Theoretical investigation of the thermodynamic stability of nano-scale systems-I: Periodic layer-structures

The thermodynamic stability of periodic layer-structures is analyzed theoretically using equilibrium statistical mechanics. While the system itself is not in complete thermodynamic equilibrium, it can be stable under appropriate constraint conditions and its stability can be determined by minimizing the free energy in the constrained state. A model binary FCC system with a miscibility gap is treated using the pair approximation of the Cluster Variation Method. A symmetric system with an overall average composition 50 atom % A and 50 atom % B is considered. It is shown that the equilibrium compositions of two phases in a periodic layerstructure depend strongly on the periodicity when the composition wavelength is decreased down to a few nanometers. The result reveals that the mutual solubilities of two materials increase significantly as the layer-thickness decreases. In an extreme case, they may become totally miscible.