shell model for cnt growth

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General hypothesis and shell model for the synthesis of semiconductor nanotubes, including carbon nanotubes S. Noor Mohammad a Sciencotech, 780 Girard St. NW, Washington, DC 20001, USA Received 1 February 2010; accepted 26 June 2010; published online 23 September 2010 Semiconductor nanotubes, including carbon nanotubes, have vast potential for new technology development. The fundamental physics and growth kinetics of these nanotubes are still obscured. Various models developed to elucidate the growth suffer from limited applicability. An in-depth investigation of the fundamentals of nanotube growth has, therefore, been carried out. For this investigation, various features of nanotube growth, and the role of the foreign element catalytic agent FECA in this growth, have been considered. Observed growth anomalies have been analyzed. Based on this analysis, a new shell model and a general hypothesis have been proposed for the growth. The essential element of the shell model is the seed generated from segregation during growth. The seed structure has been defined, and the formation of droplet from this seed has been described. A modified definition of the droplet exhibiting adhesive properties has also been presented. Various characteristics of the droplet, required for alignment and organization of atoms into tubular forms, have been discussed. Employing the shell model, plausible scenarios for the formation of carbon nanotubes, and the variation in the characteristics of these carbon nanotubes have been articulated. The experimental evidences, for example, for the formation of shell around a core, dipole characteristics of the seed, and the existence of nanopores in the seed, have been presented. They appear to justify the validity of the proposed model. The diversities of nanotube characteristics, fundamentals underlying the creation of bamboo-shaped carbon nanotubes, and the impurity generation on the surface of carbon nanotubes have been elucidated. The catalytic action of FECA on growth has been quantified. The applicability of the proposed model to the nanotube growth by a variety of mechanisms has been elaborated. These mechanisms include the vapor-liquid-solid mechanism, the oxide-assisted growth mechanism, the self-catalytic growth mechanism, and the vapor-quasiliquid-solid mechanism. The model appears to explain most, if not all, of the experimental findings reported to date on semiconductor nanotubes. It addresses various issues related to the uniqueness of the single-walled and multiwalled carbon nanotube growths; it explains why almost all carbon nanotubes are grown at a temperature between 800 and 1000 ° C; and why metals, semiconductors, oxides, and clusters serve almost equally well as FECAs to achieve these growths. © 2010 American Institute of Physics. doi:10.1063/1.3474650 I. INTRODUCTION X m Y n nanotubes X and Y are the nanotube elements; X may be metal and Y nonmetal; m and n are integers; and one of them may be zero are fascinating new quasi-one- dimensional materials with potentials for applications in nanobiochemistry, nanoelectronics, optics, and materials science. 118 These nanotubes are synthesized widely by making use of foreign element catalytic agents FECAs. They may exhibit extraordinary strength and unique electrical properties. They may also be efficient thermal con- ductors. They include carbon X=C, Y=0, m=1, n=0 nanotubes, GaN X=Ga, Y=N, m=n=1 nanotubes, BN X=B, Y=N, m=n=1 nanotubes, ZnO X=Zn, Y=O, m=n=1 nanotubes, InP X=In, Y=P, m=n=1 nanotubes, and CN X=C, Y=N, m=1, n= nano- tubes. Among them, carbon nanotubes have been studied 4,16 extensively. These carbon nanotubes are allotropes of carbon and have a cylindrical nanostructure. They are members of the fullerene structural family. They can have length-to- diameter ratio of up to 2.8 10 7 to 1, which is very large. They can be good semiconductors, and be grown as single- walled carbon nanotubes SWCNTs, double-walled carbon nanotubes DWCNTs, and multiwalled carbon nanotubes MWCNTs. Among other semiconductor nanotubes, 1729 GaN nanotubes, 19,20 synthesized first in our laboratories, are nearly transparent. They are as stable as carbon nanotubes. They can be synthesized also under extreme conditions. Pure BN nanotubes 21,24 have been produced by arc discharge and laser ablation. The realization of GaN and BN nanotubes suggests the possibility of forming also CN, AlN, and InN nanotubes. Figure 1 lists nine representative nanotubes, NT-1 to NT-9, synthesized so far by experimental techniques. Among them, NT-1 has single wall, FECA at the base but not at the head. 30 NT-2 has a single wall, FECA at the head but not at the base. 31 NT-3 has a single wall and FECA at both the head and the base. NT-4 has a single wall encapsulating FECA all throughout from the base to the head. 32,34 NT-5 has multiple walls encapsulating a FECA at the base. NT-6 has a single wall, a spherical seed at the tip of the wall but no a Associated also with the U.S. Naval Research Laboratory, Washington, DC. Electronic mail: [email protected]. JOURNAL OF APPLIED PHYSICS 108, 064323 2010 0021-8979/2010/1086/064323/26/$30.00 © 2010 American Institute of Physics 108, 064323-1

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Reasons on how CNTs grow

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Page 1: Shell Model for CNT Growth

General hypothesis and shell model for the synthesis of semiconductornanotubes, including carbon nanotubes

S. Noor Mohammada�

Sciencotech, 780 Girard St. NW, Washington, DC 20001, USA

�Received 1 February 2010; accepted 26 June 2010; published online 23 September 2010�

Semiconductor nanotubes, including carbon nanotubes, have vast potential for new technologydevelopment. The fundamental physics and growth kinetics of these nanotubes are still obscured.Various models developed to elucidate the growth suffer from limited applicability. An in-depthinvestigation of the fundamentals of nanotube growth has, therefore, been carried out. For thisinvestigation, various features of nanotube growth, and the role of the foreign element catalyticagent �FECA� in this growth, have been considered. Observed growth anomalies have beenanalyzed. Based on this analysis, a new shell model and a general hypothesis have been proposedfor the growth. The essential element of the shell model is the seed generated from segregationduring growth. The seed structure has been defined, and the formation of droplet from this seed hasbeen described. A modified definition of the droplet exhibiting adhesive properties has also beenpresented. Various characteristics of the droplet, required for alignment and organization of atomsinto tubular forms, have been discussed. Employing the shell model, plausible scenarios for theformation of carbon nanotubes, and the variation in the characteristics of these carbon nanotubeshave been articulated. The experimental evidences, for example, for the formation of shell arounda core, dipole characteristics of the seed, and the existence of nanopores in the seed, have beenpresented. They appear to justify the validity of the proposed model. The diversities of nanotubecharacteristics, fundamentals underlying the creation of bamboo-shaped carbon nanotubes, and theimpurity generation on the surface of carbon nanotubes have been elucidated. The catalytic actionof FECA on growth has been quantified. The applicability of the proposed model to the nanotubegrowth by a variety of mechanisms has been elaborated. These mechanisms include thevapor-liquid-solid mechanism, the oxide-assisted growth mechanism, the self-catalytic growthmechanism, and the vapor-quasiliquid-solid mechanism. The model appears to explain most, if notall, of the experimental findings reported to date on semiconductor nanotubes. It addresses variousissues related to the uniqueness of the single-walled and multiwalled carbon nanotube growths; itexplains why almost all carbon nanotubes are grown at a temperature between 800 and 1000 °C;and why metals, semiconductors, oxides, and clusters serve almost equally well as FECAs toachieve these growths. © 2010 American Institute of Physics. �doi:10.1063/1.3474650�

I. INTRODUCTION

XmYn nanotubes �X and Y are the nanotube elements;X may be metal and Y nonmetal; m and n are integers;and one of them may be zero� are fascinating new quasi-one-dimensional materials with potentials for applications innanobiochemistry, nanoelectronics, optics, and materialsscience.1–18 These nanotubes are synthesized widely bymaking use of foreign element catalytic agents �FECAs�.They may exhibit extraordinary strength and uniqueelectrical properties. They may also be efficient thermal con-ductors. They include carbon �X=C, Y=0, m=1, n=0�nanotubes, GaN �X=Ga, Y=N, m=n=1� nanotubes, BN�X=B, Y=N, m=n=1� nanotubes, ZnO �X=Zn,Y=O, m=n=1� nanotubes, InP �X=In, Y=P, m=n=1�nanotubes, and CN� �X=C, Y=N, m=1, n=�� nano-tubes. Among them, carbon nanotubes have been studied4,16

extensively. These carbon nanotubes are allotropes of carbonand have a cylindrical nanostructure. They are members of

the fullerene structural family. They can have length-to-diameter ratio of up to 2.8�107 to 1, which is very large.They can be good semiconductors, and be grown as single-walled carbon nanotubes �SWCNTs�, double-walled carbonnanotubes �DWCNTs�, and multiwalled carbon nanotubes�MWCNTs�. Among other semiconductor nanotubes,17–29

GaN nanotubes,19,20 synthesized first in our laboratories, arenearly transparent. They are as stable as carbon nanotubes.They can be synthesized also under extreme conditions. PureBN nanotubes21,24 have been produced by arc discharge andlaser ablation. The realization of GaN and BN nanotubessuggests the possibility of forming also CN, AlN, and InNnanotubes. Figure 1 lists nine representative nanotubes, NT-1to NT-9, synthesized so far by experimental techniques.Among them, NT-1 has single wall, FECA at the base but notat the head.30 NT-2 has a single wall, FECA at the head butnot at the base.31 NT-3 has a single wall and FECA at boththe head and the base. NT-4 has a single wall encapsulatingFECA all throughout from the base to the head.32,34 NT-5 hasmultiple walls encapsulating a FECA at the base. NT-6 has asingle wall, a spherical seed at the tip of the wall but no

a�Associated also with the U.S. Naval Research Laboratory, Washington,DC. Electronic mail: [email protected].

JOURNAL OF APPLIED PHYSICS 108, 064323 �2010�

0021-8979/2010/108�6�/064323/26/$30.00 © 2010 American Institute of Physics108, 064323-1

Page 2: Shell Model for CNT Growth

FECA at the base.35 NT-7 has multiple walls, a seed at thetips of the walls, a FECA at the nanotube head but no FECAat the nanotube base. NT-8 has multiple walls, a sphericalseed at the tips of the walls but no FECA at the base.30 NT-9has a single wall, a seed at the tip of the wall, a FECA at thehead of the nanotube, and multiple diaphragms.36,37

During the past years, significant progress has beenmade in the synthesis of XmYn nanotubes, particularly car-bon nanotubes. Yet, the growth mechanism of the nanotubeshas not been fully understood. A number of models havebeen conjectured to explain nanotube growth. These modelsinclude base growth model,1 tip growth model,1 crystalliza-tion model,2 and schooter model.4 The FECA, in the basegrowth model, remains anchored to the base while nanotubegrows. But the FECA, in the tip growth model, remains atthe nanotube tip, while nanotube grows. The formation ofnanotube, in the crystallization model,2 is actually a crystal-lization process, which begins at the surface �e.g., externalperiphery� but progresses toward the center. The FECA, inthe scooter model,4 is attached to the dangling bonds at thenanotube ends, and acts as a dynamic bridge for the incom-ing nanotube vapor species. It serves as an agent to incorpo-rate these vapor species into the open ends of the nanotubepromoting nanotube growth. Unfortunately, none of thesemodels appears to exhibit wide applicability. The catalyticrole of foreign elements in the nanotube growth is still ob-

scured. The influence of temperature, pressure, and heatingrate on the nanotube growth, and the fundamentals, for ex-ample, of bamboo shaped36,38 nanotubes, have not also beenexplained well. There is no consensus yet on the mechanismgoverning the nanotube growth. Our objective in this inves-tigation is to address them in some details, and to describe ageneral hypothesis governing the nanotube growths.

II. GROWTH TECHNIQUES

Nanotubes can today be synthesized by many physicaland chemical deposition techniques.1,3 These include boththe high-temperature and medium-temperature techniques.1,3

Among them, the high-temperature techniques �e.g., laser ab-lation, arc discharge, pyrolysis, etc.� involve simultaneousevaporation of both FECA and tube-containing materials athigh temperatures. The formation of nanotubes takes place,however, at lower temperatures. These techniques producehigh-quality nanotubes, and also provide some control intheir diameters, electronic properties, optical properties, andbiological properties. But they are not very compatible withconditions required for device fabrications. They do not suitlarge-scale technology development. In the present investiga-tion, we, therefore, resort primarily to medium-temperaturetechnique �e.g., chemical vapor deposition �CVD��. We as-sume that the nanotube-containing vapors �for instance, car-bon vapors or their precursors for carbon nanotube growth;Ga and N vapors or their precursors for GaN nanotubegrowth�, referred hereafter to as the RS species, play centralrole in the CVD growth.

For the sake of convenience, the properties of some ofthe FECAs are listed in Table I. These properties includeFECA melting temperature TM, FECA/carbon eutectic tem-perature TE, atomic percent of FECA in the FECA/carbonalloy, molar volume �FECA, liquid-solid surface energy �LS,and the enthalpy of melting HL. The FECAs include thecommonly used transition metals such as nickel, cobalt, andiron; semiconductors such as SiC, Si, and Ge; and oxidessuch as SiO2. One can see from Table I that the solubility ofcarbon in FECA solution is quite low at the eutectic tempera-ture TE. It is, for example, only 2.6 at. % for the Co/C eu-tectic solution, and 4.2 at. % for the Fe/C eutectic solution.

III. OBSERVED GROWTH ANOMALIES

A. Background

FECAs are believed to play determining roles in the syn-thesis of carbon nanotubes. Under the influence of FECA�s�,the carbon atoms, during diffusion through molten FECA�s�,organize into a graphitic nanotube structure. Bimetallic FE-CAs, such as cobalt–molybdenum,39 iron-–molybdenum,40

and iron–cobalt41 compounds, increase the carbon nanotubeyields. Transition metals are especially suitable for the exo-thermic decomposition of carbon radicals �e.g., CHx, C2Hy,C3Hz, etc.�. Metal oxide FECAs combine with hydrocarbons�e.g., CO, CH4, C2H2, C2H4, C6H6, etc.� to form carbon radi-cals. The FECA nanoparticles, if bound to the growing edge,inhibit the formation of carbon pentagons, and catalyze theformation of carbon hexagons. They anneal the defects thattend to terminate the nanotube growth.42

NT-1

NT-7

NT-5

NT-2 NT-3

NT-6NT-4

NT-8 NT-9

FIG. 1. �Color online� Schematic diagrams showing nine different represen-tative nanotubes �NT-1 to NT-9�. The nanotube sidewalls are shown in deepgreen, the nanotube seeds are shown in red, and the FECA is shown inpurple �violet�. The FECA may lie at the nanotube base �see NT-1, NT-3,NT-5� or at the nanotube head �see NT-2, NT-3, NT-7, and NT-9�. Thenanotube may also be filled with FECA �see NT-4�.

064323-2 S. Noor Mohammad J. Appl. Phys. 108, 064323 �2010�

Page 3: Shell Model for CNT Growth

B. Catalytic and size-dependent effects

Carbon nanotube �XmYn, X=C, Y=0, m=1, n=0�growth has recently been achieved also with agents believedto be noncatalytic agents. These include metals43,44 such asAu, Cu, Pt, and Pd; semiconductors45 such as SiC, Si, andGe; and oxides46 such as SiO2, Al2O3, and TiO2. Carbonnanotube growth, both with catalytic and noncatalytic agents,has been achieved at temperatures T far lower than theFECA/X eutectic temperature TE. Some of these growths,realized primarily by the CVD technique, arelisted35,38,39,43,52 in Table II. FECA species, precursors of thereactive RS vapor species, and the actual growth tempera-tures, are presented in this table. A close look of various dataof Tables I and II indicates that nanotube growths have

indeed been possible at T�TE. To be more specific, we citetwo examples. The equilibrium eutectic temperature TE ofNi/C alloy exceeds 1320 °C. The melting temperature TM ofNi is 1453 °C. Yet, using FECA�Ni, 60 to 80 nm in diam-eter, carbon nanotubes were grown47 at a temperature as lowas 650 °C. The equilibrium eutectic temperature TE of Re/Calloy exceeds 2500 °C. The melting temperature TM of rhe-nium is 3180 °C. Yet, using FECA�Re, 6 to 8 nm in diam-eter, carbon nanotubes were grown51 at a temperature as lowas 950 °C. Two reasons are put forth to justify thesegrowths. These are the size-dependent melting pointdepression53,55 of the FECA nanoparticle and the solubilityof X�C in the FECA nanoparticle. The size-dependent re-duction �TM of the melting temperature TM of a FECAnanoparticle of radius rD may be given by

TABLE I. List of input data used for the calculations of the size-dependent and solubility-dependent meltingtemperature depression of some representative FECA/carbon �FECA�Au,Al,Cu,Ag,Fe,Ni,Co, etc.� materi-als �e.g., mixtures, solid solutions, or eutectic/noneutectic alloys�. TM is the melting temperature, HL is the latentheat of fusion, �FECA is the molar volume, and �LS is the surface energy.

