Formation of sp3Bonding in Nanoindented Carbon Nanotubes and Graphite W anlin Guo,1,*C.Z.Zhu,1,2T.X.Y u,2C.H.W oo,3B.Zhang,1and Y.T.Dai1 1Institute of Nano Science,Nanjing University of Aeronautics and Astronautics,Nanjing210016,China
2Department of Mechanical Engineering,Hong Kong University of Science and T echnology,Hong Kong,China 3Department of Electronic and Information Engineering,Hong Kong Polytechnic University,Hong Kong,China
(Received19April2004;published8December2004)
Nanoindentation-induced interlayer bond switching and pha transformation in carbon nanotubes
(CNTs)and graphite are simulated by molecular dynamics.Both graphite and CNTs experience a soft-
to-hard pha transformation at room temperature at compressive stress of12and16GPa,respec-burns
tively.Further penetration leads to the formation of interlayer sp3bonds,which are reversible upon
unloading if the compressive stress is under about70GPa,beyond which permanent interlayer sp3
bonds form.During nanoindentation,the maximum nanohardness of graphite can reach109GPa,and
CNTs120GPa,which is comparable to that of diamond.
DOI:10.1103/PhysRevLett.93.245502P ACS numbers:62.25.+g,62.50.+p,81.05.Uw,81.07.De
Carbon exists in many distinct forms,such as graphite, diamond,fullerenes,and carbon nanotubes(CNTs).In graphite,the carbon atoms are arranged in a layered structure of hexagonal rings with hybridized sp2atomic bonding.Carbon atoms can also form sp3bonds with the four nearest neighbors,creating the pyramidal lattice of a superhard cubic-diamond crystal.Similar to graphite,the fullerenes and CNTs have the hexagonal ring structure bound by sp2bonds.However,the materials,particu-larly the CNTs,take on a variety of lattice structures that exhibit different mechanical and electric properties[1,2]. In the last decade,many high-pressure experiments have revealed the fascinating pha transformation of fuller-enes into superhard polymeric and disordered-amorphous carbon phas.The hardness sometimes can approach that of single-crystal diamond[3–8],even at room tempera-ture[9,10].On the other hand,in graphite subjected to high pressure up to65GPa at room temperature,no superhardness is found after the pressure is removed [10,11].Recently,a new pha hard enough to crack diamond anvils is obtained from graphite undergoing a transition of sp2to sp3bonding at a pressure of about 17GPa[12].The graphitelike hexagonal boron nitride can also form sp3bonding under compressive loading[13]. Perfect chiral CNTs are radically different from
graph-ite sheets and diamond crystals,in that unpaired electrons in a CNT cau one-dimensional superconductivity or miconductivity,depending on the chiral structure [14].As a result,its conductivity can be tuned by me-chanical deformations[15],sometimes even into single electron transistors[16].The unpaired electrons in CNTs also facilitate bond formation with other molecules or atoms,and produce tunable electric properties,which cau the CNT to function as nanonsors[17].Cross-links by sp3bondings can increa the bending modu-lus of CNT bundles by30-fold[18].Therefore,pha transition and/or bond switching in CNTs under compres-sion may have significant potential in nanotechnology. Geometrical deformation of CNT bundles under pressure of up to veral GPa have been widely studied[19,20], and the lattice structure of the tube lattice may collap when the pressure is over about4GPa[21].When single-walled CNT samples are subjected to high pressures of between3and42GPa,the electrical resistance shows a steady increa,followed by a sharp ri when the pres-sure exceeds42GPa[22].However,infirst-principles calculations[23],intertube or interlayer sp3bonding in single-walled CNT bundles is not obrved up to a stress level of20GPa,and the pressure treatment of single-wall CNTs to62GPa did not produce an after-pressure-relea superhard carbon pha[22].The Raman spectra of un-loaded single-walled CNTs do not depend on pressure treatment up to24–34GPa,but nanoindentation of single-walled nanotubes(SWNTs)can produce force-depth curves of that comparable to diamond in some experiments[24].
