Do all wurtzite nanotubes prefer faceted ones?

Abstract

First-principles computations have been preformed to investigate the stability of one-dimensional (1D) crystalline nanowires, faceted nanotubes, and conventional single-walled nanotubes (SWNTs) with various sizes, as well as the two-dimensional infinitely single layers for several wurtzite materials. Regardless of the diameters, the SWNTs are more stable than sp(3)-dominated faceted nanotubes and nanowires for BN and C, while for AlN, GaN, ZnO, ZnS, and Si, the faceted nanotubes and nanowires are always more preferred energetically than SWNTs. However, the stability of SiC SWNTs relative to other 1D nanostructures is diameter-dependent: the SiC SWNTs are more stable than thinner faceted nanotubes and nanowires, but less stable than thick ones. This indicates that SiC SWNTs and faceted nanotubes/nanowires preserving wurtzite configuration can coexist in nanoscale. The different stabilities for various nanostructures are attributed to the competition between sp(2) and sp(3) hybridization of the atoms in wurtzite materials associated with the difference in the atomic radius and electronegativity of the elements involved.

Full text

Do all wurtzite nanotubes prefer faceted ones?
Yafei Li,1Zhen Zhou,1,a兲Yongsheng Chen,2and Zhongfang Chen3,b兲
1Institute of New Energy Material Chemistry, Institute of Scientific Computing, Nankai University,
Tianjin 300071, People’s Republic of China
2Department of Civil and Environmental Engineering, Arizona State University, Arizona 85287, USA
3Department of Chemistry, Institute for Functional Nanomaterials, University of Puerto Rico,
Rio Piedras Campus, San Juan, Puerto Rico 00931, USA
共Received 2 April 2009; accepted 28 April 2009; published online 27 May 2009兲
First-principles computations have been preformed to investigate the stability of one-dimensional
共1D兲crystalline nanowires, faceted nanotubes, and conventional single-walled nanotubes 共SWNTs兲
with various sizes, as well as the two-dimensional infinitely single layers for several wurtzite
materials. Regardless of the diameters, the SWNTs are more stable than sp3-dominated faceted
nanotubes and nanowires for BN and C, while for AlN, GaN, ZnO, ZnS, and Si, the faceted
nanotubes and nanowires are always more preferred energetically than SWNTs. However, the
stability of SiC SWNTs relative to other 1D nanostructures is diameter-dependent: the SiC SWNTs
are more stable than thinner faceted nanotubes and nanowires, but less stable than thick ones. This
indicates that SiC SWNTs and faceted nanotubes/nanowires preserving wurtzite configuration can
coexist in nanoscale. The different stabilities for various nanostructures are attributed to the
competition between sp2and sp3hybridization of the atoms in wurtzite materials associated with the
difference in the atomic radius and electronegativity of the elements involved. © 2009 American
Institute of Physics.关DOI: 10.1063/1.3140099兴
I. INTRODUCTION
Inspired by the structural elucidation of carbon nano-
tubes in 1991,1one-dimensional 共1D兲nanostructures have
been attracting great research interest for their unusual prop-
erties and potential applications, associated with their low
dimensionality, quantum confinement effect, and boundary
effect. Naturally explorations of nanotubes were first ex-
tended to other layered materials. Many layered compounds,
such as metal dichalcogenides MoS2,2WS2,2共a兲,3TiS2,4ZrS2
and HfS2,5metal halide NiCl2,6and BN,7were folded into
nanotubes.8All the above mentioned layered materials have
no strong interlayer bonds and the layers are held together by
van der Waals interaction; therefore, it is easy to understand
that these compounds can be rolled into cylindrical form
under certain conditions. However, some nonlayered materi-
als, especially wurtzite crystals such as GaN 共Ref. 9兲and
AlN 共Ref. 10兲also exhibit tubular morphologies, though they
resemble their bulk phase rather than single-walled nano-
tubes 共SWNTs兲.
