D1 X-ray Diffraction (XRD)

Topic

X-ray diffraction on this metal—the experimental method described by this model—involves directing an X-ray beam at the sample and recording the intensity of the diffracted radiation as a function of the angle of incidence. Bragg's law interprets the angles at which this diffraction occurs, identifying both the crystalline phases present in the metal and the interplanar spacing of the atomic planes within each phase. Because distinct crystalline phases have different interplanar spacings, Bragg's law dictates that each phase diffracts at a different angle, allowing them to be distinguished within the same diffraction pattern.

In addition to revealing the angles at which each crystalline phase appears, this diffraction pattern also indicates the width of the corresponding diffraction peaks; the Scherrer equation converts this peak width into the crystallite size for the respective phase. The smaller the diffracting crystallite, the fewer consecutive atomic planes contribute to the constructive reinforcement of the diffraction, resulting in a broader peak. Consequently, the fact that this metal exhibits broader diffraction peaks implies, according to the Scherrer equation, a smaller estimated crystallite size. However, that same broadening of the diffraction peaks is not solely due to the crystallite size estimated by the Scherrer equation, but also to the microstrain accumulated within the sample; the Williamson-Hall analysis distinguishes the extent to which each of these two factors contributes to the broadening. By comparing how the width of the various diffraction peaks varies with their respective angles, this analysis separates the angle-independent contribution—attributable to crystallite size—from the angle-dependent contribution—attributable to microstrain. Consequently, the higher level of accumulated microstrain in the sample means that, according to the Williamson-Hall analysis, a larger portion of the total peak broadening is attributed to microstrain rather than to crystallite size.

For this reason, this model—along with the Bragg's law and diffraction pattern introduced at the outset—feeds into two other models in the set: the model describing the metal's phases (using the crystalline phases identified by Bragg's law) and the model describing the metal's grain size (using the crystallite size estimated from the diffraction pattern via the Scherrer equation). The fact that Bragg's law and the Scherrer equation are also applied—for the same purpose—to a model for a different class of materials (specifically, one describing X-ray diffraction in ceramics) demonstrates that this experimental method is not exclusive to metals; rather, it is a technique shared by many models in the set whenever a crystalline phase needs to be identified.

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