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440 nature materials | VOL 2 | JULY 2003 | www.nature.com/naturematerials

AMITESH MAITI is at Accelrys Inc., 9685 ScrantonRoad,San Diego,California 92121,USA.

e-mail: amaiti@accelrys.com

W ithin a year of the experimental discovery of carbon nanotubes (CNTs)1,theoretical calculations2 predicted that their electronic

behaviour would be highly dependent on their geometrical structure,that is, their diameter and chirality.Similar analysis has been extended in morerecent years to CNTs under mechanical deformation,such as stretch,torsion and bending3–7.As they report inPhysical Review Letters,Paul McEuen and colleagues8

have shown that by stretching a nanotube with the tip ofan atomic force microscope (AFM) and measuring itselectrical conductance,they can open an electronicbandgap (Egap) in certain metallic nanotubes,and modify the bandgap in semiconducting nanotubes.These results confirm existing theoretical predictionsthat the electronic bandgap in a strained CNT woulddepend strongly on the nanotube chirality.BecauseCNTs with varying electrical properties can already besynthesized,such experiments open the door to

fabrication of a variety of nano-electromechanicaldevices,including strain gauges and pressure sensors.Such devices are expected to be much more sensitive9

than doped-Si strain gauges widely used withmicroelectromechanical systems.

As shown in Fig. 1,a CNT can be thought ofgeometrically as a graphite sheet rolled into a seamlesscylinder, such that on rolling,a graphite lattice point(n1,n2) coincides with the origin (0,0).Thus, if a1 and a2

are the two lattice vectors of graphite, the CNTcircumference is equal to the length of the vector (n1a1 + n2a2),and the CNT chiral angle θ is defined asthe angle between vectors (n1a1 + n2a2) and a1,givenexplicitly by the formula θ = tan–1[√3n2/ (2n1 + n2)].

The CNT diameter and chirality are thereforecompletely specified by the two integers (n1, n2), referredto as the chiral indices.Owing to the symmetry of thegraphite lattice,a nanotube of any arbitrary chirality canbe defined in the range n1 ≥ n2 ≥ 0 and n1 > 0,whichimplies that the chiral angle θ lies between 0 and 30° forall CNTs.Nanotubes with the extreme chiral angles of0 and 30° have special names: a CNT with θ = 0 (that is,n2 = 0) is called zigzag,and a CNT with θ = 30° (n1= n2)

CARBON NANOTUBES

Bandgap engineering with strainMuch of the interest in carbon nanotubes arises from theinteresting interplay between their helical structure andelectronic properties. With greater understanding of the way inwhich mechanical strain changes their conductance, it maysoon be possible to continuously tune the electromechanicalresponse of nanotubes.

Crystallographers must therefore rely on powder-diffraction data for structure analysis. This complexityis magnified for structures with a large number ofsymmetry-independent atoms. Indeed, Corma’s newzeolite possesses an unusually large unit cell volume (for a zeolite) with 16 unique T atoms and 34 unique Oatoms in its asymmetric unit. This is the most complexordered zeolite ever characterized from powder-diffraction data, and, from a crystallographicperspective, it represents a remarkable feat.

References

1. Corma, A., Rey, F., Valencia, S., Jorda, J. & Rius, J. Nature Mater. 493–497 (2003).

2. Corma, A. et al. J. Catal. 189, 382–394 (2000).

3. Corma, A., Navarro, M. T., Rey, F., Rius, J. & Valencia, S. Angew. Chem. Int. Edn

Engl. 40, 2277–2280 (2001).

4. Corma, A., Díaz-Cabañas, M. J., Martínez-Triguero, J., Rey, F. & Rius, J. Nature

418, 514–517 (2002).

5. Dhingra, S. S., Weston, S. C. & Kresge, C. T. in Zeolites and Mesoporous Materials

at the Dawn of the 21st Century Vol. 135 (eds Galarneau, A., Di Renzo, F., Fajula,

F. & Vedrine, J.) 05-R-05 (Elsevier Science, Amsterdam, 2001).

MCM-68

ITQ-22

a

b

Figure 2 Only two zeolitescontaining 10- and 12MRchannels also possess largecavities formed at theintersections between the 10MRchannels.a,A germanium-freezeolite (MCM-68) obtained atMobil Corporation5 in 2000,andb, the germanosilicate zeolite(ITQ-22) recently synthesized byCorma and colleagues1.Notethat molecules within each cavityof the new germanosilicatestructure must exit through oneof the four 10MR windows beforegaining access to the 12MRchannels that lie outside thecavities.Consequently the zeoliteexhibits catalytic behaviour thatis intermediate to those that haveonly 12- or only 10MR channels.

