Carbon Nanostructures

Critical Reviews in Solid State and Materials Sciences, 27(3/4):227–356 (2002) 

Carbon Nanostructures 

O.A. Shenderova, 1,2 V.V. Zhirnov, 1,3 and D.W. Brenner 1 

1 

North Carolina State University, Raleigh, North Carolina; 2 International Technology Center, Research Triangle 

Park, North Carolina; 3 Semiconductor Research Corporation, North Carolina 

ABSTRACT: An overview of the various carbon structures with characteristic sizes in the nanoscale region is 

presented, with special attention devoted to the structures and properties of ‘nanodiamond’ and carbon nanotubes. 

The term ‘nanodiamond’ is used broadly for a variety of diamond-based materials at the nanoscale ranging from 

single diamond clusters to bulk nanocrystalline films. Only selected properties of carbon nanotubes are discussed, 

with an aim to summarize the most recent discoveries. Current and potential applications of carbon nanostructures 

are critically analyzed. 

Table of Contents 

I. Introduction ............................................................................................................................. 228 

A. Historical Overview ........................................................................................................... 228 

B. Carbon Family at the Nanoscale ....................................................................................... 230 

II. Stability of Carbon Phases at the Nanoscale ....................................................................... 233 

A. Phase Diagram of Carbon at the Nanoscale ..................................................................... 236 

B. Theoretical Studies on the Relative Stability of Different Forms of Carbon at 

the Nanoscale ..................................................................................................................... 240 

III. Selected Carbon Nanostructures, Their Synthesis, and Properties .................................. 249 

A. Diamond at the Nanoscale (‘Nanodiamond’) ................................................................... 249 

1. Types of ‘Nanodiamond’ ........................................................................................... 249 

2. Ultradispersed Diamond ............................................................................................ 266 

a. Synthesis and Post-Synthesis Treatment............................................................. 266 

b. Experimental Characterization of Ultradispersed Diamond ............................... 270 

3. Atomistic Simulation on Diamond Nanostructures................................................... 283 

a. Diamond Clusters: Structural Properties............................................................. 283 

b. Diamond Clusters: Electronic Properties ............................................................ 290 

c. Diamond Nanorods .............................................................................................. 294 

B. Carbon Nanotubes ............................................................................................................. 298 

1. Synthesis and Properties ............................................................................................ 298 

2. Mechanical Properties ................................................................................................ 302 

3. Assemblies of Nanotubes and Nanodiamond............................................................ 313 

IV. Applications of Carbon Nanostructures ............................................................................... 319 

A. Diamond-Based Nanostructured Materials for Macroscopic Applications ...................... 320 

1. Applications of Ultradispersed Diamond .................................................................. 322 

2. Applications of Ultrananocrystalline Diamond Films............................................... 326 

3. Applications of Carbide-Derived Diamond-Structured Carbon................................ 327 

B. Carbon Nanotubes in Advanced Electron Sources ........................................................... 329 

C. Carbon Nanotubes as Nanoelectronics Components ........................................................ 338 

D. Medical Applications of Fullerene-Based Materials ........................................................ 343 

E. Atomic Modeling of Carbon Nanostructures as a Tool for Developing New 

Materials and Technologies ............................................................................................... 343 

V. Conclusions and Future Outlook........................................................................................... 347 

1040-8436/02/$.50 

© 2002 by CRC Press, Inc. 

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I. INTRODUCTION 

Much of the discussion of nanotechnology 

perspectives is currently centered around carbonbased 

nanostructures. While the popularity of 

carbon nanostructures to a large extent is due to 

fullerenes and nanotubes, other members of the 

nanocarbon family are also attracting steadily 

increasing attention. For confirmation we refer to 

recent reviews 1,2 and a book 3 on nanodiamond 

materials. Accordingly, structures, properties, and 

numerous applications of nanostructured graphite, 

which belongs to a broad group of so called 

new carbon materials, has been summarized recently 

in a book by Inagaki. 4 In parallel, new 

carbon allotropes are being discovered such 

as, for example, carbolite, an esoteric chain-like 

crystalline form of carbon. 5 Clearly, carbon 

nanoscience, a discipline studying properties of 

all groups of carbon entities at the nanoscale within 

a unified framework, including interrelationships 

between the various forms of nanocarbon, conditions 

under which one form transforms to another, 

and the possibility of combining nanocarbon 

entities to hierarchical structures, is becoming a 

field onto itself. There is also a new tendency to 

bring together at scientific forums researchers from 

different carbon communities, graphite fibers, 

fullerenes, and diamond, which were developing 

before rather independently. 6 While there are excellent 

reviews 7–10 that discuss several classes of 

carbon nanostructures in one general scheme, in 

particular graphite-related and fullerene materials, 

nanodiamond has remained out of the scope 

of most recent discussions. This is despite a number 

of recent discoveries demonstrating that layered 

graphite nanoparticles can transform to 

nanodiamond and vice versa, in other words, intimate 

interrelations between different forms of 

nanocarbon exist. Moreover, a variety of interesting 

research on the thermodynamics and kinetics 

of carbon at the nanoscale have been published 

recently. We review this topic in Section II. 

In the present work we try to generalize results 

on the currently known nanocarbon materials. 

After a short historical overview on carbon 

nanostructures, we complete Section I by classifying 

the carbon family at the nanoscale. In Section 

III we discuss classes of nanodiamond and 

particularly, in more detail, ultradispersed diamond 

obtained by detonation synthesis, the topic 

of research that is popular in Russia and eastern 

countries and less known in the U.S. research 

community. Some properties of nanotubes, selected 

according to the authors’ interests, are also 

discussed in Section III. In Section IV a critical 

analysis of current and perspective applications 

of selected nanocarbon structures is provided. 

A. Historical Overview 

While the history of synthetic graphite begins 

in the 19th century, 11 artificial diamonds were not 

synthesized until the middle of the 20th century. 

Since then, both graphite- and diamond-related 

groups of carbon materials have experienced several 

waves of renewed interest in scientific communities 

when new types of materials or synthesis 

techniques had been discovered. Within the 

graphite-based group, new materials (“new carbon” 

4 ), such as carbon fibers, glass-like carbons, 

pyrolitic carbons, etc., were developed in the early 

1960s, and found broad industrial applications. 4 

The most significant relatively recent application 

of this class of carbon material is probably lithium 

ion rechargeable batteries that use nanostructured 

carbon anodes, which have made possible portable 

electronic devices. 4 Within this group of 

‘new carbon’ materials, texture on a nanometer 

scale based on preferred orientation of anistropic 

hexagonal layers play an important role in their 

properties. Some of the ‘new’ graphitic materials 

contain nanostructural units within a complex 

hierarchical structure such as, for example, 

carbon fibers consisting of carbon nanotubes in 

their cores. 

A new era in carbon materials began when in 

the mid-1980s the family of buckminsterfullerenes 

(“buckyballs”) were discovered 12 followed by the 

discovery of fullerene nanotubules (“buckytubes”) .13 

The discovery of these structures set in motion a 

new world-wide research boom that seems still to 

be growing. As mentioned above, fullerene 

nanotubules and graphite-based materials are inherently 

connected, and researchers who produced 

carbon filaments had been unknowingly growing 

nanotubes decades before Iijima’s publication. 13 

228

Some of the related topics, predictions, and discoveries 

of the carbon cage structures are summarized 

in Table 1 in chronological order. 

Diamond was synthesized from graphite by 

high-pressure/high-temperature methods in the 

1950s, and low-pressure chemical vapor deposition 

(CVD) of diamond polycrystalline films had 

been developed at the beginning of 1960s. The 

area of the CVD of diamond films experienced 

several shifts of scientific and funding activity, 

with the last peak taking place in the United States 

in the mid-1990s. The interest in diamond thin 

films has increased in the last few years as research 

activities related to nanotechnology have 

. 

229

grown world-wide, and new synthesis methods of 

nanocrystalline diamond films have been discovered. 

2,14 

Diamond powder was synthesized by shock 

waves in the beginning of the 1960s by Du Pont 

de Nemour & Co, a leader in explosive technology 

previously applied to other materials. Du 

Pont produced diamond using shock wave compression 

induced by solid explosive detonation of 

carbon materials (graphite, carbon black) mixed 

with metal powder (Ni, Cu, Al, Co) placed in a 

capsule (which was destroyed after the process). 

Produced polycrystalline diamond particles of 

micron size (1 to 60 µm) (tradename Mypolex TM ) 

consist of nanometer-sized diamond grains (1 to 

50 nm). This material has been used for highprecision 

polishing applications for a long time. 

In 1999, the DuPont Corporation was acquired by 

Spring Holding, a Swiss holding company and 

parent company of Mypodiamond Inc. The production 

volume of the company is about 2 million 

carats per year (less than half a ton). 15 

Another approach for producing diamond 

powder by a more effective means with a reusable 

detonation capsule is the conversion of carboncontaining 

compounds into diamond during firing 

of explosives in hermetic tanks. 17 The history 

of the discovery of this type of nanodiamond, also 

known as ultradispersed diamond (UDD) or detonation 

diamond, is much less known and has been 

described in a recently published book by 

Vereschagin. 3 This method was initiated in Russia 

in the earlier 1960s soon after Du Pont’s work 

on shock wave synthesis and was a very active 

area of research in the 1980s, where it was studied 

independently by different groups of researchers 

(Table 2). Publications in this area at that time 

were very scarce, with some reports appearing 

decades after the actual discoveries had been 

made. 17 The first work on nanodiamond produced 

by detonation in the United States was published 

in 1987, where the method of synthesis was described. 

18 In 1983 the NPO “ALTAI” was founded 

in Russia, the first industrial company to commercialize 

the process of detonation diamond 

production in bulk quantities (tons of the product 

per year). 3 According to a USSR government report 

(1989) on UDD production, it was planned to 

increase UDD production by up to 250 million 

carats per year. 3 At the present time the production 

of detonation diamond by “ALTAI” is limited. 

Currently, there are several commercial centers 

in the world producing UDD, particularly 

in Russia (e.g., the ‘Diamond Center’ in 

S.Petersburg), Ukraine (e.g., “Alit”), Belorussia, 

Germany, Japan, and China. A center for the production 

of UDD is being organized in India. 

B. Carbon Family at the Nanoscale 

In principle, different approaches can be used 

to classify carbon nanostructures. The appropriate 

classification scheme depends on the field of application 

of the nanostructures. For example, a classification 

can be based on an analysis of the 

dimensionalities of the structures, 4,19 which in turn 

are connected with the dimensionality of quantum 

confinement and thus is related to nanoelectronic 

applications. The entire range of dimensionalities 

is represented in the nanocarbon world, beginning 

with zero dimension structures (fullerenes, diamond 

clusters) and includes one-dimensional structures 

(nanotubes), two-dimensional structures 

(graphene), and three-dimensional structures 

(nanocrystalline diamond, fullerite). In a different 

approach, the scale of characteristic sizes can be 

introduced as the major criterion for classification. 

This scheme more naturally allows the consideration 

of complicated hierarchical structures of carbon 

materials (carbon fibers, carbon polyhedral 

particles). A summary based on different shapes 

and spatial arrangements of elemental structural 

units of carbon caged structures also provides a 

very useful picture of the numerous forms of carbon 

structures at the nanoscale. 20 Regarding the 

last approach, the spatial distribution of penta- and 

hexa-rings within structures also can provide a 

basis for classification. 21 

In terms of a more fundamental basis for the 

classification of carbon nanostructures, it would 

be logical to develop a classification scheme based 

on existing carbon allotropes that is inherently 

connected with the nature of bonding in carbon 

materials. Ironically, there is no consensus on 

how many carbon allotropes/forms are defined at 

present. From time to time publications appear 

proposing new crystalline forms or allotropic 

230

modifications of carbon. Whether fullerenes or 

carbynes are considered as new carbon allotropes 

depends to a large extent on the corresponding 

scientific community. 5,22,24–26 Sometimes the 

‘fullerene community’ appears to ignore the 

carbynes, 24 which were discovered in the 1960s. 5 

However, because it can be produced only in 

nanoscopic quantities, it was very difficult to 

measure its physical properties. Similarly, the 

‘carbyne community’ does not classify fullerenes 

as an allotrope. 25 Until the 1960s when ‘new carbon’ 

materials were synthesized, only two allotropic 

forms of carbon were known, graphite and 

diamond, including their polymorphous modifications. 

Until recently, ‘amorphous carbon’ had 

been considered as a third carbon allotrope. Pres- 

231

ently, however, the structure of amorphous and 

quasiamorphous carbons (such as carbon blacks, 

soot, cokes, glassy carbon, etc.) is known to approach 

that of graphite to various degrees. 4,5 In 

this context, it should be noted that within the 

diamond community the same term ‘amorphous 

carbon’ is used for diamond like carbon thin 

films. 27 

An interesting discussion of carbon allotropy 

and a scheme for classifying existing carbon forms 

is provided in Ref. 22. The classification scheme 

is based on the types of chemical bonds in carbon, 

with each valence state corresponding to a certain 

form of a simple substance. Elemental carbon 

exists in three bonding states corresponding to 

sp 3 , sp 2 , and sp hybridization of the atomic orbitals, 

and the corresponding three carbon allotropes 

with an integer degree of carbon bond hybridization 

are diamond, graphite, and carbyne. 22 All 

other carbon forms constitute so-called transitional 

forms that can be divided to two big groups. 

The first group comprises mixed short-range order 

carbon forms of more or less arranged carbon 

atoms of different hybridization states, for example, 

diamond-like carbon, vitreous carbon, soot, 

carbon blacks, etc., as well as numerous 

hypothetical structures like graphynes and 

‘superdiamond’. The second group includes intermediate 

carbon forms with a non-integer degree 

of carbon bond hybridization, sp n . The subgroup 

with 1

FIGURE 1. Ternary “phase” diagram of carbon allotropes. P/H corresponds to the ratio of pentagonal/hexagonal 

rings. (Reprinted from Ref. 22, Copyright (1997), with permission from Elsevier 

Science.) 

blies of the structural units, ranging from simple 

forms, such as multiwall nanotubes (MWNT) or 

carbon onions (Table 3) to more complicated 

carbon architectures such as carbon black, 

schwarzites, and agglomerates of nanodiamond 

particles with fractal structure. An example of a 

carbon structure with a complex architecture combining 

two structural units are recently discovered 

graphite polyhedral nano- and microcrystals 

with axial carbon structures having nanotube cores, 

nanotube-structured tips, and graphitic faces. 31 

Finally, at the upper micro/macroscopic scale there 

is diamond, graphite, carbolite, fullerite and recently 

discovered single wall nanotube (SWNT) 

strands of macroscopic sizes. 32 While the described 

scheme corresponds to the bottom-up approach of 

molecular synthesis, it is also necessary to add to 

the scheme for completeness the nanostructures 

obtained by top down approaches using different 

nanopatterning techniques such as, for example, 

fabrication of diamond nanorods of 40 nm diameter 

by plasma etching of diamond films. 33 Obviously, 

structural units from different families can 

be combined to form hybrid nanostructures. 

From this section, it should be obvious that 

one of the approaches to classification of carbon 

nanostructures is based on combinations of the 

type of hybridization of carbon bonds within the 

structure and characteristic size of the structure. 

II. STABILITY OF CARBON PHASES AT 

THE NANOSCALE 

It is well known that the most stable carbon 

phase on the macroscale is graphite and that diamond 

is metastable. The energy difference between 

the two phases is only 0.02 eV/atom. How- 

233

FIGURE 2. Classification of carbon nanostructures. The mark ‘sp n ‘ indicates intermediate carbon forms with a noninteger 

degree of carbon bond hybridization. 

ever, because of the high activation barrier for a 

phase transition (~0.4 eV/atom), very high temperatures 

and pressures and/or the use of a catalyst 

are required to realize the phase transformation. 

Several factors, however, prompted a number 

of researchers to reconsider the issue of carbon 

phase stability at the nanoscale at the end of the 

1980s. 72,73 It was necessary to explain the homogeneous 

nucleation of diamond at low pressures 

from the gas phase, 74 the formation of nanometersized 

diamond particles during detonation of explosives, 

18 and the observation of nanometer-sized 

interstellar diamond in meteorites, which was 

hypothesized to form from metastable carbon 

condensates. 58 While there can be alternative explanations 

for these observations, such as kinetically 

hindered formation of graphite from the gas 

phase, 75 or nucleation of diamond at the high 

pressure-temperature conditions that occur during 

detonation that correspond to the equilibrium 

diamond region, the idea that nanoscale diamond 

can be more stable than graphite was put forward. 

72,73 Several researchers have since addressed 

this question by atomistic modeling at various 

levels of sophistication. 76–81 Other research areas 

related to the stability of carbon forms at the 

nanoscale are simulations, performed back in the 

early 1980s, of very small carbon clusters (less 

than 20 to 30 atoms) to understand interstellar 

carbon as well as studies of the energetics of 

fullerene and nanotube formation after these species 

had been discovered. 

Very interesting transformations between carbon 

forms at the nanoscale had been discovered 

in the mid-1990s. After annealing at around 1300 

to 1800 K, nanodiamond particles transform to 

carbon onions with a transformation temperature 

that depends on the particle size. 60 Moreover, it 

234

235

was discovered that carbon-onions transform to 

nanocrystalline diamond under electron irradiation. 

61 Several groups performed atomistic simulations 

to understand both these phenomena. 82–84 

Recently, considering the nanodiamond-onion 

transformation, Barnard and colleagues included 

fullerenes in the ‘traditional’ analysis of the relative 

stability of diamond and graphite at the 

nanoscale and defined a size region of diamond 

stability. 81 As the system size is increased the 

most stable carbon form at the nanoscale changes 

from fullerene — to nanodiamond — to graphite. 

The crossover from fullerenes to closed nanotubes 

has also been analyzed recently. 85 In principle, a 

relatively large amount of accurate simulation 

results have been generated that create a general 

concept of the stability of carbon forms at the 

nanoscale. It is desirable, however, that the simulations 

be done using the same computational 

approach (of ab initio level) so that a quantitative 

comparison of energetics reported by different 

groups is possible. 

Another important area to achieving an understanding 

of carbon behavior at the nanoscale is 

a reexamination of the carbon phase diagram by 

introducing in addition to pressure and temperature 

a third parameter — cluster size. 86–88 

Although very important, phase diagrams 

and analysis of relative stabilities of different 

carbon forms at zero temperature are not enough 

for a general understanding of the complex relationship: 

initial carbon material – application 

of certain external conditions – final nanocarbon 

structure. At finite temperature, the stability 

depends on the transition probabilities among 

the possible configurational states of the system 

and is directly related to the height of the 

energy barrier separating the particular states. 89 

Recently, the potential energy surface controlling 

the dynamics of the graphite-diamond phase 

transformation has been investigated along a 

model reaction path using first principles and 

semiempirical total energy calculations on finite 

carbon clusters. 80,82,90 In general, the activation 

barrier is size dependent and increases 

as the size of the cluster is increased, achieving 

a value of the order of several tens of eV for the 

largest clusters (~3 nm) as found in bulk diamond. 

80,90 

Below we discuss a recent analysis of the 

phase diagram for nanocarbon, including the 

nonequilibrium phase diagram of carbon under 

irradiation as well as recent atomistic simulations 

of the stability of carbon forms at the nanoscale. 

A very important related topic for a general 

understanding of carbon behavior at the nanoscale 

is diamond nucleation from the gas phase, 75 which 

is not considered in the present review, however. 

A. Phase Diagram of Carbon at the 

Nanoscale 

The phase diagram of carbon has been reconsidered 

several times; a recent version 91 is included. 

It includes, for example, an indication of 

regions of rapid solid phase graphite to diamond 

conversion, fast transformation of diamond to 

graphite, hexagonal graphite to hexagonal diamond 

synthesis, shock compression of graphite to 

hexagonal or cubic diamond synthesis, and other 

phase transitions recently observed experimentally. 

Low pressure–high–temperature regions of 

the diagram have also been tentatively assigned 

for carbyne formation (another example including 

carbyne in the phase diagram is Ref. 5). 

Fullerenes and carbon onions were also considered 

in one of the schematic versions of the diagram. 

92 

Estimates for the displacement of the phase 

equilibrium lines for small carbon particles containing 

from several hundred to several tens of 

thousands of atoms had been made recently. 80,86,87 

In the expressions for the Gibbs free energy per 

atom of a cluster of n atoms in a given phase, the 

surface energy contribution is added to the bulk 

free energy: 

G i (T,P,n)=dE i n –1/3 + G i (T,P), (1) 

where dE i is the n-atom cluster surface energy of 

the i-th phase (it is assumed 70, 40, and 1 kcal/ 

mol for diamond, graphite, and liquid carbon, 

respectively 80 ). Then the phase equilibrium lines 

for an n-atom cluster is defined by equating the 

Gibbs energies of the corresponding phases (Figure 

3). The authors report better agreement with 

calculations for experimental shock pressure-vol- 

236

FIGURE 3. Approximate phase diagram for 1000 atom carbon clusters. Shadowed 

region corresponds to estimated uncertainties in location of equilibrium 

lines derived from available experimental data. (Reprinted from Ref. 87, Copyright 

2001, with permission from the American Institute of Physics.) 

ume and temperature data than those obtained 

with a bulk carbon equation of state. The results 

also suggest that carbon particles, of the order of 

10 3 to 10 4 atoms, can exist in the liquid state at 

lower temperatures than bulk carbon. 

Figure 4a illustrates a three-dimensional phase 

diagram where particle size is an additional parameter. 

88 It was derived based on the published 

data on properties of detonation diamond. The 

lower horizontal plane corresponds to the phase 

diagram for bulk phases. The vertical axis corresponds 

to the particle size. The diamond phase 

diminishes at a particle size 1.8 nm or below (the 

point T 1a at the figure) that corresponds to the 

experimentally observed minimum particle size. 

At particle sizes below 3 nm the diamond phase 

is considered the most stable phase, so at the 

upper part of the state diagram only the diamond 

phase is present. The striped vertical plane is 

drawn based on the fact that spherical diamond 

particles with an average size 4 nm are produced 

from the liquid state at a temperature of 3000 K. 55 

Therefore the triple point has been shifted to this 

point accordingly. Unfortunately, the positions of 

the critical points for construction of the diagram 

along the pressure axis were not discussed in Ref. 

88. In addition, the position of the triple point in 

Figure 3 and Figure 4a is different for small particle 

sizes. The triple point displaces toward higher 

pressures in Figure 3 and toward lower pressures 

in Figure 4a as the particle size is decreased. 

While calculations to derive Figure 3 are quite 

accurate, they do not explain the higher stability 

of diamond particles over graphite at the nanometer 

size scale. Thus, we suggest one more variant 

of the 3-D phase diagram based on the results 

reported in Ref. 80, but, in addition, tentatively 

introduce a change of the slope of the diamond/ 

237

238 

FIGURE 4. Three-dimensional phase diagrams for carbon. Phase diagram constructed 

according to published data on detonation diamond properties (a). 88 Schematic 3-D 

phase diagram, including fullerenes (b). 92 (Reprinted from Ref. 88 and Ref. 92 with 

permission.)

graphite equilibrium line as particle size is decreased 

(Figure 5). This change results in a higher 

stability of nanodiamond over nanographite at 

ambient conditions. 

According to the fact that at sizes below 1.8 

nm other carbon forms are abundant, such as 

fullerenes and onions, it was suggested to assign 

the corresponding region of the state diagram to 

fullerenes and onions as shown schematically in 

Figure 4b. 

Although the diagrams illustrated in Figures 

3 to 5 are rather tentative, it is a good starting 

point for constructing the nano-phase carbon diagrams 

using more accurate methods. One of the 

critical points is accurate surface energies of the 

corresponding particles as well as realism of the 

related structural models (mostly surface structure). 

Fortunately, rapidly increasing the number 

of the ab initio-based works addressing these issues 

for relatively big systems will provide a 

deeper understanding of the phase equilibrium of 

nanocarbon. 

As mentioned above, under the nonequilibrium 

conditions of intense irradiation, the phase 

equilibrium between graphite and diamond can 

be reversed so that graphite can be transformed 

into diamond even if no external pressure is applied. 

61 A detailed quantitative study of the 

nonequilibrium phase diagram of carbon under 

irradiation was presented in Ref. 93. The theoretical 

treatment is based on the master equation 

approach for incoherent phase transformation involving 

motion of the interface between two 

phases. In addition to the thermally activated exchange 

of atoms across the interface, under irradiation 

conditions atoms are ‘ballistically’ displaced 

from the lattice positions (with different 

threshold energies for different phases) to interstitial 

positions within the interface. Then, depending 

on the temperature conditions, interstitial 

atoms will relax toward particular bulk lattice 

sites. A nonequilibrium effective free energy is 

defined 93 that governs the phase stability under 

irradiation and yields quantitative predictions of 

FIGURE 5. Schematic 3-D phase diagram for carbon illustrating the change in 

the position of the triple point as a function of particle size drawn according to Ref. 

87. As shown, the nanodiamond phase is the most stable phase at ambient 

conditions. 

239

the interface velocity that can be directly compared 

to the experimental observations obtained 

by TEM. As a result of this work, the nonequilibrium 

phase diagram (irradiation intensity vs temperature) 

is illustrated in Figure 6. The kinetics of 

a reverse transition, from nanodiamond to onions 

during annealing, was described in Ref. 94. 

B. Theoretical Studies on the Relative 

Stability of Different Forms of Carbon at 

the Nanoscale 

There is a relatively large number of the theoretical 

studies devoted to the relative stability of 

diamond/graphite at the nanoscale. Within the 

earliest studies, the energy advantage of 

londsdaleite over graphite for very small particles 

elongated along the c axis was reported based on 

the comparison of the number of dangling bonds 

of graphite and londsdaleite. 76 To explain the observation 

of a 5 nm-diamond found in meteorites, 

Nuth compared the surface energies of graphite 

and diamond, but the uncertainty was too large to 

make a reasonable conclusion. Based on scaling 

the enthalpies of hydrocarbon molecules to larger 

scales, Badziag et al. 73 suggested that diamondlike 

clusters with sizes up to 3 nm are more stable 

than aromatic structures with comparable hydrogen 

to carbon ratios (the transitions are predicted 

to occur at about H/C=0.24). A similar result was 

obtained for relaxed hydrogenated graphitic and 

diamond-like structures using bond-order interatomic 

potential functions for which the transition 

in stability for diamond/graphite occures at 

H/C ratios of ~0.3. 95 Gamarnik 78 compared the 

cohesive energies of bare surface diamond clusters 

and 3-D graphite clusters using an empirical 

description of interatomic interactions. He also 

calculated the temperature dependence of the critical 

size of stable diamond clusters, including the 

entropy contribution to free energy: dF=T(Sg- 

Sd). The difference in entropy of graphite and 

diamond was chosen as Sg-Sd=3.37 kJ/mol at 

lower temperatures and 4.59 kJ/mol at 800 to 

1100 o C. A more extended discussion of these 

values can be found in Ref. 96. According to the 

prediction, 78 diamond nanocrystals formed, for 

example, at 1100 o C should be less than 5 nm in 

size and the maximum size of stable diamond 

FIGURE 6. Experimentally and theoretically (solid line) determined 

nonequilibrium phase diagram (irradiation intensity vs temperature) for irradiation 

with 1250 keV electrons. Open circles: diamond growth, black squares: 

graphite growth. (Reprinted from Ref. 93, Copyright 2000, with permission 

from American Physical Society.) 

240

crystals should not exceed 10 nm at room temperature. 

There are also several studies based on the 

‘classic’ thermodynamic functions modified to 

account for the size of the cluster. 96,97,98 Hwang et 

al. in their study of homogeneous diamond vs. 

graphite nucleation outlined a chemical potential 

model 98 and a charged cluster model, where the 

critical size for charged particles was evaluated as 

350 atoms. 97 The additional pressure contribution 

due to the curvature of the nanometer-sized particles 

was considered. 96,97 It was assumed that due 

to the additional pressure, the external pressure 

necessary for the transition of nanographite to 

nanodiamond decreases. 96 After introducing this 

contribution to the pressure-temperature analytical 

expression for the diamond/graphite equilibrium 

line in the bulk phase diagram, the authors 

obtained a size-dependent phase diagram. The 

reported critical cluster size at room temperature 

was ~6 nm. A general theory of dynamic and 

static nanodiamond formation from different solid 

carbon forms was suggested by Lin. 109 The suggested 

cluster transformation mechanism is based 

on the concept of vibrational interactions between 

objects with an anomalously high Debye temperature. 

Results from the first ab initio restricted 

Hartree-Fock calculations on the phase stability 

of a graphene sheet and cubic diamond clusters 

were reported in Ref. 77. Both bare and hydrogenated 

surfaces were considered. The cohesive 

energies obtained by extrapolation to bulk values 

of diamond and graphite were rather different 

from experimental values, indicating the low accuracy 

of the method. 

The general scheme for calculation of the 

heats of formation for graphene sheets and diamond 

clusters was outlined in Refs. 73, 77, 79. 

Below we follow the outline of Ref. 79. 

The dependence of the total energy of a 

nanocarbon system on the number of carbon atoms 

can be expressed as: 

E tot = N C E C + N db E db , (2) 

where N C is the number of carbon atoms and N db 

is the number of dangling bonds. For two-dimensional 

graphite sheets N C =6N 2 and N db =6N, where 

N is number of carbon atoms along one edge. 

This can be also estimated from the formula for 

symmetric polycyclic aromatics C 6m2 H 6m , where 

m is the number of rings along a single edge. 79 For 

a diamond octahedral with edges of n atoms, the 

cluster contains N C =N(4N 2 -1)/3 and N db =4N 2 . 73 

The parameters E db and E C are the energy per 

dangling bond and per carbon atom, respectively. 

Atomistic simulations provide a set of values of 

E tot for a particular system size and configuration 

such that the parameters E C and E db can be extracted 

from a least squares fit of E tot as a function 

of N db /N C for the graphite and carbon clusters. The 

cohesive energy of a cluster is defined as the 

difference between the total energy per atom in a 

cluster and the carbon free energy (e.g., it is E tot / 

N C ). The surface energy contribution becomes 

less and less important as cluster size increases, 

so that for an infinite cluster extrapolation of the 

cluster cohesive energy should be close to the 

bulk carbon cohesive energy, E C,, according to the 

expression: 

E tot /N C = E C + N db /N C E db . (3) 

With such tests, the accuracy of the method 

describing interatomic interactions can be evaluated 

for both diamond and graphite systems. 

Equally, instead of dangling bonds, hydrogen termination 

of a cluster surface can be considered 

within the above scheme. Such an evaluation was 

done by Winter and Ree for the density functional 

approach, using ab initio restricted Hartree Fock 

and semiempirical AM1 and PM3 methods 79 for 

both bare and hydrogenated clusters. It was concluded 

that the best accuracy was obtained utilizing 

semiempirical methods (which is not surprising 

because the enthalpies of formation of organic 

compounds are within the fitted data set). 

