First principles study on the piezoelectricity of KNN alloys

To understand the physical significance for the high piezoelectric response in K_1-xNa_xNbO₃ (KNN) material, the geometric structure, total energy, elastic constant, Born effective charge and piezoelectric constant of orthorhombic K_1-xNa_xNbO₃ perovskite solid solutions at various x (from 0 to 1) are investigated using first principles calculations for supercells. The results show that lattice parameters of K_1-xNa_xNbO₃ supercells decrease monotonously with the increasing value of x. However, the piezoelectricity exhibits parabolic-like relation with x, and the longitudinal piezoelectric coefficient d₃₃^* reaches a maximum at about x=0.5625, where the morphotropic phase boundary is expected to occur in K_1-xNa_xNbO₃ material.