本研究以鐵電材料鈦酸鉍鈉(Bi0.5Na0.5TiO3)為研究對象，探討A-site原子有序與無序排列對繞射特徵、吉布斯自由能與極化行為之影響。鈦酸鉍鈉為鈣鈦礦結構材料，其A-site由Bi與Na原子佔據，室溫下鈦酸鉍鈉為rhombohedral結構。
由於鈦酸鉍鈉的繞射結果中可觀察到額外的繞射峰，顯示其可能存在更為複雜的結構特徵。本研究開發一套排列篩選程式，篩選Bi與Na原子於A-site上的有序排列結構，並與無序排列結構進行比較。透過模擬不同排列下的繞射圖譜，結果發現無序排列最符合實際材料中的主要佔據方式，但有序排列可產生對應於文獻中觀察到的特徵繞射峰。此結果表明文獻製備之鈦酸鉍鈉的A-site以無序為基底並具備部分區域有序性。
本研究先藉由密度泛函理論計算鈦酸鉍鈉的Bader電荷、波恩有效電荷與彈性常數，再利用GULP擬合經驗位能函數。透過擬合完成之經驗位能函數由分子動力學模擬計算鈦酸鉍鈉有序與無序結構之熱力學性質以及極化能力。
吉布斯自由能的計算結果指出，由於無序排列的內能較高，在低溫時，有序排列具有較低的吉布斯自由能，較為穩定；但在常見的鈦酸鉍鈉陶瓷製備溫度條件下，無序排列因系統熵較高，其自由能反而較低，而成為穩定相。說明在高溫製程中，鈦酸鉍鈉的A-site傾向形成無序排列結構，冷卻至室溫後則傾向轉為有序排列結構，因此高溫條件製備的鈦酸鉍鈉可能具有無序為基底的部分有序性。
本研究亦透過核殼模型進行分子動力學模擬，探討鈦酸鉍鈉有序與無序排列結構的鐵電性質。結果顯示，兩者在外加電場下的極化響應與關閉電場後的殘餘極化量相當接近。

This study investigates the effects of A-site cation ordering and disordering on the diffraction characteristics, Gibbs free energy, and polarization behavior of the ferroelectric material bismuth sodium titanate (Bi0.5Na0.5TiO3).
Gibbs free energy calculations based on molecular dynamics reveal that, although the disordered structure possesses higher internal energy, it becomes thermodynamically favorable at elevated temperatures due to its greater configurational entropy. Below 1000 K, the ordered structure remains more stable; however, at higher temperatures—such as those typically used in solid-state synthesis—the disordered configuration is energetically preferred. Upon cooling, the system tends to transition toward partial ordering, which explains why experimental diffraction patterns often exhibit a predominantly disordered phase accompanied by signatures of local ordering.
Furthermore, the ferroelectric properties of both A-site ordered and disordered configurations were evaluated through molecular dynamics simulations employing a core-shell model. The results reveal that their polarization responses under applied electric fields, as well as their remanent polarization after field removal, are notably similar.

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