Analysis of the heat of formation in terms of 

bond energies provides more physical meaning to 

the parameters rather than the empirical expressions 

above. Each carbon atom in graphite forms 

three intralayer sp 2 bonds and experiences a weak 

interlayer interaction. In the diamond lattice each 

carbon atom forms identical sp 3 bonds. The heats 

of formation for sp 2 and sp 3 carbon clusters can be 

expressed in terms of the CC and CH bond energies 

and the atomic heats of formation as follows: 

241

0 2 

∆Hf 

( sp ) 3 2 N 

2 

sp H sp 1 2 

sp O 

= ECC 

+ 

⎛ 

ECH 

− ECC 

+ ∆Hf 

( H) 

⎞ 

NC 

2 N ⎝ 

C 2 

⎠ 

O 1 disp 

+ ∆Hf 

( C) 

+ ECC 

(2.4a) 

2 

0 3 

∆Hf 

( sp ) 

3 N 

3 

sp H sp 1 3 

sp O 

= 2ECC 

+ 

⎛ 

ECH 

− ECC 

+ ∆Hf 

( H) 

⎞ 

NC 

N ⎝ 

C 2 

⎠ 

O 

+ ∆H 

( C) 

(2.4b) 

f 

where N H is the number of hydrogen atoms, E CC 

and E HC are the energies of a C-C and H-C bond, 

respectively, and E disp is the C-C pair energy due 

to the interlayer dispersion (1.66 kcal/mol 79 ). 

∆H 

0 f ( H ) =171.29 kcal/mol and ∆H 0 f ( C )=52 kcal/ 

mol are the experimental values of the standard 

heat of formation of carbon and hydrogen, respectively, 

at room temperature. Equating the 

intercepts to experimental cohesive energies of 

graphite and diamond (left part of the equation at 

big N C ), bond energies can be estimated. Thus, an 

outcome of the scheme is an analytical expression 

for atomic heats of formation of hydrogenated 

nanodiamond and hydrogenated nanographite as 

functions of the number of carbon atoms. Figure 

7 illustrates an example of such dependences 

obtained by Winter and Ree using a semiempirical 

approach (PM3 cluster calculations). The curve 

crossing corresponds approximately to 33,000 

atoms (~7 nm particle size). 

Analysis of the stability of hydrogenated 

nanodiamond and nanographite is relatively 

straightforward. What is also important is that the 

relaxation of hydrogenated nanodiamond surfaces 

is in general comparable to bulk diamond, 99,100 so 

that bond energies of bulk diamond can be used 

for rough estimations. 

However, analysis of the optimized geometries 

of the bare nanodiamond surfaces showed that the 

picture is quite complicated. The first analysis of 

nonhydrogenated octahedral nanodiamond clusters 

FIGURE 7. Comparison of the cluster size dependence of the heat of formation 

∆Hf(sp3) and ∆Hf(sp 2 ) determined by the PM3 HF method. 80 The fits to the sp 3 

(open circles) and sp 2 (crosses) data are given by the dashed and solid lines, 

correspondingly. (Reprinted from Ref. 80, Copyright 1999, with permission from 

Elsevier Science.) 

242

and graphene sheets using a semiempirical approach 

was done by Winter and Ree. 79 If the surface 

orbitals are left uncapped, a finite graphene 

sheet distorts due to bond formation between adjacent 

pairs of adjacent planar dangling bonds (Figure 

8). For the example in Figure 8, 12 out of 18 

dangling bonds form 6 in-plane π bonds. In the 

case of nanodiamond, the number of dangling bonds 

for the smallest octahedral molecule C 10 is also 

reduced (Figure 8). Optimized structures of all 

other octahedral molecules with larger sizes resemble 

onion-like carbon with a diamond core and 

flattened outer layers of the octahedral cluster to 

form π bonds from the unbonded orbitals (Figure 8). 

The bonds between core and surface atoms are 

elongated by up to 1.7 to 3.0 Å, followed by round- 

FIGURE 8. Configurations of a bare graphene sheet (a) and diamond octahedral clusters (b-d) after geometry 

optimization. 79 In the case of the graphene sheet (a) six additional in-plane p bonds (1.31 Å long) formed from 12 

of the original 18 dangling bonds and the locations of the remaining six open-shell orbitals. The number of dangling 

bonds reduces from 16 to 8 for C10 (adamante-related) diamond cluster (b). The “buckification” – formation of the 

sp 2 shell over a diamond core begins with a C 35 cluster (1sp3 atom in the core) (c) and persist as a crystal size is 

increased (d). The atoms in the core of C 165 cluster are highlited by dashed lines. (Reprinted from Ref. 79, Copyright 

1998, with permission from Kluwer Academic Publishers.) 

243

ing of the cluster surface; this bond elongation is 

more pronounced for larger clusters. No cohesive 

energies had been reported for the reconstructed 

diamond clusters in Ref. 79. 

The preferential exfoliation of the diamond 

(111) surface over other low-index faces was 

considered by Kuznetsov et al. 82 using standard 

semiempirical method (MNDO) calculations of a 

two-layer cluster model for the (111) and (110) 

surfaces and physical arguments to excluding the 

(100) surface. It was shown that the activation 

barrier for (111) plane exfoliation is much lower. 

A comprehensive analysis of the stability of 

nanodiamond clusters of three specific morphologies 

was done by Barnard et al. using ab initio 

Density Functional Theory with the Generalized- 

Gradient Approximation. 99–101 The cohesive energies 

of the diamond clusters calculated by Barnard 

et al. are summarized in Table 4. The results on 

octahedral clusters are similar to those by Winter 

and Ree. 79 Cuboctahedral clusters, the surface area 

of which is comprised of 40% of (111) and 60% 

of (100)-oriented surfaces, exhibited transitions 

from sp 3 to sp 2 bonding only on the (111) planes. 

The (100) surfaces initially reconstructed (thereby 

increasing the (111) surface area), followed by a 

reorientation of the surface dimers to form curved 

graphite-like (111) cages (Figure 9). 99 The results 

of relaxation of the C 29 nanodiamond showed a 

transformation to the C@C28 endofullerene 

(Figure 9). The ‘buckification” of spherical 

nanodiamond clusters (which mostly consist of 

(111) and (100) surfaces) was also observed in ab 

initio DFT as well as Quantum Monte Carlo simulations 

90 that is discussed in Section III.A.3. Three 

cubic (100) structures that were considered contained 

28, 54, and 259 atoms. In the case of the 28 

atoms cluster, the final structure was a metastable 

amorphous structure and not a C 28 fullerene, as 

had been expected. Additional analysis did not 

reveal the transformation path of this structure to 

the fullerene. Preliminary conclusion might be 

that the lack of a (111) surface may influence the 

onset of graphitization and thus the transformation 

into fullerene-like structures. The two larger 

cubic nanodiamonds were found to have surface 

244

(a) 

(b) 

FIGURE 9. Cubic (a) and cuboctahedral (b) nanodiamond crystals before 

and after relaxation. Note surface reconstruction of the (100) surface and 

‘buckification’ of the (111) surfaces. As an extreme case of ‘buckification’ 

a C28 fullerene with an endohedral C atom is formed for the C 29 cluster. 

(Reprinted from Ref. 99 with permission.) 

245

econstructions and relaxations comparable to bulk 

diamond (Figure 9). 99 

Thus, ab initio simulations demonstrate that 

within the size range 1 nm 99–101 up to 3 nm for 

spherical clusters in Ref. 90, the crystal morphology 

plays a very important role in cluster stability. 

While the surfaces of the cubic crystals exhibit 

structures similar to bulk diamond, the 

surfaces of the octahedral and cuboctahedral clusters 

showed transition from sp 3 to sp 2 bonding. 

The preferential exfoliation of the (111) surfaces 

begins for clusters in the subnanometer size range 

and promotes the cluster transition to endofullerences 

for small clusters (~ tens of atoms) 

and onion-like shells with diamond cores for larger 

clusters. 99 

In principle, a analysis similar to that outlined 

above for hydrogenated carbon clusters can be 

done for bare reconstructed surfaces if one replaces 

parameters for hydrogen with those for 

dangling bonds. This was done by Barnard et al. 81 

Plotting the total energy per atom as a function of 

the fractional ratio of dangling bonds for nonbucky 

clusters from Table 4, and extrapolation of 

N db /N tot → 0 gave a linear fit of cohesive energy 

for the atoms within the inner region of the diamond 

cluster of 7.71 eV/atom. As can be seen 

from Table 4, the cohesive energies of diamond 

clusters are below 7 eV/atom due to the highly 

defective surface atoms. However, due to bond 

shortening and the high freedom for relaxation 

inner atoms can gain an additional energy so that 

cohesive energy becomes 7.71 eV/atom. At the 

same time, extrapolation using this procedure for 

unrelaxed clusters with dangling bonds gives a 

cohesive energy of 7.39 eV for bulk diamond. In 

principle, as the crystal size is increased, the ‘inner’ 

cohesive energy of diamond crystals should 

asymptotically decrease toward the bulk diamond 

value. With more data points for larger clusters, it 

might be possible that three (or more) groups of 

diamond clusters with specific morphologies and 

corresponding specific energetics (cohesive energy 

of the inner core) can be defined. 

Barnard et al. 81 also predicted the relative 

stability of nonhydrogenated diamond clusters, 

fullerenes and hydrogenated graphite within the 

same study. At a system size of up to 1127 atoms, 

fullerenes are the most stable structures (corresponding 

size of the cubic diamond cluster ~1.9 

nm). At a system size 1127 < N C < 24,389 atoms, 

diamond is the most stable form (‘bucky’ diamonds 

were excluded from the analysis). The size 

of a diamond cubic cluster corresponding to 24389 

atoms is ~5.2 nm. Finally, at a system size larger 

than ~24,000 atoms, graphite is the most stable 

phase. In principle, it would be interesting also to 

include in the analysis nonhydrogenated graphite 

clusters, which have not yet been thoroughly investigated. 

Results obtained in Ref. 81 are also 

important for the construction of the 3-D phase 

diagrams discussed above. 

Recently, a comparison of the stability of 

members of two other carbon families, fullerenes 

and closed nanotubes, was made 85 using first principles 

pseudopotential calculations for carbon clusters 

of C N (60 ≤ n ≤ 540). The analytical expressions 

obtained for stabilities are based on strain 

energy contributions due to the curvature effects 

as well as a contribution due to the presence of 

pentagons, which introduces nonplanarity of the 

graphitic sheet incurring incompleteness of the π 

bonding, as had been shown earlier by Adams and 

co-workers. 102 The model 85 predicts that a 

nanotube of ~13 Å in diameter (e.g., a (9,9) or 

(10,10)) is the energetically most stable form 

among various single-walled nanotubes and 

fullerenes (Figure 10), consistent with many experimental 

observations. The curve of stability of 

fullerenes in Ref. 85 is different from the previous 

predictions 102 for cluster sizes above ~200 atoms. 

There are several studies that investigated the 

stability of nanotubes relative to graphene. For 

example, graphene is the least stable structure 

until about 6000 atoms, where it becomes more 

stable than the (10,0) and (5,5) nanotubes. 108 Energy 

gain due to the arrangement of SWNT into 

arrays caused by van der Waals interactions, as 

well as faceting (flattening) of nanotube walls at 

a larger nanotube diameter, has been addressed in 

Refs. 380–383 (see also Table 3). Similarly, the 

stability of nanotubes arranged in multi-shell structures, 

as well as their faceting with increasing 

nanotube size were studied in Refs. 377–379 

(Table 3). The authors 107,373–376 discussed the energy 

characteristics of carbon onions and related 

faceting issues. In addition, the molecular dynamics 

method was used to estimate the barriers to 

246

FIGURE 10. Dependence of excess energy (relatively to an infinite 

graphene sheet) on the system size for (n,n) capped nanotubes and 

fullerenes (Reprinted from Ref. 85, Copyright 2002, with permission 

from American Physical Society.) 

relative shell rotation as well as the temperature 

dependence of the mutual arrangement of the 

shells. 107 

Regarding “small” carbon clusters, it was 

known long ago from mass spectra data of molecular 

beams 39 that the 11, 15, 19, and 23 atoms 

clusters are abundant, while between 28 and 36 

atoms the abundance of clusters is very low. Above 

36 atoms and up to hundreds of atoms, only evennumbered 

clusters are produced. An extensive 

study of the stability of “small” carbon clusters 

for a wide size range and several types of configurations 

were carried out by Tomanek and Schluter 

within a tight binding method. 103 A recent study 

using a density function formalism showed similar 

tendencies and some differences in detailed 

behavior. 104 In general, the current studies 104,105 

show three regions for the stability of small carbon 

clusters; below 20 atoms the most stable 

geometries are one-dimensional ring clusters; 

between 20 and 28 atoms clusters with quite different 

types of geometry have similar energetics; 

for larger clusters fullerenes should be more stable 

(Figure 11). Thermodynamic estimates for the 

efficiency of formation of spheroidal, flat clusters, 

and linear carbon chains depending on the 

charge of the reacting particles was analyzed in a 

recent work. 106 It was shown that charge influences 

both geometry and stability of flat clusters, 

promoting folding to curved structures as well as 

dissociation. The hierarchy of the stabilities of 

carbon forms at the nanoscale are summarized in 

Figure 12. 

A number of atomistic studies dealt with 

carbon onions. In particular, concentricshell 

fullerenes were generated from diamond 

nanoparticles of 1.2 nm to 1.4 nm diameters by 

means of molecular dynamics simulations based 

on approximate Kohn-Sham equations. 83 The diamond-to-concentric-shell 

fullerene transformation 

were observed at temperatures from 1400 K to 

2800 K and started at the surface of the diamond 

particle. The final structure consisted of two concentric 

graphitic shells with the intershell spacing 

distinctly below the interlayer distance of graphite 

with sp 3 -like cross links between the shells. 

Simulated irradiation accelerated the transformation 

and reduced the number of cross links. In a 

subsequent study, 84 structural transformations of 

carbon nanoparticles were studied by means of 

molecular dynamics using a density-functionalbased 

tight-binding method. The starting particles 

consisted of 64 to 275 atoms arranged on a graphitic 

or diamond lattice. At elevated tempera- 

247

FIGURE 11. The calculated binding energy of carbon clusters as a function of the 

number of atoms in a cluster. For the smallest sizes, the rings are the most stable 

structures. For the largest size, the fullerene structure is the most stable. For 20 and 24 

atoms, ring, bowl, and fullerene clusters have similar energies. (Reprinted from Ref. 

104, Copyright 2001, with permission from Kluwer Academic Publishers.) 

FIGURE 12. Schematic representation of the most stable carbon phase, depending on the size of 

the carbon structure. 

248

tures (1400 to 2800 K), the particles transformed 

into spherical or elongated closed cages, concentric 

shell fullerenes, carbon nanotips, and 

spiraloidal and irregularly shaped clusters. The 

type of the final cluster depended essentially on 

the size and the atomic order of the starting particles, 

and on the temperature applied. An atomic 

mechanism of transformation of nanodiamond to 

carbon onions was considered in Ref. 82. In particular, 

the observed the transformation of three 

diamond plains to two graphite planes was explained 

by a “zipper”-like migration mechanism, 

with the carbon atoms of the middle diamond 

layer being distributed equally between the two 

growing graphitic sheets. 

Besides pure thermodynamic considerations 

of the carbon phase stability outlined above kinetic 

considerations play an equally important 

role, 110 which are, however, not discussed here. 

In summary, it had been demonstrated by the 

highest level of sophistication computational approaches 

that nanodiamond is thermodynamically 

stable over graphite when the particle size is less 

than 5 to 10 nm, in contrast to the macroscale where 

diamond is metastable. At the same time, the computational 

methods indicate that nanodiamond stability 

is restricted by the smallest sizes of ~1.9 nm, 

below which fullerene structures are more stable. 

III. SELECTED CARBON 

NANOSTRUCTURES, THEIR SYNTHESIS 

AND PROPERTIES 

A. Diamond at the Nanoscale 

(“Nanodiamond”) 

1. Types of Nanodiamond 

Below is briefly summarized experimental 

evidence for diamond structures with critical 

sizes at a nanoscale as well as related methods of 

synthesis. The term ‘nanodiamond’ is used to 

identify a variety of structures that include diamond 

crystals present in interstellar dust and 

meteorites, isolated diamond particles nucleated 

in the gas phase or on a surface, and nanocrystalline 

diamond films. Methods of nanodiamond synthesis 

are diverse, ranging from gas phase nucleation 

at ambient pressure to high-pressure high-temperature 

graphite transformation within a shock 

wave. Nanodiamond materials possess different 

degrees of diamond purity, with a wide variety of 

functional groups/elements at the surface of diamond 

particles or within grain boundaries in 

nanocrystalline diamond films. The structures can 

be as-grown or compacted from previously synthesized 

diamond particles. 

There are two major groups of nanodiamond 

structures observed experimentally. The first group 

includes nanodiamond, which is the final product 

of one of the methods of synthesis (such as 

ultradispersed diamond, diamond obtained by 

transformation of carbon onions under electron 

beam irradiation, ultrananocrystalline diamond 

films). Another group includes nanodiamond nuclei 

that have been observed when conventional 

processes of micro- and macro-diamond growth 

had been interrupted at early stages to study a 

diamond nucleation process. A summary of the 

representative experimental observations of 

nanosized diamond is provided in Table 5. 

The information on nanodiamond observations 

is arranged according to the dimensionality 

of the diamond constituents. We discuss systems 

of increasing complexity beginning with the zerodimensional 

structures in the form of isolated 

particles, particles on a surface, and particles embedded 

in a matrix of another material. Some of 

the nanodiamond particles from this group had 

been observed during fundamental studies of diamond 

nucleation or transformation of carbon 

phases in specially designed experiments. Other 

types of nanodiamond such as ultradispersed diamond 

obtained by the shock wave process are 

produced in bulk quantities. The least represented 

group is one-dimensional diamond structures at 

the nanoscale, for which we discuss only three 

examples. Finally, three-dimensional assemblies 

of diamond nanocrystals grown as thin films or 

compacted from UDD powder to preformed bulk 

shapes are reviewed in more detail due to their 

importance in current technological applications. 

a. Zero-Dimensional Nano-Diamond 

Structures 

Representative observations of isolated diamond 

particles are summarized in Table 5a, with 

249

250

selected high-resolution transmission electron 

microscopy (HRTEM) images illustrated in Figures 

13 to 19. Most of the HRTEM images of 

single particles are obtained from particles etched 

out from a matrix of foreign materials or isolated 

from particle agglomerates, which are typical, for 

example, of UDD particles during storage. In 

general, these observations provide valuable information 

on diamond stability, morphology, polymorphic 

modifications, and lattice defects at the 

nanoscale, which, in turn, can be related to the 

nucleation mechanism and growth conditions. 

However, the influence of treatment conditions 

on ND surface states during ND extraction and 

purification for sample preparation is difficult to 

address. Examples of observations of ND unaltered 

by sample preparation are in situ experiments 

on the phase transformation during annealing 

60 and electron irradiation in a high-voltage 

electron microscope. 61 

i. Nanodiamond Nucleated in a Gas 

Phase 

A rather limited number of experiments have 

been conducted to examine homogeneous nucle- 

251

252 

FIGURE 13. HRTEM images of nonlinear multiply-twinned nano-diamond exhibiting Σ=3{111} coherent 

twin boundaries are present in (a-b) Murchison X, (c-d) vapor grown particles using substrate-free MPCVD 

flow reactor, and (e-f) detonation soot residues. (Reprinted from Ref. 117, Copyright 1996, with permission 

from Elsevier Science.)

FIGURE 14. High-resolution TEM image of the cluster with the diamond lattice 

observed among the clusters captured on the silica membrane for 60 s with a gas 

ratio of C 2 H 2 :O 2 =1.04 during the flame deposition of diamond. (Reprinted from 

Ref. 116, Copyright 2002, with permission from Elsevier Science.) 

FIGURE 15. HRTEM images of ultradispersed diamond particles obtained by explosive detonation 

synthesis. (After Ref. 183.) 

253

FIGURE 16. Multiple twin particles of a presolar diamond. (Courtesy of T. 

L. Daulton, Naval Research Laboratory.) 

FIGURE 17. Using particle beams, a “carbon onion,” a structure consisting of 

nested fullerene-like balls, can be converted into a diamond. A growing diamond 

is seen inside concentric graphitic layers. The diamonds can grow up to 100 

nanometers in diameter. (Reprinted from Ref. 61, with permission from Nature, 

copyright 1996. Macmillan Magazines, Inc.) 

254

FIGURE 18. HRTEM images of nanodiamond particles extracted from a graphite matrix where they had been formed 

by ion irradiation at room temperature. 122 (Courtesy T. L. Daulton, Naval Research Laboratory, after Ref. 122, 

Copyright 2001, with permission from Elsevier Science.) 

FIGURE 19. HRTEM image of a diamond crystallite (diameter ~6 nm) grown directly 

on Si with a random alignment. (After Ref. 140.) 

255

ation of diamond in the gas phase at atmospheric 

and subatmospheric pressures. 43,74,111,112 Theoretical 

arguments based on classic nucleation theory 

that homogeneous nucleation of diamond is possible 

have been presented by Fedoseev and coworkers. 

43 They also reported the formation of 

diamond particles in the gas phase using a wide 

variety of methods that are summarized in Ref. 

74. The experimental procedures included (1) an 

electric discharge between graphite or nickel electrodes 

immersed in a liquid hydrocarbon, (2) a 

drop of an organic liquid exposed to a focused 

high intensity IR laser beam, and (3) quenching 

acetylene pyrolysis by either injection of water or 

expansion of the gas in a nozzle. In the first two 

cases diamond/lonsdaleite (a hexagonal diamond 

phase) powder with average grain size 0.1 µm 

was obtained, and in the last method the particle 

size was about 20 nm. The decomposition of 

methane in a radio-frequency electric field is another 

approach used 112 in the synthesis of submicron 

size diamond/lonsdaleite particles. 

Frenklach and co-workers 74 studied nucleation 

and growth of diamond powder directly from the 

vapor phase in a substrate-free low-pressure microwave-plasma 

CVD reactor. The particles were 

collected downstream of the reaction zone on a 

filter within the tubular flow reactor and subjected 

to wet oxidation to remove nondiamond 

carbon. The homogeneous diamond nucleation 

took place when a dichloromethane- and trichloroethylene-oxygen 

mixture was used as a source 

material. The particles formed had crystalline 

shapes with an average particle size around 50 

nm. A mixture of diamond polytypes was observed 

in the powder. 

Frenklach et al. 111 also studied the effects of 

heteroatom addition on the nucleation of solid carbon 

in a low-pressure plasma reactor. The addition 

of diborane (B 2 H 6 ) resulted in substantial production 

of diamond particles, 5 to 450 nm in diameter, 

under the same conditions that show no diamond 

formation without diborane present. The observed 

yield of the oxidation-resistant powder produced in 

boron-containing mixtures reached 1.3 mg/h. 

Atomic resolution lattice images of CVD 

nanodiamond with ~5-nm particles sizes obtained 

the technique developed by Frenklach et al. had 

been thoroughly analyzed by Daulton et al. 117 (Figure 

13c-d). It was found that nanodiamonds in the 

CVD residue have an abundance of linear twins 

and star-twin microstructures consistent with radial 

(isotropic) gas phase growth conditions. Studies 

of diamond nucleation directly from an activated 

gas phase have important implications in 

revealing mechanisms of interstellar dust formation, 

which is discussed below. 

Another example of homogeneous diamond 

nucleation in the gas phase is laser-induced decomposition 

of C 2 H 4 at low pressures and temperatures 

113,114 that results in diamond powder 

formation with grain diameters 6 nm to 18 um. 

According to the authors, 113,114 high-purity homogeneously 

nucleated diamond nanoparticles had 

spherical and faceted morphologies. Homogeneous 

nucleation of diamond particles at low pressure 

by a DC plasma jet 115 has also been reported. 

A drastically different nucleation and growth 

mechanism, the so-called charged cluster model, 

was suggested by Hwang et al. 98 The model predicts 

that stabilization of diamond originates from 

charge rather than hydrogen. The authors suggest 

that charged carbon clusters of a few nanometers 

are generated in the CVD diamond and are suspended 

like colloidal particles in the gas phase 

and then subsequently deposited as diamond films. 

In an extended series of studies to confirm the 

model, the authors thoroughly analyzed the dependence 

of the nanodiamond nucleus formation 

on the deposition environment. In the most recent 

experiments they observed carbon clusters by TEM 

after capturing them on a grid membrane during 

oxyacetylene flame synthesis (Figure 14). 116 It 

was found that the captured clusters of ~1.5 nm in 

a gas mixture with an acetylene-to-oxygen ratio 

of 1.04 were mostly amorphous with a few having 

a diamond lattice. Clusters larger than 5 nm captured 

at a gas ratio of 1.09 were mostly graphite 

with a minor fraction of diamond. 116 The authors 

also emphasize, following the observation of several 

hundreds atoms clusters by HRTEM that, in 

principle, the crystallinity can be altered by interaction 

with the substrate. So far, these are the 

smallest sizes of observed diamond clusters. Regarding 

the charged cluster model, first principles 

atomistic simulations of charged diamond cluster 

stability can provide deeper insight on the reliability 

of the model. 

256

2. Ultradispersed Diamond, or Detonation 

Diamond 

A technologically important class of 

nanodiamond materials is ultradispersed diamond. 

UDD synthesis is performed by the detonation 

of solid explosives in an inert atmosphere. 

The product obtained in detonation synthesis, 

called detonation soot, contains the diamond phase, 

which is separated by chemical treatment based 

on moderate temperature oxidation of the impurities 

by nitric acid under pressure. 1 Therefore, the 

final morphology of the particles is influenced by 

the treatment conditions. Images of UDD particles 

are shown in Figure 13 and Figure 15. A 

very well-developed facet on a particle can be 

seen in Figure 15. Daulton et al. 117 performed 

extensive studies on the morphology of UDD 

particles that is described in the next subsection. 

iii. Interstellar Diamond 

Astronomical observations suggest that as 

much as 10 to 20% of the interstellar carbon is in 

the form of nanodiamonds. 125 Diamond nanograins 

are the most abundant but less understood interstellar 

matter found in metorites, where it comprises 

up to 0.15%, equivalent to about 3% of the 

total carbon. 126 The conclusion about the presolar 

nature of meteoritic nanodiamonds is based mainly 

on isotope composition measurements of trace 

elements, including noble gases. 127 There are 

uncertainties in the fraction of the presolar 

nanodiamond population in meteorites because 

the amount of trace elements is very small. 118 In 

general, questions on the places and times of the 

origin of nanodiamond particles remain open. 

The first presolar grains discovered were nanometer-sized 

diamonds isolated from meteorite 

Allende 58 (Figure 16). The diameter of presolar 

diamond particles in Allende ranged between 0.2 

to 10 nm, with an average size near 2.7 nm. 

The two main theories for presolar diamond 

formation are vapor condensation, similar to CVD 

processes, in the outer envelopes of carbon and 

red-giant stars 58 and shock-induced metamorphism 

in a supernovae. 121 It has been also suggested that 

vapor condensation of diamond could also occur 

in a supernovae. 119 The coexistence of the two 

mechanisms of ND formation (vapor condensation 

and shock-induced metamorphism) is assumed 

in the ND synthesis by explosion of a mix of 

nanocarbon species and explosives. 3 Another indication 

of the possible coexistence of the mechanisms 

is the presence of a bimodal distribution in 

the sizes of ND particles produced by shock wave 

compression, where particles within the 1 to 4 nm 

range are assumed to be condensed from the vapor 

phase. 3 

To discriminate among the most likely formation 

mechanisms, high-pressure shock-induced 

metamorphism or low-pressure vapor condensation, 

the microstructures of presolar diamond crystallites 

were compared to those of (terrestrially) 

synthesized nano-diamonds by Daulton et al. 117 

Nano-diamonds isolated from acid dissolution 

residues of primitive carbonaceous meteorites 

(Allende and Murchison) were studied using 

HRTEM. The synthesized diamonds used for 

comparison in this study were produced by explosive 

detonation (e.g., UDD particles, because it 

was assumed that their morphology should be 

close to that produced by shock wave transformation 

of carbon species) and by direct nucleation 

and homoepitaxial growth from the vapor phase 

in CVD processes (obtained from Frenklach’s 

group). Microstructural features were identified 

that appear unique to both explosive detonation 

synthesis (shock metamorphism) and to nucleation 

from the vapor phase. Diamonds produced 

by CVD have abundant twin forms with star-like 

morphologies (similar to Figure 16) indicative of 

isotropic formation conditions. Shock-produced 

diamonds have mostly planar twin forms, presence 

of dislocations, and other features consistent 

with transformation behind a planar shock front 117 

(Table 6). A comparison of these features to the 

microstructures found in presolar diamonds indicates 

that the predominant mechanism for presolar 

diamond formation is a vapor deposition process, 

suggesting a circumstellar condensation origin. 117 

It is also possible that a subpopulation of presolar 

diamonds were shock formed, because presolar 

diamonds are also linked to anomalous trapped 

specific Xe isotope (on average one presolar diamond 

out of a million contain a Xe atom). This 

isotope can only be produced in a supernovae 

where shock metamorphism conditions would 

prevail. 117,118 

257

Another theory of presolar diamond formation 

suggests that graphite grains irradiated by 

energetic particles could be transformed into diamond, 

for instance, around supernovae. 120 So far, 

there has been experimental confirmation of graphite 

transformation to diamond by MeV electron 

and ion irradiation at elevated 123 and even at 

ambient 122 temperatures. The observation of 

nanodiamonds in fine-grained uranium-rich carbonaceous 

materials from the Precambrian period 

124 also supports the theory of diamond nucleation 

by irradiation of carbonaceous materials by 

energetic particles. 

The comprehensive studies of nanodiamond 

morphology by the astrophysical community that 

reveal its relevance to the mechanism of interstellar 

diamond formation demonstrates again the 

importance of an interdisciplinary approach in 

nanoscience from unexpected, from a first sight, 

perspectives. 

iv. Direct Transformation of Carbon 

Solids to Nanodiamond 

Recent experiments have shown that heavy 

ion or electron irradiation induces the nucleation 

of diamond crystallites inside concentric nested 

carbon fullerenes. 61,93 Other carbon materials can 

also be transformed to nanodiamond by using 

laser pulses, MeV electrons or ion beams. 

Nanodiamond particles had been synthesized 

from fine particles of carbon black exposed to 

intense laser irradiation. 128,129 Similarly, the transformation 

from carbon nanotube to carbon onion 

258

and then to nanodiamond as a result of laser irradiation 

has been reported recently in Ref. 130. 

