Structural, electronic, optical and vibrational properties of nanoscale carbons and nanowires:

a colloquial review

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J. Phys.: Condens. Matter 22 (2010) 334201 (25pp) doi:10.1088/0953-8984/22/33/334201

Structural, electronic, optical andvibrational properties of nanoscalecarbons and nanowires: a colloquialreviewMilton W Cole1, Vincent H Crespi2,14, Mildred S Dresselhaus3,Gene Dresselhaus4, John E Fischer5, Humberto R Gutierrez6,K Kojima7, Gerald D Mahan8, Apparao M Rao9, Jorge O Sofo10,M Tachibana11, K Wako7 and Qihua Xiong12,13

1 Department of Physics, Penn State University, 104 Davey Lab MB123, University Park,PA 16802-6300, USA2 Department of Physics and Department of Material Science and Engineering,104 Davey Lab MB193, University Park, PA 16802-6300, USA3 Department of Electrical Engineering and Computer Science and Department of Physics,Massachusetts Institute of Technology, Cambridge, MA 02138, USA4 Francis Bitter Magnet Laboratory, Massachusetts Institute of Technology, Cambridge,MA 02138, USA5 Department of Materials Science and Engineering, University of Pennsylvania,3231 Walnut St, Philadelphia, PA 19104-6272, USA6 Department of Physics, Penn State University, 104 Davey Lab MB060, University Park,PA 16802-6300, USA7 Department of Information Science, Yokohama Soei Junior College, Miho-cho 1, Midori-ku,Yokohama 226-0015, Japan8 Department of Physics, Penn State University, 104 Davey Lab MB169, University Park,PA 16802-6300, USA9 Department of Physics and Astronomy and Center for Optical Materials Science andEngineering Technologies, Clemson University, Clemson, SC 29634, USA10 Department of Physics, Penn State University, 104 Davey Lab MB172, University Park,PA 16802-6300, USA11 Graduate School of Integrated Science, Yokohama City University, Seto 22-2,Kanazawa-ku, Yokohama 236-0027, Japan12 School of Physical and Mathematical Sciences, Division of Physics and Applied Physics,Nanyang Technological University, 21 Nanyang Link, SPMS-PAP-04-14, Singapore13 School of Electrical and Electronic Engineering, Division of Microelectronics, NanyangTechnological University, 21 Nanyang Link, SPMS-PAP-04-14, 637371, Singapore

E-mail: mwc@psu.edu, millie@mgm.mit.edu, gene@mgm.mit.edu, fischer@seas.upenn.edu,hur3@psu.edu, gdm12@psu.edu, arao@clemson.edu, sofo@psu.edu,tachiban@yokohama-cu.ac.jp, wako@soei.ac.jp and qihua@ntu.edu.sg

Received 30 December 2009, in final form 5 July 2010Published 4 August 2010Online at stacks.iop.org/JPhysCM/22/334201

AbstractThis review addresses the field of nanoscience as viewed through the lens of the scientific careerof Peter Eklund, thus with a special focus on nanocarbons and nanowires. Peter brought to hisresearch an intense focus, imagination, tenacity, breadth and ingenuity rarely seen in modernscience. His goal was to capture the essential physics of natural phenomena. This attitude alsoguides our writing: we focus on basic principles, without sacrificing accuracy, while hoping

14 http://vin.crespi.name

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J. Phys.: Condens. Matter 22 (2010) 334201 M W Cole et al

to convey an enthusiasm for the science commensurate with Peter’s. The term ‘colloquialreview’ is intended to capture this style of presentation.

The diverse phenomena of condensed matter physics involve electrons, phonons and thestructures within which excitations reside. The ‘nano’ regime presents particularly interestingand challenging science. Finite size effects play a key role, exemplified by the discreteelectronic and phonon spectra of C60 and other fullerenes. The beauty of such molecules (aswell as nanotubes and graphene) is reflected by the theoretical principles that govern theirbehavior. As to the challenge, ‘nano’ requires special care in materials preparation andtreatment, since the surface-to-volume ratio is so high; they also often present difficulties ofacquiring an experimental signal, since the samples can be quite small. All of the atomsparticipate in the various phenomena, without any genuinely ‘bulk’ properties. Peter was amaster of overcoming such challenges.

The primary activity of Eklund’s research was to measure and understand the vibrations ofatoms in carbon materials. Raman spectroscopy was very dear to Peter. He published severalpapers on the theory of phonons (Eklund et al 1995a Carbon 33 959–72, Eklund et al 1995bThin Solid Films 257 211–32, Eklund et al 1992 J. Phys. Chem. Solids 53 1391–413,Dresselhaus and Eklund 2000 Adv. Phys. 49 705–814) and many more papers on measuringphonons (Pimenta et al 1998b Phys. Rev. B 58 16016–9, Rao et al 1997a Nature 338 257–9,Rao et al 1997b Phys. Rev. B 55 4766–73, Rao et al 1997c Science 275 187–91, Rao et al 1998Thin Solid Films 331 141–7). His careful sample treatment and detailed Raman analysiscontributed greatly to the elucidation of photochemical polymerization of solid C60 (Rao et al1993b Science 259 955–7). He developed Raman spectroscopy as a standard tool for gaugingthe diameter of a single-walled carbon nanotube (Bandow et al 1998 Phys. Rev. Lett. 803779–82), distinguishing metallic versus semiconducting single-walled carbon nanotubes,(Pimenta et al 1998a J. Mater. Res. 13 2396–404) and measuring the number of graphene layersin a peeled flake of graphite (Gupta et al 2006 Nano Lett. 6 2667–73). For these and otherground breaking contributions to carbon science he received the Graffin Lecture award from theAmerican Carbon Society in 2005, and the Japan Carbon Prize in 2008.

As a material, graphite has come full circle. The 1970s renaissance in the science ofgraphite intercalation compounds paved the way for a later explosion in nanocarbon research byilluminating many beautiful fundamental phenomena, subsequently rediscovered in other formsof nanocarbon. In 1985, Smalley, Kroto, Curl, Heath and O’Brien discovered carbon cagemolecules called fullerenes in the soot ablated from a rotating graphite target (Kroto et al 1985Nature 318 162–3). At that time, Peter’s research was focused mainly on the oxide-basedhigh-temperature superconductors. He switched to fullerene research soon after the discoverythat an electric arc can prepare fullerenes in bulk quantities (Haufler et al 1990 J. Phys. Chem.94 8634–6). Later fullerene research spawned nanotubes, and nanotubes spawned a newlyexploding research effort on single-layer graphene. Graphene has hence evolved from anoversimplified model of graphite (Wallace 1947 Phys. Rev. 71 622–34) to a new member of thenanocarbon family exhibiting extraordinary electronic properties. Eklund’s career spans this35-year odyssey.

(Some figures in this article are in colour only in the electronic version)

1. Phonons in nanomaterials: carbon nanotubes, C60,graphene and semiconducting nanowires

Phonons in systems with ordered, nanometer-scale structuredemonstrate profound effects from both boundary conditionsand the new spatial symmetries that are possible at very smalllength scales. For example, many of the properties of carbonnanotubes—a cylindrically confined, cylindrically symmetricform of carbon—can be derived from the vibrational propertiesof graphene, an extended two-dimensional form of carbon(Wallace 1947). Similarly, the vibrational properties of C60—an icosahedral molecular form of carbon with the same sp2

bonding geometry as graphene (Kroto et al 1985)—are tightly

constrained by the high point group symmetry of this nanoscalesystem. All these systems ultimately relate to graphite, the bulkthree-dimensional form of sp2 carbon, whose properties havebeen well studied for over sixty years (Dresselhaus et al 1988).

The optical probes used to such great effect by Peter’sgroup mainly measured long-wavelength phonons, often innanoscale carbon systems. Hence we review the long-wavelength vibrational properties of graphene, arguably theconceptual progenitor of this large material class. The twoin-plane polarized optical phonons, one longitudinal (LO) andone transverse (TO), have identical frequencies, ωLO = ωTO =1590 cm−1 and consist of the two carbon atoms of a single unitcell vibrating against each other. The so-called ZO phonon at

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J. Phys.: Condens. Matter 22 (2010) 334201 M W Cole et al

865 cm−1 vibrates these two carbon atoms out of plane andout of phase. The three acoustic modes of graphene of coursevanish in frequency at long wavelengths. The frequency of thelongitudinal acoustic (LA) phonon varies as ω = vLAq , whereq is the wavevector and vLA = 21 km s−1. The transverseacoustic (TA) phonon disperses as ω = vTAq , with a slowersound speed of vTA = 15 km s−1. Both of these valuesare much higher than those of typical solids, reflecting thestrong covalent bonds of graphene. These two modes describein-plane vibrations of the carbon atoms and their in-planespeeds are isotropic. Finally, an unusual flexure mode displaysquadratic dispersion, ω = vLq2, where L is the effectivethickness of a layer of graphene. The precise value of L issomewhat arbitrary, since it is defined only in concert withv, but one could take L ∼ 0.1 nm for graphene. The otherfactor, v, has units of velocity. These modes describe the out-of-plane motion of the carbon atoms for a wave that travelsparallel to the plane. The flexure modes, sometimes called ZA,were observed in the first neutron scattering measurements ofgraphite phonons (Nicklow et al 1972). Unlike for graphite,nearly all measurements of graphene have this layer lying on asubstrate, and this substrate will affect the observed vibrationalmodes of graphene.

The long-wavelength phonons in a single-walled carbonnanotube (SWNT) are more interesting, in that they affordgreater room for the effects of nanoscale geometry. Thephonons of a single-walled nanotube depend on the wrappingindices (n, m) of the nanotube; these describe the tubecircumference in lattice coordinates (Dresselhaus and Eklund2000). However, at long wavelength, many of the vibrationsare independent of the wrapping indices and can be describedby elasticity theory. Some early theories used zone foldingto deduce the nanotube phonons from the known modesof a graphene sheet. Although zone folding of the scalarSchrodinger wave equation for electronic states works well,elasticity theory involves a vector wave equation, and zonefolding gives poor results. Mahan (2002) derived the vibrationsof a thin-walled hollow cylinder within elasticity theory andthereby predicted all of the long-wavelength low-frequencymodes of the nanotube. Nanotube phonons have two quantumnumbers: the wavevector q along the tube, and the angularmomentum l. The longitudinal acoustic (LA) phonon describesperiodic elongation of the tube along the axis, with a frequencyω = vLAq , an angular momentum l = 0, and a speed vLA

identical to that in graphene. The transverse acoustic (TA)phonon exerts torsion, with a frequency ω = vTAq , an angularmomentum l = 0, and a speed vTA also essentially identical tothat in graphene. The radial breathing mode (RBM), which wasfirst described by Peter (Rao et al 1997c), has no direct analogin graphene. Its speed is also vLA and its angular momentum isl = 0. He was also early to recognize the RBM as a resonantphenomenon (Pimenta et al 1998a). The flexure modes retaintheir quadratic dispersion, but now the effective thickness Lis the diameter of the nanotube. The angular momentum offlexural modes is l = 1. Flexural modes are doubly degenerate,since they describe vibrations in the two-dimensional plane

transverse to the tube axis. Since the electron states of a carbonnanotube also have an angular momentum, conservation ofangular momentum constrains the electron–phonon scattering.Eklund was also early to distinguish the differences inbehavior between semiconducting and metallic nanotubes froma spectroscopic standpoint (Pimenta et al 1998b).

