Cluster fragmentation, a laboratory for thermodynamics and phase-transitions in particular

Abstract

We present micro-canonical calculations of the fragmentation phase transition 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 back-bending micro-canonical caloric curve TP(E,V(E,P))=∂S(E,V(E,P))/∂E|P. From the Maxwell construction of βP(E/N,P)=1/TP one can simultaneously determine the transition temperature Ttr, the specific latent heat qlat, and the specific entropy-loss Δssurf linked to the creation of intra-phase surfaces. TtrΔssurf * N/(4πrws2Neff2/3)=γ gives the surface tension γ. Here 4πrws2Neff2/3=∑Ni * 4πrws2mi2/3 is the combined surface area of all fragments with a mass mi⩾2 and multiplicity Ni. All these characteristic parameters are for ∼1000 atoms similar to their experimentally known bulk values. This finding shows clearly that within micro-canonical thermodynamics phase transitions can unambiguously be determined without invoking the thermodynamic limit. However, one has carefully to distinguish observables which are defined for each phase-space point, like the values of the conserved quantities, from thermodynamic quantities like temperature, pressure, chemical potential, and also the concept of pure phases, which refer to the volume of the energy shell of the N-body phase-space and thus do not refer to a single phase-space point. At the same time we present here the first successful microscopic calculation of the surface tension in liquid sodium, potassium, and iron at a constant pressure of 1 atm. Some newer developments of the theory of statistical nuclear multi-fragmentation are also discussed. The first experimental finding of the anomaly of the micro-canonical caloric curve is presented.