The thermodynamic stability of In$_{x}$Ga$_{1-x}$N solid solutions

A group-theoretical analysis of solid solutions of indium and gallium nitrides In$_{x}$Ga$_{1-x}$N was carried out, and all the main symmetry groups were found for these solutions with the initial hexagonal structure. The thermodynamic potentials of the main phases with different compositions x are calculated using the density functional theory. It is shown that for small and large $x$, i.e. at 0 $<x<$ 0.2 and 0.8 $<x<$ 1, there is a large number of monoclinic phases $Pm$ and $P2_1$, which are stable with respect to decomposition into InN and GaN at room temperature. In the range 0.2 $<x<$ 0.8, there are only two stable orthorhombic phases Cmc2$_{1}$ with compositions $x$ = 1/3 and $x$ = 2/3. All basic geometric and thermodynamic properties of various In$_{x}$Ga$_{1-x}$N phases have been calculated. It was found that the stability of In$_{x}$Ga$_{1-x}$N epitaxial films increases with growth on InN and decreases with growth on GaN.