Eklund and colleagues were the first to realize that theradial breathing mode is Raman active (Rao et al 1997c), andthat its frequency is inversely related to the radius R of a carbonnanotube: ωRBM = vRBM/R. Measuring the frequency byRaman spectroscopy and the radius by STM, they derived vRBM

experimentally. Mahan (2002) used elasticity theory to showthat vRBM is identical to the velocity of longitudinal phonons.

Some of the early theories of carbon nanotube phononsmissed the flexure modes: all four long-wavelength modesin these treatments were acoustic, with ω ∝ q . Thiserror followed from a phonon dynamical matrix that lackedrotational symmetry. As noted by Born and von Karmanin their first paper on phonons, the dynamical matrix mustgive zero for any rigid translation or rotation of the crystal.This condition on rigid rotations is usually lost in theperiodic boundary conditions imposed on standard infinitethree-dimensional crystals. But great care must be used toensure that the dynamical matrix of lower-dimensional systemssuch as nanotubes has the required symmetries (Mahan andJeon 2004).

In contrast to the relatively direct relationship betweenflat graphene and rolled nanotubes, the vibrational modes ofa spherical C60 molecule, although derived ultimately from thesame sp2 bonding, are profoundly affected by the high pointgroup symmetry of this icosahedral molecule. An isolated C60

molecule has 180–6 = 174 intramolecular vibrational modes,but only 46 distinct mode frequencies survive the Ih symmetry(Dresselhaus et al 1992). For weak intermolecular coupling (asin C60 films) the vibrational modes of the solid state resembleclosely those of the free molecule. Group theory for an isolatedmolecule predicts that ten (8Hg + 2Ag) modes are Ramanactive and four (4F1u) are IR active (Dresselhaus et al 1992).The remaining intramolecular modes are optically silent to firstorder.

Whereas nanotubes can be described as seamlesslywrapped graphene, semiconducting nanowires made of e.g. Sior GaP are best conceptualized as cylindrical sections througha parent three-dimensional bulk solid. As such, they sufferabrupt surface terminations that are absent in the essentiallyedgeless nanotube system. Hence new surface phonons appear,and the bulk-derived phonons experience confinement from thenanowire edges.

Raman spectroscopy is a powerful technique to studythese phonons in nanostructures. The line-shape, peak positionand peak width of Raman bands can shed light on crystallinequality, doping, secondary phases, impurities and crystallinedisorder. We focus first on phonon confinement, surface opticalphonons and stimulated Raman scattering in semiconductingnanowires, guided by significant contributions from ProfessorEklund during his decade at Penn State. Later, we will discussphonons in C60, another topic of great interest to Peter, and theextension to carbon systems that polymerize to themselves or

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act as hosts for heteroatoms such as adsorbates, intercalants,and chemical functionalization.

Richter first proposed a phenomenological model tointerpret Raman line-shapes in nanocrystals (Richter et al1981). Campbell and Fauchet (Campbell and Fauchet 1986)extended it to describe cylindrical nanowires. We call it theRCF model. When a nanowire is narrower than the phononmean free path, the q = 0 Raman selection rule breaks downand the Raman band asymmetrically broadens and downshiftsdue to phonon contributions from an extended region of theBrillouin zone. Schematically, the Raman intensity for acylindrical nanowire can be expressed as

INW(ω) = A∫ qmax

0

|C(0, q⊥)|2[ω − ω0(q⊥)]2 + (�/2)2

2πq⊥ dq⊥ (1)

where C(0, q⊥) is the Fourier coefficient of a Gaussianconfinement function W (r, D) ∼ exp[−(α · r/D)2] in whichα is an adjustable parameter and q⊥ is the phonon wavevectorperpendicular to the nanowire axis, extended to a continuumlimit as a computational convenience. D is the diameter ofthe nanowire’s crystalline core (not including any amorphousoxide coating). The phonon dispersion relation ω(q) isobtained from the bulk phonon dispersion as determinedby e.g. neutron scattering (Nilsson and Nelin 1972). ForSi nanowires (Adu 2004), the downshift and asymmetricalbroadening become significant (a downshift of ∼2 cm−1) onlybelow D = 10 nm, suggesting that a previously observed largedownshift (10–20 cm−1) of the first-order Raman peak in anensemble of Si nanowires 10–20 nm in diameter arose from aphenomenon other than confinement (Li et al 1999, Wang et al2000, Zhang et al 1998).

To account for variations in nanowire diameter within anensemble specimen, Adu et al extended the RCF model byintroducing a diameter distribution (Xiong et al 2003, Adu et al2005), usually a log-normal distribution for nanowires grownby pulsed laser vaporization:

INWD(ω, D) =∫ ∞

0F(D)INW(ω, D) dD (2)

where F(D) describes the diameter distribution, INW(ω, D) isthe line-shape function for a nanowire of diameter D definedby equation (1), and D is the most probable diameter obtainedfrom the log-normal distribution. Figure 1 shows the Ramanspectra of four nanowire samples with different diameters,excited at a low power (8 μW μm−2) to minimize laser-induced heating. Again, only below 10 nm diameter doesthe Raman band downshift and broaden asymmetrically ascompared to bulk Si. The extended RCF model (solid lines) fitsthe experimental data very well (Adu 2004, Adu et al 2005).This measurement was the first clear demonstration of intrinsicconfined phonon states probed by Raman scattering.

A laser flux-dependent change in line-shape and peakposition, first observed by the Eklund group (Adu et al 2006a,2006b, Gupta et al 2003a) complicates the analysis. Since thephonon frequency and lifetime are temperature dependent, amore accurate temperature-dependent RCF line-shape can be

Figure 1. Raman scattering spectra show the evolution of 1st-orderRaman bands of four ensembles of nanowires. Open circles areexperimental data while solid lines represent the least-squares fitsusing equation (2), the RCF model extended by a diameterdistribution. Adapted from Adu et al (2005), Adu (2004).

written as (Adu et al 2006a):

INW(ω) =∫ c

−cI0e−(z/a)2

dz

×∫ qmax

0

|C(q⊥)|2[ω − ω0(q⊥, T (z))]2 + [�(T (z))/2]2

· 2πq⊥ dq⊥

(3)

where T (z) gives the temperature variation arising from laserheating. T (z) can be modeled by assuming the temperatureincrease above ambient due to laser heating follows the sameGaussian profile as the laser beam (Adu et al 2006a). Both�(T ) and ω0(T ) incorporate anharmonic interactions andthermal expansion. For narrow nanowires (D < 10 nm),Raman band asymmetry results from both phonon confinementand inhomogeneous laser heating, while laser inhomogeneousheating dominates the line-shape of wider wires, supportingthe claim of Piscanec et al (2003). A similar approach hasbeen applied to Ge nanowires (Jalilian et al 2006).

Modes localized to surfaces or interfaces that propagatealong the interface (Sernelius 2001) are particularly tractablefor well-ordered surfaces with translational symmetry (Car-dona and Guntherodt 2000). These surface phonons canbecome Raman active if the translational symmetry along thesurface is broken through surface roughness, construction of agrating along the surface, or by probing the evanescent waveusing a prism with an attenuated total reflection geometry(Falge et al 1974). In a dielectric continuum model forsurface optical phonons in a nanowire, the lattice vibrationassociated with a polar material polarizes a medium with adielectric function ε(ω) (Stroscio and Dutta 2001). Solvingthe electrostatic equations yields the dispersion relation ωSO(q)

for a surface optical mode in an infinitely long cylindricalnanowire. In the limit q � ω/c, the dispersion of the surfaceoptical (SO) mode can be written as (Gupta et al 2003b)

ω2SO = ω2

TO + ω2p

ε∞ + εm f (x)(4)

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J. Phys.: Condens. Matter 22 (2010) 334201 M W Cole et al

Figure 2. Surface optical (SO) phonon dispersion of cylindrical GaPnanowires from equation (4). The horizontal dashed line gives theschematic experimental frequency of the SO phonon. Thewavelength of the surface potential that breaks the symmetry canthen be obtained from the vertical dashed line. Adapted from Guptaet al (2003b).

where x = q R, ωp is the screened ion plasma frequency givenby ω2

LO = ω2TO + ω2

p/ε∞ where ωLO is the LO frequency at thezone center, R is the wire radius and f (x) is obtained from theeigenvalue equation for the polarization (Gupta et al 2003b).

Figure 2 plots the calculated surface optical phononfrequency ωSO versus q R for gallium phosphide nanowires inair (Gupta et al 2003b). The surface optical phonon evolvesbetween the bulk LO and TO frequencies. A horizontal linerepresents the nanowire surface optical frequency observedby Raman scattering. The corresponding wavevector q—the wavevector of the axial potential that breaks translationsymmetry and hence activates this phonon—is obtained fromthe vertical dashed arrow. Figure 3 shows the Raman spectra ofGaP nanowires carried out in three different dielectric media,revealing TO, LO and SO bands, the surface optical (SO)Raman band downshifts as εm increases, consistent with themodel of equation (4).

The surface optical phonon dispersion for a nanowire ofrectangular cross-section is more complicated, as there is noanalytical solution to the eigenvalue problem (Xiong et al2004). Nevertheless, the microscopic mechanism is similar tothat for cylindrical GaP nanowires.

What breaks the translational symmetry of the surfacepotential? Diameter modulation along the nanowire axisprovides one such mechanism. Such variations have beenseen in transmission electron microscopy for cylindrical GaPnanowires (Gupta et al 2003b, Xiong et al 2006b) and ZnSnanowires of rectangular cross-section (Xiong et al 2004).This diameter modulation is consistent with observations onmicron-sized Si whiskers grown by VLS in the 1970s, whereit was ascribed to a growth instability (Givargizov 1973).Recently, a similar diameter variation in Si nanowires hasbeen observed (Ross et al 2005). The activation of nanowiresurface optical phonons in Raman spectra suggests that suchdiameter modulations are important for the physical propertiesof nanowires.

Polarization-dependent Raman scattering from individualsemiconducting nanowires also reveals an antenna effect (Chenet al 2008, Xiong et al 2006a). Even more interesting is

Figure 3. Raman spectra of GaP nanowires collected in air (bottom)dichloromethane (middle) and aniline (top). Solid squares are thedata and the thin lines are from a Lorentzian line-shape analysis.Adapted from Gupta et al (2003b).

how the polarized Raman response depends on the nanowirelength. Nanowires with cleaved end facets behave as Fabry–Perot resonators which can support optically pumped lasing(Johnson et al 2002). Recently, such cavity modes have alsobeen seen in Raman scattering (Wu et al 2009). Figure 4shows the integrated Raman Stokes intensity of the TO phononversus laser power for a series of GaP nanowires between200 nm and 3.3 μm long, all cut from the same parentnanowire by a focused ion beam. In nanowires longer than2 μm, the Raman intensity is approximately linear in the laserpower up to 1 mW, which is characteristic of spontaneousRaman scattering, while higher laser powers induce significantheating. Nanowires shorter than 1.1 μm exhibit spontaneousRaman emission (ITO ∝ P) at low laser power, but showa strong nonlinear behavior ITO ∝ Pn above a thresholdpower, where the exponent n grows rapidly with decreasinglength, reaching n ∼ 4.3 for the 270 nm long nanowire.The threshold power decreases as the length decreases. Thisnonlinearity is a signature of stimulated Raman scattering.The low threshold power (0.1–0.5 mW) indicates that the GaPnanowire cavity has a very high quality factor Q ∼ 15 000,perhaps ascribable to whispering gallery modes similar to thoseseen in spherical microcavities (Spillane et al 2002). Peter’sdiscovery of stimulated Raman scattering in a single nanowirecavity shows promise for low threshold nanowire Raman laser(Wu et al 2009).