FECA/C FECA parameters

No. FECA

Eutectictemperature TE

�°C�Atomic

percentageTM

�°C�HL

�kJ/mol��LS

�J /m2��FECA

�cm3 /mol�

1 Au 1027 Au�99.93% 1065 36.95 1.541 13.6C�0.07%

2 Al ¯ ¯ 660 10.71 1.180 9.503 Cu 1070 Cu�99.999% 1084 13.26 1.77 7.11

C�0.001%4 Cr 1534 Cr�86% 1857 16.90 2.006 7.040

C�14%5 Mn 1232 Mn�97.1% 1246 12.05 1.298 7.35

C�2.9%6 Fe 1153 Fe�82% 1535 13.81 2.361 7.09

C�18%7 Ni 1327 Ni�99.2% 1453 17.48 2.24 6.59

C�0.8%8 Co 1320 Co�97.4% 1495 16.20 2.161 6.66

C�2.6%9 Hf 2209 Hf�97.5% 2227 24.05 1.923 13.37

C�2.5%10 Pt 1738 Pt�98.8% 1772 19.7 1.286 9.02

C�1.2%11 Pd ¯ ¯ 1552 17.60 0.886 8.7812 Re 2500 Re�99.3% 3180 33.21 2.00 8.81

C�0.7%13 Ru 1953 Ru�97.5% 2250 24.00 8.17

C�2.5%14 Mo 2221 Mo�82.5% 2617 32.00 2.510 9.35

C�17.5%15 Pb ¯ ¯ 327 4.79 0.540 18.2716 W 2720 W�78% 3407 35.40 2.990 9.50

C�22%17 Nb 2367 Nb�95% 2468 26.40 2.313 10.75

C�5%18 Ti 1643 Ti�99.5% 1660 15.45 1.92 10.55

C�1.5%19 V 1625 V�86% 1902 20.91 2.301 8.25

C�14%20 C�amorphous� ¯ ¯ 3675

064323-3 S. Noor Mohammad J. Appl. Phys. 108, 064323 �2010�

Page 4: Shell Model for CNT Growth

�TM =2�LS�LSTM

rDHL. �1�

This size-dependent melting point depression was calcu-lated for a number of FECA nanoparticles, including Ni, Co,Fe, Pt, and Re. Various parameters used for the calculationswere taken from Table I. The results for Ni, Au, and Fe aredepicted in Fig. 2. One can see that the melting point depres-sion is very high for very small FECA nanoparticles, and thatit decreases almost exponentially with increase in FECA

nanoparticle dimension. The melting point depression for Ninanoparticles, 50 nm in diameter, is 3.38%. The melting tem-perature of these Ni nanoparticles, 50 nm in diameter, is,therefore, 1404 °C. This is 754 °C higher than the oneachieved by Okai et al.47 The melting point depression forRe nanoparticles �not plotted in Fig. 2�, 8 nm in diameter, is26%. The melting temperature of Re nanoparticles, 8 nm indiameter, is, therefore, 2353 °C, which is 1403 °C higherthan that obtained by Ritschel et al.51 All these suggest that

TABLE II. List of growth temperatures, carbon sources, and FECAs used for the growths of some representative carbon nanotubes by the CVD.

No. Carbon source FECA nanoparticlesGrowth temperature

�°C� Comments Refs.

1 CO /H2 Fe/Mo nanoparticles, 900Growth by CVD for 10 min produced oriented, long SWCNT

arrays; nanoparticle size was �4.2 nm 35

2 CH4 /H2 Fe/Mo nanoparticles 900Grown by CVD for 10 min; straight individual SWCNTs up to

2.1 mm in length were realized 35

3 CO /H2 Fe/Pt nanoparticles 900Growth by CVD for 20 min produced individual, parallel,

straight SWCNTs, up to 3.9 mm in length. 354 CO /H2 Fe/Mo molecular clusters 900 Growth by CVD for 10 min produced arrays of SWCNTs 355 CH3OH /H2 /Ar Fe/Mo nanoparticles 900 Growth by CVD for 10 min produced long SWCNTs 35

6 CO /H2 Fe/Mo nanoparticles 900Growth by CVD for 10 min produced short and randomly

oriented SWCNTs. 35

7 C2H4 /NH3 Ni nanoparticles 800–900

Growth by CVD produced vertically aligned MWCNTs oflength up to 29 �m. The growth period was 10 min and the

chamber pressure was 1 atm. 38

8 CO Co, Mo precursors 700CVD growth for 3 to 60 min produced bundles of SWCNTs, 1

nm in diameter, on SiO2 �gel� substrate. 39

9 Ethanol vapor Au, Ag, Pt, Pd nanoparticles 850

CVD growth on Al-hydroxide films employing Au, Ag, Pt, orPd nanoparticles, about 3 nm in dimension, produced

SWCNTs. 43

10 Ethanol vapor Cu, Fe, Co, Ni nanoparticles 850CVD growth on Al-hydroxide films employing Cu, Fe, Co, or

Ni nanoparticles, about 3 nm in dimension, produced SWCNTs. 4311

CH4, ethanol,Cu 825–850 CVD growth on silicon substrate produced random networks of

SWCNTs. Ar and/or H2 were used as carrier gas. Cu wasderived from CuCl2.

44

Isopropanol

12 Ethanol vapor SiC, Si, Ge nanoparticles 850

Ar /H2 was used as carrier gas. The CVD growth rate with Geparticles was higher than that with SiC and Si particles. The

nanoparticle sizes were less than 5 nm. 45

13 CH4 SiO2, Al2O3, TiO2, Er2O3 900

CVD growth produced long, oriented SWCNTs, 0.8 to 1.4 nmin diameter, on Si substrate. The substrate was thermally

annealed before growth. 46

14 CH4 /H2 Ni, FeuNiuCr alloy 650

PECVD growth on �1� Ni substrate and �2� FeuNiuCr alloysubstrate under a pressure of 250–300 Pa for 30–60 min

produced SWCNTs with metal at the tips. The nanoparticlediameter varied between 60 and 80 nm. 47

15 CH4, C2H2 Co, Mo precursors 900CVD growth for 10 to 60 min produced SWCNTs andDWCNTs in an environment of SiO2 �oxidized silicon�. 48

16 CO Mo precursors 1200CVD growth for 60 min produced bundles of SWCNTs, 1 to

1.7 nm in diameter, on Al2O3 substrate. 49

17 CH4 Fe 600–800

CVD growth for 5 min produced SWCNTs, 1 to 5 nm indiameter and up to several microns in length on Al2O3

substrate. 50

18 CH4 Re nanoparticles 950–1100

CVD growth of SWCNTs, DWCNTs, and MWCNTs wasperformed. The nanotube diameters were 5 to 8 nm. ResonanceRaman spectrum suggests that carbon nanotubes resulted from

defective shell structure. 51

19 CH4 Fe, Co 800–950

CVD growth produced SWCNTs on Si substrate. The particlesize was 30 nm. The lowest growth temperature was 900 °C

for Fe but 800 °C for Co. 52

20 C2H2 /H2 Fe3C 600

CVD growth produced both SWCNTs and MWCNTs on theSiO2 surface of Si substrate. Structural fluctuation of

nanoparticles promoted the nanotube growths. 70

064323-4 S. Noor Mohammad J. Appl. Phys. 108, 064323 �2010�

Page 5: Shell Model for CNT Growth

there may be other reasons for larger melting temperaturedepression achieved in experiments. These are particularlyimportant, because they shed light on the validity/invalidityof the available growth models.1,3 Bulk diffusion of the RS

species through the FECA nanoparticles is key to these mod-els.

C. Limited solubility in FECA

Metals and oxides, such as Au, Cu, Pd, SiO2, Al2O3,TiO2, etc. do not have carbon solubility in the bulk phase.The maximum solubility of carbon in Ni is 2.7 at. % and inRe is 0.7 at. %. Yet they produced SWCNTs. The reduction�TS of the melting temperature TM of a FECA nanoparticlein an ideal solution may be given by

�TS = �kBTM2

HLxS, �2�

where kB is the Boltzmann constant and xS is the atomicpercent of the solute in the solution. For carbon nanotubegrowth employing FECA/carbon alloy, FECA is the solventand carbon is the solute. HL is again the enthalpy of meltingof the solute.

We employed Eq. �2� to carry out calculations for themelting point depression of the solutions of carbon in Ni, Co,Fe, and Re, respectively. Various parameters used for thesecalculations were taken from Table I. The results are pre-sented in Fig. 3. This figure shows that the melting pointdepression increases with increase in solubility of carbon inthe metal. This depression, for example, for carbon solubilityof 2.7 at. % in Ni, is about 2.4%. Corresponding to this solu-bility, the melting temperature of the NiuC solution is1295 °C, which is 645 °C higher than the one achieved byOkai et al.47 Carbon solubility51 in Re is less than 1.0 at. %.Corresponding to this solubility, the melting temperature de-pression is about 1.2%, which is only 38 °C. This depression�e.g. 38 °C� is about 910 °C smaller than the one obtainedby Ritchel et al.51

The solubility of carbon in Fe, Co, Ni, Pd, and Cu at themelting temperature TM, as given by Moisala et al.,3 is 20.2

at. %, 13.9 at. %, 10.7 at. %, 5.0 at. %, and 2�10−4 at. %,respectively. The solubility of carbon in Au, as given byOkamoto and Massalski,56 varies between 0.3 at. % at600 °C to 0.7 at. % at 1027 °C. Let us now examine Fig. 3.It shows that, for carbon solubility of 20.3 at. % in Fe, thedepression is about 20%. For carbon solubility of 13.9 at. %in Co, it is about 15%. And, for carbon solubility of 0.7 at. %in Au, it is about 1%. Corresponding to these solubilities, themelting temperature of the �Fe,C� solution is 1225 °C, themelting temperature of the �Co,C� solution is 1270 °C, andthe melting temperature of the �Au,C� solution is 1050 °C.These are much higher than the melting temperatures �600 to900 °C� of �Fe,C�, �Co,C�, and �Au,C� solutions listed inTable II. To be specific, a reduction in melting temperature to700 °C, for example, of the �Co,C� solution, observed ex-perimentally by Alveraz et al.,39 is much higher than thereduction in melting temperature of this solution to 1270 °C,as obtained from our calculations. This suggests that the ac-tual role of FECA particles such as Fe, Co, Ni, etc., has notyet been fully understood.

D. Others

There are other problems, as well. Based on the existingmodel, the carbon nanotube growth is either the tip growth orthe base growth. But, none of them can explain the growth ofnanotubes fully filled with metal core. The basic feature ofthe base growth model is the carbon dissolution and diffu-sion through the molten FECA nanoparticle. When super-saturated, carbon precipitates on the top of the FECA surfacein a crystalline tubular form. The nanotube grows on theFECA surface with the FECA anchored to the substrate andalso encapsulated by the growing nanotube. However, thereduction in the melting temperature of FECA, when encap-sulated by the growing nanotube, may be suppressed due toincrease in size of the FECA core.3,11 Suppression of thereduction in melting temperature counters the base growth.The surface of the nanotubes is often filled with impurities.These impurities in carbon nanotubes are multishell carbonnanocapsules, both empty and filled with FECA; amorphous

FIG. 2. The calculated variation in the size-dependent melting point depres-sion �e.g., �TM /TM� with the nanoparticle radius for Au, Ni, and Fe nano-particles, respectively. TM is the melting point of the nanoparticle.

FIG. 3. The calculated solubility-dependent melting point depression forAu, Ni, Co, and Fe nanoparticles, respectively.

064323-5 S. Noor Mohammad J. Appl. Phys. 108, 064323 �2010�

Page 6: Shell Model for CNT Growth

carbon nanoparticles; and fullerenes.57 The formation ofthese impurities may not be explained by the existing mod-els.

Recently, both SWCNTs and MWCNTs have been pro-duced employing FECAs such as Pd, Pt, Au, Cu, Ag, and Al,respectively. Even if we assume that the FECA nanoparticleson the substrate surface are molten, the most pressing ques-tion is: how could nanotubes be formed from carbon atomsthat do not really dissolve into a molten FECA? The ob-served carbon nanotube growth rate with FECA�Au iscomparable58 with that with FECA�Fe. It is unlikely that, atT850 °C, the carbon solubility in Au ��0.07 at. % car-bon solubility in the Au bulk� increases to the level of carbonsolubility in Fe �18 at. % carbon solubility in the Fe bulk�simply because both of them exhibit nanosize.59 It is alsovery unlikely that the carbon solubility increases in Au butnot in Fe. The melting point of Ge, Si, and SiC are 965 °C,1420 °C, and 2000 °C, respectively. Takagi et al.45 ob-served higher growth rate with Ge than with Si and SiC.They argued that, while mediating the carbon nanotubegrowth, Ge nanoparticles were molten but the Si and SiCnanoparticles were solid. This contradicts the finding of Gor-bunov et al.,60 which indicates that the diffusion rate of car-bon is one to two order of magnitude lower in solid than inliquid. Based on this, the carbon nanotube growth rate withSi and SiC nanoparticles would be marginally low. De Bokxet al.61 proposed that, during FECA-mediated carbon nano-tube growth, catalyst is converted into metal carbides beforedecomposing to graphene layers. This contradicts the ob-served Re-mediated carbon nanotube growth by Ritschel etal.51 The solubility of carbon in Re is too low �lower than 1at. % in bulk Re� to produce rhenium carbide. Theexperiment62 indicates that the formation of rhenium carbideis not really possible.

IV. PROPOSED MECHANISM FOR NANOTUBEGROWTHS

A. Background

To our knowledge, XmYn nanotubes are currently syn-thesized by FECA-mediated growth mechanisms63,64 �for ex-ample, the vapor-liquid-solid �VLS� mechanism�. These aresynthesized also by the self-catalytic growth �SCG�mechanism19,65,66 and the oxide-assisted growth �OAG�mechanism.67,68 The FECA-mediated growth mechanismmakes use of FECAs for growth.45,69,70 This growth can be atboth TTE and TTE. It is the VLS growth,27 if it is atT�TE. But it is the VQS �vapor-quasiliquid-solid or vapor-quasisolid-solid� growth,71 if it is at TTE. It is the SCG orOAG if it is at T�TM. Depending on growth conditions,SCG and OAG may take place at temperatures far lower thanTM. The VLS mechanism makes use of �FECA, X� eutecticdroplet to mediate nanotube growth. The VQS mechanismmakes use of �FECA, X� noneutectic droplet to mediatenanotube growth. FECA�X for the growth of XmYn nano-tubes by both the VLS and the VQS mechanisms. The OAGmechanism makes use of a X-metal oxide with or withoutthe assistance of oxygenated FECA for the growth. The SCGmechanism does not make use of any of them for the growth.

Rather, it makes use of the X element of the XmYn nanotubeto be grown. So, FECA�X for the growth of XmYn nano-tube by the SCG mechanism. Both the adatom-induced pro-cess and the diffusion-induced process contribute to thenanotube growth. We argue that seeds, rather than FECAnanoparticles, play a central role in the nanotube growth.First, a seed is formed. The seed is made of disordered �e.g.,polycrystalline, amorphous, etc.� metal X in the SCG mecha-nism, oxygenated metal X �or a combination of oxygenatedmetal X and FECA� in the OAG mechanism, and FECA/Xmaterial in the FECA-mediated mechanism. The FECA/Xmaterial may be a eutectic solution, a noneutectic solution, orjust a solid mixture of FECA and X. If the solubility of X inFECA is very low, the FECA/X material may simply beFECA with X as contaminant inside it. The material contentof the seed may be called the RL species. For the FECA-mediated growth, this RL species is the FECA/X material;RL��FECA,X�. But for the OAG, this RL species is theoxygenated X material �or a combination of oxygenated Xmaterial and FECA; RL��FECA,X,O�. The seed is eventu-ally converted into droplet, which should preferably be mol-ten �semimolten� to mediate growth. The RS species diffusesthrough the droplet, and is supersaturated/nucleated to pro-duce nanotubes. The droplet remains at the nanowall tip �oreven the entire nanotube head� as the nanotube grows. Thenanotube growth takes place at the liquid/solid �L/S� inter-face by two-dimensional nucleation. The solid of the L/Sinterface is the substrate at the initiation of the growth but isthe nanotube tip during the subsequent stages of the growth.The nanotube tip is the edge of the nanotube just underneaththe droplet. The liquid of the L/S interface is always thedroplet �e.g., molten or semimolten seed�.

