selected-area electron diffraction
Imagine you have a whole city photographed from above, but you only want to know how the streets are laid out in one small neighbourhood. So you drop a mask over the photo with a single small window cut in it, and study only what shows through that window. Selected-area electron diffraction (SAED) does exactly this inside a transmission electron microscope. The electron beam passes through a thin slice of crystal, and instead of forming a picture of the crystal, the microscope is switched to show the pattern of spots the crystal scatters. An aperture (a tiny hole) placed in the image lets you pick out just one small region, and you record the diffraction pattern from that region alone.
What you get is a pattern of sharp spots, and here is the beautiful part: that pattern is a direct, magnified photograph of a flat slice through the crystal's reciprocal lattice. Because fast electrons have a tiny wavelength (about 2.5 picometres at 200 kilovolts, roughly two hundred times smaller than an X-ray), the Ewald sphere that picks out which reflections appear is enormous — radius about 400 nm^-1 — so it cuts the reciprocal lattice almost like a flat plane rather than a curved shell. That flat cut is the layer of reciprocal-lattice points perpendicular to the beam, so the spot pattern is essentially a scaled map of one plane of reciprocal space. The scaling obeys a simple rule, R d = lambda L: the distance R of a spot from the centre, times the plane spacing d it comes from, equals the electron wavelength lambda times the camera length L (a fixed instrument constant). Measure R, know lambda L, and you read off d.
SAED is the crystallographer's quick-look tool. From one pattern you can tell whether a region is a single crystal (a neat grid of spots), many tiny randomly oriented crystals (continuous rings, like a powder), or amorphous (diffuse haloes). You can index the spots to identify a phase, read the orientation, and measure how two crystals line up across an interface (epitaxy). The honest caveat: SAED is not as accurate for lattice parameters as X-ray diffraction. The camera length drifts and must be calibrated, the intensities are distorted by strong multiple scattering (dynamical scattering), and the region you actually sample is limited by lens aberration to roughly half a micrometre, often larger than the aperture image suggests.
Point the beam down a cube axis of an aluminium grain and the SAED pattern is a square grid of spots. Measuring a spot at R = 10 mm with the instrument's lambda L = 20 mm.angstrom gives d = lambda L / R = 20/10 = 2 angstrom — the (200) spacing of aluminium — confirming both the phase and that you are looking down the [001] zone axis.
One SAED pattern gives phase, orientation, and interplanar spacings from a sub-micron region in seconds.
The 'selected area' is defined by an aperture in the image plane, not the beam, so lens aberration lets electrons from a wider region leak in — the true sampled area can be much larger than the aperture image, which is why SAED from very small features can be unreliable.