Structure of boron nitride nanoscale cones: Ordered stacking of 240° and 300° disclinations

Article abstract of DOI:10.1103/PhysRevB.61.7686

Recently discovered boron nitride (BN) nanoscale cone particles are shown to consist of an ordered stacking of seamless conical shells. High-resolution transmission electron microscopy and nanobeam electron diffraction allowed the orientation of the BN hexagonal rings to be determined. In all but one case, the results conformed with a model of orderly stacked 240° disclinations, which is the smallest cone geometry ensuring the presence of B-N bonds only. One case of a nanoscale cone constituted of 300° disclinations was found, implying that structures containing line defects of non-B-N bonds may form. 2000 The American Physical Society.

Full text of DOI:10.1103/PhysRevB.61.7686

PHYSICAL REVIEW B
VOLUME 61, NUMBER 11
15 MARCH 2000-I
Structure of boron nitride nanoscale cones: Ordered stacking of 240° and 300° disclinations
†
L. Bourgeois,* Y. Bando, W. Q. Han, and T. Sato
National Institute for Research in Inorganic Materials, Namiki 1-1, Tsukuba Ibaraki 305-0044, Japan
͑
Received 24 September 1999͒
Recently discovered boron nitride ͑BN͒ nanoscale cone particles are shown to consist of an ordered stacking
of seamless conical shells. High-resolution transmission electron microscopy and nanobeam electron diffrac-
tion allowed the orientation of the BN hexagonal rings to be determined. In all but one case, the results
conformed with a model of orderly stacked 240° disclinations, which is the smallest cone geometry ensuring
the presence of B-N bonds only. One case of a nanoscale cone constituted of 300° disclinations was found,
implying that structures containing line defects of non-B-N bonds may form.
I. INTRODUCTION
ate and lead to the formation of fullerene cages. For example,
the difficulty with which BN shells form under electron irra-
diation has been interpreted by some authors as showing
Cones are interesting because their departure from a flat
surface can be solely determined by the topological defect
located at their apex. For a two-dimensional lattice with hex-
agonal symmetry, as in graphitic carbon and trigonal boron
nitride, the simplest such defects are pentagonal and square
rings. A single one of these defects inserted into the hexago-
nal lattice will result in a cone whose apex angle is directly
related to the size of the ring. Ring defects larger than hexa-
gons ͑e.g., heptagons͒ will not generate cones, but saddle-
shaped surfaces. A cone’s apex may also consist of a com-
bination of ring defects. However complicated this
combination may be, for a two-dimensional array with dis-
crete symmetry elements, there will only be a discrete num-
ber of possible apex angles. This can be understood by real-
izing that a cone can be obtained through the operation
where a sector of angle D␪ ͑the disclination angle͒ is re-
moved from a flat sheet, and the two cut sides of the sheet
are joined together. Continuity at the junction is only satis-
8
that two dimensionally curved surfaces of BN are not ener-
getically stable, in contrast with carbon where they easily
9
form. Yet the fabrication of BN fullerene analogs would be
an important extension of the concept of perfectly closed
cages of atoms. Until now, the only system other than carbon
which has been observed to exhibit perfect fullerene geom-
etry is MoS2.10 It is therefore of significant interest to esti-
mate the stability of ring defects in BN.
Conical morphologies have been observed for a variety of
layered materials: graphite,11 BN ͑Ref. 12͒, and
aluminosilicates.1
3,14
Despite the fact that these particles are
helical, i.e., that they consist of a single conical layer
wrapped helically about the cone axis, information about the
nucleation of ring defects could be obtained ͑see Ref. 15 for
C, and Ref. 16 for BN͒. These results were confirmed in a
transmission electron microscopy study where the morpholo-
gies of coproduced BN and C helical cones were compared:
C cones had apex angles compatible with pentagonlike api-
cal defect, whereas BN exhibited sharper tips more consis-
fied if D takes certain values. A cone can then be defined by
its disclination angle, although this does not always allow a
unique determination of the apical defects.
Ring defects are necessary to the emergence of curvature
in layered structures on the nanometric scale. This was sug-
gested some time ago for microporous carbon, a highly dis-
␪
7
tent with a squarelike apical defect. The helical nature of the
particles meant that the ring defects were not closed. In this
paper, unambiguous evidence of the existence of seamless
conical BN shells is presented. This follows an initial report
by the authors of the discovery of BN nanoscale cones,
where apex angles were always observed to be very close to
the 38.9° value for a 240° disclination.17 A 240° disclination
is one of five possibilities for a sheet of trigonal symmetry.
Here, it is shown that the nanoscale cones are indeed perfect
240° disclinations. A 300° disclination was also found, sug-
gesting that odd-membered rings, and more importantly, line
defects of non-B-N bonds, may form in BN.
1
ordered material. More recently, it was found that an or-
dered arrangement of some specific ring defects within a
hexagonal lattice would lead to closed cage structures, the
simplest and most famous one of them being the fullerene
2
C . In C the defects are pentagons, of which there are
6
0
60
twelve. In boron nitride ͑BN͒ however, even-membered
rings, and in particular squares, are thought to be the pre-
ferred defects because they do not necessitate the inclusion
of B-B or N-N bonds, which are weaker than B-N bonds.3
The presence of odd-membered rings becomes more and
more costly the larger the shell, as line defects of B-B or
,4
II. EXPERIMENTAL DETAILS
5
N-N bonds between ring-defects become longer. The com-
mon occurrence of flat caps — presumably constructed from
The nanoscale cones are part of a material constituted
primarily of BN nanotubes. The material was synthesized
5
17
three squares — in BN nanotubes, the more faceted appear-
ance of BN shells produced by electron beam irradiation6
and the sharper tips exhibited by BN helical cones compared
by reacting boron oxide vapor with chemically vapor-
deposited carbon nanotubes under the flow of nitrogen, at
7
18
with C cones indicate that squares are indeed the favored
1500 °C. Observations were carried out on a JEOL 3000F
ring defects in BN. Nevertheless, there is still some degree of
uncertainty as to whether BN square rings can readily nucle-
field-emission high-resolution transmission electron micro-
scope ͑HRTEM͒ operated at 300 kV and equipped with a
0
163-1829/2000/61͑11͒/7686͑6͒/$15.00
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7686
©2000 The American Physical Society

