D2 X-ray Diffraction and Microscopy

Topic

X-ray diffraction of a ceramic sample serves as the common starting point for this model: a single diffraction pattern obtained from the sample provides the data needed to identify its crystalline phases, lattice parameter, and crystallite size. Because all three measurements rely on the same diffraction pattern, a single experimental measurement suffices to obtain all three results.

Bragg's law uses this same diffraction pattern to identify the crystalline phases present in the sample as well as their lattice parameter. By analyzing the positions of the peaks in the diffraction pattern, Bragg's law allows for the identification of the specific crystalline phase and the determination of the characteristic spacing between its crystal lattice planes.

The Scherrer equation utilizes this same diffraction pattern—focusing on peak width rather than position—to estimate crystallite or grain size. Wider peaks in the pattern lead the Scherrer equation to estimate smaller crystallites, while narrower peaks result in an estimate of larger crystallites.

The relationship between the areas of these diffraction peaks and the area corresponding to the pattern's amorphous background determines the sample's crystalline fraction relative to its amorphous fraction. A larger area occupied by crystalline peaks compared to the amorphous background indicates a higher crystalline fraction and a lower amorphous fraction.

Consequently, because all three techniques originate from the single X-ray diffraction pattern that initiates this model, that one measurement is sufficient to characterize three distinct aspects of the ceramic sample: the crystalline phases present and their lattice parameter (via Bragg's law); and the size of the crystallites (via the Scherrer equation); ...and what fraction of the sample is crystalline versus amorphous, based on the ratio of their peak areas. For the first two techniques, this model reuses Bragg's law and the Scherrer equation—already established in the metal diffraction model—without redefining them here.

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