Where the signal comes from

Fire electrons into a solid and they random-walk: forward-peaked scattering at first, then diffusion, filling a teardrop whose size is set by voltage and by the material's stopping power. In EBSD geometry the pattern-forming electrons are the minority that scatter back out near the entry point of the 70°-tilted surface. In TKD the sample is a foil thinner than the first few steps of that walk; the electrons leave through the bottom before they can spread.

Interaction-volume sandbox A schematic Monte Carlo: caricature physics, honest geometry

Accelerating voltage

Foil thickness (TKD)

Kanaya–Okayama range

–

µm

Pattern source width

–

nm, lateral (schematic)

– –

Switch Ni → W at fixed voltage: the cloud shrinks (stopping power), so heavy materials give EBSD its best resolution. Then switch to TKD and note the scale bar change: the foil turns a micron-scale problem into a tens-of-nanometres problem by amputation, not by focus.

R_KO = 0.0276 · A · E^1.67 / (Z^0.889 ρ) [µm; E in keV] the Kanaya–Okayama electron range: the depth scale of the full teardrop. For Ni at 20 kV it is about 0.9 µm; for Al, 4 µm. The pattern-relevant zone is far smaller: diffraction contrast survives only for electrons that exit having lost little energy, which confines the useful EBSD source to roughly the top 10–40 nm and a lateral patch of tens of nanometres, smeared ~3× along the tilt direction by the 70° geometry. The teardrop sets the background; the sliver sets the signal.

Go deeper: what this cartoon gets right, and what it waves at

The trajectories above are a toy: fixed step length, Gaussian deflections, no energy-loss physics, enough to make the geometry honest (range scaling, tilt asymmetry, foil truncation) and nothing more. Real answers come from proper Monte Carlo (CASINO and friends) and, for the pattern-forming fraction specifically, from Zaefferer's analysis of where backscattered Kikuchi patterns actually originate: a thin, high-energy-exit sliver, not the whole plume, which is why EBSD resolution is tens of nanometres while the plume is microns.

The TKD numbers have their own subtlety: resolution is set by beam broadening through the foil, so it degrades with thickness and improves with voltage, opposite in sign to EBSD, where higher kV means a bigger plume and worse resolution. That reversal is why TKD runs happiest at 30 kV, the top of most SEM columns.

The same film, both ways

Here is a nanocrystalline film (true grain structure known, mean size on the slider) mapped twice. Each technique's probe averages over its own source region: where that region covers one grain, the pixel indexes; where it straddles several, the pattern is a superposition and the pixel dies (or worse, lies). This is part 5's speckle and holes, given their physical cause.

One nanostructure, two source sizes Black = mixed patterns, unindexable

Film grain size

Accelerating voltage

EBSD indexed

–

% of pixels · – of – grains seen

TKD indexed

–

% of pixels · – of – grains seen

– –

Slide the grain size down to 15 nm. TKD keeps drawing a map; EBSD returns a black field with orphan pixels, and every orphan that does index is a real orientation measured from a real grain, which is how nanocrystalline EBSD papers end up reporting beautiful statistics about an unrepresentative minority. Raising the voltage makes EBSD worse and TKD better.

The price

TKD's resolution is bought, not free, and the currency is the specimen. The sample must be electron-transparent (a FIB lamella or an electropolished foil, hours of preparation instead of minutes of polishing) and the foil's own thickness becomes a new resolution limit.

Thickness cuts twice. Too thick, and the beam crosses several grains stacked in depth: the pattern is a superposition again: the same disease EBSD had laterally, now vertical. Too thin, and there is barely any diffracting material: patterns go faint and noisy, and the foil bends and drifts under the beam. Between the two sits a window, and the window narrows as grains shrink:

The thickness window A model curve: the shape is the lesson, not the numbers

Foil thickness

Grain size

Grains stacked per column

–

foil thickness / grain size

Indexable fraction

–

model estimate

– –

The working rule falls out of the geometry: the foil should be comparable to or thinner than one grain. For a 30 nm nanocrystalline film that means a ~30 nm foil, which is exactly why TKD sample prep is the hard part of TKD.

The ledger. Neither column wins; the microstructure picks.
Property	EBSD (bulk, 70°)	TKD (foil, transmission)
Lateral resolution	~30–100 nm, tilt-smeared	~2–10 nm
Sample prep	polish; minutes–hours	FIB lamella / foil; hours, skilled
Mappable area	mm², large statistics	µm², tens of grains
Voltage preference	lower kV → smaller source	higher kV → less broadening
New failure modes	charging, tilt distortion	foil bending, drift, depth overlap
Best at	bulk microstructure, texture, large-area statistics	nanocrystalline films, ODS particles, heavily deformed metal, fine precipitates

The thing to remember

EBSD and TKD are one technique wearing two geometries: same detector, same Hough, same vote. The only thing that changed is how much material the electrons were allowed to visit, and that one variable moves the resolution by an order of magnitude and the sample-prep cost by about the same factor, in opposite directions.

Next · Part 7

Pattern quality as data

IQ and band-contrast maps as strain and damage fingerprints: the signal hiding in the channel everyone treats as decoration.

Part 1

From Kikuchi bands to an orientation

The pattern, the Hough and the vote that both geometries share.

Sources & further reading

K. Kanaya, S. Okayama, “Penetration and energy-loss theory of electrons in solid targets,” J. Phys. D 5, 43 (1972): the range formula above.
S. Zaefferer, “On the formation mechanisms, spatial resolution and intensity of backscatter Kikuchi patterns,” Ultramicroscopy 107, 254 (2007): why the pattern source is a sliver, not the plume.
R. R. Keller, R. H. Geiss, “Transmission EBSD from 10 nm domains in a scanning electron microscope,” J. Microsc. 245, 245 (2012): the paper that started TKD.
P. W. Trimby, “Orientation mapping of nanostructured materials using transmission Kikuchi diffraction in the scanning electron microscope,” Ultramicroscopy 120, 16 (2012): TKD made practical.
G. C. Sneddon, P. W. Trimby, J. M. Cairney, “Transmission Kikuchi diffraction in a scanning electron microscope: a review,” Mater. Sci. Eng. R 110, 1 (2016): the standard review, including the thickness window.
R. van Bremen, D. Ribas Gomes, L. T. H. de Jeer, V. Ocelík, J. Th. M. De Hosson, “On the optimum resolution of transmission-electron backscattered diffraction (t-EBSD),” Ultramicroscopy 160, 256 (2016): beam broadening vs foil thickness, measured.
D. Drouin et al., “CASINO V2.42: a fast and easy-to-use modeling tool for scanning electron microscopy and microanalysis users,” Scanning 29, 92 (2007): the real Monte Carlo this page's cartoon gestures at.