How to Read and Interpret XRD Data Patterns

An X-ray diffraction (XRD) pattern is a plot of scattered X-ray intensity against the diffraction angle, and every feature on that plot carries specific structural information about your sample. Peak positions tell you what crystalline phases are present and how their atoms are spaced. Peak widths reveal crystallite size and internal strain. Relative peak heights reflect how atoms are arranged within the unit cell and whether your sample has any texture. Reading an XRD pattern well means knowing which features to trust, which to question, and where common pitfalls hide.

What the Axes Actually Tell You

The horizontal axis of a standard powder XRD pattern is labeled 2θ (two-theta), measured in degrees. This is twice the angle between the incoming X-ray beam and the planes of atoms inside the crystal that are doing the diffracting. The vertical axis is intensity, usually in arbitrary counts or counts per second. Together, they produce the characteristic “barcode” of sharp peaks sitting on a low background that most people picture when they think of XRD data.

Each peak appears at a specific 2θ value because X-rays scattered from parallel planes of atoms reinforce each other only when the geometry satisfies Bragg’s law, which links the X-ray wavelength, the spacing between atomic planes, and the angle at which the beam hits those planes.¹ When the path-length difference equals a whole number of wavelengths, you get constructive interference and a bright peak. When it doesn’t, the scattered waves cancel out. The practical upshot: a peak at a lower 2θ angle corresponds to wider atomic-plane spacing, while a peak at a higher angle means the planes are packed more closely together.

Because the X-ray wavelength is fixed for a given instrument (copper Kα radiation is the most common lab source), each peak position maps directly to a specific interplanar distance, often called a d-spacing. That d-spacing is the single most diagnostic number you can pull from a diffraction pattern. It tells you which set of crystal planes produced that peak, and by extension, what crystal structure you’re dealing with.

Phase Identification by Matching Peaks

The first thing most people do with a new XRD pattern is figure out what crystalline phase or phases are in the sample. This is essentially a fingerprinting exercise: you compare the positions and relative intensities of your experimental peaks against reference patterns stored in databases like the International Centre for Diffraction Data (ICDD) Powder Diffraction File. If your pattern lines up with a reference, you’ve identified the phase.

The standard is strict. Every peak predicted by the reference pattern should appear in your experimental data at the right angle and in roughly the right proportion. Arbitrary peaks in the reference cannot simply be missing from your data without a good explanation.² If three out of five expected peaks match but two are absent, you don’t have a confirmed identification. You might have a mixture of phases, or the sample might have strong preferred orientation that suppresses certain reflections.

Mixtures are common in real samples, and they show up as overlapping sets of peaks from different phases. Sorting these out requires patience: you identify the strongest phase first, “subtract” its contribution mentally or with software, then look at what’s left over and try to match the residual peaks to another reference pattern. Software tools with built-in databases speed this up enormously, but the final judgment call is still yours. A match that looks right statistically can still be wrong if it doesn’t make chemical sense for the sample you prepared.

What Peak Positions Shift Can Mean

Sometimes your peaks line up almost, but not quite, with a reference pattern. Every peak is shifted by a similar small amount in the same direction. Before you conclude that your crystal has an unusual structure, consider a simpler explanation: the sample might have been slightly mispositioned in the instrument. Even a vertical displacement of about one millimeter in a standard Bragg-Brentano setup can shift peaks by roughly 0.8 degrees, which is enough to throw off your d-spacing calculations and make phase identification unreliable.³ In capillary geometry, the effect is different but still real: displaced specimens can cause peaks to split, shifting simultaneously to both lower and higher angles than their true positions.⁴

If the shift is systematic and uniform across all peaks, sample displacement or a zero-point error in the instrument is the most likely cause. Analytical corrections exist to fix this after the fact.⁵ But if some peaks shift more than others, or shift in opposite directions, something more interesting is going on. Compositional variation, solid solutions, or residual stress can all produce non-uniform peak shifts. A solid solution, for instance, changes the unit-cell dimensions depending on how much of a dopant element is incorporated, and that changes all d-spacings by a consistent fraction, expanding or contracting the lattice. Stress, by contrast, affects different crystallographic directions differently, so peak shifts won’t be uniform.

