Poisson Ratio and Biaxial Relaxation Coefficient in $In_{x}Ga_{1-x}N$ and $In_{x}Al_{1-x}N$ Alloys

We present theoretical results showing dependence of Poisson ratio and biaxial relaxation coefficient on composition and atomic arrangement in wurtzite $In_{x}Ga_{1-x}N$ and $In_{x}Al_{1-x}N$ alloys. Our calculations reveal that the Poisson ratio determined for $In_{x}Ga_{1-x}N$ and $In_{x}Al_{1-x}N$ alloys subjected to a uniaxial stress parallel to the c axis of the wurtzite structure shows significant superlinear dependence on composition. The superlinear bowing in Poisson ratio is enlarged by the effect of In clustering. The biaxial relaxation coefficient determined for $In_{x}Ga_{1-x}N$ and $In_{x}Al_{1-x}N$ alloys subjected to a biaxial stress in the plane perpendicular to the c axis of the wurtzite structure changes superlinearly and linearly with x in $In_{x}Ga_{1-x}N$ and $In_{x}Al_{1-x}N$, respectively. The effect of In atom clustering results in sublinear dependence of the biaxial relaxation coefficient in both $In_{x}Ga_{1-x}N$ and $In_{x}Al_{1-x}N$ alloys.