© 2003 Nature Publishing Group

NEWS & VIEWS

is called armchair (the names zigzag and armchairsimply reflect the shape of the open edges of theseCNTs,Fig. 1b and 1c).The chiral indices (n1,n2)strongly influence the electronic structure of a CNT,and therefore its electrical conductance. In particular,allarmchair tubes are predicted to be metallic (zerobandgap); tubes with n1– n2= 3n (n = any positiveinteger),which includes the (3n,0) zigzag tubes as aspecial class,are quasi-metallic (small bandgap); tubeswith n1– n2 ≠ 3n are semiconducting (finite bandgap).Experimental measurements are often not able to makethe distinction between metallic and quasi-metallictubes because of the presence of contact resistance andthermal effects.Thus for simplicity,experimentalistsoften classify CNTs as either metallic orsemiconducting,and we follow the same convention in the discussion below.

The unusual dependence of the electronic structureof nanotubes on chirality,and their potentialapplications in nanoscale devices,have promptedresearchers to investigate the effect of structuraldeformation on the electrical conductance ofnanotubes. In a pioneering experiment10,Hongjie Daiand colleagues applied a force to a suspended metallicnanotube with an AFM tip normal to the tube axis,simultaneously bending and stretching the nanotube.This deformation generated a conductance drop of twoorders of magnitude at a deformation angle of ~13°,much higher than that predicted for bent tubes3,4.The origin of such a large conductance drop promptedseveral theoretical explanations, including theformation of new C–C bonds within the CNT, leadingto fourfold coordination of some atoms10,11,and theopening of a bandgap in a metallic tube under thetensile strain resulting from AFM deformation12.

In their experiment8,McEuen and colleagues haveconclusively demonstrated that the conductancechanges observed in nanotubes under AFMdeformation are due to strain-induced changes of thebandgap (Fig.2a).The researchers used an AFM tip tosimultaneously vary the strain and electrostatically gate the tube by applying a voltage (Vtip) to the tip.The electrical conductance (G) of a nanotubesuspended between two gold contacts (Fig. 2b) wasmeasured as a function of Vtip for various degrees ofAFM deformation (corresponding to different CNTstrains).Seven different CNTs (four metallic and threesemiconducting) were used,and they all showeddifferent results as a function of strain.Two of themetallic tubes displayed a significant drop in G, asobserved previously10,whereas the other two metallictubes did not show any significant conductance change.One semiconducting tube had decreasing G with strainwhile the remaining two had increasing G.

To explain these results,McEuen and colleaguesturned to previous theoretical work on strainedCNTs5–7,which predicted that the rate of change of thebandgap as a function of strain depends on the CNTchiral angle θ.For semiconducting tubes, the bandgapcan either increase or decrease with strain.An increasedbandgap leads to a drop in conductance (as observedexperimentally for the first semiconducting tube),whilea reduced bandgap produces a conductance increase (asobserved for the other two semiconducting tubes).Stretched armchair tubes do not open any bandgap,

and always remain metallic.All other metallic tubes (n1– n2 = 3n) can open a bandgap with strain, thelargest gaps being in the (3n,0) zigzag tubes,where anEgap ~100 meV can be induced by only 1% stretching(Fig. 2a).This bandgap increases linearly with strain,thus transforming the metallic nanotube into asemiconductor at a strain of only a few percent.The different electrical response of the four metallictubes studied by McEuen and colleagues could therefore be explained by assuming that two of themwere of the type n1 – n2 = 3n, and the other two werearmchair nanotubes.

By fitting the resistance (1/G) as an exponentialfunction of strain, the authors were able to estimateboth the variation of the bandgap with strain and thechiral angle of the CNTs.However,an accuratequantitative comparison with theory5–7 requires anindependent determination of the chiral indices ofeach CNT.This may soon become possiblethroughrecent advances in high-resolution transmissionelectron microscopy13.Another interesting aspect of thework by McEuen and colleagues8 is that if thesuspended nanotube is a doped semiconductor,one caneffectively think of the experimental setup of Fig. 2b as a

a2

a1

(1,1)

(2,2)

(3,3)

(3,1)

(0,0) (1,0) (3,0) (5,0)θ

a b c

Figure 1 Carbon nanotube (CNT) basics. a,A graphite sheet with lattice vectors a1, a2.A few latticepoints are indicated, as is the chiral angle θ for a (3,1) CNT. Orange and purple lines are drawn along thecircumferences of armchair and zigzag tubes, respectively. b,A (5,5) armchair tube.c,A (9,0) zigzag tube.

Figure 2 Metal-semiconductortransition in carbon nanotubes(CNTs).a,A metallic zigzag CNT(left) opens up a bandgap (Egap)under tensile strain (right),whichturns the nanotube into asemiconductor and decreases itsconductance.b,Theexperimental geometry used byMcEuen and colleagues tomeasure the response of a CNT totensile stretching by an AFM tip.

Adapted from ref. 8, © 2003 AmericanPhysical Society.

