我們利用小顆粒X光繞射理論來擬合奈米粉末的X光繞射譜圖，以判定奈米粉末之平均粒徑與粒徑分佈。若考慮粉末為單一粒徑，發現理論值與實驗值在繞射峰形底部甚不吻合。我們進而假設奈米粉末之粒徑分佈為高斯分佈或Lognormal分佈，將此粒徑分佈的因素利用峰形疊加的方法加入X光繞射譜圖之計算。一般實驗室用的X光繞射儀皆包含銅靶的Kα1及Kα2，我們在理論模擬中也加入了Kα1及Kα2兩種不同波長X光的組合效應。用此一模型去對奈米粉末的繞射峰形做擬合，由擬合的結果我們可以得到奈米粉末粒徑分佈的形式，再將此一分佈的結果與原子力顯微鏡所觀察到的結果相互比較，發現由擬合X光繞射峰形所得到的粒徑分佈結果與原子力顯微鏡所觀察到的結果十分相近。本方法也發展成利用X光繞射譜圖來判定奈米粉末的平均粒徑與粒徑分佈的方法。 Finite size X-ray diffraction theory was used to determine the mean particle diameter and size distribution of powders composed of nano-scale particles. The X-ray diffraction patterns were analyzed assuming a single size as well as multi sizes for the powder. Better fits were frequently obtained when a size distribution for the powder was assumed, as expected. Gaussian and Lognormal distributions were then considered. Through the process, we were able to determine the size distribution of the powder by using the x-ray diffraction pattern. Comparisons of the results to that obtained from the AFM images were also presented.
