鈦酸鉛為鈣鈦礦型之鐵電材料，在鈣鈦礦型材料家族中有著相對較高的居禮溫度、熱電係數，且可在無外加電場情況下產生自發極化現象，在應用上可以做為機電轉換裝置、轉換器、電容器等。
過去文獻指出藉由摻雜稀土元素（本研究以鑭摻雜為例）可以改善材料性質，例如：鑭摻雜會使得鈦酸鉛材料居禮溫度、介電常數及焦電性等性質改變，因此若想改變鈦酸鉛電性可以透過摻雜方法實現。
但鐵電材料在製造或是退火的過程中容易有本質缺陷的產生，而缺陷的生成又會進一步影響材料的性質。本研究第一部分是利用第一原理計算(Ab initio calculation)方法探討鈦酸鉛材料中對於不同缺陷和帶電狀態處在不同化學勢能環境下的缺陷形成能，確認與過去文獻結果吻合後，再利用相同方法套用到鑭摻雜鈦酸鉛的模型中，預測在有鑭摻雜下各種帶電缺陷的形成可能性。另外為了更全面的模擬實驗上的環境條件，考慮熵效應的自由能計算結果顯示對於缺陷生成能並沒有明顯的改變。
由於鑭摻雜是在原本鉛位置，會造成電荷的不平衡，因此會伴隨其他陽離子空缺的產生機制達到電荷補償，然而若想使用第一原理計算鑭摻雜情況下各種離子補償機制是相當耗時的，因為缺陷位置可以任意改變，故有許多缺陷位置排列可能性。因此第二部分是利用前述提到的帶電點缺陷生成能使用線性組合的方式湊成複合缺陷的形式加上缺陷間庫倫作用能修正和直接使用第一原理計算複合缺陷之生成能作比較，預測該方法之可行性，結果告訴我們鉛空缺與鈦空缺之補償機制皆有機會發生，符合文獻提到之結果。然而在修正值的部分會與實際不符，因此無法使用此法來直接修正複合缺陷的生成能。另一方面原先預期可以使用這個概念先找到最低庫倫能和所對應之距離，接著應用在多缺陷系統中缺陷分佈的配置。但在本研究最後的結果顯示並非在所有複合缺陷中，庫倫能與晶體結構的總能都有正相關，因此要用於找尋能量最低的缺陷模型仍有一定的疑慮。

In this study, defect formation energy are determined to investigate the point defect mechanism under various conditions such as oxygen atmosphere or defects with different charge state by first-principles calculation. When lanthanum ion doped lead titanate, it tend to replace lead ion site due to the similar ionic radius, and it will cause an unbalanced charge system. Therefore, it will accompany the compensation mechanism of vacancies formation. However it is time-consuming to calculate the defect formation energy of these kinds of complex defect. In this study, a relatively fast method in first-principles calculation about the single point defect in a linear combination will be used, and then consider the corrections of coulomb interaction between defects. By comparing different ways to calculate the defect formation energy, the results show that the formation of lead vacancy and titanium vacancy are more likely to form. And it is agreed to the result of literature referred to. But we find that the value after correction is not same with complex defect result and it can be interpreted due to the corrected Coulomb energy can only be used as a reference for relative corrections and cannot be directly corrected for energy. The other goal is to use the result of Coulomb energy versus distance between defects to predict the trend of defect distribution. However, Coulomb energy can’t be positively correlated with total energy of crystal structure. That is to say, only take Coulomb interaction into consideration is not enough to well predict the complex defect form.

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