In this Letter,the transformation of the bonding struc-ture in single-walled or multiwalled CNTs and graphite during nanoindentation is investigated from a mechanis-tic point of view using molecular dynamics simulation.A sharp ri in hardness occurs at12GPa in graphite and at 16GPa in the CNTs,but the interlayer sp3bonds,which first form under a pressure of36GPa in graphite and 46GPa in CNTs,are reversible until large-scale sp3 hybridization occurs at a stress level of about90GPa. As the pressure increas during indentation,the sp3 bonds at the center of the indentation zone are destroyed. The peak stress attained is about120GPa in the CNTs, which is higher than the compressive strength of single-crystal diamond that is lightly below100GPa[25].The compressive ,the maximum load before fail-ure,for graphite is109GPa.
In the prent simulation,the cond-generation reac-tive empirical bond order potential,developed for solid carbon on the basis of the Tersoff-Brenner expression [26],is ud.The potential has been modified to specifi-cally describe the interatomic interaction of carbon atoms in diamond and graphite lattices.In addition,non-
local effects have also been incorporated via an analytic function.The capability of the potential to correctly describe the bond breaking and switching between multi-carbon atoms [27–29]has been verified.A nonbonding interatomic interaction in the form of a Lennard-Jones 6-12potential [30]has al
so been included.Simulations of the indentation of single-walled 6;6 ,biwalled 6;6 = 11;11 ,and triwalled 6;6 = 11;11 = 16;16
CNTs with length of 98.38A
˚on substrates are performed.For comparison,a trilayered graphite sheet is simulated as well.The indenter ud has a spherical apex of radius
elites
of R 25 A
.Both the indenter and the substrate are simulated by virtual force via a repulsive potential [31]V r A R ÿr R ÿr 3to avoid the interlinking with the carbon atoms,where A is a force constant, x is the step function,R is the indenter radius,and r is the distance from the atom to the center of the indenter sphere.In this work,we take the force constant A
200eV = A
.In all simulations,the indenter is presd at the center of the samples and penetrates with a speed of 5m =s at a constant temperature of 300K controlled by the Berendn scheme [32],and a time step of 1fs is ud.The nanohardness for graphite is prented in Fig.1as a function of the indentatio
n depth.Here the nanohard-ness is defined as the indentation load divided by the contact area,which is determined from the number of atoms entering the repulsive virtual force field of the indenter.There are three distinctive regions in Fig.1:from a to b (region I)is the soft linear region where the
hardness is low and increas slowly with the in-dentation depth with a modulus of about 10GPa;the region from b to f (region II)shows the hard pha where the hardness increas sharply,but still linearly,with the indentation depth.The slope is 73times that in region I,and reprents a modulus of about 730GPa,which is comparable to the corresponding value for diamond (700to 1200GPa)[33].In the third region,from f to g (region III),the hardness becomes unstable,and the strength starts to drop.No interlayer bond forms,up to the transition point b ,at which all the interlayer spaces of
the graphite approach 2A
˚(e the int at b ).Beyond that,the interlayer interaction may be dominated by the Brenner potential and by the formation of the interlayer sp 3bonds,particularly when the thermal motion of the atoms at 300K is considered.The first interlayer bonding
(bond length less than 1.7A
˚)can be en to occur at c ,at a hardness of 36GPa,following a small hardness drop (e int).With increasing indentation depth,the hardness continues to increa to about 75GPa,where another small drop in hardness is obrved with the formation of more interlayer bonds (e int at d )and a uniform sp 3structure at the center of the cond graphite layer (int D).Beyond that,the hardness continues to increa to its peak value 109GPa at f ,keeping the same overall steep slope,with some slight drops.At f ,interlayer bond-ing occurs over a larger area,but at the center of the indented region,some sp 3structures have been destroyed and an amorphous pha with a mixture of sp 2and sp 3-bonded carbon atoms starts to appear (e int F).The area of amorphization increas with the indentation depth,until the whole structure finally becomes unstable.The uniform sp 3pha f
ormed at the pressure center of the graphite sample can bear ultrahigh compressive stress,up to 109GPa before destruction.Its strength is comparable to the compressive strength of diamond [25]and can explain why graphite under high-pressure can crack the diamond anvil [12].
