論文摘要
X光繞射對於材料的分析上是一個非常有力的工具，本論文之目的就是藉由分析繞射峰線形來判定奈米微粒粉末的粒徑分佈。基本理論是由E. F. Bertaut所提出，主要技術是對繞射峰形作富立葉分析。藉由共同體積函數（common volume function）及晶柱長度分佈（column length distribution）可以找出繞射峰形和微粒的粒徑分佈間的關係，我們引進解析函數，並藉由擬合來處理繞射譜圖的統計誤差問題。經由一些基本假設我們得到共同體積函數，並得到繞射峰線形函數及其對應到的粒徑分佈函數，用此峰形函數擬合繞射峰形後即可從粉末繞射譜圖獲得其粒徑分佈。
本實驗室採用真空冷凝法備製奈米微粒粉末，其繞射峰形遠遠偏離高斯函數或洛仁子函數的峰形，其特徵為具有尖銳的峰和向左右延伸的兩翼，因此我們將繞射峰分成兩個高度寬度不同的成分峰，而這兩個成分峰有相同的中心位置，如此我們可以將這一類的繞射峰形做很好的擬合，最後我們發現這種特殊峰形是由於粉末樣品粒徑的高分散性（highly dispersive）所造成。

Abstract
X-ray diffraction is a very powerful tool for structural analysis, from which information on composition, structure, and particle size may be obtained. The aim of this thesis is to determine the particle size distribution function (PSD) of powder samples consist of ultra small nano-particles employing the Fourier analysis to the diffraction profiles. We related the powder diffraction line profile to the particles size distribution through the common volume function and the column length distribution function. We followed the idea introduced by E. F. Bertaut in 1950, but using an analytic function to account for the statistical fluctuations which is intrinsic to the experimental data. Assuming that the common volume function us analytic, the line profile function and the corresponding particle size distribution may then be obtained.
The nano-particle powders were synthesized by the gas condensation method. These samples have a common feature: the line profiles are far from Gaussian and exhibit a narrow tip with wide spread wings. We concluded that such deviation from Gaussian type can be explained to be due to the highly dispersion of the particle size distribution. In order to account for high degree of dispersion, two distributions of different widths and heights were allowed in the analysis. By considering such criteria, very good fitting to the powder patterns can generally be obtained.

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