The extension of the phase rule to nano-systems and on the quaternary point in one-component nano phase diagrams.
The phase rule of Gibbs has been extended to nano-systems in this paper. For that, first the total number of atoms or stable molecules (N) in the system is selected as a new independent thermodynamic variable to characterize the size of nano-systems. N is preferred to r (the radius of the system) as the volume and radius are functions of other independent variables (p, T, composition) and therefore r is not an independent variable. As follows from the extended phase rule, the maximum number of phases and the degree of freedom at a given number of phases is increased by 1 for nano-systems compared to macro-systems, due to the new independent thermodynamic parameter N. The extended phase rule can serve as the basis to work out topological details of nano phase diagrams. As an example, an existence of a quaternary point is predicted in one component nano phase diagram of thallium (in contrast to usual one component phase diagrams with triple points at most). At given values of p = 7.2E-12 bar, T = 544 K, and N = 1.2E5, HCP (hexagonal closely packed solid), BCC (body centered cubic solid), liquid and vapour phases of pure TI are predicted to be in equilibrium.
BAY-NANO Research Institute for Nanotechnology, Department of Nano-Composites, University of Miskolc, Department of Nanotechnology, 3515 Miskolc, Egyetemvaros, E/7, 606, Hungary.
George
G
Kaptay