Various processes for nanotube growth by the RS vaporspecies are shown schematically in Fig. 4, where the dropletis the NSC droplet �defined in Sec. IV D in the following�.The RS species may have four components: RSI, RSS, RSW,and RSV. So, RS=RSI+RSS+RSW+RSV. Among the fourcomponents, the RSI species participates in the adatom-induced process, the RSS and RSW species participate in thediffusion-induced process, but the RSV species remains in thevapor phase. It participates in none of them. As shown inFig. 4, one or more of the following events �related to RSI,RSS, RSV, and/or RSW� takes place during growth: �1� Directlanding of the RSI species on the droplet surface. �2� Desorp-tion, if any, of the RSI species from the droplet surface. �3�Direct impingement of the RSS species on the substrate sur-face �at location P�. �4� The diffusion of the RSS species fromthe location P of impingement to the nanotube base Qthrough the substrate surface. �5� The diffusion of the RSS

species from the nanotube base to the droplet. �6� The directimpingement of the RSW species at or very near the nanotubebase. �7� The diffusion of the RSW species from the nanotubebase to the droplet �not shown in Fig. 4�. These are followedby the adsorption of the RS species into the droplet, and thenucleation of this species at the L/S interface. The diffusionof the RSS species from the point P to the point Q woulddepend on the distance PQ=rM. The nanotube length LNT

would similarly depend on the diffusion rate of the RS spe-cies through the droplet. The nanotube thickness �e.g., the

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distance between the outer wall D1 and the inner wall D2�would be the function of growth conditions. Depending ongrowth conditions, the concentration of the RSW species at orvery near the nanotube base may be very low. The growth bythe RSW species at the nonactivated nanotube walls may alsobe marginally low. All these are shown schematically in Fig.4.

B. Nanotube growth features

The CVD technique is a good example for the medium-temperature �for example, �1200 K for carbon nanotube�growth. It provides high purity, high yield; and produces ver-tically aligned nanotubes. The salient features of the nano-tube growth by the CVD technique are shown in Table III.As apparent from this table, a thin matrix is first formed onthe substrate. This is followed by the formation of a very thinactive layer on the matrix. Rapid thermal annealing is thenperformed. During this annealing, the active layer materialdiffuses into the matrix and reacts with it creating the seedlayer. Also, the seed layer, thus formed, is split into tiny

nanoparticles. The seed layer for the OAG is made of sub-oxide �e.g., SiO for SiO2-assisted growth, Ga2O forGa2O3-assisted growth; In2O for In2O3-assisted growth�. Alarge number of nuclei are generated on the substrate surface.The nuclei grow independently. We cite some examples. ForSCG of GaN nanotubes,19,20 the matrix is made of polycrys-talline GaN, the thin layer on the top of it is made of Ga, andthe seed layer is Ga-rich GaN layer. For OAG of InPnanotubes,25 the matrix is made of In2O3, the thin activelayer on the top of it is made of In, and the seed layer madefrom them is In2O. For FECA-mediated carbon nanotubegrowth,1,3 the matrix is made of one or more of FECAs �forexample, FECA�Fe,Ni,Co,Mo, etc.�, the thin active layeris made of carbon, and the seed layer is made of FECA/carbon material. Based on these, it may be noted that FECAnanoparticles are different from seed nanoparticles. For Fe-mediated carbon nanotube growth, the FECA nanoparticle isFe; but the seed nanoparticle is Fe/C material.

The size of the seed nanoparticles may be on the sameorder as the desired diameter of the XmYnnanotubes. Duringgrowth, the substrate is heated to an optimal temperature.The carrier gas �for example, argon, ammonia, nitrogen, orhydrogen� and the tube-containing RS�X and RS�Y spe-cies are fed into the chamber. The tube-containing gases forcarbon nanotubes are C vapors but for GaN nanotubes are Gaand N vapors. The precursors of the tube-containing gasesfor carbon nanotubes may be CO, acetylene, ethylene, etha-nol, and methane. They release RS�X�C upon landing �orprior to landing� on the matrix surface. RS�X�C is pro-duced by the catalytic decomposition of the precursor. Henceit is extremely mobile on the matrix surface. If driven by atemperature or concentration gradient under appropriategrowth conditions, it diffuses readily into the FECA matrixcreating FECA/X seed nanoparticle. The diffusion of X intothe FECA nanoparticle may be nonuniform. This diffusion ofX may be the highest at the center and the lowest at theperiphery of the FECA nanoparticle.

Nucleation is key to XmYn nanotube growth. For thisnucleation, RS�X and RS�Y vapors or their precursors areflown into the chamber together with carrier gases �H2, N2,NH3, etc.�. The RS�X and RS�Y vapor atoms produceactive RS�XmYn molecules, which diffuse through thedroplet. The RL species of the droplet fluctuates. Upon su-persaturation at the L/S interface, the RS�XmYn moleculesprecipitate to form crystalline tube. The diffusion of RS

�XmYn molecules through the fluctuating RL species andtheir supersaturation at the L/S interface facilitate the orga-nization of the XmYn molecules into tubular form. The tubeis collected from the synthesis zone of the reactor.

P

Q

RSIRSS

X

Z

Y

3 5

3 4

R

LNT

rM

6

1 2

D2

D1

Droplet capHollowNT core

FIG. 4. �Color online� The nanotube growth by the adsorption-induced pro-cess �e.g., by direct landing of the RSI species on the droplet surface� and thediffusion-induced process �e.g., impingement of the RSS species on the sub-strate surface�. The numeral 1 corresponds to landing and adsorption of theRSI species directly into the droplet surface; the numeral 2 to desorption ofthe RSI species from the droplet surface; the numeral 3 to impingement ofthe RSS species on location P of the substrate surface; the numeral 4 todiffusion of the RSS species from the substrate surface location P to thenanotube base Q; the numeral 5 to diffusion of the RSS species from thenanotube base to the droplet surface; and the numeral 6 to impingement ofadatoms at or near the nanotube base. The nanotube length is LNT, theexternal nanotube diameter is D1, and the internal nanotube diameter is D2.The center of the nanotube base is the origin of the coordinate system, andthe distance between the points P and Q is rM.

TABLE III. List of material Layer structures created for the nanotube growth by various mechanisms.

Mechanism Substrate Matrix Thin active layer Seed material Core Shell

SCG Si XmYn material X X-containing XmYn XXmYn material

OAG Si X-oxide X X-suboxide X-oxide XFECA-mediated growth Si FECA material�s� X FECA/X solid solution FECA FECA/X

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C. Segregation

Segregation is central to the nanotube growth. Depend-ing on the material characteristics of the active layer, mate-rial characteristics of the matrix, the size of the seed nano-particle, the temperature and pressure gradients, and the Xconcentration, the solubility limit of X �X=C, Y=0, m=1,and n=0 for carbon nanotube growth; X=Ga, Y=N, m=n=1 for GaN nanotube growth; X=In, Y=P, m=n=1 for InPnanotube growth� in the seed material decreases during cool-ing. During this cooling, X of the seed material starts tosegregate. The segregation increases as the temperature de-creases. The segregation is the highest near the solidificationpoint. At or below the solidification point, there is equilib-rium but no further segregation. The segregation is completeat the equilibrium at which there is a core surrounded by ashell. The core and the shell are attached to each other.

For FECA-mediated growth, the core may be made ofFECA but the shell may be made of FECA/X. This happensif X is completely segregated to, near, or even beyond thenanoparticle periphery from the FECA/X nanoparticle core.Let the diameters of the shell and the nanoparticle be DSL

and DNP, respectively; and SLNP=DSL /DNP. The concentra-tion of FECA in the FECA/X shell for SLNP�1 may bequite low if the segregated X to �or near� the periphery of thenanoparticle is very high. It may even be negligible. FECAand X may just form a FECA/X solid solution or a solidmixture. And hence the shell is polycrystalline or amor-phous. The shell is amoprhous even if X slips onto the sub-strate surface beyond the nanoparticle periphery, e.g., SLNP1. The amorphicity �semiamorphicity� results fromthe lattice mismatch between the X and the substrate. Due tothe influence of surface effect of the FECA core, this shellmight be polycrystalline �amorphous� even when its FECAcomponent is insignificant or zero. It is true particularly ifthe shell is thin or very thin. An important material charac-teristic of carbon is that it has a very low surface energycompared to that of FECA �particularly, the transition metalssuch as Ni, Co, Fe, etc.�. So, it has higher tendency to seg-regate from the FECA/carbon seed nanoparticle bulk to,near, or beyond the periphery of the nanoparticle duringcooling. This tendency to segregate is accelerated by the sub-strate and/or nanoparticle fluctuations. For the SCG, there isno FECA, and hence the shell, upon segregation of X fromthe XmYn core is made of X. It lies around the XmYn core. Itcreates a heterostructure with the XmYn material. It may con-tain oxygen. Under the influence of surface and interfaceeffects of the core �or matrix�, it is amorphous. It serves asthe seed for the SCG. For the OAG, the shell is made ofhighly oxygenated X. It is also amorphous, and serves as theseed for the OAG.

We may envision three different situations for theFECA-mediated growth. First, the FECA/X shell is formedaround a tiny FECA �DNP=1 to 2 nm� core. Second, a bundleof tiny FECA/X shells is created in a relatively large seednanoparticle. Each of these shells surrounds a tiny FECA�DNP=1 to 2 nm� core. Third, a single FECA/X shell is cre-ated from a moderately large �DNP=2 to 25 nm� seed nano-particle. The atomic percent of X in the FECA/X shell is

high. It is polycrystalline, and even amorphous. The highresolution transmission electron microscopy �HRTEM� im-ages confirm the segregation of X from the FECA/X seednanoparticle.72,73 It is substantiated also by the electron en-ergy loss spectroscopy �EELS� analyses.73 The experimentsshow that the X material in the FECA core, thus formed fromthe FECA/X seed nanoparticle after segregation and solidifi-cation, may be insignificant. For similar reasons, the FECAof the FECA/X shell, thus formed after segregation and so-lidification, may be insignificant. Again, if the seed nanopar-ticle is relatively large, it may contain a large number of tinyseed nanoparticles �each with a FECA/X shell and FECAcore� in it. These tiny seed nanoparticles may actually be thefragments of the same large seed nanoparticle created by thephase separation during precipitation of X on the matrix orduring the decay of X from it. Due to fluctuations, they mayhave random orientations.

If a single FECA/X shell is formed around a relativelylarge FECA core, the diffusion of X toward the peripherytakes place from the entire inside of the nanoparticle. Obvi-ously, the thickness of the shell would be large. Also, theatomic percent of X in the FECA/X shell would have con-centration gradient. The X at. % may be higher in the regionnear the exterior wall of the shell than in the region near theinterior wall of the shell. The end result of all these would bethe eventual splitting of one single thick shell into severalthin subshells. In an alternative scenario, the splitting of thesame thick shell into thin concentric subshells would takeplace if �1� FECA in the FECA/X shell is very insignificant,�2� there is no concentration gradient of X along the lateralwidth of the shell, �3� but there is a lateral variation in theinfluence of the surface effects of the core on the shell. Eachof the thin subshells would obviously be separated from theneighboring ones by grain boundaries. They would be poly-crystalline. Due to mesoscopic size effect, they would alsobe molten �semimolten�. They would all act as droplets fornanotube growth. The nanotube thus grown would be a mul-tiwalled nanotube. To reiterate, the condensate would haveamorphous FECA/X shell and FECA core. The shell wouldcomprise of concentric circles of subshells, each of themhaving FECA/X composition different from that of the othersubshells. While the outermost subshell would have low, ifany atomic fraction of FECA, the innermost subshell wouldhave high atomic fraction of FECA. There would be struc-tural inhomogeneity at the interface of two subshells, andalso between the FECA core and the innermost subshell.Stress would be generated at these interfaces, which wouldgive rise to grain boundaries, semigrain boundaries, or grain-boundarylike regions. These would be concentric circles ofgrain boundaries, semigrain boundaries, or grain-boundarylike regions. Interestingly, these would be absent invery thin shells having one or a few graphite layers.

Multiwalled nanotubes may be formed by also alterna-tive means. In one of them, there would be no splitting of thesingle thick shell into thin concentric subshells. So, only asingle nanotube, having a thick wall, would be grown fromthe nucleation of RS species inside a single seed. However,during subsequent growth, or during cooling after growth,this thick wall would split into thin concentric subwalls. This

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would happen because each monolayer of the tube, duringsupersaturation and cooling, would lose surface energy.These monolayers would, therefore, tend to be contracted involume and separated from each other. The multiple nano-tubes, thus formed, would be concentric. They would all befrom one single FECA/X seed. Ma et al.22 carried out aself-catalytic CVD growth of BN nanotubes. Boron served asa catalytic agent for the synthesis of these nanotubes. It wasobserved that multiwalled nanotube was generated from asingle hemispherical droplet at the nanotube tip. This dropletwas made of NSC seed �see Sec. IV D� of amorphousBuNuO composition. Similar observation was made byGohier et al.30 during carbon nanotube growth. ForMWCNTs, each of the subwalls should be that of a graphene,and the interwall separation should be very close to the in-terlayer separation of graphite. That this is true is manifestedfrom experiments, which show that the interwall separationfor MWCNTs is about 0.340 nm, while the interlyer distancein graphite is about 0.335 nm. The very small difference,0.005 nm, between the two is the result of strain imposed bythe MWCNT curvature.

Gavillet et al.73 investigated the atomic level of theFECA/carbon segregation process. They performed first-principle quantum molecular dynamics simulations of thedynamic behavior of FECA/carbon cluster during coolingfrom high temperature. Cobalt was chosen to be the FECAfor the study. The impact of temperature reduction on themotion of the atoms was monitored. The forces acting on theatoms were derived from the instantaneous electronic groundstate. This ground state was accurately described by the localdensity approximations of the density functional theory�DFT�. The DFT exhibited the quantum mechanical frame-work for the electronic system. Hence, it was quite efficientto address the dynamical behavior of the system during tem-perature reduction. The interactions between valence elec-trons and ionic cores were accounted for by pseudopotentialsfor carbon and cobalt atoms. A sphere, 1.3 nm in diameter,was formed from a hexagonal close-packed Co structure.This sphere included a 153 atoms-mixed CouC cluster. Thewhole system was heated to a temperature of 2000 K. It waskept at this temperature for 5 ps to achieve thermalization. Itwas then cooled down gradually at a rate of 100 K/ps untilthe temperature reached to about 1500 K. It was found that,after 5 ps at 1500 K, most of the carbon atoms ��80%�segregated to the surface of the cluster. The Co atoms mi-grated at the same time to the center of the cluster. A periph-eral shell and a central core were thus formed. The carbonatoms in the shell had a network of connected linear chains,aromatic rings, and hexagons. The catalyst provided a fluc-tuating CouC bonds which facilitated the incorporation ofnew carbon atoms into the chains.

D. Seed structures

We argue again that seed, and droplet from this seed, areintegral elements of nanotube growth. As shown in Fig. 5,depending on the interplay between the surface energy andthe strain energy per unit volume, a seed may exhibit one ofthree different structures, viz., NSA �nanoseed type-A�, NSB

�nanoseed type-B�, and NSC �nanoseed type-C� structures.Among them, the NSA structure has the form of a shell. Asthe nanotube grows, it �e.g., the seed� moves up and stays atthe nanowall tip. The seeds found by Andrews et al.74 �seeFig. 2�f� by these authors� have the NSA structure. The NSBstructure is hemispherical. It has two parts: a core and ashell. The core is made of FECA. It is formed if, during theinitiation of growth, the FECA core is detached from thesubstrate but remains attached to the FECA/X shell. Theseeds observed by Kukovitsky et al.75 are good examples ofthe NSB seed. The NSC structure is spherical or hemispheri-cal. It covers the nanotube head, and appears as a cap. It isformed under X-rich conditions, in which X is segregatedfrom FECA/X seed nanoparticle, creating X-rich FECA/Xshell but X-poor FECA/X core. Under X-rich conditions, theconcentration of X in the FECA/X seed nanoparticle is high.So, some X atoms still remain in the core after the creationof a shell due to segregation of X toward the periphery. TheFECA/X core is then detached from the substrate but re-mains attached to the FECA/X shell. There are two reasonsfor the FECA core of the NSB seed and the FECA/X core ofthe NSC seed to be detached from the substrate: First, thereis high level of stress at the core/substrate interface. Thisstress arises from the lattice mismatch and the mismatch ofthe thermal expansion coefficients of the two materials. Sec-ond, due to size-dependent melting point depression, thereoccurs melting of the interface between the core, and thesubstrate underneath this core. We cite one example. InPnanotubes were grown from In and P vapors.29 For thisgrowth, an Au film was placed on silica substrate. At the endof the growth, Au and In were, however, found at the nano-tube cap. It happened because Au film was converted intoAu/In alloy due to diffusion of In vapor into the Au film.Under In-rich condition, Au/In seed nanoparticle, thusformed, had Au/In alloy core even when In was segregated tothe periphery of the seed nanoparticle to create In-rich Au/Inshell. The Au/In core and the silica substrate are differentmaterials. So, there was abrupt interface between the Au/Incore and the silica substrate. On the other hand, the Au/Incore and the Au/In shell had the same material. And hencethere was no abrupt interface between them. Au/In core wastherefore detached from the silica substrate but remained at-

NSA seed NSB seed

Open edge

NSC seed

FECA

(a) (b) (c)

FIG. 5. �Color online� Schematic diagrams of three possible structures �e.g.,NSA, NSB, and NSC� of nanotube droplets �e.g., molten/semimolten seeds�.

