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.

掺杂KSr ₂ Nb ₅ O ₁₅的高价阳离子（La ³⁺，Bi ³⁺，Y ³⁺，Ti ⁴⁺，Ta ⁵⁺和W ⁶⁺）的极化率和自发极化。利用第一原理和实验结果计算出无铅四方钨青铜铁电体。阳离子掺杂剂给出不同的结果，这主要是由于缺少可忽略缺少原子的离子极化性和原子相互作用引起的极化性的可加性规则所致。基于介电常数的极化率与实验值非常吻合，特别是对于具有三价阳离子掺杂的结构。利用第一性原理计算出的极矩自发极化与实验得出的基于极矩的自发极化是一致的。这表明了预测的可靠性，以及高价阳离子掺杂的KSr ₂ Nb ₅ O ₁₅的自发极化被确认。这项工作为具有四方钨青铜结构的铁电材料的自发极化铺平了道路。