CLUSTER FRAGMENTATION, A LABORATORY FOR THERMODYNAMICS AND PHASE-TRANSITIONS IN PARTICULAR

A micro-canonical formulation of thermodynamics is presented which all ows for a consistent application to small as also large systems and th e unambiguous identification of phase transitions even in mesoscopic s ystems. Then the development of this most dramatic thermodynamic pheno menon with rising particle number can be systematically studied. I pre sent micro-canonical calculations of the fragmentation phase transitio n in Na-, K-, and Fe- clusters of N = 200 to 3000 atoms at a constant pressure of 1 atm. The transition is clearly of first order with a bac k-bending micro-canonical caloric curve Tp (E, V(E, P)) = partial deri vative S(E, V(E, P))/partial derivative E/p. From the Maxwell construc tion of beta p (E/N, P) = 1/Tp one can simultaneously determine the tr ansition temperature T-tr, the specific latent heat q(lat), and the sp ecific entropy-loss Delta s(surf) linked to the creation of intra-phas e surfaces. All these characteristic parameters are for approximate to 1000 atoms similar to their experimentally known bulk values. This fi nding shows clearly that within micro-canonical thermodynamics phase t ransitions can unambiguously be determined without invoking singularit ies of some thermodynamic quantities in the thermodynamic limit. The m icro-canonical ensemble allows insight into the mechanism of the separ ation of phases in inhomogeneous configurations as a change-over from the smaller phase-space of the bound degrees of freedom (dof) in the l iquid to the much larger one of the Gee translational gas-dof under th e expense of binding energy. At the same time we present here the firs t successful microscopic calculation of the surface tension in Liquid sodium, potassium, and iron at a constant pressure of 1 atm.