High-energy electron irradiation (1.2 MeV, 

>10 24 e/cm 2 ; ~100 dpa) was used successfully to 

convert the cores of concentric-shell graphitic 

onions into nanometer-size diamonds at irradiation 

temperatures above 900 K (Figure 17 ). These 

experiments were performed in situ in an electron 

microscope, which allowed continuous observation 

of the formation process. A strong compression 

in the interior of the onion was inferred by 

the observed reduction in the spacing between 

adjacent concentric shells during irradiation. 

Ion beam irradiation of carbon solids also 

resulted in formation of nanodiamond. Irradiation 

with Ne+ (3 MeV, 4 × 10 19 cm –2 ; ~600 dpa) and 

temperatures between 700˚C and 1100˚C converted 

graphitic carbon soot into nanometer-size 

diamonds. 123 Again the diamonds were found to 

nucleate in the cores of graphitic onions that developed 

under irradiation. The increased diamond 

yield when compared with electron beam irradiation 

is explained by the higher displacement cross 

section, the higher energy transfer, and the higher 

total beam current on the specimen. 

ND nucleation occurs inside graphite under ion 

irradiation at ambient temperature when implanted 

by Kr + ions (350 MeV, 6 × 10 12 cm –2 ). 122 The residue 

of the ion-irradiated graphite was found to contain 

nanodiamonds with an average diameter of 7.5 nm. 

Nanodiamond particles extracted from graphite irradiated 

by ions are illustrated in Figure 18. 

Another example of nanodiamond formation 

is the irradiation of highly oriented pyrolytic graphite 

surfaces using a highly charged ion (HCI). 131 In 

contrast to the above work, the transformation of 

spherical carbon onions to diamond by low-temperature 

heat treatment at 500 o C in air without 

electron and ion irradiation was reported. 136 

HRTEM images showed that diamond particles 

several tens of nanometers in diameter as well as 

the carbon onions coexist after the heat treatment 

in air. From detailed HRTEM and electron energyloss 

spectroscopy studies, the authors 136 suggest 

that sp 3 sites in the onions and the presence of 

oxygen during the heat treatment play important 

roles in the transformation without irradiation. 

Diamond nucleation resulting from the impact 

of energetic species corresponding to the 

conditions of a bias-enhanced CVD process 132 or 

diamond film growth using direct ion beam bombardment 

133 have been also studied extensively. 

The biased enhanced nucleation method, in which 

the substrate is negatively biased and ions are 

extracted from the CVD plasma, 132 provides the 

most versatile tool for the control of the density of 

the nucleus. These synthesis conditions create a 

rather harsh environment that decreases the probability 

of any nucleus that is formed of surviving 

in a gas phase or on a surface; therefore, a new 

explanation of the nucleation mechanism was 

required. 129 Diamond nuclei 5 to 10 nm in diameter 

have been observed recently in amorphous 

carbon films grown using bias-enhanced CVD 139 

or exposed to an ion beam. 130 A proposed model 139 

for diamond nucleation by energetic species corresponding 

to these two conditions involves the 

spontaneous bulk nucleation of a diamond embryo 

cluster (several tens of atoms) in a dense, 

amorphous hydrogenated carbon matrix; stabilization 

of the cluster by favorable interface conditions 

of nucleation sites and hydrogen termination; 

and, as a final step, ion bombardment induced 

growth through a preferential displacement mechanism. 

134 The preferential displacement mechanism 

has been used also by Banhart 135 to explain the 

transformation of graphite to diamond by MeV 

electron impact. The displacement energy of sp 2 

bonded atoms is considerably lower than that of 

sp 3 bonded atoms, so that electron bombardment 

leaves the diamond atoms intact but displaces the 

graphitic atoms to sp 3 or diamond-like positions. 

On the basis of this mechanism, the explanation 

of the diamond embryo growth under continuous 

bombardment during bias enhanced CVD is due 

to preferential displacement and transformation 

of amorphous carbon to diamond. The described 

mechanism has wide implications in understanding 

diamond nucleation and growth in/from other 

carbon-containing phases when sufficient activation 

energy is provided by means of highly activated 

species/radiation. 

v. Diamond Nucleation on a Substrate 

In the development of diamond films by CVD, 

studies of the nucleation and early growth mechanisms 

on a wide variety of substrates had been 

259

quite intensive (see, for example, review Ref. 

137). This is due to the fact that the nucleation 

process is critical in determining the films properties, 

morphology, homogeneity, defect formation, 

and adhesion. 

Because diamond heterogeneous nucleation 

has been a topic of numerous papers, 137,138 we 

include one representative study here. HRTEM 

images of the nucleation sites responsible for 

epitaxial growth of diamond by CVD on silicon 140 

revealed 2 to 6 nm diamond clusters at steps on 

the Si substrate (Figure 19). 

b. 1D Nanodiamond Structures 

The least represented group is one-dimensional 

diamond structures at the nanoscale. Aligned 

diamond whiskers have so far been formed only 

by a ‘top down’ approach by air plasma etching of 

polycrystalline diamond films, particularly of asgrown 

diamond films and films with molybdenum 

deposited as an etch-resistant mask 33 (Figure 

20). As for the as-grown diamond films, 

nanowhiskers were found to form preferentially 

at grain boundaries of diamond crystals. Dry etching 

of diamond films with Mo deposits created 

well-aligned whiskers 60 nm in diameter that were 

uniformly dispersed over the entire film surface 

with a density of 50/µm 2 . 

Micron-diameter filaments formed by colloidal 

assemblies of UDD particles have been observed 

in Ref. 64 (Figure 21). After extracting 

and drying, the filaments were similar to glass 

fibers, but no measurements of mechanical properties 

had been performed. Koscheev et al. also 

succeeded in the synthesis of submicron-diameter 

filaments consisting of UDD particles obtained 

by laser ablation of pressed nanodiamond pellets 

64 (Figure 21). In contrast to the dense filaments 

in colloids every laser-ablated fiber is a 

network of nanoparticle chains. Studies of elemental 

composition, IR, and Raman spectra of 

filaments confirmed that they consisted of origi- 

FIGURE 20. Magnified SEM micrograph of diamond nanowhiskers 

(2.5 µm across the picture). (Reprinted from Ref. 33, Copyright 

2000, with permission from Elsevier Science.) 

260

FIGURE 21. Diamond filaments grown by self-assembly of UDD particles in a colloidal suspension (a) and filaments 

obtained by laser oblation of pressed UDD pellets (b). 63 (Images courtesy of A. Koscheev.) 

nal nanoparticles that retained a diamond structure. 

After extraction from the vacuum chamber, 

the whole assembly behaved like an aerogel. In 

both examples of UDD-based filaments, the filament 

networks were rather tangled. 

c. 3D Nanodiamond Structures 

i. Ultra-Nanocrystalline Diamond (UNCD) 

Films 

A novel diamond-based material, called 

ultrananocrystalline diamond, with 2 to 5 nm 

grains (both H-containing and H-free) has been 

synthesized recently at the Argonne National 

Laboratory by Gruen and colleagues 2,62,141–143 using 

a microwave plasma assisted chemical vapor 

deposition (MPCVD) process. 

UNCD thin films were synthesized using argon-rich 

plasmas instead of the hydrogen-rich 

plasmas normally used to deposit microcrystalline 

diamond. By adjusting the noble gas/hydrogen 

ratio in the gas mixture, a continuous transition 

from micro- to nanocrystallinity was achieved. 

The controlled continuous transition from the 

micro- to nanoscale is a unique capability of the 

method. 2 

The use of small amounts of carbon-containing 

source gases (C 60 , CH 4 , C 2 H 2 ) with argon leads to 

the formation of C 2 -dimers, which is the growth 

species for all UNCD thin films. The nanocrystallinity 

is the result of a new growth and nucleation mechanism 

that involves the insertion of C 2 into the 

π-bonds of the nonhydrogenated reconstructed (100) 

surface of diamond. Unattached carbon atoms then 

react with other C 2 molecules from the gas phase to 

nucleate new diamond crystallites. 2 This results in 

an extremely high heterogeneous nucleation rate 

(10 10 cm –2 s –1 , which is 10 6 times higher than from 

conventional CH 4 /H 2 plasmas). UNCD grown from 

C 2 precursors consists of ultrasmall (2 to 5 nm) 

grains and atomically sharp grain boundaries. 

More subtle control of the properties of UNCD 

films can be accomplished via the addition of 

supplementary gasses to the plasma (N 2 , H 2 , B 2 H 6 , 

PH 3 ) and growth conditions (biasing, power). For 

instance, the addition of hydrogen leads to highly 

insulating films with large columnar grains. The 

addition of nitrogen, however, yields films that 

are much more electrically conductive than UNCD 

made with pure CH 4 /Ar plasmas. The added nitrogen 

leads to the formation of CN in addition to 

C 2 in the plasma. The presence of CN results in 

decreased renucleation rates during growth, which 

leads to larger grains and grain boundary widths. 

Up to 10% of the total carbon in the 

nanocrystalline films is located within 2 to 4 atomwide 

grain boundaries. Because the grain boundary 

carbon is π-bonded, the mechanical, electrical, 

and optical properties of nanocrystalline 

diamond are profoundly altered compared with 

more conventional grain structures. 

261

UNCD films are superior in many ways to 

traditional microcrystalline diamond films. They 

are smooth, dense, pinhole free, phase-pure and 

can be conformally coated on a wide variety of 

materials and high-aspect-ratio structures. 2 

Here it should be emphasized that, although 

the term ‘ultra-nanocrystalline diamond’ and 

‘ultradispersed diamond’ have the same prefix 

‘ultra-’, these two materials are completely different. 

The latter are single diamond clusters that 

form agglomerates with loose bonds between 

particles within a powder or in solution where 

they are stored, and the former is a bulk material 

with strong chemical bonds and atomically sharp 

grain boundaries between nanodiamond crystals. 

ii. Crystalline Diamond-Structured Carbon 

Films 

Recently, a completely different method from 

what had been discussed so far for the synthesis 

of diamond-structured carbon in bulk quantities 

has been developed by Gogotsi et al. 14 The method 

is based on extracting silicon from silicon carbide 

or metal carbide in chlorine-containing gases at 

ambient pressure and temperatures not exceeding 

1000 o C. Nanocrystalline diamond with an average 

crystallite size of 5 nm is formed after the 

extraction of silicon from the carbide. Figure 22 

shows diamond nanocrystals surrounded by amorphous 

carbon regions formed near the SiC/carbon 

phase interface. However, if no hydrogen was 

added to the gas, nanocrystalline diamond slowly 

transformed to the graphite phase during the longterm 

treatment at 1000°C, and only amorphous 

and graphitic carbon at a distance of more than 

3 µm from the SiC/carbon interface was observed. 

Following continued heat treatment at low hydrogen 

content, a typical film microstructure consisting 

of a nanocrystalline diamond layer (Figure 

22b) several microns wide near the SiC/carbon 

interface, followed by a region of diamond 

nanocrystals surrounded by carbon onions and 

disordered carbon was observed. The third region, 

closest to the surface layer, consists of carbon 

onions as well as curved graphite sheets, 

some planar graphite, and porous and disordered 

amorphous carbon. 145 

The specific feature of diamond-structured 

carbon is multiple diamond structures including 

FIGURE 22. High resolution TEM micrographs showing the structure of the carbon coating within a micrometer of 

the SiC/carbon interface (a), where nanocrystals of diamond are surrounded by graphitic carbon, including onionlike 

structures. The sample was treated in Ar/3.5% Cl 2 . Typical TEM micrograph of nanocrystalline layer of diamondstructured 

carbon produced with hydrogen present in the gas (b): Ar / 2.77% Cl 2 / 1.04% H 2 . (Reprinted from Ref. 

14, with permission from Nature, copyright 1996. Macmillan Magazines, Inc.) 

262

cubic, hexagonal (londsdalite) structures as well 

as a variety of other diamond polytypes. 145 For a 

stable conversion of silicon carbide to the diamond 

phase, the presence of hydrogen in the gas 

mixture to saturate dangling bonds on the surface 

of diamond particles is key. Nanocrystalline diamond 

films grown up to 50 µm thick at high 

hydrogen content have been demonstrated. 146 Once 

the process is optimized, the linear reaction kinetics 

allows transformation to any depth, so that the 

entire silicon carbide sample can be converted to 

nanocrystalline diamond. A specific feature of 

the carbide-derived coating is the possibility of 

varying the pores size from angstrom to a few 

nanometers, depending on the carbide precursor 

type leading to the growth of nanoporous carbon 

or nanoporous diamond. Thus, the morphological 

difference between carbide-derived and CVD-produced 

nanodiamond is a wide range of diamond 

poly types and the nanoporosity of the former. 

Because random orientation of diamond 

nanocrystals is typical for carbide-derived carbon, 

it was assumed that the growth of nanocrystalline 

diamond occurred mainly from highly disordered 

sp 3 carbon produced by selective etching of SiC. In 

most cases, SiC was first converted to amorphous 

sp 3 carbon, and then the formation of diamond 

occurred within nanometers of the SiC/carbon interface. 

The role of hydrogen is primarily to stabilize 

the dangling bonds of carbon on the surface of 

diamond nanocrystals. Correspondingly, if the starting 

material is SiC powder, a powder of diamond 

structured carbon can be synthesized. 

Figure 23 shows diamond particles with an 

average size of 5 nm embedded in an amorphous 

matrix formed during chlorination of TiC. 144 It is 

worth noting the absolutely round particle that are 

formed as illustrated in Figure 23. 

iii. Nanocomposite Material from UDD 

Bonded by Pyrocarbon 

Another interesting bulk form of nanodiamond 

particles is the so-called nanodiamond composite 

(NDC), 146 which consists of UDD particles connected 

by a pyrocarbon (PyC) matrix. Nanodiamond 

FIGURE 23. High-resolution TEM image of diamond nanocrystals embedded in amorphous 

carbon in a carbide derived carbon produced by chlorination of TiC. 144 (Reprinted from Ref. 144 

with permission from Y. Gogotsy.) 

263

powder is placed in a container of a predetermined 

shape, which is then bonded together by pyrocarbon 

formed by means of methane decomposition 

through the entire volume of the diamond powder. 

146 This material is characterized by a high 

porosity (50 to 70%). The reported pores size is not 

greater than 20 to 30 nm with average radius of 4.5 

nm. The Young’s modulus is 30 GPa. 

Due to the high density of nanopores, the 

material posses a high sorption activity, particularly 

for large biomolecules (such as tripsin). 146 

The production of the material is realized at Skeleton 

Technologies, Inc. 

iv. ND by Shock-Wave Process 

Polycrystalline diamond powder can be produced 

by shock synthesis. 16 Under suitable conditions, 

explosively produced shock waves can create 

high pressure (~140 GPa) high-temperature 

conditions in confined volumes for a sufficient 

duration to achieve partial conversion of graphite 

into nanometer-sized diamond grains that compact 

into micron-sized, polycrystalline particles. 

There are two characteristic ranges within the size 

distribution of the primary diamond nano-crystals: 

1…4 nm and 10…160 nm. 3 

An essential component that is mixed with 

graphite utilized in shock wave synthesis is copper, 

which provides fast heat dissipation in order 

to avoid the transformation of the diamond back 

to graphite at the high temperatures that are reached 

during the explosion. 

There are several modifications of the shockwave 

process. Particularly, graphite (or other carbonaceous 

materials such as carbon black, coal, 

etc.) can be loaded into explosives 57 vs. loading in 

a fixture vessel external to the explosives. 

The shock-wave process was commercialized 

by Du Pont de Nemour & Co to produce polycrystalline 

diamond particles of micron size (1 to 

60 µm) that is more friable than monocrystalline 

diamond microparticles (natural or produced by 

HPHT) and is widely used in fine polishing applications. 

Recently, low dynamic pressures up to 15 

GPa have been reported to be enough to produce 

diamond from ordered pyrolytic graphite (with 

voids between particles) using planar shock waves 

parallel to the basal plane of the graphite. 147 Diamond 

particles consisting of crystallites with grain 

sizes of several tens of nanometres were observed 

in the upper and middle regions of the post-shock 

sample by HREM. 

An interesting set of experiments was done 

by applying dynamic shock wave pressures (50 

GPa) on samples containing carbon nanotubes 

and polyhedral nanoparticles. 148 HRTEM studies 

of the samples recovered from the soot revealed 

that layers of the outer shells of the 

nanotubes break and transform into curled graphitic 

structures, and the inner nanotube walls 

and bulk material display structural defects. 

Therefore, no one-dimensional nanodiamond is 

produced by this method. The shock-wave compression 

of polyhedral particles, present in the 

starting material, resulted in nanodiamond production 

(Figure 24). In this context, it should be 

mentioned that the book by Vereschagin 3 contains 

a reference to work where aggregates of 

needle-like diamond crystals and particles with 

sharp edges of about 10 nm in size were produced 

by a modified shock wave process. Therefore, 

in principle, the production of diamond 

nanowhiskers by explosive detonation might be 

possible. 

Interesting results on diamond production by 

shock-wave compression of carbyne materials 

have been discussed by Heimann. 149 Linear carbon 

allotropes were found to transform readily 

into diamond at comparatively weak dynamic 

pressures below 5 GPa (when compared with pressures 

above 100 GPa for graphite conversion) 

without external thermal activation. Because the 

diamond particle sizes were not reported, we do 

not discuss this method in more detail, but in 

analogy with other carbon precursors we presume 

that their characteristic sizes should be within the 

nanometer scale range. These data emphasize the 

importance of the carbon precursor material for 

diamond production. 

v. High-Pressure High-Temperature 

Process 

We are not aware of publications reporting 

the production of nanosize diamond by traditional 

HPHT methods, because the method was tradi- 

264

FIGURE 24. An HRTEM image showing nanocrystals of diamond in the post-shock 

sample that are the results of carbon polyhedral particles transformation under shock 

compression. The inset is a higher magnification of the region marked by the solid arrow. 

(Reprinted from Ref. 148, Copyright 1998, with permission from Elsevier Science.) 

tionally aimed at the growth of high-quality macroscopic 

diamonds and the identification of 

nanodiamonds would require special equipment. 

There are no obvious obstacles to the production 

of nanodiamonds by this method if the volume of 

the carbon precursor material was small enough 

and these small volumes are well separated in 

space to prevent growth to microscopic sizes. 

Another issue is the practicality of the method — 

there are many other more economical ways to 

produce nanodiamonds. 

As there is no special emphasis on the size of 

diamond produced by HPHT methods, here we 

only refer to recent reports on HPHT production 

of diamond from exotic precursor materials such 

as fullerenes (Refs. 150, 154, and recent review 

151) as well as carbon nanotubes 152 that allow 

much lower temperatures and externally applied 

pressures when compared with graphite. For example, 

the transformation of buckyballs to diamond 

at high static pressure can be done at room 

temperature and does not require a catalyst. 154 

Alternatively, the production of diamond from a 

metallofullerite matrix at high temperature and 

ambient pressure has also been reported. 153 Another 

group of authors reported the conversion of 

fullerenes to diamond under ‘moderate’ conditions 

5.0 to 5.5 GPa and 1400˚C. 150 

Carbon nanotubes have been converted to 

diamond at 4.5 GPa and 1300˚C using NiMnCo 

catalyst. 152 According to their HRTEM observations, 

the authors suggest that under HPHT conditions 

the tubular structures collapse and broken 

graphitic shells curl up and close into spheroidal 

networks to eliminate the dangling bonds at the 

edges. The high curvature of the formed nested 

graphitic shells and cross-links between the layers 

in the onion-like structures that are formed 

lead to an increased fraction of sp 3 bonds that 

facilitate the formation of diamond. 

In Ref. 155 multiwalled carbon nanotubes 

were heated in a diamond anvil cell by a laser 

above 17 GPa and 2500 K. The recovered product 

consisted of nano-sized octahedral crystals (diamond) 

of less than 50 nm. The tubular structure 

completely changed to granular and grain sizes 

corresponded to the diameter of nanotubes. The 

grain size of the diamond suggests that the trans- 

265

formation took place by direct conversion of 

nanotubes that might provide a control over diamond 

size by the choice of the MWNT size. 

The aim of the present section was to summarize 

reports on the synthesis/observation of 

nanodiamond. In general, it is formed under a 

wide variety of nonequilibrium conditions. The 

methods of diamond synthesis reported in this 

section are summarized in a tentative scheme 

(Figure 25). 

2. Ultradispersed Diamond 

As has already been mentioned above, 

ultradispersed diamond — a material consisting 

of isolated diamond particles — is not well known 

in the U.S., while it has been on the market and 

used widely in different technologies in the Former 

Soviet Union for more than a decade. The areas of 

application of UDD are completely different from 

those, for example, for UNCD films, the material 

being actively developed now in the U.S. While 

UNCD as grown is a very hard, very smooth, and 

chemically inert coating, a single particle of UDD 

consists of a chemically inert diamond core and 

chemically active surface, with controllable properties. 

In the macro-world they exist in the form 

of powders (where UDD form agglomerates) and 

suspensions (aggregated or isolated particles). 

Below we provide more details on the synthesis 

and properties of UDD. 

a. Synthesis and Post-Synthesis Treatment 

At the beginning we would like to emphasize 

the differences between the major methods for 

diamond synthesis using explosives, because the 

materials that are produced are very different, and 

it is necessary to be aware of this difference when 

making a choice of the material for particular 

applications. There are three major methods that 

had been commercialized. 3 The first is the transformation 

of carbon precursors (e.g., graphite, 

coal, and carbon black) to diamond in a capsule 

compressed by a shockwave (~ 140 GPa) generated 

outside the capsule (the ‘Du Pont method’). 

FIGURE 25. Tentative scheme summarizing the methods of synthesis of diamond nanostructures. 

266

To prevent diamond regraphitization, a mixture 

of graphite (6 to 10%) with metallic powder (Cu, 

Al, Ni) is used. The diamond yield is about 60 

mass percent of the carbon phase or about 5% of 

the initial mixed material loaded into a capsule. 

The synthesized nanodiamond had a bimodal size 

distribution; the first maximum was within the 

1 to 4 nm size range and the second was within 

the 10 to 150 nm range. The product of the synthesis 

always contained the londsdalite phase due 

to the martensitic type of transformation graphiterombohedral 

graphite-londsdelite–diamond. 3 

There are several modifications of this method, 3 

however. 

The second method of ND production is based 

on the detonation of a mixture of carbon-containing 

material with explosives. In this case diamond 

formation takes place both within the carboncontaining 

particles as well by condensation of 

carbon atoms contained in the explosives. The 

explosion can be done in air or in an inert atmosphere 

relative to the product of synthesis. 3 In the 

latter case, a diamond cubic phase not more than 

20 nm in size is formed. When the formation is in 

an atmosphere of air, the samples always contain 

londsdalite and the particle size is smaller — 

about 8 nm. The diamond yield constitutes up to 

17% of the mass of the initial carbon material or 

about 3.4% of the mass of the explosives. 

The characteristic feature of the diamond 

obtained by these two methods based on the shock 

wave compression of the initial graphite phase is 

formation of polycrystalline material with particle 

sizes comparable to the particle sizes of the 

precursor carbon material. The particles consist 

of nanocrystalline diamond grains. After purification 

the particles produced by detonation are classified 

by fractions (from 1 to 60 µm ) for use in 

polishing applications. 3 

In the third method of using explosion energy 

for diamond production, diamond clusters are 

formed from carbon atoms contained within explosive 

molecules themselves, so only the explosive 

material is used as a precursor material (Figure 

26). A wide variety of explosive materials can 

be used, including products for military applications 

(so that UDD synthesis is a good way of 

utilizing of the stock pile materials). A typical 

explosive is a mixture of TNT (2-methyl-1,3,5- 

trinitrobenzene) and hexogen (in proportion 60/ 

FIGURE 26. Schematic illustration of the steps in the controlled detonation synthesis of nanodiamond from carboncontaining 

explosives (1). During explosion (2) the highly dispersed carbon medium condenses from free explosive 

carbon in a fraction of a microsecond. Depending on the detonation conditions, the resulting detonation soot (3) 

contains 40 to 80 wt.% of ultradispersed diamond. After disposal, the product has to undergo several stages of 

purification. Big industrial detonation reactors are able to deliver tons of detonation diamond per month. The 

composition of detonation soot is provided based on 163 (pictures of the detonation process courtesy of PlasmaChem 

GmbH, Mainz/Germany). 

267

40) composed of C, N, O, and H with a negative 

oxygen balance (i.e., with the oxygen content 

lower than the stoichiometric value), so that ‘excess’ 

carbon is present in the system. A negative 

oxygen balance in the system is an important 

condition for UDD formation. The explosion takes 

place in a nonoxidizing medium (Figure 26) of 

either gas (N 2 , CO 2 , Ar, or other medium — that 

can be under pressure) or water (ice) — ‘dry’ or 

‘wet’ synthesis, correspondingly, that plays the 

role of a coolant. To prevent the UDD formed in 

the detonation wave from transforming into graphite 

at the high temperature generated by the detonation, 

the cooling rate of the reaction products 

should be no less than 3000 K/min. 3 The initial 

shock from a detonator compresses the high-explosive 

material, heating it and causing chemical 

decomposition that releases enormous amounts 

of energy in a fraction of a microsecond (Figure 

26). As the detonation wave propagates through 

the material it generates high temperatures (3000 

to 4000K) and high pressures (20 to 30 GPa) that 

correspond to conditions of thermodynamic stability 

for diamond. During detonation, the free 

carbon coagulates into small clusters, which grow 

larger by diffusion. 80,86,87 The product of detonation 

synthesis, called detonation soot or diamond 

blend, contains 40 to 80 wt.% of the diamond 

phase depending on the detonation conditions. 

The carbon yield is 4 to 10% of the explosive 

weight for the most effective of the three industrial 

methods of diamond production using explosives. 

In summary, there are two major technical 

requirements for UDD synthesis using explosives. 

First, the composition of the explosives must provide 

the thermodynamic conditions for diamond 

formation, and second the composition of the gas 

atmosphere must provide the necessary quenching 

rate (by appropriate thermal capacity) to prevent 

diamond oxidation. The diamond yield depends 

to a large extent on the explosive mixture 

(Figure 27). 86 The shape of the explosive also 

influences the yield; the ideal shape is spherical, 

but for convenience a cylindrical shape is used 

regularly. The relationship between the mass of 

the explosives and the mass of the surrounding 

media influences also yield (e.g., 5 kg of explo- 

FIGURE 27. Diamond weight fraction recovered from soot as a function of the 

composition of the explosive mixture. The abbreviation for explosives is as 

follow: TNT — 2-methyl-1,3,5-trinitrobenzene; HMX — octahydro-1,3,5,7- 

tetranitro-1,3,5,7-tetrazocine; TATB — 2,4,6-trinitro-1,3,5-benzenetriamine; 

RDX — hexahydro-1,3,5-trinitro-1,3,5-triazine. (Reprinted from Ref. 86, Copyright 

2000, with permission from American Institute of Physics.) 

268

sive requires ~11 m 3 of detonation camera with 

gas media at ambient pressure to provide the necessary 

quenching rate). 3 The mechanisms of diamond 

formation as well as factors influencing 

yield during explosive detonation have been discussed 

in numerous publications by different 

Russian research groups (summarized in Ref. 3). 

In the U.S., fundamental studies of carbon particle 

phase transformation in detonation waves 

have been performed at Laurence Livermore 

National Laboratory, primarily by Francis Ree 

and colleagues 80,86,87 and Los Alamos National 

Laboratory primarily by Sam Shaw and colleagues. 

158 Both the thermodynamics of chemically 

reactive mixtures and the kinetics of carbon 

coagulation have been modeled. 86,87,158 The kinetics 

of the formation and growth of finite carbon 

particles contribute significantly to the detonation 

properties of carbon-rich CHNO explosives. As 

detonation proceeds, the most important products 

behind the reaction zone are carbon dioxide, water, 

nitrogen, and carbon residues that undergo 

phase changes. The relatively slow growth rate of 

carbon particles gives rise to an extended reaction 

zone. As a consequence, the detonation is more 

sensitive to the system configuration, with the 

observed Chapman-Jouguet pressure reflecting the 

condition of a partially reacted state rather than 

that of the final detonation product. Carbon clustering 

is a slow reaction in the detonation regime 

as demonstrated by Shaw and Johnson at the end 

of 1980s 158 using a diffusion-limited model. Carbon 

particles build up from random collisions, 

while the hot dense background fluid maintains 

the equilibrium temperature, allowing the clusters 

to anneal to compact spherical objects. The final 

particle size was estimated to be 10 4 to 10 5 atoms 

(50 Å), which explained the experimental particle 

sizes. The model did not distinguish between 

the various forms of carbon present during the 

detonation process. The model has been reconsidered 

taking into account the diamond/graphite 

transitions within the carbon particles. 80,86,87 Estimates 

of the displacement of the phase equilibrium 

lines for small carbon particles containing 

from several hundred to several tens of thousands 

of atoms 87 was also included in the analysis of the 

kinetics of carbon coagulation. A simplified hydrodynamics 

model yielded a time and pressuretemperature 

path-dependent value for the 

nonequilibrium diamond fraction of the soot mixture. 

86 

i. Purification 

The diamond blend in addition to UDD contains 

graphite-like structures (35 to 45 wt.%), and 

incombustible impurities (metals and their oxides 

— 1 to 5wt.%). 1 Using X-ray diffraction and 

small angle X-ray scattering, it was shown that an 

UDD cluster in detonation soot has a complex 

structure consisting of a diamond core of about 

4.3 nm in size and a shell made up of sp 2 coordinated 

carbon atoms (Figure 27). 164 The shell structure 

and thickness vary with the cooling kinetics 

of the detonation products (dry vs. wet synthesis) 

and conditions of chemical purification of theUDD 

clusters from the detonation soot. 164 According to 

the X-ray diffraction spectra and the results of 

electron microscopy, UDD of the highest degree 

of purification contain no intermediate amorphous 

phase, graphite, or londsdalite. 161,162 

UDD purification is performed by mechanical 

and chemical methods. After mechanical removal 

of process admixtures, the diamond-carbonic 

powder is subjected to thermal oxidation 

with nitric acid under pressure to separate the 

diamond phase. 1 The method of acid purification 

at elevated temperatures is the most efficient purification 

method at the present time because it 

comprehensively influences all admixtures: metals 

are dissolved and non-diamond carbon is oxidized 

simultaneously. The diamond should be 

flushed with water after separation from the acidic 

media. After a typical purification step, powders 

of UDD can be considered as a composite consisting 

of different forms of carbon (80 to 89%), 

nitrogen (2 to 3%), hydrogen (0.5 to 1.5%), oxygen 

(up to 10%), and an incombustible residue 

(0.5 to 8%). 1 The carbon consists of a mix of 

diamond (90 to 97%) and non-diamond carbon 

(3 to 10%). 

