本研究主要以分子動力學法研究石墨烯及奈米碳管的聲子性質，如色散關係與態密度等，並嘗試確立一套容易計算且準確的分析方法，接著再對各模型改變不同尺寸、缺陷等條件來探討它們對聲子性質的影響。本文首先以分子動力學模擬一維原子系統的色散關係和態密度，同時與色散關係和態密度的理論結果相比較，來進行方法的測試，從中確認色散關係和態密度的結果完整且正確。接著對二維石墨烯進行不同勢能、尺寸和缺陷比例之色散關係分析，分別探討它們對聲子性值的影響，發現使用不同勢能去模擬相同完美模型的結果會不同，但調整不同尺寸或缺陷比例對色散關係影響不顯著，色散關係結果與文獻比較也非常吻合，也無須如文獻所述採用單位晶胞內的單一種原子進行分析，即可得到完整之色散關係，而本文中所使用的兩種態密度方法也能呈現非常相似的結果。最後對奈米碳管進行聲子特性分析，其中模擬不同螺旋性、尺寸和缺陷比例之模型，發現尺寸差異對色散關係之差異不大，而不同缺陷比例的影響也不顯著，但會造成態密度峰值之頻率位置有些許差異，而在不同螺旋性其餘尺寸相同的結果中兩者色散關係有較明顯的不同，色散關係與文獻比較其趨勢也相符合。在態密度的分析結果中，使用兩種方法進行比較，分別為計算原子速度的自相關函數方法和由色散關係結果直接將波數域疊加的方法，可發現未施加週期性邊界時的模擬，使用第一種方法計算態密度能夠顯示較完整的細節，而在施加週期性邊界的模擬中兩個方法則相同。
本研究成功確立一套健全的聲子色散關係與態密度的分析方法，分析石墨烯與奈米碳管的聲子性質，可提供往後奈米材料對熱傳相關研究的一個分析依據。

Phonon properties of graphene and carbon nanotubes, i.e., dispersion relation and density of state, were studied using molecular dynamics simulation. We were trying to establish a correct and simple procedure to analyze the thermal conduction mechanism for nanomaterials. First, the phonon properties of one dimensional atom chain interacting using harmonic potential were calculated and compared with the theoretical results in order to confirm the validity of the procedure. Next, we analyzed pristine graphene with different size and defected one with various number of vacancies. Meanwhile, the effects of size, defect and boundary condition on the phonon properties of carbon nanotube were also simulated. It was found that these effects were not easy to observe when inspecting the dispersion curves. However, the density of state shows obvious differences. In this study, we successfully established the analysis procedure to extract phonon dispersion relation and density of states for nanomaterials from molecular dynamics simulation. This research could pave the way to correlate the thermal conduction mechanism and phonon behavior in the near future.

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