由於間接能帶間隙的存在，鈣鈦礦中需要聲子輔助的載子復合顯著延長了載子的生命期。甲基銨碘化鉛鈣鈦礦中，間接能帶間隙的形成對應於碘化鉛八面體籠的變形，而此變形是由甲基銨陽離子的特定方位指向所引起。然而，由熱紊變導致的甲基銨陽離子特定方位指向以及相對應的碘化鉛八面體籠變形的清晰路徑尚未完全釐清。我們提出了四方甲基銨碘化鉛鈣鈦礦的簡正模分析，以完整觀察一平衡附近的所有熱紊變；對於簡正模分析每一模態下的甲基銨方位指向研究，我們開發了正交分解簡正模分析，使用投影矩陣進行包括正交分解方法和天平動識別方法；最後，我們發現了具有以下條件的特殊簡正模態（a）在室溫下活躍（b）同時包含碘化鉛八面體籠的變形以及甲基銨方位指向的天平動變化，因此預期（c）此類特殊簡正模態包含形成間接能帶間隙的特定甲基銨方位指向。

The phonon-assisted carrier recombination through the indirect bandgap remarkably elongates the lifetime of carriers in perovskites. The formation of indirect bandgaps in the methylammonium (MA) lead iodide perovskite (MAPbI3) corresponds to the distortion of the lead iodide octahedral cage induced by specific orientations of the MA cation. However, clear routes to reach these specific orientations and the distortion thereof during thermal fluctuations have not been fully specified. Here we present the normal mode analysis of the tetragonal MAPbI3 perovskite for a complete observation of all thermal fluctuations in the vicinity of an equilibrium; for the MA orientation studies within each mode of the normal mode analysis, we develop the orthogonal decomposition normal mode analysis consisting of the orthogonal decomposition method and the librational identification method both using projection matrices; in the end, we find distinct normal modes that (a) are active at room temperature, (b) each contains the lead iodide distortion together with librationally varying MA orientations, and therefore (c) are anticipated to involve indirect-gap MA orientations.

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