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We present detailed investigations of the structural, elastic, dielectric, and piezoelectric properties of scandium aluminum nitride (ScxAl1−xN) with the wurtzite crystal structure by means of first-principles calculations based on density functional theory in order to enable a detailed comparison to the corresponding physical properties of GaAlN and InAlN. The goal of our approach is to use atomistic simulations to extract the novel solid state characteristics of ScxAl1−xN crystals by the determination of complete sets of coefficients for the elastic, compliance, and piezoelectric tensor and to confirm the theoretical predictions by experimental measurements of selected tensor coefficients. The calculation of the tensor components is accompanied by a detailed analysis of the crystal structures, e.g., average bond length, bond angles, lattice parameters, and mass density in dependence on alloy composition of ScxAl1−xN. If an increasing number of Al atoms of up to x = 0.5 are replaced by Sc atoms, we observe a nonlinear change of the ratio of lattice parameter c (x) a (x) and average bond angles of about 10% and 5%, respectively, which give an indication of an increasing deviation of the crystal structure of ScxAl1−xN from an ideal hexagonal lattice. As a consequence of the deformed crystal structure and the iconicity of the Sc–N bond, we predict a change in value of the elastic coefficient C 33 S c A l N (x) , the piezoelectric coefficient e 33 S c A l N (x) , and the value of spontaneous polarization P S P S c A l N (x) of up to 65%, 150%, and 230%, respectively. Based, on these simulation results, physical features of practical use are derived, like the average bulk, shear, and the Young modulus as well as the reciprocal Young's modulus and Poisson ratio. Furthermore, the spontaneous polarization of ScxAl1−xN is approximated, taking nonlinear effects into account as well as the piezoelectric polarization caused by uniaxial, biaxial, and hydrostatic stresses in dependency on alloy composition and strain. A detailed comparison of the structural and polarization related properties of GaAlN and InAlN allows us to point out the peculiarity of wurtzite ScAlN crystals within the group III-nitrides. [ABSTRACT FROM AUTHOR]