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tached to the Au/In shell. Seeds created by Bakkers andVerheijen,29 Gohier et al.,30 and Huang et al.35 are good ex-amples of the NSC seeds. The RS adatoms, landing on thecap, slide down to the peripheral shell before they undergosupersaturation to produce nanotubes.

E. Melting/semimelting of seeds into droplets

We assume that the seed is made of FECA/X alloy, solidsolution, or solid mixture. FECA is made of a metal �Fe, Ni,Co, Au, Cu, Re, etc.�, a semiconductor �Si, Ge, SiC, etc.�, oran oxide �SiO2, Al2O3, etc.�. The nanotube is made of XmYn

material. And the substrate is made of a material totally dif-ferent from all of them. For the convenience of readership,eight different variations, NSA-1 to NSA-8, of NSA seed, areshown in Fig. 6. There can be similar variations also in theNSB and NSC seeds. A droplet is essentially a seed, which ismolten �semimolten� in the entire region or in certain parts ofit. This happens if the seed, being at the nanotube tip �or thesubstrate surface�, exhibits the following characteristics.First, it has lattice mismatch and mismatch in the thermalexpansion coefficients at the seed/substrate or the seed/nanotube interface. Such mismatches give rise to lattice dis-orders �e.g., twins, nanopipes, grain boundaries, grain-boundarylike regions, etc.� in the seed. If made of anoneutectic solid solution or a solid mixture, its RL content�e.g., RL��FECA,X� material� may have lattice disorders.There may also be traces of foreign elements �e.g., dopants,contaminants, etc.� inside the RL species. If made ofFECA/X eutectic solution, noneutectic solution, or just solidmixture, FECA and X may be inhomogeneously distributedinside the RL species. All these disturb RL lattice structure,and weaken the interatomic �intermolecular� interactions in-side it. A large concentration of the RS species may cover theexterior seed surface �see NSA-5�. The surface atoms of theseed may be disturbed by the influence of the RS speciesaccumulated on its exterior �external� surface. Vacancies anddangling bonds may thus be created on or near the seedsurface. The RL species are affected also by growth param-eters such as, temperature, pressure, precursor flow rate,FECA nanoparticle size, etc. We suggest that, in view ofthese, the lattice structure of the seed during growth, andeven prior to the growth, may be different from its single-crystal lattice structure in the bulk.

Defects, dopants, and contaminants disturb the seed lat-tice structure. The inhomogeneous distribution of FECA andX in the RL��FECA,X� species during the FECA-mediatedgrowth, and the presence of oxygen in the RL species duringthe OAG may also be the causes of seed lattice disturbance.The oxygen may originate from the support material; it mayeven appear as precursor contaminant in the non-OAGs. At-oms in the vicinity of defect-infected sites are less tightlybound to one another than the atoms in defect-free sites ofthe seed. On the same ground, atoms at grain boundaries,semigrain-boundaries, grain-boundarylike regions, and inter-faces are also less tightly bound to one another than those inthe bulk. The melting point of the seed in the grain bound-aries and grain-boundarylike regions is consequently lowerthan that in the bulk.36 Interfaces also suffer from similar

Solid seed

Narrow stripes seed/nanotube interface stripe

Molten/Semi-molten seed

Nanotube wallNanotube wall

NSA-3

NSA-1 NSA-2

NSA-4

Seed stripe

RS accumulation on the seed

NSA-7NSA-8

Spherical tiny defect sites

Interfacestripe

RSRS

NSA-5 NSA-6

RSRS

Molten/semimoltennanopore

Solid seed

FIG. 6. �Color online� Schematic diagrams of narrow stripes �nanopores�formed in NSA �NSA-1 to NSA-8� seeds made of X or FECA/X material.The solid seeds are shown as red shells, the molten �semimolten� seed isshown as orange shell; and the accumulation of the RS species on the exte-rior surface of the seed is shown as patterned blue shell. The seed NSA-1 isentirely solid; the seed NSA-2 is entirely molten �semimolten�; and theseeds NSA-3 to NSA-8 are solid but have disturbed and disordered regions.Narrow white stripes and tiny white spheres resulted from disturbance anddisorder in the seed. The landing of the RS species directly from the vaporphase is shown by arrow.

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reduction in melting points.53–55 Taking all these into ac-count, one may thus argue that FECA/X seed, at TTE �andeven at T�TE�, may have lattice structure with numerousnanopores. This lattice structure may be much looser than theone of its single-crystal bulk. That it is true is evident from arecent experiment76 which shows that, at a certain tempera-ture T�TM, both Si and metal are solid but the Si/metalinterface is partially molten.

Different seeds mediating nanotube growth can have dif-ferent characteristics. For example, the NSA-1 seed made ofFECA/X alloy is not molten or semimolten at TTE.Rather, due to lattice disturbance and weakened interatomicinteractions, it has loose lattice structure even at TTE.However, the NSA-2 seed made of FECA/X alloy is fullymolten or semimolten at T�TE. It is influenced by eutecticeffect. The NSA-3 seed has grain boundaries, semigrain-boundaries, and grain-boundarylike regions. The narrow sur-roundings of these regions are semimolten at TTE. TheNSA-4 seed has grain boundaries, semigrain boundaries,grain-boundarylike regions, and also interfaces. The narrowsurroundings of these regions and interfaces are semimoltenat TTE. The external surface of the NSA-5 seed is coveredwith high concentration of the RS species, and has disorder atthe seed/nanotube interface. It is semimolten both at the ex-ternal �exterior� surface and at the seed/nanotube interface atTTE. The NSA-6 seed has tiny defect sites �e.g., the sitesof foreign elements, dopants, and contaminants� inside itslattice structure. These defect sites are semimolten at TTE. The NSA-7 seed has a single shelled nanopore due tograin boundaries or grain-boundarylike regions. It is molten�semimolten� due to mesoscopic size effects. There could bemultiple nanopores of the same shape in NSA-7. These nano-pores may merge together to create a thicker shelled nano-pore. The NSA-8 seed is free from the influence of the RS

species, and has no foreign elements. Yet it has seed/nanotube interface state disorder, which, at TTE, gives riseto a narrow semimolten stripe at this interface.

Fluctuations of substrate and/or nanoparticles and thethermodynamic imbalance�s� in disturbed/disordered re-gions, particularly during annealing prior to growth, playcrucial role in dictating the seed characteristics. They causethe formation of molten �semimolten� stripes and/or pockets.Depending on the growth conditions, the number density ofthese stripes may be quite high. They may be vertical �asshown in NSA-3 and NSA-4 seeds�, nonvertical, or nonper-pendicular to the substrate surface. They may interact withone another. They may arise also in nonalloyed droplets�such as those for SCGs�, but at TTM. As temperatureand/or pressure are increased, the lattice disorder increases;and together with it, the molten �semimolten� stripes becomelarger and wider. They may merge together to create mul-tiple, concentric, thin nanopores, or just one single thicknanopore of the shape of the one in NSA-7. The seed mate-rials in regions of disturbed �disordered� lattice and weak-ened interatomic interactions are generally amorphous �orsemiamorphous�. And these regions are quite small �dimen-sion: less than 2 nm�. They are different from the normalbulklike lattice structure of the seed. So, they undergo sub-stantial melting temperature depression. This depression, for

example, for a nanopore, 3 nm in dimension, in Re/C mate-rial would, according to Eqs. �1� and �2�, be 2250 °C. Themelting point would thus be only 900 °C down from TM

=3180 °C.Based on above discussions, the NSA-1 seed may not

have molten or semimolten regions. Yet it may serve as adroplet at TTE owing to loose lattice structure from latticedisturbance and weakened interatomic interactions. Veryslow diffusion of the RS species through this droplet maytake place if the shape, size, and mass of the RS species arerelatively small. This diffusion may be called “solid diffu-sion.” The NSA-2 seed is molten or semimolten at T�TE

due to eutectic effect but at TTE due to mesoscopic sizeeffect. It becomes droplet if molten �semimolten� in the en-tire region, or in only certain parts of it. The RS speciesdiffuse through it. The NSA-4 seed has narrow semimoltenstripes, which serve as diffusion paths for the RS species.These species may enter the semimolten narrow stripeformed around the seed/nanotube interface. The RS speciesreach the L/S interface through these stripes. Then they un-dergo supersaturation and nucleation to produce nanotubes.The NSA-5 seed has semimolten region at the external �ex-terior� surface and also around the seed/nanotube heteroint-erface. These regions are connected together as paths for theRS species to diffuse to the L/S interface. The NSA-6 seedhas tiny semimolten spherical regions formed around defectsites. They may merge together to form a shelled nanopore.The RS species may diffuse through them. They may, other-wise, tunnel and/or hop through them to reach the L/S inter-face. The NSA-8 seed has narrow semimolten stripe onlyaround the seed/nanotube interface. This seed serves as drop-let for the RS species that slide down the droplet surfacefrom the top, and then enter the L/S interface. They undergosupersaturation/nucleation at the L/S interface. The nanotubedirection is dictated both by the direction of semimoltenstripes and the direction of motion of the RS species.

F. Modified definition of droplet

In the light of the above discussions, we may put forth amodified definition of droplet. A droplet is a seed, which issolid, molten, or semimolten in the entire region or in somespecific regions of it. It may have disturbed, disordered,amorphized, semiamorphized, loose, and/or anisotropic lat-tice structure due to stress, strain, defects, vacancies, thermo-dynamic imbalances, and grain boundaries. Under the com-bined influence of them, this seed may have molten orsemimolten nanopores. The RS species diffuse through them.It happens at TTE if the seed is made of FECA/X material.It happens at TTM if, however, the seed is made of X oroxygenated X. It has fluctuating RL species, which interactswith the diffusing RS species facilitating the RS reorganiza-tion. The seed is semimolten in the sense that, even when itappears to be a solid, it has loose lattice structure and/orsemimolten nanopores needed for smooth, ordered, and con-fined diffusion of the RS species through it. If the droplet is aseed, which �a� is solid, �b� has disturbed/disordered latticebut no semimolten nanopores, a very slow solid diffusion ofthe RS species may be possible through it. The nanopores

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may be concentric, very close to one another, separated fromone another, or may have intersections. Some or all of themmay merge together, as it happens in a FECA/X seed at T�TE. The droplet has generally the shape of a shell, nanopo-res�s�, and a small thickness. It is stable. The thickness maybe small enough for it �e.g., droplet� to undergo size-dependent melting point depression even without lattice dis-turbance. Depending on confinement, it may produce even aone-atom thick layer of seamless cylinder �for example,SWCNT from sp2-bonded graphene�. The semimolten state,structural flexibility, fluctuations, small size, and confine-ment capability of the RL species of the droplet are requiredfor interactions with the diffusing RS species, and for reor-ganization of the RS species into a tubular form. The con-finement capability of the shelled RL species may result atleast partly from its interfacing with the central core. Thesemimolten state of the droplet provides the flexibility, forexample, for diffusing carbon atoms to be reorganized intoABAB type of stacking to create graphene. Isolated carbonatoms tend to form pentagons. This is minimized because thediffusing carbon atoms form clusters with the fluctuatingFECA/carbon material of the RL species in the droplet. Suchclustering is crucial as it allows carbon of the FECA/carbonmaterial to react with the adsorbed carbon, and to form ahexagon before any pentagon is formed and stabilized. Anincoming carbon atom compensates for the carbon of theFECA/carbon. The droplet should have in situ or induceddipole moment. It may or may not have a cap. If it has a cap,this cap may or may not serve as part of the seed. Due tosegregation of X from the FECA/X seed nanoparticle, thecore may be made primarily of FECA, while the shell maybe made primarily of X or FECA/X material. Being molten�semimolten�, it should have surface tension, and good stick-ing coefficient.

G. Adhesive property of seeds

The adhesive property of the growing nanotube tip iscrucial for nanotube growth. This adhesive property resultsfrom the presence of dangling bonds.77 It results also fromthe electronegativity and polar characteristics of the RL andthe RS species. The charge distribution QS and the electrone-gativity �S of the RS species �e.g., X and Y atoms, and par-ticularly XmYn polar molecules� are also important for thisgrowth. Both the charge distribution QS and the electronega-tivity �S of the RS species should be different from thecharge distribution QL and the electronegativity �L of the RL

species. Defects, materials characteristics, L/S interface, het-erostructures at the L/S interface, and the structural aniso-tropy �see Fig. 5� of the RL species influence together thecharge redistribution, electronegativity, and the creation ofdipole moment �ML, all in the RL species. We cite severalexamples. Chemical compositions of FECA and X are differ-ent. Due to inhomogeneous distribution of charges, aFECA/X seed may have dipole moment �ML under nonequi-librium conditions. Due to charge asymmetry, a FECA/X orX seed at the tip of XnYm nanotube may also have permanentdipole moment �ML. This dipole moment gives rise to anelectric field78 E� DM�r��. The electric field E� DM�r�� and the sur-

face tension �L are essential tools to govern the electrostaticattraction between the RS and the RL species. They are re-sponsible for preferential landing of the RS species on thedroplet surface. They are responsible also for the orderedalignment of the RS species inside the RL species.

V. CHARACTERISTICS OF NANOTUBE PRODUCTS

A. Plausible scenarios for nanotube growths

Depending on growth conditions �e.g., growth tempera-ture, chamber pressure, precursor flow rate, nanoparticlesize, etc.�, a number of scenarios may be envisioned duringthe FECA-mediated nanotube growth. We present a few ofthem. FECA vapor may, for example, be formed inside thechamber. There can be a variety of reasons for this. The rapidthermal annealing prior to growth is one of them. Sharpedges of the FECA nanoparticles formed during this anneal-ing may melt due to size-dependent melting point depres-sion, which, upon vaporization, gives rise to vapor. Tempera-ture and pressure fluctuations may contribute to it. X atomsgenerated from catalytic decomposition of precursors arehighly energetic. They may collide with the FECA heatingthe FECA surface, and ejecting the FECA atoms from thissurface. As RS vapor species is flown into the chamber, theFECA vapor competes with it. Scenario S1: the chamber isX-rich but FECA-poor. So, the concentration of the FECAvapor is lower than that of at least the X-component of theRS vapor. Scenario S2: the chamber is FECA-rich. The con-centration of the FECA vapor is, therefore, higher than thatof the RS vapor. Scenario S3: the segregation of X fromFECA of the FECA/X seed nanoparticle is complete. So, thecore is now made of FECA but the shell � SLNP�1� is madeof FECA/X material. The interface between the two is abruptand small. There is a size-dependent melting point depres-sion of the interface. Due to this depression, while both theFECA core and the FECA/X shell remain solid, the interfacebetween the two becomes molten �semimolten�. Scenario S4:X is segregated from FECA to the periphery of the FECA/Xseed nanoparticle. But this segregation is not abrupt. It israther graded. So, the interface between the FECA/X shell� SLNP�1� and the FECA core does not undergo size-dependent melting point depression. There is no melting�semimelting� of the interface between the two. Scenario 5:both the core and the shell have FECA/X composition. How-ever, while the core is FECA-rich, the shell is X-rich. Sce-nario S6: the core/substrate interface is abrupt and undergoesmelting point depression. Due to this depression, while boththe FECA core and the substrate remain solid, the interfacebetween the two is molten �semimolten�. Scenario S7: beingcollided by the RS species, and under the influence oftemperature/pressure fluctuations, the FECA core lattice isdisturbed. It is not molten but semimolten and yet stable.Scenario S8: the pressure and/or temperature inside thechamber are nonuniform; there is also fluctuation of the tem-perature and/or the pressure. They create scratches on theFECA core, or even tear it apart.