Raman scattering can also shed light on the dopantdistributions in nanowires (Imamura et al 2008) and zonefolding in twinned nanowires (Lopez et al 2009). Outstandingpuzzles remain. For example, radial breathing modes in siliconnanowires have been predicted (Thonhauser and Mahan 2005,Peelaers et al 2009), but not yet observed experimentally.

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J. Phys.: Condens. Matter 22 (2010) 334201 M W Cole et al

Figure 4. TO Raman band intensity dependence on length and laser power. Panel (a) gives a linear plot of the integrated TO band intensityversus laser power for seven nanowires of different lengths. For wires shorter than about one micron, nonlinearity is observed. Panel (b) is alog–log plot for the data shown in (a). Stimulated Raman scattering is seen for wires shorter than 1 μm. The threshold depends on nanowirelength. Adapted from Wu et al (2009).

Figure 5. Normalized Raman spectra of C60 films on Si(100) taken under different environmental conditions and laser power densities �:(a) in 1 atm of He and � = 5 W cm−2, (b) in 1 atm of O2 and � = 75 W cm−2, and (c) in 1 atm of He and � = 75 W cm−2. The inset showsthe XRD scan of the C60 film that produced the Raman spectrum of (a). Adapted from Zhou et al (1992).

2. Pristine carbon nanostructures: polymerizationand photophysics of C60

Peter was fascinated by the high symmetry of the C60 moleculeand his initial studies focused on understanding its vibrationalproperties (Eklund et al 1995b). His group sublimed high-purity C60 micro-crystalline powders in an inert atmosphere toprepare thin films of C60 on silicon and quartz substrates. Ina thin film, C60 molecules assemble into a face centered cubic(fcc) lattice. The weak intermolecular interaction (Pacheco andRamalho 1997) and nearly spherical molecular shape allow C60

to spin rapidly about its lattice positions above 260 K (Heineyet al 1991b).

Figure 5 show the first Raman spectra of C60 films reportedby the Eklund group (a), (b), compared to another early C60

film Raman spectrum (c) which differed significantly fromthat reported by Peter. When using an Ar ion laser at 488 or

514 nm to excite the Raman spectra, the most prominent peakoccurs at either 1458 or 1469 cm−1. Different results wereobtained if the experiments were carried out in air or oxygen,as opposed to vacuum or an inert atmosphere. Throughmeticulous studies, the Eklund group traced this diversity ofresults to two photochemical transformations which alter thestructure of pristine solid C60 while leaving the fullerene shellslargely intact: photopolymerization of C60 and photo-enhanceddiffusion of O2 into interstitial voids in the fullerene lattice.In the former case, covalent carbon–carbon bonds interlinkfullerene molecules (Rao et al 1993b). In the latter case,O2 molecules under the action of UV/visible light exhibitenhanced diffusion into the lattice (Rao et al 1993a, Eloi et al1993).

The vibrations of C60 in the solid state are very similarto those of the isolated molecule, comprising 46 distinct

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J. Phys.: Condens. Matter 22 (2010) 334201 M W Cole et al

Figure 6. The Eklund group exercised extreme caution in the thinfilm preparation of C60 to uncover the role of oxygen in the observedRaman data. A thin film deposition apparatus was installed inside aHe glove box, and sample transfer procedures from the glove box tospectrometers were developed to facilitate complete exclusion ofoxygen from the C60 film during all stages of sample preparation andRaman measurements. Pictured from left to right are Rao, Wang,Professor Eklund, Ren (behind), Wang and Zhou. Photo circa 1993.

frequencies of which ten are Raman active, eight with Hg

symmetry and two with Ag symmetry. The two Ag modesappear at 493 and 1469 cm−1 in figure 5(a); these are calledAg(1) and Ag(2). The early literature disagreed on thefrequency of Ag(2). This high-frequency tangential modeinvolves the symmetric, simultaneous contraction of all 12pentagonal rings in the molecule. Using a low laser powerdensity of 5 W cm−2 on an oxygen-free sample, the Eklundgroup reported a polarized mode at 1469 cm−1 and assigned itto the Ag(2) pentagonal pinch mode (Zhou et al 1992). Ramanmeasurements performed in the presence of air or O2, as infigures 5(b) and 6, encounter O2 molecules physisorbed in theoctahedral interstices in the fcc C60 lattice. Initially, theseguest molecules produce almost no measurable change in theRaman spectrum relative to that observed in pristine, oxygen-free C60 films (figure 5(a)). However, in the continued presenceof UV/visible light this interstitial O2 eventually oxidizes the

fullerene shell at which point changes in the Raman and IRspectra can be detected (Rao et al 1993a).

A line at 1458 cm−1 (also sometimes seen at 1460 cm−1,as in figure 5) that was incorrectly assigned in early research tothe Ag(2) mode in oxygen-free C60 films was shown later bythe Eklund group to be only ∼80% (i.e. not 100%) polarized(Eklund et al 1992), and therefore not the Ag(2) mode. TheEklund group demonstrated that the 1458 cm−1 line is instead aclear signature of solid C60 in the phototransformed, polymericstate (Rao et al 1993b). A well-known photochemical 2 + 2cycloaddition was proposed as the mechanism of covalentattachment between C60 molecules. If carbon–carbon doublebonds on two adjacent molecules are oriented parallel to oneanother and separated by less than ∼4.2 A, then photochemicalassistance can break these double bonds and produce a four-membered ring, as in the left panel of figure 7 (Venkatesan andRamamurthy 1991).

The simplest example of 2 + 2 cycloaddition is thedimerization of ethylene (C2H4) to cyclobutane (C4H8), shownin figure 7(a). Two C60 molecules can dimerize by a similarmechanism, as shown in figure 7(b). Solid C60 satisfies thegeneral topochemical requirement for 2 + 2 cycloaddition,since each C60 molecule contains 30 double bonds tangentialto the ball surface, and the double bonds on adjacent moleculescan be separated by as little as 3.5 A in pristine solid C60

(Heiney et al 1991b). In this photochemical mechanism,an incident photon prepares one molecule in the lowestexcited triplet state T1. This molecule then reacts withan adjacent molecule that is in the singlet ground state S0.Three photophysical properties of C60 lead to a significantoptically pumped population of the T1 state: efficient dipole-allowed transitions (above ∼2.3 eV) from the ground state toexcited singlet states (Wang et al 1992), nearly 100% efficientintersystem crossing of the excited molecule into T1 (Hung andGrabowski 1991), and a long T1 lifetime of ∼40 ps (Arbogastet al 1991). If air or O2 is present, the lifetime of the firstexcited triplet state of C60 is significantly reduced (Hung andGrabowski 1991) and the photopolymerization is quenched.

This phototransformation mechanism was confirmed inthe Eklund group through time evolution studies of the Ag(2)

mode in oxygen-free films under increasing exposure to a high

Figure 7. The 2 + 2 cycloaddition reaction between parallel carbon double bonds on adjacent molecules is shown schematically in (a) of theleft panel, while (b) shows a C60 dimer produced by the same reaction. The right panel shows: (a) a bimolecular photochemical reaction inwhich a C60 monomer in the excited triplet state 3M∗ reacts with a monomer in the ground state M to form a dimer D and (b) a schematicenergy level diagram for the C60 monomer, showing the principal levels involved. The ki are the respective rate constants and the othersymbols are described in the text. Adapted from Eklund et al (1995c).

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J. Phys.: Condens. Matter 22 (2010) 334201 M W Cole et al

laser flux (Wang et al 1993). A narrow line at 1469 cm−1

is initially observed, indicating that the film is pristine C60.With increasing photon dose, a broader peak appears at1458 cm−1 and grows at the expense of the 1469 cm−1

line. This characteristic evolution is the Raman signatureof photopolymerization in solid C60 (Rao et al 1993b).Additional evidence for the photopolymerized phase includesthe observation that a pristine C60 film is readily soluble inorganic solvents such as toluene, whereas photopolymerizedC60 is not. In addition, the laser desorption mass spectrum ofpristine C60 shows the presence of (C60)n clusters with n < 4;these clusters are identified with cross-linked C60 moleculesinduced by the desorption laser itself. Laser desorption massspectra of a phototransformed C60 film show more than 20clear peaks; these are identified with large clusters of fullerenemolecules such as (C60)20. Furthermore, the number of thefirst-order Raman and IR intramolecular vibrational modesincreases in the phototransformed phase, as in figure 5(c), dueto the reduction in symmetry below Ih . Finally, a new low-frequency Raman-active mode appears at ∼118 cm−1 in thephototransformed phase, one which has been identified withan interball mode (Wang et al 1994, Rao et al 1993b).

Theoretical studies of C60 dimerization have taken severalapproaches, including generalized tight-binding moleculardynamics (Menon et al 1994), modified neglect of differentialoverlap and tight-binding methods (Strout et al 1993), andlocal-orbital-based first principle molecular dynamics (Adamset al 1994). All of these studies indicate that 2+2 cycloadditionyields the most stable dimer geometry. Two years afterthe report of photopolymerized C60, other research groupsshowed that polymerization can also be induced in solid C60

through simultaneous application of high temperature andhigh pressure, yielding the one, two and three-dimensionalpolymerized structures depicted in figure 8 (Iwasa et al 1994,Nunez-Regueiro et al 1995).

Raman spectroscopy has become an indispensablecharacterization tool in carbon science. The Eklund groupplayed a pivotal role in advancing our understanding of allforms of carbon, ranging from the graphite intercalationcompounds in the 1970s (described below), through thefullerene studies described above, to carbon nanotubes in thepast decade and graphene in the present era (Bandow et al1998, Dresselhaus and Eklund 2000, Eklund et al 1995a, Guptaet al 2006, Pimenta et al 1998a, 1998b, Rao et al 1998, 1997b).Eklund was also interested in the molecular spectra of C60 interms of the very large number of harmonics and combinationmodes (more than 200) observed in the IR and Raman spectra,a phenomenon essentially unique to fullerenes. His group didthe pioneering work in this research area, as described in hisbook (Dresselhaus et al 1996).