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STRUCTURE OF BORON NITRIDE NANOSCALE . . .
7687
continuity of the BN hexagonal lattice along the entire sur-
face of the cone. For carbon the possibilities increase to five
͑
disclination angle D ϭ60°,120°, . . . ,300°), which corre-
␪
spond to apex angles ␪apexϭ2a sin(1ϪD /360)ϭ112.9°,
␪
8
3.6°, . . . ,19.2°, respectively.19 Therefore the type of dis-
clination observed here, with D ϭ240°, is consistent with
␪
the symmetry requirement for BN. Such a 240° disclination
is sketched in Fig. 2. Note that the apex is shown to consist
of two hexagons sharing a B-N bond, i.e., the apical defect is
a single two-membered ring. This kind of defect is probably
highly unstable as a result of the large strain associated with
non-120° bond angles. More likely configurations will be
discussed later. Two different orientations about the cone
axis are shown in Fig. 2. As the conical sheet is rotated about
its disclination axis, the hexagons of a given surface element
rotate about their local normal. For a 240° disclination there
are four orientations, 90° apart, where hexagons from oppo-
site sides of the cone will be the mirror image of each other,
the mirror plane being parallel to the viewing plane and con-
taining the disclination axis. Figure 2 shows the cone near
two of these positions. In Fig. 2͑a͒, the hexagons which are
more or less parallel to the viewing plane are in the zigzag
orientation, whereas in Fig. 2͑b͒ they are in the armchair
orientation. In Fig. 3 the cone of Fig. 2 is rotated about the
cone axis and set in an arbitrary orientation, which is mea-
sured by the angle ␾. ␾ϭ0 is defined to correspond to the
zigzag position, and ␾ϭ␾ as the direction normal to the
a
viewing plane and intersecting the cone axis. Since the par-
ticle is viewed normal to its cone axis, atoms from opposite
sides of the cone, near the ␾ direction, will appear mirror of
a
each other relative to the cone axis. This is a characteristic of
2
40° and 120° disclinations only, and reflects the fact that
they exhibit twofold and fourfold symmetry, respectively ͑if
one makes abstraction of the difference between B and N
atoms, which cannot be detected by elastic scattering of the
electron beam and therefore does not manifest itself in the
diffraction patterns or the high-resolution images͒. If the
cone axis is not exactly parallel to the viewing plane, as will
often be the case during TEM observations, the mirror sym-
metry between hexagons from opposite sides of the cone will
still be apparent, albeit approximately. Tilting of up to 20°
was found to preserve this feature.
FIG. 1. High-resolution transmission electron micrographs of
two BN nanoscale cone particles with apex angles close to 39°.
Enlargements of the core regions exhibit hexagonal fringe patterns,
each dot representing a BN hexagon; taking the fast Fourier trans-
form of these regions ͑see insets͒ gives the orientation of the BN
hexagons with respect to the cone axis: zigzag orientation in ͑a͒,
and armchair orientation in ͑b͒.
Enlargements of the core region of the particles in Fig. 1
reveal hexagonal fringe patterns exhibiting the same orienta-
tions with respect to the cone axis as those shown in Fig. 2.
Furthermore, observation of such two-dimensional fringe
patterns for a number of other nanoscale cones always cor-
responded with hexagons in one of the two orientations of
Fig. 2; in many cases no clear fringe patterns could be found
in the particles’ core, which was probably the result of the
arbitrary orientation of the cones about their axis. Therefore,
it may be suggested that the nanoscale cones of Fig. 1 are
Ϯ30° double-tilt stage. Electron diffraction of the particles
was performed with a 1.6-nm diameter beam. The image
simulations are multi slice calculations done with the
MacTempas software, and fast Fourier transforms of the
HRTEM images were computed with the DigitalMicrograph
software.
III. RESULTS
2
40° disclinations seen along the two different directions
In Fig. 1, HRTEM micrographs of two typical nanoscale
cone particles are shown. The nanoscale cones consist of
slanted walls approximately 10 nm in width separated by a
thin, possibly empty core ͑diameter Ϸ1 nm͒. The observed
apex angle ͑i.e., the angle measured on the image͒ is 42
Ϯ1° in both cases. This is fairly close to the theoretical
value of 38.9° for the apex angle of a 240° disclination.17
The value of 240° is one of two cases ͑with 120°) ensuring
shown in Fig. 2.
In order to give more weight to this claim, nanobeam
electron diffraction ͑NBD͒ patterns were taken for all ob-
served particles. The electron beam was focused onto the
cone axis, in an almost normal position ͑i.e., with the pro-
jected apex angle close to its minimum value͒. This allowed
probing of the local orientation of the hexagons along the
path of the electron beam and hence, indirectly, of the sym-