Gold Gold

θ

Egap

Ferm

i lev

el

Tube axis

Ea

b

nature materials | VOL 2 | JULY 2003 | www.nature.com/naturematerials 441

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field-effect transistor, in which the two metal contactsact as the source and drain,and the AFM tip acts as thegate.For instance, if the CNT is p-doped,a positive biasvoltage applied to the AFM tip creates an electron-richregion in the middle of the tube,effectively making it ap-n-p transistor.This establishes an immediateconnection with the rich field of semiconductor-basedmicroelectronic devices.Using AFM tips tomechanically stretch or deform molecular systems,andapply a gate voltage at the same time,opens up a newdimension in the rapidly emerging fields of molecularand nanoelectronics.This could potentially lead to thefabrication of novel nanoscale devices such as pressuresensors, transducers,amplifiers,and logic devices.

References

1. Iijima, S. Nature 354, 56–58 (1991).

2. Mintmire, J. W., Dunlap, B. I. & White, C. T. Phys. Rev. Lett. 68, 631–634 (1992).

3. Rochefort, A., Avouris, P., Lasage, F. & Salahub, D. R. Phys. Rev. B 60,

13824–13830 (1999).

4. Nardelli, M. & Bernholc, J. Phys. Rev. B 60, R16338–R16341 (1999).

5. Heyd, R., Charlier, A. & McRae, E. Phys. Rev. B 55, 6820–6824 (1997).

6. Yang, L., Anantram, M. P., Han, J. & Lu, J. P. Phys. Rev. B 60, 13874–13878

(1999).

7. Yang, L. & Han, J. Phys. Rev. Lett. 85, 154–157 (2000).

8. Minot, E. D., Yaish, Y., Sazonova, V., Park, J.-Y., Brink, M. & McEuen, P. L. Phys.

Rev. Lett. 90, 156401 (2003).

9. Cao, J., Wang, Q. & Dai, H. Phys. Rev. Lett. 90, 157601 (2003).

10. Tombler, T. W. et al. Nature 405, 769–772 (2000).

11. Liu, L. et al. Phys. Rev. Lett. 84, 4950–4953 (2000).

12. Maiti, A., Svizhenko, A. & Anantram, M. P. Phys. Rev. Lett. 88, 126805 (2002).

13. Kociak, M. et al. Phys. Rev. Lett. 89, 155501 (2002).

442 nature materials | VOL 2 | JULY 2003 | www.nature.com/naturematerials

MATERIAL WITNESS

Secular science

The extent to which materials technology has become secularized is evident from thefact that most materials scientistswill wonder what such a

statement could possibly mean. What couldbe more materialistic than materials?

But it wasn’t always so. Once ThomasAquinas reconciled aristotelian ‘science’with Christian theology in the thirteenthcentury, it was hard to debate matters ofelemental composition in the Western world without treading on theological territory. Arguments about the constitution of the sacramental wafer in the Christian Masshindered a unified Reformation in the Germanic countries.Theological scholastics debated the nature of Christ’s fleshin pedantic detail.

Gold was valued before the Enlightenment not just for itsbeauty but because it was deemed to embody a divine purity.That’s why alchemy was as much a spiritual as a metallurgical enterprise (at least for those who took it seriously). The naming of the first distilled alcohols andother volatile organic compounds as ‘spirits’ was more thanan idle metaphor. The alchemists of Eastern Asia, mean-while, sought gold because of its supposed life-lengtheningproperties: because it was so ‘incorruptible’, it could makethe human body so too.

I was moved to ponder on these roots of the chemical andmaterial sciences by the news that some families have hadthe cremated remains of their loved ones transformed intodiamond crystals by a Chicago company called LifeGem.Who is to judge whether this is macabre or touching, or sim-ply exploitative? What is, perhaps, more illuminating is thatthe enterprise was connected to a project by the British artistMarc Quinn.

Quinn had some of his carbonized hair transformed at hightemperature and pressure into a diamond and mounted in awork called Now I’m Perfect. It would of course be unwise toassume that such an action acquires profundity simply bybeing conducted by an artist, but Quinn’s work does showhow advances in materials technology can resonate in soci-ety in a non-materialistic way.

Diamond as a symbol of perfection — here, indeed, of per-sonal perfection — collides with the notion of graphite, sootand ashes as messy stuff, which is no doubt one reason why,when researchers at General Electric first performed thehigh-pressure transformation of graphitic carbon into diamond in 1955, some gem merchants called it ‘unnatural.’

So although a diamond made from cremated ashes is inone sense not so different from the lock of hair treasured asa memento in Victorian times, in another way it is somethingmore. The material is regarded as somehow sanctified and‘purified’ by squeezing, as though GE’s process is perform-ing the role of a priestly blessing, making a body more ‘perfect’ in death than in life. Yet of course it is diamond’svery perfection that makes it hard and lifeless, cold even tothe touch.

Materials, then, have not altogether lost their symbolicvirtues. But would LifeGem’s clients feel differently if theyknew that the original GE team demonstrated their technique’s versatility by making diamond from roofing tar,bits of moth and peanut butter?

Philip Ball

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