X-RAY-DIFFRACTION BY A ONE-DIMENSIONAL PARACRYSTAL OF LIMITED SIZE

An explicit equation for X-ray diffraction by a finite one-dimensional paracrystal is derived. Based on this equation, the broadenings of re flections due to limited size and disorder are discussed. It depicts t he paracrystalline diffraction over the whole reciprocal space, includ ing the small-angle region where it degenerates into the Guinier equat ion for small-angle X-ray scattering. Positions of diffraction peaks b y paracrystals are not periodic. Peaks shift to lower angles compared to those predicted by the average lattice constant. The shifts increas e with increasing order of reflections and degree of disorder. If the heights and widths of the paracrystalline diffraction are treated as r educed quantities, they are functions of a single variable, N(1/2)g. T he width of the first diffraction depends mostly on size broadening fo r a natural paracrystal, where N(1/2)g = 0.1-0.2. A method to measure the paracrystalline disorder and size using a single diffraction profi le is proposed based on the equation of paracrystal diffraction. An in itial value of size may be obtained using the Scherrer equation, that of the degree of disorder is then estimated by the alpha* law Final va lues of the parameters are determined through least-squares refinement against observed profiles. An equation of diffraction by a polydisper se one-dimensional paracrystal system is presented for 'box' distribut ion of sizes. The width of the diffraction decreases with increasing b readth of the size distribution.