Fragmentation phase transition in atomic clusters .1. Microcanonical thermodynamics

The volume W of the accessible N-body phase space and its dependence on the total energy is directly calculated. The famous Boltzmann relation S = k * ln(W) defines microcanonical thermodynamics (MT). We study how phase transitions appear in MT. Here we first develop the thermodynamics of microcanonical phase transitions of first and second order in systems which are thermodynamically stable in the sense of van Hove. We show how both kinds of phase transitions can unambiguously be identified in relatively small isolated systems of similar to 100 atoms by the shape of the microcanonical caloric equation of state < T(E/N) > and not so well by the coexistence of two spatially clearly separated phases. i.e. within microcanonical thermodynamics one does not need to go to the thermodynamic limit in order to identify phase transitions. In contrast to ordinary (canonical) thermodynamics of the bulk microcanonical thermodynamics (MT) gives an insight into the coexistence region. Here the form of the specific heat c(E/N) connects transitions of first and second order in a natural way. The essential three parameters which identify the transition to be of first order, the transition temperature T-tr, the latent heat q(lat), and the interphase surface entropy Delta s(surf) can very well be determined in relatively small systems like clusters by MT. It turns out to be essential whether the cluster is studied canonically at constant temperature or microcanonically at constant energy. Especially the study of phase separations like solid and liquid or, as studied here, liquid and gas is very natural in the microcanonical ensemble, whereas phase separations become exponentially suppressed within the canonical description. The phase transition towards fragmentation is introduced. The general features of MT as applied to the fragmentation of atomic clusters are discussed. The similarities and differences to the boiling of macrosystems are pointed out.