X-ray diffraction by a one-dimensional paracrystal of limited size.
X-ray diffraction by a one-dimensional paracrystal of limited size.
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DOI：
10.1107/s0108767398003067
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发表时间：
1998-09
期刊：
影响因子：
--
通讯作者：
X. Mu
中科院分区：
文献类型：
--
作者：
X. Mu
推导了有限一维副晶体 X 射线衍射的显式方程。基于该方程，讨论了由于有限的尺寸和无序而导致的反射展宽。它描述了整个倒易空间上的旁晶衍射，包括退化为小角度 X 射线散射吉尼尔方程的小角度区域。副晶体的衍射峰位置不是周期性的。与平均晶格常数预测的峰相比，峰移动到更低的角度。这种转变随着反射顺序和无序程度的增加而增加。如果将副晶衍射的高度和宽度视为约化量，则它们是单个变量 N1/2 g 的函数。第一次衍射的宽度主要取决于天然副晶体的尺寸加宽，其中 N1/2 g = 0.1-0.2。基于副晶衍射方程，提出了一种使用单一衍射轮廓测量副晶无序和尺寸的方法。可以使用Scherrer方程获得尺寸的初始值，然后通过α*定律估计无序程度的初始值。参数的最终值是通过针对观察到的轮廓进行最小二乘精炼来确定的。提出了尺寸“盒”分布的多分散一维副晶系统的衍射方程。衍射宽度随着尺寸分布宽度的增加而减小。
An explicit equation for X-ray diffraction by a finite one-dimensional paracrystal is derived. Based on this equation, the broadenings of reflections due to limited size and disorder are discussed. It depicts the paracrystalline diffraction over the whole reciprocal space, including the small-angle region where it degenerates into the Guinier equation for small-angle X-ray scattering. Positions of diffraction peaks by paracrystals are not periodic. Peaks shift to lower angles compared to those predicted by the average lattice constant. The shifts increase with increasing order of reflections and degree of disorder. If the heights and widths of the paracrystalline diffraction are treated as reduced quantities, they are functions of a single variable, N1/2 g. The width of the first diffraction depends mostly on size broadening for a natural paracrystal, where N1/2 g = 0.1-0.2. A method to measure the paracrystalline disorder and size using a single diffraction profile is proposed based on the equation of paracrystal diffraction. An initial value of size may be obtained using the Scherrer equation, that of the degree of disorder is then estimated by the alpha * law. Final values of the parameters are determined through least-squares refinement against observed profiles. An equation of diffraction by a polydisperse one-dimensional paracrystal system is presented for 'box' distribution of sizes. The width of the diffraction decreases with increasing breadth of the size distribution.