Wurtzite structure is adopted by many crystals, such as
BN, Si, SiC, AlN, GaN, ZnO, and ZnS. All these materials
have wurtzite structure as the stable phase except BN, which
crystallizes in cubic and hexagonal phases. However, hex-
agonal BN can transform into wurtzite structure under high
pressure. A wurtzite structure can be seen as nonlayered or
layered with strong interlayer interaction. Atoms in wurtzite
crystals, except for the surface atoms, are all fourfold-
coordinated with tetrahedral configurations
In recent years, wurtzite nanostructures, especially nano-
tubes, have been well studied for their promising applica-
tions in electronic devices, such as optoelectronics and
biochemical sensors. Initially, single-walled carbon nano-
tubelike structures were assumed for these inorganic nano-
tubes. Theoretical studies on GaN,11 AlN,12 ZnO,13 and ZnS
共Ref. 14兲demonstrated that the SWNTs of wurtzite materials
are rather stable since the strain energies of these tubes are
lower than those of BN and carbon nanotubes. The silicon
SWNTs and nanowires were also investigated theoretically.15
However, these SWNTs are rather artificial and hypo-
thetical. Goldberger et al.9synthesized the single-crystalline
GaN nanotubes using ZnO nanowires as templates; Wu et
al.10 synthesized the single-crystalline h-AlN nanotubes
without templates. Instead of the layered tubular structure
and smooth tube walls, they found that the as-obtained AlN
nanotubes have the faceted geometry with hexagonal cross
sections. Via the thermochemistry process, Yin et al.16 suc-
cessfully synthesized the highly faceted wurtzite-type single-
crystalline ZnS nanotubes also with hexagonal cross sec-
tions. Among several experiments to synthesize Si
nanotubes,17,18 none has achieved the SWNT structure. By
means of density functional theory 共DFT兲computations, sev-
eral groups showed that the Si nanotubes prefer puckered
structures instead of smooth tubes,19 and Chen et al.20 veri-
fied that the faceted model of AlN nanotube is energetically
more favorable than the cylindrical one, which was also con-
firmed by others.21 The following theoretical studies demon-
strated that the faceted tube models are also favored by
GaN,22 ZnO,23 ZnS,24 and Si.25 To our best knowledge, the
single-walled AlN, GaN, ZnO, ZnS, and Si nanotubes are
a兲Electronic mail: zhouzhen@nankai.edu.cn.
b兲Electronic mail: zhongfangchen@gmail.com.
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still hypothetical materials up to now. Does this mean that
the cylindrical forms of wurtzite materials are all impos-
sible?
The answer is absolutely no. Sun et al.26 reported the
formation of SiC nanotubes by reacting silicon with multi-
walled carbon nanotubes 共also as templates兲. The produced
SiC nanotubes are multiwalled with 3.5–4.5 Å interlayer
spacing, indicating that coupling between the layers is quite
slight and each layer can be considered as a SiC SWNT. This
finding is quite remarkable since bulk SiC has no layered
structure as graphite and h-BN, which also stimulated the
theoretical investigations on SiC SWNTs.27 Hence one ques-
tion arises: why can SiC form the single-walled tubular
structure while other wurtzite materials cannot? In this paper
we report the evolution rule of nanostructures of wurtzite
materials, including BN, Si, AlN, GaN, ZnO, ZnS, and SiC,
to address the above question by means of DFT computa-
tions. Several structures, including nanowires, faceted nano-
tubes, and SWNTs with different sizes as well as two-
dimensional 共2D兲infinite single layer were considered for
each wurtzite material, and the corresponding carbon nano-
structures were also studied for comparison.
II. COMPUTATIONAL METHODS
In this work, crystalline nanowires and faceted nano-
tubes with various sizes were compared with conventional
SWNTs and 2D infinite single layers. The models of hexago-
nal single-crystal nanowires and faceted tubes were con-
structed from the experimental wurtzite structures, as exem-
plified by BN in Fig. 1. First, a large bulk supercell is
constructed, and then the initial models of several crystalline
nanowires and faceted nanotubes of different sizes are ob-
tained by cutting the supercell with cylinders of various di-
ameters. The atoms outside the cylinder are removed to
achieve crystalline nanowires with different diameters. The
atoms outside a large cylinder and inside a small cylinder are
removed to obtain the faceted nanotubes with different outer
and inner diameters, and the nanostructure surfaces are not
passivated. All the 1D nanostructures are placed in a tetrag-
onal supercell, and periodic boundary conditions are applied
along the axis direction to simulate the infinitely long
nanowires/tubes.
DFT-based ultrasoft pseudopotential28 plane-wave
method implemented in the Vienna ab initio simulation pack-
age 共VASP兲29 was adopted for all the computations. The
generalized gradient approximation 共GGA兲with PW91
functional,30 and a 360 eV cutoff for the plane-wave basis
sets were used. For all the systems studied, the coordinates
of all the atoms within the supercell were fully relaxed with-
out symmetry constraint during geometry optimizations; the
lattice constant cwas also optimized to minimize the total
energy along the tube/wire axis. Five Monkhorst–Pack spe-
cial kpoints were used for sampling the 1D Brillouin zone,
and the convergence threshold was set as 10−4 eV in energy
and 10−3 eV/Å in force.