In detonation synthesis of nanodiamonds, the 

impurity content is higher when compared with 

other artificial diamonds (i.e., HPHT diamonds 

contain no less than 96% carbon). Therefore, the 

effect of impurities is more pronounced for UDD 

compared with other diamonds. 1 Impurities in 

269

UDD, in principle, can be divided into the following 

groups: 1 (1) water-soluble ionized species (free 

electrolytes); (2) chemically bonded to diamond 

surfaces and prone to hydrolysis and ionization 

(salt forms of functional surface groups); (3) water 

insoluble; and (4) incorporated into the diamond 

lattice and encapsulated. The impurities of the 

first and second groups are formed in the chemical 

purification of UDD by acid stage. 1 The major 

water-soluble admixtures (first group) are removed 

by washing the UDD with water. The surface 

functional groups (second group) can be efficiently 

removed by ion-exchange resins that involve demineralization 

of surface groups. The water-insoluble 

impurities represent both individual 

microparticles of metals, oxides, carbides, salts, 

and metal oxides that do not dissociate. For their 

removal, UDD particles are treated with acids. By 

using different methods of UDD purification, one 

can remove 40 to 95% of the impurities of these 

three groups. It is practically not possible to remove 

the impurities of the fourth group by chemical 

methods. The UDD of the highest purity available 

at ‘Diamond Center’, Inc. contains 98.5% of 

diamond. 

Commercial products of purification have 

the following grades: a water suspension of diamond 

and powder obtained from suspensions by 

drying and grinding of UDD are a gray powder 

containing up to 99.5 wt.% of a pure diamond 

(without counting adsorbed gases). 1 To remove 

non-carbon impurities, the chemically purified 

product is subjected in some cases to additional 

purification using ion-exchange and membrane 

technologies. 

In general, the UDD production consists of 

detonation synthesis, chemical purification and 

acid washing of UDD, product conditioning, and 

modifying of diamond. 

b. Experimental Characterization of 

Ultradispersed Diamond 

The properties of UDD particles are mainly 

defined by their nanometer-scale sizes (4 to 6 nm 

in diameter) that are within a transitional size 

range between macromolucules and crystalline 

solids. About half of all atoms in such particles 

are on the surface, and thus are unavoidably bound 

to adsorbed atoms, molecules, and functional 

groups. These adsorbed atoms, which can exceed 

the number of atoms in the diamond particle, can 

strongly affect the physical and chemical properties 

of the particles. 

To minimize surface energy, the primary UDD 

particles with diameters of ~4 nm form larger 

clusters 20 to 30 nm in size that, in turn, form 

larger weakly bound aggregates (of an order of 

magnitude of hundreds of nanometers). The UDD 

aggregates have a fractal nature. 1 This hierarchy 

of nanodiamond blocks needs to be taken into 

account in the interpretation of all experimental 

results. 

The smallest amount of diamond matter, which 

can be prepared and studied in isolation are primary 

particles of UDD. In addition, the particles 

of UDD are thermodynamically stable at ambient 

conditions, due to their very small size (

While by traditional dynamic synthesis from 

graphite diamond particles of both cubic and hexagonal 

(a=0.252 nm) structures are produced, UDD 

obtained from explosives has only the cubic structure 

without any traces of the hexagonal phase. 1 

Raman Spectroscopy 

All experimental Raman studies of ultradisperse 

diamond quote practically the same frequency position 

of the peak within 1321–1322 cm –1 . 167 Typical 

Raman spectra of UDD and bulk diamond are 

shown in Figure 30. 167 The observed spectrum can 

be explained by the phonon confinement model 

(see references in Ref. 167). The authors of Ref. 

167 calculated from this spectrum based on the 

phonon confinement model that the size of the 

diamond nanoparticles is 5.5 nm (the X-ray size 

obtained by the same authors was 4.3 nm). 

Aleksenskii et al., 165 using the same Raman 

technique, obtained two numbers for the size of 

the diamond crystallites using two different sets 

of constants in the phonon confinement model: 

3.6 and 4.3 nm. The authors 165 noted that the 

estimates of crystalline size based on the photon 

confinement model are very sensitive to the choice 

of the dispersion relation for the photon modes. 165 

Annealing Effects and Diamond-Graphite 

Phase Transition 

The narrow size range of UDD nanoparticles 

of 4 to 5 nm was quoted in a number of studies. 165 

The usual explanation is that nanodiamond is more 

stable than graphite (see Section II). However, the 

thermodynamic stability reasoning, while explaining 

the upper bound does not give the lower bound 

for the size, thus the narrow size distribution still 

needs to be clarified. 

Aleksenskii et al. 165 used Raman spectroscopy 

to study the annealing effects on the 

nanodiamond structure. Starting from an anneal- 

271

FIGURE 28. Model structures of detonation-produced carbon. Depending on purification 

conditions, different layers of the UDD shell can be ‘stripped-off’. (Reprinted from Ref. 164, 

with permission from American Institute of Physics.) 

ing temperature of T=720 K, remarkable changes 

in the Raman spectra were observed. The peak 

due to diamond nanoparticles decreased significantly 

in intensity while not exhibiting any shift 

in frequency. With further increases of T ann 

a monotonic decrease of intensity of the 

nanocrystalline diamond line at 1322 cm –1 was 

observed, without any change in position. At 

T ann =1200 K this line was no longer observed. 

The constancy of the position of the 1322 cm –1 

Raman line up to T ann =1000 K indicates that no 

changes occur in the structure of the diamond 

nuclei at such annealing temperatures. X-ray diffraction 

data indicated the formation of a graphitic 

phase for T>1200 K. 165 The authors 165 

pointed out that because UDD exists in aggregated 

form, the amorphous phase is apparently 

distributed inside the aggregates on the surface of 

diamond nuclei. The presence of an amorphous 

phase was supported by X-ray diffraction, which 

yielded about 1.5 nm for the size of amorphous 

particles. 

The diamond-graphite phase transition temperature 

observed in UDD (T pt >1200 K) is considerably 

lower than the phase transition temperature 

of bulk single-crystal diamond (T pt >1900 K). 

An interesting result was reported by 

Obraztsova et al. 169 The authors developed a special 

annealing procedure that provided an effective 

means of reducing the size of diamond 

nanoparticles while preserving the diamond crystal 

structure. The procedure allowed them to reduce 

the size of diamond particles step by step 

from the initial 4.5 nm down to 2 nm by changing 

the annealing temperature. Obraztsova et al. found 

that for the smaller size the complete particle 

transformation into the onion-like carbon structure 

takes place. The size and phase transformations 

were characterized by Raman spectroscopy. 

The authors also observed a strong photolumines- 

272

FIGURE 29. X-ray diffraction from UDD. (Reprinted from Ref. 167, 

Copyright 1995, with permission from the American Institute of Physics.) 

cence (PL) simultaneously with the Raman signal 

of diamond. The maximum of the PL shifted from 

2.14 to 2.3 eV, while the annealing temperature 

was increased over the range from 1100 to 1600 K, 

and correspondingly the particle size changed from 

4.5 to 2 nm. The PL signal disappeared simultaneously 

with the disappearance of the Raman 

signal of diamond. These authors estimated the 

size of diamond crystals from the phonon confinement 

model to be 4.5 nm. 

X-ray Spectroscopy 

Quantum confinement effects are expected in 

nanocrystalline semiconductors when the size of 

the particle is smaller than some critical value. 

However, details of the electronic structure of 

nanodiamonds are still unknown. Chang et al. 

studied CVD diamond films with various crystallite 

sizes by X-ray absorption spectroscopy. 170 

The size of the diamond crystallites in the films 

ranged from 3.5 nm to 5 µm. Figure 31 shows the 

exciton state and conduction band edge of the 

nanodiamonds as a function of the crystallite 

size. 170 According to this plot, the conduction 

band edge shifts to higher energy with a decrease 

in the crystallite size. A strong change in energy 

structure, which is believed to be due to quantum 

confinement, takes place for sizes smaller than 10 

nm. The authors applied a standard analytical 

approximation for quantum confinement shift of 

energy levels in a one-dimensional quantum box 

of size a ∆E ≈ π 2 h 

2 

* 2 

and derived the value of 

2ma 

effective mass for nanodiamond of about 0.1m 0 . 

The above results and their interpretation raise 

several questions. First, the objects of this study 

were not isolated diamond crystallites but a complex 

composite material consisting of diamond 

crystallites of different sizes, grain boundaries, 

amorphous and possibly graphitic inclusions, etc. 

Second, Ley et al. 171 questioned the validity of the 

273

FIGURE 30. Raman spectra from UDD and bulk diamond. (Reprinted from Ref. 167, 

Copyright 1995, with permission from the American Institute of Physics.) 

method the authors used for the extraction of the 

values of energy shifts. Third, the calculated effective 

mass of nanodiamond of 0.1m 0 is considerably 

smaller than the bulk value. Note that in 

the limiting case of a→0, when the particle approaches 

one atom, m*→m 0 , that is, the effective 

mass increases. Fourth, the reported widening 

energy gap, remarkable already at a diamond 

particle size of about 10 nm, is in contradiction 

with theoretical results predicting the critical size 

for the band structure size-effect onset to be 2 to 

2.5 nm. 172 In 2002, Raty et al. presented theoretical 

results suggesting that the widening of the 

energy gap is remarkable only for the size of the 

diamond particle

FIGURE 31. The exciton state and conduction band edge of the 

nanodiamonds as a function of the crystallite size. (Reprinted from Ref. 

170, Copyright 1998, with permission from the American Physical Society.) 

to obtain bonding information. For example, it 

clearly shows sp 3 or sp 2 bonding of carbon atoms. 

In principle, the EELS sensitivity in compositional 

analysis can be extended to the single-atom 

limit, as was shown by Suenaga et al. 173 Because 

EELS is usually associated with high-resolution 

TEM, it is possible to collect information about 

bonding with very high spatial resolution within 

a nanoparticle. EELS in a TEM can in principle 

improve the accuracy of size measurements. In 

Ref. 174 the approximate diameters measured in 

a TEM were later adjusted by fitting theoretical 

and experimental EELS spectra. The fitting procedure 

was based on the spherical model shown 

in Figure 33, and both the amorphous layer thickness 

and crystalline diamond core diameter were 

varied to obtain the best fit. Table 8 shows measured 

diameters of diamond particles of three different 

sizes compared with calculated values derived 

by matching experimental EELS data. 

It should be noted that the assumption of a 

spherical shape for the diamond nanoparticles led 

to a considerable difference between the direct 

TEM measurements and EELS adjusted values. 

After more detailed investigations of TEM images, 

it was found that the particles were not 

really spherical. Taking into account the 

nonspherical shape resulted in better agreement 

between the EELS predicted and TEM measured 

diameters. Also, from their analysis the authors 

conclude that theoretical predictions for the case 

of crystalline diamond surrounded by a surface 

layer of sp 2 (e.g., graphitic) material were definitely 

not capable of reproducing the experimental 

results. 174 

Shape of Diamond Nanoparticles 

The shape of UDD particles 3 to 5 nm in size 

is often assumed to be spherical. As a model, a 

275

FIGURE 32. Histogram of diamond crystallites of various sizes directly measured in a HREM lattice image 

of a CVD nanodiamond film. (After Ref. 2.) 

spherical shape is easier for calculations. At the 

same time, there are experimental reports that 

most of the diamond particles have very spherical 

shape. 174,175,176 This led to speculation that the 

diamond nanoparticles are formed from liquid 

drops. Chen and Yun 175 argued that from the point 

of view of the carbon phase diagram, thermodynamic 

conditions created by explosive detonation 

(temperature range 3000 to 3500 K, pressure 30 

to 35 GPa do not correspond to the liquid state 

region of diamond crystal). The authors 175 suggested 

that this contradiction could be resolved 

by assuming that while bulk diamond cannot melt 

under the detonation conditions, for the nanometer-sized 

diamond particles the effective melting 

point might decrease. Thus, Chen and Yun concluded 

that the formation mechanism of nanosized 

diamond is through coagulation of liquid 

droplets. 175 One should mention that the statements 

about the spherical shape of diamond 

nanoparticles are usually based on TEM pictures 

without considerable magnification, where the 

particles appears so small (as for example, in 

Ref. 175) that it is impossible to make any assessments 

about shape. Sometimes particles are 

shown in TEM with larger magnification, but 

without isolation from each other and from the 

amorphous matrix so again it is difficult to assess 

the shape. 

Vereschagin and Sakovich also argued in favor 

of a spherical shape for UDD nanocrystals 

and the liquid carbon drop formation mechanism. 

168 Also, they compared the density of 

nanodiamonds calculated from the lattice parameters 

(3.527 g/cm 3 ) with the experimental values 

of the helium pycnometric density of UDD, which 

276

FIGURE 33. A model for a diamond nanoparticle consisting of a 

sphere of crystalline diamond with diameter d c , surrounded by a 

layer of amorphous carbon with thickness t a . The resulting diameter 

of the particle is d=d c +t a . 

277

is 3.05 to 3.10 g/cm 3 . Their conclusion was that 

the difference between calculated (X-ray) and 

pycnometric densities supports the liquid phase 

model of nanodiamond formation. Moreover, the 

authors 168 suggested that diamond nanoparticles 

formed by rapid crystallization are hollow spheres! 

They estimated from the density difference that 

the cavity inside 4 nm particle should be 1.77 nm 

in diameter. 

Surface Properties 

Maillard-Schaller et al. investigated the surface 

and electronic properties of nanometer-sized 

diamond particles (UDD Ndp2) by X-ray photoelectron 

spectroscopy (XPS) and UV photoelectron 

spectroscopy (UPS). 177 In these experiments, 

nanodiamonds were deposited on flat Si(100) 

substrates by electrophoresis. Figure 34 shows 

the XPS spectra of a nanodiamond powder film 

on Si(100). According to the XPS analysis, the 

UDD powder did not contain any detectable impurities 

except nitrogen. The N content was estimated 

to be 1 to 2 at. %. The as-deposited UDD 

films showed a strong oxygen peak. After treatment 

in a hydrogen microwave plasma and transfer 

in air to the XPS system, the nanodiamond 

films were found to be almost free from oxygen 

contamination, as can be seen in Figure 34. 

HeI (hν=21. 2 eV) and HeII (hν=40.8 eV) 

UV photoelectron spectroscopy measurements 

have been performed on the as-deposited and 

hydrogen plasma-treated nanodiamond films. 

Based on the UPS spectra (Figure 35), the energy 

band diagram of nanodiamond has been proposed 

(Figure 36). The electron affinity χ of UDD films 

was calculated using the emission width W and 

the low kinetic energy cut-off in the experimental 

UPS spectra (Figure 35): χ=hν-E g -W. 

The emission width of the as-deposited sample 

was 15.0 eV with a low-energy cut-off at 3.1 eV, 

which results in a positive value of electron affinity 

of +0.7 eV, assuming that the band gap E g =5.5 

eV. After H 2 plasma treatment, the samples showed 

an emission width of 15.9 eV with a very sharp 

low-energy cut-off at 2.1 eV, indicating a negative 

electron affinity of –0.2 eV (Figure 36). 

Electrical Characterization 

There are only a very few experimental reports 

on electrical and electronic properties of 

UDD. Some measured collective electrical characteristics 

of powders and suspensions are given 

FIGURE 34. Survey XPS spectra of the UDD film (a) before and (b) after the H 2 

plasma treatment. (Reprinted from Ref. 177, with permission from Elsevier Science.) 

278

FIGURE 35. HeI and HeII UPS spectra of as deposited and H 2 plasma-treated 

UDD surfaces. (Reprinted from Ref. 177, with permission from Elsevier Science.) 

FIGURE 36. Energy band diagram of the hydrogenated nanodiamond powder film. (Reprinted 

from Ref. 177, with permission from Elsevier Science.) 

279

in Table 7. Gordeev et al. reported a resistivity for 

bulk nanodiamond composites obtained by pressing 

UDD powders. 178 Such materials have very 

high porosity typically in the range 60 to 70 vol.%. 178 

The room temperature resistivity of such UDD 

composites was 1.2 × 10 9 W-m, consistent with the 

resistivity reported by Dolmatov (Table 7). 

Belobrov et al. reported results of studies of 

UDD powders with different surface modifications 

by electron parmagnetic resonance and 

nuclear magnetic resonance (NMR) spectroscopies. 

179 An example of a nanodiamond EPR 

spectrum is shown in Figure 37. The authors 179 

found that the nanodiamond EPR signal is independent 

from the chemical modification of the 

nanodiamond surface. The g-factor for UDD was 

found to be 2.0027(5). 179 Belobrov et al. concluded 

that the paramagnetic properties of the 

nanodiamond are determined only by the sp 3 core 

of the diamond particle. 

A 13 C NMR spectrum for nanodiamond is 

shown in Figure 38. According to the authors, 179 

the resonance line is assymetric and well decomposed 

into two Gaussian components, 

whose numerical values are presented in the 

table in Figure 38. The authors interpreted the 

narrow line with δ=35.1 ppm as relating to 

diamond carbon, while the wide line with δ=34.2 

ppm is caused by distortion of the tetrahedral 

coordination. The authors 179 concluded that only 

30% of bonds in nanodiamond are nondistorted 

sp 3 bonds, while the remaining 70% of carbon 

bonds are distorted but still with sp 3 hybridization. 

For comparison, natural jewel-quality diamonds 

have a characteristic chemical shift δ=50 

ppm. 

Zhirnov et al. characterized UDD particles 

using electron field emission measurements by 

putting small a amount (0.2 µm in thickness) of 

UDD on metal or silicon tips by electrophoresis. 

180,181 In these experiments, the field emission 

characteristics of tips with UDD coatings were 

compared to characteristics of bare tips. The 

emission experiments showed that the emission 

characteristics differ significantly for different 

UDD coating conditions. The different UDD 

coating conditions were obtained from one original 

UDD powder (marked as Nd) using different 

physical and chemical treatments. The modifications 

differed in concentration of impurities, 

pH of water suspension, and density as shown in 

Table 9. 180 

FIGURE 37. Central part of the EPR spectrum of nanodiamond with the Li standard (g=2.0023). 

The scan and the modulation are 50 and 0.01 mT (After Ref. 179, with permission from P. 

Belobrov.) 

280

FIGURE 38. 13 C spectrum for nanodiamond. The numerical values of chemical shifts, intensities, and line widths after 

decomposition into Gaussian components are given in the table. (After Ref. 179, with permission of P. Belobrov.) 

281

A summary of the emission characteristics 

for different UDD coatings is given in Table 10. 

The emission characteristics of UDD are discussed 

in more detail in Ref. 180. An interesting result is 

the difference in the emission characteristics of 

UDD with modifications NdP and NdP1 (Figure 

39). NdP1 was prepared using the heavier (bottom) 

fraction of the original NdP modification, 

and the main difference between the two was the 

average crystallite size (larger for NdP1). This 

result indicates critical role of diamond crystal 

size in the nanoscale regime on the emission properties 

of UDD-coated tips. 

Characterization of Isolated Nanodiamond 

Particles 

At this point, most of reported results on characterization 

of nanodiamond describe collective 

properties of multiparticle systems such as CVD 

nanodiamond films, agglomerates of UDD, etc. 

Such systems are composite materials, consisting 

of sp 3 -bonded diamonds often surrounded by 

amorphous carbon, sp 2 -bonded graphitic inclusions, 

etc. Correspondingly, it is often difficult to 

extract specific information about 3 to 6 nm primary 

nanodiamond crystallites. Moreover, in some 

cases the properties of nanodiamonds can be 

modified due to the presence of surrounding materials. 

For example, the surface energy, and correspondingly 

shape of particles, is very sensitive 

to their surroundings. The characterization of isolated 

nanodiamond particles is an important but 

challenging task. There are few reports of characterization 

of isolated diamond particles 40 to 100 

nm in size (see, for example, the next section). 

However, the smallest nanodiamond crystallites 

with a size of 3 to 6 nm are very difficult to 

characterize in isolation, due to their natural trend 

to form agglomerates. 

Tyler et al. recently reported a new technique 

for isolating individual nanodiamond particles by 

depositing them on sharp (radius 10 to 50 nm) 

metal tips by pulsed electrophoresis from alcohol 

suspensions of UDD. Apparently, the very high 

electric fields near the sharp tips breaks the agglomerates, 

and thus it is possible to manipulate 

individual nanodiamond particles. 182 Examples of 

metal tips with nanometer-size diamonds are 

shown in Figures 15 and 40. The typical size of 

diamond nanoparticle as measured in TEM was 

about 3 nm (Figure 40). It should be noted that in 

all cases only particles with faceted shapes were 

observed. 

More detailed information about the preparation 

procedure and results of characterization can 

be found elsewhere. 183,184 Preliminary results of 

field emission characterization of UDD reveal a 

considerable difference in emission behavior of 

single isolated diamond nanoparticle and multiparticle 

nanodiamond thin film. 184 

Nonclassical Fluorescence from 

Diamond Nanoparticle 

A new area for physical experimentation with 

possible applications in advanced information processing 

is the generation of light sources that are 

able to emit individual photons on demand. 

Beveratos et al. investigated the quantum properties 

of the light emitted by diamond nanocrystals 

containing a single nitrogen-vacancy color center. 

185 The typical size of diamond particles used in 

these experiments was 40 nm. According to the 

authors, there are several very important optical 

properties of diamond nanocrystals that are impor- 

282

FIGURE 39. Current-voltage characteristics of Si tips with UDD coatings of the same 

modification with different size of diamond crystallites: NdP and NdP 1 . (Reprinted from 

Ref. 180, Copyright 1999, with permission from the American Institute of Physics.) 

tant for their use as individual photon light sources. 

First, the subwavelength size of these nanocrystals 

renders refraction irrelevant. A nanocrystal can be 

regarded as a point light source. Second, the very 

small volume of diamond excited by the pump 

light yields very small background light. This is 

very important for single photon sources. 

By exciting nanodiamond crystals using a 

YAG laser (l=532 nm), the authors were able to 

observe fluorescence with almost backgroundfree 

photon antibunching from single nitrogenvacancy 

centers in diamond nanocrystals at room 

temperature. The excited state lifetime in the bulk 

is t b =11.6 ns. The measured lifetime in the 

nanocrystals was 25 ns. The authors argue that 

this lifetime modification is a quantum electrodynamic 

effect. 

3. Atomistic Simulations on Diamond 

Clusters 

a. Simulations of Diamond Clusters: 

Structural Properties 

Below we discuss two questions related to the 

number of atoms, the fraction of surface atoms in 

a diamond particle of a particular size, and possible 

shapes of a single nanodiamond particles. Although 

in reality diamond nanoparticles contain functional 

groups at the surface (Section III.B.2), the present 

analysis is restricted to hydrocarbon systems. 

How Many Atoms Are in a Single ND 

Particle? 

Plotted in Figure 41a is the number of atoms 

in a spherical diamond particle as a function of 

particle size estimated from the formula: 

Ntot = 4 

3V 

R 3 

π , (5) 

0 

where V 0 = 5.667 Å 3 is atomic volume in bulk 

diamond. For example, a particle with a diameter 

of 4.3 nm the equation yields about 7200 atoms, 

while a particle with diameter 10 nm is predicted 

to contain about 92,000 atoms. 

Another important characteristic that influences 

particle properties is the number of surface 

atoms. Assuming 

n 

S 

= ( n ) 23 / 

(6), 

Bulk 

283

FIGURE 40. Isolated nanodiamond particle on molybdenum tip. 184 

where n s and n bulk are surface and bulk atomic 

densities, respectively, the following analytical 

expression is often used to estimate the number of 

surface atoms in a spherical particle: 

N 

S 

3 

/ Ntot 

= 

13 / 

(7) 

4Rn 

Bulk 

It is possible to cut out a sphere of a given radius 

and count the number of atoms with a coordination 

number less than four at the surface of the 

sphere. The difference between the fraction of the 

surface atoms evaluated this way and from Eq. 6 

can be as big as 2 to 2.5 times. This difference 

arises from the presence of various surface facets 

in the second method for counting the number of 

surface atoms that are not accounted for in Eq. 6, 

which assumes a density of surface atoms equal 

to that for a (001) facet. The number of surface 

atoms for a spherical cluster as a function of 

cluster diameter taking into account surface 

faceting is plotted in Figure 41. 

What is the Shape of a Nanodiamond 

Cluster? 

Until recently, most of the experimental work 

dealing with nanodiamond produced by means of 

detonation described the shape of clusters as being 

spherical (Section III.A.2.b). Indeed, HRTEM 

pictures of nanodiamond agglomerates resemble 

spherical forms (Figure 42a) as well, as, for example, 

nanodiamond clusters embedded in metal- 

284

FIGURE 41. Total number of atoms and the number of surface atoms in a spherical nanodiamond 

particle as a function of particle size. Bottom image provides more details for smaller particles. 

lic matrices after chlorination of metal carbide 

(Figure 23). However, recent HRTEM images of 

a single nanodiamond cluster on the surface of a 

Mo tip clearly indicate the presence of facets at 

the particle surface, with the cluster resembling a 

polyhedral shape (Figure 15). This shape is similar 

to that of microscopically sized diamond particles 

formed in the gas phase during a CVD 

process as first was reported by Matsumoto and 

Matsui 29 (Figure 42b). The typical habit of these 

clusters was regularly shaped cubo-octahedron 

and twinned crystals, that is, twinned cubo-octahedron, 

an icosahedron and a decahedral-Wulffpolyhedron. 

The particles have exposed (100) and 

(111) facets and often possess chamfered edges 

along certain directions (such as ) (Figure 

42b). Multiply twinned nanodiamond particles 

have had been observed in meteorites (Figure 16). 

The shape of a diamond cluster is inherently 

connected to its stability, which in turn depends 

on the state of the surface atoms. Important factors 

that impact cluster stability include the presence 

of active groups on the surface of UDD 

particles after different types of purification treatments, 

hydrogenation of the surface, and possible 

surface reconstructions on a bare surface that eliminates 

(or at least reduces) the number of dangling 

bonds. As discussed in Section II based on ab 

285

FIGURE 42. TEM images of diamond clusters revealing different 

shapes: spherical (a) shapes of nanodiamond particles (After Ref. 

90, courtesy of G. Galli) and well-faceted diamond particles of 

micron and submicron sizes (b). (After Ref. 29.) 

initio simulations, bare diamond surfaces, containing 

(111) planes undergo ‘buckification’, 90,99–101 

that might be responsible for the observed spherical 

shapes of diamond particles. Particles containing 

(100) bare surfaces reconstructed in a 

manner similar to bulk diamond surfaces. 99–101 In 

addition, relaxation and geometrical parameters 

of hydrogenated nanodiamond surfaces were quite 

similar to those of bulk diamond. 99–101 Based on 

these facts, we performed simple evaluations of 

binding energies of hydrogenated clusters with 

different morphologies. 

Results of binding energies of fully hydrogenated 

spherical, cubo-octahedron and truncated in 

one direction octahedron clusters are plotted in 

Figure 43. Binding energies have been calculated 

relative to systems with the same number of carbon 

atoms in bulk diamond and hydrogen atoms 

as H 2 molecules. The results of DFT/LDA calculations 

by Kern and Hafner 186 on energetics of 

reconstructed (001)(2 × 1):H and (111)(1 × 1):H 

diamond surfaces were used for the calculations 

(summarized in Table 11). A dimer reconstruction 

of all (100) diamond surfaces has been assumed. 

The calculations suggest that a truncated octahedron 

cluster is more stable than a cubo-octahedron 

or a spherical cluster with the same number 

of atoms (Figure 43a). As apparent from the 

figure, the difference in binding energy between 

286

FIGURE 43. Binding energies of hydrogenated diamond clusters as a function of particle size. 

Binding energies calculated relative to systems with the same number of carbon atoms in bulk 

diamond and hydrogen atoms as H 2 molecules. LDA data 186 (Table 11) on energetics of (001) and 

(111) diamond surfaces are used for the calculations. 

287

spherical and cubo-octahedron clusters is small, 

on the order of ~0.01 to 0.02 eV/atom (for a 

comparison, the difference in cohesive energies 

of bulk diamond and graphite is about 0.02 eV/ 

atom). These results can be explained using simple 

arguments about the relative fractions of surface 

atoms with favorable and unfavorable energies 

for clusters with particular shapes. As follows 

from Table 11, one-, two-, and three-coordinated 

carbon atoms at a diamond surface have different 

energies. Thus, a larger number of atoms with 

unfavorable on-site energies (such as, for example, 

twofold coordinated atoms at a (001) facet) would 

result in lower cluster stability. Indeed, as illustrated 

in Figure 44, the fraction of two-coordinated 

atoms (accordingly dimerized and hydrogenated 

in a final structure) is larger for cubo-octahedron 

clusters, resulting in the greatest cluster stability 

compared with the spherical and octahedron structures. 

It should be noted that spherical clusters resemble 

truncated octahedrons (Figure 45a) with 

additional adatoms (for bigger clusters — atomic 

islands) at the center of their facets and are intermediate 

shapes between octahedron and cubo-octahedron 

regarding the number of surface atoms with 

nonfavorable energies. The fraction of atoms with 

three dangling bonds at the surface of a spherical 

cluster is relatively small (Figure 45a). An analysis 

of their location at a surface of a spherical cluster 

show that they do not have undercoordinated nearest 

neighbors with which to form a (2 × 1) surface 

reconstruction. Thus, singly coordinated atoms would 

be rather etched or terminated by three hydrogen 

atoms. In general, from the analysis above, it can be 

concluded that the most stable shape of a fully hydrogenated 

diamond cluster is that with the maximum 

number of ‘energetically favorable’ surface 

atoms, for example, hydrogenated atoms with three 

carbon atoms as neighbors. The octahedron or slightly 

truncated octahedron cluster are primary candidates 

satisfying this condition. 

Due to the very small difference in stability 

between different carbon structures, it can be also 

expected that excitation (for instance, by an electron 

microscope) may be sufficient to induce transitions 

in particle shape. This may be the primary 

reason that different shapes of diamond clusters 

such as spherical (Figure 42a) or faceted (Figure 

15) are observed. As discussed in Section II, electron 

beam irradiation can even induce phase transitions, 

such as carbon onions to nanodiamond 

structures and vice versa. Similarly, Ijima and 

Ichihasi 187 showed that at the nanoscale, the shape 

of metallic particles is not necessarily constant 

because the energy of a nanoparticle shows many 

local minimum energy configurations, corresponding 

to different structures. A gold particle ~2 nm 

in size that was exposed to strong electron beam 

irradiation with a beam intensity between 15 and 

80 amp/cm 2 fluctuated between the cubo-octahedral, 

icosahedral, and single-twinned structures. 187 

Although not quite realistic, energetic characteristics 

of all-carbon nonreconstructed diamond 

clusters were evaluated using a bond order potential, 

188 which indicated stable relaxed diamond 

structures contrary to the first principle simulations. 

