Structural and Elastic Properties of Wurtzite Al-Rich In$\text{}_{x}$Al$\text{}_{1 - x}$N Alloys

We present theoretical study of lattice parameters and elastic constants of wurtzite Al-rich In$\text{}_{x}$Al$\text{}_{1 - x}$N (x = 0.125, 0.1875 and 0.25) alloys using self-consistent ab initio calculations with a supercell model. Two different atomic arrangements have been considered for a given x, by either distributing the In atoms as uniformly as possible over the supercell or by clustering the In atoms together in a small part of the supercell. Our calculations reveal that the a and c lattice parameters show almost linear dependence on composition for the alloys with uniform distribution of In atoms, while for the case of alloys with clustered In atoms the c lattice parameter deviates from linearity quite significantly. For the alloys with clustered In atoms, we observe that the values of C$\text{}_{11}$, C$\text{}_{12}$, and C$\text{}_{44}$ elastic constants are significantly smaller than the linear interpolated values between the elastic constants of AlN and InN, and the values of C$\text{}_{33}$ elastic constant are significantly larger than the corresponding interpolated values. For the alloys with uniform distribution of In atoms, only C$\text{}_{11}$ elastic constant deviates significantly from linear dependence on composition.