3. Carbon nanostructures with heteroatoms:physical adsorption, intercalation, and chemicalfunctionalization

The structure and properties of graphite and other carbonpolymorphs can be greatly modified by adding atoms or

Figure 8. Schematic arrangement of C60 molecules in(a) one-dimensional orthorhombic and two-dimensional tetragonal(b) and rhombohedral (c) polymeric phases.

molecules to the all-carbon host (Fischer et al 2000). Closed-shell atomic or molecular species generally interact weaklywith the carbon sheet, leading to a diverse range of physicaladsorption phenomena focused upon the dynamics and phasebehavior of the adsorbates themselves. Open-shell specieswith weak ionization potentials or strong electron affinities,such as the alkali metals, alkaline metals or sulfuric acid,experience stronger charge-transfer interactions with an sp2

carbon sheet. Hence, these species can dilate the spacebetween weakly bound carbon layers and thereby infiltrate thecarbon host, whether graphite (Dresselhaus and Dresselhaus1981, 2002), solid C60 (Murphy et al 1992), carbon nanotubes(Lee et al 1997, Rao et al 1997a) or even one-dimensionalcarbon polymers such as polyacetylene, (CH)x (Heiney et al1991a). Finally, species such as hydrogen or fluorine cancovalently bind to carbon, changing the hybridization from sp2

to sp3, with profound effects on the electronic and structuralproperties.

Adsorption onto graphitic materials has played animportant role historically in surface science, including Peter’sown elegant investigations using transport measurements toelucidate the physical adsorption of cyclic hydrocarbonswith varying degrees of aromaticity onto graphene andnanotubes (Sumanasekera et al 2002) and his careful studieson the interaction of hydrogen with nanoscale carbons, whichprovided some of the critical clarifying measurements on thephysics of these systems (Williams et al 2002, Narehoodet al 2002, Pradhan et al 2002). Fundamental questionsinclude the nature of the adsorption potential, as influencedby the unusual electronic properties of nanotubes and graphene(Castro Neto et al 2009) and the various adsorbate phenomena,such as unusual phases and transitions between them. Potentialapplications are diverse, including gas separations, storage andsensing (Romero et al 2005, Sholl and Johnson 2006, Coleet al 1981). To understand physical adsorption onto nanotubesand graphene, it helps to recall a previous generation’sexperience with adsorption onto graphite. Single-surfaceexperiments are challenging due to the low surface-to-volumeratio. For physical adsorption, scanning tunneling microscopyis generally not useful, except for the most strongly boundgases like Xe (Weiss and Eigler 1992). Fortunately, exfoliated

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graphite has a high surface area (>20 m2 g−1) with uniform,extended honeycomb facets. As such, gas can imbibe withina macroscopic porous sample, yet experience an adsorptionenvironment nearly identical to that on a flat surface. Weakbinding to a surface in physical adsorption also implies smallkinetic barriers, hence the adsorbate mobility is high andthe heat of adsorption is small, so equilibration is rapid.Therefore experiments can determine both the film coverageN (by subtracting the number of gas atoms from the totalnumber of atoms) and the chemical potential μfilm of theadsorbed film, since it equals μvapor. For an ideal monatomicgas, μfilm(N, T ) = μvapor = β−1 ln(nλ3), where λ ≡(2πβh2/m)1/2 is the thermal de Broglie wavelength, m isthe atomic mass, n = Pβ is the coexisting vapor density atpressure P , and β−1 = kBT . In principle, one thermodynamicmeasurement (an adsorption isotherm) could determine all ofthe thermodynamic properties of the adsorbed gas. In practice,however, P is immeasurably small at low T . Fortunately,one can measure another thermodynamic function, the specificheat C(N, T ) of the physisorbed film, because the backgroundspecific heat of the graphite is small and can be subtracted.Since the temperature integral of C/T is the entropy, onecan merge data from the two thermodynamic techniquesusing a Maxwell relation, (∂S/∂ N)T = (∂μfilm/∂T )N .Complementing these thermodynamic measurements are x-ray and neutron scattering probes, NMR, Raman spectroscopyand other experimental studies. Electron diffraction and TEMcan provide useful structural information on a single exposedsurface of graphene or graphite. These various methods havebeen reviewed extensively (Dash et al 1994, Zeppenfeld 2001,Bruch et al 2007a, 2007b).

Studies of films on graphite yield a wide variety ofmonolayer phase diagrams, depending on the commensuration,i.e. the degree of mismatch between the graphite hexagons andthe natural lattice constant of the adsorbate, which is controlledmainly by the Lennard-Jones diameter σ . At low filmcoverage, one obtains a gas in a quasi-2D periodic potentialwith atomic band structure effects (Cole et al 1981). Athigher coverage, a sub-monolayer film undergoes one or moretwo-dimensional phase transitions. For weakly corrugatedpotentials (e.g. Ar or CH4), the phase diagram resembles thatof an ideal 2D system. A 2D condensation transition occursat moderate temperatures, typically about one-half of the 3Dvalue. The measured critical exponent of the coexistencecurve (Kim and Chan 1984) agrees nearly perfectly with thevalue (βc = 1/8) predicted by the 2D Ising model, oneof the most fundamental measurements in surface science.At lower temperature, even a small corrugation affects theincommensurate solid, whose 2D lattice exhibits orientationalepitaxy, a temperature-dependent rotation of the film relative tothe graphite substrate, which terminates in a distinct transitionwith Bragg diffraction spots evolving into liquid-like structurefactor (Shrimpton et al 1988, D’amico et al 1990). Forthe quantum fluids, the corrugation gaps the long-wavelengthphonon spectrum by ∼0.94 meV (Lauter et al 1992) andforces a high-temperature transition to a

√3 × √

3R30◦commensurate phase at Torder ∼ 3 K for helium isotopes and∼20 K for hydrogen isotopes. This transition displays the 2D

critical exponents of the three-state Potts model (Schick et al1977).

Adsorbed films on graphene have only recently begunto be explored. Physical adsorption on graphene wouldappear straightforward because the key difference, compared tographite, is a presumably small shift of the adsorption potential(Gordillo and Boronat 2009). From a qualitative point of view,we therefore expect physically adsorbed films on grapheneto be similar to those on semi-infinite graphite. In contrast,many novel phenomena result from the reduced dimensionalityof atoms adsorbed onto or inside carbon nanotubes (Calbiet al 2001a). Taking the adsorption potential U(ρ) to becylindrically symmetric, the solutions of the single-particleSchrodinger equation assume the form:

n,ν,k(ρ, θ, z) = �n,ν(ρ) exp[i(νθ + kz)]. (5)

The longitudinal wavevector k = pz/h with pz the momentumalong the tube axis. The rotational quantum number ν ∼=±1,±2, . . . corresponds to angular momentum Lθ = νh. To agood approximation (Stan and Cole 1998), the energy is a sumof radial, rotational and longitudinal contributions:

En,ν,k = En,ν + p2z /(2m) ≈ En,0 + L2

θ /(2m〈ρ〉2) + p2z /(2m).

(6)Here, 〈ρ〉 is the mean distance of the gas atom from the tubeaxis. The subscript n = 1, 2, 3, . . . labels the nth solutionof the radial Schrodinger equation for a specified ν, witheigenvalue Enν . If the tube is narrow, then the spacing betweenradial energy levels is large, so that only the ground state (n =1, ν = 0) is excited at low temperature and the lowest energyexcitations are axial with a quasi-continuous spectrum: a one-dimensional gas. Even when collisions become important, thissystem remains essentially a quasi-1D fluid. The rotationaldegree of freedom is excited at Trot ∼ k−1

B h2/(m〈ρ〉2), whichis a few Kelvins for He or H2 and smaller for a heavier particle.For temperatures slightly above Trot the system manifests twodegrees of freedom, z and θ , and therefore acts as a 2D gas:C/(NkB) = 1. This dimensional crossover has been exploredin detail for quantum fluids inside narrow nanotubes (Gaticaet al 2000).

Classical gases within nanotubes do not exhibit low-temperature transverse or angular delocalization due to zero-point motion, so the molecules localize in the region ofminimum potential. The ratio of the molecular size σ to thenanotube radius R defines two limiting cases. The limit σ ∼= Ris exemplified by the peapod geometry, wherein C60 moleculesare imbibed within a narrow nanotube in single file alongthe tube axis (Smith et al 1998). This remarkable situationis simple to model if one considers only the translationaldegree of freedom along the tube axis, in which case oneobtains an analytical expression for the 1D equation of state(Gursey 1950). However, this model’s application to theC60 peapods requires further approximations: only nearest-neighbor interactions and negligible transverse motion ordiffusive friction (i.e. the nanotube simply constrains the C60

molecules to a line). Also, the molecules are implicitlyassumed to be freely rotating, insofar as rotational couplingis ignored. At room temperature and above, all of these

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J. Phys.: Condens. Matter 22 (2010) 334201 M W Cole et al

Figure 9. Adsorption isotherms of krypton on the outside of ananotube. Used with permission of the Cobden-Vilches group (Wanget al 2010).

assumptions should be accurate (Calbi et al 2003). In theother limiting classical case, σ � R, low-coverage adsorptionoccurs close to the nanotube wall, at the adsorption potentialminimum. When the density of molecules increases to thepoint that their that mutual repulsion dominates the substrateattraction, subsequent molecules are obliged to adsorb in a lessattractive region, near the center of the pore. Such a capillarycondensation transition is familiar from porous media (Gaticaand Cole 2005).

Although few experiments have studied adsorption withinindividual nanotubes (Buttner et al 2009), many experimentshave investigated adsorption onto bundles of nanotubes (Calbiet al 2008, Johnson and Cole 2008, Migone 2008). Onekey finding is the importance of heterogeneity in the bundlepacking. Interstitial adsorption occurs primarily in the widerchannels, as determined by the distribution of nanotuberadii and the kinetics of bundle formation. Very strongadsorption occurs in the V-shaped grooves between nanotubesalong the outside surface of the bundle. This space isoccupied at the lowest pressures, followed by monolayerformation on the rest of the bundle surface, then adsorptionin a second-layer groove defined by the intersection betweensemicircular monolayer films on adjacent tubes. Experimentsare in semi-quantitative agreement with calculations basedon semi-empirical adsorption potentials that are derived fromadsorption on graphite (Calbi et al 2001b, Talapatra et al 2002).

Recent adsorption experiments from the Cobden-Vilchesgroup at the University of Washington measure adsorptionon the outside of a single carbon nanotube, achieved bymeasuring the resonant frequency shift of a vibrating nanotubein equilibrium with a gas (Wang et al 2010). Figure 9displays one such data set. These low-temperature adsorptionisotherms exhibit two near-discontinuities. The larger jump isattributed to a transition from a gas to a commensurate phase,shown schematically in figure 9, analogous to that of Kr onplanar graphite below 130 K (Fain et al 1980). The smallerjump at higher coverage is interpreted as a transition to anincommensurate solid. The flat region between the jumps may

reflect a reentrant fluid phase conjectured to occur for kryptonon graphite (Specht et al 1987). These data, one of the firststudies of nano-matter on a single cylindrical surface, raisenumerous fundamental questions about adsorbate structure anddynamics and their effect on electronic transport.

One general point needs to be addressed: since single-nanotube adsorption is a one-dimensional problem, no phasetransition in the strict thermodynamic sense is possible. Theapparent discontinuities in simulations and experiments mustbe rounded close to a nominal transition pressure. Numericalstudies suggest that this rounding covers an exceedinglynarrow pressure interval for the systems discussed here (Swiftet al 1993, Trasca et al 2004). One interesting question, yet tobe explored, is how the fluctuations near these quasi-transitionsare revealed through electron transport or scattering. Densityfluctuations will nearly diverge according to the generalrelation 〈�N2〉 = (∂ N/∂ ln P)T , derived from equation (5).One anticipates behavior analogous to critical opalescence orthe critical scattering of electrons at the Curie point of aferromagnet.