7688
L. BOURGEOIS, Y. BANDO, W. Q. HAN, AND T. SATO
PRB 61
FIG. 2. A 240° disclination, i.e., a cone with apex angle 38.9°, for BN. The only defect is a two-membered ring at the apex. Two
orientations of the cone about its disclination axis are shown: so that the hexagons of the surface element perpendicular to the viewing
direction are in the zigzag orientation ͑a͒, and in the armchair configuration ͑b͒. The two positions are separated by a 90° rotation about the
cone axis.
metry of the disclination axis. NBD patterns taken for the
nanoscale cones of Figs. 1͑a͒ and 1͑b͒ are presented in Figs.
beam. The two faint spots with ͉g002͉ magnitude in Figs. 4͑a͒
and 4͑b͒ are spurious reflections. The cone axis is perpen-
4
͑a͒ and 4͑b͒, respectively. Common to these diffraction pat-
terns are the following features. First, two g002 reflections
g002 is the scattering vector corresponding to the layer pe-
¯
dicular to the median of the two 002/002 rows ͑defined as
the line M in the figures͒. Second, and most importantly, two
sets of hexagonal ͉g100͉ reflections mirror of each other
(
riodicity d002ϭ3.42 Å͒ separated by an angle equal to ␪obs
They are caused by scattering from the two opposite sides of
the cone’s walls, which are parallel to the incoming electron
.
through M. These spots are located in positions consistent
with the hexagonal fringe patterns observed in the high-
resolution images: zigzag orientation in Figs. 1͑a͒ and 2͑a͒,
and armchair orientation in Figs. 1͑b͒ and 2͑b͒. The exis-
tence of two sets of hexagonal diffraction spots symmetrical
about the cone axis can be taken as strong indication that the
nanoscale cones possess twofold symmetry and are therefore
2
40° disclinations. From the NBD patterns it is indeed clear
that the particles are composed of individual seamless cones
FIG. 4. Electron diffraction patterns taken with a nanobeam
probe ͑nominally 1.6 nm in diameter͒ very close to the cone axis for
the two particles of Fig. 1, respectively. Explanatory sketches of the
diffraction spot patterns are included. The fact that the cone axis is
a mirror line confirms that the cones are 240° disclinations all in the
FIG. 3. Arbitrary rotation angle of the cone about its disclination
axis: for a 240° disclination, the cone axis ͑arrow͒ is a twofold
symmetry axis.
same ␾ orientation.
a

