The Changes in the Thermodynamic Properties of a Germanium Nanocrystal with a Decrease in Its Size under Various P–T-Conditions

Abstract

The equation of state P(v/v_o) and the baric dependences of both the lattice and surface properties of germanium macro- and nanocrystals have been determined on the basis of the Mie–Lennard–Jones pairwise interatomic potential and the RP-model of a nanocrystal. It has been shown that the isothermal dependences P(v/v_o) of macro- and nanocrystals intersect each other at a certain value of the relative volume (v/v_o)₀. The surface pressure becomes zero at the intersection point (at (v/v_o)₀). The relative volume (v/v_o)₀ decreases with both an isomorphic–isomeric increase in the temperature and an isomorphic–isothermic decrease in the number of atoms in a nanocrystal or upon the isomeric–isothermic deviation of a nanocrystal from its energetically optimal shape (a cube for the RP-model). Based on the derived equation of state, the changes in 23 properties of germanium with both an isochoric (v/v_o = 1) and isobaric (P = 0) decrease in the number of atoms in a nanocrystal at temperatures of 100, 300, and 1000 K have been studied. It has been shown that the higher the temperature of a nanocrystal is, the greater the increase is in the specific volume of a germanium nanocrystal under an isobaric (P = 0) decrease in its size.