Prediction of distinct surface segregation effects due to coordination-dependent bond-energy
variations in alloy nanoclusters
Leonid Rubinovich and Micha Polak*
Department of Chemistry, Ben-Gurion University, Beer-Sheva 84105, Israel
Received 30 March 2009; revised manuscript received 27 May 2009; published 7 July 2009
The first implementation of a recently introduced method based on the extraction of the coordination
dependence of surface bond-energy variations CBEV from density-functional theory DFT computed pure-
metal surface-energy anisotropy is reported. In particular, polynomial functions fitted to DFT data computed
previously for Pt, Pd, and Rh are used as input energetics for statistical-mechanical computations of Pt-Pd
923-atom cuboctahedron-cluster compositional structures and Pt-Rh111 as a test case using the free-energy
concentration expansion method FCEM. The major findings concern the roles of preferential strengthening of
intrasurface and surface-subsurface interlayer bonds leading to quite unique segregation characteristics: i
strong Pt segregation at certain 111 surface sites of the Pt-Pd clusters, accompanied, at relatively high overall
Pt composition, by weaker Pt segregation forming Pt-Pd ordered 100 structure, whereas Pd segregates mainly
at the edge and vertex sites; ii dominant Pd subsurface segregation. The high computation efficiency of the
CBEV/FCEM approach allows the determination of the complete temperature dependence of atomic-exchange
processes among surface sites, as well as between subsurface and deeper sites, reflected in the corresponding
configurational heat-capacity curves. Compared to other approaches, the high transparency of this method
helps to elucidate the origin of the distinct bond-energy-variation effects on site-specific segregation in alloy
nanoclusters.
DOI: 10.1103/PhysRevB.80.045404 PACS numbers: 61.46.Df, 68.35.Dv, 82.60.Qr, 68.35.Md
I. INTRODUCTION
Considerable efforts have been made to model composi-
tional and geometrical structures specific to alloy nanoclus-
ters compared to the corresponding bulk alloys, with empha-
sis on the outer surface shell.
1
These theoretical-
computational studies are motivated by the relevance of
chemical and physical properties, which depend on the clus-
ter structure and size, for applications in catalysis, magnetic
media, or electronic devices. Pt-Pd and Pt-Rh modeled in
this work are widely used as catalysts in the detoxication of
car exhaust gases. Limitations of current experimental char-
acterization techniques make modeling almost the only tool
to obtain atomic-scale geometrical and compositional infor-
mation concerning nanosized alloy clusters. Several ap-
proaches that differ in the level of accuracy and efficiency
have been reported in the literature.
1
In particular, as far as
energetics are concerned, the currently most common meth-
ods are based either on the density-functional theory DFT
or on empirical or semiempirical many-body potentials
EP such as the second moment approximation to the tight-
binding theory TB-SMA, or preferably, on a combination
of both.
2
The former can be of high accuracy but the rather
time consuming computations limit their practical applicabil-
ity to relatively small size alloy clusters. For the study of
medium or large clusters the generally less accurate but
computationally much more efficient EP methods have been
often used. For the exploration of cluster properties at finite
temperatures, the interatomic energetics has to be combined
with thermodynamic/statistical-mechanical formalism or
computer simulations. Employing statistical-mechanical ex-
plicit expressions for the alloy free energy has certain advan-
tages. In particular, the free-energy concentration expansion
method FCEM, which takes into account short-range order
SRORef. 3 in a system of equilibrated atom-exchanging
clusters, has proven to be highly efficient in computation of
site-specific concentrations obtainable by F minimization
vs overall composition, temperature and cluster size,
4
as
compared to Monte Carlo simulations, for example.
Our first attempts to go beyond simple empirical energet-
ics as input in the FCEM for the study of alloy nanoclusters
incorporated
4,5
elemental bond energies and their surface-
induced variations as obtained by means of the Naval Re-
search Laboratory-tight-binding method NRL-TB.
6
How-
ever, it appears that quantitative evaluation of the role of
elemental bond-energy variations in surface segregation in
bulk alloys and alloy clusters necessitates more reliable en-
ergetics. Therefore, we introduced most recently another ap-
proach to the issue of near-surface interatomic bonding.
7
Our
aim was to develop a DFT-based method of high efficiency,
namely, to retain a reasonable accuracy in relatively fast
computations of medium- and large-cluster compositional
structures. The idea was to derive a procedure for extracting
the coordination dependence of intrasurface and surface-
subsurface pair-bond-energy variations CBEV from DFT-
computed surface-energy anisotropy.
The paper is organized as follows. After describing briefly
the introduced method, the results computed for Pt-Pd 923-
atom clusters are divided between surface and subsurface
segregation effects. Pd clusters of this size were predicted to
have the cuboctahedron Oh shape.
8
Computational vs ex-
perimental data for segregation in Pt
0.25
Pd
0.75
111 are given
as a test case. The discussion deals with the origins of the
two respective driving forces in the context of bond-energy
variations involving the two outer shells and assesses previ-
ous theoretical and experimental studies of the Pt-Pd system.
A summary of the research results and prospects concludes
the article.
PHYSICAL REVIEW B 80, 045404 2009
1098-0121/2009/804/0454048 ©2009 The American Physical Society 045404-1