Spontaneous electric polarization of high-valance-ion-doped lead-free ferroelectric KSr₂Nb₅O₁₅ by first-principles calculations

The polarizability and spontaneous polarization of high-valent cations (La³⁺, Bi³⁺, Y³⁺, Ti⁴⁺, Ta⁵⁺ and W⁶⁺) doped KSr₂Nb₅O₁₅ lead-free tetragonal tungsten bronze ferroelectrics are calculated by using the first principles and experimental results. The cation dopants give different results, mainly due to the shortage of the additivity rule that ignores the ion polarizability of the missing atoms and the polarizability caused by the interaction of the atoms. The polarizability based on the dielectric constants is in good agreement with experimental values, especially for the structures with trivalent cation doping. And the spontaneous polarization calculated by the polar moment by using first principles result is consistent with that based on the polar moment from experiment. This shows the reliability of the prediction, and the spontaneous polarization of high-valent cations doped KSr₂Nb₅O₁₅ are confirmed. This work paves a way for the spontaneous polarization of the ferroelectric materials with tetragonal tungsten bronze structure.