The electronic, structural, and thermodynamic properties of cubic (zinc blende) group-III nitride ternary In xGa1-xN and quaternary Al xIn yGa1-x-yN alloys are investigated by combining first-principles total energy calculations and cluster expansion methods. External biaxial strain on the alloys are taken into account in the calculations. While alloy fluctuations and strain effects play a minor role in the physical properties of AlGaN, due to the small lattice-mismatch, in the InGaN alloys we found a remarkable influence of strain on the phase separation. The effect of biaxial strain on the formation of ordered phases has been also investigated, and the results are used to clarify the origin of the light emission process in In xGa1-xN based optoelectronic devices. The dependence of the lattice constant and energy bandgap in quaternary Al xIn yGa1-x-yN alloys was obtained as function of the compositions x and y. PACS: 61.66.Dk, 64.75.+g, 71.20.Nr