Beyond this weakly bound physical adsorption regime,a wide class of other ‘adsorbates’ interact more stronglywith carbon, but still preserve the sp2 bonding geometryof the carbon host. Since these species interact stronglyenough to infiltrate between the layers of the bulk graphitelattice, they are no longer normal adsorbates, but genuinedopants, with substantial charge transfer to the host carbonlattice. In fact, the so-called graphite intercalation compoundsmotivated Peter’s initial contact with several contributors tothis festschrift. Intercalation occurs when the charge-transferdopants form their own ordered sublattice, the most dramaticexample being the ordered stacking sequence of N graphenelayers alternating with one or more intercalant layers inone-dimensional superlattices, a so-called ‘stage N’ graphiteintercalation compound.

Guest–host charge transfer is a common feature of allthe carbon-based intercalation compounds. Although theliterature from the 1960s calls these materials ionic salts, theywere actually good metals. Graphite intercalation compoundsdisplay textbook signatures of the nearly free electronmodel: temperature-dependent in-plane resistivity followingMatthiessen’s rule with weak electron–phonon interactions,a temperature-independent Pauli spin susceptibility withminimal Stoner enhancement, a Drude-like reflectivity spectrawithout complications from overlapping inter-band transitions,and a linear specific heat coefficient whose magnitude isconsistent with other measures of the density of states at theFermi energy (Claye et al 2000). All of the forms of alkali-doped carbon depicted in figure 10 constitute synthetic metalswith conduction by delocalized π electrons or (in conductingpolymers) solitons. The π -derived states are broadly dispersivealong the direction of conjugation and weakly dispersive alonginterlayer, intermolecular or inter-tube directions.

Peter was the most important contributor to the Ramanspectroscopy of graphite intercalation compounds. Ramanspectroscopy turned out to be a very important tool for studyingthese systems, largely because of his excellent pioneeringwork. Early graphite intercalation research offered the

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Figure 10. Schematic structural models for alkali-intercalatedcarbonaceous host lattices. Clockwise from upper right: stage 1potassium-intercalated graphite KC8; saturated phase ofNa-intercalated polyacetylene in which close-packed Na chainsoccupy all available interstitial channels; potassium fulleride whereboth tetrahedral and the single octahedral site in the fcc host aresingly occupied; a hypothetical saturation-intercalated SWNTtriangular lattice corresponding approximately to KC13. All but thelast have been identified crystallographically; the intercalatednanotube superlattice is entirely hypothetical. Peter studied all ofthese systems, except for doped polyacetylene. Adapted from Fischer(2000).

possibility of studying individual graphene layers separatedfrom each other by layers of the intercalant; hence it was avery early example of a nanostructure. In certain compoundsone could separately study the Raman spectra of the carbonlayer and the intercalant layer, because the relevant modesoccurred at different frequencies. In stage 1 compounds, anintercalant layer separates each graphene layer from the others.In stage 2 compounds, each graphene layer has a grapheneneighbor to one side and an intercalant layer to the other.Compounds of stage n > 2 have two types of grapheneconstituents: two layers like those in stage 2 compounds andthe remainder with only graphene neighbors. Peter measuredthe frequencies, intensities and line-shapes of the Ramanfeatures due to the graphitic host material and the intercalant,studying the perturbations of each upon the other as a functionof intercalant species and staging. In this way he obtainedgreat insights into intercalation. Peter performed inspirationalwork on staging in H2SO4 intercalation compounds where hemonitored both the electrochemistry and the Raman spectra insitu as staging proceeded (Chan et al 1987a, Sumanasekeraet al 1999). He did complementary pioneering work onacceptor compounds in the bromine intercalant system, wherehe could study the spectra of both sp2 carbon and bromine(Eklund et al 1978, Chen et al 2003). This work was seminalto the field, advancing both materials physics and Ramanspectroscopy in highly novel ways.

Superlattices in graphite intercalation compounds (Safranand Hamann 1979, Dahn et al 1982) and doped polymers(Ma et al 1988) arise from competition between anisotropicdopant–dopant and dopant–host interactions, as modulatedby temperature-dependent entropic contributions, the dopant

Figure 11. The Princess and the Peas model of elastically mediatedintercalant interactions. Elastic interactions between layerdeformations caused by intercalants produces an effective in-planeattraction U between the intercalants. These elastic dipoles produceweaker attraction in hosts with stiffer layers, thus TiS2 does notexhibit staging at T = 300 K whereas graphite does. The schematicphase diagram shows staged phases as a function of Li intercalantconcentration (Fischer and Kim 1987). The large shaded arearepresents stage-ordered regions (pure phase and two-phasecoexistence) in which enthalpy dominates (the ‘ferromagnetic’regime). Solid lines and curves within the shaded region demarcatedifferent stage-ordered configurations, while the boundary betweenshaded and unshaded regions is the locus of transitions from stageordering to dilute stage 1 (lattice gas or liquid, or the ‘paramagnetic’regime).

chemical potential μ, and the pressure P . Staging is onlystable when the effective in-plane dopant–dopant interactionis attractive while the effective out-of-plane dopant–dopantinteraction is repulsive. In intercalated graphite at lowtemperatures, the in-plane attraction between intercalantsdominates. Hence, an interlayer gallery is fully occupied byintercalants at a spacing consistent with their mutual hard-core repulsion and the strength of potential energy corrugationsimposed by the honeycomb lattice. This interlayer fillingoccurs in a sequence of stages with increasing dopantconcentration, including multiphase coexistence over mostof the range of μ. Near saturation doping, the systemattains stage 1 plus random vacancies. At sufficiently hightemperature, each two-dimensional layer of intercalants meltsand the system becomes a dilute, stage-1 lattice gas, with theintercalants distributed randomly.

What is the source of the effective attraction betweenintercalants within the same gallery? The effect is counter-intuitive, since charge-transfer dopants should repel eachother through direct Coulomb interactions. At low dopantconcentration, the layers of the carbon host deform elasticallyaround well separated intercalant ions, creating elastic dipoles(Safran and Hamann 1979) whose magnitude and decay lengthdepend on the strain gradient (see figure 11). Crucially,nearby dipoles in the same interlayer gallery attract each other,since this minimizes the total elastic deformation of the host.Elastically stiff hosts such as the TiS2, which is composedof thick, covalently bonded, S–Ti–S trilayers, support onlyweak strain dipoles that decay slowly with distance fromthe intercalant ion. Consequently, the elastically mediateddopant–dopant attraction in transition metal dichalcogenidesis weak, and the only stable intercalated structure is stage1 with random in-plane site occupancy. In contrast, the

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constituent carbon layers within graphite are floppy. The in-plane attraction is strong, so graphite intercalation compoundsare the prototypical multi-staged layer intercalants. Althoughbeautiful, these staging transitions can be impractical: Li ionbatteries with well-ordered graphitic anodes are degraded bythese staging transitions over many charge and discharge cycles(Dahn et al 1995).

Molecular C60 solid in the fcc structure offers tetrahedraland octahedral interstitial sites suitable for intercalation(Murphy et al 1992). Solid C60 is readily n-doped viareduction by alkali or alkaline earth metals, but apparentlycannot be p-doped since oxidizing acids destroy the molecule.Doping solid C60 with alkali metals M = K, Rb and Csgenerates a series of well-defined crystallographic phasesMxC60, where x = 1, 3, 4 and 6. At low concentration,alkali ions preferentially occupy the larger octahedral sitesup to 1:1 alkali:C60 stoichiometry, accompanied by slightlattice contraction due to ionic interactions, because evenCs+ is too small for hard sphere repulsion to be a factor.Approaching M3C60, the smaller tetrahedral sites, two permolecule, begin to fill. The system either phase separatesor behaves as a lattice gas depending on the intercalant(including alkaline earth alloys). Beyond M3C60 the hostlattice transforms to tetrahedral, which accommodates fourintercalants per fullerene since the latter are no longer close-packed. Finally, bct gives way to body-centered cubic ata limiting composition of M6C60. Of particular interest,given the molecular character of fullerene-based solids, isthe moderately high-temperature superconductivity at x =3 (Hebard 1992). Very narrow conduction bands producethe high density of states at the Fermi level favorable tosuperconductivity (Gunnarsson 2004). Careful considerationof Jahn–Teller distortions, exciton binding, and electron–electron correlation is required to reconcile the high Tc (up toat least 33 K) with a BCS-like pairing mechanism.

Lattice gas behavior of the intercalant is not observedbeyond the fcc limit, but a continuously variable doping perfullerene, in principle from 0 to 12 electrons, can be realizedwith mixed alkali/alkaline earth site occupancy. This featurewas exploited to settle a controversy about the physical originof fulleride superconductivity (Yildirim et al 1996). Recentreports of superconductivity above 11 K in CaC6 (Emery et al2008) may stimulate a re-examination of non-Fermi liquidbehavior in doped carbon hosts.

The Eklund group prepared Mx C60 samples using theglove box of figure 6, and discovered several interesting effectsthrough Raman analysis (Eklund et al 1995b). The Ag(2) modefrequency is sensitive to doping—downshifting by ∼6 cm−1

for each electron transferred to the ball—and can be used tomonitor the diffusion of the alkali during intercalation. Thismode softening due to charge transfer is roughly 70% aslarge as that observed in graphite intercalation compounds.In contrast to the Ag(2) mode, the Ag(1) radial breathingmode at 493 cm−1 in C60, seen in figure 5(a), hardens by∼7 cm−1 upon doping to M6C60. Apparently a competingeffect overwhelms the carbon–carbon bond elongation thatis associated with charge transfer. Theoretical calculationsindicate that an electrostatic interaction arising from the

Figure 12. X-ray diffraction patterns of (a) starting material andsingle-walled nanotube bundles doped to saturation by K (b), Rb (c)or Cs (d) (Duclaux et al 2003).

charged C60 ball is partly responsible for the observed upshift(Jishi and Dresselhaus 1992).

What about ordered bundles of single-wall carbonnanotubes, also called ropes (Thess et al 1996)? Sincecylinders are, crudely speaking, stiffer than sheets, the elasticdeformation dipole in the tubes surrounding an intercalantin a nanotube bundle should be weaker than in graphite.Although rigid rotations about tube axes may yield localcommensurability between adjacent tubes, the weakness ofthe interlayer corrugation and the incompatibility between(n − m) mod 3 �= 0 tubes and the 3-fold symmetry of thetwo-dimensional bundle lattice frustrates long-range order.In addition, the large separation between the centers ofadjacent nanotubes should result in a weak interaction betweenhypothetical parallel chains of intercalants. One suspectsthat intercalated nanotube bundles are unlikely to showstaging, instead favoring lattice gas behavior with randomfilling. Guest–host charge transfer and the resulting Madelungenergy should then govern the phase stability, rather than theelastically mediated dopant–dopant interactions of graphiteintercalation compounds.

