What Is XRD? 10 Basic Questions and Answers on X-Ray Diffraction

Step 1 — What are X-rays? X-rays are the same kind of thing as visible light, just far more energetic and with a much shorter wavelength (about 0.05–0.25 nanometres). Wavelength simply means the length of one wave, the distance from one crest to the next.

Step 2 — Why that wavelength matters. Inside a solid, atoms sit roughly 0.1–0.5 nanometres apart. X-ray wavelengths land in the same size range. That is the whole trick: to "see" a spacing, you need a wave of about the same size. Visible light is thousands of times too long, so it can never sense individual atomic layers.

Step 3 — What is diffraction? Diffraction is what happens when waves meet a regularly repeating obstacle and then combine with each other. In some directions the waves line up crest-on-crest and become strong (this is called constructive interference). In all other directions a crest meets a trough and they cancel out (destructive interference). So the material does not glow evenly in every direction — it sends out strong beams only along a few special angles.

Step 4 — What we actually record. A detector travels around the sample and counts how many X-rays arrive at each angle. The result is a graph called a diffraction pattern or diffractogram: angle on the horizontal axis, counted intensity on the vertical axis. Every sharp spike on that graph is one family of atomic planes announcing itself. If you are looking at a diffractogram for the first time, our companion guide on how to read an XRD graph in 7 easy steps walks through a real pattern line by line.

Two materials can contain exactly the same elements and still behave completely differently, because what changes is how the atoms are stacked. Graphite in a pencil and diamond in a drill bit are both pure carbon. A chemical test cannot tell them apart; XRD separates them in two minutes.

That is why XRD sits at the entrance of almost every materials laboratory. Before you measure strength, conductivity, catalytic activity or drug performance, you first want to know what phase you are actually holding. XRD answers that question quickly, cheaply and without damaging the sample.

• XRD uses X-rays whose wavelength is about the same size as the spacing between atoms, which is why it can sense atomic order.
• Only crystalline (orderly) material produces sharp peaks; the sharp peak is the signature of repetition.
• The output is a graph of intensity versus angle, called a diffraction pattern or diffractogram.
• Peak positions tell us about spacing; peak heights and widths carry further information.
• The technique is non-destructive and usually needs only a small amount of sample.
• It identifies phases (specific compounds and structures), not just chemical elements.

Start with the picture of planes. In a crystal the atoms are not scattered randomly; they line up so that you can slice through them along flat sheets called lattice planes (this ordered arrangement is explained from scratch in our introduction to crystal structure). Think of a multi-storey car park: the floors are evenly spaced and perfectly parallel. The gap between neighbouring floors is written as d, the interplanar spacing.

Send in the waves. An X-ray beam arrives at an angle θ (theta) measured from the plane surface — note carefully, from the plane, not from the normal as in optics. Part of the beam scatters from the top layer, part continues and scatters from the layer below.

The wave from the lower layer walks further. That extra journey has a length of exactly 2d sinθ. Geometry gives one d sinθ on the way in and one on the way out.

The condition for a peak. If that extra distance equals a whole number of wavelengths, the two waves come back in step and reinforce each other, producing a measurable peak. If it is any other value, they fall out of step and cancel. Because a crystal contains millions of layers, cancellation is almost perfect — which is why XRD peaks are sharp rather than smeared.

Bragg's law is the bridge between something you can measure (an angle) and something you want to know (a distance inside the crystal). Rearranged as d = λ / (2 sinθ), every peak on your pattern converts directly into a d-value in Ångström. Those d-values are what search-match software compares against reference databases, what you feed into unit-cell calculations, and what you track when a material is strained, doped or heated.

• Bragg's law: nλ = 2d sinθ — learn it by heart, everything in Module 1 depends on it.
• θ is measured from the atomic plane; instruments report 2θ.
• Constructive interference gives peaks; destructive interference gives the flat baseline in between.
• Large d-spacings appear at low angles; small d-spacings appear at high angles.
• Diffraction is only possible when λ is smaller than 2d.
• Each peak is a message from one particular family of planes, labelled by Miller indices (h k l).

1. Generating X-rays. Inside a sealed tube, a hot filament releases electrons which are accelerated by a high voltage (typically 40 kV) and slammed into a metal target, usually copper. The collision knocks out inner electrons of the copper atoms; when outer electrons drop down to fill those gaps, they emit X-rays of a very specific wavelength called Cu Kα (1.5406 Å).

2. Cleaning the beam. A nickel filter or a monochromator removes unwanted wavelengths, and slits trim the beam to the right shape. We want a beam that is as close to a single wavelength as possible, because Bragg's law assumes one λ.

3. Meeting the sample. The prepared sample — often a fine powder pressed flat into a shallow holder — sits at the centre of the instrument. In a powder there are millions of tiny crystals pointing in every possible direction, so whatever the angle, some crystals are always correctly oriented to satisfy Bragg's law.