Reading Peak Widths for Crystallite Size and Strain

Narrow, sharp peaks indicate large, well-ordered crystals. Broad, rounded peaks point to smaller crystallites, internal strain, or both. This is one of the most practically useful features of an XRD pattern, especially if you work with nanomaterials, thin films, or any sample where grain size matters.

The simplest way to estimate crystallite size from peak broadening is the Scherrer equation, which relates the full width at half maximum (FWHM) of a peak to the average size of the coherently diffracting domains.⁶ The idea is intuitive: fewer planes contributing to diffraction means less perfect constructive interference, which smears out the peak. There are caveats. The Scherrer equation only gives a lower bound on crystallite size, and it assumes that all broadening comes from size effects alone. Strain broadens peaks too, and the instrument itself adds some width to every peak just from optics and geometry.

To separate size broadening from strain broadening, researchers commonly use the Williamson-Hall method, which plots peak width against diffraction angle and uses the different angular dependence of the two effects to disentangle them.⁷ There are several flavors of Williamson-Hall analysis, each making slightly different assumptions about how strain is distributed in the crystal.⁸ None of them gives a perfect answer for every material, but they provide a much better estimate than Scherrer alone.

For nanoscale materials, peak broadening is the dominant visual feature. A pattern from particles only a few nanometers across can look like gently rolling hills rather than sharp spikes. The peak positions stay the same as for the bulk material, and for spherical nanoparticles the relative intensities stay the same too, but the widths increase dramatically.⁹ If your peaks are so broad they start overlapping with their neighbors, extracting reliable size numbers becomes tricky and you may need whole-pattern fitting rather than single-peak analysis.

Why Relative Intensities Change

In an ideal powder sample, every possible crystal orientation is represented equally, and the relative heights of the peaks reflect the intrinsic scattering power of each set of crystal planes. That scattering power depends on the types and positions of atoms in the unit cell. This is encoded in a quantity called the structure factor, and it’s the reason XRD can ultimately reveal where atoms sit inside a crystal.

In practice, intensities deviate from the ideal for several reasons, and the most common one is preferred orientation, sometimes called texture. If your crystallites aren’t randomly oriented, if they tend to lie flat like stacked plates or stand on end like pencils in a cup, some sets of planes will be over-represented in the diffraction geometry while others are under-represented. The peak positions stay put, but the relative peak heights change, sometimes dramatically. For spherical particles dried into a powder, orientations tend to be random and intensities match the bulk reference well. Plate-like or needle-shaped crystals are much more prone to texture effects.⁹

This matters for phase identification because a textured sample can fool you. Peaks that should be strong may appear weak, and vice versa. If your experimental pattern matches a reference in peak positions but not in intensities, preferred orientation is a likely culprit before you start suspecting a new phase. Grinding the sample more finely, spinning the sample during measurement, or using a different sample geometry can reduce the problem.

Quantifying How Much of Each Phase Is Present

Once you know what phases are in your sample, you often want to know how much of each. Quantitative phase analysis (QPA) goes beyond fingerprinting to put numbers on the weight or volume fraction of each component. Two widely used approaches are the Rietveld method and the reference intensity ratio (RIR) method.

Rietveld analysis fits a calculated diffraction pattern to the entire measured profile, adjusting crystal structure parameters, peak shapes, background, and phase fractions simultaneously until the calculated pattern matches the experimental one as closely as possible. It’s powerful but demands that you know the crystal structures of all phases present.¹⁰ When a phase in the mixture has an unknown or only partially known structure, standard Rietveld breaks down. Newer hybrid approaches allow partial crystal-structure modeling to be combined with model-free methods for the unknown phases, broadening the range of mixtures that can be quantified.

The RIR method is simpler and more accessible. It compares the strongest peak of each phase to that of a standard (usually corundum, α-Al₂O₃) to obtain a scaling factor. If you know the RIR values for your phases, you can estimate their proportions from the relative intensities of their strongest peaks. The approach works well for routine multi-component analysis, and approximate RIR values can be estimated from atomic scattering properties even when experimental RIR data aren’t available.¹¹ Both Rietveld and RIR methods have been tested head-to-head on synthetic sandstones of known composition, and both perform reasonably well when sample preparation is careful, though Rietveld generally handles complex mixtures with overlapping peaks better.¹²

Whichever method you use, sample preparation matters enormously. Poor grinding, large crystallites, or preferred orientation will distort intensities and corrupt your quantitative results. The numbers that come out of a quantitative analysis are only as good as the data that go in.

