ISOMERISM AND THE VIBRATIONAL PARTITION FUNCTION OF VERY SMALL ATOMIC MICROCRYSTALLITES

Abstract

A systematic investigation into the problem of structural isomerism in very small precrystalline nuclei is undertaken with the mechanical systems interacting through central forces of Lennard-Jones (6-12) and Morse (α= 3) type. The investigation involves the growth of nuclei from tetrahedral and octahedral seed-structures, as well as from those structures described in the Bernal theory of liquids. The number of isomers which possess enantiamorphic twins is determined. An extremely striking feature of the results obtained is the marked sensitivity of the number of possible stable minimal configurations to the range and softness of the pair potential : only 36 13-atom Morse (α = 3) minima exist compared to 988 13-atom Lennard-Jones (6-12) minima. This result is less surprising at second sight when the tree-like interrelationship of the potential energy minima is considered : the removal of a particular structure in one growth generation removes progressively more minima from subsequent generations. Certain tetrahedral configurations open-up to give octahedral configurations on softening of the potential. Of the 988 13-atom Lennard-Jones isomers 131 possess enantiamorphic twins : knowledge of these additional clusters is required for the construction of the multi-configuration partition function. The harmonic oscillator approximation is used to obtain the vibrational frequencies of each geometrically distinct isomer. The zero point energies calculated from these frequencies are shown to be an order of magnitude lower than the corresponding cluster potential energies at absolute zero. Finally the vibrational partition function derived from the single, most stable cluster (single-configuration partition function) is compared to that obtained by summation over all comparable isomers (multi-configuration partition function). It is seen that the validity of the single-configuration approximation depends strongly upon the distribution of the cluster potential energies, and less strongly upon the number of isomers. Details of the morphology of very small microcrystallites have already been published [1] : subsequent publications will expand upon the present work.