NEW CARBON NANOPARTICLE - ICOSAHEDRAL DIAMOND
Vladimir Ya. Shevchenko1, Alexey E. Madison1, Alan L. Mackay2
1
Grebenshchikov Institute of Silicate Chemistry, Russian Academy of Sciences,
Saint-Petersburg, Russia
2
School of Crystallography, Birkbeck College, University of London,
London, UK
ABSTRACT. Regular structures need not be crystalline1. The most striking example of
such structures is icosahedral packing2. It has a definite structure, which is not that of a
crystal, nor that of a molecule; it is not one of the space-groups (or even point groups)
listed in the International Tables; it is not a twin (although it could be described in terms
of twinning). Describing a great variety of “unusual”, “unprecedented”, “magic”
structures and so on any reference to a pre-existing crystal lattice is meaningless1.
Structural inhomogeneity and coherence are characteristic of structures of nanosized
particles3,4. Spatially inhomogeneous structures, for which a local short-range order
slightly differs from a short-range order of one of stable or metastable structural
modifications, or one of non-crystallographic packings, whereas different fragments are
coherently joined into a whole, should exist in the nanoworld. Here we show that
icosahedral carbon nanoparticles in which the local arrangement of atoms is virtually
identical to that in diamond can be formed in nanometer range. They can be transformed
reversibly into onion-like shell structures without disturbance of their topological
integrity. Icosahedral diamond-like core can coexist coherently with onion shells. The
general principle that governs the formation of such structures takes as a basis the nonEuclidean geometry.
Although nanodiamonds have long been the subject of the close attention of
researchers, the question as to their structure remains open. Diamond nanoparticles are
not at all the small-sized diamond crystals. For example, the detonation carbon particles
consist most probably of a diamond core coated with shells having an onion (onion-like)
structure with graphite inclusions5. Recently, the structural properties of nanodiamond
particles synthesized by detonation and the products of their transformation into carbon
onions via vacuum annealing have been studied by various experimental techniques6. It
has been shown that the detonation nanodiamond particles have a composite core-shell
structure comprising an ordered diamond core of ~3 nm covered by a partially
disordered outer shell of ~0.8 nm. The transformation of the nanodiamond into carbon
onions proceeds from the amorphous outer shell of the particles inwards towards the
particles’ diamond core. A reconstruction of carbon atoms located in the outer shell
leads to the bonding similar to those in nanocrystalline graphite. The observed structure
was comparable with the structure of the bucky diamond clusters7,8. The ab initio
calculations showed that at about 3 nm the reconstructed surfaces become more
reasonable, thus providing an atomistic structural model based on the topology of a
diamond core surrounded by a fullerene-like carbon network7,8.
Recently, the structural models of icosahedral diamond nanoparticles compatible
with onion-like structures were developed9-11. Different structural fragments are
coherently joined into a whole. The local arrangement of atoms in these particles is
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universally tetrahedral (not only inside the fragments but also at their interfaces) and
virtually no different from that in the diamond.
The fivefold symmetry in diamond-like nanoparticles has been experimentally
observed by a number of researchers. In particular, particles with an icosahedral
morphology were observed among the diamond nanoparticles synthesized in an
acetylene flame12. The icosahedral morphology was interpreted as a result of multiple
twinning of cubic crystals. It was noted that, among several forms of these multiple
twins, there exist almost perfect icosahedra. The fivefold symmetry clearly manifests
itself in the electron diffraction patterns. Some grate particles had semi-coherent
boundaries but the small particles of several nanometers in size had fully coherent
interfaces.
Let us demonstrate how an icosahedral diamond-like nanoparticle (icosahedral
diamond) can be constructed if it is treated as a nanostructure that has coherent
boundaries and is composed of insignificantly distorted fragments of diamond and
lonsdaleite (hexagonal diamond). The geometric principles used for assembling such
structures are based on the local approach13,14. Within this approach, nanoparticles with
coherent boundaries in the general case are assembled from a limited set of building
blocks determined by the fundamental manifolds and the principles of assembling are
governed by the topological properties of a fiber space. The great diversity of “unusual”
structures can be obtained by mapping or projecting fragments of highly symmetrical
structures from different non-Euclidean spaces onto the three-dimensional Euclidean
space or mapping these fragments onto curved manifolds embedded into the Euclidean
space. Their particular cases are substructures of polytopes, i.e., regular tilings of the
three-dimensional Riemannian space (of positive curvature).
An icosahedron can be assembled by joining twenty slightly distorted regular
tetrahedra. The number of atoms in the icosahedral packing can be increased by
performing the geodesic design of tetrahedra or by filling the tetrahedra by
corresponding crystalline fragments (by a fragment of diamond packing, for example).
Constructed in such way diamond nanoparticles9-11 have a shell structure and a nearly
spherical shape. Each shell contains 20k2 atoms (20, 80, 180, 320, 500, …), and the
particle as a whole consists of 20k(k+1)(2k+1)/6 atoms (20, 100, 280, 600, 1100, …),
where k is the number of the shell. Their size varies within several nanometers. Special
cases of this “magic” series are provided by endohedral nanodrops of the (H2O)100
water, which were found in cavities of giant oxomolybdate clusters15, and the (H2O)280
Dzugutov clusters16. These numbers are characteristic of carbon onions17, and
icosahedral diamond-like particles can easy (layer-by-layer) undergo into onions and
vise versa just only by puckering and smoothening consecutive shells without migration
of atoms over considerable distances.
Fig. 1 shows the consecutive shells of icosahedral nanoparticles. The core of
these particles consists of 20 atoms forming a regular dodecahedron. Fragments in the
form of barrels are attached to each of the 20 dodecahedral faces. The gaps are regularly
filled with fragments of diamond and lonsdaleite. So, inserting the consecutive shells
(Fig. 1, left) each into another one obtains the diamond-like particle9. The smoothened
shells (Fig.1, right) form nested fullerene – onion17. Both sets of shells are equal
topologically, and may be reversibly transformed each into another by smoothing and
puckering of atomic nets11. It should be emphasized that, in the framework of the
mechanism under consideration, the transformation of an icosahedral diamond-like
nanoparticle into a shell nanoparticle is not accompanied by breaking of any chemical
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bonds and leads only to a change in their character and direction. In terms of atomic
orbitals, the reversible structural transformations in carbon nanoparticles correspond to
dehybridization and rehybridization of the bonds. The topological integrity of the
network as a whole remains unchanged.
Figure 1 Formation of icosahedral nanoparticles with coherent boundaries. The
consequent shells (from top to bottom) consist of 20, 80, 180, 320, and 500 atoms,
respectively (view along the two-fold axis of icosahedron). left, Shells forming the
diamond-like particle. right, Shells forming the onion-like particle. Both sets of shells
are equal topologically, and may be reversibly transformed each into another by
smoothing and puckering of atomic nets. Combining shells from both sets results to the
composite icosahedral core-shell particle with diamond core coherently joined with
onion shell.
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Another possibility is the coherent coexistence of diamond-like core with onionlike shells. Let us suppose that outer shells undergo the smoothening transformation,
whereas the inner core remains diamond-like. This case corresponds to the composite
icosahedral core-shell particle without any grain boundaries (in the classical sense)
between “diamond” and “graphite” fragments.
Thus, the structures of icosahedral diamond-like nanoparticles can
simultaneously involve fragments with specific features of diamond, lonsdaleite,
graphite, and carbon onions joined coherently. They can serve as a good model
accounting for the structure of detonation nanodiamonds, as well as for the structural
transformations
of
nanodiamonds
into
onion-like
carbon
structures
and vice versa5-8,23-30.
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