations about the electronic and vibrational energy levels. Due to the dimerization of C60, the LUMO t1u states split into a quasi- doublet and singlet state but the HOMO hu state mixes strongly with the lower gg and hg levels leading to a gener- Figure 40. Schematic 3D structure for an endohedral fullerene ally broader DOS [932]. molecule. C60-Based Materials 453

5.3.1. M@C60,M= Metal 5.3.3. X@C60,X= Noble Gases

The first evidence for endohedral metallofullerenes based Noble gas atoms can also be trapped in C60 cages. In fact, on C60 (M@C60 was proposed from a magic number due to the C60 molecule cage is large enough to enclose all of the LaC60 in a mass spectrum prepared by laser vaporization of noble gases including helium, neon (Ne), argon (Ar), kryp- ton (Kr), and xenon (Xe) [952, 953]. a LaCl2-impregnated graphite rod [936]. Further evidence + The noble-gas endohedral fullerenes are usually prepared showing that the La C60 ions did not react with H2,O2, No, by treating the fullerene with the gas under high tem- and NH3 confirmed that the active metal atoms are indeed perature and pressure [952, 953]. Treatment at ∼650 C encapsulated inside the C60 cage [937]. and ∼3000 atm yields a C /X@C (X = He, Ne, Ar, Original soot containing M@C60 (M = Y, Ba, La, Ce, 60 60 Pr, Nd, Gd, Er, Eu, and Dy) is usually produced by arc- Kr, Xe) mixture with the ratio of encapsulated to empty fullerenes only on the order of 10−3. Recently, remark- discharge-heating of an MxOy/graphite (MxOy = Y2O3, able enrichment of Ar@C60 (with a purity of 40%) [954], BaO, La2O3, CeO2,Pr6O11,Nd2O3,Gd2O3, Er, and Eu2O3 composite rod under a 50–100 Torr He atmosphere [938– Xe@C60 (with a purity of 31%) [955], and Kr@C60 sam- 941]. But the extraction of M@C from the soot is diffi- ples [956] with a purity as high as 90% has been realized by 60 HPLC using a semipreparative PYE[2-(1-pyrenyl)ethylsilyl] cult because of almost all known M@C60 so far showing high reactivity and they are insoluble and unstable in nor- column (10 × 250 mm) with toluene as the eluent [957]. mal fullerene solvents such as toluene and carbon disulfide The fact that noble gases with smaller masses do not interact significantly [952, 953] (the interaction is suggested (CS . Ca@C has been extracted by pyridine or aniline 2 60 to be van der Waals force mainly) with the inner parts of [942], M@C (M = Y, Ba, La, Ce, Pr, Nd, Gd, and Sr) can 60 -orbitals of the C cage implies that the chemical and be extracted by aniline [943], and Li@C prepared by an 60 60 physical properties of these compounds will not differ much ion implantation technique can be extracted by CS [942, 2 from those of empty C molecules. But 129Xe NMR spec- 943]. 60 troscopy study shows that in the case of Xe, the 5p elec- Pure samples of Eu@C , Er@C , and Dy@C have 60 60 60 trons of the Xe are much closer to and interact much more obtained by combining sublimation and HPLC with ani- strongly with the -electrons of the C [955]. line as an eluent [939–941]. The X-ray-absorption near edge 60 structure spectrum showed that the valence of Eu atom in 5.4. C M Eu@C60 was +2 [939], while the Raman spectrum indicated 60 n that the valence of Dy atom in Dy@C is +3 [941] with 3 60 The exohedral metal complexes of C60, usually written as electrons transfering from the Dy atom to the C cage. It 60 C60Mn, where M is the metal species, can be categorized as has also been indicated that the Dy in Dy@C is located 60 the third type of C60 complex compared to the hetero- and at an off-center position 1.25–1.30 Å from the center of the endohedral fullerenes (see Fig. 41). The study of gas phase

C60 cage, and the UV-visible–IR spectrum suggested that C60Mn compounds has been stimulated by the discovery of the HOMO–LUMO gaps of Dy@C60, Er@C60, and Eu@C60 the superconductivity of alkali doped fullerites. C60Mn com- molecules are small [939–941]. plexes are suitable model systems for studying the electronic properties of nanostructures and understanding the fundamental interactions between two nanosystems, particularly 5.3.2. R@C60,R= N, P metal–covalent interfaces.

