Electron & Neutron Diffraction: How Matter Waves Reveal Structure

Electron diffraction proves that particles behave as waves. Fire a beam of electrons at a thin crystal, and they do not bounce off like tiny bullets. They spread into a pattern of bright spots and concentric rings on a detector — exactly the same kind of diffraction pattern you get when you shine X-rays through a crystal or laser light through a narrow slit. The only explanation is that the electrons are interfering with themselves like waves. This is not a metaphor. It is a direct experimental fact, and it is one of the cornerstones of quantum mechanics.

Think of it like ripples in a pond. If you drop two stones at once, their ripples cross and produce a pattern of peaks where they reinforce and flat spots where they cancel. A beam of electrons fired at a crystal does the same thing — the electrons scatter off the regularly spaced atoms, and the scattered waves interfere. Where they reinforce, you get a bright spot. Where they cancel, you get darkness. The resulting pattern is a direct map of the atomic spacing inside the crystal.

The de Broglie wavelength: why electrons act like waves

In 1924, the French physicist Louis de Broglie proposed a radical idea in his PhD thesis: if light — which everyone thought was a wave — could behave as a particle (the photon), then perhaps particles like electrons could behave as waves. He suggested that every moving particle has an associated wavelength, now called the de Broglie wavelength:

λ = h / p

Where h is Planck's constant (6.626 × 10⁻³⁴ J·s) and p is the momentum of the particle (mass × velocity). The equation says that the wavelength gets shorter as the momentum increases — so a faster electron has a shorter wavelength.

For an electron accelerated through a voltage V (in volts), the wavelength in nanometres is approximately:

λ (nm) ≈ 1.226 / √V

A practical example: in a transmission electron microscope running at 200 kV, the electron wavelength is roughly 0.0025 nm (2.5 pm) — about 200,000 times shorter than visible light. This tiny wavelength is what gives electron microscopes their atomic-scale resolution.

The critical point for diffraction: when the electron wavelength is comparable to the spacing between atoms (typically 0.1–0.3 nm in crystals), the electrons will diffract. The Davisson-Germer experiment confirmed this in 1927.

The Davisson-Germer experiment: the proof

In 1927, Clinton Davisson and Lester Germer at Bell Telephone Laboratories were studying the surface of a nickel crystal by firing electrons at it. An accidental break in their vacuum system caused the nickel sample to oxidise. When they heated it to remove the oxide layer, the surface recrystallised into large flat crystal planes.

They then measured the intensity of electrons scattered from the nickel surface as a function of angle. Instead of a smooth curve, they found a sharp peak at a scattering angle of 50° for 54 eV electrons. The peak was a diffraction maximum — the electrons were behaving like waves and satisfying Bragg's law, just like X-rays.

The angle of the peak gave an interplanar spacing of 0.091 nm, which matched the known spacing of nickel atoms. And the de Broglie wavelength for 54 eV electrons is about 0.165 nm — consistent with the measured diffraction angle. It was a perfect match between theory and experiment.

Separately, George Paget Thomson (son of J.J. Thomson, who discovered the electron) passed high-energy electrons through thin metal foils and observed ring diffraction patterns on a photographic plate. The ring diameters matched the de Broglie wavelength prediction. Both experiments won Nobel Prizes — Davisson and Thomson shared the 1937 Nobel Prize in Physics.

How electron diffraction works in practice

Electron diffraction is now a standard analytical technique, performed in dedicated instruments or as a mode within electron microscopes. The basic setup is straightforward:

The electrons interact so strongly with matter that the sample must be very thin — otherwise they would be absorbed before they could form a diffraction pattern. This is the main practical difference from X-ray diffraction, where samples can be millimetres thick.

The resulting pattern depends on the sample type:

• Single crystal: a regular array of sharp spots, each corresponding to a set of atomic planes (Bragg reflections)
• Polycrystal: rings made of many small spots (Debye-Scherrer rings), because the crystallites are randomly oriented
• Amorphous: diffuse halos, because there is no long-range order

Electron backscatter diffraction: mapping crystals in the SEM

Electron backscatter diffraction (EBSD) is a technique used in scanning electron microscopes (SEM) to determine the crystal orientation of individual grains in polycrystalline materials. The sample is tilted to about 70°, and the electron beam is scanned across the surface. At each point, backscattered electrons form a diffraction pattern called a Kikuchi pattern, which reveals the local crystal orientation.

EBSD is widely used in materials science and geology. It can map grain boundaries, identify phases, measure strain, and determine texture (preferred orientation) in metals, ceramics, and rocks. The spatial resolution is about 50 nm — far better than X-ray-based texture analysis.

Neutron diffraction: a complementary probe

Neutron diffraction is the third major diffraction technique, alongside X-ray and electron diffraction. Neutrons have a de Broglie wavelength given by the same equation λ = h/p, and thermal neutrons from a nuclear reactor or spallation source have wavelengths around 0.1 nm — ideal for crystal diffraction.

Neutron diffraction has two unique advantages:

1. Light atom sensitivity. Neutrons scatter from atomic nuclei, not electrons. This means they can detect light atoms like hydrogen and lithium even in materials containing heavy elements — a task that is very difficult with X-rays or electrons.

2. Magnetic sensitivity. Neutrons have a magnetic moment (they behave like tiny bar magnets). When they diffract from a magnetic material, the pattern includes extra peaks from the magnetic structure — revealing how atomic spins are arranged. This is how scientists discovered antiferromagnetism and continue to study magnetic materials.

The major trade-off is that neutron sources are large and expensive. There are only a handful of high-flux neutron facilities worldwide (such as the ILL in France, ISIS in the UK, and SNS in the USA), and beam time is competitive.

Common misconception: electron diffraction shows the path of electrons

It is natural to think of diffraction as electrons being "deflected" by atoms like marbles bouncing off posts. That is not what happens. Electron diffraction is an interference phenomenon. Each electron behaves as a wave that passes through the entire crystal at once, and the pattern builds up as many electrons — or even a single electron fired repeatedly — interfere with themselves. The spots in the pattern are not images of atoms; they are Fourier transforms of the atomic arrangement. The same mathematics that describes X-ray diffraction applies to electrons, just with the scattering strength scaled differently.

For more on the basic physics of wave diffraction, see what is diffraction. For a comparison with X-ray and optical techniques, our guide on examples of diffraction covers everyday and scientific cases. The X-ray diffraction guide explains the related XRD technique in detail.

External resources

• Britannica: Electron diffraction — overview and history of the technique
• Harvard Natural Sciences: Electron Diffraction Demo — classroom demonstration setup and theory
• DoITPoMS Cambridge: Electron Diffraction Patterns — detailed materials science treatment