The results of these calculations indicated 

that cohesion energy, surface excess energies, and 

stiffness of spherical diamond clusters with 

nanoscale dimensions deviate considerably from 

their macroscopic values. For clusters of 2.2 nm 

(1100 atoms) and 4.8 nm (10 4 atoms), the calculated 

cohesive energy, was about of 95% and 99% 

of the bulk value, respectively. From an analysis 

of the asymptotic value of surface energy it was 

concluded that the spherical surface possess primarily 

a (100) character. Regarding stiffness, it 

was found that for clusters 2.2 nm and 5.8 nm 

(2 × 10 4 atoms) in diameter the stiffness was about 

92% and 99% of the bulk value, respectively. 

A current conclusion is that hydrogenated alldiamond 

clusters are the most energetically preferable 

forms, especially octahedrons and partially 

truncated octahedrons. Starting with CH 4 , 

adamante (C 10 H 8 ), etc., all hydrogenated diamond 

clusters are mechanically stable. 

In contrast, if the (111) surface of a 

nanodiamond particle is not hydrogen terminated, 

the resulting structure would be an encapsulated 

fullerene at small particle sizes and ‘bucky diamond’ 

with a diamond core and fullerene-like 

outer shell 91,99–101 (Figure 45c). Buckification has 

been observed for spherical particles at least up to 

3 nm in diameter. 91 The authors 91 performed ab 

initio calculations using the GGA density functional 

for the smallest size clusters, and a 

semiempirical tight-binding Hamiltonian for systems 

up to 3 nm (2425 atoms) in diameter. Both 

288

FIGURE 44. Fractions of one-, two-, and three-coordinated surface atoms 

(relative to the total number of surface atoms) for cubo-octahedron (a), spherical 

(b), and truncated in one direction octahedron clusters (c) as a function of 

number of atoms in a cluster. 

289

FIGURE 45. Structural models of nanodiamond clusters. Spherical (a) or polyhedral (b) (cubo-octahedron) shapes 

with all four-coordinated carbon atoms can be preserved if the cluster surface is terminated by hydrogen. Twocoordinated 

atoms on the surface of a spherical cluster are dark colored (a). This illustrates that a spherical cluster 

represents truncated octahedron with several adatoms in the center of its (001) or (111) facets. Bare surface of 

nonhydrogenated diamond clusters experience surface reconstruction resulting in a cluster with a diamond core and 

a fullerene-like shell(c) (courtesy of Guilia Galli 90 ). 

methods gave similar structural models for the 

smallest cluster sizes, indicating validity of the 

results for structures of larger clusters obtained 

with the tight-binding method. According to Ref. 

91, starting from ideally terminated diamond particles, 

the reconstruction occurs spontaneously at 

low temperature. The barrier between the ideal 

surface structure and the reconstructed surface is 

size dependent and increases as the size of the 

cluster is increased, achieving a value of the order 

of several tens of eV for the largest clusters as 

found in bulk diamond. 189 It is interesting to define 

the critical size, when diamond clusters will 

have an all-diamond structure (probably with reconstructed 

(111) surfaces forming Pandey chains 

similar to bulk diamond surfaces). 

In support of their fullerene-like structural 

model, the authors provide an X-ray absorption 

spectra of nanodiamond agglomerates. 90 The preedge 

signal of the nanodiamond spectra differs 

significantly from those of diamond and graphite 

and exhibits a characteristic 2-peak feature resembling 

that of a buckyball and C 70 . These 

nanodiamond peaks had been interpreted as the 

signature of a mixture of pentagons and hexagons 

on the reconstructed surface of the diamond core. 

b. Simulations of Diamond Clusters: 

Electronic Properties 

Relationships between various electronic properties 

and cluster size were explored with a selfconsistent 

environment dependent tight-binding 

(SCEDTB) model with the C-H terms fit to first 

principles electronic structure results for ethane, 

290

methane, benzene, and hydrogenated and 

diamond surfaces. 191 Plotted in Figure 46 

is the density of states for four diamond clusters 

and for bulk diamond. The bulk density of states 

is shifted by the averaged Coulomb potential due 

to the surface dipole layer (cf. Figure 47) experienced 

by carbon atoms in the cluster. All four 

clusters demonstrate a size dependence of the 

band gap (Figure 48). Dimensional effects are 

most apparent with respect to the states in the 

valence band; the highest-occupied molecular 

orbitals for the 34 and 161 atom clusters lie approximately 

2.5 eV and 1.25 eV, respectively, 

below the bulk valence band edge. At the same 

time even for the smallest cluster the energy of 

the lowest-unoccupied molecular orbitals coincide 

with the bulk conduction band edge. This 

result can be intuitively expected because the states 

with higher energies and smaller wavelengths are 

less sensitive to the dimensions of the system. 

Dimensional band gap widening is less than 0.4 

eV for the largest cluster examined (913 carbon 

atom; ~2 nm diameter), which leads to the conclusion 

that any band gap size effect is insignificant 

for cluster sizes larger than about 2 to 2.5 

nm. Minor deviations from the bulk spectrum for 

the largest cluster are due mainly to the presence 

of hydrogen states and not to the finite dimensions 

of the cluster. This result apparently disagrees 

with indirect X-ray measurements, which 

indicate that in a 3.6-nm cluster the conduction 

band edge position is 1.2 eV above the conduction 

band edge for bulk diamond. 170 At the same 

time, however, the results are consistent with recent 

ab initio calculations 90 (Figure 48b). Depending 

on the simulation approach, the authors 

conclude, the band gap for diamond clusters approaches 

that for bulk diamond at cluster sizes of 

about 2 nm according to Quantum Monte Carlo 

calculations, and about 1 to 1.2 nm according to 

density functional calculations using the generalized 

gradient approximation. 90 According to the 

FIGURE 46. Electronic density of states for the four clusters with a truncated octahedron shape (histogram) and for 

bulk diamond (solid line). The histogram at the bottom of the pane (a) is a spectrum generated from density functional 

theory. (After Ref. 191.) 

291

FIGURE 47. Coulomb potential distributions for the nanodiamond clusters\plotted along the and 

directions passing through the centers of mass of the clusters. Octahedron clusters are truncated along the 

axis and contain 34 (a), 161 (b), 435 (c) and 915 carbon atoms (d), correspondingly. (After Ref. 172.) 

FIGURE 48. Band gap vs. cluster size for fully hydrogenated diamond clusters calculated with a SCTB model 190 (a), 

and DFT /GGA (generalized gradient approximation) and DFT/TDLDA (time dependent LDA) methods 90 (b). In 

Figure 48b the HOMO-LUMO gaps are indicated by triangles. The dashed line indicates the bulk (indirect) gap 

calculated with DFT/GGA. Open circles correspond to calculations with TDLDA. 90 The fact that for larger clusters 

the band gap is lower than that for the bulk structure is due to a stress effect induced by hydrogen on the surface. 90 

The bulk band gap calculated with the SCTB approach (a) is 5.5. eV. 

292

esults on X-ray adsorbtion and emission experiments, 

no appreciable changes in band gap is 

observed for nanodiamond clusters with sizes 

exceeding 2 nm. 90 

Illustrated by Figure 49 are electronic properties 

of carbon nanoclusters with highly distorted 

bonds (consisting completely of 5 to 7 rings) as 

well as clusters with sp 2 /sp 3 bonding. According 

to the figure, the band gap becomes filled with the 

presence of sp 2 bonding. 

Coulomb potential distributions for the clusters 

obtained with the self-consistent environment 

dependent tight binding calculations 191 are plotted 

in Figure 47. The main feature of the potential 

distribution is a sharp rise at the cluster surface 

produced by hydrogen termination. Cluster size 

effects are apparently only significant for the 

smallest cluster. For the larger clusters the calculations 

predict that the potential inside the cluster 

does not change appreciably with increasing cluster 

size. In conjunction with the spectra plots the 

potential rise at the boundary gives a -1.4 5 eV 

electron affinity of the hydrogenated surface. 

This value is close to the experimentally 

FIGURE 49. Density of states of two nanocarbon clusters with highly disordered 

sp3 bonds (a) as well as with mixed sp 2 /sp 3 bonding (b). Clusters contain 435 

carbon atoms. (After Ref. 190.) 

293

measured electron affinity, 192 while density functional 

theory usually overestimates experimental 

values by ~0.6 to 0.8 eV. 193 

One of the major focuses in nanoelectronic 

applications of nanodiamond is the possibility of 

n- and p-type doping of the clusters. Recent first 

principles calculations addressed the structural 

stability of nanodiamond clusters doped with B, 

N, and P in substitutional positions. 194,195 Small 

hydrogenated diamond clusters (a few tens of 

C atoms) containing B, N, or P atoms in the center 

maintained the diamond lattice during relaxation. 

For future research, it would be interesting to 

evaluate substitutional energies of different 

dopants in the subsurface positions vs. position in 

the inner parts of nanoparticles, as well as their 

diffusional properties. Another interesting issue 

would be the difference in dopant behavior in 

nanoclusters as compared to that in bulk diamond 

when well with diamond surfaces at the 

macroscale. 

A major conclusion of the studies of electronic 

properties of nanodiamond clusters is that 

quantum confinement effects disappear at cluster 

sizes larger than approximately 2 nm, in contract 

to silicon and germanium clusters where quantum 

confinement effects persist up to 6 to 7 nm clusters. 

90 A practical realization of the size dependence 

of quantum confinement effects in ND clusters 

is likely difficult because of the very small 

cluster size (below ~1000 atoms for 2 nm cluster). 

In addition, according to the size distribution function 

of the UDD particles, only a small fraction of 

the clusters is produced with a 2 nm diameter. 

c. Diamond Nanorods 

Would Diamond Nanorods be Stronger 

than Fullerene Nanotubes? 

Diamond was always considered the strongest 

material in the macroscopic world until the 

extreme mechanical properties of carbon 

nanotubes were discovered (Table 13). After that 

discovery, numerous papers claimed that carbon 

nanotubes were the strongest material. It is difficult 

to make a fair comparison between two representatives 

from the macro- and nano-worlds 

unless some assumptions related to particular structures 

are made. Below we compare the mechanical 

properties of these two materials at equal conditions, 

assuming that it is possible to make diamond 

nanorods, and briefly discuss the routes for synthesis 

of one-dimensional diamond. 

When extrapolating the mechanical properties 

of carbon nanotubes to the macroscale, an 

ambitious assumption has to be made regarding 

their wall thickness; it is usually assumed to be 

equal to the interplanar spacing of graphite. At the 

nanoscale, an unambiguious characteristic of 

strength would be maximum force before failure 

for a given structure, rather than maximum stress. 

At least, it would be a useful characteristic for 

comparison of fiber-like nanostructures from different 

materials with similar diameters. For this 

force–based definition of a nanostructure strength, 

Figure 50 illustrates the dependence of fracture 

load vs. diameter for single wall nanotubes and 

diamond nanorods for three orientations, corresponding 

to the low-index axis (,, 

). 196 The calculations for nanotubes were 

done using ideal strength values for graphene 

sheets from ab-initio pseudopotential total energy 

calculations within the local density approximation 

228 (values are summarized in Tables 12 and 

13). Similar strength values for different diamond 

orientations were obtained by the same authors 197 

and by similar techniques, 198 so all the input parameters 

for the evaluations are self-consistent. 

Fracture forces are evaluated for MWNTs with a 

variable outer diameter and a fixed inner diameter 

of 4 nm, which corresponds to typical experimental 

values. 39 

The results of Figure 50 demonstrate that at 

small diameters, carbon nanotubes are stronger than 

diamond rods because of the superior strength of 

the single bonds in graphene over those in diamond 

(Table 13). However, as the load-bearing area and, 

correspondingly, the number of bonding sites increases 

with diameter, the diamond rods become 

stronger than SWNTs. The corresponding critical 

diameters for the three orientations of diamond 

nanorods are summarized in Table 13. While the 

strength of SWNT increases linearly with diameter, 

the strength of nanorods grows as the square 

of diameter. Figure 50 also illustrates that the 

strength of a MWNT is comparable to that of a 

294

diamond rod oriented in the direction and 

exceeds those for and -oriented 

nanorods. Although the load-bearing properties of 

MWNTs are quite impressive, in practical applications, 

special precautions must be taken to exploit 

this property. Experiments by Yu et al. 249 have 

shown that when clamps of a particular kind are 

applied to the outermost shell of a tensile loaded 

MWNT, failure occurs only in the outermost shell. 

This result suggests little load transfer between the 

outer shell and inner shells, and therefore the inner 

shells do not contribute to the load bearing crosssectional 

area of the system. Because of the integrity 

of diamond rods, this problem is absent from 

the structures. It was also shown 196 that by no 

means do carbon nanotubes posses the highest 

strength-to-weight ratio. 

To futhur explore whether diamond nanorods 

represent an important and viable target structure 

for synthesis, molecular modeling has been used 

to explore structures and to characterize binding 

energies for several example diamond nanorod 

configurations illustrated in Figure 51a. 196 Plotted 

in Figure 51b are energies as a function of the 

hydrogen-to-carbon ratio for the four diamond 

nanorods illustrated in Figure 51a, calculated with 

the bond-order analytic potential. 218 Also plotted 

are energies for (17,0) nanotubes of finite length 

whose ends have been hydrogen terminated. The 

energies reported are relative to systems with the 

same number of carbon and hydrogen atoms in 

graphite and as H 2 molecules, respectively. For 

large carbon-to-hydrogen ratios, the diamond 

nanorods and the single-walled fullerenes are 

roughly comparable in binding energy, while for 

small ratios the sp 3 -bonded structures are energetically 

favored, in agreement with a previous 

analysis of carbon-hydrogen clusters (Section II). 

295

To explore the size dependence of the 

Young’s modulus of diamond nanorods, the 

second derivative of strain energy in the system 

was been calculated 196 as a function of strain 

for a nanorod of 1.4 nm in diameter (Table 13). 

This value is an unambiguious characteristic 

and can easily be converted to Young’s modulus 

(see Section III.B.2 below). While an average 

value of the second derivative of strain 

energy is similar to that of bulk diamond, the 

strain energy changed in a different manner for 

subsurface carbon atoms and those in the rod 

center. The ‘strengthening’ of the atoms in the 

rod center (Table 13) had been observed Ref. 

196. 

Atomistic simulations 196 indicate that diamond 

nanorods represent an important and viable target 

structure for synthesis. Given the number of methods 

that have been used to produce covalently 

bonded whiskers, the prospects for synthesizing 

diamond nanorods appears to be very promising. 

For example, impressive results have been 

achieved in the growth of β-SiC nanorods and 

whiskers with radii as small as 10 nm. Synthesis 

has been accomplished by a number of methods, 

including hot filament chemical vapor deposition, 

219 laser ablation, 220 reduction-carburization, 226 

and sol-gel reactions followed by carbothermal 

reduction of xerogels. 267 However, as described 

in Section III.A.1, aligned diamond whiskers have 

296

FIGURE 50. Fracture force as a function of diameter for different one-dimensional carbon 

structural components: diamond nanorods with different crystallographic orientations, SWNTs 

and MWNTs. The types of nanotubes correspond to those with a zigzag arrangement of 

atoms. In the case of MWNTs, the outer diameter is a variable and the inner diameter is 

assumed 4 nm for all MWNTs. (After Ref. 196.) 

FIGURE 51. Illustrations of representative diamond nanorods (a). Binding energies given by a bond-order potential 

as a function of hydrogen-to-carbon ratio (b). Energies were calculated using a dimer reconstruction for all surfaces 

with structures corresponding to the (100) diamond surface. Open triangles: diamond nanorods. Solid circles: (17,0) 

nanotubes of different lengths whose ends are hydrogen terminated. (After Ref. 196.) 

297

een formed so far only by a ‘top down’ approach 

using air plasma etching of polycrystalline diamond 

films, particularly of as-grown diamond 

films and films with molybdenum deposited as an 

etch-resistant mask. 33 In addition to the ‘top-down’ 

methods of diamond nanorod synthesis, direct 

conversion of carbon nanotubes to diamond 

nanorods might be also considered. It is known 

that carbon onions can be converted to structures 

containing nanodiamond cores under MeV e-beam 

irradiation 93 or ion beam irradiation. 123 So far, 

electron beam induced formation of amorphous 

carbon nanorods 10 to 20 nm in diameter from 

CVD-deposited carbon nanotubes has been realized 

in situ under HRSEM. 268 Similarly, it has 

been observed that carbon nanotubes can be transformed 

into amorphous carbon rods under irradiation 

with an Ar ion beam. 269 

Interestingly, diamond rods with diameters as 

small as 10 µm and several hundred micrometers 

long were fabricated by a variety of techniques 

back in the 1960s. 270–272 The monocrystalline rods 

were grown epitaxially on diamond seed crystals 

from a gaseous phase under low pressure conditions 

in the presence of a Ni, Fe, or Mn catalyst. 270 

Diamond whiskers were also grown in an electron 

microscope on the sharp edges of diamond or 

other dielectric crystals under electron beam irradiation 

from carbon-containing residual gases at 

low pressure. 271 Diamond whisker growth in a 

metal-carbon system at high pressures and temperatures 

conditions was also reported. 272 

B. Carbon Nanotubes 

1. Synthesis and Properties 

Synthesis and properties of nanotubes are 

topics comprehensively addressed in a variety of 

books. 39,199–203 Below we provide a brief summary 

of these topics. 

There are three most commonly used methods 

to produce carbon nanotubes: arc discharge, 

laser ablation, and chemical vapor deposition. 

There are also several nontraditional methods that 

have been developed (discussed, for example, in 

Ref. 39, 224). CVD methods have been used for 

at least 4 decades for the production of filamentous 

carbon; 203 this method is based on the decomposition 

of carbon-containing gases on metal 

catalysts at reaction temperatures below 1000 o C. 

Arc discharge and laser ablation methods are based 

on the condensation of carbon atoms generated 

from the evaporation of solid carbon sources. The 

evaporation temperature involved in these processes 

is close to the melting temperature of graphite, 

3000 to 4000 o C. The multiwall nanotubes 

reported by Iijima 13 in 1991 were produced by an 

arc-discharge method. Before the discovery of 

nanotubes, both arc discharge and laser ablation 

techniques had been used to produce fullerenes, 

but the optimal conditions to produce fullerenes 

is different that the optimal conditions required to 

produce nanotubes. In 1985 Smalley and colleagues 

12 reported that they had produced 

fullerenes by a laser vaporization method. The 

chronology of the major events in the synthesis of 

nanotubes and fullerenes is summarized in Table 

14. 

In an arc-discharge, carbon atoms are evaporated 

by a helium plasma generated by high a 

current between the anode and cathode. This 

method can produce both high-quality MWNTs 

and SWNTs (Figure 52). Growth of MWNTs by 

this method does not require, in principle, a catalyst. 

39,204 MWNTs can be obtained by controlling 

the growth conditions such as the pressure of the 

inert gas (optimal for MWNT ~500 Torr, for C 60 – 

below 100Torr 39 ) and the arc current. The synthesized 

MWNTs typically have a length on the 

order of 10 µm and diameters in the range of 5 to 

10 nm. They typically form tight bundles, but 

nanotubes themselves are very straight. The purification 

of MWNTs can be achieved by heating 

as-grown material in an oxygen environment. 

While a standard arc-evaporation method produces 

only multilayered nanotubes, the addition 

of metals such as cobalt to the graphite electrodes 

results in extremely fine nanotubes with singlelayer 

walls. 47,48 The optimization of SWNT growth 

was achieved using a carbon anode containing 

yttrium and nickel as a catalyst. 204 

An alternative method of growth of highquality 

SWNTs in large quantities was suggested 

in 1996. 49 Like the original method of preparing 

C 60 , this involved the laser vaporization of a graphite 

target containing a small amount of catalyst 

298

and resulted in a high yield of single-walled 

nanotubes with unusually uniform diameters. 

These highly uniform nanotubes had a greater 

tendency to form aligned ropes than those prepared 

using arc evaporation. The ropes consist of 

tens of individual nanotubes close-packed into 

hexagonal crystals. The initial experiments indicated 

that the rope samples contained a very high 

proportion of nanotubes with a specific armchair 

structure, but later other types of SWNT were 

grown. SWNTs grown both by laser ablation and 

arc discharge typically contain by products of 

fullerenes, graphitic polyhedrons with encapsulated 

metal particles, and amorphous carbon particles 

or overcoatings on SWNT walls. A widely 

used purification method developed by Smalley 

and co-workers 207 involves refluxing the as-grown 

SWNTs in a nitric acid solution for an extended 

period of time. 

The CVD growth process involves heating a 

catalyst material to high temperatures in a furnace 

and flowing a hydrocarbon gas through the 

reactor (Figure 52). The key parameters of the 

CVD nanotube growth are the hydrocarbons, 

catalysts, and growth temperature. The catalyst 

species are typically transition-metal 

nanoparticles formed on a support substrate such 

as alumina. For MWNT growth, mostly ethylene 

or acetylene is used as a hydrocarbon feedstock, 

and the growth temperature is typically in the 

range of 550 to 750 o C. 204 There are the same 

typical catalytic metals (iron, cobalt, nickel) for 

the CVD process, as for laser ablation and arc 

discharge methods. The drawback of the CVD 

growth of MWNT is the high defect density, a 

problem that still needs to be addressed. 204 Recent 

progress in the fabrication of MWNT using 

the catalytic CVD method shows that narrow 

diameter double and triple walled nanotubes can 

be grown with high yield. 210 Growth of bulk 

amounts of SWNTs with a high degree of structural 

perfection was enabled by a CVD method 204 

using an appropriate catalyst, a temperature range 

of 800 to 1000 o C, and preferably methane as the 

carbon feedstock. Optimization of the catalyst to 

grow highly aligned SWNTs nanotubes is described 

in Ref. 204. The maximum length of 

individual SWNTs grown by this method is 150 

micrometers. 204 The SWNT produced can be 

separated from the support material by acidic 

treatment. The high interest in CVD nanotube 

growth is also due to the fact that aligned and 

299

FIGURE 52. Schematic representation of the experimental setup for the three most common 

methods of nanotube growth (adapted from Ref. 204). Type of nanotube grown (MWNT or 

SWNT), necessity to use a catalyst, as well as the possibility to grow fullerenes by the same 

method are also specified. Available data on nanotube yield are also provided. 

ordered nanotube structures can be grown on 

specific growth sites of prepatterned substrates 

with control that is not possible with the arc 

discharge or laser ablation techniques. 204 Thus, 

using the CVD method in combination with 

microfabrication techniques, individual SWNT 

can be integrated into nanotube-based electronic 

and chemical-mechanical devices that are functional 

on the molecular scale. The relatively low 

temperatures of the process and the ability to 

pattern the catalyst material directly on device 

substrates make catalytic CVD the method of 

choice for nanotube device development. 

To illustrate how the diameter of the nanotubes 

depends on the method of growth and specific 

growth conditions, we refer the reader to Table 15 

(adapted from Ref. 205). On the basis of the 

analysis of experimental data in the literature, 

summarized in Table 15, the authors 205 concluded 

that the majority of the catalytic mechanisms underlying 

the formation of various nanocarbon 

deposits on catalytic substrates include some com- 

300

mon steps. A thermodynamic analysis of carbon 

nucleation on the metal surface demonstrates that 

a variation of the reaction parameters, such as the 

temperature and the nature of the metal catalyst 

and promoters, can lead to the formation of different 

carbon deposits, such as filamentous carbon, 

multiwall nanotubes, or single-wall nanotubes. 

As an opposite extreme to the challenge of 

growth of an individual nanotube at a predetermined 

site, the synthesis of large uniform and 

ordered micro- and eventually macrostructures of 

SWNTs has been pursued rigorously. Recently, 

the self-assembly of single crystals of SWNTs 

using thermolysis of nanopatterned precursors has 

been reported. 51 Micrometer-sized crystals of 

SWNTs were composed of arrays of thousands of 

SWNTs with identical diameters and chirality. 

The precursor material for SWNT growth consisted 

of a heterostructure composed of alternate 

layers of buckyballs and thermally evaporated 

nickel that resulted in very small nucleation sites 

and subsequent self-assembly of the SWNT crystals. 

Even more recently, 32 long nanotube strands, 

up to several centimeters in length, consisting of 

aligned SWNT were synthesized by the catalytic 

pyrolysis of n-hexane with an enhanced vertical 

floating technique. The long strands of nanotubes 

were assembled from arrays of nanotubes, which 

were intrinsically long. 

The industrial capacity for the production of 

carbon nanotubes is steadily increasing. Information 

on leading commercial suppliers of carbon 

301

nanofibers and nanotubes is provided in Ref. 224. 

As a particular example of services provided by 

one of the current SWNT suppliers, we refer the 

reader to Carbon Nanotechnologies, Inc, (CNI) 

Texas. In addition to the production of SWNTs 

(in the CNI case, by laser ablation method), the 

list of services provided by the vendors includes 

derivatization of end-of-tube and the sidewall of 

nanotubes, which is important for modifying physical 

properties, cross-linking, and enhancing solubility 

and dispersion; enabling technology for enduse 

applications such as cutting, alignment, 

dispersion, solubilization, and wrapping with polymer 

surfactants. 

In general, major challenges in nanotube 

growth remain the ability to gain control over the 

nanotube chirality and diameter, and the ability to 

directly grow semiconducting or metallic 

nanotubes from and to any desired sites. 204 

There is a long list of unique properties of 

nanotubes that make them one of the most important 

structural and functional materials for 

nanotechnological applications. One of the striking 

features of nanotubes is their combination of 

widely variable electronic properties and extreme 

mechanical properties. These are discussed in detail 

in a later section. Depending on their precise 

structure, nanotubes can be either metallic conductors 

or semiconductors. The semiconducting 

nanotubes are of two types: one has a band gap of 

a few hundredths of an electron volt, while others 

have about a 1-eV band gap depending on the 

radius. Ropes have been measured with a resistivity 

of 10 –4 ohm-cm at 300 K, 49 making them the 

most conductive fibers known. Individual 

nanotubes have been observed to conduct electrons 

ballistically, for example, without scattering, 

with coherence lengths of several microns. 211 

In addition, they can carry the highest current 

density of any known material, measured 212 as 

high as 10 9 A/cm 2 . Quantum conductance of 

SWNTs has been reported 213 as well as their intrinsic 

superconductivity. 214 Selected properties 

of SWNTs are summarized in Table 16. 

2. Mechanical Properties of Carbon 

Nanotubes 

The mechanics of carbon nanotubes is a topic 

of very intensive research as confirmed by the 

number of excellent reviews published within the 

302

last year. 221–225 The focus of much of the research 

has been on properties of individual NTs, such as 

their Young’s modulus, bending stiffness, buckling 

criteria, tensile and compressive strength. 

Advanced mechanical properties of nanotubes are 

important in projected applications such as 

nanoelectromechanical systems, nanosensors, 

nanocircuits, drug delivery devices, and reinforcing 

structures in nanocomposites. 223–225 Recently, 

a super-hard bulk material consisting solely of 

nanotubes has been created, suggesting that macroscopic 

structures consisting exclusively of 

nanotubes might be possible. 51 

Below we summarize experimental and theoretical 

data reported to date on two important mechanical 

characteristics of nanotubes, their Young’s 

modulus, and tensile strength. There is a surprisingly 

wide variation within the measured and predicted 

values of these properties. For example, there 

is fivefold variation in measured properties of 

SWNTs and a 40-fold variation in the predicted 

fracture strengths of SWNT. 227,228 To a large extent, 

this discrepancy can be attributed to the fact that 

definitions characterizing macroscopic material behavior 

under load should be used with caution in 

describing nanometer-scale objects. To address this 

important issue, the area of nanomechanics is emerging 

as a new discipline that describes the behavior of 

materials and structures at the nanoscale. 221–223 New 

mechanical characteristics that are different from 

those used in conventional continuum mechanics 

will likely be defined to describe the deformation 

behavior of nanostructures in the near future. Depending 

on the demands of applications taking place 

solely at the nanoscale (in contrast to macroscopic 

applications in composites, for instance), mechanical 

characteristics might be introduced along with 

materials characteristics that depend on a specimen’s 

geometry. This issue has been partially addressed in 

the Section III.A.3.c on the comparison of the fracture 

strengths of carbon nanotubes and hypothetical 

diamond nanorods and is briefly touched on in the 

discussion of the fracture strengths of nanotubes. 

a. Young Modulus of Nanotubes 

The definition of Young’s modulus relies on 

the continuum hypothesis that assumes spatial 

uniformity of a material and is defined as a material 

property (a characteristic intrinsic to the 

material independent on specimen geometry). As 

the specimen size diminishes, the discrete structure 

of the material can no longer be homogenized 

into a continuum. As has been pointed out 

by Yakobson et al., 221 if one considers graphene 

as a two-dimensional material, a MWNT should 

be considered as an engineered structure composed 

of rolled graphene sheets rather than a 

material. However, the definition of material-like 

characteristics, such as Young’s modulus, nevertheless 

has been applied to nanotubes when considering 

their application as an engineering material. 

Below we consider in more detail the 

discrepancy between Young’s modulus calculated 

by two means, both of which originate in continuum 

mechanics, that do not contradict one 

another if applied to macroscale materials, but 

give a fivefold difference in predicted Young’s 

modulus of nanotubes. This result has been pointed 

out by Yakobson et al. by applying a shell model 

to carbon nanotubes 235 that served an otherwise 

very useful role in predicting of buckling behavior 

of nanotubes. This is probably the most striking 

inconsistency in the application of continuum 

mechanics approaches to the nanoscale. 

Yakobson’s Paradox 

Calculating a Young’s modulus is straightforward 

if the potential energy functions describing 

interatomic interactions are known. The calculations 

involve the second derivative of the 

strain energy with respect to the applied strain: 

Y 

b = 

⎛ 

2 

1 ∂ E⎞ 

V 

⎜ 2 ⎟ 

⎝ ∂ε 

⎠ 

ε = 0 

(8) 

where V=Sh is the volume of the object, h in the 

object’s thickness, and S is the surface area of the 

nanotube at zero strain. The value of ∂ 2 E/∂ε 2 is a 

unique characteristic independent of the structure 

or material under consideration. The average value 

for nanotubes obtained from recent first principle 

simulations is 56 eV/atom and that of graphite is 

57.3 eV/atom (Table 17). 229 For simulations using 

303

many-body interatomic potentials, the value of 

∂ 2 E/∂ε 2 is comparable. 221 Assuming h=0.34 nm 

(the interplanar distance in graphite), the calculated 

Young’s modulus of nanotubes with Eq. 6 

using first principles data 229 are slightly lower 

than that of graphite (1030 GPa). This value is 

comparable to the lowest reported experimental 

values of SWNT extracted from data on thermal 

oscillations and bending tests, which are about 

1.2 to 1.3 TPa, 233,234 where the same assumption 

on the tube thickness had also been made in the 

corresponding expressions for the thermal vibrations 

amplitude and for the nanotube deflection 

under bending used to extract the Young’s modulus. 