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STRUCTURE OF BORON NITRIDE NANOSCALE . . .
7689
FIG. 5. Monolayer cones stacked on top of each other with the same ␾ orientations: ␾ ϭ10° in ͑a͒; ␾ ϭ80° in ͑b͒; both have their cone
a
a
axis tilted by about 10° relative to the incoming electron beam. The interlayer distance is 3.42 Å, that of turbostratic BN. Despite the fact
that there are very few coincidental lattice sites, hexagonal fringe patterns are visible in the simulated images ͑as indicated by six-branch
star͒.
stacked on top of each other, and not of a helically wrapped
conical sheet with disclination angle close to 240°. Since at
least 30 conical layers contribute to each diffraction pattern
probably a result of the viewing direction not being perpen-
dicular to the cone axis, an effect likely to be particularly
strong due to the steep slope of the disclinations. Tilting of
the cone parallel to the viewing direction will strongly affect
the direction of local ͑hk.0͒ scattering vectors positioned
along the slope, but not that of ͑hk.0͒ vectors perpendicular
to the slope. On the other hand, faceting of the nanoscale
cones, observed for some particles seen almost along their
cone axis, and sometimes manifested as slightly different
͑002͒ lattice fringe contrast on HRTEM images, would affect
the symmetry relationship exhibited by all ͑hk.0͒ diffraction
spots. This was not detected in the NBD patterns. Therefore
it may be inferred that either faceting is minimal, or that it
retains the two-fold symmetry characteristic of the 240° dis-
clination.
As mentioned before, all but one of the twenty or so ob-
served nanoscale cones exhibited features consistent with the
model of 240° disclinations stacked in an ordered way. Fig-
ures 6͑a͒–6͑b͒ show HRTEM images and NBD of this ex-
ception. The projected apex angle measured on the images is
20°, which is only slightly larger than the value of 19.1° for
a 300° disclination. Enlargement of the nanoscale cone’s
core ͓Fig. 6͑b͔͒ shows hexagonal dots in an orientation that
is different from that observed for all 240° disclinations.
This is confirmed by the diffraction pattern. A model for a
300° disclination ͓see Fig. 6͑c͔͒ in the orientation where op-
posite sides of the cone map each other presents hexagons in
exactly the same arrangement as observed experimentally.
Again, this brings strong support to the model of seamless
conical shells stacked on top of each other in an ordered
manner. A seamless 300° disclination for BN entails the
presence of a line defect, consisting of B-B bonds presum-
ably, since they are energetically preferable to N-N bonds
͓see Fig. 6͑d͔͒. This result indicates that structures contain-
ing non-B-N bonds may form and remain stable, although
they are less likely to do so than those containing B-N bonds
only.
͑the cones’ lateral size is 12 nm or larger͒, and that a
helicity-caused overall rotation of the ͑hk0͒ spots greater
than about 5° would be detected, the helicity must be less
than about 0.17°. In our view, the existence of extremely
small helicities for all investigated cones ͑about twenty͒ is
highly unlikely, as relaxation of a helically wrapped mono-
layer of BN ͑or C͒ leads to a rather broad distribution of
7
,20
helicities.
The presence of only two sets of reflections also indicates
that individual conical monolayers making up the particles
are aligned so as to have their orientation angle ␾ equal.
a
This explains why hexagonal fringe patterns could often be
observed in the nanoscale cone cores. Yet, when building
structure models of cone stackings, one realizes that inter-
layer distances in the range 3.3–3.5 Å are not compatible
with obtaining regions of hexagonal͑h͒-BN-like ordered
stacking, even along the four zigzag and armchair orientation
directions. Despite this lack of h-BN-like ordering, image
simulations of cone models exhibiting the typical turbostratic
BN interlayer distance of 3.42 Å, and with their constituent
cone layers aligned in the same ␾ orientation ͑see Fig. 5͒
a
displayed hexagonal fringes when ␾ ϭ10° ͓Fig. 5͑a͔͒ or
a
␾aϭ80° ͓Fig. 5͑b͔͒, and with the cone axis tilted by about
10° from the normal position relative to the incident electron
beam. Larger cone stacking models could not be used in
order to generate more realistic simulated images, and in
particularly confirm whether dozens of conical layers over-
lapping in an ordered way would also produce clear hexago-
nal lattice fringes. However, a significant improvement in
fringe definition was observed from a single cone to two
superimposed cones; this is taken as sufficient evidence that
alignment of individual cones is enough to result in the ob-
served fringe patterns, without the intervention of
polygonization and local h-BN-like ordering.
Returning to Fig. 4, a more accurate assessment of the
mirror relationship expressed by the hexagonal sets of reflec-
tions shows that it holds very well when the diffraction spots
IV. DISCUSSION
(
g100 or g110) are close to M, but does not always do so for
It has been noted that the nanoscale cones all displayed a
hollow or amorphous core surrounding the cone axis. In
reflections closer to the cone axis ͓see Fig. 4͑a͔͒. This is