III. RESULTS AND DISCUSSION
A. Carbon and BN nanostructures
For C and BN nanostructures, it is interesting to find that
the faceted nanotubes F1 and F2 both quit their initial con-
figurations and become double-walled nanotubes after the
optimization 共Fig. 1兲. F1 consists of an outer zigzag 共15,0兲
SWNT and an inner 共9,0兲SWNT, while F2 consists of an
outer zigzag 共21,0兲SWNT and an inner 共15,0兲SWNT. Simi-
lar results have been reported by Pan and Feng31 in a recent
paper. In contrast, the nanowires NW1, NW2, NW3, and the
faceted nanotube F3 still keep their initial bulk configuration,
though significant reconstruction happens to the surfaces. Es-
pecially, the 共12,0兲single-walled C and BN nanotubes are
more stable than all the other C and BN nanostructures con-
sidered except the 2D layer 共Table I兲, and F1 and F2 are
more stable than F3 after changing into cylindrical forms.
The above results are not difficult to understand, since it is
well known that C, B, and N atoms all prefer sp2hybridized
multiple bonds,32 and layered graphite and h-BN are their
stable phases for bulk materials, respectively. Thus, cylindric
forms of BN and C nanostructures, where C, B, and N atoms
all adopt sp2hybridization, are energetically more favorable
than those C and BN nanostructures in wurtzite configuration
with sp3hybridization.
B. AlN, GaN, ZnO, ZnS, and Si nanostructures
The evolution rules of AlN, GaN, ZnO, ZnS, and Si
nanostructures are quite similar, but significantly different
from C and BN 共Table I兲. The NW3 nanowires always have
the largest binding energies, followed by the NW2 nanowires
and F3 faceted nanotubes. The binding energies of 共12,0兲
SWNTs of these wurtzite materials are even lower than those
of the thinnest NW1 nanowires and the thinnest F1 faceted
nanotubes. Since the binding energies of SWNTs increase
with increasing tube diameters due to the smaller strain en-
ergies, 2D single layer can be seen as a limit of SWNTs with
FIG. 1. 共Color online兲Top view of atomic configuration of BN nanostruc-
tures. Both initial and optimized structures for BN faceted nanotubes F1 and
F2 are also given. Moreover, the nomenclature of BN nanostructures is also
applicable to other wurtzite materials considered in this work.
204706-2 Li et al. J. Chem. Phys. 130, 204706 共2009兲
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an infinitely large diameter and the highest stability. Thus,
we computed the single-layered structures of these five ma-
terials to estimate the binding energies of infinitely large
SWNTs. Our computations show that such single layers have
even lower binding energies than those of NW1 and F1. The
above results demonstrate that SWNTs of AlN, GaN, ZnO,
ZnS, and Si can never be more stable than the faceted ones,
even with very large diameters. Although previous
studies11–14 showed that the strain energies for these tubes
are comparable or lower than those of BN and carbon nano-
tubes, they are only metastable since the faceted tubes are
more stable. The SWNT form may be only hypothetical for
the above wurtzite materials.
The instability of Si and ZnS SWNTs can be easily un-
derstood since Si, Zn, and S are reluctant to adopt sp2
hybridization.32 However, AlN, GaN, and ZnO all contain a
first-row element, which prefers to form sp2-hybridized mul-
tiple bonds; what is the reason for the instability of their
SWNTs compared with BN? It is mainly due to the signifi-
cant difference in the atomic radius and electronegativity of
the elements in these wurtzite compounds 共Table II兲. Due to
the large atomic radius difference, the orbital overlap in the
SWNTs of these wurtzite compounds is quite small, resulting
in much weaker
␲
bonding and less stability. Also the sig-
nificant difference of electronegativity gives more ionic com-
ponent to Al–N, Ga–N, and Zn–O bonds which would there-
fore diminish the conjugated effect of
␲
bonding. In contrast,
the atomic radius difference between B and N is relatively
small, and the sufficient overlapping of pzorbits between B
and N brings strong delocalized
␲
system and makes BN
SWNTs rather stable.
C. SiC nanostructures
In contrast to the above both catalogs of wurtzite mate-
rials, the binding energy of 共12,0兲SiC SWNT is higher than
those of F1 and F2, but lower than those of NW2, NW3, and
F3 共Fig. 2兲. This result is amazing since in the previous stud-
ies of wurtzite nanostructures,11,21–24 SWNTs are always less
stable than faceted nanotubes. Very recently, Wang et al.35
have systematically studied the energetics of single-
crystalline 2H-SiC nanowires and nanotubes through first
principles computations. They claimed that faceted SiC
nanotubes are all energetically more favorable than the cy-
lindrical ones. However, the chosen single-walled SiC nano-
tubes in their study are rather thin. To get more insight, we
compared the binding energies of 2D SiC single layer and
SiC nanowires and faceted nanotubes, since the SiC single
layer can model the infinitely large SiC SWNT with the
highest stability. Like 共12,0兲nanotube, the computed binding
energy of SiC single layer is also higher than those of NW1,
F1, and F2, and lower than those of NW2, NW3, and F3. It
implies that SiC SWNTs can never be more stable than
NW2, NW3, and F3. However, since SiC SWNTs are more
favorable than thinner faceted nanotubes and nanowires en-
ergetically, it gives a reasonable explanation why cylindric
form has been realized experimentally for SiC.