However,if the pressure is removed before reaching a value of 74GPa,all the sp 3bonding structures return to the original sp 2graphite layer structure and the sample resumes its soft pha.This result is consistent with experimental obrvations [10,11].It should be noted that the 100GPa strength of the graphite and the dia-mond is obtained under a nonuniform compressive con-dition where shear stress may play important role.Under uniform compression,the pressure-induced sp 3structure in a graphite sheet with periodic boundary condition is difficult to destructed even up to 1TPa ,but the soft-hard pha transition is nearly the same.
Nanoindentation of CNTs yields similar results.A typical hardness-indentation depth curve of a biwalled CNT is shown in Fig.2.Two linear regions can be en:the soft region a-b and the hard region c-d .The small ri in the hardness in b-c is due to the strength of the vertical C-C bond of the inner tube,who diameter is much smaller than the indenter tip radius.The slope is
030
60
90
1200
2
4
6
d
b a
I
Indentation depth (Å )
)
a P G ( s s e n d r a H D
F
FIG.1(color).Hardness versus indentation depth curve of a
abductgraphite sample with three distinct regions:soft region I,hard region II,and unstable region III.The ints at points b ,c ,d ,and f on the curve show the geometry deformation and inter-layer sp 3bonding at the points.Ints D and F are the bonding conditions of atoms on the cond layer of the sample where the red atoms are in a sp 2state and the green ones are in a sp 3state.
考研时间20140:297GPa = A
in ction a-b and 1:56GPa = A in c-tion b-c .At point c ,a sharp transition from the soft to the hard pha occurs,as all the interwall spaces approach 2A
˚.The hardness at c is about 16GPa,higher than the critical value of 12GPa for graphite (point b in Fig.1).The slope of the hard pha is about 62times of that in the soft ction b-c .Interlayer bonding does not occur until the hardness reaches a value of 43GPa at d ,where the first interlayer bonding is obrved,as shown by ints A and D in Fig.2.The sp 2to sp 3bonding transition is reversible when
the unloading occurs before the applied pressure reaches a value of about 90GPa.In this ca,no perma-nent change occurs to the CNT after unloading.This is consistent with the experimental findings that show no change in electric property,hardness,or Raman spectra of CNTs after unloading from applied pressures of up to 65GPa [22–24].Slightly beyond 90GPa,large-scale interwall sp 3bonds form and cau a drop in the hardness-depth curve from e to f .Ints B and E show the interwall bonding and the uniform distribution of sp 3atoms on the inner tube at point f .Further indentation beyond f leads to a continuous increa in the hardness until the maximum at about 119GPa is reached at g .At the maximum pressure,the uniform sp 3structure at the center of the indented region is destroyed and an amor-phous sp 2and sp 3pha is obtained,as shown by Fig.3.Further indentation leads to the ont of instability,lead-ing to the decrea of the hardness and,ultimately,to the complete destruction of the CNT .
Figure 4shows the residual interwall bonding structure after unloading from point f and point h in Fig.2.It is obvious that when the compressive stress is higher than 90GPa,the interlayer bonding is irreversible.Comparing Figs.4(a)and 4(b)with ints B and E of Fig.2indicates that all but a few of the interwall sp 3bonds are broken during unloading.W ell beyond the point of the maximum hardness on the indentation curve in Figs.4(c)and 4(d),
an amorphous pha with a structure formed from mixed sp 2and sp 3bonding is obtained after unloading (from point h ,Fig.2),indicating that the CNTs must be loaded well beyond 65GPa to produce a superhard amorphous pha of sp 2and sp 3.