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B. Diversities in nanotube characteristics

During growth under Scenarios S1 and S3, the FECA/Xshell serves as NSA droplet. The RS�X and RS�Y land onthe droplet surface, diffuse through it, and react together toform XmYn molecules. Upon supersaturation at the L/S in-terface they crystallize to form nanotube. The nanotube, thusformed around the FECA core, increases in length. The drop-let remains at the nanowall tip of the nanotube but the FECAcore remains at its base. At the end of the growth, the FECAcore constitutes the nanotube base.

During growth under scenarios S1, S4, and S6, theFECA/X shell serves as NSB droplet. The FECA core, al-ready attached to the shell but detached from the substrate,becomes part of this droplet. The nanotube, formed duringgrowth, increases in length, and the droplet remains attachedto the nanotube tip. At the end of the nanotube growth, theNSB seed is still at the nanotube tip, and the original FECAcore is part of this seed. That this is true is apparent from anexperiment by Dai et al.,49 which produced SWCNTs byemploying CO as carbon source and Mo as FECA. The tube,1 to 5 nm in diameter, had FECA nanoparticle attached to thenanotube head. It did not though participate in the nanotubegrowth. It served only as an interface with the FECA/X drop-let. If the droplet is sufficiently molten, it may be too weak�soft� to carry the FECA core with it up to the nanotube tip.The FECA core may then be left, not at the base but some-where inside the tube.

During nanotube growth under scenarios S2, S4, and S7,the droplet at the tip of the FECA/X shell serves as NSAdroplet. The RS�X and RS�Y land on the droplet surfacebut the FECA vapors land on the semimolten FECA/X core.So, while RS�X and RS�Y contribute to the formation andlengthening of the nanotube, the FECA vapors contribute tothe thickening of the FECA core. Both the nanotube andFECA core simultaneously grow. FECA vapors entering thedroplet are also segregated to the surface into the FECA core.The FECA vapors contribute to the thickening of the FECAcore. At the end of the growth, the nanotube, thus formed, isfilled up with FECA. Tang et al.25 grew InP nanotubes by theOAG mechanism under In-rich conditions. These nanotubeswere filled with In metal at the core. Hu et al.26 synthesizedCdS and CdSe nanotubes via Sn-templated route under ther-mal annealing. These nanotubs were filled with Sn metal.Che et al.33 grew carbon nanotubes employing Pt/Ru cata-lyst. These nanotubes were also filled with the Pt/Ru cata-lysts.

During nanotube growth under the combined impact ofthe scenarios S2, S4, S6, and S7, RS�X and RS�Y land onthe droplet surface, and the FECA vapors land on the semi-molten FECA core curved downward due to weight. Asnanotube grows, the FECA core, attached to the FECA/Xshell, but detached to the substrate, eventually hangs fromthe tip. While nanotube grows and lengthens by the adsorp-tion of the RS�X and RS�Y, the FECA core thickens bythe adsorption of FECA vapors. However, the rate of length-ening of the nanotube is higher than the rate of thickening ofthe FECA core. The adsorption of FECA vapors may be thehighest at the center but lowest at the edge of the FECA core.

Some of the FECAs, adsorbed at the edge of the core, slideto its center. As a result, it is elongated downwards assumingthe shape of a cone �or a pear�. It is also attached to theFECA/X shell but detached from the substrate. So, it movesup with the droplet. At the end of the growth, the nanotubehas FECA attached to its head. Only the tip of this FECA isanchored at the nanotube head; the rest of it hangs from thetip. If the FECA particle is too heavy, it may break apart withpieces lying somewhere inside the hollow core. Bower etal.79 employed FECA�Co to synthesize MWCNTs on Sisubstrate. TEM micrograph showed cone-shaped cobalt par-ticle fully enclosed at the nanotube tip. Only the tip of thisparticle was attached to the nanotube; the rest of it was hang-ing from the tip downward. Similar cone-shaped FECA par-ticle by Okai et al.47 was found hanging from the SWCNTtip. Almost broken Ni particle was found by Kokuvitsky etal.80 �see Fig. 4�b� by these authors� to hang from theSWCNT tip. We believe that the diffusion of FECA vaporsinto FECA core may not solely contribute to the invertedcone �pear� shape of the hanging FECA particle. The diffu-sion of FECA vapors through the droplet, and the eventualsegregation and migration of them �e.g., FECA vapors� intothe attached FECA particle may, at least, be partly respon-sible for it. This is an added cause of the inverted cone-shaped FECA particle hanging from the nanotube head.

During nanotube growth under the combined impact ofscenarios S1, S3, S6, and S8, RS�X and RS�Y land on thedroplet surface but there is no FECA vapor to land on theFECA core. The nanotube, formed from the droplet, length-ens, while the droplet remains at its tip. A part of the frag-mented FECA core remains at the base. But another part of itmoves up with the droplet. At the end of the growth, thenanotube head is partly covered with FECA. The nanotubebase is also partly covered with FECA. There may be piecesof the FECA sticking to the internal sidewall of the tube.Andrews et al.74 carried out CVD growth of MWCNTs em-ploying the catalytic decomposition of ferrocene-xylene mix-ture at �675 °C. Elemental analysis of the aligned MWCNTarray showed FECA�Fe near both the head and the base ofthe nanotubes; it was there also sticking to the inner wall ofthe hollow nanotubes.

Let us consider the nanotube growth from single-component material �for example, X=C, Y=0, m=1, n=0for carbon nanotube�. A number of situations may arise afterthe system shutdown. First, the RS species is no longer flowninto the chamber. And the chamber cools down slowly. Thegrowth also stops. At the end of the growth, the FECA and Xof the FECA/X droplet remain at the nanotube head. Second,the growth continues for some time after system shutdown. Itoccurs with X of the FECA/X droplet serving as the RS

species. X of the FECA/X droplet is thus consumed for thegrowth. Hence, at the end of the growth, only FECA remainsat the nanotube head. Third, there are fluctuations in tem-perature and/or pressure in the chamber during system shut-down. The FECA, left at the nanotube head after the growth,is consequently ejected away from the nanotube head. At theend of the growth, there is, therefore, neither FECA nor X atthe nanotube head. These are all consistent with experimen-tal findings. For example, Kokuvitsky et al.80 grew carbon

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nanotubes at 800–950 °C employing Ni nanoparticles asFECA. The experimental electron diffraction data obtainedby them80 unambiguously indicated that the nanotube headswere capped with Ni, nickel–carbon solid solution, ornickel–carbon mixture. Iijima and Ichibashi7 preparedSWCNTs by covaporizing graphite and FECA�Fe in anAruCH4 environment. At the end of the growth, they foundno trace of FECA at the nanotube tip.

VI. INHOMOGENEOUS DISTRIBUTION OF FECAAND X IN FECA/X SHELL

A. Background

Let us consider the growth of XmYn �X=C, Y=0, m=1, n=0� nanotubes from NSA droplet �see Fig. 5�a�� hav-ing nanopore�s�. There may just be one thick nanopore or anumber of thin concentric nanopores. Depending on growthconditions, these nanopores may have variation�s� in struc-tural composition. These nanopores, if molten or semimol-ten, become the diffusion paths for the diffusion of the RS

species to the L/S interface. The variation in composition�porosity� of the nanopores may arise from FECA and Xcomponents of the FECA/X seed varying laterally along thewidth of the FECA/X shell. There may also be differences insurface tension near the inner and the outer walls of the shell.The areas near the inner wall of the shell may be called AIW,and the areas near the outer wall of this shell may be calledAOW. The nanopore in AIW may thus be thicker than thenanopore in AOW, or vice versa. Three situations may arise.First, AIW, as compared to AOW, has the FECA atomic per-cent higher than the X at. %. Second, AOW, as compared toAIW, has the FECA atomic percent higher than the X at. %.Third, the atomic percent of FECA is comparable to theatomic percent of X in both the AIW and the AOW. Therewould be two types of diffusion of the RS species through thedroplet. These are the vertical diffusion to the L/S interface,and the lateral diffusion to the sidewall. The vertical diffu-sion would be continuous, which would produce nanotubes.But the lateral diffusion would be periodic, which wouldproduce diaphragms or impurities. The periodic diffusionwould take place under FECA-rich and/or X-rich conditions.

B. Growth of bamboo-shaped nanotubes

We now consider the RS�X rich condition and the NSAtype seed �droplet� for carbon nanotube growth. Under nor-mal circumstances, RS�X atoms land uniformly on all ar-eas, including the AIW and the AOW, of the droplet. Thisdoes not however happen if AIW �which is adjacent to FECAcore�, as compared to AOW, has the FECA atomic percenthigher than the X at. %. AIW is now X-deficient which al-lows RS�X to land more �e.g., in larger number� in the AIWthan in the AOW. Suppose, the number densities of RS�Xatoms landing in the AOW and AIW are � nm−2 s−1 and��+��� nm−2 s−1, respectively. The fraction of these atomsdiffusing to the L/S interface from both the AIW and theAOW must be equal. Let it be �. This is necessary for asmooth supersaturation to take place at the L/S interface andto contribute to nanotube growth. This means the excess of Xatoms �e.g., �� nm−2 s−1� remains stuck in the AIW. With

time, there occurs an accumulation of the excess X atoms inthe AIW. This continues until the AIW is supersaturated withthem. Being supersaturated, AIW is no longer in thermalequilibrium. It experiences stress, and tends to revert back tothermal equilibrium. To achieve it, AIW tries to release theaccumulated RS�X atoms. But they cannot be released tothe L/S interface. The only option left for the AIW is, there-fore, to release them out through the inner wall of the shelleddroplet. To restate, depending on materials characteristics,growth conditions, and stress, the AIW gradually swells �seeFig. 7�a��. Ultimately, the swelling reaches a stage when thedroplet can no longer hold the accumulated X atoms. So, the

D

D

D

D

D

Outer wall Outer wall

Inner wall

Swollen X-richsection of the

droplet

(a) (b)

D

D

D

D

D

Outer wall Outer wall

Swollen X-richsection

Inner wall

(c) (d)

FECA

D

D

D

D

D

D

D

D

D

FIG. 7. �Color online� Schematic diagrams showing the creation of bamboo-shaped nanotubes. �a� Swelling �extension� of the inner wall of the NSAseed due to the accumulation of the X atoms; blue-green shell is the swollenX-rich segment of the droplet. �b� Formation of cone �or umbrella� shapeddiaphragms and �c� almost horizontal diaphragms formed from NSA seed.�d� Formation of inverted cone �or inverted umbrella� shaped diaphragmsformed from NSB and/or NSC seeds. The ejection of the accumulated Xatoms to the side surface of the seed is shown by black arrows but thediffusion of the RS species through the droplet/nanotube interface is shownby blue arrows.

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X atoms are ejected out through the inner wall. As this innerwall is circular, the ejected X atoms create together umbrella�or cone� shaped diaphragm. To be more specific, increase inthe number of RS�X atoms precipitated in the AIW overtime leads to the formation of X–X chains �strings� of poly-gons. The chain lying near the inner wall is circular. Otherchains formed underneath it are also circular. At elevatedtemperature, the kinetic energy of the atoms forming thechains is sufficiently high. So, they overcome the surfacetension and also the attraction by FECA. They lift off thesurface of the inner wall and continue to grow creating ulti-mately a diaphragm.

The inner diameter shrinks in locations where the ejectedX atoms create the diaphragm. The shrinkage results fromthe ejection of the accumulated X atoms. There is no accu-mulation in AOW. So, the outer diameter, in contrast, mayremain unchanged all throughout the nanotube length. Fol-lowing the ejection of the X atoms, the droplet achieves ther-mal equilibrium. However, due to X-rich condition of thevapor environment, the process of excess adsorption of Xatoms in the AIW begins again. It continues until the AIW issupersaturated with the accumulated X atoms, and createsthe next diaphragm. The nanotube, thus grown, has a bam-boo shape �see Fig. 7�b��. Interestingly, these are consistentwith the characteristics of the bamboo-shaped carbon nano-tubes observed experimentally by Lee and Park.36 The dis-tance between the two successive diaphragms depends on theaccumulation rate of X atoms in the AIW. It depends onother growth conditions �e.g., temperature, pressure, etc.�, aswell. That this is true is manifested from experiments byJuang et al.37 Depending on the kinetic energy of atomsforming the polygons, the diaphragm may also appear asnear horizontal �see Fig. 7�c��.

The situation is slightly different for diaphragms formedfrom NSB or NSC droplet �see Figs. 5�b� and 5�c��. Theinner wall of the NSB droplet is attached to the FECA; it isinterfaced with this FECA. So, there is no room for the lat-eral swelling of the AIW. This swelling takes place onlyupward or downward at an angle with the interface. Theswelling upward at the interface creates a graphitic cap onthe FECA �see Fig. 5�b��. But the swelling downward createsa diaphragm. The inner wall of the NSC droplet is attachedto the FECA/X core. The X component of this FECA/X coreis, though, quite low. It has slightly loose structure at rela-tively high temperature, and also surface tension and weight.As a result, it has the bottom surface curved out downward.The RS species diffuses through it very slowly to its bottomsurface, where it is accumulated with time. Once supersatu-rated, the accumulated content is ejected out to form a dia-phragm. As nanotube grows, the NSC seed moves up withit leaving the diaphragm attached to the inner wall ofthe tube. Nanoparticles do fluctuate in vacuum at roomtemperature.81,82 Such fluctuation contributes to the separa-tion of the diaphragm from the FECA/X core �around nano-tube tip�. A series of diaphragms is formed during nanotubegrowth. As shown, in Fig. 7�d�, these diaphragms are in-verted downward. They appear as inverted umbrella �or in-verted cone�. They are identical to those observed experi-mentally by Zhang et al.38 and Wang and Wang.83

C. Impurity generation at the nanotube surface

We now consider the FECA-rich condition of vapor andAOW, rather than AIW, having FECA atomic percent lowerthan the X at. %. Under these conditions, AOW is FECA-deficient. So, FECA atoms tend to land more �e.g., in largernumber� in the AOW than in the AIW. However, for smoothnucleation for nanotube growth, the diffusion of FECAthrough all areas, including AOW, of the droplet to the L/Sinterface is suppressed. This occurs if FECA of AOW re-mains stuck to the droplet. While stuck to the droplet, theFECAs hinder the diffusion of the RS species to the L/Sinterface. They create various by-products including FECAclusters; and multishell carbon nanocapsules, both empty andfilled with FECA. The AOW swells as the by-products areaccumulated in the droplet. It experiences also stress. To berelieved of this stress, it eventually ejects them out throughthe outer wall. It happens periodically until the vapor re-mains rich in FECA. We believe that these are the reasons ofimpurities being formed on nanotube surface.57 These arealso the reasons of impurities being abundant more on theouter surface than on the inner surface.

VII. EXPERIMENTAL SUPPORT FOR THE PROPOSEDHYPOTHESIS

A. Evidence of the creation of shell

Hofmann et al.84 performed atomic-scale environmentaltransmission electron microscopy �ETEM� of the surface-bound CVD growth of carbon nanotubes. They used FECA�Ni. They found �see Fig. 3�b� by these authors� thatFECA�Ni remained crystalline as C2H2→2C+H2 dissocia-tion yielded a carbon-rich shell and a FECA�Ni core. Therewas no trace of Ni3C in the FECA core. Zhang et al.85 per-formed laser ablation of a compressed mixture of carbon,BN, SiO, and Li3N. The selected area diffraction pattern con-firmed that the laser ablation created a crystalline core of�-SiC plausibly from the reaction: C�solid or vapor�+2SiO �gas�→SiC�solid�+SiO2�solid�. SiC core, thusformed, was surrounded by an amorphous shell made of amixture of carbon and BN. The observations by Hofmann etal.84 and Zhang et al.85 are consistent with those by Arenalet al.24 and Gao and Wang.86 All of them lend support to oursuggestion that the shell formation is a prerequisite for nano-tube growth, and that these shells are amorphous.

