From TEM Kikuchi lines to a map in the SEM
Guide 1 handed you a beautiful gift and then a limitation. The gift was Kikuchi lines: those crisp bands that appear in a thick-ish TEM foil and act like a crystal's own protractor, telling you exactly which way the crystal is tilted. The limitation is that a TEM sees one tiny, ultrathin patch at a time. Guide 2 pushed the other way — down to atomic columns on an even thinner foil. Electron backscatter diffraction, EBSD, spins the Kikuchi trick in a completely different direction: it drags it out of the TEM, plants it in an ordinary scanning electron microscope, points it at a chunk of bulk material, and asks not 'which way does this one spot point' but 'which way does every spot point, everywhere, as I sweep across the surface.' The answer is a map.
Picture a mosaic floor made of a single kind of stone, but with every tile cut from the quarry block at a random angle, so the grain of the stone runs a different way in each tile. From across the room the floor looks uniform; only if you could read the grain direction of every single tile would the patchwork of tiles reveal itself. That is exactly a polycrystal, and EBSD is the instrument that reads the grain direction of each tile. The setup is deliberately lopsided: the flat sample is tilted steeply, about 70 degrees, away from facing the beam. The electron beam parks on one spot, dives a few tens of nanometres into the crystal, and a fraction of the electrons scatter back out. On their way out those backscattered electrons diffract off the crystal planes and spray a Kikuchi pattern onto a flat phosphor screen sitting close by, which a fast camera photographs. The steep tilt is what throws enough backscattered electrons forward onto the screen to make the pattern bright.
Reading one pattern: bands, poles, and Hough indexing
Freeze on a single spot and look at what the camera caught. The pattern is a web of bright, straight bands crossing the screen. Each band is one family of crystal planes seen edge-on: the band's centre line is the trace of that plane, and the band's width is set by the Bragg angle for those planes. Wide bands come from widely spaced planes (small d needs a bigger angle, narrow band; large d, small angle, wide band — the same inverse-spacing feel from the reciprocal-lattice rung). Where several bands cross, they meet at a bright intersection: that is a zone axis, a direction shared by all those planes, a crystallographic pole. So one Kikuchi pattern is a flattened road map of the crystal's whole geometry, projected outward onto the screen like a shadow cast from the sample point.
EBSD GEOMETRY (in the SEM, flat sample tilted ~70 deg to the beam)
electron beam
|
v
[ tilted crystal surface ]
|
| backscattered electrons diffract on the way out
v
+--------------------------+
| phosphor screen | the KIKUCHI PATTERN
| ====== band A ====== | each BAND = one (hkl) plane family
| band B + band C | band CROSS + = a zone axis / pole
| band D | band WIDTH ~ 2 x theta_B
+--------------------------+
one pixel of the map -> one full crystal orientation
band width, worked (20 kV: electron lambda = 0.086 A)
d = 2 A -> theta_B = arcsin( 0.086 / (2 x 2) ) = 1.23 deg
full width ~ 2 x theta_B ~ 2.5 deg (narrow: electron lambda is tiny)
Put a number on that band width and the physics from earlier rungs snaps into place. Speed a beam electron through 20 kilovolts and its wavelength is about 0.086 angstrom — roughly eighteen times shorter than the 1.54-angstrom copper X-rays of the diffraction rung. Feed that into Bragg's law for a plane spacing of d = 2 angstrom: sin theta = lambda / (2 d) = 0.086 / 4 = 0.0215, so the Bragg angle is only theta = 1.23 degrees and the band spans about 2 theta = 2.5 degrees. That is why Kikuchi bands are narrow, gently curved stripes rather than fat wedges — the electron wavelength is so tiny that every Bragg angle is tiny too. It is the same 2 d sin theta you have used all along, just wearing electron clothes.
- The camera grabs the raw Kikuchi pattern from the parked spot — a webful of faint straight bands.
- Software runs a Hough transform, which turns each straight band into a single peak, so detecting bands becomes finding bright spots — far easier for a computer.
- It measures the positions and widths of the strongest bands and the angles between them.
- It matches that geometry against the known crystal structure (loaded beforehand) to find the one orientation that lines every band up correctly.
- It records that orientation as three angles for this pixel, together with a confidence and fit score, then the beam steps to the next spot.
Rastering the beam: a map where grains appear
Now do that not once but a million times. The beam steps across the surface on a fine grid — steps of anything from a few nanometres to a micron — and at every pixel it indexes a fresh pattern and stores a full crystal orientation. The result is an image where each pixel carries not a brightness but a direction. To see it, we paint each pixel by which crystal axis happens to point along the sample's surface normal, using the standard-triangle colour key you met as the inverse pole figure: red for a <001> axis pointing out at you, green for <101>, blue for <111>, and blends in between. Each pixel's colour is, in effect, a compass reading of the crystal beneath it — a direct picture of the microstructure coloured by orientation.
