An eggshell is made up primarily of calcium carbonate. In most cases magnesium is also present in the carbonate lattice in trace amounts. Quantitative analysis of the amounts of each element in the eggshell crystalline lattice can be done with X-ray diffraction data by employing the Rietveld analysis method.
Figure 1 shows an XRD pattern collected from a powdered using the Rigaku's Ultima IV multipurpose diffraction system. To obtain the amount of Mg present in the predominantly CaCO3 lattice, a Rietveld refinement was performed using the experimental data. In general Rietveld methods use model structures to calculate theoretical diffraction data that can be mathematical fit to experimental data. The model structures are systematically altered until the best fit is obtained.
Figure 2 shows the Rietveld refinement results for the eggshell. The orange difference pattern at the top is a visual indicator of the quality of the refinement as it depicts the difference between the model's theoretical pattern (blue) and the raw data (red).
In Figure 3, a screen shot from the WPF module, displays the refinement of the phase content and a composition of Ca0.963Mg0.037CO3 can be derived from this refinement. a model that contained 0.03 Mg atoms per 0.97 Ca atoms in the asymmetric unit of the crystal structure.