Baker et al.77 proposed a model for the carbon nanotubegrowth. They assumed that the FECA particle is semimoltenat the growth temperature, and that carbon absorbates fromcatalytic decomposition of hydrocarbon gases are formed onthe semimolten FECA surface. Driven by concentration gra-dient, they diffuse then through the bulk of the FECA beforeprecipitating as graphene on another FECA surface. Lin etal.87 made use of selected area electron diffraction patterns toobserve real-time catalytic state of FECA��Ni,MgO� dur-ing carbon nanotube growth. They followed the crystal struc-ture of FECA��Ni,MgO� before and during the carbonnanotube growth. The observation was startling: the crystalstructure of FECA��Ni,MgO� during the carbon nanotubegrowth was identical to that prior to this growth. There wasno trace of C in the FECA core during carbon nanotube

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growth. Helveg et al.11 also found no carbon transportthrough the bulk of the FECA. These observations invalidatethe proposal of Baker et al.77 So, the only vehicle left for thecarbon nanotube growth is the molten �semimolten� FECA/Xseed created as a shell around the FECA. That such a shelldoes exist is evident from an experiment by Gorbunov etal.72 In this experiment, Ni film, about 1 nm thick, was ther-mally evaporated on a free standing carbon layer. At theas-deposited state no Ni was observed by TEM. However,upon in situ annealing at 400 °C, Ni particles, 2–4 nm insize, appeared. A carbon-rich shell, formed around Ni par-ticle, also appeared. Obviously these happened due to segre-gation of carbon from Ni during cooling. The shell wasamorphous, which encaged the catalytically inactive solid Nimetal. That the shell indeed encaged the solid Ni metal wasapparent from the axial elongation of Ni nanoparticle. It be-came larger �7 nm from 2–4 nm in size� and softer at highertemperature �e.g., 700 °C�. So it needed extra room. It couldnot, however, extend �swell� radially as there was a carbon-rich shell around it; this shell did not enlarge at higher tem-perature equally as the Ni metal. So, FECA had to be elon-gated axially.

We go back to the experiment by Helveg et al.11 andHofmann et al.84 These experiments indicate that, duringSWCNT growth, the FECA nanoparticle was elongated axi-ally from its equilibrium semi-rounded form. We believe itcould not extend laterally because of the presence of a shellaround the FECA nanoparticle. It would not happen withoutthe resistance and confinement by the shell. Semimoltennanopore�s� created in this shell mediated the growth ofgraphene layer. They provided the confinement needed alsofor nucleation and alignment of the carbon atoms into a well-ordered tubular form. The organization of carbon atoms intotubular graphene during diffusion through the molten �semi-molten� nanopores, and their supersaturation at the L/S inter-face were both driven by a need for the graphene layer toattain minimum energy. And it was achieved by the transferof energy from it �e.g., the tubular graphene� to the FECA�Ni �nanoparticle core� surface. The surface energy of theFECA was consequently increased. The FECA, as a result,was elongated. This continued until the transfer of energyfrom the tubular graphene satisfied the energy requirementfor the FECA’s elongation. The FECA went back to its origi-nal shape as soon as it ceased. The observed elongation ofFECA, and the sudden collapse of this elongation are testi-monies for the crucial role played by the shell and the molten�semimolten� nanopores created in this shell. The assumptionof shell explains the atomic-scale in situ observations of bothHelveg et al.11 and Hofmann et al. What they perceived to bethe interface transport, is actually the ordered, confined trans-port through the shelled nanopore around the FECA core.Without a narrow confinement, the experiments11,84 couldyield DWCNTs or even MWCNTs. Hofmann et al. spoke of“liquidlike” FECA�Ni. It is actually the molten �semimol-ten� FECA/X material inside the nanopore. The present studyexplains also the atomic-scale observation of Yoshida et al.70

It confirms this observation in that the molten �semimolten�nanopore of the FECA/X shell, rather than FECA, is the bestvehicle for the RS transport to the L/S interface.

The CVD growth experiments by Contoro et al.,88 Lolliet al.,89 and Miyauchi et al.90 show that nanotube diameterincreases with temperature. This is possible if the growth ismediated by molten �semimolten� seed �e.g., droplet� encap-sulating the FECA core. Increase in temperature acceleratedthe segregation �see Sec. IV C�. It influenced the chiral se-lectivity and structural subtlety of the nanotube. Increase insegregation accompanied increase in the size of the FECAcore and also increase in the shell diameter DSL. So, theincrease in nanotube diameter with temperature is a reflec-tion of the increase in shell diameter with temperature.

B. Evidence of dipole moments and electric field

Otani et al.91 performed first-principle total-energy cal-culations to examine the creation of intrinsic dipole momentin carbon nanotubes exhibiting hemispherical NSC cap. Thelattice structure of this cap is generally disturbed and disor-dered due to the presence of FECA/X solid solution. Thenanotube neck lies just underneath the cap of the nanotube.There occurs transfer of charges between the hemisphericalcap and the cylindrical neck of the nanotube. Otani et al.confirmed that, such charge transfer does occur. And due tothis charge transfer, the electron density increases in the capbut it decreases in the neck. This gives rise to an intrinsicdipole moment around the hemispherical cap. It is about 3.5D for carbon nanotubes. The dipole moment has two com-ponents: DM1 and DM2. DM1 originates from the charge in-homogeneity between the cylindrical neck and the hemi-spherical cap; but DM2 results from charge transfer from thenanotube neck to the hemispherical cap. The dipole momentthus induced around the cap allows nanotubes to respond toexternal electric field. The dipole interaction inside the RL

species of the cap acts also as a motive force for the seed’sself-organization, and for the reorganization of the RS spe-cies diffusing through it �see Sec. VII A�. The open-endedtubes exhibiting NSA seeds �and not covered by caps� havehighly reactive unsaturated dangling bonds. The bond orbit-als of the tips are polarized. They are aligned parallel to theexternal electric field.

In an experiment by Zheng et al.,92 SWCNTs were syn-thesized directly on flat substrates using monodispersedFECA��Fe,Mo� nanoparticles, RS�CO, the CVD growthtechnique, and H2 carrier gas. A number of substrates, allhaving the same density of FECA��Fe,Mo� nanoparticles,were prepared for the experiments. The SWCNT yield wasextremely low if pure CO was used as the RS species. Therewere almost no nanotubes formed on the substrate. TheSWCNT yield was greatly increased if, however, 20% H2

was added to CO. The SWCNT yield was highest if the H2

concentration was between 35% and 65%, respectively. Theyield was also good if the reaction temperature was set to800–900 °C. RS�CO underwent the reaction: 2CO→C+CO2 before or after landing on the droplet surface. Addi-tional reaction, such as CO+H2→C+H2O, might also havetaken place. Carbon atoms, thus released, lacked dipole mo-ment. So, they were not attracted by the RL species, andcould not readily land on the droplet surface. With pure COused as the RS species, the SWCNT yield was, therefore,

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extremely low. Unlike carbon atoms, H2, N2, etc. have dipolemoment. The carbon atoms had induced dipole momentwhen they were bound by carrier gas such as H2. If carriedby H2, they were attracted by the RL species. The RS speciesconsequently landed on the droplet surface, and underwentdiffusion through the droplet. Once supersaturated, they pre-cipitated on the nanotube tip just underneath the droplet. Allthese demonstrate that dipole moments for both the RS andthe RL species are important for successful growth of nano-tubes.

Let us cite some other examples. Ni is an effective cata-lyst for SWCNT growth. Yet Saito et al.93 could not growSWCNTs employing Ni clusters or particles; they grew in-stead SWCNTs employing Ni carbide seed particles. Similarsituations were observed by Saito94 with La �lanthanum�, bySubramoney et al.95 with Gd �gadolinium�, and by Zhou etal.96 with Yt �yttrium�. The tubes grown by RL��La,C�,RL��Gd,C�, and RL��Yt,C� had, however, smaller lengths�e.g., �100 nm�. Seraphin and Zhou97 produced high-density SWCNTs in the presence of mixed FECA��Fe,Ni� and FECA��Fe,Co� in an Ar atmosphere.SWCNTs, thus produced, had diameters ranging from 0.9 to3.1 nm and length over 5 mm. The number density of thetubes was much higher when produced with FECA��Fe,Ni� and FECA��Fe,Co� than with FECA�Fe,FECA�Co, and FECA�Ni. Also, RL��Fe,Ni,C� and RL

��Fe,Co,C� produced nanotube diameters much larger thanthose by RL��Fe,C�, RL��Ni,C�, and RL��Co,C�, re-spectively. The most plausible scenario for all of these maybe described as follows: RL�Ni, RL�La, RL�Gd, andRL�Yt are nonpolar. But RL��Ni,C�, RL��La,C�, RL

��Gd,C�, and RL��Yt,C� are polar. The dipole moment ofRL��Ni,C� is larger than those of RL��La,C�, RL

��Gd,C�, and RL��Yt,C�. With weak dipole moment, RL

��La,C�, RL��Gd,C�, and RL��Yt,C� could not effec-tively attract the RS species. So, the nanotubes thus grownwere quite short. RL��Fe,Ni,C� and RL��Fe,Co,C� arelarger, more porous, and more polar than RL��Fe,C�, RL

��Ni,C�, and RL��Co,C�, respectively. Due to the pres-ence of two different metals, RL��Fe,Ni,C� has highercharge inhomogeneity than RL��Fe,C� and RL��Ni,C�.For the same reason, RL��Fe,Co,C� has higher charge in-homogeneity than RL��Fe,C� and RL��Co,C�. FollowingOtani et al.,91 RL��Fe,Ni,C� and RL��Fe,Co,C� have,therefore, larger dipole moment than RL��Fe,C�, RL

��Ni,C�, and RL��Co,C�, respectively. Due to the pres-ence of two metals, RL��Fe,Ni,C� and RL��Fe,Co,C�have also higher structural inhomogeneity �disorder� thanRL��Fe,C�, RL��Ni,C�, and RL��Co,C�. RL

��Fe,Ni,C� and RL��Fe,Co,C� are, therefore, more poly-crystalline and have larger number of molten �semimolten�nanopores than RL��Fe,C�, RL��Ni,C�, and RL

��Co,C�. These nanopores are circular and concentric. TheRS species could diffuse through RL��Fe,Ni,C� and RL

��Fe,Co,C� in greater number and with higher mobility.The experimental observation3 suggests that carbon solubil-ity is indeed higher in alloys than in single metals. The ex-perimental observation98 also indicates that the FECA clustersize of the RL species correlates well with reaction rate. All

these demonstrate that RL��Fe,Ni,C� and RL

��Fe,Co,C� were more polar, and that they could readilyattract the RS species to produce high density of long nano-tubes. The requirement for a bimetallic RL species, viz., RL

��FECA1,FECA2,X� to achieve the highest dipole mo-ment is to optimize the �1� FECA1, FECA2, X mixture; �2�FECA1:FECA2:X atomic ratio; �3� miscibility of X in the�FECA1,FECA2� mixture; and �4� growth conditions �e.g.,temperature, pressure, etc.�.

C. Evidence of nanopores

In a CVD experiment by Cassell et al.,99 the chemicalcomposition and texture of the FECA used for the growthwere optimized to accomplish high yield of high-qualitySWCNTs. Two different FECAs: FECA��Fe,Mo,Al2O3�and FECA��Fe,Mo, �Al2O3uSiO2–hybrid��, respectively,and RS�CH4 were used for this growth. The SWCNTyield was much higher with the FECA��Fe,Mo, �Al2O3uSiO2–hybrid�� than with the FECA��Fe,Mo,Al2O3�. And this was due to the more texturalstructure of the FECA��Fe,Mo, �Al2O3uSiO2–hybrid��compared to that of the FECA��Fe,Mo,Al2O3�. TheFECA��Fe,Mo, �Al2O3uSiO2–hybrid�� had the largestpore volume among all the catalysts investigated. The largepore volume resulted from high density of mesopores createdinside the seed due to lattice disturbance and disorder. Itallowed smoother diffusion of the RS species through the RL

species of the droplet. The SWCNT yield was consequentlyhigh. This experiment thus lends support to our idea put forthin Sec. IV, and demonstrates that, for growths at TTE,molten �semimolten� mesopores are actually the preferredpaths for the diffusion of the RS species through the RL spe-cies. The density of these pores increased if two or moreelements were used together to catalyze the growth.

Alvarez et al.39 observed that SWCNT growth began10–30 min after the introduction of hydrocarbon into thechamber. Only amorphous carbon, which is detrimental fornanotube growth, was formed during the first 3 min. Thefastest nanotube growth took place only when the FECA hadoxidelike characteristics. This growth rate was, however,substantially reduced when the oxidelike material was gradu-ally converted into metal. An oxidelike material has disor-dered lattice; it is generally porous. But a metal is single-crystalline and nonporous. So, the oxidelike material hadnanopores, which became molten �semimolten� due to thesize-dependent mesoscopic effect. The droplets were thusformed, and the RS species could smoothly diffuse throughthem to the L/S interface to produce nanotubes. The nano-pores were reduced and even eliminated when the oxidelikematerial was converted into metal. There were then a few, ifany, droplets available to mediate nanotube growth. Conse-quently the SWCNT yield became very low. Homma et al.58

found that pretreatment of SiO2 substrate at T�950 °C inH2 prior to CVD led to higher density of SWCNTs. This maybe attributed to higher density of molten �semimolten� nano-pores and droplets generated due to greater amorphizationand higher defects created on the substrate surface. The ex-periments by Alvarez et al.39 and Homma et al.58 attest to the

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hypothesis that the formation of nanopores, and dropletsfrom these nanopores, is central to the nanotube growth.

D. Evidence of FECA/carbon material at the nanotubehead

Pan et al.31 grew carbon nanotubes employing FECA��Fe,silica� nanocomposite particles. EDX spectra showedthe presence of carbon, iron, silica, and oxygen �62.5 wt %,30.4 wt %, 6.8 wt %, 1.3 wt %, respectively� at the nanotubetip. While growing carbon nanotubes in the temperaturerange of 1100 °C, Benissad et al.100 observed small metalcarbide droplet at the nanotube tip. Kokuvitsky et al.80 grewcarbon nanotubes, using arc discharge under a pressure of550 Torr helium gas, and employing graphite electrodes asthe carbon source. The growth was performed on silica sub-strate with FECA�Ni. The growth temperature was800–950 °C. The experimental electron diffraction data80

indicated that the nanotube tips had nickel and nickel–carbonsolid. All these suggest the following: The seed, for theFECA-mediated growth, was actually made of FECA/X ma-terial, and was amorphous. The droplet was formed from themolten �semimolten� FECA/X seed. And this seed had nano-pore�s� inside it. The presence of FECA�Ni at the nanotubetip inhibited the formation of carbon pentagons but facili-tated the formation of carbon hexagons. The FECA/carbonsolid solution had unsaturated bonds at the nanotube tip.They were actually the dangling bonds that created dipolemoment at the nanotube edge. This very dipole moment keptthe nanotube tip chemically active, and as an attraction sitefor the RS species. The RS adatoms landed on the dropletsurface, were converted into small clusters, and were thenadsorbed on the droplet surface before being supersaturatedat the L/S interface. The inert gas used in the synthesis car-ried away excess energy from the adsorption site.

E. Evidence of seed melting and adatom-inducedgrowth

The rapid deposition of long, oriented SWCNTs byHuang et al.35 is a good example of the adatom-inducednanotube growth. This growth made use of RSwCH4. Wecite three compelling reasons to substantiate our suggestion.First, the nanotubes, produced after 20 min, had length up to1.5 cm and diameter around 1.25 nm. The growth rate, about12.5 �m /s, was very high. Such a high growth rate couldnot be achieved with the RS=RSS species �see Sec. IV A andFig. 4� landing on the substrate surface, and then diffusing tothe droplet via the substrate surface. The RSS species under-goes surface scattering during diffusion through the substrateand the nanotube sidewall. So, they are slowed down duringtransport. Second, the nanotubes had spherical NSC seed atthe nanotube tips. The seed dimension was larger than thelateral dimension of the nanotube. It happened because theside surface of the seed was curved out. And it could happenonly because the seed was molten �semimolten�. It was mol-ten �semimolten� owing to structural inhomogeneity and het-erointerface at the seed/nanotube interface. The tube wasmade of carbon. So, the seed was made of FECA/carbonmaterial �e.g., noneutectic alloy, mixture, solid solution, or

even eutectic alloy�. Otherwise, there would be no heteroint-erface. Third, the nanotubes were straight and oriented in thedirection of the RS adatom flow. It is possible only when theRS=RSI species lands directly on the droplet surface from thevapor phase. This means the growth was carried out by theadatom-induced process. Noting that the nanotube neck wasmade of carbon, and the seed was made of FECA/carbon,one may assume that there was a charge transfer between thenanotube neck and the NSC seed. It gave rise to dipole mo-ment. The growth rate was very high because the RS speciescould be effectively attracted by the RL species under theinfluence of this dipole moment.