The Background and What Lives in It

Between the peaks sits the background, and it’s tempting to ignore it. The background comes from several sources: X-ray fluorescence from the sample, air scatter, diffuse scattering from amorphous phases, thermal vibration of atoms, and detector noise. For routine phase identification, you just need to subtract it cleanly so your peak-fitting software can work. But the background contains real information too.

A broad hump in the background, especially centered around 15 to 30 degrees 2θ for copper radiation, is the hallmark of an amorphous component in the sample: glass, polymer, or a disordered solid. If you’re characterizing a pharmaceutical formulation or a composite, knowing whether the active ingredient is crystalline or amorphous can be critical. Rietveld-based quantification of amorphous content typically requires spiking the sample with a known amount of a crystalline internal standard, then seeing how much of the “missing” intensity can’t be accounted for by any crystalline phase.

Pharmaceutical and Materials Applications

XRD pattern interpretation has become essential in pharmaceutical development because many drug molecules can crystallize in multiple forms, called polymorphs, that have identical chemical composition but different crystal packing. These polymorphs can have very different solubility, stability, and bioavailability, so telling them apart is a regulatory requirement. Powder XRD can distinguish polymorphs even at low concentrations in a mixture; synchrotron-based measurements have identified four distinct polymorphic forms of the drug tiotropium bromide present at just 0.4% by weight in a lactose powder blend.¹³

The choice of diffraction geometry also affects what you see. A recent study comparing capillary transmission, foil transmission, and standard Bragg-Brentano reflection setups on two polymorphs of the antidiabetic drug metformin embonate found that geometry influenced the accuracy of both identification and quantification.¹⁴ This is worth knowing if you’re setting up a new analysis: not every instrument configuration is equally suited to every sample type, and running the same powder in a different holder can change the outcome.

Beyond static snapshots, in situ XRD during crystallization has revealed how pharmaceutical polymorphs evolve over time. Synchrotron-based flow crystallization experiments have captured the real-time progression from one polymorph to another in systems where two forms have nearly equal thermodynamic stability.¹⁵ Watching this unfold in a diffraction pattern, seeing one set of peaks grow while another set shrinks, is one of the more compelling demonstrations of what XRD data can tell you when you collect it continuously rather than at a single point in time.

In Situ and High-Temperature XRD

Standard XRD gives you a snapshot of a sample at room temperature and ambient pressure. But materials change under extreme conditions, and in situ XRD lets you watch those changes happen. High-temperature XRD, for instance, heats the sample on the diffractometer stage while collecting patterns at each temperature step. You can track phase transitions, thermal expansion, oxidation, and decomposition as they occur.

In situ high-temperature measurements on a high-entropy alloy revealed distinct phase transitions at intermediate temperatures, with different crystal structures appearing and disappearing between 600 °C and 1000 °C.¹⁶ Interpreting these patterns is the same as interpreting any XRD data, peak positions, widths, and intensities, but now you’re watching them evolve in real time. Peaks from a new phase appear, grow, and sometimes vanish again as conditions change. Thermal expansion shifts all peaks gradually toward lower angles as the lattice expands with heating.

The technique has also been pushed into extreme territory. Researchers have combined laser-heated diamond anvil cells with time-resolved synchrotron XRD to follow structural transitions in iron at compression rates of hundreds of gigapascals per second and temperatures reaching 2000 K, capturing changes on millisecond timescales.¹⁷ The data interpretation principles remain the same: you’re still looking at where peaks sit, how broad they are, and how their intensities change. The challenge is that you’re extracting that information from weaker, noisier patterns collected in fractions of a second.

Thin Films and Grazing-Incidence XRD

Thin films present a special challenge for XRD because a conventional beam passes through only a tiny volume of film before plowing into the substrate below, which can dominate the pattern with its own diffraction peaks. Grazing-incidence XRD (GIXD) solves this by directing the X-ray beam at a very shallow angle to the surface, keeping most of the beam path inside the film rather than the substrate.