4. Scanning. The goniometer (the precision rotating stage) turns the sample by θ while the detector turns by 2θ, keeping the geometry correct at every step. A typical scan runs from 2θ = 10° to 80° in steps of about 0.02°, taking anywhere from ten minutes to a few hours.

5. Detecting and plotting. The detector counts arriving photons. Where Bragg's law is satisfied, counts shoot up and a peak appears. The instrument software draws intensity versus 2θ.

6. Interpreting. Each peak position is converted to a d-spacing using Bragg's law, and the full list of d-values plus relative intensities is compared with reference patterns in a database such as the ICDD PDF. A good match names the phase.

Knowing the working sequence is what separates a button-pusher from an analyst. If you understand that the beam must be monochromatic, you will suspect the filter when strange extra peaks appear. If you understand that the sample must sit exactly at the centre of the circle, you will recognise sample-height error when every peak shifts slightly. Almost every artefact in a real diffractogram can be traced back to one of these six steps.

• The six stages: generate → filter → strike the sample → scan → detect → interpret.
• Cu Kα (1.5406 Å) is the most common laboratory radiation; Co and Mo are used for iron-rich and dense samples.
• The goniometer keeps the θ : 2θ relationship exact throughout the scan.
• Random crystallite orientation in a powder guarantees that every plane family gets its chance to diffract.
• Modern strip and area detectors collect a whole scan in minutes instead of hours.
• The final step is always a comparison with a reference database (ICDD PDF, COD, or similar).

The central idea of materials science is a simple chain: processing decides the structure, the structure decides the properties, and the properties decide the performance. XRD sits precisely on the "structure" link of that chain, which is why it appears in almost every research paper about solids.

Same atoms, different structure, different material. Carbon is the classic proof. Arrange carbon atoms in weakly bonded flat sheets and you get graphite: soft, grey, electrically conducting, useful as a lubricant. Arrange the same carbon atoms in a rigid three-dimensional network and you get diamond: the hardest natural material, transparent, an electrical insulator. Chemical analysis reports "100 % carbon" for both. Only a structural method such as XRD can tell them apart.

It confirms that your synthesis actually worked. Suppose you heat a mixture to make a perovskite for a solar cell. XRD tells you whether you formed the target phase, whether unreacted starting powder remains, and whether an unwanted secondary phase appeared. That single measurement can save weeks of chasing confusing property data.

It follows a material through its life. Heat treatment, doping, mechanical deformation, corrosion, battery cycling and ageing all leave fingerprints in the diffraction pattern — peaks shift, broaden, weaken or split. XRD therefore works as both a quality gate and a research tool.

• Properties follow structure; XRD is the standard way to measure structure.
• Chemistry alone cannot distinguish polymorphs — XRD can.
• It verifies that a synthesis produced the intended phase and nothing else.
• It measures crystallite size, strain, texture and phase fractions from the same scan.
• It is non-destructive, so precious or limited samples are not wasted.
• Nearly every materials journal expects an XRD pattern as basic evidence.

• Phase identification is the number one application worldwide.
• Quantitative analysis gives weight percentages of mixed phases.
• Peak width → crystallite size; peak position → lattice parameter and stress.
• Grazing incidence geometry extends XRD to very thin coatings.
• Heating, cooling and electrochemical stages allow in-situ, time-resolved studies.
• Industries from cement to pharmaceuticals rely on XRD for routine quality control.

1. Amorphous materials give no peaks. Glass, most polymers, gels and many biological materials have no long-range order, so they produce only a broad hump. You can confirm that something is amorphous, but you cannot solve its structure this way. The two cases are compared side by side in our article on amorphous vs crystalline XRD patterns.

2. Poor sensitivity to minor phases. Below roughly 1–5 wt %, a phase usually disappears into the background. Trace impurities that badly affect properties may stay invisible.

3. It is an averaging technique. The beam covers millions of crystallites and reports their average behaviour. It will not show you one unusual particle, a single defect or a local inhomogeneity.

4. Light elements scatter weakly. X-rays interact with electrons, so hydrogen (one electron) is almost invisible and lithium is very difficult. Neighbouring elements in the periodic table, such as iron and cobalt, are also hard to tell apart.

5. No direct chemical analysis. XRD names phases, not elements. If a phase is absent from the reference database, identification can stall.

6. Overlapping peaks. In a mixture of several phases, or in low-symmetry crystals, peaks crowd together and interpretation becomes ambiguous.

7. Preferred orientation distorts intensities. Plate-like or needle-like crystals tend to lie down in the holder, exaggerating some peaks and suppressing others.

8. Sample preparation strongly affects results. Coarse grinding, uneven filling and wrong sample height all shift or distort the data.

9. Limited depth and spatial resolution. Conventional XRD probes a surface layer roughly a few micrometres deep and cannot map micro-scale features the way an electron microscope can.

Knowing what a technique cannot do protects you from over-claiming. A referee will not accept "no impurity was detected by XRD" as proof of purity, because a few per cent could easily be hidden. The professional habit is to state the limit honestly and, when it matters, combine XRD with a complementary method such as XRF for chemistry, SEM for morphology, or Raman spectroscopy for short-range order.