VIII. CATALYTIC ACTION

Takagi et al.43 grew carbon nanotubes at 800–950 °Con Al-hydroxyl film employing Au, Ag, Pt, Pd, Cu, Fe, Co,and Ni as FECAs. Yuan et al.69 grew carbon nanotubes at900 °C on quartz film employing Fe, Co, Ni, Cu, Pt, Pd, Mn,Mo, Cr, Sn, Au, Mg, and Al as FECAs. Takagi et al.45 grewcarbon nanotubes on silicon substrate at 850 °C employingSi, Ge, and SiC as FECAs. Huang et al.46 grew carbon nano-tubes at 900 °C employing SiO2, Al2O3, TiO2, and Er2O3 asFECAs. All these FECAs exhibit wide variations in materialstructure. They have large differences in melting points, andalso in the eutectic phases with carbon. While some of themare transition metals, others are noble metals, semiconduc-tors, clusters, or even oxides. Transition metals �e.g., Fe, Co,Ni, etc.� are known to have strong catalytic action on graph-ite formation.101 But the semiconductors �e.g., Si, Ge, SiC�,oxides �e.g., SiO2, Al2O3, TiO2, etc.�, and even noble metals�e.g., Au, Ag, etc.� are known to lack catalytic action ongraphite formation. The binding energy of carbon is muchlarger with the Fe-family of metals102 than with others. Car-bon atoms cannot, therefore, stay long on FECA nanopar-ticles lacking catalytic function for graphitic formation. Yetall of them serve as FECA producing carbon nanotubes.Also, all of them exhibit catalytic action on graphite forma-tion in a relatively narrow temperature range �e.g., 800 to1000 °C�. This is remarkable considering that they havevery large differences in materials characteristics, meltingtemperatures, and eutectic phases with carbon. We cite anexample �see Table II�: both Al/C and Re/C materials pro-duce carbon nanotubes at temperatures between 800 and1000 °C. However, the melting point of aluminum is only660 °C but the melting point of rhenium is 3180 °C. One ofthem is lower than the growth temperature, and the other oneis much higher than the growth temperature.

We believe that the primary reason for all the aboveobservations is simple: The graphite formation does not re-ally require the catalytic function of the Fe-family of metals.It does not also require the nanoparticles to be in a crystallinestate, or even in a eutectic-alloyed state with carbon. Instead,it requires them to cause segregation, and to form just a solidmixture, solid solution, or noneutectic alloy with carbon at-oms. Almost all of the FECA/carbon materials produce car-bon nanotubes at 800 to 1000 °C simply because there ishardly any need for chemical reaction, Fe-type catalytic ac-tion, or structural modification of the FECA/carbon material

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into eutectic form during growth. There may though be needfor interatomic interactions between FECA and carbon. Theymust create an amorphous material that facilitates smoothdiffusion of the RS�X=C through the droplet. Based onthese observations, we may define the catalytic function ofFECAs as follows: First, a FECA should cause segregationyielding a shelled seed and a central core. Second, it shouldassist the formation of a droplet defined in Sec. IV. Thiswould involve the creation of lattice disorder, grain bound-aries, structural amorphicity, dipole moment, and molten�semimolten� nanopores in the shelled seed even at a tem-perature TTE. We call this temperature T�TDRP. The mol-ten �semimolten� state of the nanopores, which gives rise todroplets, is created from the seed due to structural distur-bance�s�. The temperature T�TDRP of this droplet should beoptimal enough to engineer the yield, upon nucleation andsupersaturation, of the XmYn crystal from the RS�X andRS�Y species. Again, the shape, organization, molten�semimolten� state, materials characteristics, and temperatureT�TDRP of the molten �semimolten� nanopores, should to-gether provide the confinement for appropriate alignment,and the flexibility for reorganization �nucleation� of X and Yatoms into tubular lattice structure of the XmYn crystal units.The FECA/X species of the droplet is amenable to deforma-tion needed for interaction with the diffusing XmYn mol-ecules. The complex interactions of the X and Y atoms withthe FECA of the FECA/X droplet species are crucial for thereorganization and the nucleation of the XmYn moleculesinto tubular form. The mechanism of growth at T�TDRP

might be the VQS mechanism.71 The nanotube would not beformed if one of them is unsuitable for crystal formation. Allof these may be achieved irrespective of whether the FECAis a metal, a semiconductor, a cluster, or an oxide. Thus theFECA exhibits a platform on which FECA/X material canform NSA, NSB, or NSC seeds. These seeds may exhibitphase separation from the FECA core, and may produce car-bon nanotubes even at T�TE.

The main features of the present model are the atomicreorganization, chiral selectivity, and structural realignmentof the RS vapor species �for example, RS�C for carbonnanotubes, and RS�BN for BN nanotubes� during diffusionthrough the FECA/X molten �semimolten� seed. It has strongdipole action. So, the RS adatoms land on the molten �semi-molten� seed, diffuse through it, and undergo supersaturationto achieve chirality distribution and to produce nanotube.Carbon atoms are organized into graphitic form during dif-fusion through the droplet, and also during supersaturation.Carbon nanotubes are grown in the temperature range of800–1000 °C simply because this temperature range is mostfavored for the transformation of carbon atoms into thesp2-bonded graphitic tubular form.

IX. DEPENDENCE OF GROWTH ON CONDITIONSFOR DROPLET FORMATION

Based on our discussions in Sec. VIII, the nanotubegrowth is mediated by droplets. These droplets by the VLSmechanism are created at a temperature T�TE due to theeutectic alloying of FECA and X. These droplets by the VQSmechanism are created at a temperature TTE due to the

noneutectic mixing �alloying� of FECA and X. FECA and Xcreate FECA/X mixture, FECA/X solid solution, FECA/Xnoneutectic alloy, or FECA/X eutectic alloy, for the forma-tion of droplets. These droplets by the SCG, and OAGmechanisms are, however, created at T�TM. Lattice disor-der, grain boundaries, and/or structural amorphicity, alwaysplay a role in noneutectic growth to yield molten �semimol-ten� nanopores in the shelled seed. Droplet formation is in-deed the most important figure of merit for growths by allmechanisms. Droplet �as defined in Sec. IV F� is the vehiclefor smooth diffusion of the RS species through the RL speciesto the L/S interface. The interactions of the RS species withthe RL species have always a certain specific pattern for thegrowth of a certain XmYn nanotube. No matter what thegrowth parameters �e.g., RS species, carrier gas, temperature,pressure, etc.� are, the end product of these reactions is al-ways the same XmYn molecule, and essentially the samecharacteristics of this molecule. This is the fundamental rea-son of why nanotubes �in particular, carbon nanotubes� al-ways have similar morphologies, no matter what synthesistechniques, growth conditions, carrier gases, FECAs, orcombinations of FECAs, are employed to produce thesenanotubes. Remarkably, depending on even wide variationsin the synthesis parameters, SWCNTs can have diametersvarying only between 0.7 and 3 nm. Almost always theygrow either isolated or self-assembled in crystalline bundles.

The droplets have been observed previously in works byHuang et al.,35 Kukovitsky et al.,80 and Yin et al.103 Whilevery high temperature or pressure may cause oversupply ofX on FECA, very low temperature or pressure may causeundersupply of X on FECA. None of them is favorable fordroplet formation. The requirements for droplet formationare satisfied differently under different growth conditions�e.g., temperature, pressure, RS composition, seed nanopar-ticle size, etc.�. Only certain temperature or pressure can cre-ate lattice disorders, grain boundaries, and structural amor-phicities needed for the generation of molten �semimolten�nanopores, and droplets from these nanopores. While theymay be realized for a certain noneutectic composition, forexample, of Au/C alloy �solid solution� at a certain tempera-ture �or pressure�, they may be realized for some other non-eutectic composition of Fe/C alloy �solid solution� at someother temperature �or pressure�. While they may be realized,for example, with RS�CH4 at a certain temperature, pres-sure, flow rate, and ambient condition, they may be realizedwith RS�C2H2 or RS�CO at some other temperature, pres-sure, flow rate, and ambient condition. Similarly, while theymay be realized, for example, for a certain eutectic/noneutectic composition of Au/C alloy at a certain combina-tion of temperature, pressure, flow rate, and ambient condi-tion, they may be realized also for the same eutectic/noneutectic composition of Au/C alloy but at some othercombination of the same temperature, pressure, flow rate,and ambient condition. All these suggest that, although met-als such as Fe, Co, Ni, Cu, Pt, Pd, Mn, Mo, Cr, Sn, Au, Mg,and Al; semiconductors such as Si, Ge, SiC; and oxides suchas SiO2, Al2O3, TiO2, and Er2O3; can serve as FECAs, and

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can produce situations conducive to the creation of molten�semimolten� nanopores and droplets, they can do so onlyunder certain specific conditions.

Let us put forth some illustrations. Takagi et al.43 exam-ined the impact of atmospheric heating of FECA�Au andFECA�Fe on the SWCNT growths. Using FECA�Fe, theyobserved higher SWCNT growth with atmospheric heatingthan without atmospheric heating. Thus Fe acted as FECAproducing SWCNTs even without atmospheric heating. Thisis drastically different for FECA�Au. Using FECA�Au,the SWCNT growth was significant with atmospheric heat-ing but insignificant without atomspheric heating. These sug-gest that the noneutectic composition of the RL��Fe,C��mixture, solid solution or noneutectic alloy� had some nano-pores even without atmospheric heating, and that dropletswere formed from these nanopores due to the size-dependentmesoscopic effect. This noneutectic composition of RL

changed due to atmospheric heating. And it led to an increasein the number of the nanopores, and hence of the droplets.The density of nanotubes thus formed became much higherunder higher atmospheric heating. In contrast, the noneutec-tic composition of the RL��Au,C� �mixture, solid solutionor noneutectic alloy� had no nanopore in the absence of at-mospheric heating. It produced no nanotube without atmo-spheric heating. However, it was very sensitive to atmo-spheric heating. The number of nanopores and the possibilityof melting �semimelting� inside the RL increased substan-tially under atmospheric heating. The atmospheric heatingled also to the removal of contaminant�s�, if any, from thetips of some �or all� of the nanopores.

Homma et al.58 observed that, under identical growthconditions, SWCNTs grown with FECA�Al2O3 were shortand straight; but with FECA�Fe were long and curved.While the average growth rate with FECA�Al2O3 was 200nm/min, the average growth rate with FECA�Fe was 1200nm/min. Yuan et al.69 observed that, under identical growthconditions, SWCNTs produced by different FECAs had dif-ferent alignments. While these alignments, for example, withFECA�Pd were poor, these alignments with FECA�Mnwere rich. Interestingly, the alignments with FECA�Pdwere greatly improved under optimized growth conditions.Yin et al.103 produced chains of hollow GaN nanospheres�diamerer 20–25 nm� at T700 °C but GaN nanotubes �di-amerer 20–25 nm� at T�700 °C. Chains of hollow GaNnanospheres were converted into GaN nanotubes at T�700 °C. Some simple reasons for lower nanotube growthrate under certain condition are �a� longer time taken by theprecursor to yield nanotube elements/molecules; �b� resistivepath created by the nanopores for the diffusion of the RS

species to the L/S interface; �c� undersupply or oversupply ofnanotube atoms/molecules to the growth front; and �d� com-position of the RL species not very conducive to growth.

X. APPLICABILITIES AND DISCUSSIONS

A. Nanotube growth by the SCG mechanism

So far our attention has been focused primarily to eluci-dating the FECA-mediated carbon nanotube growth. Here,we show that the present model is applicable also to the

nanotube growth by the SCG mechanism. To demonstrate it,we describe the growth of GaN �a=3.189 Å, c=5.185 Å�nanotubes.19,20 A GaN matrix, 10 to 30 �m thick, wasformed on Si substrate prior to the growth. A thin Ga layerwas then formed on the matrix. It was next annealed, whichproduced GaN nanoparticles �platelets� with Ga on the top ofGaN nanoparticles �platelets�. Some of the nanoparticleswere on a flat surface, while others were on clusters andhillocks formed during annealing. As the temperature waslowered before growth, there occurred phase separation. Ga,lying on the GaN surface, thus segregated to the periphery.GaN nanoparticles were consequently surrounded at the pe-riphery by Ga-rich shells, which might have oxygen fromcontamination. These shells were still on GaN. So, the shellssuffered from stress due to differences in lattice structuresand thermal expansion coefficients at the interface with GaN.They became therefore amorphous, and served as seeds fornanotube growth. Figure 8�a� shows them formed on plate-lets but Fig. 8�b� shows them formed on clusters and hill-ocks. One can see from these figures that the Ga seeds sur-round the GaN core. RS�GaN molecules were generated bythe reaction: 2Ga+2NH3→2GaN+3H2 before or after Gaand NH3 vapors landed on the seed surface. These RS

�GaN molecules diffused through the shelled seed underappropriate growth conditions producing GaN nanotubes.These growth conditions include a growth temperature of�850 °C, a chamber pressure of 15 Torr, and an ammonia

(a)

(b)

50 nm

50 nm

FIG. 8. Gallium seeds formed on �a� GaN matrix and �b� GaN clusters andhillocks during GaN nanotube growth by the SCG mechanism.

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flow rate of 50 to 100 SCCM �SCCM denotes cubic centi-meter per minute at STP�. Under these conditions, thinnanostripes were created inside the shelled seeds, which be-came molten �semimolten� due to size-dependent meltingpoint depression. The shelled seeds were thus converted intoshelled droplets. They had nanopores. Figure 9�a� showsGaN nanotubes grown from the shelled seeds. As evidentfrom this figure, the nanotubes have several different forms.While some of them are circular, others are hexagonal, pen-tagonal, and even irregular in shape. Figure 9�b� shows in-teresting nanotube structures.104 They resulted from defec-tive segregation of Ga from GaN nanoparticle prior to thegrowth, and also from the lack of uniform diffusion of the RS

species through the nanopores�s�. The nanotubes have con-sequently open sidewalls. One of the nanotubes was splitinto two nanotubes, and has open sidewalls.

B. Nanotube growth by the OAG mechanism

The present model explains the oxide-assisted nanotubegrowth, as well. Let us consider the growth of InP nanotubesunder the In-rich condition. For this growth, the matrix ismade of In2O3. During annealing In vapor reacts with In2O3

matrix to produce In2O seed layer: 4In+In2O3→3In2O. Dur-ing this annealing, the In2O seed layer, thus formed, alsosplits into seed nanoparticles. As temperature goes down af-

ter annealing, In2O loses energy. So, In tends to be separatedfrom In2O; it tends to create a metal core. This is vapordisproportionation.105 Under the influence of this vapor dis-proportionation, some of the In2O molecules revert back toIn2O3 producing In core: 3In2O→ In2O3+4In. The In2O3 ox-ide created from the reaction is expelled to the periphery.The In2O seed nanoparticle now has In core and In2O shell.The In2O shell is amorphous, and has grain boundaries. So itundergoes size-dependent melting point depression creatingsemimolten nanopores. RS�P and RS� In vapors diffusethrough them. While diffusing through them, they react to-gether to produce InP �e.g., In+P→ InP�. Being highly reac-tive, In2O suboxide may react with the RS�P species pro-ducing InP:4P+3In2O→4InP+In2O3. The InP moleculescreated from them undergo supersaturation yielding InPnanotube. The In2O3 molecules released from various reac-tion�s� create a thick In2O3 sheath around the InP nanotube.Under In-rich conditions, RS=In lands also on the In core.As a result, In core also grows together with the InP nano-tube. They grow simultaneously. The InP nanotube producedby the experiment is filled with In metal, and has thick In2O3

oxide sheath. That the proposed mechanism is correct ismanifested from experimental observation of InP nanotubeby Tang et al.25 This nanotube was encapsulated by In core,and had thick In2O3 oxide sheath. The nanotube tip had theIn:P:O ratio as 87:10:3, which confirms that the seed wasmade of either In2O or some derivative of In2O.

The present model explains carbon nanotubes46 growneven with FECA�SiO2. They were grown at 900 °C underSiO2-rich conditions. During annealing, SiO2 produced SiOseed nanoparticles. However, during cooling after annealing,SiO lost some energy and became unstable. To regain stabil-ity it reacted with C �solid or vapor�106–108 producingSiC:C+2SiO→SiC+SiO2. This SiC formed the core; SiO2

was expelled to the periphery of the core. Some of the SiOmolecules simply reverted back to SiO2 molecules: 2SiO→Si+SiO2. In this growth environment, Si produced fromthis reaction, became amorphous. Together with SiO2, it cre-ated a shell, which served as the seed for nanotube growth.Si has a melting point of 1410 °C, and SiO2 has a meltingpoint of 1610 °C. But they also have grain boundaries. So,the seed was converted into a droplet due to size-dependentmelting point depression of the grain boundaries. RS�C va-por species diffused through nanopore�s� of this droplet, andunderwent supersaturation yielding carbon nanotubes.