Endohedrals of group-V elements N@C60 and P@C60 can be prepared by an ion implantation method [944, 945]. The C60 5.4.1. Alkali Metals and Alkaline Earth Metals fullerene is continuously evaporated onto a substrate and In a pioneering experimental work, Wang and co-workers simultaneously bombarded with low-energy (40 eV) nitro- − first studied the photoelectron spectra of C60Kn clusters, n = gen or phosphorous ions. The resulting film is subsequently 0–3, and they found evidence for charge transfer from the scratched from the substrate and dissolved in toluene and alkali atoms to the C60 molecules [958]. The electron affini- filtered. The soluble part contains only intact fullerenes, ties of the species were found to have a linear relationship with the ratio of encapsulated to empty fullerenes typically on the order of 10−4. HPLC techniques are used to obtain pure endohedral fullerenes. These two systems are soluble in organic solvents and stable at room temperature while

As@C60 is calculated to be unstable [946]. Experimentally, ESR studies [944, 945, 947–950] revealed that the encapsulated nitrogen and phosphorus are located at the center of the cage, the N or P atom is in quartet electronic spin 4 4 ground state S = 3/2 S3/2, and the highly reactive S spin states of N and P do not interact with the C60 cage. The fact of well-isolated electron spin of group-V atoms encapsulated Figure 41. Schematic 3D structures for two types of exohedral metal– in fullerenes and the easy positioning of endohedral C60 fullerene clusters (C M . (a) A “wet” structure where metal atoms offer a very ﬂexible possible implementation of quantum- 60 n spread over the fullerene cage. Here a C60M12 molecule with one metal information bits for a promising spin quantum computer atom on each 12 pentagon facet. (b) A “dry” structure where metal

[951]. atoms form an adsorbed droplet on C60. 454 C60-Based Materials

with the number of K atoms. This indicated that C60Kn are cannot be explained by a metal shell around the C60 with quite ionic because each K atom donates its outer 4s elec- a regular distribution but are in agreement with a sodium

tron to the t1u LUMO of C60. A dipole-supported state is cluster bound to the C60 molecule (i.e., a sodium droplet − found in KC60, yielding an inter-K-C60 stretching vibration on C60) [964]. For clusters with more than one sodium atom of 140 cm−1. (n>2), it was suggested that there is a strong decrease Zimmermann et al. have given a systematic study on alkali in ionization potential as the sodium cluster size increases,

metal–fullerene clusters by using photoionization time-of- and a full electron transfer from sodium atoms to the C60 flight mass spectrometry [959]. The C60Mn clusters were pro- molecule is expected. duced by coevaporation of fullerenes and metal in a gas The electric dipole moment of isolated single-alkali-atom- aggregation cell. It was suggested that the stability of the C60 molecules (C60Li, C60Na, C60K, C60Rb, and C60Cs) has alkali metal–fullerene clusters seems to be determined pri- been measured by molecular beam deflection experiments marily by the electronic rather than the geometric config- [965]. It was shown that the dipole increases from 12.4 D for uration. The C60M6 clusters are found to be particularly C60Li to 21.5D for C 60Cs. These results indicated a strong stable formations for any alkali metal. Coating a fullerene electron transfer from the alkali atom to the C60 cage, which with more than seven alkali metal atoms led to an even–odd is partial for Na and almost complete for K and Cs. It was

