Changes of the thermodynamic properties at isochoric and isobaric decrease of the silicon nanocrystal size

Equation of state $P(\nu/\nu_o)$ and the baric dependences of the lattice and surface properties of silicon macro- and nanocrystals have been calculated using the method of calculation of crystal properties from the pair Mie–Lennard-Jones interatomic potential and the RP-model of nanocrystal. The isothermal dependences of $P(\nu/\nu_o)$ for the macro- and the nanocrystal are shown to be intersected at a certain value of relative volume $(\nu/\nu_o)_0$. The surface pressure becomes zero at the intersection point (at ($\nu/\nu_o)_0$). The value of $(\nu/\nu_o)_0$ decreases upon isomorphic–isomeric increase in temperature and also at isomorphic–isothermic decrease in the number of atoms N in the nanocrystal, or at isomeric–isothermic deviation of the nanocrystal shape from the most energetically optimal shape (in the RP-model, this shape is a cube). The obtained equation of state is used to study the changes of the silicon properties at isochoric ($\nu/\nu_o$ = 1) and also isobaric $(P = 0)$ decrease in $N$ at temperatures 300 and 1000 K.