Local icosahedral structures in binary-alloy clusters from molecular-dynamics simulation
Stefano Cozzini
Dipartimento di Fisica, Universita ` di Trento, 38100 Trento, Italy;
INFM, I-38050 Povo, Italy;
and Departamento de Fisica Atomica, Molecular y Nuclear, Universidad de Sevilla, Apartado 1065, 41080 Sevilla, Spain
Marco Ronchetti
Dipartimento di Informatica e Studi Aziendali, Universita ` di Trento, 38100 Trento, Italy
Received 22 November 1995, revised manuscript received 6 February 1996
We investigate the structure of 13-particle clusters in binary alloys for various size ratios and different
concentrations via molecular-dynamics simulation. Our goal is to predict which systems are likely to form
local icosahedral structures when rapidly supercooled from the melt. We calculate the energy spectrum of the
minimal energy structures, and characterize all detected minima from both their relative probability and a
structural point of view. We identify regions in our parameter space where the icosahedral structure is domi-
nant like in the corresponding monatomic case, regions where the icosahedral structure disappears, and others
where icosahedral structures are present but not dominant. Finally, we compare our results with simulations
reported in the literature and performed on extended binary systems with various size ratios and at different
concentrations. S0163-18299605018-7
I. INTRODUCTION
Over the last decade, chemists and solid state physicists
have been greatly interested in the platonic solid with the
highest symmetry: The icosahedron. Chemists became inter-
ested in icosahedra because several clusters have been found
to be icosahedral or polyicosahedral. In particular, the recent
synthesis and structural determinations of metal carbonyl
clusters resulted in a variety of icosahedral clusters contain-
ing transition metals and main group elements.
1
Solid state
physicists believed until recently that icosahedral symmetry
played no role in extended structures because it is not com-
patible with periodic arrangement of structural units i.e.,
with crystalline order. It is now known that icosahedral
symmetry is compatible with quasiperiodic translational or-
der, and states of matter arranged in such a way have been
found i.e., quasicrystals
2
. Moreover, icosahedral structures
are suggested to be important in disordered systems, like
supercooled liquids and glasses.
3
The presence of icosahedra
in simple supercooled liquid and glasses was revealed by
means of computer simulations: From the pioneering work
of Steinhard, Nelson, and Ronchetti
4
up to the most recent
works,
5
there is evidence in the literature that it is so for
monatomic supercooled liquids and glasses interacting via
Lennard-Jones LJ and a variety of different metallic
potentials.
6
So far, however, studies of LJ binary systems
yield contrasting results.
7
The study of icosahedral clusters is
therefore important both in itself and because it can give
hints on the presence of such structures in disordered sys-
tems and on the nucleation of extended icosahedral quasi-
crystals. Computer simulations performed by Honeycutt and
Andersen
8
on homogeneous LJ systems showed that icosa-
hedrally symmetric clusters are the lowest in energy up to a
size of 5000 atoms. A similar study in binary systems would
be interesting, but unfortunately it is difficult because the
parameter space to be investigated is far more complex. In
fact in the case of monatomic species only the interaction
potential and the cluster size i.e., the number of particles
have to be specified, while in binary systems the relative
abundance of the two species, geometric factors i.e., size
ratios, and parameters relative to the binding energy have to
be taken into account. For this reason computational studies
on mixtures are rare and focused on specific aspects, like the
study of impurities in clusters
9
or the dynamics of phase
separation.
10
To start exploring clusters in a binary system it
is therefore necessary to reduce the search space by fixing a
few parameters and studying the dependence on the remain-
ing ones. For instance, both the above referred works by
Garzon et al.
9
and Clarke et al.
10
keep the geometric param-
eters fixed and vary the energetics. In the present work we
decided to cut the parameter space in an orthogonal direction
by fixing the energetic parameters and the size of the cluster,
and varying particle size and concentration. We therefore use
the same depth of the potential well for both atomic species
and for the interaction between unlike particles. For the clus-
ter size we focus on 13-particle clusters, since our aim is to
determine the importance of icosahedral structures. We
therefore study the geometric structure and energy spectrum
of 13-atom clusters for four different atomic size ratios and
for all possible relative concentrations. In Sec. II we present
the details of the computational model. In Sec. III we discuss
the methods of measurements that we used. The results are
presented in Sec. IV, followed by a discussion and a com-
parison with the literature Sec. V.
II. COMPUTATIONAL MODEL
We studied a system composed of 13 particles belonging
to two different species ( L and S ) and interacting with a LJ
isotropic potential. The two species differ because of geo-
metric factors: The radius of L atoms is larger than the radius
of S atoms. The interaction between S atoms is characterized
PHYSICAL REVIEW B 1 MAY 1996-II VOLUME 53, NUMBER 18
53 0163-1829/96/5318/1204010/$10.00 12 040 © 1996 The American Physical Society