alternation in the mass spectra, which signals the beginning also found that the C60K molecules have a giant polarizabil- 3 of metal–metal bonding [959]. But C60Li12 was found to be ity at room temperature, equal to 2506 ± 250 Å , but no an exception to the electronically determined cluster stabil- permanent dipole by using the molecular beam deflection ity. It retains the iscosahedral symmetry of the C60 molecule technique [966]. The addition of a potassium atom enhances because each Li atom was found to be stable when above by more than a factor of 20 the polarizability of a pure C60 one of the pentagonal faces. C60Li12 is very stable both in molecule. This giant polarizability is caused by the free skat- the singly and the doubly ionized state. The origin of the ing of the K atom on the C60 surface. C60K behaves like a enhanced stability might be interpreted to be of geometric paraelectric system with an electric dipole of 17 7 ± 0 9D. origin [959, 960]. Alkaline earth metal covered fullerenes C M (n = 0–500; M = Ca, Sr, Ba) were also studied in 60 n 5.4.2. Transition Metals these works [959, 961]. It was suggested that these clusters are formed by the completion of metal layers around a cen- In the case of transition metals, the compound clusters tral C molecule; the first layer is complete when one metal C60Mx (x = 0 150; M = Ti, Zr, V, Y, Ta, Nb, Fe, Co, 60 Ni, Rh) have been produced using modified laser vapor- atom is situated above each of the 32 facets of the C60 cage. Recently, the electronic and geometric properties of ization of a transition metal target in a low-pressure inert C Na− and C Au− cluster anions were investigated by gas condensation cell [917, 967, 968]. It was found that the 60 n 60 n metals form complete layers around the central fullerene TOF-MS and PES [962]. The C60–Na and C60–Au clusters were produced in a double-rod laser vaporization source. molecule (i.e., forming transition metal coated fullerenes). Both the adiabatic electron affinity and the vertical detach- Mass spectrometric studies on these free metal–fullerene ment energy, extracted form the PES spectra, exhibit even– clusters showed that upon heating with a intensive laser odd alteration with the successive addition of Au atoms on pulse, these metal–fullerene clusters transform into metal carbides (M = V, Ti) and bulklike metallo-carbohedrene C60. So odd-n species have high relative stability. C60Aun takes a “dry” structure where Au atoms aggregate as a clus- clusters (M = Nb, Ta where x<2) [967]. Photofragmenta- tion mass spectra of metal–fullerene clusters C M (M = ter (see Fig. 41a). In contrast, C60Nan adopts the direct bind- 60 x ing of the Na atoms into stable trimers, each sodium atom Fe, Co, Ni, Rh; x = 0 30) reveal the existence of a reaction channel which yields clusters having the composi- lying above a pentagonal ring; thus C60Nan takes a “wet” structure where the Na atoms spread over the fullerene tion of metal in-cage doped heterofullerenes C59−2nM(n = 0 10) [917]. Additional tandem TOF experiments on cage (see Fig. 41b). For C60Nan clusters, strong periodi- cal oscillations are observed with a high cluster stability at mass selected C59M indicated that the initial fragmentation smaller sizes (n = 3, 6, 9, and 12). When n>12, the sodium step of this new kind of substitutionally doped fullerene atoms begin to exhibit a metallic layer behavior considering is the loss of a neutral MC molecule [917]. Recently, evi- the much smoother adiabatic electron affinity (AEA) and dence for the existence of C60Mx (M = Sm, Pt) has also vertical detachment energy (VDE) variations [963]. Addi- been observed in photofragmentation study by excimer laser tional PES experiments, performed with a 5.83 eV pho- ablation-TOF mass spectrometry [969]. todetachment energy, have shown that for n = 1to3the charge transfer from the valence orbital of the Na atoms to 5.5. C @Carbon Nanotubes the fullerene LUMO is approximately complete, whereas at 60 n = 4 this charge transfer is only partial. This result not only C60 can be encapsulated into carbon nanotubes in the points out the specificity of Na compared with the larger form of self-assembled one-dimensional chains and form a alkali elements but also suggests a full rearrangement of the new type of self-assembled hybrid structure called “bucky- cluster geometric configuration at the intermediate sizes. peapods” (see Fig. 42). The novel structure may give In contrast to the previous work, another individual study potential applications in data storage [970] and promising based on the measurement of the polarizability and dipole high-temperature superconductors [971]. of isolated C60Nan (n = 1–34) molecules in a static electric Pulsed laser vaporization of graphite with certain metal- field showed the existence of a permanent electric dipole lic catalysts can produce both carbon nanotubes and C60 for every size with increasing n from 1 to 34; these results molecules [972]. To obtain nanotube production, most of C60-Based Materials 455