C. Nanotube growth by the VLS mechanism

The present model explains also the VLS growth ofnanotubes. We cite an example. Kong et al.27 have reportedthe Au-mediated VLS growth of the ZnO �a=3.249 Å, c=5.207 Å� nanotubes from a mixture of ZnO powder andgraphite. During annealing, the solid mixture of ZnO andgraphite underwent the reaction: 2ZnO+C→2Zn�vapor�+CO2. The Zn atoms resulting from this reaction diffusedinto the Au solvent of the Si substrate surface, producingAu/Zn seed nanoparticles. The CO2 vapor, thus created,served, however, as the RS species for growth of ZnO nano-tubes. During cooling after annealing, there occurred phase

(a)

(b)

50 nm

FIG. 9. GaN nanotubes grown from the seeds; �a� various structural forms�e.g., circular, hexagonal, pentagonal, irregular, etc.� of the nanotubes; �b�nanotubes with incomplete �broken� walls.

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separation. So, some of the Zn atoms were segregated fromthe Au/Zn solid solution creating a central core and a shell.While the shell had higher concentration of Zn than Au, thecore had higher concentration of Au than Zn. Eventually theZn-poor Au/Zn core was separated from the Si substrate dueto the size-dependent melting of the core/substrate interface.However, it was still conjoined with the Zn-rich Au/Zn shell,which served as seed for nanotube growth. The core, sepa-rated from the substrate, produced the NSC cap for the seed.The Au/Zn solid solution has no eutectic phase. It has aperitectic phase at 438 °C �phase composition is 96 at. %Zn; 4 at. % Au�. The Au/Zn compound of the shell becamedroplet at 900 °C, which is higher than the peritectic tem-perature T=438 °C. The RS�Zn and RS�CO2 vapors,landing on the cap, slided down to the peripheral droplet.When diffusing through the droplet, they reacted together toyield ZnO:Zn+CO2→ZnO+CO. The ZnO molecules fromthis reaction underwent supersaturation producing ZnOnanotubes. Energy dispersive spectroscopy shows that theseed at the tip of the nanotube was made of Zn and Au; butthe nanotube was made of ZnO.

D. Nanotube growth by the VQS mechanism

The growth of almost all SWCNTs and MWCNTs, aslisted in Table II, is performed by the VQS mechanism.71

The liquid droplet observed by Mardonero109 during growthof carbon fibers was made of C12H24 �melting point�435 °C�. The FECA used for this growth provided an in-terface but the growth was performed by the VQSmechanism.71 Although Kukovitsky et al.80 suggested thatthe VLS mechanism was responsible for the growth of theircarbon nanotubes using carbon vapor and Ni catalyst, thisgrowth took place at a temperature 300–400 °C below theNi/C eutectic temperature TE �TE1319 °C�. It was per-formed, in fact, by the VQS mechanism.71 In situ TEMobservations70 reveal that MWCNTs grow continuously fromFe3C alloy particles at 600 °C. This temperature is far belowthe eutectic temperature TE=1153 °C for the Fe/C alloy. TheFe3C alloy particles have cementile structure and lattice va-cancies. Depending on growth parameters, these vacanciescan be numerous. The particles undergo fluctuations underthe gas environment at elevated temperatures. They are alsodeformed slowly and slightly, which leads to changes incrystal orientations. So, they suffer from disturbances in thecrystal structure, and have nanopores. Liquid droplets resultfrom size-dependent melting point depression of these nano-pores. Fe3C was identified before by Yoshida et al.110 as theagent for carbon nanotube growth, and by Oberlin et al.111 asthe agent for carbon nanofibre growth. Ni3C was similarlyconsidered to be responsible112 for carbon nanotube growth.They were believed to be “liquidlike.” The simple reason forthis is the formation of liquid droplets at TTE.

Recently, Takagi et al.113 observed carbon nanoparticlesto act as seeds for carbon nanotube growths. These nanopar-ticles do not fuse with each other even when agglomeratedfor use for the CVD growth of carbon nanotubes. In an ear-lier experiment114 for carbon nanotube growth employingFECA�Ni, the formation of graphene islands was consid-

ered to be crucial. It was not different in Takagi’s experi-ment. The islands had five-member rings formed on thesp2-relaxed solid carbon surface. Five-member solid ringsformed on the six-member solid rings caused defects, andwere the causes of lattice disturbance. And this very distur-bance led to the formation of nanopores and liquid dropletsfor the VQS growth of nanotubes.

XI. SOME BASIC PRINCIPLES GOVERNINGNANOTUBE DESIGN

A. Description

The structure and morphology of nanotubes should bedictated by at least four basic principles. First, the nature ofchemical bonds in nanotube material should be such thatthese bonds can appropriately be tailored to achieve desirednanotube characteristics. The nanotube length and thenanowall thickness depend on the in-plane bonding and theout-of-plane bonding of various monolayers of the nanotubematerial. If both of them are strong, the nanotube lengthwould be long, and the nanotube wall would be thick. If themonolayers exhibit strong in-plane bonding but weak vander Waals-type out-of-plane bonding, the nanotube lengthwould be large but the nanotube wall would be thin. If themonolayers exhibit weak in-plane bonding but strong out-of-plane bonding, the nanotube length would be small but thenanotube wall would be thick. Second, if the nanotube ma-terial is designed to engineer and produce a multiwallednanotube, then the interwall strain for this material must below. In general, the interwall spacing of a nanotube increaseswith decrease in its diameter.115 Again, the smaller the diam-eter of the nanotube, the larger is its curvature, and hence thelarger is its interwall strain. This strain would be extremelylarge for a very thin nanotube of very small diameter. Thismeans, a very thin nanotube, with very large curvature, couldhardly be a double-walled or a multiwalled nanotube. In or-der for a nanotube to be multiwalled nanotube, it must haverelatively large inner-wall diameter �e.g., the diameter of theinnermost wall�, or the material be free from interwall strain.Third, depending on the nature of segregation, SLNP �seeSec. IV C� can be larger than, equal to, or smaller than unity.Fourth, FECA-mediated growth of a single-walled nanotubemust be tuned with appropriate nanoparticle size. The prob-ability of diffusion of X into FECA to form FECA/X mate-rial varies with FECA nanoparticle size. So, the formation ofdroplet depends on the FECA size. X solubility in FECAincreases with decreasing FECA nanoparticle size. Thismeans X at.% of the FECA/X nanoparticle is higher �e.g.,FECA:X atomic ratio is smaller� in smaller FECA/X nano-particle, which is created by the diffusion of X in the FECAnanoparticle. The melting point of this nanoparticle de-creases with decreasing particle size.116 Based on FECA/Xbinary phase diagrams,117 the X solubility in FECA, there-fore, increases with decreasing FECA nanoparticle size,which promotes the formation of FECA/X core. This solu-bility dictates also the nature of segregation of X from theFECA/X core during cooling. In general, the smaller thenanoparticle, the higher should be the probability ofsmoother and more uniform segregation of X to, near, or

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even beyond the nanoparticle periphery from the nanopar-ticle bulk. The shell, thus formed, would be very narrow andhomogeneous with high concentration of X. Also, SLNP

would nearly equal to one if the narrow shell is formed at theperiphery of the nanoparticle. If the FECA is made of anoxide �e.g., SiO2, Fe2O3, Al2O3, etc.�, the FECA/X shell,with X accumulated on FECA, would have disturbed anddissordered lattice structure. It would preferrably have asingle nanopore guaranteeing the formation of single-wallednanotube. With high concentration of X in the FECA/X shell,the nanopore and the droplet would be deep. The deep con-finement would be essential to relieve the torsional stress onthe CuC bonds during initial nucleation of the RS speciesin a highly curved nanopore around a very small nanopar-ticle. Special growth conditions would be required to realizevery large-diameter nanotubes. If these nanotubes are formedon FECA, the diffusion of X into FECA to create uniformlycompositioned FECA/X nanoparticle would not be easy. Thesegregation of X to �or near� the periphery of a largeFECA/X nanoparticle would not therefore be very uniform.While diffusing to �or near� the periphery, X would furthersuffer from scattering by the FECA/X particle surface. Theshell resulting from the segregation would not, therefore,have nanopores and droplets appropriate for good nanotubegrowth.

B. Experimental demonstration

To demonstrate that the proposed principles for nanotubematerial would be feasible, we highlight features of someexisting experiments. The inner wall diameter was 58 nm butthe outer wall diameter was 122 nm for the GaN nanotubessynthesized by He et al.19 The inner wall diameter �e.g., thediameter of the innermost wall� was 5.2 nm, and the outerwall diameter �e.g., the diameter of the outermost wall� was13.1 nm for multiwalled BN nanotubes �MWBNTs� obtainedby Ma et al.22 The interlayer spacing of these nanotubes was0.33 nm. The average diameter was 2 nm and the largestlength was 1 �m for single-walled BN nanotubes�SWBNTs� synthesized by Arenal et al.24 The average nano-tube diameter was 27 nm, and the thickness of the nanotubewall varied between 2 and 4 nm for single-walled InP nano-tubes fabricated by Bakkers and Verheijen.29 The averagenanotube diameter was very small, about 1.25 nm, and thenanotube length was very large, about 1.5 cm, for SWCNTsfabricated by Huang et al.35 The average diameter was verysmall, 0.95–1.21 nm for SWCNTs synthesized also by Gavil-let et al.73 However, the growth of carbon nanotubes of di-ameters larger than 100 nm was found to be exceedinglydifficult.75 MWCNTs employing FECA�Fe were synthe-sized by Sinnott et al.118 For these nanotubes with Fe /C=0.75, the average inner diameter �e.g., the diameter of theinnermost wall� was 5.8 nm and the average outer diameter�e.g., the diameter of the outermost wall� was 33.6 nm. Butfor these nanotubes with Fe /C=0.075, the average inner di-ameter was 4.3 nm and the average outer diameter was 28.3nm. SWCNTs were synthesized also from discrete FECAnanoparticles of various sizes.119 These nanoparticles had di-ameters in the range of 1–2 nm and 3–4 nm, respectively.

Interestingly, the syntheses of nanotubes, describedabove, comply well with the proposed basic principles. Thenanotubes produced by Huang et al.35 could be very thin andvery long simply because carbon is very robust; and graphitehas strong in-plane bonding but weak van der Waals-typeout-of-plane bonding. The van der Waals-type out-of-planebonding is weak equally in MWCNTs and MWBNTs. This isevident from interlayer spacings of 0.34 and 0.33 nm inMWCNTs and MWBNTs, respectively. The diameters of theinnermost walls of both MWBNTs �Ref. 22� and MWCNTs�Ref. 118� are quite large. These nanotubes could be multi-walled for two simple reasons: �a� the curvature of thesenanotubes was relatively small, and �b� the interwall strainfor them was too small to destabilize the walls. The multiplewalls for them could be created because the van der Waals-type out-of-plane bonding among various monolayers isquite weak. The InP and GaN are not as robust as graphite.The outer-of-plane bonding for them is large. For these rea-sons, InP and GaN nanotubes, produced so far, have thickwalls but not large lengths. While SLNP�1 for someSWCNTs,75 SLNP�1 for some other SWCNTs,87 and SLNP1 for some other SWCNTs.119 These are completelyin line with the proposed principle. In line with this prin-ciple, Sinnott’s observation118 shows that higher C content�e.g., smaller Fe:C atomic ratio� in Fe/C nanoparticle corre-sponds to smaller nanoparticle size, smaller shell, andsmaller external and internal diameters of the nanotube thusformed.

XII. CONCLUSIONS

A. General conclusion

A general hypothesis and a unified shell model havebeen presented for nanotube growth. The hypothesis is anextension of the one proposed recently for nanowires.120 Inthe same way as the original one, it may be called the SNM�simple, novel, malleable� hypothesis. The present model de-scribes growths by the FECA-mediated process, the OAGprocess, and the SCG process. It explains almost all experi-mental observations on nanotube growths reported to the lit-erature. It explains the growth of nanotubes with FECA atthe base, nanotubes with FECA at the tip, nanotubes withimpurities at the nanotube sidewalls, bamboo-shaped nano-tubes, single-walled, and multiwalled nanotubes, and nano-tubes open with broken �incomplete� sidewall. It presents anew definition of the catalytic action of FECA, and demon-strates that metals, semiconductors, and even oxides canserve as FECA to mediate nanotube growth. It elucidates thebasic foundation of nanotube growth at TTE, which ap-pears to be crucial for carbon nanotube growth. During thisgrowth amorphous carbon is transformed into graphite. Thechange in phase during this growth takes place when theRS�C adatoms diffuse through the molten �semimolten�FECA/carbon droplet and undergo supersaturation. Andthese take place at temperatures lower than the eutectic tem-perature of the FECA/carbon alloy. It is widely believed thatthe nanotube diameter depends on the size of the seed nano-particle. The present study suggests that it depends rather onthe equilibrium shape and size of the liquid droplet. The

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shape and size of the droplet are dictated by several param-eters including surface tension, vibration/fluctuation, dipolemoment, and capilary forces. It may depend also on the sizeand surface roughness of the seed nanoparticle. Nanotubegrowth stops if the droplet breaks away from the nanotubetip under the influence of parameters such as temperature andpressure which govern the surface tension, capilary forces,and the equilibrium condition of the droplet.

B. Special features of SWCNTs

For the ease of readership, we start from the basics.Three of the four carbon atoms shared covalently with neigh-bors in a plane but the fourth one delocalized among theatoms, give rise to sp2-type bonding. The sp2-type bonding isstronger than the sp3-type bonding, which creates diamond.The basic constitution of the SWCNT is hexagon made ofsp2-bonded CuC covalent bonds. These bonds are amongthe strongest in nature. Because of this, the hexagons sustainextreme strains �up to �40%� in tension without showingsigns of breakage and rupture. Elastic stretching elongatesthe hexagon until the strain is very high. The local defectexhibits mobility. Owing to this mobility, the local defect isredistributed over the entire surface in the two-dimensionallattice. Graphene is a single planar sheet made of hexagons.Graphite is made up of many graphene layers stacked to-gether. Graphite exhibits strong in-plane bonding but weakvan der Waals-type out-of-plane bonding. So, graphite isvery weak normal to its plane. The chemical bonding ofSWCNTs is composed entirely of sp2 bonds, similar to thoseof graphite. This means SWCNT has also strong in-planebonding but weak van der Waals-type out-of-plane bonding.This is unique. This, together with five prevailing character-istics of the RL species of the droplet, dictates the SWCNTgrowth. These five characteristics are as follows: �1� verythin nanopore created around the core. It is about a mono-layer thick; so it resists the nucleation and aggregation ofeven DWCNTs. If very close to the inner wall of the shell, itmay, for example, be created under the influence of the sur-face energy of the core, vibration �fluctuation� of the centralcore, or the core/shell interface states. �2� The RL species inthe shell is very homogeneous implying that there is no lat-eral concentration gradient of any of the components of theRL species of the shell. This may result from a relativelyhigh �but not too high� heating rate, which leads to segrega-tion velocity conducive enough for smooth incorporation ofatoms into a thin shell. �3� The nanopore is molten or semi-molten by mesoscopic size effect creating droplets. The RS

species diffuses smoothly to the L/S interface through themolten �semimolten� RL species of the droplets in the shell.�4� It has dipole moment, which promotes the alignment andreorganization of the RS species into a helical tubular form.�5� The optimal temperature Topt, and the judiciously chosenrelatively large initial heating rate to reach this temperature,give rise to fluctuations and yield deformation�s� of the RL

species. This is critical. There occurs no deformation of theRL species, and no interactions between the RS and RL spe-cies, unless the temperature Topt is optimally high, and theheating rate to reach this temperature is sufficiently large. All

these provide flexibility and extra energy to the RS speciesfor interaction with the RL species, and for organization intohexagonal ring. They together facilitate smooth growth. Thehigh temperature Topt attained with lower heating rate mayproduce pentagons or few hexagons, if any but no appre-ciable concentration of hexagons. These are some of the rea-sons of why Huang et al.35 achieved very high SWCNTgrowth rate resorting to high optimal temperature Topt andhigh heating rate. In contrast, Ugarte121 produced only nano-particles but no nanotubes, at T=Topt arrived at with lowheating rate. Even though SWCNT has a single-walled struc-ture, only a monolayer thick, it is extremely strong.

ACKNOWLEDGMENTS

The author wishes to thank Maoqi He, Arif Khan, AlbertDavydov, Chip Eddy, Fritz Kub, Ron Carter, and PratulAjmera for help and discussions. He is grateful to the refereeof the paper for highly constructive comments, criticisms,and suggestions.

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