The contradiction with the values reported 

above appears when the Young’s modulus of 

SWNT and wall thickness are estimated from the 

in-plane stiffness and flexural rigidity calculated 

in the shell model, 235 where a SWNT is approximated 

by a continuum isotropic shell. The deformation 

energy of a nanotube is a function of inplane 

strain ε and the changes of curvature k in the 

axial and circumferential directions of a shell. 

Using the shell model, a wide variety of shell 

buckling behavior, particularly critical strains or 

curvatures vs. applied load such as compression, 

bending, torsion can be predicted. Molecular dynamics 

simulations of transformations of shapes 

of SWNTs subject to large nonlinear deformations 

demonstrated remarkable agreement with 

tube buckling behavior predicted from the shell 

model. 235 The only material parameters required 

in the shell model are in-plane stiffness C, 

Poisson’s ratio ν, and the flexural rigidity D that 

can be obtained from first principle simulations. 

The simulation of the axial tension of a nanotube 

provides values for Poisson’s ratio ν and the inplane 

stiffness C 

⎛ 

2 

1 ∂ E⎞ 

C = S 

⎜ 2 ⎟ 

⎝ ∂ε 

⎠ 

ε = 0 

(9a) 

The flexural rigidity, the dependence of the strain 

energy on its curvature, D can be calculated from 

304

a comparison of strain energy U of tubes of different 

diameters d: 

D= 

Ud 

2 

/ 2 

(9b) 

Recent first principles-based estimations 229 provide 

D=3.9 eVÅ 2 /atom and show no dependency 

on tube chirality. The in-plain stiffness for different 

types of nanotubes are given in Table 17. 

As we can see so far, the nanotube thickness is 

not involved in the estimations of C and D in the 

shell model. On the other hand, a continuum 

shell can be assigned the modulus Y sh and the 

thickness h unambiguously, to formally match 

the ν, C and D: 

C= Yshh, (10a) 

3 

Yshh 

D = 

2 

12( 1−ν 

) 

(10b) 

Using the first principles parameters reported 

above for C and D and a first principle’s Poisson 

ratio ν=0.15, 229 the shell Young modulus would 

be 3.86 TPa (~5 TPa with an analytic potential for 

describing interatomic interactions) and with a 

shell thickness h=0.9 Å. These values differ significantly 

from those reported above. Based on 

this discussion, these questions remain until we 

can apply a material definition to an atomically 

thick structure, as well as on limitation of the 

applicability of Eq. 10 to nanostructures. 

The in-plane stiffness C is an unambiguous 

parameter, and considering only axial tension, 

according to Eq. 8a and h can take any values 

satisfying . If we assume h=0.34 nm, the resulting 

Young’s modulus of a SWNT will be of the order 

of ~1 TPa using the first principles in-plane stiffness 

value. 229 It should be noted that for nanotubes 

with diameters less than 0.68 nm (doubled 

interplanar space in graphite), using h=0.34 nm 

makes no sense, although in many articles this 

value is used for estimations of Y for nanotubes 

of any diameter. Nanotubes with small radii in 

principle should be considered as rods with corresponding 

cross-sectional areas. 230 

For SWNT ropes, which are a three-dimensional 

material and therefore the classic definition 

of Y is valid, the Young’s modulus would unambiguously 

be recovered as: 

2 

ρb 

∂ E 

Y = 

2 

(11) 

m ∂ε 

where ρ b is the bulk density and m is the mass of 

the atom. First principles Y values for SWNT 

ropes are of the order of ~1 TPa (Table 18). 

Thus, there is an interesting situation in the 

application of the continuum shell model to tubular 

nanostructures. On the one hand, the description 

of nanotube characteristics within the shell 

model is intrinsically self-consistent and is very 

useful for predicting tube buckling behavior. On 

the other hand, there is remarkable discrepancy 

between the Young’s modulus of SWNT recovered 

from the shell model and that corresponding 

to SWNT ropes or graphite. To avoid this problem, 

Ru 236 proposed an intrinsic bending stiffness 

for carbon NTs in order to decouple the bending 

shell stiffness of NTs from their ill-defined effective 

thickness and to ensure a consistent use of the 

classic shell theory (i.e, shell thickness — only 

for shell theory). 

At present, theoretical issues on the Young’s 

modulus of nanotubes can be summarized as following. 

221,229,236 

1. The elastic properties of a cage graphite 

structure can be characterized unambiguously 

only by its in-plane and flexural rigidity 

parameters (Eq. 9), both of which can be 

calculated from first principles. 

2. Using these rigidity parameters (and Poisson 

ratio), SWNT buckling behavior can be 

predicted very well from the macroscopic 

shell model, as confirmed by atomistic simulations. 

3. Using rigidity parameters, the shell Young’s 

modulus and shell thickness can be defined 

unambiguously (Eq. 10). Currently, the fact 

is that these characteristic are inconsistent 

with Young’s modulus and thickness of 3-D 

materials such as SWNT ropes and MWNTs 

and therefore are attributed only to the shell 

model for understanding its high resilience. 236 

4. If cage structures are distributed statistically 

uniformly over a large cross-sectional area 

305

306

(as SWNT ropes or MWNT with relatively 

big radius), the bulk Young’s modulus can 

be recovered unambiguously (Eq. 4). 

5. An appropriate estimation of the bulk 

Young’s modulus of a SWNT cannot be 

made using Equations 9 and 8a due to the 

uncertainty of nanotube bulk density or an 

arbitrary geometrical thickness, respectively. 

Nevertheless, by convention, h=0.34 nm is 

usually presumed so that calculated results 

on in-plane rigidity of SWNTs are reported 

in terms of Young’s modulus. 

6. Experiments addressing the Young’s modulus 

of SWNT (Table 18) use analytical expressions 

relating measured values and 

Young’s modulus. An assumption on SWNT 

wall thickness is also required in these estimations, 

and it is assumed to be 0.34 nm. 

Within the above summary, questions still 

exist such as, for example, when can a MWNT be 

considered a ‘bulk’ material so that the Eq. 4 can 

be applied. For example, Govindjee and 

Sackman 237 considered an elastic multisheet model 

to show the explicit dependence of material properties 

on the system size when a continuum crosssection 

assumption is made for a multishell system 

subjected to bending. The continuum 

assumption is shown to hold when more than 201 

shells are present in the macromechanical system 

considered. 

There is an additional consideration in the 

nanomechanics of SWNT related to the possible 

changing of the nature of bonding when π− and 

σ- bonds experience a different influence of deformation 

during, for example, a bending test, so 

that when, for example, a nanotube is bent, its 

effective tension-related properties are different 

from those in a pure tension test. 

Probably useful atomistic simulations can be 

done with sheets of diamond of different thickness. 

Unlike nanotubes, the thickness can be continuously 

increased and tendencies in in-plane 

stiffness and flexural rigidity can be analyzed. 

A different approach for analyzing the linear 

elastic modulus of a SWNT is described in, 239 

where nanoscale continuum theory is established 

to directly incorporate interatomic potentials into 

a continuum analysis without any parameter fitting. 

The theory links interatomic potentials and 

atomic structure of a material to a constitutive 

model on the continuum level. Reported Young’s 

moduli are within the range 500 to 700 GPa, 

depending on the type of the interatomic potential 

used in the calculations. These values are somewhat 

lower than those obtained from first principles 

or pure atomistic simulations with analytic 

potentials. 

Experimental and Theoretical Young’s 

Modulus for CNTs 

Currently, measured Young’s moduli of CNTs 

are typically of the order of 1.0 to 1.3 TPa (Table 

18), and those predicted from first-principle simulations 

are of the order of 1 TPa (Table 19). 

However, the maximum observed and predicted 

values are up to 5 Tpa, which is probably an 

artifact in the experimental measurements and the 

Young’s modulus for the shell model in the theoretical 

analysis as discussed above. 

A number of experimental methods have been 

used to date to deduce Y (Table 18). These methods 

include transmission electron microscopy 

(TEM) observations of thermally excited vibrations, 

240 thermal stresses monitored by micro- 

Raman spectroscopy, 241 atomic force microscopy 

(AFM)-based measurements of lateral deflection 

of CNTs, 242 and a direct pulling technique by 

applying an axial force to a long NT rope 23,24 or to 

a single MWNT 25 (Figure 53). 

According to Table 18, the TEM-based methods 

suffer from relatively large margins of error 

margin of the order of 100%. For AFM-based 

techniques, the error margin can be of the order of 

50%. Significant errors mostly arise from difficulties 

in anchoring the ends of the nanotube. 246 

In addition, to extract a Young’s modulus most 

experimental techniques make some assumptions 

regarding the mechanical behavior of the system 

and assume that continuum elasticity theory is 

valid so that well-established expressions from 

elasticity theory for loaded tubes can be used at 

the nanoscale. However, the resulting values can 

be very sensitive to geometrical assumptions. For 

example, measured values of Y of Mo-based nanowhiskers 

varied by about a factor of two depending 

on the assumed geometry of the cross-sec- 

307

308

FIGURE 53. Illustration of a multiwall carbon nanotube (~11 nm diameter) prior to 

tensile testing (a). Arrows indicate direction of loading (white is the actual pulling 

direction); (b) fracture surfaces of both ends of the tube after breakage. (Reprinted from 

Ref. 245, with permission from Elsevier Science.) 

tional area of the nanocrystal. 246 An excellent review 

of instrumentation for measuring Young’s 

moduli is provided in Ref. 223. 

In contrast to the experimental results, there 

are no appreciable differences between the 

Young’s modulus for nanotubes and for a single 

graphene sheet predicted from first principles 

simulations (Table 19). Also, the results from 

Table 19 indicate that the effect of curvature and 

chirality on the elastic properties of NTs is small. 

More detailed analysis of variations in the strength 

of C-C bonding as the graphene sheet is rolled 

into a tube had been performed in Ref. 227. Based 

on a first principles cluster method, the authors 

adopted the Mulliken population analysis to estimate 

the overlap integrals between carbon atoms 

that measure the strength of the covalent bond. 

According to these results, the binding energy, 

elastic modulus, and tensile strength of carbon 

nanotubes must be less than that of graphite. Indeed, 

results of first principles calculations 232 and 229 

indicate an increase in the in-plane rigidity of 

nanotubes (approaching that of graphene) with 

increasing radius (Table 17). The Poisson’s ratio 

also retains graphitic values except for a possible 

slight reduction for small radii. It shows, however, 

chirality dependence (Tables 17 and 19). 

Limitations of Continuum Mechanics at 

the Nanoscale 

Atomistic simulations of buckling of selected 

nanotubes 235 demonstrated that bifurcation-buckling 

equations from shell theory can be applied, in 

principle, at the nanoscale. However, the deformation 

behavior of every nanotube cannot be satisfactorily 

described using a shell model. A comprehensive 

analysis of the limitations on the 

applicability of continuum shell models to the 

entire class of nanotubes has been performed by 

Harik. 230,248 

A scaling analysis has been used to identify 

the key nondimensional geometrical parameters 

that control the buckling behavior of NTs. Based 

309

on the relationship between buckling behavior 

and NT structure, four broad classes of CNTs had 

been identified (Figure 54a): thin and thick shells, 

high aspect ratio (long) NTs, and NT beams. A 

representative applicability map according to the 

NT classes had been also constructed (Figure 54b). 

The descriptive name of each class indicates the 

structural properties of NTs as well as the potential 

continuum models that can be used to predict 

their global mechanical behavior. Thus, NT shells 

behave either as thin shells or thick shells (hollow 

cylinders) depending on the thickness-to-radius 

ratio. The long NTs (class II) have structural behavior 

similar to the behavior of columns. The 

NT beams (class III) deform like macroscopic 

beams. 

The results of the analysis have important 

practical applications. For NTs with the same 

FIGURE 54. Schematic representation of four classes of nanotube geometries (a) used in the applicability 

map for the continuum beam model (b). Ranges of values for non-dimensional geometric parameters 

of nanotubes define NT classes and indicate the limits in the applicability of the thin-shell model 

for NTs. Parameters L NT , R NT , and a 1 represent the three length scales involved in the nano-mechanical 

problem. a 1 is the width of the hexagonal carbon rings, which is about 0.24 nm. L NT, R NT, d NT are nanotube 

length, radius and diameter, respectively. (Reprinted from Ref. 230 with permission from V. Harik.) 

310

values of the nondimensional parameters, they 

must have identical critical strain and buckling 

modes, even if the individual structural features 

are different. This can help to reduce the number 

of MD simulations needed to describe a whole 

class of NTs. In experimental studies, specific 

equivalent-continuum models should be used for 

a system under investigation according to the 

applicability map for data reduction or NT probe 

design. 

b. Nanotube Tensile Strength 

CNT tensile strengths predicted using first 

principles calculations and obtained experimentally 

are summarized in Tables 19 and 20, respectively. 

Measurements were done on individual 

MWNTs and SWNT ropes. Yu et al. obtained the 

tensile strength of individual MWNTs by scanning 

electron microscopy. 249 The MWNTs broke 

in the outermost layer, and the tensile strength of 

the MWNT layer ranged from 11 to 63 GPa. 

Analysis of the stress-strain curves for the individual 

MWNTs indicated that the corresponding 

Young’s modulus of the outer layers varied from 

270 to 950 GPa. More recently, the first observation 

of the actual breaking of a MWNT in tension 

in TEM has been reported 245 (Figure 53). Figure 

53b reveals that the nanotube has apparently 

‘healed’ itself after failure by forming a closed 

311

end-cap. Based on the observation of the force 

required to break the nanotube a tensile strength 

of 150 GPa (experimental uncertainties ~30%) 

was estimated. The corresponding deformation 

was ~5%. This is the highest reported fracture 

strength of any material and is relatively close to 

the ideal fracture strength of graphene. From corresponding 

bending studies on such nanotubes, 

the Young’s modulus was estimated to be 0.9 TPa 

(±20%). Ab initio estimations of ideal fracture 

strengths along the directions corresponding to 

the zigzag and armchair atoms arrangements at 

the edge are 209 GPa and 226 GPa, respectively. 228 

This ideal tensile strength had been obtained for 

an ideal situation where there is no symmetry 

breaking (no defects, no stress inhomoginities 

due to temperature, for example), and hence it 

establishes an upper limit on the strength. In similar 

simulation conditions, ideal fracture strengths 

for diamond range from ~95 GPa in the 

direction 198,228 to 225 GPa in the direction. 

198 It would be valuable to study the failure of 

deformed graphene in conditions of small perturbations 

using the first principles approaches. 

The only reported first principles-based estimation 

of a (6,6) nanotube tensile strength in 

elongated nanotubes is surprisingly very low (~6 

GPa). 227 1 ⎛ ∂Etot 

⎞ 

It was calculated as σ TH = ⎜ ⎟ , 

s ⎝ ∂ε 

⎠ 

ε= 

ε 

where s is the surface area of cross-section, and 

εCR is maximum strain in the system (~0.4). The 

corresponding Young’s modulus is also lower 

(0.76 TPa) than those reported in other studies 

(Table 19). Thus alternative first principles calculations 

are required. Recently, the ductile behavior 

of carbon nanotubes was investigated by largescale 

quantum calculations. 256 While the formation 

energy of strain-induced topological defects determines 

the thermodynamic limits of the elastic 

response and of the mechanical resistance to applied 

tension, it was found that the activation 

barriers for the formation of such defects are much 

larger than estimated previously. Unfortunately, 

ultimate tensile stress values had not been evaluated 

in Ref. 256. A comprehensive analysis of 

nanotube ductile behavior is provided in the review, 

221 but recent results 256 should be taken in 

the account. 

CR 

Molecular dynamics simulations of nanotubes 

under tension had been performed using a bond 

order analytic potential in Ref. 261 However, 

while using the bond order potential for estimating 

elastic properties for moderate deformation 

(up to 15%) is reasonable, the bond-order potential 

used in the simulations 261 is not appropriate 

for simulating system behavior at deformations 

above approximately 15% due to acut-off via a 

switching function of the interatomic potential. 

When bond lengths exceed 1.7 Å (the beginning 

of the cut-off range), a steep nonphysical increase 

in the interatomic forces results in very high values 

of ultimate tensile strength. When developing 

an interatomic potential suitable for fracture simulations, 

it is important that any cut-off function be 

used at distances beyond the inflection point in 

the potential function. The inflection point relates 

to the peak interatomic force and therefore influences 

fracture stresses in a system. In our previous 

work on diamond cleavage, we avoided this 

problem by shifting the cut-off function beyond 

the inflection point and keeping a list of nearest 

neighbors during the run. 42 Recently, 43 a modified 

Morse function was developed to specifically 

address fracture of CNTs by adjusting the position 

of the inflection point to provide an ultimate 

fracture strain of nanotubes that reproduces the 

value obtained from the Yu et al. experiment 

(~10%). 249 The corresponding fracture stress under 

conditions of symmetry breaking (temperature, 

presence of vacancies) was estimated to be 

~90 GPa. However, a reliable value can probably 

only be obtained with quantum mechanics–based 

dynamic simulations. 

Interesting results on the tensile strengths of 

SWNTs under hydrostatic pressure have been 

reported in Ref. 44. Simulations used the bondorder 

potential with DFT simulations of selected 

configurations. Hydrostatic pressure on the 

nanotube walls was simulated by encapsulating 

hydrogen molecules to capped nanotubes. The 

reported failure strength under hydrostatic pressure 

was 63 GPa for a (5,5) nanotube, and that for 

a nanotube containing twinned 7-5-5-7 pairs was 

only 3 GPa lower. 

Finally, regarding the practical aspects of 

nanotube strength, the first kinetic approach to 

CNT real-time strength has been discussed in 

312

Ref. 45 predicting the yield strain range. It was 

found that the value depends on the NT chirality, 

in a way very different from the thermodynamic 

assessments. 

Estimating a three-dimensional ideal strength 

for nanotubes suffers from the same problem of 

uncertainty in defining the cross-sectional area of 

a nanotube as in the estimation of Young’s modulus. 

According to Roundy, 266 depending on the 

application a more useful metric might be force 

divided by the mass per unit length (i.e., the stress 

divided by mass density) (Figure 55). This would 

assume a strength-to-weight ratio characteristic 

of the structural material and can provide a single 

nanotube with an ideal strength that would be 

independent of the spatial arrangement of the tubes 

(e.g., MWNT vs. NT ropes). It would also be 

convenient to perform a comparison of the characteristic 

for nano-specimens from different materials. 

For example, the ratio between the strengthto-weight 

characteristic for graphite and diamond 

(using data from Tables 12 and 21) would be 1.56 

and 3.7 for and diamond orientations, 

correspondingly. The higher the value, the 

more weak/heavy is the nano-specimen. 

3. Assemblies of Carbon Nanotubes and 

Nanodiamond 

Certain types of nanocarbons such as 

fullerenes, nanotubes, and diamond clusters can 

serve as basic building blocks for constructing 

more complicated structures that might exhibit 

new properties and find novel applications. In this 

section the feasibility of assembling carbon 

nanotubes and nanodiamond clusters is discussed. 

There is a geometrical similarity between the 

{111} planes of diamond and individual graphene 

sheets in which pairs of diamond planes resemble 

“puckered” graphite. This relationship, together 

with the lengthening of carbon-carbon bonds from 

1.42 Å in graphite to 1.54 Å in diamond, results 

in the near epitaxial relations 

FIGURE 55. Illustration as a convenient strength characteristic of a nanostructure can be defined. It 

would be the maximum force before failure divided by the mass per unit length. This definition does 

not involve the problematic definition of cross-sectional area and is independent of the dimensionality 

of the nanostructure. 

313

Graphite (0001) || diamond (111) 

Graphite [ 1120 ] || diamond [ 11 0] 

between graphite and diamond planes. These relations 

have been utilized in several models for 

understanding important structures and processes 

in carbon materials, including diamond nucleation 

on graphite 275 and graphitization of diamond 

surfaces and clusters. 82,189,276,277 There are also similar 

but less obvious relations between fullerene 

nanotubes and diamond that lead to a number of 

mechanically and chemically stable structures with 

potential structural materials and nanoelectronic 

device applications. 

Several recent experiments have provided 

compelling evidence for stable hybrid carbon 

nanotube-diamond structures. In experiments by 

Kuznetsov et al., 82,277 the formation of nanometric 

closed curved graphitic structures with tubular or 

conical forms attached to the surface of a diamond 

particle were observed in HRTEM images 

of diamond particles after high-temperature annealing. 

The TEM images show concentric graphitic 

shells corresponding to the top view of 

nested carbon nanotubes (Figure 56a) as well as a 

side view of nanotubes on the edges of particles 

(Figure 56b). The authors suggest that multilayered 

graphitic caps that form during the initial 

annealing of micron-sized diamond particles at 

1800 to 2000 K transform into closed carbon 

nanotubes attached to the diamond surface via 

reconstruction of the edges of diamond (111) 

planes orthogonal to the surface into graphite 

(0001) planes. 277 

FIGURE 56. TEM images of carbon nanotubes/nanofolds attached to a diamond surface. Top 

view (a) and side view (b). (Reprinted from Ref. 277, with permission from Elsevier Science.) 

314

Guidelines for creating a range of robust 

nanotube-diamond structures have been developed 

recently 278 and tested with the bond-order 

potential. 218 The analysis was restricted to (n,0) 

and (n,n) nanotubes perpendicularly attached to 

diamond (001) and (111) facets. These rules were 

derived based on geometrical considerations in 

combination with energies and stresses estimated 

from atomic modeling using an analytic potential 

function. 278 Geometrical considerations include 

analysis of the total and local mismatches between 

a nanotube and the diamond surface. A 

total mismatch is a mismatch between the perimeter 

of a nanotube and the perimeter of a polygon 

on a diamond surface formed by atoms participating 

in bonding (Figure 57). For example, the total 

mismatch for a (6,0) nanotube is 6.7%, while that 

for (24,0) nanotube would be only 2.6%. To create 

a strong chemical interface between a (n,0) 

nanotube and the corresponding n-sided polygon 

formed by dangling bonds on a diamond surface, 

the shape of the polygon should be as close to 

circular as possible to match that of a nanotube 

edge. Thus, in addition to total mismatch, a local 

mismatch can be defined as the distance between 

a single vertex of a polygon on a diamond surface 

and the point of the projection of a corresponding 

atom from a nanotube edge. Atomic level simulations 

have suggested that local lateral mismatches 

as large as about 1 Å do not necessarily inhibit 

FIGURE 57. Schemes of the possible connection between the (111) diamond surface and zigzag nanotubes. Dots 

connected by solid lines correspond to the atomic sites available for bonding at nanotube edges. Crosses 

correspond to atomic sites at the (111) diamond surface. Dashed lines connect sites on the diamond surface 

participating in the bonding with the specific nanotube. Stars at the contours of nanotubes (e,f) denote the dangling 

bonds at the interface diamond/nanotube after the nanotube attachment. (Reprinted from Ref. 278.) 

315

strong bond formation. For (6,0) and (24,0) 

nanotubes this local mismatch would be 0.17 Å 

and 0.68 Å, respectively. Nanotubes with larger 

radii posses less total mismatch but higher local 

mismatch, thus the interface energy of the relaxed 

structures is higher for nanotubes with larger radii 

(Table 22). 

Based on criteria related to the total and local 

mismatches and relative symmetry of a nanotube 

and site available for bonding on a diamond surface, 

six distinct groups of (n,0) nanotubes with 

different degrees of bond formation with a diamond 

(111) facet can be identified depending on 

the nanotube parameter n (Figure 56). 278 The strongest 

interfaces are formed by nanotubes from the 

first two groups that correspond to nanotubes with 

sixfold (6 × M,0) and threefold (6 × M+3,0) symmetry, 

where M is an integer. The energetic characteristics 

of nanotubes of different groups are 

summarized in Table 22. 

The symmetry of (n,n) nanotubes do not 

match well with that of a defect-free diamond 

(111) facet, and therefore interfaces of this type 

will not in general show strong bonding. However, 

there is a strong similarity between the 

five-fold symmetric (111) facets of adiamond 

pentaparticle and the ends of (5 × M, 5 × M) 

nanotubes that can result in strong bonding. 278 

The total mismatch between a pentaparticle of a 

nanoscopic size and (5,5) nanotube (Figure 58a) 

is about –4.1%. Simulations predict that the local 

mismatch can be accommodated for (5 × M, 

5 × M) nanotubes at least up to M=3. As discussed 

in Section III.A, pentaparticles are often 

observed among nanodiamond clusters. 

Because of the fourfold symmetry of (100) 

diamond facets, a general scheme like that outlined 

above for the attachment of nanotubes to 

(111) facets could not be developed. Analysis of 

bonding geometries together with molecular modeling 

studies, however, has been able to identify 

specific cases of strong bonding. 278 One such example 

is a (12,0) nanotube attached to the (100) 

facet of a diamond cluster, which is illustrated in 

Figure 58b. The total mismatch between the surface 

sites and the nanotube is only 4.9%. Interface 

energies for selected zigzag nanotubes attached to 

an (001) diamond surface are provided in Table 

22. 

Depending on a nanotubes morphology, some 

types of open nanotubes can be chemically connected 

with different diamond surfaces, atom-toatom. 

Structures without dangling bonds at the 

interface can be formed; this is important for 

nanoelectronic applications, because dangling 

bonds at the interface can trap electrons and suppress 

conductivity through the interface. By combining 

metallic or semiconducting nanotubes with 

diamond clusters or substrates, different types of 

heterojunctions can be designed for carbon-based 

nanoelectronics applications. For example, a hybrid 

structure consisting of a short nanotube sandwiched 

between two diamond clusters mimics the 

double barrier structure of a resonant tunneling 

diode. 

The nanotube/nanodiamond composite, illustrated 

in Figure 58, may, in principle, serve as tips 

for a field emitting array. 172,191 According to selfconsistent 

tight binding simulations, 191 the work 

functions of a single closed nanotube and a single 

316

FIGURE 58. Illustration of the relaxed hybrid interface structure between a diamond pentaparticle and a (5,5) 

nanotube (a) and diamond truncated octahedron cluster and the (12,0) nanotube (b). The nanotube is attached to 

the (100) facet of the cluster. (Reprinted from Ref. 278.) 

317

nanotube with an edge terminated by hydrogen are 

about 4.5 to 5 eV. The barrier at the back contact 

of the diamond cluster/metallic nanotube varies 

from 4.5 to 2-3 eV, depending if the nanodiamond 

cluster consists of pure diamond phase (Figure 58) 

or contains the tetrahedrally coordinated (ta-C) 

carbon phase. 191 Taking into account the negative 

electron affinity at the hydrogenated surface of a 

diamond cluster, the resulting emission barrier for 

the hybrid structure is comparable or lower than 

that for a single nanotube (Figure 59). Calculations 

also indicate the presence of the wave functions 

with energies near the Fermi level that are continuously 

extended along both the nanotube and diamond 

cluster. 191 This enhances the possibility of 

current flow from a nanotube to a diamond cluster. 

Probably, the major advantage of the above 

design of a nanotube capped with a nanodiamond 

particle is the potential reduction of nanotube 

erosion resulting in increased device lifetime. 

Indeed, the current density for emission from a 

single nanotube is high in compared with a 

nanotube capped with a nanodiamond particle 

that posses more emission sites. Based on estimates 

using the bond order potential, an hydrogenated 

diamond surface is more mechanically stable 

than a capped or hydrogenated nanotube edge. 

Recently, 279 partitioned real-space density functional 

calculations of field evaporation of carbon 

clusters from SWNT were performed. The calculations 

demonstrate that the activation-energy barrier 

for field evaporation of carbon clusters and 

hydrocarbon clusters from SWNT’s decreases as 

the electric field increases. It was also found that 

evaporation from an open-ended carbon nanotubes 

occurs more easily than from capped nanotubes. 

Another interesting result is that adsorbed hydrogen 

weakens the C-C bonds and significantly reduces 

the activation-energy barrier for field evaporation. 

Regarding nanotechnology applications, a 

nanotube forming strong chemical bonds with a 

diamond cantilever can be a good candidate for a 

proximal probe tip. 

The nanodiamond/nanotube hybrid structures 

discussed above can, in principle, be synthesized 

by manipulating diamond clusters with a proximal 

probe tip with a nanotube mounted at the end 

of the tip. While this method of assembling 

nanoscale building blocks would be a powerful 

tool to test a concept, it is not suitable for the mass 

production. One of the more practical ways of 

fabricating the suggested hybrid structures might 

be electrophoresis/dielectrophoresis techniques 

FIGURE 59. Homogeneous emission through a nanodiamond cluster. Band structure for graphite/ 

diamond/vacuum when (a) no field is applied and (b) under applied field. The difference between the 

Fermi level and CB edge depends on geometry and may vary between 5.5 eV and 3.0 eV. CB edge 

position in tetrahedrally coordinated a-C depends on the amorphization degree. Band structures in 

applied fields for a-C with zero (c) and positive (d) EA. (Reprinted from Ref.191.) 

318

involving directional movement of charged/polarized 

diamond particles in the suspensions under 

an applied electric field. Electrophoretic deposition 

of nanosized diamond particles from 

isopropyl alcohol suspensions on highly oriented 

pyrolytic graphite (HOPG) substrates has 

been thoroughly investigated in Ref. 71. The 

nanoparticles acquire a negative surface charge in 

aqueous and organic suspensions. However, in 

isopropyl alcohol suspensions, H+ ions generated 

in situ by the reaction between iodine and acetone 

adsorbed on the diamond particles, resulting 

in a positive surface charge and deposition 

of particles on a cathode. SEM and AFM pictures 

demonstrated that nanodiamond deposited 

as individual particles has a spherical shape. It 

was also revealed that the defect sites, such as 

steps on HOPG surface, are favorable for the 

deposition of particles. These techniques have 

been also used successfully for the deposition of 

nanodiamond powder on arrays of silicon tips 

for cold cathode fabrication. 180,181 Similar to the 

above results, deposition of nanodiamond powder 

on arrays of carbon nanotubes can be considered. 

IV. APPLICATIONS OF CARBON 

NANOSTRUCTURES 

In the worldwide study “Nanostructure Science 

and Technology” 1999, 281 four broadly defined 

and, in principle overlapping, application 

areas for nanostructure science and technology 

were suggested as a classification scheme. These 

areas are dispersions and coatings, high surface 

area materials, functional nanodevices, and consolidated 

materials. Figure 60 illustrates how this 

classification can be applied specifically for carbon-based 

nanostructures, which due to their abundant 

forms fill all four categories of the application 

fields. 

FIGURE 60. Schematic representation of four major areas of the applicability of the carbon nanostructures drawn 

according to the general classification of nanostructures in Ref. 281. 

