Melting Point of the Crystal-Like Structures in the Heterogeneous Smoky Plasma—Fractal Geometry and Spectral Approximations

Abstract

In a smoky plasma, crystal-like structures (clusters) are formed which contain less than $10^{3}$ particles and are characterized by significant anisotropy of thermodynamic characteristics. Here, the influence of the clusters’ size on their melting temperature is studied. It was revealed that the phonon spectrum density of a nanometer-sized cluster cannot be represented by the classical Debye model. Therefore, to describe the real phonon spectrum of nanoclusters, two control parameters are introduced: the fractal dimension and the scale parameters. Based on the fractal shape of the phonon spectrum density, a method has been developed for calculating the relative melting temperature of clusters in the most real parameter range: $N = $ 100–500, $D = $ 2.4–2.8 where $N$ is the number of particles in the cluster and $D$ is its fractal dimension.