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Surface Entropy of Argon Clusters
Mikael Kjellberg, Sergey Prasalovich, Vladimir Popok, Klavs Hansen, Eleanor E. B. Campbell
Department of Physics, Göteborg University, SE-41296 Göteborg, Sweden
The enhanced stability of certain cluster sizes is traditionally inferred from the enhanced
abundance of these species in mass spectra. For rare gas clusters, the stability pattern can be
described as due to a close packing of atoms into closed structures (shells) with the symmetry of
Mackay icosahedra. The mere presence of shell closings does not give any information on the
magnitude of the energies involved. A quantitative comparison requires knowledge of the
binding energies of the clusters. It is possible to extract this information from the mass spectra
by making reasonable general assumptions [1] with the restriction that only relative values can
be found. The flat abundance spectrum (after background subtraction) is related to relative
I ∝ D + C D − D G.
energies as ( )
N N+ 1 v N N+
1 /
This has been done in Fig 1(A) for masses around the N = 55 “magic number”. The amplitude
in the relative energy variations does not follow the same trend as the local abundance
variations. In particular the maximum in the relative energy is shifted to smaller N. The reason
for this is that the relative energies obtained in this procedure are not the dissociation energies,
DN, of the clusters but the free energies, FN = DN – TSN, where SN is identified with the surface
entropy (the natural logarithm of the number of ways the configurational ground state can be
contructed). This can be estimated from the structures calculated by Northby [2] and used to
extract the dissociation energies. This is shown in Fig. 1(B) and compared with the calculated
dissociation energies, where the absolute scale was obtained by scaling with the bulk and
surface energy. The agreement of the trend in the values is very satisfactory.
∆F (meV)
80
75
70
65
60
Figure 1. A, Left:Integrated peak intensities from Ar N + mass spectrum filled squares, (right y-axis) and the
dissociation energies extracted from the spectrum (free energies) (open squares, left y-axis). B, Right: Extracted
dissociation energies (free energies) (open circles), dissociation energies after subtraction of the entropy term (open
squares), calculated energies from Northby [2] (filled squares).
References
50 51 52 53 54 55 56 57 58 59 60
0
61
N
[1] K. Hansen and U. Näher, Phys. Rev. A , 60 1240 (1999).
[2] J.A. Northby, J. Xie, D.L. Freeman, J.D. Doll, Z. Phys. D 12 69 (1989)
∆F
I N
3
2
1
I N
Energies [meV]
85
80
75
70
65
60
55
50
45
∆F N,exp
D N,exp
D N,Northby
50 52 54 56 58 60
N