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標題: | 以非平衡分子動力學計算固體材料熱傳導係數之工具研發 Development of a Non-equilibrium Molecular Dynamics Simulation Tool for Calculating the Thermal Conductivity of Solid Materials |
作者: | Chun-Ying Chiu 邱俊穎 |
指導教授: | 黃美嬌(Mei-Jiau Huang) |
關鍵字: | 熱傳導係數,非平衡分子動力學,尺寸效應, thermal conductivity,nonequilibrium molecular dynamics,finite-size effect, |
出版年 : | 2007 |
學位: | 碩士 |
摘要: | 本論文使用一非平衡分子動力學之數值模擬方法來計算Si塊材的熱傳導係數,並探討取平均步數M、熱通量q'、加熱區或移熱區之長度δ、模擬區域熱流方向長度Lz、模擬區域在垂直熱流方向的橫截面積A、線性擬合溫度曲線區與加熱區或移熱區之距離σ對計算所得的熱傳導係數k 的影響。我們在模擬系統中,藉著Jund和Jullien[19]的方法,調整在加熱區和移熱區中原子的速度來加入熱流,當整個模擬區域達到穩態後,由模擬區域的溫度分布曲線可得到溫度梯度。因熱流大小為已知,由傅利葉定律,我們可以求得Si在模擬區域的k。模擬中發現,較大的q'要花較長的模擬時間才能達到穩態。大致上隨著σ愈大,線性擬合溫度曲線區的溫度曲線會趨近線性,且k會愈大;q'愈大,則k 愈大,這與實驗觀察不符;δ 和A 的大小對k 的影響很小;Lz 愈長,求得的熱傳導係數愈大,可驗證尺寸效應。在模擬中觀察到,當q'過大,或者是δ過小時,達到穩態後,在加熱區的溫度上升的幅度會比在移熱區的溫度下降的幅度來的大,造成模擬區域溫度分布曲線的不對稱。這現象可能是由於k 會隨著溫度上升而下降所造成。在此要特別感謝張泰鳴學長提供本論文程式的主要部份-計算原子間作用力的副程式、Verlet list + Cell link 法副程式、計算薄層溫度副程式以及在週期性邊界條件下,如何排列晶格原子初始位置的方法,使本論文的研究得以順利完成。 A nonequilibrium molecular dynamics method is used to compute the thermal conductivity of bulk silicon and the influence of numerical parameters involved in the method on the computed thermal conductivity k is studied numerically in this thesis. Numerical parameters involved in the method are as follows, M(the number of steps which we take for average), q'(heat flux), δ(the length of the region where heat is added or removed), Lz(the length of the simulation cell in the direction of heat flux), A(the area of the cross section which is perpendicular to the direction of heat flux), and σ(the distance between the region where heat is added or removed and the region we take for linear fitting). By Jund and Julien’s method[19], we rescale the velocity of atoms in heat source and heat sink to add heat flux in the simulation cell. As the simulation cell has reached steady, we can get temperature gradient from a stationary temperature profile and compute the thermal conductivity by Fourier’s law. In the simulation We find the lager q', the longer simulation time is needed for the system to achieve steady state. In general, the bigger σ, the more linear temperature profile and larger k is got. The Larger q', the larger k is got, but the result does not agree with experiments. k is almost not affected by δ and A. Because of the finite-size effect, the Longer Lz, the larger k is got. When q' is too large or δ is too small, we find the stationary temperature profile of the simulation cell is asymmetric. This may be due to the fact that k is smaller at higher temperature. All k's we get in this simulation are smaller than that of bulk Si measured in experiment because the mean free path of phonon is limited by the boundaries at the edge of heat source and sink. Specially, I am grateful to my senior, Tai-Ming Chang for his programs-the subprogram which calculate the force between atoms, the subprogram of Verlet list + Cell link method, the subprogram of computing temperature of slices of the simulation cell, and the method of how to set the initial position of atoms at lattice sites of the periodic boundary condition. Those programs and the method make the research in this thesis completed successfully. |
URI: | http://tdr.lib.ntu.edu.tw/jspui/handle/123456789/27567 |
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顯示於系所單位: | 機械工程學系 |
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