Growth simulations of 3-dimensional Lennard-Jones (LJ) clusters/nuclei from the vapour phase were carried out in order to estimate the role of kinetic and energetic effects in determining the internal structure of the clusters. The kinetic effects have been clearly observed recently [1] in case of defected clusters LJ₃₂₈₁ with internal structure proposed by van de Waal [2], where they lead to overgrowth of fcc structure instead of more energetically preferred hcp structure. The 3281-atom LJ cluster of ideal octahedral shape determined by eight dense-packed planes {111} and of the fcc internal structure, analysed here, is free from growth stimulating surface defects and therefore is an ideal candidates for comparison.

Growth simulations of LJ clusters were realised using the two-temperature-region model [3] based on Monte Carlo method. The initial ideal cluster LJ₃₂₈₁ was thermally equilibrated at a selected growth temperature and put into supersaturated vapour. The used value of the vapour atom concentration n_v = 0.002 (in reduced units of LJ system) was selected since it proved to be optimal to form well-arranged cluster structure in a reasonable simulation time [3]. The simulated growth was realised from N = 3281 up to 6000 atoms at two reduced growth temperatures T^* = 0.30 and 0.50 corresponding to 36 K and 60 K for argon clusters. The internal structure in final clusters was precisely analysed by determining the number of fcc and hcp units and their location in the cluster. For this purpose, the structural analysis based on the Coordination Polyhedron Method [4] and visualisation using the PovRay program were used.

Growth of the ideal fcc clusters is strongly temperature-dependent: at low temperature clusters evolve from octahedral to an irregular shape, while at the higher one they are close to spherical. The internal structure in new cluster regions built at the low temperature is characterised by many stacking-fault layers of fcc and hcp character. This is caused by approximately the same binding energies for fcc and hcp structure and a low adatom movement on the cluster surface. The temperature increase up to T^* = 0.50 removes partly this ambiguity in cluster structure formation showing preference for the fcc structure. This is evident from statistics of newly created structural units, where the fcc units are approximately four times more numerous than those of the hcp character.

The possible explanation of this preference is in energetic effects caused by different interaction energy of two fcc or two hcp layers located on the neighbouring (111) planes of the initial fcc cluster. Such layers should contact at the edge of octahedral cluster where they are inclined one to another at the obtuse angle of about 109^o. Two neighbouring hcp planes avoid such contacts at this position, while this angle is ideal to make contact of two fcc layers. This means that the fcc layer, when initiated on one surface, can easily propagate to the neighbouring planes. The higher temperature facilitates this kinetic process of the fcc layer propagation by higher surface diffusion of adatoms. The second mechanism, which helps to form fcc surface layer from adatoms, involves structural rearrangement of hcp islands [5] before they are able to originate stacking-faults hcp layer.

Literature
[1] W. Polak, Europhys. Lett., accepted for publication.
[2] B. W. van de Waal, J. Chem. Phys. 98 (1993) 4909.
[3] W. Polak, Phys. Rev. B 71 (2005) 235413.
[4] W. Polak, Phys. Rev. B 67 (2003) 115402.
[5] S. Somasi, B. Khomami R., and Lovett, J. Chem. Phys. 114 (2001) 6315.

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1. Formation of regular polyicosahedral and defected crystalline structures in growing Lennard-Jones clusters