conductive paths form via the ﬁlling of interior C60 chains, which can effectively bridge defects on the tube walls, reduce the electrical resistivity, and also reduce the effects of charge carrier localization at low temperature [982]. It can also

be indicated from the measurements that the ﬁlling of C60 also increases the photon scattering, enhances the thermal conductivity in some sense, and effectively prevents other molecules (such as oxygen molecules) from doping into SWCNTs [982]. Another direct-current electric resistance measurement carried out by the four-probe method using

Figure 42. Schematic 3D view for C @carbon nanotubes. the matlike ﬁlms of C60@SWCNTs showed somewhat dif- 60 ferent results in that, for the temperature range 5

C60 molecules [979]. Both experimental results based on very short range, investigations of C60 clusters are focused on HRTEM observation [974] and theoretical results using structure behavior. Experimental studies of fullerene clus- molecular dynamical calculation [980] suggested an opti- ters indicate they probably have icosahedral structure, sim- mum temperature range from 350 to 450 C and that the ilar to inert gas clusters [985]. Systematic optimization of

ﬁlling mechanism is most likely through the defect on the the lowest energy structures of the (C60n (n ≤ 57) clus- surface of SWCNTs but not through the ends of them. ters has been carried out with a genetic algorithm and

EELS experiments study on C60@SWCNTs showed that database conjugate-gradient method [986]. These structures the electronic and optical properties of the encapsulated C60 show transitions at n = 17 from icosahedral to decahedral molecules are very similar to fcc C60 with only small changes and at n = 38 from decahedral to fcc. The second energy suggesting a weak van der Waals interaction between the difference curve indicates that n = 13, 38, 55 (C60n clusters SWCNTs and the C60 molecules [981]. are especially stable. However, taking account of the ther- Refined measurements of electrical resistivity, thermal effect, the icosahedral structure instead of decahedral mopower, and thermal conductivity of highly C60-filled and close-packed ones is the most stable structure when the SWCNTs and unfilled controls from 1.5to 300 K have cluster is cooled from a high-temperature state by a molec- been performed recently [982]. It was shown that additional ular dynamics simulation. 456 C60-Based Materials [41] [55] [55] [55] [55] [55] [55] [55] [55] [55] [55] [55] [55] [55] d h h h d h h v v v v v v v v v 3 3 3 3 5 3 2 2 2 5 2 3 3 2 2 2 3 2 2 2 2 2 2 s 2 s s 1 1 2 D C D D C D C C C C D C D D D D C D C D C D C C C C D C C C 727.2 ( 735.4 ( 763.7 ( 757.5 ( 839.3 ( 878.3 ( 836.7 ( 852.2 ( 702.6 ( 793.9 ( 733.6 ( 750.8 ( 804.6 ( 840.8 [54] 702.3 ( 7.26 [52] 697.8 ( 7.57 [52] 7.36 [52] 7.34 [52] 2.5[49] 723 [53] 2.666 [36] 3.28 [50] 7.13 [52] 694.6 [55] 3.42 [50]3.39 [50] 6.96 [52] 6.92 [52] 3.10 [50] 7.05 [38] 694.3 ( 2.3 (second) [51] 3.21 [50]3.28 [50] 6.963.26 [52] [50] 6.923.32 [52] [50] 813.0 ( 3.38 6.95 [50] [52] 820.1 ( 6.95 [52] 822.0 ( 6.89 [52] 794.8 ( 806.1 ( 3.23 [50]3.20 [50] 7.16 [52] 7.093.20 [52] [50] 776.2 ( 745.2 ( 7.03 [52] 826.7 ( h v 3 2 D C 8( 22 ( ) [41] 697.8 ( [41] 2.89 [50] 7.10 [38] 699.1 [55] 3 h 3 v D 2 2 h D 6 D C D 13 ( 8( 1 2.25[48] 4 [41] 3.09 [50] 7.31 [52] 704.8 [55] [47] 3.27 [50] 7.09 [52] 784.0 ( 1 , 3.14 (first) 7.15[38] 716.4 ( C 2 D 16 ( [45, 46] [50, 51] 7.17 [52] 768.1 (

