液態鎵的結構、動力學及熱力學性質之研究

Abstract

在本論文中，我們將以 molecular dynamics (MD) 作為模擬的方法，以一具有排斥核 (repulsive core) 和Friedel震盪 (oscillation) 項所組成的液態鎵pseudo-potential作為模擬系統的作用位能，來探討真實液態鎵微觀尺度下的結構、動力學行為及其熱力學特性。於此，我們將這些動力學行為和熱力學特性分成兩部分各自討論。 一、 經由非彈性X-ray 散射 (IXS) 和非彈性中子散射 (INS) 實驗，發現液態鎵的靜態結構因子 (static structure factor) 有一突起結構，動態結構因子 (dynamic structure factor) 的頻譜寬 (line-width) 函數 有一平台結構。這兩異常結構的成因及其物理原理是近年來熱門的話題。故為了解其物理原理，我們以上述所提的液態鎵模型作為系統之作用位能，由粒子流動之縱向分量相干函數頻譜 (longitudinal current spectra) 所估計出的系統聲速，和經由計算所得到的動態結構因子幾乎和實驗值吻合。這證明我們所使用的液態鎵模型足以取代真實液態鎵。同時，在我們的模擬系統發現，靜態結構因子 中的凸起結構與頻譜寬函數 中的平台結構都約略發生在相同處，但在 中凸起結構的產生，需有效位能範圍含蓋到第三個震盪位能井， 中平台結構的產生，需有效位能範圍卻只需要含蓋到第二個震盪位能井。 二、 Mansoori-Canfield / Rasaiah-Stell提出以硬球為基本要件的MCRS微擾理論，不但無需沉重的計算且能經濟地幫模型系統找到ㄧ有效粒子尺度。再加入Mon的修正項，推廣為Extend-MCRS微擾理論。此理論更能精確地估計模擬系統的有效粒子尺度和其熱力學性質。利用具有和真實液態鎵相似物理特性的液態鎵模型作為模擬系統的作用位能，除了前章節在此液態鎵模型發現的奇異結構外，其徑向分布函數 (radial distribution function) 的峰值隨密度變化曲線有一不連續跳躍。此外，額外的熵值 (excess entropy) 隨著密度增加而減少，但在某段密度區間內額外的熵值卻不正常增加。此奇異行為可以由系統的粒子最密堆積 (packing fraction) 在此區間內隨密度增加而減少獲得解釋。

In this thesis, to investigate the structures, dynamic behavior, and thermodynamic properties of liquid gallium, we use molecular dynamics (MD) method with a liquid gallium pseudo-potential, which consists of a repulsive core and a Friedel-oscillation tail. The discussions for the dynamic behavior and thermodynamic properties of liquid gallium will be separated into two chapters. According to inelastic neutron scattering (INS) and inelastic x-ray scattering (IXS) experiments, A shoulder appears on the static structure factor and a dynamic anomaly appears on the linewidth function of dynamic structure factor . The causes of these two anomalous structures are popular issues in recent decade. In order to investigate the physical origins of these two anomalies, the interatomic pair potential, described above will be the simulated model. The sound velocity of our model which is estimated from longitudinal current spectra and the dynamic structure factors of our model agree well with the experimental results. Therefore, it suggests that the simulated model is good for describing realistic liquid gallium. On the other hand, we report the shoulder of the and the dynamic anomaly of the roughly locate at the some position. The contribution of interaction range of interatomic pair potential to cause the shoulder of should include the first three attractive wells, but the contribution of interaction range of interatomic pair potential to cause the dynamic anomaly of should include the first two attractive wells only. Mansoori-Canfield / Rasaiah-Stell (MCRS) theory, which is based on hard sphere perturbation theory, can estimate effective diameter of particle efficiently without heavy computing time. By adding a correction term originally proposed by Mon to remedy the deficiency of the MCRS theory, the extended-MCRS theory can accurately predict the effective diameter and thermodynamic properties of simulated system. By using MD simulation with interatomic pair potential given above, there is a discontinuous jump on the main-peak position of the radial distribution function at some critical density. Moreover, an anomaly of excess entropy is found to be associated with the anomalous packing fraction of the hard sphere (HS) fluid in the almost same density region.