It is the relatively strong preference of the
sp2-hybridization and moderate differences in atomic radius
and electronegativity between Si and C that make SiC
SWNTs rather competitive in SiC nanostructures. The atoms
in SiC SWNTs are all sp2-hybridized, and the pzorbitals of C
and Si are sufficiently overlapped and will form strong con-
jugated
␲
bonding on the surface of slab and nanotubes,
which could lower the total energies. Therefore, graphitic
SiC and SiC SWNTs are more stable than those thinner
nanowires and faceted nanotubes. However, as the diameter
and thickness increase, the ratio of surface saturated atoms
versus total ones in nanowires and faceted nanotubes de-
creases gradually, and then nanowires and faceted nanotubes
will be eventually more stable than SWNTs, since wurtzite
SiC is the more stable phase than layered structure 共which
does not exist actually兲for bulk material. In comparison, the
TABLE I. Binding energies per atom 共eV兲aof all nanostructures for each wurtzite material.
NW1 NW2 NW3 F1 F2 F3 共12,0兲Single layer
C 8.609 8.750 8.817 8.966 9.057 8.751 9.100 9.192
BN 8.256 8.355 8.405 8.510 8.574 8.354 8.613 8.865
SiC 6.848 7.026 7.117 6.862 6.865 7.028 6.871 6.920
AlN 6.694 6.846 6.924 6.705 6.707 6.846 6.651 6.679
GaN 5.775 5.905 5.972 5.783 5.785 5.904 5.745 5.774
ZnO 3.593 3.662 3.698 3.599 3.599 3.662 3.564 3.585
ZnS 3.150 3.191 3.211 3.145 3.141 3.187 3.032 3.058
Si 4.800 4.960 5.040 4.815 4.815 4.965 4.595 4.627
aThe binding energy per atom is computed with respect to dissociation into atoms, and also as exemplified by
BN, Eb=共nEB+mEN−EBnNm兲/共n+m兲, where nand mare the number of B and N atoms, respectively. EBand EN
are the energy of B and N atoms, respectively.
TABLE II. Atomic radius 共angstrom兲共Ref. 33兲and electronegativities 共using the Pauling scale兲共Ref. 34兲of
elements contented in the studied wurtzite materials.
C B/N Si/C Al/N Ga/N Zn/O Zn/S Si
Atomic radius 0.67 0.87/0.56 1.11/0.67 1.18/0.56 1.36/0.56 1.42/0.48 1.42/0.88 1.11
Electronegative 2.55 2.04/3.04 1.90/2.55 1.61/3.04 1.81/3.04 1.65/3.44 1.65/2.58 1.90
204706-3 Wurtzite nanotubes J. Chem. Phys. 130, 204706 共2009兲
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thinner nanowires and faceted nanotubes of SiC have high
ratio of unsaturated surface atoms which leave unfavorable
dangling bonds on the surface and thus increase the total
energies. Overall, the above results can vigorously explain
why SiC SWNTs can be a stable phase in experiments, and
account for their high stability even superior to some thin
faceted nanotubes. SiC is the transition of nanostructures
from sp2-dominated to sp3-dominated for wurtzite crystals.
IV. CONCLUSION
In summary, the evolution rule of nanostructures for a
series of wurtzite materials have been systematically studied
using first principles computations. The evolution of wurtzite
nanostructures is highly related to their compositions. For C
and BN, the single-walled cylindric forms are energetically
more favorable than faceted nanotubes and nanowires since
C, B, and N all prefer to adopt sp2hybridization. In contrast,
the more preferable hybridization for Si, Zn, and S is sp3;
therefore, the Si and ZnS SWNTs are much less stable than
the faceted nanotubes and nanowires. For AlN, GaN, and
ZnO, the nanostructures of these materials are dominated
with fourfold-coordination, since the single-walled forms are
rather unstable due to the significant difference of atomic
radius and electronegativity between two elements involved,
which would lower the orbital overlapping and the conju-
gated effect of delocalized
␲
bonding. Overall, we answer
why SiC can form the single-walled tubular structure, while
other wurtzite materials, Si, AlN, GaN, ZnO, and ZnS, al-
ways form the faceted ones. We hope that our study can
bring a deeper understanding of wurtzite nanostructures.
ACKNOWLEDGMENTS
Support in China by NSFC 共Grant No. 20873067兲,
and in the USA by NSF under Grant No. CHE-0716718, the
U.S. Environmental Protection Agency 共EPA Grant No. RD-
83385601兲, and the Institute for Functional Nanomaterials
共NSF Grant No. 0701525兲is gratefully acknowledged.
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FIG. 2. 共Color online兲Variation in binding energies with number of atoms
for various 1D SiC nanostructures. The dot line denotes the binding energy
of 2D SiC single layer.
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