金屬叢集的熔化行為: 依據瞬間正則模分析的次序參數

Abstract

在此論文中，我們探討兩種金屬叢集Ag17Cu2和Ag14的熔化行為，並利用isothermal Brownian type 的分子動力模擬搭配Gupta位能產生其低溫至高溫的組態。在這兩種叢集的比熱隨溫度的變化中，皆在較高溫度顯示出一主峰，我們定義為其熔化溫度，但它們之間的差別在於，在較低的溫度，Ag14具有一個額外的前峰而Ag17Cu2沒有。我們利用瞬間正則模（INM）分析剖析兩種叢集的動力學行為，並提出了一個新的次序參數，可以具體描述兩種叢集的熔化行為。 INM分析表明，一個叢集的次序參數可以被其瞬間振動態密度所定義，或者可由該叢集旋轉運動的三個正交特徵向量所描述，在此該叢集可視為一轉動剛體。對於所研究的兩種金屬叢集，我們的計算結果顯示，這兩種定義所求得的次序參數大致是一致的，對於低溫至高溫的熔化相變過程的闡述也與此兩種叢集各自的比熱曲線所推論的結果相吻合。此外，此次序參數也提供了更深入的圖像，關聯了叢集的熔化行為與過去成功地應用於塊材系統的熔化相變之對稱性破缺的概念。

In this thesis, we investigate the melting behaviors of two metallic clusters, Ag17Cu2 and Ag14, which are generated by an isothermal Brownian-type molecular dynamics simulation with the empirical many-body Gupta potential from low to high temperatures. The temperature variations in the specific heat of these two clusters exhibit at higher temperature a main maximum, at which we define as the melting temperature, but at lower temperature they differ by Ag14 possessing an additional prepeak and none in Ag17Cu2. The instantaneous normal mode (INM) analysis is used to dissect dynamics of the two clusters. We propose a new order parameter that specifically describes the melting behaviors of the two clusters. Our INM studies show that the order parameter of a cluster can be defined either by the INM vibrational density of states, or in terms of three orthogonal eigenvectors describing the rotational motions of the cluster by considering it as a rigid body. For the two metallic clusters studied, our calculated results indicate the mutual agreement of the order parameter by these two methods and also the consistent interpretation of the melting transitions at both lower and higher temperatures with those inferred from their respective specific heat. Furthermore, the new order parameter provides an insightful picture between the melting of clusters and the concept of broken symmetry, which is successfully applied to bulk systems for understanding the melting transition.