Direct determination of doped nanotube structuresis hindered by the difficulty of obtaining well-orderedhost lattices of single-walled nanotubes with monodispersediameter (Thess et al 1996). X-ray diffraction of bundles dopedto saturation by K, Rb and Cs (Duclaux et al 2003) showsa shift in the first-order (1, 0) peak—a characteristic of the2D triangular bundle lattice—to lower wavevector, a shift thatincreases with atomic number of the alkali (see figure 12). Thisshift suggests a dilation of bundles which remain crystallineupon doping. However, the starting material in this experimentresults from high-temperature annealing, which is known toincrease the average tube diameter, since small-diameter tubesare less thermally stable than large-diameter ones. Thus, thesmall shift of the (1, 0) peak between pristine and saturation-doped materials may correspond not to lattice dilation, butto a change in the average diameter of the constituent tubes.Curiously, the compositions determined by weight uptakecorrespond to one alkali atom per eight carbons, the same as the

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Figure 13. In situ powder x-ray profiles measured at fixed cell potentials during Li insertion (left, bottom to top) and de-insertion (right,bottom to top). As Li insertion progresses, the first-order rope peak at q = 4π sin θ/λ = 0.43 A−1 decreases in intensity without shifting orbroadening. Crystalline ropes are restored after de-insertion only after washing followed by a high-temperature anneal. Adapted from Clayeet al (2000).

saturated stage-1 phase of graphite intercalation compounds.This correspondence suggests that electrostatics governs thestability of these compounds. Despite a relatively highconcentration of inserted alkali atoms, the observed diffractionpatterns do not exhibit new lattice symmetries and do notcorrespond to the ordered structures proposed by simulations(Gao et al 1998, Fischer et al 2000).

In situ experiments exploiting electrochemical control,where the sample serves as a working electrode, canaccommodate measurement of x-ray diffraction, Ramanscattering, reflectivity, resistivity and Pauli susceptibility (viaconduction electron spin resonance) during charge/dischargecycles. In addition, a plot of cell potential versus dopantconcentration can reveal general features of the phase diagram,such as staging transitions and coexistence regimes. Eklundrecognized the beauty of this approach, exploiting it toperform in situ neutron diffraction during staging transitionsof sulfuric acid in graphite (Chan et al 1987b). Muchlater, Peter measured resonant Raman scattering in p-dopednanotubes while electrochemically tuning the Fermi energy(Sumanasekera et al 1999).

Reversible electrochemical insertion of Li and K intosingle-walled nanotube bundles has been investigated bygalvanostatic charge–discharge on half-cells consisting ofpurified single-walled nanotube buckypaper and Li or Kmetal, using LiPF6 or KCN salts in organic solvents. Insitu acquisition of x-ray scattering data used a magneticallyactuated piston to raise and lower the electrolyte (Claye et al2000). Figure 13 plots the x-ray results across one lithiumcharge/discharge cycle. The reference spectrum shows a broad(1, 0) reflection at q = 0.43 A

−1from the 2D triangular rope

lattice and a sharp (002) peak at q = 1.87 A−1

from residualgraphite impurities. Doping reduces the intensities of thesepeaks, but does not change their positions. Near the maximum

doping level (i.e. the lowest cell potential), the (002) peakdevelops a shoulder at lower q; this signature of the ∼10% c-axis dilation of stage-1 LiC6 confirms the proper operationof the cell. Reversing the current recovers pristine graphite,but not ordered bundles: the (1, 0) peak does not recover.Bundle crystallinity was restored only by high-temperatureannealing after disassembling the cell. Similar results forpotassium, (whose higher scattering power would certainlyreveal 2D lattice gas filling or lattice dilation), suggest thatelectrochemical doping simply frays the bundles somewhatby progressive solvent co-intercalation rather than irreversiblyexfoliating them. In contrast, samples that are vapor-dopedby alkali atoms retain crystalline bundles, but the relative x-ray peak intensities are inconsistent with appreciably filledchannels in the doped state (Gao et al 1998, Fischer et al 2000).A convincing fit of scattering data has not yet been achieved forany structural model for any dopant.

Charge transfer in these electrochemically K-dopednanotube arrays has been studied by several in situprobes: four-probe conductivity, microwave conductivity,electron paramagnetic resonance spectroscopy and Ramanspectroscopy (Claye et al 2000). Samples of a givenconcentration were anaerobically transferred to a cryostat fortemperature-dependent measurements. An EPR signal is adefinitive proof of a metallic state, since it measures thetemperature-independent concentration of Pauli spins, whichis proportional to the density of states at the Fermi energy.In addition, doping-induced redshifts of certain Raman-activemodes reflect carbon–carbon bond softening due to n-doping,or conversely for p-doping (Rao et al 1997a). Figure 14collects the room-temperature results. The top panel showsa smooth 15-fold increase in the conductivity (normalized tographite) with increasing K concentration from zero to aboutKC27, a quarter of the saturation doping. For comparison,

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15 (a)

(b)

(c)

10

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1595

1590

1585

0.00 0.02

K/C atomic ratio

0.04

Doping

μwave dopingDC 4-probe

μwave de-doping

De-doping

Figure 14. In situ measurements of the electrical conductivity (a),spin susceptibility (b) and shift of the Raman-active tangentialG-band (c) as functions of K/C ratio during galvanostaticallycontrolled insertion and de-insertion. The maximum K/C is limitedby coinsertion of the THF solvent. Panel (a) shows that theconductivity enhancement saturates at K/C ∼ 0.04, is completelyreversible (solid and open circles), and is the same when measured atmicrowave and low audio frequencies. Panel (b) shows that the spinsusceptibility also evolves reversibly with K concentration, morerapidly above K/C = 0.007. Panel (c) shows that the Raman shift, asignature of charge transfer, also evolves continuously (andreversibly, not shown) and exhibits non-monotonic behavior belowK/C = 0.007. Adapted from Claye et al (2000).

vapor-phase doping to saturation, i.e. KC8, yields a 40-fold conductivity enhancement at 300 K (Lee et al 1997).The microwave data shows that the process is reversibleunder de-doping. The conductivity is linear in cell potentialbut nonlinear in potassium concentration, since most of theK uptake occurs below 0.5 V. The smooth evolution ofthe conductivity provides no evidence for phase transitionsor staging under doping, consistent with the x-ray resultsdiscussed previously.

Microwave ESR measurements required the weakly polarKCN electrolyte, for which the maximum K/C ratio is 1/24,since THF (tetrahydrofuran) co-intercalates to form a partiallysolvated ternary compound at higher doping levels. Themiddle panel of figure 14 plots the Pauli spin susceptibility χP,proportional to N(EF), as a function of doping. No conductionelectron signal was detected in the undoped state due to de-phasing of the induced spin alignment through interaction withapproximately 1 at% of ferromagnetic Ni impurity from thecatalyst. A well-defined resonance emerges upon doping, with

a monotonically increasing intensity. Despite the large errorbars, one is tempted to identify an induction period belowK:C ∼0.007 after which the susceptibility increases rapidly.However, the threshold at 0.007 most likely simply representsthe potassium concentration at which all of the semiconductingtubes are doped into the metallic regime. The Raman shiftshows a similar threshold, above which a continuous andreversible redshift reflects charge-transfer-induced softeningof the carbon–carbon bonds, consistent with the behavior ofthe conductivity and Pauli susceptibility. Below this dopingthreshold the Raman shift is not monotonic; this is also theregion where χP depends only weakly on K:C.

Alternatively, the induction period might suggest behaviorreminiscent of the soliton doping regime in polyacetylene, i.e. alarge conductivity enhancement with no spins. Charge transferin doped conjugated polymers, in particular polyacetylene, ismore subtle than in graphite due to the existence of solitons:one-dimensional objects, spread over about ten carbon sites onthe (CH)x chain, which carry charge but no spin (Chiang et al1977, Heeger et al 1988). Solitons can originate at defects orcan be induced by doping up to some maximum concentrationabove which the conductivity increases dramatically, withthe onset of Pauli spins signaling the transition from asoliton-doped semiconductor to a normal metal. Nanotubesdo exhibit a low energy elastic excitation, the twiston, whichmight provide the necessary quenched distortion to stabilize alocalized lattice distortion on individual tubes (Kane and Mele1997).

With the advent of graphene as the latest nanocarbonpossessing readily tunable properties, we have come fullcircle. Wallace’s landmark band structure published 63 yearsago contained the seeds of graphene physics, in particularband degeneracy and linear dispersion at the Fermi energy(Wallace 1947). It significantly influenced Peter’s early workon intercalation compounds. We now describe graphene asunrolled nanotubes; less than 20 years ago nanotube conceptswere introduced by starting from the fiction of rolled-up single-layer graphite. For now graphene doping is generally limitedto modulation by a capacitively coupled gate, as in field effecttransistors. One suspects that it would not be long beforesomeone rediscovers the surface science literature devotedto alkali metal adlayers (see, for example, (Ancilotto andToigo 1993) and references therein) and develops a chemicalprocedure to induce permanent property changes in graphene.

Effects more dramatic even than intercalant dopingare possible through chemisorption to graphene sheets(Boukhvalov and Katsnelson 2009). Chemisorption is morecomplex than physisorption, since one must explicitly accountfor the pronounced electronic and ionic response of thecarbon atoms. One striking prediction of chemisorptionmodels is graphane, in which hydrogen reacts with grapheneto form an infinite, buckled sequence of C–H bonds, agiant planar molecule (Sofo et al 2007, Flores et al2009). Tentative experimental evidence for this novel two-dimensional crystal exists (Elias et al 2009), in that graphenereacts reversibly with atomic hydrogen. Exposure to cold-hydrogen plasma increases the electrical resistivity of grapheneby two orders of magnitude. The resulting insulator remains a

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hexagonal crystal, and the Raman spectrum shows vibrationalcharacteristics of fully hydrogenated graphane. This materialreturns to its pristine graphene form after thermal annealing(Elias et al 2009), without substantial damage to the graphenelattice. However, the lattice constant of the hydrogenatedmaterial currently presents an interesting puzzle. Transmissionelectron microscopy indicates that the insulating materialproduced by graphene hydrogenation has a lattice constantalmost 5% smaller than graphene, but theory predicts thatthe lattice constant should be 3% larger than graphene (Sofoet al 2007). Also unknown is the maximum degree ofhydrogenation that can be obtained by this method.

4. Electron energy-loss spectroscopy at the nanoscale

As an excellent experimentalist, Peter was always awarethat a complete picture of nature required one to correlatea nanostructure’s physical behavior with its structural,morphological and chemical characteristics. Although heappreciated the power of spectroscopic techniques such asRaman spectroscopy, Fourier transform infrared spectroscopy,photoluminescence and visible–UV absorption, these probespresent intrinsic limitations in spatial resolution. Hence healso dedicated great attention to complementary techniquessuch as atomic force and electron microscopy that offer muchhigher spatial resolution, whether studying ensembles (Aduet al 2006a, 2005, Gutierrez et al 2005, Kim et al 2008,2005, Furtado et al 2004, Liu et al 2008) or individual (Chenet al 2008, Wu et al 2009) nanostructures. In the lateryears of his career, Peter expanded his research interests toencompass many new kinds of nanostructures. He studiedplasmons in nanoparticles, magnetic doping of semiconductornanowires (Wu et al 2008), the local properties of graphene(Gupta et al 2009) and boron doping in carbon nanotubes(Liu et al 2008). In many cases he successfully correlated,one-to-one, the physical behavior of individual nanostructureswith their structure, chemistry and morphology, combiningoptical techniques with electron microscopy. We now reviewhow recent technological advances in electron microscopy willadvance Peter’s vision of the scientific method for research innanoscience.