Interpreting GIXD data requires extra care. The measured intensities are distorted by several geometry-specific effects: the polarization of the beam, variations in the solid angle subtended by different parts of the detector, absorption within the film, and the Lorentz correction.¹⁸ If you skip these corrections, your measured peak intensities won’t match reference patterns, and any attempt at quantitative analysis or structure refinement will be unreliable. Peak positions are less affected, so phase identification from GIXD is usually straightforward, but getting the intensities right demands applying the full set of correction factors appropriate to your particular setup.

Software Tools and Database Matching

Very few people interpret XRD patterns entirely by hand anymore. Software ranges from manufacturer-supplied packages bundled with diffractometers to free, open-source tools. Programs like ReciPro offer a built-in database of over 20,000 crystal models, three-dimensional crystal structure visualization, stereographic projection tools, and semi-automatic indexing of diffraction spots.¹⁹ For Rietveld refinement, widely used packages include TOPAS, GSAS-II, and FullProf, each with its own learning curve and quirks.

The database you search against matters as much as the software. The ICDD PDF (Powder Diffraction File) is the most comprehensive commercial database, with hundreds of thousands of reference patterns. The Crystallography Open Database (COD) is a free alternative that covers a large range of inorganic and some organic structures. When you run a search-match, the software typically ranks candidate phases by how well their reference peaks align with your data. But automated search-match is not infallible. It can be fooled by strong preferred orientation, by overlapping peaks from multiple phases, or by the presence of phases not in the database. Treat the software’s top suggestion as a hypothesis to test, not a verdict.

Common Mistakes When Reading Patterns

A few interpretation errors come up over and over. One is confusing a sample-holder peak with a real phase. Aluminum sample holders, for instance, have their own diffraction peaks, and if your sample layer is thin enough, those peaks will poke through. Knowing what your holder contributes saves you from chasing phantom phases.

Another common mistake is over-interpreting small peaks near the noise floor. Statistical noise in the detector can produce bumps that look like weak diffraction peaks, especially at high 2θ angles where overall intensity is low. A real peak should be reproducible across repeated scans and should have a width consistent with the other peaks in the pattern. If a bump shows up in one scan but disappears in a longer-count repeat, it’s noise.

Misidentifying Kα₂ splitting as a doublet from a second phase is another trap. At higher 2θ values, the slight wavelength difference between the Kα₁ and Kα₂ components of the X-ray source becomes resolvable, splitting single peaks into closely spaced pairs. This is a purely instrumental effect and has nothing to do with the sample. Most analysis software can strip the Kα₂ contribution, but if you’re eyeballing a raw pattern, the splitting can be confusing.

Finally, people sometimes report crystallite sizes from the Scherrer equation as if they were particle sizes. A single particle can contain multiple crystallites separated by grain boundaries, so the Scherrer size is typically smaller, sometimes much smaller, than the actual particle size measured by electron microscopy or laser diffraction. The two quantities answer different questions, and conflating them leads to confusion when other measurements don’t agree.

When XRD Reaches Its Limits

XRD is fundamentally a technique for crystalline materials. If your sample is entirely amorphous, a glass or a liquid or a fully disordered polymer, you won’t get sharp Bragg peaks. You’ll see a broad hump in the background, and while pair distribution function analysis can extract some structural information from that hump, it’s a different kind of analysis from the peak-by-peak interpretation discussed here.

Light elements are also a challenge. Hydrogen, lithium, and other low-atomic-number elements scatter X-rays weakly, so their positions in a crystal are hard to pin down from XRD alone. Neutron diffraction is often a better tool for locating hydrogen atoms. Similarly, elements close together on the periodic table (iron and cobalt, for example) have very similar X-ray scattering strengths, making them hard to distinguish in a mixed site. Anomalous (resonant) scattering techniques at a synchrotron can help with this, but they require access to a tunable X-ray source.

Detection limits for minor phases vary with the instrument and the phase in question, but a rough rule of thumb for a lab diffractometer is that a crystalline phase needs to be present at around one to five percent by weight to show identifiable peaks above the background. Synchrotron sources push this limit considerably lower, as demonstrated by the pharmaceutical studies identifying polymorphs below one percent concentration.¹³ If you need to detect trace crystalline phases on a routine basis, a lab instrument may simply not have the sensitivity, and you’ll need either synchrotron time or a complementary technique.