Practical XRD with Confidence

Webinar summary

In this webinar, the second in the series Practical XRD with Confidence, Akhilesh discusses quantitative X-ray diffraction, which is used to determine both the identity and relative abundance of crystalline phases in a material. A diffraction pattern contains several kinds of information at once: peak positions identify phases and reflect lattice parameters, peak intensities relate to atomic arrangement and phase amount, peak widths can reveal crystallite size or strain, and broad humps indicate amorphous content. A material may be fully crystalline, fully amorphous, or a mixture of ordered and disordered components, and the choice of analysis method depends heavily on that structural complexity.

Accurate quantification begins with careful sample preparation. The powder should be representative, homogeneous, evenly packed, and level with the sample holder. Particle size should generally be small enough to provide good averaging but not so fine that grinding introduces strain or excessive peak broadening. A practical range for many quantitative measurements is roughly 10 to 40 µm, with somewhat tighter control preferred for Rietveld refinement. The X-ray beam should remain fully on the sample, because spillover onto the holder increases background and can obscure weak peaks. Sample displacement, underfilling, overfilling, loose packing, or an uneven surface can shift peak positions and distort intensities, leading to incorrect identification or quantification.

The sample holder must also be chosen carefully. Aluminum holders are suitable for many inorganic powders, but weakly absorbing or low-density materials may allow the X-ray beam to penetrate through the sample and scatter from the holder. In those cases, deeper wells, glass holders, or zero-background holders may be more appropriate. The wrong holder can contribute unwanted peaks or background, especially when analyzing low-concentration phases or amorphous content.

Several methods are available for quantitative phase analysis. The relative intensity ratio method is a relatively simple semi-quantitative approach that uses database values comparing a phase’s strongest peak to a reference material such as corundum. It works best for simple mixtures with only a few phases, little peak overlap, and minimal preferred orientation. Its main weakness is dependence on selected peaks; if those peaks overlap or are affected by orientation, the results can be unreliable.

Calibration methods can provide high accuracy when suitable standards are available. External standard curves compare unknowns to prepared reference mixtures of known composition. Internal standard methods add a known amount of a reference material directly to the sample, which is especially useful for estimating amorphous content. Standard addition methods involve spiking the sample with known amounts of the phase of interest, then extrapolating back to the original concentration. These approaches are powerful but depend on matrix matching, instrument stability, good peak selection, and predictable intensity response. Matrix effects, microabsorption, preferred orientation, amorphous material, and peak overlap can all introduce error.

Rietveld refinement is the most powerful general-purpose method for complex mixtures. Rather than relying on one or two peaks, it models the entire diffraction pattern using known crystal structures. The calculated pattern is refined against the observed pattern by adjusting parameters such as scale factors, lattice constants, background, peak shapes, preferred orientation, and sometimes occupancies or thermal parameters. Because it uses the full pattern, Rietveld refinement is especially useful when phases overlap or when many phases are present.

Good Rietveld results require good data. A sufficiently broad 2θ range should be collected, especially for inorganic materials, minerals, clays, and cements. Organic and pharmaceutical materials often require a smaller angular range because their useful scattering typically decreases at higher angles. The step size should be fine enough to define peak shape, usually with several data points across each peak. Data should not be smoothed before refinement, because smoothing alters the counting statistics used for weighting. Background should normally be modeled during refinement rather than subtracted beforehand, because background can contain real contributions from amorphous material, holders, capillaries, Compton scattering, and detector effects.

Rietveld refinement depends on correct phase identification and appropriate structural models. If a phase lacks a known crystal structure, conventional Rietveld refinement cannot be performed for that phase, but profile-fitting methods such as Pawley or Le Bail fitting may still be used. This is useful for disordered materials such as some clays, where a full structural model may not exist. The quality of a refinement should be judged by both the visual fit and numerical indicators such as Rwp and goodness of fit. Difference plots are especially useful because unexplained residual peaks may indicate missing phases, poor background modeling, preferred orientation, or incorrect peak-shape parameters.

Preferred orientation is a major source of error in quantitative XRD. Plate-like, needle-like, and layered crystals often align during sample preparation, making some peaks artificially strong and others too weak. RIR and calibration methods have limited ability to address this problem beyond avoiding affected peaks. Rietveld refinement can include preferred-orientation corrections, but it is still better to reduce orientation through careful preparation. Peak overlap is another common problem; when peaks from multiple phases occur at similar angles, single-peak methods become unreliable, while full-pattern methods are better able to separate contributions using the rest of the pattern.

Microstructure also affects quantification. Small crystallite size, strain, defects, and stress can broaden peaks and complicate analysis. Instrument broadening should be characterized with standards such as silicon or lanthanum hexaboride so that sample-related broadening can be interpreted more accurately. Overgrinding should be avoided because it may introduce strain or change the material itself.

The direct derivation method provides another option when conventional structure-based approaches are difficult. It uses the relationship between diffraction intensity, structure factors, electron density, and chemical composition. When a reasonable chemical formula is known, it can estimate phase quantities using reference profiles or extracted phase patterns. This method can be useful for materials lacking complete structural data, samples with texture or large crystallites, and mixtures containing amorphous or trace phases.

Amorphous content can be estimated in several ways. A simple crystallinity analysis compares the area of crystalline peaks with the total scattering area, including the amorphous hump. More advanced approaches can incorporate amorphous components into whole-pattern fitting or use internal standards to calculate how much non-crystalline material is present. Results should be interpreted realistically, since amorphous quantification is sensitive to background modeling, sample preparation, reference selection, and assumptions about composition.

The best quantitative method depends on the sample and the available information. RIR is appropriate for simple, clean mixtures. Calibration curves are best when high-quality standards and stable measurement conditions are available. Rietveld refinement is preferred for complex multiphase materials, overlapping peaks, and preferred-orientation correction. Direct derivation can be valuable when structural information is incomplete or amorphous material must be quantified. For routine or high-throughput work, clustering tools, templates, and macros can streamline analysis by grouping similar patterns and applying consistent refinement strategies across related samples.

Reliable quantitative XRD is not achieved by software alone. It requires representative sampling, careful specimen preparation, appropriate data collection, and a method matched to the material. Errors from poor preparation, peak overlap, preferred orientation, background treatment, matrix effects, and amorphous content can easily dominate the final numbers. When these factors are controlled, XRD becomes a powerful tool for measuring phase composition in materials ranging from minerals and cements to pharmaceuticals, clays, batteries, and complex industrial powders.