Ab initio study of elastic constants in In_xGa_(1-x)N and In_xAl_(1-x)N wurtzite alloys

摘要

Dependence of elastic constants on composition and atomic arrangement in wurtzite In_xGa_(1-x)N and In_xAl_(1-x)N alloys is studied by self-consistent ab initio calculations within a supercell model. It is found that a Vegard's-like law, i.e., linear dependence on the alloy content, x, can be accepted for C_(12), C_(13), and C_(44) in In_xGa_(1-x)N, and for C_(12), C_(13), and C33 in In_xAl_(1-x)N, whereas significant sublinear deviations are obtained for C and C33 in In_xGa_(1-x)NN and for C_(11) and C44 in In_xAl_(1-x)N. The effect of In atoms clustering, modeled by grouping In atoms in a part of a supercell, leads to a decrease in C_(11), C_(12) and C44, and an increase in C_(33), in both In_xGa_(1-x)N and In_xAl_(1-x)N alloys. Therefore, in the alloys with clustered In atoms, C_(12), C_(13), and C_(44) show significant sublinear behavior on composition in both In_xAl_(1-x)N and In_xAl_(1-x)N, whereas the composition dependence of C_(33) is almost linear in In_xAl_(1-x)N and significantly superlinear in In_xAl_(1-x)N. The dependence of the bulk modulus on composition is slightly sublinear in In_xGa_(1-x)N and In_xAl_(1-x)N alloys and changes little due to the In clustering effect.