319

Nanocarbon materials possess remarkable 

properties, and the potential applications look 

unlimited. While nanostructural materials from 

the graphite family have a well-established reputation 

in a variety of applications, 4 broad market 

acceptance of more esoteric nanocarbon-based 

technologies, however, will be enabled only if the 

fabrication costs are reduced and bulk production 

realized. For example, in 1998 a standard price of 

first gram- and subgram-sized nanotube samples 

was about $2000 per gram. Currently, prices vary 

from $500 a gram down to tens of dollars a gram 

for unpurified multiwall nanotubes. According to 

Fortune Magazine, 282 Carbon Nanotechnologies, 

Inc., TX, projects that as nanotube prices drop, 

more and more markets will open up with a total 

market value totaling $100 billion a year. According 

to Ref. 282, projecting the price of nanotubes 

down to $15,000 a pound, or about $33 a gram, a 

yearly supply of one ton would be able to support 

the manufacture of several billion dollars’ worth 

of flat-panel displays for PCs and television sets. 

In Table 23 we provide a tentative price list for 

nanodiamond particles, carbon nanotubes, and 

fullerenes as of 2002. Because the quality, purity, 

and exact form of the final product (powders, suspensions, 

etc.) vary, it is difficult to make meaningful 

price comparisons between different foundries, 

so the information provided does not pretend 

to advertise or diminish products of any of the 

companies listed. As can be seen from Table 23, 

prices for the highest purity nanodiamond particles, 

fullerenes, and nanotubes are all different by 

an order of magnitude in increasing order. An 

analysis of the economic impact of nanocarbon use 

shows that it increases the price of traditional products. 

For example, the utilization of ultradispersed 

diamond for polymer (rubber) composites in the 

amount of 1 gram per 1 kg of polymer 1 requires an 

additional investment of $2 per 1 kg of polymer 

composite. This sounds reasonable. 

Nanodiamond production by a single company 

currently can be of the order of tons per 

year, 1,3 so it is a quite mature technology. Technologies 

for purification and application in different 

areas are quite developed also (at least in 

countries of the Former Soviet Union (FSU)). 1,3 

Novel applications continue to emerge as the technology 

is developed on an industrial scale. For 

example, aggregate-free nanodiamond-metal solutions 

for electroplating have been developed for 

industrial production in Germany. 285 Among 

nanotube foundries, bulk quantity production is 

listed on the websites of Hyperion (MWNT), 

Rosseter Holdings Ltd, INP Toulouse France 

(MWNTs), Nanoledge (arc-grown SWNTs). For 

example, Guangzhou reports production of 

MWNT as 10 kg/day (95% purity) and SWNT as 

of 100 g/day (50% purity). 

In addition to the necessity of having effective 

and inexpensive methods of fabricating high 

quality nanostructures in bulk quantities (e.g., 

for applications in nanocomposites), it is also 

important to develop controllable methods of 

nanostructure integration that can be scaled-up 

for volume production of functional devices. For 

example, for nanotube-based electronics, the 

strategies under development for achieving scaleup 

are self-assembly of nanospecies or self-alignment 

through controlled CVD growth on surfaces 

patterned with catalytic particles combined 

with microfabrication techniques. 204 

Below we discuss the applications of UDD in 

more detail as a field less familiar to many audiences. 

The applications of ultrananocrystalline diamond 

films and carbide-derived diamond are 

briefly outlined because these topics are thoroughly 

described in a number of recent publications. 

2,14,63 Among the most popular nanotube applications 

that have been described in recent 

reviews, we have chosen to discuss only the rapidly 

evolving areas of cold cathodes and functional 

devices. We conclude the section with a 

brief description of medical applications of 

fullerenes and the ever-increasing role that computational 

methods play in the development of 

new applications of carbon materials. 

A. Diamond-Based Nanostructured 

Materials for Macroscopic Applications 

Below we discuss in more detail current and 

potential applications of three different classes of 

nanodiamond, which, in our opinion, are the major 

classes of diamond-based materials on the 

nanotechnology market. Those materials are 

ultradispersed diamond particles (UDD), which has 

320

321

een on the market in FSU countries for decades, 

and two recently synthesized nanodiamond structures, 

namely, ultrananocrystalline diamond films 

and carbide-derived nanodiamond. While UNCD 

films possess very unique properties, carbide-derived 

diamond is distinct by the simplicity of its 

production. These three materials are synthesized 

by completely different techniques and have rather 

different properties, providing each of them specific 

application niches (Figure 61). 

1. Applications of Ultradispersed 

Diamond 

An extended review on the technological applications 

of UDD had been written recently by 

Dolmatov. 1 The material is used in the form of a 

powder, suspension, or paste. Below we provide 

the digest of UDD applications according to Ref 

1. 

a. Metal-Diamond Galvanic Coatings 

Electrochemical and chemical deposition of 

UDD together with metals using standard galvanic 

equipment has been demonstrated to be 

beneficial in a variety of applications in machine 

building, shipbuilding, the aircraft industry, tools 

for electronics, electrical engineering, medicine, 

and the watch and jewelry industry. The advantages 

of adding UDD to galvanic coatings include 

an increase in wear-resistance and microhardness 

FIGURE 61. Schematic representation of major areas of current and prospective applications of UDD, 

ultrananocrystalline diamond films and carbide-derived diamond films. 

322

(Table 24); an increase in corrosion resistance 

and a decrease in porosity; a dramatic decrease of 

friction coefficient; considerable improvement of 

adhesion and cohesion; and high throwing power 

of electrolyte. According to Ref. 1, 283, the service 

life of products is increased 2 to 10 times, 

even when the coating thicknesses is decreased 

by a factor of 2 to 3. The strengthening effect is 

observed in coatings of many metals, including 

silver, gold, and platinum, which are employed in 

numerous electronics applications. Particularly, 

UDD is most widely used in strengthening chromium 

coatings deposited using an electrolytic 

process. In this process, UDD-containing additives 

are added to the chrome-plating electrolyte 

without any modification to the standard production 

line. Such coatings increase by a few times 

the operating life of molds, high-precision bearing 

surfaces, and other similar components. UDD 

is also used in the production of cutting and razor 

tools. 

The UDD content in a metal coating averages 

0.3 to 0.5 wt. %. The amount of UDD consumed 

for a metal layer thickness of 1 mm is 0.2 g 

(1 carat) / m 2 . Table 24 provides more detailed 

information for different metals where UDD has 

been used successfully to enhance the performance 

of galvanic coatings. According to Dolmatov, 284 

metal-UDD galvanic coatings are a major market 

niche for the current UDD consumption from Diamond 

Center, Inc. followed by applications such as 

polishing materials and nanocomposites. 

In the near future PlasmaChem GmbH, Inc. 

will commercialize a new high purity aggregatefree 

ND product for application in the electroplating/electroless 

processes based on industrial processes/compositions 

developed in the framework 

of a European project. 285 

b. UDD for Polishing Pastes and 

Suspensions 

UDD pastes are being used for finishing precision 

polished materials for electronics, radio 

engineering, optics, medical, machine building, 

and jewelry industries 1 . The compositions with 

UDD allow one to obtain a surface of any geometrical 

form with a relief height roughness of 

2 to 8 nm. Recently, 4 Å roughness has been 

323

achieved for Al 2 O 3 , and SiC surfaces using UDD 

suspensions (according to the Alit, Inc., Ukraine). 

UDD is employed in polishing compositions used 

for the final treatment of silicon wafers in the 

microelectronics industry. UDD has been also 

used in the electronics industry as a component of 

heat-removal pastes and compounds for chip packaging, 

replacing the highly toxic beryllium oxide 

that has been used traditionally. 

The amount of UDD consumed for this application 

is 1 to 10 g/m 2 . 

c. UDD for Polymer Compositions 

Polymer composites with enhanced mechanical 

properties are required by the aircraft, 

motor and tractor, ship building, medical, chemical, 

and petrochemical industries, as well as in 

the manufacture of seals, stop valves for various 

purposes, and protective and antifriction 

coatings. The addition of UDD to polymers 

provides an increase in their mechanical 

strength, wear-resistance, and heat-ageing resistance 

(Table 25). Highly effective coatings 

based on the incorporation of UDD in fluoroelastomers 

and polysiloxanes were developed; 

the elastic strength of rubbers based on 

polyisoprene, butadiene-styrene, butadiene-nitrile, 

and natural rubbers were considerably improved. 

1,286 For example, for fluoroelastomers 

filled with UDD particles the stretch modulus 

at 100% elongation and the conditional rupture 

strength increased more than tenfold (from 8.5 

to 92 MPa and from 15.7 to 173 MPa, respectively). 

In this case, the elongation increased by 

a factor of 1.6 (from 280 to 480%). One of the 

mechanisms that have been attributed to the 

influence of UDD particles on the strength properties 

of polymer composites is an increase in 

cross-linking. 1 Additives of UDD into the rubbers 

decrease attrition wear by an average of 3 

to 5 times, increase rupture strength by 30%, 

and breaking temperature by 15%. Epoxy adhesives 

that incorporate UDD have high adhesion 

and cohesion properties. 

The specific consumption of UDD or diamond 

blend (mix containing UDD and significant 

percent of other carbon based products of detonation 

explosion) is 1 to 5 kg per 1000 kg of rubber 

(polymer) and 1 to 5 kg per 1000 m 2 of polymer 

coating or film. 

324

d. UDD for Lubricating Oils, Greases, and 

Lubricant Coolants 

Modified lubricant compositions are used in 

machinery, metal treatment, engine building, ship 

building, and the aircraft and transportation industries. 

The addition of UDD and diamond blend to oils 

allow one to obtain sedimentation-stable and environmentally 

safe systems with particle sizes of less than 

0.5 µm. 1 The use of nanodiamonds in oils increases 

the service life of motors and transmissions. Friction 

torque is reduced by 20 to 40%, and the wear of 

rubbed surfaces is decreased by 30 to 40%. 

The specific consumption of UDD or DB in 

these applications is 0.01 to 0.2 kg per 1000 kg of 

oil. 

e. UDD for Systems of Magnetic Recording 

UDD is also used as an antifriction additive 

and a physical modifier for ferro-lacquer coatings 

of magnetic tapes and disks, and also as an additive 

to electrochemical deposition of composite magneto-recording 

tapes to improve the properties of 

magnetic recording devices. 287 The addition of UDD 

decreases ferro-magnetic grain size, thus allowing 

an increase in recording density while reducing 

abrasive wear and friction coefficient 

f. UDD for Application in Intermetallics 

Based on Copper, Zinc, and Tin 

UDD can be used in specific application fields 

such as when surfaces experience high frictional 

forces produced by very harsh working conditions 

that displace plastic and liquid lubricating 

materials. UDD is an ideal composite material for 

intermetallics based on copper with zinc or tin 

(the UDD content is no more than 15 volume %). 

The addition of UDD decreases the frictional 

forces two to six times. 288 

g. UDD for Biology and Medicine 

According to Refs. 1, 289 UDD is considered 

a potential medical agent (not just drug delivery 

agent) in oncology, gastroenterology, vascular 

disease, and an efficient remedy for the aftereffects 

of burns and skin diseases. The beneficial 

property of UDD for medical applications is its 

anomalously high adsorbtion capacity, high specific 

surface areas, abundance of free electrons on 

the surface (a multiple radical donor), nanoscale 

size, significant amount of oxygen-containing 

functional groups on the surface, chemically inert 

cores and hydrophoblicity of the surface. Due to 

their high adsorption capacities, UDD exhibits 

extremely high absorbing/bonding activities with 

respect to pathogenic viruses, microbes, and bacteria. 

The absorbing/bonding may be selective to 

particular drugs, which can enhance the drug’s 

activity. According to Refs. 1, 289, UDD exhibits 

no carcinogenic or mutagenic properties and is 

not toxic. 

The use of UDD in the form of aqueous and 

oil suspensions showed promising results for curing 

cancer by removing toxins from organism, 

normalizing peristaltic of the bowels, and improving 

blood characteristics. 289 The use of UDD 

in chemical and radiotherapy appears to be promising 

in the cure of malignant tumors by preventing 

the mutagenic effect of drags. According to 

Ref. 289, a theraupeutic course requires ~0.02 to 

0.5 g of UDD. While preliminary results, particularly 

in oncology, are encouraging, 289 this area of 

reseach has been explored very little because of 

insufficient funding for the research in the countries 

of the FSU where the application was first 

developed. 

A research group from the Ukraine also recently 

reported a study on the use of UDD as an 

adsorbent for the purification of biological media. 

290 

h. UDD Dinter as an Adsorbent of a New 

Type 

Carbon-containing adsorbents are widely used 

in various industries such as medicine and pharmacology. 

The most abundant of these adsorbents 

are activated coals and graphitized thermal carbon 

black. Synthetic diamond, particularly submicron 

diamond composites as well as sintered 

UDD, represents a new class of carbon containing 

325

adsorbents, 291 characterized by chemical inertness 

and high strength. Another beneficial effect is the 

possibility of using the adsorbent repeatedly by 

modifying and recovering the diamond surface. 

In addition to the application areas listed 

above, UDD is used as a component in the production 

of diamond ceramics and molds made of 

diamond-containing materials. UDD had also been 

employed for seeding substrates used in the CVD 

growth of diamond films. Dry UDD is known to 

absorb and retain water in amounts that are four 

times the weight of the UDD. This allows its use 

as an inert solid water absorber in materials whose 

quality is determined by the residual water content, 

for example, in magnetic carriers. 

2. Applications of Pure Phase 

Ultrananocrystalline Diamond Films 

As discussed in Section III.A, ultrananocrystalline 

diamond is grown using a new plasma deposition 

process that utilizes a high content of noble gas. This 

process was developed at Argonne National Laboratory 

and produces films with ultrasmall (2 to 5 nm) 

grains with atomically abrupt grain boundaries. UNCD 

films are superior in many ways to traditional microcrystalline 

diamond films: they are smooth, dense, 

pinhole free, and phase-pure, and can be conformally 

coated on a wide variety of materials and high-aspectratio 

structures. The set of unique properties include 

mechanical (high hardness ~100 GPa, and Young’s 

modulus ~960 GPa), tribological (extremely low friction 

~0.01), transport (tunable electrical conductivity, 

high thermal conductivity), electrochemical (wide 

working potential window), and electron emission 

(low, stable threshold voltage) characteristics. The 

UNCD has been considered for a variety of applications, 

including MEMS and moving mechanical assembly 

devices, surface acoustic wave (SAW) devices, 

biosensors and electrochemical sensors, coatings 

for field emission arrays, photonic and RF switching, 

and neural prostheses. 

Studies of UNCD-coated flat substrates and 

microtip arrays for cold cathodes applications 2,292 

have yielded consistently low threshold fields 

(1 to 2 V/µm), high total emission currents (up to 

10 mA), and stable emission during long-duration 

testing (up to 14 days). 

Ultrananocrystalline diamond has been also 

grown with the incorporation of nitrogen up to 8 

× 10 20 atoms/cm 3 with the addition of nitrogen to 

plasmas during the CVD growth of diamond 

films. 292 This is the highest carrier concentrations 

seen for any n-type diamond material to date 

resulting in several orders of magnitude increase 

in UNCD conductivity that promise applications 

in heterojunction electronic devices. 

UNCD electrodes exhibit a wide working 

potential window, a low background current, and 

high degree of electrochemical activity for redox 

systems. These results, in combination with the 

biocompatibility properties of UNCD, could lead 

to the application of UNCD electrodes for nerve 

stimulation. 2 

Future MEMS applications that involve significant 

rolling or sliding contact (MEMS moving 

mechanical assemblies (MEMS MMAs)) will require 

the use of new materials with significantly 

improved mechanical and tribological properties 

and the ability to perform in harsh environments. 

Because the feature resolution in polycrystalline 

MEMS is limited by grain size, the use of MEMS 

made by conventional CVD diamond methods is 

limited. In addition, the conventional CVD diamond 

films typically have large grain sizes (~1 

mm), high internal stress, poor intergranular adhesion, 

and rough surfaces (rms ~1 µm). Alternatively, 

diamond-like coatings, generally grown by 

physical vapor deposition, cannot cover high aspect 

ratio MEMS features conformally and require 

high-temperature post-deposition processing to 

relieve stress, which compromises their mechanical 

properties. Ultrananocrystalline diamond coatings 

possess morphological and mechanical properties 

that are ideally suited for MEMS applications 

in general, and MMA use in particular. 2,293 The 

roughness of the film is about 20 to 40 nm and the 

friction coefficient can be as low as 0.01. The 

surfaces are very smooth (rms~30 to 40 nm) and 

the hardness is as high as ~100 GPa. When compared 

with Si-based MEMS, the brittle fracture 

strength is 23 times that of Si, and the projected 

wear life of MEMS MMAs from diamond is 10,000 

times greater than that of Si MMAs. The group 

from Argonne National Laboratory demonstrated 

three-dimensional MEMS structures fabricated 

from UNCD material, including cantilevers and 

326

multilevel devices, acting as precursors to 

microbearings and gears (Figure 62). 

Applications of UDNC as biocompatible MEMS 

devices, biosensors and biological electrodes are being 

also explored. A special program is funded by the DOE 

to develop UDNC-based artificial retinas to restore 

sight to people blinded by the retinitis picmentosa 

condition. 294 Functionalization of UNCD to attach DNA 

molecules has been demonstrated also. 294 

Nanocrystalline diamond coatings on suitable 

substrates are promising materials for medical 

implants, cardiovascular surgery, and for the coating 

of certain components of artificial heart valves 

due to their extremely high chemical inertness, 

smoothness of the surface, and good adhesion of 

the coatings to the substrate. 295 Nanocrystalline 

diamond coatings (reported grain size ~nm) deposited 

by RF-PCVD of methane with nitrogen 

on mm-sized steel implants that had been inserted 

to tissue and bones for up to 52 weeks 295 demonstrated 

excellent biocompatibility and biostability 

(Figure 63). 

We would like to conclude this subsection by 

outlining the medial application of diamond from a 

completely different perspective. Within the concepts 

of the molecular nanotechnology, 308 carbonbased 

materials could play an important role in building 

“nanorobots”, structures that have been 

envisioned for applications in nanomedicine 309 (Figure 

64). Nanomedicine may be defined as the monitoring, 

repair, construction, and control of human 

biological systems at the molecular level using engineered 

nanodevices and nanostructures. 309 

Fullerene nanotube–based rotors, shuffles, and 

gears 310 have been computationally designed as well 

as those based on so-called diamonoid materials. 311 

3. Applications of Carbide-Derived 

Diamond-Structured Carbon 

Recently, a method for the synthesis of diamond-structured 

carbon in bulk quantities by extracting 

silicon from silicon carbide or metal car- 

FIGURE 62. A UNCD MEMS cantilever strain gauge with a 100-nm feature resolution 

produced by UNCD blanket film deposition and etching through a hard oxide mask. 

The UNCD film is 3.3 µm thick, and it is separated from the substrate by 2 µm. 

(Reprinted from Ref. 293, with permission from Elsevier Science.) 

327

FIGURE 63. Illustration of a very good biotolerance of the implants coated with the nanocrystalline 

diamond layers. In subcutaneous tissue, muscles and bones, thin connective tissue capsules 

built from fibrocytes and collagen fibers were formed. Optical microscope analysis of the wall 

of the capsule after 52 weeks did not reveal any phagocytic reaction or products of corrosion. 

(Reprinted from Ref. 295, with permission from Elsevier Science.) 

FIGURE 64. Science fiction: using diamond in medical nanorobots. The picture is adapted 

from M. D. Lemonick, “...And Will They Go Inside Us? Given the Promise of Nanotechnology, 

It’s a Safe Bet,” Time Magazine 154 (8 November 1999):93. Artist: Joe Letrola. 

328

ide was developed. 14 In principle, chlorination of 

carbides for the production of carbon-based materials 

and, particularly, nanoporous carbon, is a relatively 

mature technology that has been commercialized (see, 

for example, http://www.skeleton-technologies.com). 

However, the synthesis of nanocrystalline diamond 

by this technique 14 is a recent achievement. Coatings 

of diamond-structured carbon produced by this route 

show hardness values in excess of 50 GPa and Young’s 

moduli up to 800 GPa. 

The carbide-derived carbon and diamond coatings 

show excellent tribological behavior in both room 

air and dry nitrogen and are at the stage of commercialization 

for tribilogical applications, particularly as 

nanodiamond coatings for SiC dynamic seals for 

water pumps. 296 The coatings are self-lubricating, with 

remarkably low friction coefficients that can be tailored 

by altering the reaction parameters and show no 

measurable wear. 296 Favorable tribological properties 

of carbide-derived nanodiamond make it a favored 

candidate for applications in the manufacturing of 

different types of prosthesis. 297 

Conformal coatings produced by selective etching 

can be useful in micro-electro-mechanical systems 

(MEMS) applications, where very thin and 

uniform coatings are required. In addition, permeability 

of the films produced by chlorination of SiC 

and an extremely narrow pore size distribution in 

carbide-derived carbon provide effective molecular 

sieves, high-surface area electrodes and other 

applications, where vapor-deposited diamond films 

cannot be applied. The large-scale solid-state synthesis 

of technical diamond at ambient pressure 

and moderate temperatures with no plasma activation 

can provide diamond materials at a low cost 

for a variety of high-volume applications such as 

brake pads, where diamond could not be used before 

because of its cost. 

B. Carbon Nanotubes in Advanced 

Electron Sources: Are Carbon 

Nanotubes Exceptional Electron 

Sources? 

Advanced electron sources often are regarded 

as the most important short-term application of 

carbon nanotubes. In this section, we summarize 

the technical parameters of nanocarbon electron 

emitters and provide critical assessments of their 

status and prospects. Electron emission properties 

of carbon nanotubes are considered. 

329

330

1. Practical Issues of Field Emission 

Electron Sources 

Field emitters are cold electron sources whose 

operation is based on geometry effects. Despite 

their apparent simplicity and the expectations about 

device applications, field emitters are rarely used 

in real-world devices. The reason is that so far 

field emitters do not satisfy the practical technical 

requirements of high current density and emission 

stability, 314,315 as well as a low operating 

voltage. 

The two major designs of electron sources are 

a single point electron source (e.g., a single 

nanotube) and a large area electron source, which 

could be either an array of tips (e.g., nanotubes) 

or a continuous film of emitting material. 

In this section we provide critical assessments 

of the status of carbon emitters by comparison 

with their most recently reported emission parameters 

to those of field emitters made from other 

materials (Figures 65 and 66). 

2. Carbon Nanotubes Emitters 

Typical carbon nanotubes field emitters are 

shown in Figure 67. With their high aspect ratio 

and unique conducting properties, there has been 

a great deal of recent speculation regarding field 

emission from carbon nanotubes, with some researchers 

claiming properties that are far superior 

to more conventional field emitting structures. In 

this section we attempt to critically review carbon 

nanotubes field emission cathodes from the viewpoint 

of the field emission community, including 

candid comparisons to other well-established field 

emitters. In our comparison, we categorize different 

types of field emitters as “low-voltage emitters”, 

“high-current emitters”, and “gated emitters”. 

a. Low-Voltage Emitters 

Low-voltage (10 to 20 V) field emission from 

carbon nanotubes was reported recently in Ref. 

319, where a very small emitter-to-anode distance 

(6 µm) was used. We note that similar 

effects can be achieved with other types of field 

emitters. The first field emission diode that operated 

at less than 10 V applied was reported in 

1989 by Makhov. 314 It consisted of sharp wedges 

of single crystal silicon operated at a cathode-toanode 

distance of less than 1 µm. Since then, 

several similar devices have been demonstrated, 

including recent results from diamond tips (see 

Table 26). In all cases, the low-voltage operation 

FIGURE 65. Conventional field emission technologies: (a) Single Mo tip field emitter (etched wire); 

(b) ungated Si field emitter arrays. (Reprinted from Ref. 316, Copyright 1994, with permission from 

American Institute of Physics.) 

331

FIGURE 66. Gated Mo field emitters. (Reprinted from Ref. 317, Copyright 

1998, with permission from American Institute of Physics.) 

was achieved by using very small vacuum gaps of 

less than 10 µm. Unfortunately, this type of device 

has limited usefulness; they are all essentially 

diodes with little or no advantages compared 

with solid-state diodes. Table 26 compares 

recently reported low-voltage operation of carbon 

nanotubes field emission diodes with previously 

reported field emission devices. 

b. High-Current Emitters 

The potential for high-emission currents has 

always been an attractive feature of field emitters, 

and there are many reports of “high current densities” 

from novel emission materials. However, 

these reports can be misleading and must be interpreted 

carefully in terms of practical applications. 

For example, a small total current of 10 µA can 

result both in very high and very low current 

density depending on the choice of emission area. 

The emission area of practical merit is the total 

cathode area α total (independent of the number of 

emission sites). All of the reported data regarding 

carbon nanotubes field emission has been obtained 

using a proximity probe of very small area 

(1 to 100 µm 2 ), with the total current measured in 

these experiments typically only 1 to 100 µA. 

Nevertheless, claims of high-current densities and 

device applications for microwave tubes have been 

made. The practical question, however, is “what 

will the current be when the anode diameter is 

increased to 1 cm?” It is likely that the current 

will be much less than 10,000 amperes. As was 

shown by Göhl et al., 323 an increase in probe 

diameter results in a drastic decrease in probe 

current density. 

The parameter of merit for device applications 

is the integral current density, that is, the 

total current emitted divided by the entire cathode 

area. That is, a very high current density is 

obtained only from a very small cathode area. 

(The record current density of about 2500 A/ 

cm 2324 was obtained from an array of emitters 

332

FIGURE 67. Fragments of typical CNT field emitters: (a) supported single nanotube; 329 (b) 

array of CNT grown by CVD (at different magnifications); 326 (c) attached CNTs. 332 (Reprinted 

from Ref. 329 with permission from Springer-Verlag GmbH & Co. KG (a) and Ref. 

326 (b) and Ref. 332 (c) with permission from the American Institute of Physics.) 

333

with an integral area of 25 × 25 µm 2 and a total 

current of a few mA.) A realistic challenge is to 

demonstrate a total current of 1 A (or more) from 

a macroscopic area of 1 cm 2 . Overall judgements 

about the potential usefulness of new cathode 

materials cannot be made without data from a 

minimum set of practical parameters: maximum 

total current at failure I max , integral current density 

J max , operating voltages V th (threshold voltage), 

and V max (voltage for maximum current or 

failure) and transconductance g m ~ I max / V max . 315 

Note that the typical maximum current of “highcurrent” 

carbon nanotubes emitters is within 0.1 

to 2 mA. For comparison, 4 mA of current was 

obtained from a single ZrC tip. 327 Table 27 compares 

maximum current and transconductance of 

different field emitters. 

c. Gated Emitters 

Gated field emitters shown in Figure 66 are 

basic components of field emission displays (FED) 

and microtriodes for vacuum microelectronics 

devices. 314 Typical gate voltages of metal field 

emitters prepared by standard technique is in the 

range 50 to 100 V. To date, only a few reports on 

gated carbon nanotubes emitters have been published. 

Hsu and Shaw 328 grew multiwalled carbon 

nanotubes on conventional silicon gated field 

emitters with 2.5 µm gate aperture. The silicon 

tips in these particular emitters were relatively 

blunt. A gated field emitter cell with carbon 

nanotubes grown on Si tips is shown in Figure 68. 

However, it was found from SEM examination 

that only 10% of Si tips had carbon nanotubes. 328 

Figure 69 shows emission current-voltage characteristics 

from Si field emission arrays with and 

without carbon nanotubes. As can be seen, emitters 

without carbon nanotubes had a much higher 

threshold voltage. Field emission arrays with carbon 

nanotubes showed threshold voltages near 20 

V. Table 28 compares emission characteristics of 

carbon nanotubes 328 and Mo 317 gated field emitters. 

Indeed, carbon nanotubes allow for the reduction 

of the operational voltage for emitters 

with relatively large gate aperture. However, the 

current per cell and total current of a carbon 

nanotubes field emission array is considerably 

lower than metal field emitters. 

d. Maximum Current from Individual 

Nanotubes 

Experiments with individual carbon nanotubes 

s mounted on metal tips have shown maximum 

emission currents of the order of 100 µA. 329 

334

FIGURE 68. Gated carbon nanotubes-on-silicon post field emitter cell. 

(Reprinted from Ref. 328, Copyright 2002, with permission from the 

American Institute of Physics.) 

335

336 

FIGURE 69. Emission current-voltage characteristics (anode current vs gate 

voltage) from arrays with and without CNTs. (Reprinted from Ref. 328, Copyright 

2002, with permission from the American Institute of Physics.)

Nilsson et al. 330 studied the emission-degradation 

behavior of carbon nanotubes thin-film electron 

emitters. The authors investigated MWNT arrays 

grown by CVD on a silicon wafer. They found 

that current-dependent emission degradation 

started at about 300 nA per emitter. This result is 

consistent with Ref. 328 (see Table 28). In the 

authors’ opinion, the primary degradation mechanism 

of a carbon nanotubes film on Si was the 

Joule heating at the carbon nanotubes /silicon 

interface. 330 The authors 330 discuss the difference 

between their result and the result reported by 

Bonard et al., 329 where a maximum current of 100 

µA was obtained from an individual MWNT 

mounted on the tip of an etched gold wire. This 

difference can be explained in part by the different 

contact resistance between carbon nanotubes 

and gold and carbon nanotubes and Si. 329 

In general, the average current per emission 

site in a carbon nanotubes emitter is smaller than 

in metal field emission arrays. The maximum 

current of 100 µA obtained from individual 

nanotubes is also typically the maximum current 

for metal (e.g., Mo) emitters, 314 though emitters 

from metal carbides, 327 or metal tips with diamond 

coatings, 331 result in larger maximum currents, 

up to few mA per tip. 327 

has to keep in mind that such an application must 

compete with existing fluorescent tubes. In general, 

to achieve a brightness of 10 000 cd/m 2 , the 

emission current density should be about 0.5 to 1 

µa/cm 2 at voltages of 3 to 5 kV. For luminescent 

tubes of practical size these conditions will result 

in high power consumption. Indeed, the power 

consumption of the reported carbon nanotubes 

field emission lamp is more than 10 times higher 

than for a conventional fluorescent tube. 334 The 

authors 334 believe that it would be possible to 

decrease the power consumption by phosphor 

optimization. It should be noted, however, that 

the phosphor efficiency by electron excitation is 

always lower than the efficiency by UV excitation 

for fundamental physical reasons, and therefore 

it may not be possible to fabricate field emission 

lamps with efficiencies comparable with 

fluorescent tubes. 

Among other proposals for using carbon 

nanotubes as field emission electron sources, we 

mention X-ray tubes, 335 electron guns for electron 

microscopy, 336 and vacuum microtriodes. 337 However, 

unless considerable improvement in integral 

current density and emitter lifetime is shown, 

major breakthroughs in the performance or application 

of these devices will be difficult to achieve. 