Spectroscopic techniques of absorption exploit theinelastic scattering suffered by the probe (photons or electrons)while traveling across a material, through interactionswith vibrational modes (i.e. phonons), electronic transitions(excitons), and collective oscillations of free charge carriers(plasmons). Here we survey recent advances in usingelectron probes to study the physical and chemical propertiesof individual nano-objects, focusing on electron energy-lossspectroscopy (EELS) as performed in a transmission electronmicroscope.

The synthesis and fabrication of novel nanostructuresimposes a growing need for analytical techniques withvery high spatial resolution. Recently, electron energy-loss spectroscopy performed in a spherical aberration (Cs)

corrected scanning transmission electron microscope (STEM)has reached record sub-nanometer, even atomic resolutions(Haider et al 1998, Krivanek et al 1999, 2003, Muller et al2006, Muller 2009, Maigne and Twesten 2009, Pennycook et al

Figure 15. Schematic of an STEM-EELS system. The microscopecolumn (electron source and electromagnetic lenses) isoversimplified in order to highlight the detection elements: theannular dark field detector and electron spectrometer.

2009). An electron beam with an energy of a few hundredkeV can be focused to a scanned probe ∼0.1 nm in diameter,making possible a transmitted image of a sample with atomicspatial resolution.

Figure 15 shows the main components of an STEM-EELSsystem. The high energy electron beam is focused to a sub-nanometer spot and can be passed through a thin crystallinesample along a single atom column. An annular dark fielddetector collects electrons elastically scattered at high anglesby Rutherford scattering, forming an image as the probe scansthe sample. Simultaneously, inelastically scattered electronsare collected in the forward direction; an electron spectrometerdisperses these to resolve the energy-loss spectrum, correlateddirectly to the position of the beam on the sample.

Elastic scattering mainly arises from interactions withatomic nuclei. Since a nucleus has a much higher rest massthan an electron, the energy exchanged between them is toosmall to resolve in a TEM-EELS system. Elastic scatteringproduces the so-called zero-loss peak; in a very thin sample,this peak essentially reproduces the energy distribution of theelectron source. Inelastic scattering arises from the interactionswith conduction, valence and inner-shell electrons. TheEELS spectrum presents two important regimes of inelasticscattering: the low-loss and high-loss regions. The low-lossregion up to ∼50 eV involves interactions with the least-boundatomic orbitals, transferring energy into plasmons, inter-bandtransitions, and intra-band excitations. The high-loss regionabove 50 eV is associated with inner-shell electrons and henceit reveals the elemental composition of the sample.

The electrons in the outer shells (i.e. conduction electronsin a metal or valence electrons in a semiconductor) are weaklybound to the atoms, with significant delocalization into energybands. Since they couple to each other by Coulomb forces,an electromagnetic perturbation (via photons or electrons)can induce collective oscillations with a characteristic energy

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Figure 16. Deconvoluted EELS spectra measured at the corner (A),edge (B), and center (C) of a triangular Ag nanoparticle. Comparedto the mica support (D). The different regions display characteristicplasmon modes. The colored insets map the spatial distribution ofeach plasmon mode. Adapted from Nelayah et al (2007).

signature. Fast electrons from the probe can displace outer-shell electrons in the specimen through Coulomb interaction,leaving behind a positively charged correlation hole. Thisperturbation can initiate a longitudinal charge oscillationalong the probe trajectory (Egerton 2009): a plasmon wakeoscillating at a frequency ωp.

The energy loss is proportional to Im[−1/ε(E)] =ε2/(ε

21 + ε2

2), where ε(E) = ε1 + iε2 is the energy-dependent complex dielectric function of the medium. Thisquantity is routinely measured by optical techniques. Recently,techniques which exploit enhanced electromagnetic fields,such as resonant Rayleigh dark field optical microscopy,have measured the spatially averaged optical response fromindividual nano-objects (Sherry et al 2006). However, eventhe most sophisticated optical methods, such as tip-enhancedoptical spectroscopy (Cancado et al 2009), cannot providespatial resolution better than a few tens of nanometers. Thesub-nanometer electron probe of an STEM-EELS systemcan also activate these optical excitations; this suggests thepossibility of imaging localized excitations in a single nano-object through the near infrared, visible, and ultraviolet regionsby STEM-EELS spectroscopy. Depending on the electronsource, the lowest energy (i.e. near infrared) region of theEELS spectrum can be masked by the tail of the zero-loss peak. However, high-brightness, small-energy-dispersionelectron sources, such as cold field-emission electron gunsand e-beam monochromators (especially within Cs-correctedSTEMs), now provide the right tools to make these spatiallyresolved measurements. Note, however, that optical techniqueslike those that Peter pioneered still provide a finer energyresolution for measuring vibrational mode shifts.

For example, Nelayah et al (2007) mapped three distinctsurface plasmon modes at 1.7, 2.7 and 3.2 eV within a single

Figure 17. High-resolution annular dark field image and thecorresponding Ti, O and Ca elemental maps of a misfit dislocation ata SrTiO3/CaTiO3 interface. The color-coded map gives the Ca/Tisignal ratio. Maps are 128 pixels × 128 pixels; the acquisition time0.01 s/pixel and the beam current is ∼200 pA. Adapted fromPennycook et al (2009).

triangular Ag nanoparticle ∼50 nm across, as depicted infigure 16. The lowest energy mode is confined to the corners ofthe triangle. The energy of this corner-localized mode stronglydepends on the particle size and shape. Mapping plasmons innanostructures facilitates plasmon engineering by tuning thenanoparticle geometry.

Recently, N’gom et al (2009) investigated the elec-tromagnetic coupling of surface plasmon modes on twointeracting Au nanorods. The isolated nanorods each showtwo plasmons, a longitudinal mode at ∼1.9 eV that is confinedto the rod ends and a transverse mode at ∼2.4 eV thatis homogeneously distributed along the nanorod. Whentwo such rods are close to each other, the EELS spectrummeasured in the gap between them shifts to lower energies.The experimental plasmon intensity distributions correlateswell with the theoretical distribution of the electromagneticfield calculated by the discrete dipolar approximation method.The results also agree with previous optical measurementsof interacting nanoparticles, wherein the spatially averagedplasmon intensity shows similar energy shifts (Rechberger et al2003, Atay et al 2004).

The high-loss region of the EELS spectrum provideselemental analysis. The binding energies of inner-shellelectrons (labeled K, L, M, N and O) range from hundredsto thousands of electron volts. When electrons from thebeam ionize inner-shell electrons, the resulting features in theEELS spectrum, called ionization edges, characterize each

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Figure 18. Structural defects in a (6, 6) carbon nanotube, showingschematic and reconstructed vacancies and di-vacancies, plus aStone–Wales defect and an adatom–vacancy pair.

chemical element. These ionization edges are superimposed ona rapidly decreasing background from electrons that undergomultiple random scattering events. This background isusually interpolated and removed for quantitative elementalor structural analysis. K-edges typically have a sawtooth-like shape, i.e. an abrupt increase in intensity followed bya more gradual monotonic decay. The edge may containa subtle energy-loss near-edge structure (ELNES) that arisesfrom bonding effects. After background removal, the core-lossintensity Jc(E) is given by the Fermi golden rule: Jc(E) ∝M(E)2 N(E) ∝ (d f/dE)N(E). Here M(E) is an atomicmatrix element closely related to the atomic oscillator strengthd f/dE , and N(E) is the local density of final states for theelectronic transition (Egerton 2009). N(E) varies for differentcrystallographic sites. Changes in the chemical environment ofan atom can also shift the threshold of the ionization edge by afew electron volts.

Atomic-resolution spectroscopic mapping of near-edgestructures is now feasible with the new generation of Cs -corrected STEM. Figure 17 gives a beautiful example, wherePennycook et al (2009) use a fifth-order aberration correctedSTEM to obtain EELS spectrum images that clearly showa misfit dislocation core at a SrTiO3/CaTiO3 interface. Theindividual Ti, O and Ca maps correlate with the high-resolutionannular dark field image.

The EELS spectrum does not depend on the crystalorientation relative to the electron beam for isotropic materialssuch as cubic crystals. However, structures based on graphenesheets, such as graphite, nanotubes or nanohorns, are extremelyanisotropic, with graphene being the ultimate two-dimensionalmaterial (and the basis of much of Peter’s research program).The σ electrons of these sp2 hybridized carbon atoms providestrong inter-atomic bonding in the basal plane, while the π

orbitals are oriented perpendicular to the plane. The K-edgeof graphene-like materials is associated with transitions fromthe 1s state to empty π∗ and σ ∗ anti-bonding orbitals. Theπ∗ component produces a sharp loss peak at 285.4 eV, whilethe broader σ ∗ contribution centers around 292.5 eV. ScanningTEM-EELS of individual multi-walled carbon nanotubesreveals a strong orientation dependence to the K-edge (Stephanet al 2001, Maigne and Twesten 2009). Maigne and Twesten(2009) mapped the π∗/σ ∗ K-edge intensities in an individual

Figure 19. Formation energies of single vacancies and doublevacancies in armchair (a) and zigzag (z) single-walled tubes ascalculated in density-functional-based tight-binding (Frauenheimet al 2002) and density-functional theory (Kresse and Furthmuller1996). The inset shows a double vacancy in an (8, 8) armchair tube.Reprinted from Krasheninnikov et al (2006) with permission fromElsevier.

multi-walled carbon nanotube, showing maximum intensitywhen the beam is parallel to the graphene planes. Asimilar approach can in principle measure the sp2/sp3 ratio inhybrid nanostructures, but this experiment is more challenging(Berger et al 1988). The mapping of ionization edges has alsorevealed the chemical distribution and structure of multi-shellhybrid B–C–N nanotubes (Stephan et al 2001).

TEM instrumental development now enables scannedatomic-resolution EELS to reveal detailed field distributionsin nanostructures, while simultaneously providing valuableinformation on their chemistry, structure and bonding at theatomic scale.

5. Defects in carbon nanostructures

Beyond the properties of ideal, well-ordered periodic sp2

carbons discussed so far, defects play a prominent role.Defects in carbon nanotubes specifically greatly influencephysical properties such as mechanical strength (Zhang et al1998a, Salvetat et al 1999, Sammalkorpi et al 2004, Penget al 2008), optical response (Uchida et al 2007, Fujimoriet al 2010), and electron (Charlier et al 1996, Chico et al1996, Crespi et al 1997, Yao et al 1999, Bockrath et al2001, Gomez-Navarro et al 2005, Zhou et al 2006, Charlieret al 2007, Vijayaraghavan et al 2010) and thermal transport(Yamamoto and Watanabe 2006, Mingo et al 2008). Theyactivate the D-band in Raman spectroscopy, a topic of greatinterest to Peter. These deviations from translational symmetryinclude vacancies (often reconstructed to optimize carbon ringstructures), Stone–Wales bond rotations (Stone and Wales1986) and heteroatoms such as hydrogen or fluorine. Defects

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Figure 20. A Stones–Wales defect can split into a dislocation dipole,the two dislocations gliding apart through a series of successive 90◦bond rotations that shift bonds from the current seven-fold to thecurrent five-fold ring.