• Works only on crystalline material; amorphous samples give a broad hump.
• Minor phases below about 1–5 wt % are usually invisible.
• Results are averages over a large illuminated volume, not local information.
• Hydrogen and other light elements scatter X-rays too weakly to locate easily.
• Gives phases, not elemental composition.
• Peak overlap, preferred orientation and poor sample preparation degrade the data.

Peak position (2θ) converts through Bragg's law into a d-spacing. The full list of d-spacings is the fingerprint that identifies the phase and, after indexing, gives the unit-cell and lattice parameters. A small shift in position means the spacing has changed — because of doping, temperature, or residual stress.

Peak intensity (height or area) depends on which atoms sit on the planes and how the crystallites are oriented. Relative intensities help confirm an identification, allow quantitative phase analysis in a mixture, and reveal preferred orientation when they deviate strongly from the reference.

Peak width (FWHM) is controlled by crystallite size and by non-uniform strain. Nanocrystalline powders give visibly broad peaks; well-annealed, defect-free crystals give very narrow ones. FWHM stands for full width at half maximum — the width of the peak measured at half of its height. How to measure it correctly, and what it really means, is covered in detail in FWHM of X-ray peaks in XRD.

Background and broad humps carry the amorphous story. Comparing the area under the sharp peaks with the area under the broad hump gives the percentage crystallinity, a routine number in polymer and pharmaceutical laboratories.

Rather not do the arithmetic by hand? Enter your peak angle and width into the free Scherrer crystallite size calculator and it returns D in nanometres.

• Peak position → d-spacing → phase identity, unit cell, stress.
• Peak intensity → phase amount and preferred orientation.
• Peak width → crystallite size and micro-strain.
• Background → amorphous fraction and degree of crystallinity.
• The Scherrer equation gives a quick average crystallite size, valid up to about 100–150 nm.
• Rietveld refinement extracts many of these numbers together from the whole pattern at once.

• Any solid with crystalline order is a valid XRD sample.
• Fine, randomly oriented powder gives the most trustworthy data.
• Bulk pieces work if a flat surface can be presented to the beam.
• Thin films need grazing incidence to avoid drowning in substrate signal.
• Semi-crystalline polymers give sharp peaks sitting on a broad hump.
• Air-sensitive and precious samples are run in sealed capillaries or domes.

What happens in XRD. The incoming X-ray is scattered by the electrons around the atoms without losing energy. Because the atoms repeat regularly, these scattered waves interfere and produce peaks at particular angles. The instrument therefore measures angle.

What happens in XRF. XRF stands for X-ray fluorescence. The incoming X-ray is energetic enough to knock an inner electron completely out of an atom. An outer electron immediately drops into the empty place and releases the surplus energy as a new X-ray whose energy is characteristic of that element — iron always emits its own energy, calcium always emits its own. The instrument therefore measures energy, not angle.

Why they complement each other perfectly. Suppose XRF reports 60 % iron and 30 % oxygen. That is consistent with several different iron oxides. XRD then tells you which one you actually have: hematite, magnetite or wustite. Used together, you get both the composition and the structure — the complete description of the material.

• XRD identifies phases; XRF identifies elements.
• XRD measures angles; XRF measures photon energies.
• XRD works only on ordered material; XRF works on anything.
• Only XRD can separate polymorphs such as anatase and rutile.
• Only XRF gives you direct elemental percentages.
• Both are non-destructive and are frequently run on the same sample.

SEM in one paragraph. SEM stands for scanning electron microscope. A fine beam of electrons is scanned across the sample surface line by line. Electrons knocked out of the surface are collected and converted into brightness values, building up a photograph-like image with magnifications from a few hundred to several hundred thousand times.

The key contrast: real space versus average structure. SEM works in real space — you literally look at a specific spot and see the particles there. XRD works on the whole illuminated volume at once and returns a statistical average. If your powder contains one strange particle, SEM might find it; XRD almost certainly will not notice it.

Different kinds of "size". SEM measures particle size, the size of the lump you can see. XRD measures crystallite size, the size of the perfectly ordered region inside that lump. One particle may contain hundreds of crystallites, so SEM often reports a larger number than the Scherrer calculation, and both can be correct.

They answer different questions, so they are usually used together. A typical nanomaterials paper contains an XRD pattern proving the phase and an SEM image proving the morphology. Adding EDS (an elemental detector attached to the SEM) also brings in local chemistry.

• XRD uses X-rays and reports structure; SEM uses electrons and reports morphology.
• XRD output is a pattern; SEM output is an image.
• XRD averages over millions of crystallites; SEM looks at one small area.
• Crystallite size (XRD) and particle size (SEM) are different quantities.
• SEM usually needs vacuum and often a conductive coating; XRD normally does not.
• SEM plus EDS adds local chemistry; XRD plus Rietveld adds quantitative structure.