3. Field Emission Devices 

a. Displays and Lamps 

Field emission flat panel displays are often 

cited as one of the most promising applications of 

carbon nanotube field emitters, and several groups 

have demonstrated the operation of carbon 

nanotubes displays. Probably, the most advanced 

FED prototypes were made at Samsung. 332,333 We 

note somewhat pessimistically, however, that 

many different kinds of field emission displays 

have been demonstrated during the last 12 years, 

with but so far none have proven to be a successful 

commercial alternative to other technologies 

such as LEDs, electroluminescent, and plasma 

displays. 

One of the recently proposed applications of 

carbon nanotubes was in the luminescent tubes 

for general lighting purposes. 334 However, one 

4. Emission Mechanism and Specific 

Features of Carbon Nanotubes 

In general, carbon nanotubes emitters are 

based on the same operation principle as more 

traditional emitters, such as metal tips. As a general 

observation, the open-ended carbon nanotubes 

appear to emit better than those with caps, and 

SWNTs emit better than MWNTs. 

The key factor determining emission properties 

of carbon nanotubes is the geometrical field 

enhancement, which for individual emitters is 

roughly proportional to their aspect ratio. The 

difference between carbon nanotubes and conventional 

field emitters and the potential advantage 

of carbon nanotubes is their cylindrical shape, 

which may enable higher field enhancement. 

However, this advantage turns into a drawback 

when we consider the maximum current from 

individual nanotube emission sites. It is limited to 

337

hundreds of nA, 328,330 for example, very different 

from tens of µA for metal tips. 314,317 

Another difference between carbon nanotubes 

and conventional metal field emitters is the fact 

that carbon nanotubes can be flexed, bent, and 

reoriented by an electric field. 338 For moderate 

electric fields, the flexing and reorienting is reversible, 

but under high-field conditions sufficient 

to extract large field emission currents, the 

nanotube remains irreversibly deformed. 

Nanotubes that field emitted at a high currents 

for long times were foreshortened 338 , suggesting 

a lifetime-limiting mechanism for vacuum 

microelectronic devices. 

Conclusion on Field Emission from Carbon 

Nanotubes 

Despite statements claiming carbon nanotubes 

to be “excellent”, high-current, and low-field 

emitters, realistic assessment suggests that carbon 

nanotubes may ultimately offer few advantages 

over alternative field emission technologies. In 

fact, a more precise comparison of conventional 

metal field emitters and carbon nanotubes emitters 

(see Tables 26 to 28) does not reveal any 

remarkable advantages of the latter. 

C. Carbon Nanotubes as 

Nanoelectronics Components 

Carbon nanotubes are considered as a very 

important subset of nanoelectronic materials. 339 

Semiconducting properties of carbon nanotubes 

made them interesting for electronics applications. 

One of the requirements for a material for active 

electronic devices is the ability to control its electron 

transport properties. In CNTs such control 

can be achieved by geometry (e.g., diameter, shape, 

helicity) or surface adsorbates. 

The operational principle of most electronic 

devices is based on either conductivity modulation 

of a channel or on highly nonlinear I-V 

characteristics. Both field effect transistors 

(FETs) and intratube p-n junctions made from 

individual semiconducting nanotubes have been 

demonstrated. 

Doped Carbon Nanotubes Structures 

As-grown semiconducting carbon nanotubes 

have p-type conductivity. 340–343 Carbon nanotubes 

can be doped chemically by controlling surface 

adsorbates. 341–343 Doped structures with p-n junctions 

were formed on individual single-walled 

carbon nanotubes by doping with alkaline metals 

and organic molecules. Doped structures with both 

negative differential conductance 341 and unipolar 

conductance (rectification) 342 were demonstrated. 

In a recent work by Kong et al. 340 a p-n-p junction 

was chemically defined on an individual carbon 

nanotubes. The n-doped region was produced by 

local deposition of potassium on a p-type carbon 

nanotubes. From transport measurements, the 

authors 340 concluded that nanometer-scale width 

tunnel barriers at the p-n junctions dominate the 

electrical characteristics of the system. Figure 70. 

shows a schematic p-n-p carbon nanotubes device 

and the corresponding band diagram. At low temperatures, 

the structure can be regarded as a quantum 

dot confined between the two p-n junctions. 

Single electron transistor behavior of this carbon 

nanotubes p-n-p structure was reported. 340 In principle, 

by local doping of carbon nanotubes, the 

realization of such functional devices as Esaki 

tunnel diodes or Shokley p-n-p-n diodes should 

be possible. 

Field Effect Transistors 

The possibility for modulating the conductance 

through a carbon nanotubes by a gate electrode 

was first demonstrated by Dekker et al. in 

1998. 344 Since then, several groups have demonstrated 

field effect transistor (FET ) device structures 

in which a gate electrode modulates the 

conductivity of a conducting channel by a factor 

of 10 5 . 345 Large arrays of carbon nanotube FETs 

have been fabricated. 346 Simple prototypes of electronic 

circuit elements were demonstrated, such 

as a voltage inverter or NOT gate circuit using 

one n-channel and one p-channel FET. 

In carbon nanotubes FETs, the carbon 

nanotubes acts as a channel, connecting two metal 

electrodes. The channel conductance is modulated 

by third gate electrode. Several different 

338

FIGURE 70. (a) Schematic CNT p-n-p structure; (b) AFM image showing a 200- 

nm wide window (dark), corresponding to potassium doped n-type region; (c) 

corresponding band diagram. (Reprinted from Ref. 340, Copyright 2002, with 

permission from American Institute of Physics.) 

types of carbon nanotubes FET were reported: 

“bottom gate”, 344 “top gate”, 347 and vertical. 348 

The top gate structure shown in Figure 71 347 appears 

the most promising one, because it allows 

for a thinner gate insulator, protects the carbon 

nanotubes channel from exposure to air, and can 

be made suitable for high-frequency operation. 347 

Wind et al. 347 recently reported top gate 

p-channel carbon nanotubes FET with channel 

length of 260 nm and having a maximum 

transconductance of 3.25 µS. The authors compared 

the parameters of the carbon nanotubes FET 

to the state-of-the art Si transistors (see table in 

Figure 71c). In the authors’ opinion, the dc performance 

of a carbon nanotubes FET is much better 

than a Si FET. It should be noted, however, that in 

their comparision the authors used electrical 

charcteristics normalized per channel width, which 

was assumed to be 1.4 nm. Another assumption 

was that only one nanotube was present in the 

channel. The third assumption is that the 

transconductance will increase proportional to the 

number of parallel nanotubes in the channel. All of 

these assumptions need to be carefully investigated. 

For circuit operation of a FET, the total 

transconductance is one of the key parameters. The 

total transconductance reported in Ref. 347 is 

3.25 µS, which is much smaller than the 

339

340 

FIGURE 71. (a) Schematic cross-section of the top gate CNT FET showing the gate 

and source and drain electrodes. (b) Output characteristic of a top gate p-type 

CNFET with a Ti gate and a gate oxide thickness of 15 nm. The gate voltage values 

range from 20.1 to 21.1 V above the threshold voltage, which is 20.5 V. Inset: 

Transfer characteristic of the CNFET for V ds = 20.6 V. (c) Comparison of key device 

parameters for CNT and Si FET. (Reprinted from Ref. 328, Copyright 2002, with 

permission from American Institute of Physics.)

transconductance of practical Si FETs. Javey et 

al. 349 reported fabrication nanotube FET arrays with 

local bottom gates. 

While as-made FETs are all p-type, a local 

electrical manipulation method was used to convert 

specified nanotube FETs into n-type. The authors 

349 found that a p-type FET can be converted 

into n-type by applying a high local gate voltage 

combined with a large source-drain bias for a certain 

duration. This conversion is shown in the current 

vs bottom gate voltage (I-V g ) curves in Figure 

72a for a transistor before and after applying a 

local gate voltage of -40 V and a source-drain bias 

of 20 V for 5 min. The authors note, however, that 

some of the p-FETs become rather insulating over 

a large gate range after this electrical manipulation 

step. The yield of p- to n-conversion by our local 

manipulation method was about 50%. 

This local doping approach leads to multiple 

n-FETs coexisting with p-FETs on a chip. Complementary 

logic gates with up to six complementary 

transistors and three stage ring oscillators were 

realized by connecting the n- and p-transistors. 

Figure 72b shows the output characteristics of an 

FIGURE 72. Local manipulation for n-type tube FETs for complementary devices. (a) 

Source-drain current vs. gate voltage (I-Vg) curves of a SWNT-FET in air and after local 

electrical manipulation in vacuum, showing the p- to n-type conversion. Bias = 10 mV. (b) 

Transfer characteristics of an inverter made from a p-type nanotube FET and an n-type FET 

obtained by electrical manipulation. The operating voltage applied is V DD = -5 V. (Reprinted 

from Ref. 349, Copyright 2002, with permission from the American Chemical Society.) 

341

inverter (NOT gate). It consists of an as-made p- 

type tube FET and an n-type FET, and obtained 

by electrical manipulation. This complementary 

NOT logic gate exhibits a high voltage gain of 8. 

Complementary NOR, OR, NAND, and AND 

logic gates are built with up to six (3 p-type/3 n- 

type) SWNT-FETs. 349 

All published characteristics of carbon 

nanotubes electronic logic gates are static I-V 

characteristics. Data on the dynamic time-dependent 

response of these components are very important 

for fair assessments of their usefulness for 

practical nanoelectronic devices. At this point, 

there are only very few reports on the operational 

speed of carbon nanotubes devices. Ring oscillators 

with an oscillation frequency of 5 Hz made 

using three unipolar p-type carbon nanotubes FETs 

and resistors were reported in Ref. 350. Javey et 

al. 349 reported a complementary carbon nanotubes 

FET ring oscillator with three SWNT based inverters. 

The oscillating frequency of the device 

was measured to be about 220 Hz (Figure 73). 

Thus, the speed of carbon nanotubes devices, reported 

at this point, is very slow. The authors 349 

explain this as due to “extrinsic” factors such as 

external resistance and capacitance of the circuit. 

The demonstration of high-speed operation of 

nanotube electronic devices is probably the most 

important issue for assessments of the feasibility 

of nanotube electronics. 

The theoretical understanding of the operation 

of a carbon nanotubes FET remains incomplete. 

351 While initially it was believed that the 

gate voltage changes the conductivity of carbon 

nanotubes channel, later there was increasing 

evidence that the Schottky barriers at the carbon 

nanotubes/metal contacts may play a key role. 

Heinze et al., 351 based on their theoretical results, 

concluded that carbon nanotubes FETs operate as 

unconventional Schottky barrier transistors in 

which switching occurs primarily by modulation 

of the contact resistance rather than the channel 

resistance. Clearly, more work is needed for a 

complete understanding of carbon nanotubes FET 

operation. 

Besides the specific technical issues discussed 

above, there is a more fundamental question concerning 

possible nanoelectronic applications of 

carbon nanotubes: What is the best direction to 

pursue for alternate information processing technologies, 

for example, carbon nanotubes, molecular 

electronics, etc.? Today’s attempts in most 

cases replicate silicon technology with new 

switches, or integrate nonsilicon components, such 

FIGURE 73. Ouput characteristics of a ring oscillator made of three complementary nanotube 

inverters. The output frequency is 220 Hz. V DD = -4 V. (Reprinted from Ref. 349, Copyright 2002, 

with permission from American Chemical Society.) 

342

as carbon nanotubes with silicon, for example, 

CMOS channel replacement technologies. However, 

as long as electron transport and energy 

barriers govern device operation, use of carbon 

nanotubes to replace the channel of a silicon 

MOSFET would not measurably extend silicon 

CMOS technology. 

Three important parameters in the realization 

of digital systems are the device switching speed, 

switching energy dissipation, and integration density. 

The question that should be examined is 

“What are the ultimate limits to the speed, size, 

density and dissipated energy of a carbon 

nanotubes switch (e.g., a FET switch)? 

In addition, several issues need to be addressed 

to assess the practical feasibility of nanotube based 

integrated electronics. Possibilities for integration 

of individual carbon nanotubes components 

in a complex circuit (billions of components per 

cm 2 ) are unclear at this point. 

D. Medical Applications of Fullerene- 

Based Materials 

The field of fullerene and carbon nanotube 

biology, as well as applications of fullerene derivatives 

in biology and medicine, has become increasingly 

popular. 298,299 In the mid-1990s it was demonstrated 

that fullerene compounds have biological 

activity and their potential as therapeutic products 

for the treatment of several diseases had been reported. 

Recently, a private biopharmaceutical company, 

C Sixty Inc. was created with a primary 

focus on the discovery and the development of a 

new class of therapeutics based on the fullerene 

molecule. C Sixty’s lead products are based on the 

modification of the fullerene molecule and are 

aimed at the treatment of cancer, AIDS, and 

neurodegenerative diseases. 301 

The flexible chemical reactivity of C 60 has 

already resulted in numerous fullerene compounds 

that are now available for study. In addition, at 7.2 

Å in diameter, C 60 is similar in size to steroid 

hormones or peptide alpha-helices, and thus 

fullerene compounds are ideal molecules to serve 

as ligands for enzymes and receptors. 298 While 

fullerene C 60 itself shows no solubility in water, 

many fullerene compounds can be very water 

soluble. Such derivatives of C 60 contain polar side 

chains, and the water solubility increases with the 

number of polar groups. A number of useful 

fullerene-based therapeutics have been reported, 

including antiviral agents and anti-cancer drugs, as 

well as biosensors for diagnostic applications; 300,301 

as a protective agent against iron-induced oxidative 

stress; 306 or as an in vitro antibacterial agent. 307 

Fullerenes had been demonstrated to be useful 

in DNA-templated assemblies of inorganic-organic 

building blocks. 312 The fullerene-DNA complexation 

significantly altered the structure of DNA 

(DNA become very condensed). This complexe 

might be potentially useful for gene delivery. 

The exploration of nanotubes in biomedical 

applications is also underway. Cells have been 

shown to grow on nanotubes, so they have no 

toxic effect. 313 The cells also do not adhere to the 

nanotubes, potentially giving rise to applications 

such as coatings for prosthetics, and antifouling 

coatings for ships. The ability to chemically modify 

the sidewalls of nanotubes can be considered for 

biomedical applications such as vascular stents, 

and neuron growth and regeneration. 313 

Thus, all major forms of carbon at the 

nanoscale appear to be valuable resources for 

biomedical applications. 

E. Atomic Modeling of Carbon 

Nanostructures as a Tool for Developing 

New Materials and Technologies 

The results of a number of modeling and simulation 

studies on carbon nanostructures have been 

discussed in appropriate places elsewhere in this 

article. For completeness, we include in this section 

a brief discussion of some situations in which 

theory and modeling has led to experiments in 

developing new technologies and applications involving 

carbon nanostructures. In some cases the 

experiment has confirmed the theoretical predictions, 

while in other cases the corresponding experimental 

measurements have yet to be made. 

1. Fullerene Structures 

Probably the most celebrated triumph of theory 

in the area of carbon structures is the prediction 

that the electronic properties of carbon nanotubes, 

343

specifically the absence or presence of a band 

gap, depends on the tubule’s helical structure and 

radius. 199,280,353,354 Using simple tight binding 

theory based on near-neighbor π bonding, it can 

be shown that when the relation (2n 1 +n 2 )=3q is 

satisfied, a nanotube is predicted to have a zero 

band gap, with all other structures being semiconductors. 

In this expression, n 1 and n 2 are the integer 

values of the in-plane graphite lattice vectors 

that define the wrapping of a nanotube, and q is an 

integer. Further analysis shows that with the exception 

of the n 1 =n 2 structures, the zero band gaps 

predicted by simple tight binding theory are due 

to a degeneracy of the highest occupied molecular 

orbital (HOMO) and the lowest unoccupied molecular 

orbital (LUMO) at the Gamma point, that 

is, these structures are semimetals. More detailed 

calculations show that s-p mixing removes this 

degeneracy and introduces a band gap, albeit with 

a value that is much smaller than the structures 

predicted to be semiconductors by simple tight 

binding theory, and that the magnitude of the 

small band gap decreases with increasing nanotube 

radius. 354 In the case of the n 1 =n 2 structures, theory 

has shown that the zero band gap is due to a 

crossing of the HOMO and the LUMO, resulting 

in a true metal. 

Based on the predicted nanotube wrappingband 

gap prediction, several groups have suggested 

that joining two nanotubes with similar 

radii but different helical structures could create a 

metal-semiconductor junction. 355,356 Calculations 

have shown that such a junction is energetically 

feasible without introducing undesirable radical 

electronic states. Similarly, theory proposed that 

the electronic properties of nanotubes could be 

tuned further by chemisorbing species to their 

walls. 95,357 An example structure of this type is 

illustrated in Figure 74, where ethylene molecules 

are chemisorbed along part of a (6,0) nanotube at 

positions that are predicted to open a band gap. 

Based on tight binding calculations, the structure 

shown is predicted to have a Schottky barrier of 

0.44 eV, and metal-induced gaps states that decay 

from the metallic to the semiconducting region of 

the nanotube. 95,357 The decay behavior of these 

states is quantitatively similar to those at more 

conventional interfaces such as Al-Si boundaries. 

White and Todorov have predicted that 

nanotubes display ballistic electron conduction, 

with localization lengths of the order of hundreds 

of nanometers (or more) .358 This is exceptional 

behavior, which strongly suggests applications of 

nanotubes as efficient nanoscale wires. Additional 

FIGURE 74. Illustration of a region of a nanotube containing a metal-semiconductor junction due 

to ethylene chemisorption. 

344

details regarding transport in nanotubes can be 

found in Ref. 359. 

Theory has also predicted that the value of a 

band gap in a semiconducting nanotube can be 

changed by an applied stress, and that band gaps 

can even be added or removed for large 

stresses. 357,360,361 This has led to suggestions of 

nanoscale strain and vibration gauges using 

nanotubes as sensors in which changes in conductivity 

due to strain are utilized. 357 Structures with 

this specialized function have not yet been constructed. 

Recently, Srivastava and co-workers have 

modeled the structure and electron transport 

through both symmetric and asymmetric nanotube 

“Y junctions”. 362,363 These structures, which when 

appropriately connected resemble neuro-networks, 

were found to be energetically stable and electronically 

robust with respect to defect states. The 

transport calculations suggest that switching and 

rectification properties of these structures depend 

strongly on the symmetry, and to a lesser degree 

on chirality. For symmetric junctions, for example, 

the calculations show that perfect rectification 

across a junction is possible depending on the 

helical structure of the nanotubes, but that for 

asymmetric junctions rectification is not possible. 

Recent simulations and experiments have indicated 

that nanotube junctions can be created by 

electron beam heating of cross nanotubes. 364 Taken 

together, the predictions relating band gaps to 

structure and chemisorption, ballistic electron 

transport models, and the apparently rich behavior 

and structures possible with Y junctions makes 

a strong case for using these structures for 

nanoscale electronic device applications, with the 

caveats mentioned above. 365 

As discussed above, molecular modeling in 

conjunction with continuum treatments of 

nanotubes showed that severely bent nanotubes 

will kink (much like a garden hose), and that kink 

formation is largely reversible as nanotubes are 

straightened. 366,235 The kink structures observed 

in these early simulations were remarkably similar 

to those subsequently seen with electron and 

atomic force microscopies. 366,367 Both indicate a 

flattened region behind the kink, and ridges along 

the top and the bottom of the kink. Reversible 

kink formation has also been characterized theoretically 

for nanotubes used as molecular 

indentors, 368,369 a property that supports experimental 

applications of nanotubes in nanometerscale 

metrology. 370 Similar to kink formation, 

theory predicted that nanotubes with large radii 

will collapse into ribbon structures due to van der 

Waals attraction between opposing walls of the 

nanotube. 371,372 These structures have been observed 

experimentally. 372,302 

An interesting example of theory and experiment 

working together is the prediction that kinks 

in nanotubes may act as sites of enhanced reactivity. 

303 Using molecular modeling and a tight binding 

model, theory predicted that the ridges along 

the top and bottom of kinks on nanotubes produce 

atomic geometries that resemble sp 3 bonding, 

which result in the formation of radical states in 

the band gap of a (17,0) nanotube. Furthermore, 

these radical states, theory predicted, are sites for 

strong chemisorption of hydrogen atoms, and 

therefore kinks should display enhanced reactivity. 

Experimental studies carried out in parallel 

with the calculations showed that kink sites are 

more susceptible to attack by dilute nitric acid 

than are nonkinked regions of nanotubes. From a 

technology viewpoint, these results suggest that 

combining mechanical bending with chemical 

interactions is a viable route for controlling the 

cutting of nanotubes to precise lengths for various 

electronic device applications. 

Several modeling studies have been carried 

out to explore the properties of nanotube-polymer 

composites, particularly how load transfer between 

the nanofiber and matrix can be maintained. 

Molecular modeling has suggested that polymers 

can optimize nonbonded interactions with a 

nanotube by wrapping helically around the 

nanotubes. 304 Molecular modeling studies have 

also shown that chemical cross-linking between a 

nanotube and a polymer matrix can significantly 

enhance load transfer, 305 and that somewhat surprisingly 

such cross links may not significantly 

decrease the high modulus that make nanotubes 

attractive for composite applications in the first 

place. 95 

Molecular modeling studies using classic, tight 

binding, and first principles atomic forces have 

also been used to characterize the plastic deformation 

of uniaxially strained nanotubes. 66,256 These 

345

calculations predicted a Stone-Whales transformation 

that leads to what can be interpreted as 

dislocation formation and motion. Because the 

kink motion involves bond rotation, and bonds 

can have different orientations with respect to the 

nanotube axis for different helical wrappings, the 

calculations predicted that the strength of 

nanotubes depends strongly on their structure. 

Interestingly, the formation of a dislocation results 

in an interface between two nanotubes with 

different helical properties but similar radii, which, 

depending on the structures of the nanotube, can 

result in a metal-semiconductor junction like that 

discussed above. Hence, these calculations lead 

to predictions for specific conditions under which 

these junctions could potentially be made, as well 

as predictions of structures with optimized plastic 

properties for structural materials applications. 

Modeling has indicated that another potentially 

important application of nanotubes is the 

separation of organic molecular mixtures. 70 Simulations 

of diffusive flow of methane/isobutene, 

methane/n-butane, and methane/ethane binary 

mixtures through single nanotubes and nanotube 

bundles were carried out. The simulations showed 

effective separation of the butane structures from 

methane, but that because of the similarity in size 

separation of methane and ethane was as effective. 

The simulations also showed that the helical 

structure of nanotubes has little effect on the diffusion 

coefficients and hence the separation properties, 

but that the radius had a large effect with 

smaller radii structures showing better discrimination 

between different molecules. 

Molecular modeling and tight binding methods 

have also been used to characterize the structural 

and electronic properties of fullerene 

nanocones and nanostructures assembled from 

nanocones. 352 The calculations suggested that depending 

on their radius, these carbon nanocones 

can exhibit conventional cone shapes or can form 

concentric wave-like metastable structures. Furthermore, 

the calculations showed that single 

nanocones can be assembled into extended twodimensional 

structures that can be in a self-similar 

fashion with fivefold symmetry. Predicted electronic 

properties of nanocones indicated that the 

pentagon in the center of a cone is the most probable 

spot for electron field emission, suggesting 

the application of these structures as localized 

electron sources for templating at scales below 

more traditional lithographies. 

2. Nanodiamond Clusters 

The high symmetry of nanotubes helped to 

facilitate much of the successful theory and modeling 

done on these and related systems. In the 

case of nanodiamond clusters, there is a much 

greater variation in structure and perhaps fewer 

clear-cut technological applications, and so less 

has been done in terms of theory leading applications. 

Galli and co-workers used accurate first principles 

methods to characterize the dependence of 

band gap on the size of hydrogen-terminated nanodiamond 

clusters, as well as to predict surface 

reconstructions of clusters without chemisorbed 

hydrogen that are unique to these clusters. 90 The 

calculations indicate that for the hydrogen-terminated 

structures the HOMO-LUMO gap, which is 

given as 8.9 eV for methane, becomes comparable 

to the band gap for bulk diamond for clusters 

as small as 1 nm. This result is in sharp 

contrast to silicon and germanium clusters, which 

show quantum confinement effects for larger clusters. 

The lack of quantum confinement effects in 

diamond clusters is consistent with experimental 

emission and adsorption studies. The first principles 

calculations also predicted surface reconstructions 

without hydrogen termination that had 

significant π character. These structures resemble 

diamond clusters encapsulated in fullerenes and 

have been termed “bucky diamond” clusters. 

While not necessarily suggesting new technological 

applications of these structures, the results of 

these studies do point toward potential limitations 

and opportunities for using nano-diamond clusters 

for nanoelectronics applications. 

Modeling has also been used to characterize 

the bonding and stability of hybrid nanodiamondnanotube 

structures. 278 The modeling studies, 

which included both a many-body classic potential 

and tight-binding calculations, showed that 

several classes of hybrids exist with reasonably 

low-strain structures interfaces. There are several 

possible applications of these systems, including 

346

as arrays of field emitters (Figure 75) and as 

nanoscale diodes (Figure 76). While there are 

indications that such structures have been realized 

experimentally, deliberate experimental studies 

aimed at technological applications of these 

structures have not to date been carried out. 

In an interesting set of calculations, Park, 

Srivastava, and Cho used first principles calculations 

to examine a 31 P atom positioned at the 

center of a diamond nanocrystallite as a solidstate 

binary qubit. 195 The calculations indicated 

that the impurity is much more stable at a substitutional 

site than an interstitial site, and that the 

placement of the impurity is robust with respect 

to diffusion. The calculations also indicated that 

coupling between the nuclear spin and the weakly 

bound (valance) donor electrons is suitable for 

single qubit applications. This result, together with 

the stability of nanotube-diamond hybrid structures, 

suggests that nano-diamond clusters could 

be useful in computing applications. 

V. CONCLUSIONS AND FUTURE 

OUTLOOK 

It is an interesting period in the science of 

carbon, when the different communities such as 

those conducting research on graphite-based materials, 

fullerene nanotubes, and diamond, which 

were working rather independently and are now 

merging into one discipline as their interests converge 

at the nanoscale. There is a clear tendency 

to understand the properties of all-carbon entities 

at the nanoscale within a unified framework, including 

interrelationships between the various 

forms of nanocarbon, conditions under which one 

form transforms to another, and the possibility of 

FIGURE 75. Illustration of a “mushroom” array of nanodiamond-tubule hybrid structures. 

347

FIGURE 76. Illustration of a resonance tunneling diode created from a nanodiamondfullerene 

hybrid structure. 

combining nanocarbon entities into hierarchical 

structures. 

There is increased research activity in the thermodynamics 

and kinetics of carbon at the nanoscale. 

Ab initio level of sophisticated computer simulations 

outlined the sequence of the most stable forms 

of carbon at the nanoscale, which are rings, 

fullerenes, diamond clusters, and graphite particles 

as the system size is increased. Interesting forms of 

nonhydrogenated nanodiamond such as bucky-diamond 

have been discovered, and experimental 

confirmation has been provided. Presumably, there 

are enough data accumulated for the development 

of the three-dimensional carbon phase diagram at 

the nanoscale, where the third parameter is ths size 

of the carbon entity. Tremendous tasks remain to 

be done in order to develop an understanding of the 

general mechanisms of the nucleation and the 

growth of carbon nanospecies under a variety of 

conditions as well as the kinetics of transformation 

between different carbon forms. 

Special attention in the current review had 

been devoted to nanodiamond, which has very 

diverse structures at the nanoscale, ranging from 

individual clusters to high-purity films. As discussed 

in the review, these nanodiamond forms 

can be produced by very diverse techniques, ranging 

from the detonation explosive method to the 

low-pressure CVD method or by the method of 

chlorinating carbides. It is interesting that 

ultradispersed diamond has a long history of application 

in the countries of FSU, before 

nanotechnology became a popular topic, in such 

traditional areas as galvanic coatings, polymer 

composites, polishing, and additions to lubricants. 

It can be easily produced in ton quantities; however, 

it is very hard to produce UDD completely 

free of contamination due to the incombustible 

impurities (metals, nonmetals, and their oxides) 

that are located in interparticle areas within agglomerates 

of UDD particles. A high purity of 

UDD is not required, however, for the traditional 

applications mentioned above. Depending on the 

application, earlier developed technologies for 

UDD purification, surface modification as well as 

aggregate-free UDD suspensions are being developed 

for industrial-scale use. It should be emphasized 

that developing an understanding of the 

relationship between the complex structure of the 

surface of UDD and their physical properties are 

areas of recent very active research. 384 Especially 

important, although very challenging, is developing 

an understanding of the properties of individual 

nanodiamond particles. Regarding novel 

applications of UDD, we pointed out their biomedical 

applications, an area of research that has 

just started to emerge. 

The properties of carbon nanotubes as well 

as their prospective applications have been the 

focus of a variety of reviews and books. In the 

348

present work, we discussed carbon nanotube 

mechanical properties in the context that they 

are very instructive test systems with which 

new concepts for describing the mechanical 

behavior of nanostructures are required. This is 

being addressed by an emerging discipline — 

nanomechanics. We also discussed the prospects 

of the application of carbon nanotubes in 

field emission and nanoelectronic devices. 

While carbon nanotubes are very interesting 

research objects for materials science and solidstate 

physics, their potential electronic applications 

may be somewhat overstated. We believe 

that a more critical assessment of the potential 

of carbon nanotubes for electronics is needed. 

To emphasize the increasing role of atomic 

modeling of carbon nanostructures as a tool 

for developing new materials and technologies 

we included a brief discussion of some 

situations in which theory and modeling has 

led to experiments in developing new technologies 

and applications involving carbon 

nanostructures. 

In conclusion, the carbon family of materials 

at the nanoscale, with its wide diversity of forms, 

is a rapidly developing area from both the point of 

view of fundamental research as well as the current 

and perspective nanotechnological applications. 

ACKNOWLEDGMENTS 

The authors greatly acknowledge the help of 

Gary E. McGuire and John Hren for the critical 

reading of the manuscript; A. Barnard and G. 

Galli for providing their results before publication; 

as well as V. Kuznetsov, V. Dolmatov, A. 

Koscheev, A. Kalachev, T. Daulton, Y. Gogotsy, 

D. Gruen, D. Areshkin, D. Roundy, R. Ruoff, F. 

Ree, J. Viecelli, C. Pickard, V. Harik for very 

fruitful discussions. OAS acknowledges support 

from the Office of Naval Research through contract 

N00014-95-1-0270. DWB acknowledges 

support from the Office of Naval Research through 

contract N00014-95-1-0270 and through a subcontract 

from the University of North Carolina at 

Chapel Hill, and from NASA-Ames and NASA- 

Langly. 

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