The indentation curves of single-walled and triwalled CNTs are compared with tho of the biwalled CNT in Fig.5.The maximum nanohardness of 121 2GPa re-mains almost the same in all three cas and is higher than that of the graphite sample (109GPa)but compa-rable to the reported microhardness of single-crystal diamond, 100GPa [25],and 88to 147GPa from the data ba [33].Similar to the biwalled tubes,no perma-nent change occurs to the triwalled CNTs after unloading from a compressive stress up to 93GPa.
Detailed simulations show that when the force constant
A reduces to 20eV = A
,the hardness-depth curve for bi-walled CNTs is nearly the same.When A changes from
200to 2eV = A
,the predicted strength has an increa less than 7%.Increasing the indenter size from 25to 50A
˚has a very weak in fluence on the hardness curve.The soft-hard pha transition is rather innsitive to the indenter size and hardness,and the boundary conditions and
the
FIG.3(color).Snapshot of the middle part of the CNT from Fig.2at point g .The outer tube is in gray and the inner one is in red.Intermediate amorphous pha with a mixture of a hex-agonal and a pyramidal structure is shown with interlayer hexagon in green,pentagon in yellow,and triangle in
西藏英文blue.
(a)(b)(c)
(d)
FIG.4(color).Geometry and permanent interlayer bonding structures of the biwalled CNT:(a),(b)after unloading from point f in Fig.2;(c),(d)after unloading from point h in Fig.2.(a)and (c)are the geometry of ction in the middle part of the CNTs where the inner tube is in red and the outer one is in gray;(b)and (d)are the inner tube with sp 2atoms in red and sp 3atoms in green.
50
100
150
2
16GPa
(6,6)/(11,11) BWNT
a
Indentation depth (Å )
H a r d n e s s (G P a )
B
C
D
E
F
FIG.2(color).Hardness-depth curve of nanoindentation of
the biwalled CNTs.The ints A,B,and C show the geometry and interlayer bonding at points d ,f ,and g on the curve;the ints D,E,and F show the bonding conditions of atoms on the inner tube of the sample where the red atoms are in a sp 2state and the green ones are in a sp 3state.
number of layer and in-plane size of the sample graphite sheets.
In conclusion,both graphite and CNTs transform be-tween soft and hard phas during indentation,with the transition compressive stress being about 12and 16GPa,respectively.In graphite,deeper penetration leads to the formation of interlayer sp 3bonding,resulting in a nano-hardness that increas linearly with the penetration depth with a modulus of about 730GPa =nm .The pha transition between the soft and hard phas is recoverable up to a compressive stress of 74GPa,beyond which uniform sp 3bonds form at the center of the indented region.At higher stress some of the interlayer sp 3become permanent and remain even after unloading.The nanohardness can reach 109GPa in the graphite sample,and about 120GPa in the CNTs,which is com-parable to the reported microhardness of single-crystal diamond.The results may explain the emingly para-doxical experimental obrvation that,while no increa in nanoindentation hardness can be detected in graphite and CNTs after-pressure treatment up to 65GPa [10,11,22],graphite sheets can be hard enough to crack the superhard diamond anvil during a compressive test of over 23GPa [12],and CNTs may be as hard as a diamond during indentation [24].
The work is supported by the National Science Foun-dation of China,Croucher Foundation,and RGC (CA02/03.EG01)at the Hong Kong University of Science and Technology.It is also supported by a gra
nt from the Hong Kong Rearch Grant Council
(PolyU5312/03E).
*Corresponding author.
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5
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Indentation depth (Å )
)
a P G ( s s e n d r a H FIG.5(color online).Hardness versus indentation depth
curves of single-walled CNT (SWNT),biwalled CNT (BWNT),and triwalled CNT (TWNT)with the inner tube of 6;6 ,and all the tubes are armchair tubes.
