Sending a beam of electrons through or onto a crystal and recording the pattern of spots it scatters into. Electrons behave as waves far shorter than the distance between atoms, so a regular lattice sends them out in sharp directions, and the pattern is a map of the lattice. Because electrons interact strongly with matter, even a of atoms gives a clear pattern – something X-rays, which pass almost straight through, cannot do.
As the site uses it
What photoemission, optical absorption and electron diffraction show for Ca2N, a layered electride exfoliated in liquid into flakes 0.2 to 10 µm across.
Identify the phase first: 2H and 3R α-In2Se3, β and β′ look alike under an optical microscope but differ in Raman spectra, second-harmonic generation and electron diffraction.
A crystal scatters electrons into a pattern of spots that maps its lattice – a hexagon for graphene or MoS2, two hexagons turned by the twist angle for a twisted bilayer, rings for a film of many grains. In LEED, slow electrons reflected from a surface show the extra spots of a layer whose repeat differs from its substrate’s.
Waves from particles
Electrons accelerated through a voltage have a wavelength that shrinks as their energy grows – a few picometres in a , far below the 0.1 to 0.3 nm between atoms in a crystal. Rows of atoms scatter such waves only in particular directions, where the waves from all the rows add up. Recorded on a detector, those directions form a pattern of spots: for a single layer of graphene or MoS2, a hexagon whose distance from the centre gives the and whose rotation gives the orientation of the crystal.
Electrons interact with matter far more strongly than X-rays do, which is why electron diffraction works on a single atomic layer or a a few micrometres across, where needs much more material. The price is that in thicker crystals electrons scatter more than once, so the brightness of the spots is harder to interpret than in X-ray diffraction.
In the microscope and on the surface
In a transmission electron microscope, selected-area diffraction records the pattern of a chosen patch of a flake. A gives one set of spots, two layers twisted against each other give two hexagons turned by the , and a film of many grains gives rings. Electron microscopy of graphene suspended in vacuum showed that a sheet one atom thick is a crystal with long-range order – and that it is not flat, rippling out of plane by up to a nanometre (Meyer and colleagues, 2007).
Low-energy electron diffraction, LEED, sends slow electrons at a surface and records those scattered back. They reach only the top few atomic layers, so LEED is the standard check of layers grown in ultrahigh vacuum, which rarely share their ’s lattice. Few-layer germanene on gold gave sharp patterns dominated by one-eighth-order spots, an 8 × 8 superstructure of the gold lattice, which ruled out the alternative of a germanium film covered by a layer of gold (Dávila and colleagues, 2016). Reflection high-energy electron diffraction does the same job at grazing incidence while a film grows.
Symmetry and speed
Focusing the beam into a cone instead of a parallel beam spreads each spot into a disc, and the pattern inside the discs carries the crystal’s point-group symmetry. Convergent-beam electron diffraction can therefore tell, on a single small crystal, whether it has a centre of inversion – the question that decides whether it can be or produce light.
With pulsed beams, diffraction becomes a film. In ultrafast electron diffraction a laser pulse excites the sample and an electron pulse arriving a set time later records its pattern; the spots dim as the atoms vibrate more strongly. In monolayer WSe2, fitting all the spots together separated the two elements: tungsten and selenium both vibrated more within the first two picoseconds; over the next two, selenium kept gaining while tungsten lost much of its gain, before the changes slowed (Jung and colleagues, 2024).
For specialists
Diffraction of electrons, whose wavelength at transmission-microscope energies is a few picometres, by the periodic potential of a crystal; the spot pattern samples its reciprocal lattice. Strong scattering makes it work on single layers: selected-area diffraction in a TEM gives the orientation, twist angle and lattice constant of a flake; low-energy electron diffraction (LEED), at tens to hundreds of electronvolts, sees only the top layers of an film in ultrahigh vacuum and reveals its superstructure; convergent-beam diffraction tests point-group symmetry, including whether there is a centre of inversion; and ultrafast electron diffraction follows the lattice after a laser pulse, picosecond by picosecond.
Convergent beam electron diffraction (CBED), recently demonstrated on , offers a number of interesting applications such as imaging atomic in- and out-of plane shifts, , and individual adsorbates. In this study, we show how CBED allows for atomic-precision imaging of…
This work combines experimental investigations and calculations to study hexagonal boron nitride (hBN) growth on a curved Pt(331) substrate. Low-energy electron diffraction (LEED) and (STM) were employed to investigate the structural properties, observing that hBN growth…
We report a direct observation of the of monolayer SnTe on graphene by . By combining low-energy electron diffraction, momentum microscopy, , and first-principles calculations, we show that the observed monolayer-limit electronic…