8 d 2 × D 45

8 50( 54 [44] 19 ( ), 6.918 (min.) ( axes (Å) carbon atoms afﬁnity (eV) energy (eV) (kcal/mol)

1 × 8 6 C × × 79

Diameter or length 30 50

8 7 × × 90 75 5[42] 3 (

7.10 [23]7.76 [43]8 1 [41] 5 [41] 2.65 [50] 2.73 [50] 7.95 [38] 618.1 [55] 7.48 [38] 657.7 [55] ∼ , 3.14 [50] 7.25 [52] 720.1 ( h v , 3.17 [50] 7.30 [52] 724.6 ( 5 2 2 v 2 D a ,C ,C , C s v 3 , 8.20 [43] 21 ( , 3 v v D 2 2 ,C h , [42] ,C 2 3 C C v (two major 8.70 [43] 7 , h 3 d , D 2 2 I v ,C d , ( 2 s d 2 D D h ,C 3 2 T C s , , D , , , h h h h d ,C D C D isomers) 7 6 5 6 3 2 3 5 2 2 h h I I D D D D D D D D 10 10 10 21 51 7 9C 2419 10 35 4686 9.542 (max.)( 134 187 259 450 616 10 0 150 0 Inserting Properties on horizontal axis and Fullerenes on Vertical axis. Non-IPR IPR isomers Chiral isomers of the 3 principal Distinct Electron Ionization Heat of formation 1812 [19] 1 0 Some higher fullerenes have too many isomers, structures, point groups therefore all are not listed here. a 20 36 60 70 72 74 76 78 80 82 84 86 88 90 92 94 96 98 100 102 104 106 C C C C C C C C C C C C C C C Fullernes isomers [40] [41] Point group C C C C C C Appendix A. C C60-Based Materials 457 [256] 2 D 84 C and -green 6 (at 950 K) [268] d 6 [264] -yellow brown [257] 2 d 2 2 ± D ± two major isomers of D D 15.935 Å [250] (fcc) 11.34 [43] greenish yellow (mix of 1.2 [262] 210 181 K, 235K [260] 20 GPa [252] (hcp) 15.92 Å [255], [263] 78 v ) 2 C v 2 C 18 [264] 59 C -chestnut brown ± -golden-yellow [41] v 3 2 D 0.85( (hcp) 11.12 Å (fcc) 15.6 Å [43] C 10 [259]

0 76 C ± 18 (at 803 K) [266] 7 (at 764 K), 4 [267] ± ± ± 16

color both in solution and crystalline state [41] 7 202 206 (hcp) 11.00 Å [43] (fcc) 15.3 Å [254] 170–135K, glass [259] bright yellow–green − 11 [259] 71 [271]

0 0 70 C ± ± 6 (at 298 K) [265] 190 5[264] 47 ± 85 82

± reddish brown [14] 4.6 [269] 4–5[262] 5–6[270] 7 8 43 ∼ (hcp) 10.70 Å [43] (fcc) 15.01 Å [253] [253, 258] 25[252] port-wine red/ − − 33 [271] 10 [259]

