Change in the thermodynamic properties of a Si–Ge solid solution at a decrease of the nanocrystal size

The equation of state and the thermodynamic properties of the substitutional solid solution Si$_{0.5}$–Ge$_{0.5}$ are calculated in the framework of the “medium atom” model. The changes in the equation of state and the thermodynamic properties upon the transition from a macrocrystal to a nanocrystal of 222 atoms with the geometric Gibbs surface are calculated using the RP-model of nanocrystal. The calculations have been performed along isotherms $T$ = 100, 300, and 1000 K in the pressure range -1 $<P<$ 7 GPa. The changes in the properties is studied at the isochoric and also isobaric ($P$ = 0) decrease of the number of atoms in the nanocrystal. It is shown that, at the isobaric ($P$ = 0) decrease in the size, the specific volume of the Si$_{0.5}$–Ge$_{0.5}$ nanocrystal increases the more significantly, the higher the nanocrystal temperature.