Physical cluster mechanics: Statistical thermodynamics and nucleation theory for monatomic systems
- 1 September 1975
- journal article
- research article
- Published by Taylor & Francis in Advances in Physics
- Vol. 24 (5), 645-678
- https://doi.org/10.1080/00018737500101481
Abstract
We extend previous computations of mechanical stability of atomic microclusters to the realm of statistical thermodynamics, obtaining thermodynamic functions for small, solid-like Van der Waals clusters of less than some 100 atoms possessing non-crystalline structures of ‘polytetrahedral’ type. These are shown to be almost invariably at a thermodynamic advantage over alternative lattice structures of the same number of atoms, at least for the Lennard-Jones potential in the harmonic-oscillator/rigid-rotor approximation. The dependence of thermodynamic functions upon cluster size appears to be essentially monotonic in the number of internal degrees of freedom; although there are certain exceptional structures, particularly with icosahedral symmetry, there proves to be little evidence for the occurrence of ‘magic numbers’ for stability at any temperature and within the size-range considered. Particular attention is given to the heat capacity of model systems in relation to their vibrational spectra. The Debye T 3 law appears reasonably well obeyed at low temperatures with no evidence for the existence of either ‘soft modes’ or distinct surface contributions. The results for the free energy of formation of minimal clusters ΔG f are then applied to the computation of nucleation rates in terms of the Becker-Döring-Volmer-Zeldovitch quasi-equilibrium theory. Gibbsian behaviour in the form of a maximum in the curve of ΔG f versus size is observed with a critical nuclear size at realistic temperatures and pressures of the order of that predicted by macroscopic liquid-drop theories. These figures and those derived for nucleation rate and critical supersaturation appear remarkably insensitive to the details of the model used, in particular to the distinction between ‘microcrystalline’ and ‘amorphous’ atomistic models. The general status of atomistic nucleation theory is critically examined in the light of these and similar results.Keywords
This publication has 38 references indexed in Scilit:
- On the equilibrium pressure of phases with very small dimensionsThe Journal of Chemical Physics, 1973
- Computation of Dense Random Packings of Hard SpheresThe Journal of Chemical Physics, 1972
- The entropy of small clusters of atoms using an Einstein modelChemical Physics Letters, 1971
- A kinetic theory of cluster formation in the condensation of gasesTransactions of the Faraday Society, 1969
- The structure and orientation of crystals in deposits of metals on micaSurface Science, 1967
- A Dense Packing of Hard Spheres with Five-fold SymmetryNature, 1965
- HOMOGENEOUS NUCLEATION FROM THE VAPOR PHASEIndustrial & Engineering Chemistry, 1965
- A Geometrical Approach to the Structure Of LiquidsNature, 1959
- Dissociation Treatment of Condensing SystemsThe Journal of Chemical Physics, 1939
- Kinetische Behandlung der Keimbildung in übersättigten DämpfenAnnalen der Physik, 1935