Computer relaxation of fragments of an atomic bee crystal, using a Lennard-Jones atom-atom interaction potential, yields a variety of close-packed polycrystalline structures, with well-defined grain boundaries between ordered fcc and hcp domains. The strong dependence of the results on shape and size of the fragments, as well as on their orientation and precise position with respect to the bee matrix, is attributed to the surface structure, which apparently determines in detail what will happen upon relaxation, and suggests that the new phase starts ('nucleates') at the surface and proceeds inwards. Although the nature of the relation between surface structure and final result remains obscure, and no trends are apparent, single crystals with fee or hcp structures can be obtained, with hcp being dominant. Possible effects of non-hydrostatic pressure are discussed in connection with constrained relaxations. The results are affected by simulated 'thermal' disorder, however small. Radial distribution functions, and simulated diffraction patterns are presented, the latter in comparison with some experimentally observed traces of small Argon clusters. (C) 2007 Elsevier B.V. All rights reserved.