|
Cluster Structure
One of the unique properties of clusters is the possibility of structures containing
five-fold axes - unlike crystalline structures there is no requirement for translational periodicity.
Two examples are shown below. The Mackay icosahedron
has six five-fold axes through the twelve vertices, and the Marks decahedron
has a single five-fold axis. Both structures are common in a wide variety of
atomic clusters.
Fig. 1. Three examples of the structures clusters can adopt:
(a) a 38-atom truncated octahedron,
(b) a 55-atom Mackay icosahedron, and (c) a 75-atom Marks' decahedron.
These clusters have the optimal shape for the three main types of regular packing seen in clusters:
face-centred cubic, icosahedral and decahedral, respectively.
When a cluster's interactions can be described by a pair potential the main contribution
to the energy comes from nearest neighbours. Therefore, one might expect those structures
with the greatest number of nearest-neighbour contacts to be lowest in energy. This would
favour structures, such as the Mackay icosahedron, which are both spherical and have {111}
surface facets. However, there is another factor. In icosahedra and decahedra the structures
must be strained in order to eliminate the gaps that result
if the structures are composed of regular tetrahedra (see below). There is an energetic penalty
associated with this strain.
Fig. 2 Examples of the strain involved in packing tetrahedra.
(a) Five regular tetrahedra sharing a common edge leave a gap of 7.36 degrees.
(b) Twenty regular tetrahedra sharing a common vertex leave gaps amounting to a solid angle
of 1.54 steradians.
As the strain energy increases with size, it is common
to see a cluster's structure change from icosahedral to decahedral to
face-centred-cubic as the size increases. A similar series of structural changes can
be induced by narrowing the width of the potential well, because this also disfavours
strained structures.
As I have worked on the structure of a variety of clusters,
I have obtained a large database of structures. These are accessible from
the Cambridge Cluster Database.
Associated Publications
- R. H. Leary and J.P.K. Doye, Phys. Rev. E 60, R6320-R6322 (1999)
Tetrahedral
global minimum for the 98-atom Lennard-Jones cluster
- J.P.K. Doye and D.J. Wales, Phys. Rev. B 59, 2292-2300 (1999)
Structural
transitions and global minima of sodium chloride clusters
- J.P.K. Doye and D.J. Wales, New J. Chem. 22, 733-744 (1998)
Global
minima for transition metal clusters described by Sutton-Chen potentials
- J.P.K. Doye and D.J. Wales, J. Chem. Soc., Faraday Trans. 93, 4233-4244
(1997)
Structural
consequences of the range of the interatomic potential: a menagerie of
clusters
- J.P.K. Doye, A. Dullweber and D.J. Wales, Chem. Phys. Lett. 269, 408-412
(1997)
Structural
predictions for (C60 )N clusters with an all-atom
potential
- J.P.K. Doye and D.J. Wales, Chem. Phys. Lett. 262, 167-174 (1996)
The
structure of (C60 )N clusters
- J.P.K. Doye and D.J. Wales, Chem. Phys. Lett. 247, 339-347 (1995)
Magic
numbers and growth sequences of small face-centred-cubic and decahedral clusters
- J.P.K. Doye, D.J. Wales and R.S. Berry, J. Chem. Phys. 103, 4234-4249 (1995)
The
effect of the range of the potential on the structures of clusters
|