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Composition dependence of elastic constants in wurtzite AlGaInN alloys

In this paper, we analyze the dependence of elastic constants c_ij on composition for random wurtzite quater- nary AlGayInN alloy in the whole concentration range. The study takes as its starting point the c_ij parameters for zinc blende phase calculated earlier by the authors on the basis of valence force field model. To obtain the wurtzite constants from cubic material parameters the Martin transformation is used. The de- viations from linear Vegard-like dependence of c_ij on composition are analyzed and accurate quadratic fits to calculated moduli are presented. The influence of nonlinear internal strain term in the Martin transformation is also investigated. Our general results for quaternary AlGaInN alloys are compared with the recent ab initio calculations for ternaries GaInN and AlInN (Gorczyca and Lepkowski, Phys. Rev. B 83 203201, 2011) and good qualitative agreement is found.