Practical XRD with Confidence

Webinar summary

This webinar, the first in the series Practical XRD with Confidence, introduces the fundamentals of powder X-ray diffraction, focusing on how diffraction patterns relate to crystal structure and composition. 

Powder X-ray diffraction is used to analyze crystalline materials by measuring how X-rays scatter from ordered atomic planes. Because hard X-rays have wavelengths similar to the spacing between atoms in crystals, they can interact with those planes and produce diffraction patterns that reveal structural information. The resulting peak positions, intensities, and widths provide a characteristic fingerprint that can be used to identify crystalline phases and evaluate data quality.

X-rays for diffraction are generated in an X-ray tube. Electrons are emitted from a heated tungsten filament and accelerated toward a metal target by high voltage. When the electrons strike the target, they produce both continuous Bremsstrahlung radiation and characteristic X-rays. The process is inefficient: most of the energy becomes heat, so cooling is essential. Instability in cooling conditions, such as fluctuations in water temperature, can affect X-ray intensity and therefore data stability.

For diffraction analysis, characteristic radiation is preferred, especially the Kα1 line, because it has high intensity and a well-defined wavelength. A stable, well-defined wavelength produces sharper and more accurate diffraction peaks, which improves confidence in phase identification.

A diffractometer directs X-rays from the source through optics, onto the sample, and then to a detector. The goniometer controls and measures the relevant angles. In common powder diffraction measurements, Bragg-Brentano geometry is often used because it maintains focusing conditions and provides high intensity when the sample surface is properly positioned between the incident and diffracted beams.

Bragg’s Law describes the condition for constructive interference: nλ=2dsinθ. Here, (n) is an integer, λ is the X-ray wavelength, (d) is the spacing between crystal planes, and θ is the diffraction angle. When this relationship is satisfied, scattered X-rays reinforce one another and produce a diffraction peak. Each peak corresponds to a specific d-spacing and a specific set of crystal planes. These planes are labeled using Miller indices, written as (hkl).

A crystal is defined by a repeating atomic arrangement, described by a unit cell with three lattice vectors and three angles. The symmetry of the unit cell determines the crystal system. High-symmetry systems, such as cubic materials, generally produce simpler diffraction patterns, while lower-symmetry systems, such as hexagonal materials, tend to produce more complex patterns.

Peak positions are controlled primarily by lattice parameters and the X-ray wavelength. However, they can also be affected by instrumental and sample-related errors. One of the most important sources of systematic peak shift is sample displacement, especially when the sample surface is not level with the reference height of the holder. A small shift of roughly 0.02° to 0.04° can be common, but a shift around 0.5° is significant and usually indicates a sample-height or alignment problem.

Peak width contains information about crystallite size and lattice distortion. Small crystallites broaden peaks, a relationship commonly described using the Scherrer equation. Lattice strain or distortion can also broaden peaks and may be treated using approaches such as the Wilson equation. Peak intensity depends on the structure factor, preferred orientation, and particle statistics. Because intensity is sensitive to sample preparation and particle distribution, peak positions are often more reliable than intensities for initial phase identification.

Phase identification depends on comparing measured diffraction data against reference databases using search-match software. Common databases include ICDD products such as PDF-5+ and PDF-4/Axiom, the Inorganic Crystal Structure Database, and the open-access Crystallography Open Database. Search reliability can be improved by narrowing the possible entries, for example by using elemental information or creating subfiles tailored to the expected sample chemistry.

Good sample preparation is essential for trustworthy powder XRD results. Powder should generally be ground to less than 45 μm to improve particle statistics and reduce missing or misleading peaks. The sample holder cavity should be completely filled, and the sample surface should be flat and level with the holder. Coarse grains, such as particles around 200 μm, can lead to poor particle statistics and may cause some peaks to be absent or unreliable.

Preferred orientation is a common problem when particles are needle-like or plate-like. In these cases, crystallites tend to align in certain directions rather than being randomly oriented, which changes relative peak intensities. Preferred orientation can make some peaks appear much stronger or weaker than expected, complicating phase identification. Back-loading, side-loading, and capillary transmission geometry can help reduce this effect.

For low-absorbing materials, such as many polymers, transparency effects can cause peak shifts because X-rays penetrate too deeply into the sample. These effects can be reduced by using thinner sample layers or transmission geometry. For very small sample amounts, a zero-background holder can be used by sprinkling a monolayer of powder. If the sample must be spun during measurement, a thin layer of grease can help hold the powder in place and may also help reduce preferred orientation.

Data quality can be judged using several practical metrics. Resolution is commonly evaluated by the full width at half maximum of diffraction peaks. The peak-to-background ratio indicates how clearly peaks stand out from the background. The signal-to-noise ratio reflects the reliability of weak features and can be improved by longer counting times or by averaging repeated scans.

Crystalline and amorphous materials are distinguished by their diffraction patterns. Crystalline samples produce sharp diffraction peaks because their atoms are arranged periodically. Amorphous materials lack long-range periodic order and typically produce a broad halo rather than sharp peaks.

When identifying phases, the measured peaks should be compared against reference patterns. Ideally, all major characteristic peaks from the reference pattern should be present in the measured data, and all measured peaks should be accounted for. Missing peaks may result from preferred orientation, insufficient particle statistics, weak signals below the detection limit, or poor data quality. Extra peaks may indicate additional phases, impurities, or an incorrect match.

Software-assisted phase identification commonly includes automatic peak evaluation, background subtraction, and model generation. A residual plot is useful for comparing the modeled pattern with the measured pattern and identifying unmatched features. Weak peaks may be easier to inspect using a square-root intensity scale, which compresses intense peaks and makes smaller peaks more visible.

In the example discussed, the major phase was identified as strontium sulfate, also known as celestine. Additional phases included barite and a minor amount of strontium chloride hydrate. The phase assignment was confirmed by checking both peak positions and relative intensities and ensuring that all observed peaks were accounted for.

Overall, reliable powder XRD phase identification depends on three connected factors: high-quality data collection, careful sample preparation, and informed interpretation of the diffraction pattern. Correct sample height, fine and representative powder, control of preferred orientation, adequate counting statistics, and thoughtful database filtering all contribute to more trustworthy phase assignments.