And now the grains simply appear, for free. A grain is a patch of pixels that all share nearly the same orientation — one continuous colour. Trace the line where the colour suddenly jumps and you are tracing a grain boundary, the mismatched seam where two crystal patches meet, exactly the floor-tiles-at-different-angles picture. Better still, EBSD hands you the misorientation across that seam as a hard number of degrees. A gentle jump of only a few degrees is a low-angle boundary; a large jump is a high-angle boundary, and the convention draws the line between them at about 10 to 15 degrees. Some boundaries even show a special, exact misorientation: a 60-degree twist about a <111> axis in an FCC metal is the coherent twin boundary (a Sigma 3 relationship in the coincidence-site-lattice language), and EBSD flags every one of them automatically. What used to be eyeballed from an etched micrograph is now measured.
From map to texture: pole figures, IPF, ODF
Zoom back out from individual grains and a bigger question waits: are the grains pointing every which way, or do they cluster around preferred directions? That statistical bias is texture, and it is one of the most consequential things about a real polycrystal. A freshly cast metal is often nearly random, but roll it into sheet, draw it into wire, or grow it as a film and its grains swing toward a few favoured orientations. Texture is why a rolled sheet is stiffer or easier to bend one way than another — it is structure driving property, with the grain population, not any single grain, doing the driving. Because EBSD has just handed you the orientation of thousands of grains at once, you can measure the whole distribution rather than guess at it.
There are three standard ways to draw that distribution, and they answer three different questions. A pole figure fixes on one chosen plane normal — say every grain's {111} — and plots, on a stereographic projection in the sample's frame, where all those normals point; clustering into blobs is the visible signature of texture. An inverse pole figure asks the mirror-image question: for one chosen sample axis (say the sheet's rolling direction), which crystal directions line up with it. And the full orientation distribution function, the ODF, is the complete statistical description — the probability of finding a grain at every possible orientation, from which both kinds of figure can be computed. A cold-rolled brass sheet, for instance, shows a characteristic texture that a metallurgist can read off the pole figure at a glance, and that predicts how the sheet will behave in the press.
But be honest about the statistics. EBSD measures texture grain by grain, yet it only ever looks at one small, thin surface patch, so it may see only a few hundred or few thousand grains — and if the grains are coarse, that is far too few to trust as a bulk average. This is exactly where the next guide's neutron diffraction shines: a neutron beam passes through a whole centimetre-sized sample and averages over millions of grains, giving bulk texture with real statistical weight. EBSD gives you the where and the local detail; neutrons and X-rays give you the trustworthy bulk average — the same question answered at different scales.
Choosing EBSD, and its honest limits
Line EBSD up against its cousins and its niche is obvious. The SAED, CBED and Kikuchi patterns of guide 1 read orientation from a single thin-foil patch in the TEM; the HRTEM and STEM of guide 2 image the atomic columns themselves. EBSD sits at the characterization scale in between: it does not resolve atoms, but it maps orientation over millimetre-wide areas of ordinary bulk material, thousands of grains at a sweep. Its lateral resolution is tens of nanometres, its angular resolution around half a degree in the ordinary form — and a cross-correlation refinement called high-resolution EBSD sharpens that to about a hundredth of a degree, sensitive enough to map elastic strain, residual stress, and even dislocation-density gradients from the faint distortions of the pattern. When your question is which way do the grains point, how big are they, and what are the boundaries, EBSD is the natural tool.
Now the fine print, because every probe lies a little if you let it. First, EBSD is a surface method through and through — that few-tens-of-nanometres sampling depth means it says nothing about what lies beneath, and it lives or dies by surface preparation. Second, it maps ORIENTATION, not atomic positions: a pixel tells you which way the crystal points, never where the individual atoms sit. For that you go back up to the HRTEM and STEM of guide 2. Third, and easy to forget, a single EBSD map is a two-dimensional section through a three-dimensional solid. The grains you see cut are chords, not full grains, so the apparent grain size on the map is systematically smaller than the true 3D size unless you correct it with stereology — or physically slice down through the sample layer by layer to build a genuine 3D map. A flat map is a slice, and a slice is not the whole.
Hold all three probes in your head at once and the choice becomes a matter of matching the question to the scale. Need the atoms? HRTEM or STEM on an ultrathin foil. Need one crystal's orientation locally? Kikuchi lines in the TEM. Need an orientation and texture map over a real, bulk microstructure? EBSD in the SEM. Need a trustworthy bulk-averaged texture, or the light atoms and magnetism that electrons cannot see? Neutrons, waiting in guide 4. No single instrument answers every structural question — the skill is knowing which one to reach for, and EBSD owns the middle ground where orientation, grains and texture live.