Powder X-ray Diffraction Basic Course - Fifth Installment: Quantitative analysis

It is used to determine the amounts of different phases in a material, not just to identify which phases are present. This is important because a material’s performance often depends on the relative amounts of its crystalline components, so quantitative XRD is useful in research, development, and quality control.

The RIR method estimates phase amounts from the integrated intensity of a strong diffraction peak and a reference intensity ratio stored in a database. In practice, once the phases have been identified, quantification can be done quickly. It is most reliable when the selected peaks do not overlap and when the sample’s peak intensity ratios match the reference behavior reasonably well.

Its biggest weaknesses are peak overlap and preferred orientation. If a phase’s strongest peak overlaps with peaks from other phases, or if crystal alignment changes the observed peak intensities, the method can produce inaccurate results. Because it often depends heavily on one peak per phase, errors can become significant in more complicated samples.

The Rietveld method uses the whole diffraction pattern rather than relying on one peak. It refines structural and profile parameters by fitting a calculated pattern to the measured one. Because of that full-pattern approach, it can separate overlapping contributions more effectively and can correct for effects such as preferred orientation, making it better suited to multiphase or structurally complex materials.

Yes. The Rietveld approach can include preferred-orientation corrections, such as March-Dollase or spherical harmonic functions. That said, these corrections should be used carefully. They are appropriate when a phase is known to show preferred orientation, but forcing such corrections just to improve the fit can hide other problems, such as missing phases or an incorrect starting structure.

They help judge how well the calculated pattern matches the measured data. Rwp is commonly used, and S compares the observed fit quality with the statistically expected ideal case. A value of S near 1 suggests a good refinement, but these numbers are not enough by themselves. It is still necessary to inspect the residuals, check each phase fit, and make sure the refined results are physically reasonable.

Amorphous material does not give sharp Bragg peaks, so it cannot always be treated like a normal crystalline phase. It can still be quantified by combining Rietveld analysis with other strategies. One option is the internal standard method, which estimates amorphous content indirectly. Other options, such as PONKCS/Rietveld and RIR/Rietveld, model the amorphous halo more directly and can provide rapid evaluation once the needed parameters have been established.

Collect high-quality data and make sure phase identification is correct before trying to quantify anything. Even a sophisticated refinement cannot fully rescue poor measurements or a wrong phase model. Reliable quantitative results come from a combination of good sample preparation, good scan quality, appropriate modeling, and critical review of the final fit.