Two invisible images fix a Burgers vector. This page tells you which two to take before you spend the session finding out.
Pick the crystal, the zone axes you can reach and the candidate Burgers vectors, and the table gives g·b for every reflection and every candidate, marks the invisibility conditions, applies the g·(b×u) criterion for edge components, finds the smallest set of reflections that tells all candidates apart, and, once you record which images showed the dislocation and which did not, lists the Burgers vectors that survive.
Green: g·b = 0 and the edge term small, the dislocation is invisible. Amber: g·b = 0 but g·(b×u) above 0.64, residual contrast from the edge component remains. Grey: |g·b| = 1/3, the faint image of a partial. The first column records your observation for that reflection: click to cycle through unused, visible and invisible.
Compact indices separated by spaces or commas, a minus sign before a negative index (1-10 is [1 −1 0]); three-index directions for hexagonal crystals. Reflections of each zone with a structure factor above the threshold are listed; a reflection in several zones is listed once with all of them.
One lattice vector per line in fractional coordinates (1/2 1/2 0 means a/2[110]); the symmetry-equivalent directions are generated for cubic sets and the in-plane variants for hexagonal ones.
With a line direction the page evaluates g·(b×u) as well: for an edge or mixed dislocation with g·b = 0 the residual contrast is weak only when |g·(b×u)| is below about 0.64 (Howie and Whelan). Leave blank for the g·b = 0 rule alone.
A dislocation is out of contrast in a two-beam image when the operating reflection g is normal to its displacement field, and for a screw dislocation that is exactly the condition g·b = 0. For an edge or mixed dislocation the field also has a component along b×u, so a residual image survives at g·b = 0 unless g·(b×u) is also small; Howie and Whelan's criterion, that the residual contrast is faint when |g·(b×u)| is below about 0.64, is what the page applies when a line direction is given. The Burgers vector is determined by finding two reflections, not parallel to one another, in which the dislocation is invisible: b is then along g1×g2, and its magnitude follows from the crystallography.
In practice the difficulty is planning: which zone axes to reach, which reflections in them make which candidates invisible, and whether the reflections available in a given foil can separate the candidates at all. The page takes a crystal from the library or a CIF, lists the reflections of the zone axes you name (those with a structure factor above the threshold, one of each ±g pair), and computes g·b exactly, as hb1 + kb2 + lb3 with b in fractional lattice coordinates, for every candidate vector. The candidates come from the usual sets for the structure type (perfect and partial dislocations of fcc, bcc, hcp, diamond, B2 and L12 crystals) expanded over the symmetry-equivalent directions, or from a list you type. A greedy search then finds the smallest set of reflections whose pattern of visible and invisible images differs between every pair of candidates, which is the minimum experiment.
Once images exist, click the first column of each reflection used to mark the dislocation visible or invisible in that image. The page keeps the candidates whose predicted pattern matches every observation and says which reflections would separate the survivors. The comparison uses g·b = 0 for invisibility; a candidate marked amber (residual contrast expected) is kept when you report visible and also when you report invisible, because a faint residual image is easily missed, and a candidate at |g·b| = 1/3 is treated the same way, since the image of a partial at g·b = ±1/3 is faint but not absent.
The rules are those of the two-beam theory of a dislocation in an elastically isotropic crystal, which is how the g·b analysis is always taught and usually applied. In anisotropic crystals the displacement field is not exactly normal to b×u and the invisibility at g·b = 0 is not exact (Head, Humble, Clarebrough, Morton and Forwood's programs handled that case by full simulation); in that situation the g·b = 0 images can show weak contrast even for a screw, and the image-matching route is the one to take. The candidate lists are the common ones and are not exhaustive: dislocations in intermetallics, ceramics and low-symmetry crystals may have Burgers vectors outside these sets, which is what the custom list is for. The threshold on the structure factor removes weak and forbidden reflections from the tables; a kinematically forbidden reflection that appears by double diffraction cannot be used for a g·b analysis anyway, because its contrast is not two-beam. The page does not compute images: the companion two-beam defect simulator does, including the g·b = 0 residual contrast of an edge dislocation.
@misc{tripathy2026gbinvisibilityplanner,
author = {Tripathy, Manisha},
title = {g.b Invisibility Planner},
year = {2026},
howpublished = {\url{https://untetheredatom.com/tem/gb-planner}},
note = {Interactive web tool}
}