Every band is a road, every crossing a town. This is the map, with the tilt angles written on the signposts.
A live Kikuchi map for any crystal. Hover a band to see every zone axis strung along it, hover a zone to see the bands that meet there, and pick where you are and where you want to be: the tool names the band to follow, how far to tilt, and the double-tilt holder settings that get you there.
The list here follows the last band or zone you pointed at. Click a zone axis to tilt to it (the view re-centres on it); click empty space to clear.
A family is every symmetry-equivalent orientation of one plane, drawn all together or not at all ({311} in fcc is 12 bands). The map considers the 12 strongest families; hover a zone axis to see every band through it, including the ones not drawn, and pin them.
Major, intermediate and minor are set by zone strength: the summed |F| of every band through the zone, as a fraction of the strongest zone at this index limit. Big dots are major zones; small faint dots are minor ones.
Scroll, double-click, or the + and − buttons zoom; drag to pan. Shift-drag (or right-drag) tilts the crystal freely; arrow keys tilt in steps when the map has focus.
α is the rod axis (horizontal on the map); β is carried by α. Zones outside the shaded region are drawn hollow: no holder setting reaches them from this zero.
Stitched-map mode draws, around every zone axis in view, the spot pattern you would see with the beam on that axis, sized by |F|² against one common scale, so as you pan across the screen each band crossing carries its own labelled net (a composite, as on a textbook Kikuchi map; a real screen shows one net at a time). Nearest-zone mode shows that one net; the Ewald mode keeps only what a flat foil of thickness t would actually excite. By default each net stops at three times the spacing of its nearest spot, so three spots line up along each row out from the centre; "the whole net" goes out to d = 0.022 nm (about 6° around each axis at 200 kV).
Scroll to zoom and drag to pan, here and on the map (Reset view puts everything back). Every spot with room for its label gets one, brightest first; zoom in and the rest fill in.
Gnomonic projection, viewed along the beam from above. Band widths are true here (the exaggeration setting applies to the map only), so at a zone axis each pair of lines passes halfway between 000 and its spots. Spot intensity is kinematical, |F|² times the thin-foil shape factor at thickness t, drawn with a compressed scale (I0.3) so weak outer spots stay visible; a thinner foil brings outer spots up, as in the Ewald sphere guide.
Every Kikuchi band is one family of lattice planes seen edge-on. The two lines of a band sit one Bragg angle either side of the plane's trace, so the band is 2θB wide: narrow for widely spaced planes, wider as d shrinks. Its darkness here follows the structure factor |F|, which is roughly how strong the band looks in a real pattern (the excess and deficient contrast of a real band is not modelled; this is the geometric map, the one you carry in your head at the microscope). Bands come in symmetry families and are drawn family by family, never a few members of one: {311} in fcc is twelve bands and you get all twelve or none. The map keeps the twelve strongest families in reserve, draws the strongest six by default, and shows the hidden ones dashed whenever you hover a zone axis, so every intersection can be seen in full and any band can be pinned onto the map.
A zone axis [uvw] is a direction that lies in many planes at once. On the map it is the point where all those bands cross. The test is the Weiss zone law, hu + kv + lw = 0, and it is exact in every crystal system. Hover any band and the list under the map names every zone axis on it, in order along the band, with the tilt from where you are now. Hover a zone axis and the list names the bands that meet there.
The map is a stereographic projection of the hemisphere of directions around the beam, with the beam at the centre. Angles from the centre are true; a band that passes through the centre is a straight line, and every other band is an arc. The screen tab shows the same geometry as the camera sees it, a gnomonic projection in which every band is a straight pair of lines, over the few degrees a real pattern covers.
Not every crossing on the map is worth the same. A major zone axis is a low-index direction that lies in many low-index planes at once: [011] in fcc sits in {111}, {200}, {220}, {311} and {331} planes, so fourteen bands converge there, most of them strong. Its diffraction pattern is dense and bright, the spots sit close together, and many beams are excited at once, which is why major zones are where you do high-resolution imaging and why two-beam conditions are hard to reach there. A minor zone axis is a higher-index direction such as [133]: only a handful of weak, high-index bands pass through it, its pattern is sparse, and it is easy to tilt slightly off it into a clean two-beam condition. On the map, major zones are the big dots where the thick bands meet and minor zones are the small faint dots on the thin bands in between; in a real pattern you recognise a major zone by the crowd of bands running into it.
The tool ranks zones by a simple number it calls zone strength: add up |F| for every band through the axis (using the twelve-family reserve, not only the drawn set), and compare with the strongest zone at the current index limit. Major is at least 45% of that, minor is below 22%, intermediate is in between. It is a ranking of how busy the map is at that pole, not a symmetry ranking: a highly symmetric but sparse zone like fcc [111], with its three strong {220} bands and little else, lands in the intermediate tier, and the hover panel always shows the number so you can judge for yourself.
Tilt the crystal about a plane's normal and that plane stays edge-on: its band stays where it is while every other band slides across the screen. The zone axes strung along the band come to the centre one after another. That is the whole trick of navigating reciprocal space with Kikuchi lines, and it is what the route panel computes. Pick where you are and where you want to be. The band to follow is the plane that contains both directions, (hkl) = [u1v1w1] × [u2v2w2], and the tilt is the angle between the two directions in the crystal's own metric, so a hexagonal cell gets its c/a-dependent answer, not the cubic shortcut. If that band is too weak to see in the current set, the tool looks for a two-leg route through an intermediate zone using only bands that are drawn.
The classic fcc triangle is the first thing to try: [001] to [111] runs 54.7° along the (1-10) band; [111] to [011] runs 35.3° along (01-1); [011] back to [001] runs 45° along (100), which is drawn from its (200) reflection because (100) itself is absent in fcc. Press Go and watch the band stay put while the rest of the map turns.
A double-tilt holder gives you two angles, not three. α turns the whole rod; β turns a cradle carried by the rod, so its axis moves with α. The holder panel treats whatever orientation you choose as α = β = 0, solves for the pair that brings a target zone on axis, and shades the region the holder can reach at all. A zone outside the shaded patch cannot be reached from this zero, whatever route you take; you would need to remount the specimen or use a rotation holder. The in-plane rotation of the pattern is not something a double-tilt holder controls, so the readouts ignore it: the spin slider under Orientation rotates the map without changing α or β.
Band contrast is geometric with |F| weighting: there is no dynamical excess and deficient shading, no thickness dependence and no HOLZ lines. Spots on the screen tab are, by default, the whole zero-order net of the nearest zone axis sized by |F|2, which is what an indexed pattern shows and what lets a minor zone display its sparse net; the Ewald-sphere mode instead keeps only what a flat foil of thickness t excites kinematically, with a sin2(πts)/(πs)2 shape factor. Neither includes absorption, multiple scattering or HOLZ rings. Scattering factors are the Peng 1996 five-Gaussian fits with no Debye-Waller factor. Camera flips are provided because every microscope's camera orientation differs; match them to a known pattern before trusting handedness.
@misc{tripathy2026kikuchimapnavigator,
author = {Tripathy, Manisha},
title = {Kikuchi Map Navigator},
year = {2026},
howpublished = {\url{https://untetheredatom.com/tem/kikuchi-map-navigator}},
note = {Interactive web tool}
}