0 0 60 C ± ± 2 (at 298 K) [39] 200 8 5[264] − ± 33 38

. ± brown [14] 4 4 [262] 10 12 [114] 4 84 − 181 ∼ ∼ fcc(fcc) 14.17 Å [236] fcc/hcp fcc/hcp [43] fcc/hcp [43] fcc/hcp [43, 251, 252] ∼ 18 [252] 38 [120] 39 magenta/black − to C 36 36 [42] 7 − (pyridine)/black [42] 10 > fcc [250] (polymerized) 1.05 (cal.) [250] 1.72 [109] 1.64 (estim.) [254] ] 1 1 − 3 − cm) Properties of solid fullerenes from C 1 − enthalpy (kJ mol (kJ mol susceptibility (cgs ppm per mole of carbon) Sublimation standard Resistivity [( Heat of sublimation Dielectric constant Static magnetic Unit-cell parameter 6.68 Å [42] (hcp) 10.02 Å Appendix B. PropertyStructure hcp [42] C Transition temperature 260 K, 90 K [116] 280 K, 340 K Bulk modulus (GPa)Bandgap 70 (eV) (cal.) [250] 0.9 [261] 6.8 [113] 1.7 [262] 1.8 [262] 1.3 [262] 0.7 ( Mass density (g/cm Color of solution/solid yellow–brown 458 C60-Based Materials

EQUATIONS metals, and transition metals), forming gas-phase stable compounds. T = h/2e2R−1 (1) Fullerene superconductivity Some kinds of metal doped C60 compounds have superconductivity. The M3C60 (M = n2 n = 1 − (2) alkali metal) system is the most widely studied of them. The 2 0 720 highest Tc found in M3C60 is about 30 K (Rb3C60). It is widely believed that M3C60 are s-wave BCS-like supercon- "t = "t0 expEAt/kBT (3) ductors, driven by the coupling to the intramolecular Hg PT = P0 exp−5H/kT (4) phonons and probably with some strong-coupling effects. = exp−E /kT (5) Fullerene Any of a class of carbon molecules in which the 0 ' carbon atoms are arranged into 12 pentagonal faces and 2 0 = 00 exp−E'/kT0 (6) or more hexagonal faces to form a hollow sphere, cylinder, or similar ﬁgure. The smallest possible fullerene molecule T ∼ e2kT 9NE :2'−59ln; /:4 (7) F ph may have as few as 32 atoms of carbon, and fullerene-like

# = #1 + i#2 (8) molecules as few as 20 carbon atoms. The most common and stable fullerene is buckminsterfullerene (C ). # = # + i# (9) 60 1 2 Fullerite Solid state form of fullerene; usually means solid N = 9n + ik: (10) state C60. It usually forms black powders or black–brownish crystals. # = 9N:2 = 9n + ik:2 (11) Heterofullerene Fullerenes in which one or more carbon C = #1#0A/d (12) atoms in the carbon cage structure is substituted by a noncarbon atom (heteroatom), also called “dopeyballs” or D = #2/#1 (13) heterohedral fullerene, including borafullerenes (C59B ), 3 CP T = C1T + C3T (14) azafullerenes (C59N C58N2 C69N ), and heterofullerenes with heteroatoms other than N, B. k = CvsB/3 (15) Metal doped C60 compound Or metal doped fullerite. 2 C;T = C44 (16) A kind of material formed by intercalating metal atom into the interstitial sites of C host lattice. The metal usu- C;2 = C − C + C /3 (17) 60 T 11 12 44 ally used includes alkali metal, alkaline earth metal, and 2 C;L = C11 (18) some lanthanide metals. Some kinds of these materials have superconductivity. K = C11 + 2C12/3 (19) Metal/C60 composite A kind of phase-separated solid of G = 9C − C /2C :2/5 (20) 11 12 44 M/C60. These metals (such as Al, Cu, Ag, etc.) usually have high cohesive energy and cannot be intercalated C lattice. H T /H 0 = 1 − T /T 2 (21) 60 c1 c1 c The most common composites are multilayer ﬁlms and the

Jc = AM+ − M−/R (22) nanodispersion ﬁlms. J ∼ J 091 − T /T 2:n (23) Polymerized C60 Solid C60 can be polymerized by c c c irradiation of intense visible or ultraviolet light, or under C = 0 079exp1/T 1/4 − 1: (24) high-temperature, high-pressure treatment. During poly-

merization, some of the internal C–C bonds of C60 molecules are broken and connected via intermolecular GLOSSARY cycloaddition.

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