Figure 21. Snapshots of atom emission from a bent double-wallednanotube in tight binding molecular dynamics in a microcanonicalensemble (Wako et al 2007). Dark gray, light gray, and black atomsdenote the inner wall, outer wall, and emitted atoms, respectively.The arrow indicates a hole which relieves compressive stress.

can occur during growth (Crespi 1999) or be introduced viachemical treatment (Zhang et al 2003, Datsyuk et al 2008),mechanical deformation (Yakobson 1998, Nardelli et al 1998,2000, Huang et al 2006, Ding et al 2007) or irradiation(Krasheninnikov and Banhart 2007, Crespi et al 1998, 1996).Although defects of many kinds have been closely examinedtheoretically via both first-principles (Hohenberg et al 1964,Kohn et al 1965, Car and Parrinello 1985) and empirical(Tersoff 1988, 1989, Xu et al 1992, Tang et al 1996) methods(reviewed in Rafii-Tabar (2008)), experimental studies aremore limited in number.

Figure 18 shows examples of point defects in a (6, 6)nanotube. The single-atom vacancy reconstructs to a morestable structure with a single dangling bond and a five-membered ring. A di-vacancy similarly reconstructs to forma 5-8-5 defect (which can be transformed into a 555-777configuration by rotating a bond out of the eight-fold ring).A Stone–Wales defect comprises a 90◦ rotation of a C–Cbond to create two oppositely-oriented 5–7 pair dislocations:a dislocation dipole. Finally, the last panel depicts an adatom–vacancy pair. Table 1 provides experimental and theoreticalformation and migration energies for many of these defects.(Note that the reference state for the carbon chemical potentialis not always explicitly described in the literature on defectswith variable atom number, but one consistent definition couldbe the energy of an isolated carbon atom.) The vacancy and

Figure 22. Multi-vacancies produced by removing two, four, six oreight carbon atoms from a tube wall and subsequently relaxing thestructure, all within an (8, 8) nanotube. Open circles on left denoteremoved atoms. The 5-8-5 defect of the di-vacancy evolves throughdislocation climb as successive dimers marked in black are removed.Reproduced with permission from Wako et al (2008).

di-vacancy energies decrease with decreasing tube diameterdue to the greater defect-induced release of curvature strainenergy in narrower tubes; the di-vacancy energy is lower,since the dangling bonds can be satisfied under reconstruction.The Stone–Wales defect typically has the lowest formationenergy, and hence is favored for formation under e.g. electronor ion irradiation. Helicity dependence arises from variationsin the alignment of C–C bond relative to the tube axis andalso electronic effects, visible most clearly in the period-threevariation in figure 19 for zig-zag tubes.

Direct observations of point defects by scanning tunnelingmicroscopy (Ouyang et al 2001, Ishigami et al 2004) andtransmission electron microscopy (TEM) (Hashimoto et al2004, Huang et al 2006) can image 5–7 pair defects andmonitor the accumulation of topological defects near kinksin deformed nanotubes. Activation energies for vacancy–interstitial recombination (0.4 eV) and vacancy migration(0.7 eV) are also accessible to time-resolved, temperature-dependent Raman spectroscopy (Uchida et al 2007), as shownin table 1.

A dislocation within the wall of a nanotube changeswrapping indices and hence is not point-like. (Dislocationsalso form perpendicular to the basal plane in multi-wallednanotubes, as seen by TEM (Huang et al 2006).) The lowest-energy edge dislocation core contains a 5–7 pair defect; two

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Table 1. Formation energies for a range of defects in carbon nanotubes.

Wrapping indices Diameter (A)Formationenergy (eV)

Migrationenergy (eV) Method

Defect type: Vacancy

Berber and Oshiyama (2006) (3, 3)–(6, 6) 4-8 4.5–5.5DFT(6, 0)–(12, 0) 5–9 6.0-7.0

Carlsson (2006) (n, n) 5.5–11 5.2–6.4DFT(n, 0) 5.5–11 5.2–6.0

Krasheninnikov et al (2006) (n, n) 6–17 5.4–6.7 0.5–2.1 Tight binding(TB), DFT(n, 0) 4–16 5.0–6.8 0.3–1.0

Kotakoski et al (2006) (5, 5) and (10, 10) 7 and 14 5.3 and 6.5 TB, DFT

Di-vacancy

Carlsson (2006) (n, n) 5.5–11 3.6–4.4DFT(and certain chiral tubes) (n, 0) 5.5–11 3.4–4.0

Krasheninnikov et al (2006) (n, n) 5–17 4.4–5.5TB, DFT(n, 0) 4–16 2.7–4.7

Kotakoski et al (2006) (5, 5) and (10, 10) 7 and 14 4.0 and 5.2 TB, DFT

Amorim et al (2007) (5, 5)–(10, 10) 7–14 4.1–4.9DFT(8, 0)–(18, 0) 6–14 3.6–4.4

Berber and Oshiyama (2008) (n, n) 4–8 3.9–4.3DFT(n, 0) 5–9 3.5–3.8

Stone–Wales

Zhou and Shi (2003) (12, 0)–(60, 42) 9–70 4.5–7.5 ExtendedHuckel(curved clusters, not tubes)

Carlsson (2006) (n, n) 5.5–11 2.6–3.4DFT(n, 0) 5.5–11 2.2–3.4

Dinadayalane and Leszczynski (2007) (5, 5) 7 1.4–2.3 DFT, MP2

Ertekin et al (2009) (6, 6)–(10, 10) 8–14 2.8–4.1 Continuummechanics(8, 0)–(20, 0) 6–16 3.0–4.5

Adatom-vacancy

Okada (2007) (9, 0)–(11, 0) 7–9 8.1–10.0 DFT

Vacancy recombination and migration

Uchida et al (2007) Mixed 0.4 and 0.7 Ramanpulsed laser,T -dependent

such defects can originate from the splitting of a Stone–Walesdefect, as shown in figure 20 (Yakobson 1998). Plastic tensiledeformation is associated with the glide of these 5–7 pairdislocations—through successive bond rotations—to lengthenthe tube (Dumitrica and Yakobson 2004, Dumitrica et al 2006,Jiang et al 2004, Nardelli et al 1998, 2000), particularly atelevated temperature; this process has also been seen in TEM(Huang et al 2008, 2006). If bond rotation cannot occur,a stretched nanotube may fracture (Tserpes and Papanikos2007). While the 5–7 defect glides by the bond rotation, itclimbs through emission or adsorption of atoms (Ding et al2007).

Dislocation dipoles also form under bending (Mori et al2006, 2007), either as the split Stone–Wales defect describedabove or as a reconstruction of a multi-vacancy (Wako et al2007). In simulations of a bent double-walled nanotube atfinite temperature, a chain of the atoms is emitted on thecompressed side, as shown in figure 21, with subsequent

reconstruction into a 5–7 defect dipole. Figure 22 depictsthe formation and migration of this dislocation dipole dueto successive atom emission. The left-hand panels showinitial states for successively larger multi-vacancies in a(8, 8) nanotube, with their relaxed structures—minimizingdangling bond energy—shown on the right. The di-vacancyreconstructs as a 5-8-5 defect. Tetra-, hexa- and octa-vacanciesall reconstruct as 5–7 defect dipoles. Treating the 5-8-5 defect as a special case of coincident 5–7 defects, thedistance between the constituent 5–7 pairs in the dislocationdipole increases with increasing number of removed atoms.These separated 5–7 defect dipoles—formed from linearmulti-vacancies—are more stable than comparable structuresformed by relaxing more compact multi-vacancy clusters(Sammalkorpi et al 2004, Kotakoski et al 2006, Lee et al2009). The dislocation dipoles stabilize the bent tube, withlarger separations generating larger bend angles, as shown infigure 23 for a (5, 5) tube (Wako et al 2008). Hence the

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Ben

ding

ang

le (

degr

ees)

Bin

ding

ene

rgy

(eV

/ato

m)

Figure 23. The bending angle and binding energy of a (5, 5)nanotube with a 5–7 dislocation dipole as functions of the number ofatoms removed from one side. The nanotube shown has themaximum bending angle, 24.2◦, caused by the removal of 8 atoms.The original unit cell contains 400 atoms. Reproduced withpermission from Wako et al (2008).

5–7 defect dipole facilitates plastic bending, in addition to axialextension.

Being formed by atom emission, these same defects can beannihilated through atom addition. To simulate this process,carbon dimers were impacted onto a 5-8-5 defect in tight-binding molecular dynamics (Xu et al 1992) (the followingdescribes new work by KW, MT and KK, not previouslypublished). A relaxed 5-8-5 defect within a (5, 5) nanotubeis impacted at the site of the eight-fold ring by C2 dimers withkinetic energies from 8 to 30 eV. Figure 24 depicts the resultingdefect annihilation: for initial kinetic energies above 18 eV, thedimer successfully inserts into the 5-membered rings.

Electron and ion beams can cut and weld carbon-basednano- and micro-devices (Jang et al 2004, Krasheninnikovand Banhart 2007, Kosynkin et al 2009, Elias et al 2010),perforce introducing defects during these operations; thesemust be understood and controlled to produce reliabledevices. Computational studies currently dominate researchon such defects in carbon nanotubes, revealing strong effectsof tube diameter and helicity, and underpinning emergingexperimental efforts in resolving and characterizing thesedefects.

Figure 24. Snapshots of the annihilation of a 5-8-5 defect throughcollision with a carbon dimer (in black), in tight binding moleculardynamics. The dimer has an incident kinetic energy of 18 eV.

As we look back on Eklund’s scientific career, hiscontributions had a large impact on carbon nanostructures,from his earliest attempts to probe single-layer and few-layer graphene in graphite intercalation compounds; to hisstudies on fullerenes in their pristine, doped and polymerizedforms; to carbon nanotubes as they appear in their single-walled, double-walled and multi-wall pristine and dopedforms; and finally to graphene which again appears in thecorresponding layered forms. Although his own researchwork largely focused on optical and spectroscopic studies,where he did pioneering work, he followed the entire field ofnanocarbons broadly and related his own scientific advancesto this broader context. This approach was also apparent inhis pioneering work on nanowires, to which he brought tobear his extensive knowledge about carbon nanostructures tosearch for quantum confinement phenomena in other nanowiresystems. He applied his deep appreciation for the designof clever experiments and new experimental approaches toadvancing research and in discovering new physics in quantumwires during the last decade of his career.

Acknowledgments

The authors acknowledge the DOE and NSF for financialsupport. JOS also thanks the American Chemical SocietyPetroleum Research Fund, QX acknowledges the SingaporeNational Research Foundation, KW and KK acknowledgesupport from Yokohama Soei Junior College, and MTacknowledges support from Yokohama City University. Theauthors all express their sincere thanks to all of the Eklundgroup alumni and others who have contributed to the researchdescribed here. We also thank Silvina Gatica, Kurt Binderand Marc Monthioux for helpful discussions and figures. Thisreview article is dedicated to Peter’s memory.

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