金屬鋅叢集靜態結構因子之研究

Abstract

我們討論八種不同原子數的鋅金屬叢集，分別是Zn6、Zn13、Zn29、Zn33、Zn36、Zn42、Zn49與Zn53。在模擬的部分使用的是Brownian-type分子動力模擬，搭配Gupta-type經驗位能，得到金屬鋅叢集在不同溫度的組態。 在本論文中，我們會針對鋅叢集在不同溫度下的結構進行探討。共使用了三種辦法，分別是配對分佈函數(Pair distribution function)，角度分佈函數(Angular distribution function)以及靜態結構因子(Static structure factor)。 配對分佈函數是將一個鋅叢集中的兩原子間之距離統計後獲得的分佈情形。角度分佈函數則是將鋅叢集中三原子之間的夾角的分佈情形。靜態結構因子則是利用散射公式(Debye scattering equation)來計算鋅叢集的散射情形。 運用上述的三種辦法所繪出的配對分佈函數、角度分佈函數與靜態結構因子之圖形在低溫下（約為10K、20K）皆會有明顯不同於高溫時圖形之特徵。其中我們又對低溫下的靜態結構因子做進一步的靜態結構因子分群分析。 同時我們會利用OpenGL繪製出鋅叢集的3D立體圖形，讓我們可以更加清楚的將上述的分佈函數用圖像的方式加深理解。

We discuss eight different atomic numbers of zinc metal clusters, namely Zn6, Zn13, Zn29, Zn33, Zn36, Zn42, Zn49 and Zn53. The Brownian-type molecular dynamics simulation and empirical Gupta-type potential are used in the simulation to obtain the configuration of the metal zinc clusters at different temperatures. In this thesis, we will discuss the structure of zinc clusters at different temperatures. Three methods are used, namely the pair distribution function, the angular distribution function and the static structure factor. The pair distribution function is a distribution obtained by counting the distances between two atoms in a zinc cluster. The angular distribution function is the distribution of the angle between the three atoms in the zinc cluster. Static structure factor is the use of scattering formula (Debye scattering equation) to calculate the scattering of zinc clusters. The pair distribution function, the angular distribution function and the static structure factor are plotted at the low temperature (about 10K, 20K) using the above-mentioned three methods, which are obviously different from those of the high temperature. In this thesis, we further analyze the static structure factor at low temperature. At the same time, we will use OpenGL to draw zinc clusters of 3D graphics, so that we can more clearly the above distribution function with the image to deepen understanding.