Kikuchi Map Navigator

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 2θ_B 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.