First-principles calculations of defect formation energy and carrier concentration of Ti⁴⁺, Ta⁵⁺ and W⁶⁺ doped KSr₂Nb₅O₁₅

The formation enthalpy, chemical potential, defect formation energy and charge carrier concentration of Ti⁴⁺, Ta⁵⁺ and W⁶⁺ doped KSr₂Nb₅O₁₅ (KSN-Ti, KSN-Ta and KSN-W) are obtained using first principles calculations for the purpose of predicting the influence of high valence cations on the structures and dielectric properties. It shows that when Ti⁴⁺, Ta⁵⁺ and W⁶⁺ doped into KSN, a phase transition from tetragonal to orthogonal occurs, where the KSN-Ti structure has a larger distortion than that of KSN-W, and KSN-Ta has the smallest lattice distortion. Both the band gap and the carrier concentration increase and of the trends are KSN-Ti > KSN-Ta > KSN-W and KSN-W > KSN-Ti > KSN-Ta, respectively. It is indicated that KSN-Ta is the most stable compound and KSN-Ti has the largest dielectric constant. The stability of KSN-Ti, KSN-Ta and KSN-W are in corresponding to the results of Gibbs energy that KSN-Ta < KSN-W < KSN-Ti, and the thermal expansion coefficient satisfies to KSN-Ta > KSN-W > KSN-Ti. This work paves the way to further understand the inner doping mechanism of cations and the method to improve dielectric properties of ferroelectric materials with tetragonal tungsten bronze structure like KSN.