7690
L. BOURGEOIS, Y. BANDO, W. Q. HAN, AND T. SATO
PRB 61
breaking. All observed nanoscale cones exhibited a fairly
uniform diameter of about 15 nm, and therefore this idea
could not be tested by looking at whether smaller particles
displayed an intact apex. Nonetheless, the high degree of
order detected in the cones’ structure provides strong indica-
tion that the ring-defect containing part of the shells was a
stable configuration at the start of the growth process.
The ordered stacking of individual conical shells may
seem surprising considering that, as has been pointed out, it
is not possible to obtain the stacking arrangement typical of
h-BN, even locally. On the other hand it is plausible that a
2
40° disclination will possess some degree of faceting near
its apex, especially if it resulted from the nucleation of two
squares ͑rather than four pentagons, where the strain would
be more evenly distributed͒. Such faceting might cause
‘‘locking’’ of the cones’ apexes into the same orientation, in
order to allow greater interlayer interaction. Polygonization
was found to be weak, if present at all. This indicates that
there are no large areas with h-BN-like three-dimensional
ordering, which in turns suggests that growth of additional
layers started around the apical region.
The sole case of a 300° disclination amidst about twenty
2
40° disclinations confirms the preference for even-
membered rings or even numbers of odd-membered rings in
BN. Concurrently, it signifies that nucleation of an odd num-
ber of pentagons has a non-negligible probability, and that
the subsequent development of a line defect of non-B-N
bonds may lead to an apparently stable structure. In contrast,
C nanoscale cones synthesized in conjunction with C nano-
tubes are almost always 300° disclinations.21 Interestingly,
the ratio of BN cone numbers between the unfavored and the
favored configurations is roughly the same (Ϸ20%) for
nanoscale cones and for helical cones.7 These figures
should be taken with caution due to the small size of the
statistical sample. Moreover the nucleation and growth con-
ditions of the two types of cones are very different. Never-
theless, these results point to a fundamental property of the
BN system: squares and pentagons can lead to stable nano-
structures. Consequently, it should be expected that BN
fullerenes will be successfully synthesized in the near future,
despite the fact that the slightly more complicated structure
of BN compared with carbon means it is more difficult to
find the appropriate kinetical conditions.
,16
FIG. 6. ͑a͒ Nanoscale cone with projected apex angle measured
V. CONCLUSION
to be 20°, which is close to the value of 19.2° for a 300° disclina-
tion. Enlargement of the core region ͑b͒ reveals hexagonal fringes
oriented as one would expect for a 300° disclination in the orienta-
tion shown in ͑c͒. The nanobeam diffraction pattern inset in ͑a͒ is
consistent with the high-resolution image and 300° disclination
model. ͑d͒ shows the line defect consisting of like bonds.
BN nanoscale cones were determined to consist of conical
monolayers corresponding to disclinations of integral num-
bers of 120°. In all but one case, the disclination angle was
2
40°, the smallest value compatible with preservation of the
BN lattice’s symmetry. Observation of a nanoscale cone par-
ticle comprised of 300° disclinations suggested that the re-
quirement that only B-N bonds should form is not so strin-
gent energetically.
some cases, ͓e.g., Fig. 1͑b͔͒ low-curvature ‘‘bridges’’ appear
to join the two opposite sides of the cone’s walls, but gener-
ally the apical region clearly seems empty or highly disor-
dered. Since the formation of 240° disclinations results from
the nucleation of one or several ring defects ͑two squares or
four pentagons͒, it may be suggested that the apical region
did exist early during the growth stage of the cones, but that
excessive strain imposed by the growing size of the particles,
and concentrated at the defective area, the apex, led to its
ACKNOWLEDGMENTS
The authors wish to acknowledge Dr. D. Golberg for
making helpful suggestions. L. B. is grateful for the support
of the Science and Technology Agency.

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*
STRUCTURE OF BORON NITRIDE NANOSCALE . . .
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