Piezoelectricity in K_1−xNa_xNbO₃: First-principles calculation

The piezoelectric properties of K_1−xNa_xNbO₃ are studied by using first-principles calculations within virtual crystal approximation. To understand the critical factors for the high piezoelectric response in K_1−xNa_xNbO₃, the total energy, piezoelectric coefficient, elastic property, density of state, Born effective charge, and energy barrier on polarization rotation paths are systematically investigated. The morphotropic phase boundary in K_1−xNa_xNbO₃ is predicted to occur at x = 0.521, which is in good agreement with the available experimental data. At the morphotropic phase boundary, the longitudinal piezoelectric coefficient d₃₃ of orthorhombic K_0.5Na_0.5NbO₃ reaches a maximum value. The rotated maximum of is found to be along the 50° direction away from the spontaneous polarization (close to the [001] direction). The moderate bulk and shear modulus are conducive to improving the piezoelectric response. By analyzing the energy barrier on polarization rotation paths, it is found that the polarization rotation of orthorhombic K_0.5Na_0.5NbO₃ becomes easier compared with orthorhombic KNbO₃, which proves that the high piezoelectric response is attributed to the flattening of the free energy at compositions close to the morphotropic phase boundary. (paper)