The thermodynamic properties of small clusters of rare-gas atoms are determined from a biased random-walk Monte Carlo procedure. The cluster sizes studied range fro.n N = 3 to N = 13 atoms. The internal energy is calculated as a function of temperature. Each cluster exhibits an abrupt liquid-gas phase transition at a temperature much less than for the bulk material. An abrupt solidliquid transition is also observed for N = 11 and 13. The entropy of fusion is S = 1.76 e.u, For smaller clusters, the solid-liquid transition is more gradual. The bond-length distributions are calculated for each cluster at various temperatures.The fluctuations of bond lengths from their average valu:" increase gradually with temperature until the melting temperature is reached, at which point there is a large, abrupt increase. The indications are that a harmonic normal-mode analysis is applicable only at temperatures substantially below the melting point and even there, the frequency spectrum is temperature dependent. For N = 3, the equilibrium structure is an equilateral triangle. An N = 5 cluster forms a trigonal bipyramid and for N = 7 the form is a pentagonal bipyramid. The nine-particle structure has symmetry C» and is a pentagonal bipyramid with two additional atoms, and the N = 13 cluster forms an icosahedron.
The Monte Carlo method is used to calculate the average thermodynamic properties of small (N?13) clusters of atoms. All cluster sizes studied exhibit fairly sharp solid–liquid, as well as liquid–gas, transitions. In addition, some of the larger clusters also undergo structural transitions between different isomeric forms. The solid–liquid transition temperature is determined by four independent tests. The melting points predicted by these tests do not differ by more than 5%.
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