Glossary

Short definitions of the terms used throughout this documentation, with links to where each is developed properly. Terms that are easy to confuse with one another are defined next to each other rather than strictly alphabetically.

Directions and crystals

Antipodal - the flag marking a quantity as an axis rather than a direction, so that it and its opposite are the same thing. It changes angles, means and densities, and nothing warns you if it is missing. See Axes.

Miller indices - the notation for planes and directions in a lattice. Round brackets (hkl) name a plane, square brackets [uvw] a direction; braces {hkl} and angle brackets uvw name the whole symmetric family. The two are not interchangeable: in quartz the plane (100) and the direction [100] are 30 degrees apart. See Miller Indices.

Point group - the symmetry operations that leave one point of the lattice fixed. There are 32. Space group - the same allowing translations as well, of which there are 230. Laue group - a point group with an inversion centre added, of which there are 11, and what a diffraction experiment can actually determine. See Crystal Symmetries.

Crystal frame - the Cartesian axes glued to the lattice. Specimen frame - the axes the sample is described in. Nearly every confusing result comes from a quantity being read in one when it was written in the other. See Reference System.

Fundamental sector - the patch of the sphere holding exactly one of each symmetrically equivalent direction; what an inverse pole figure is drawn on. Fundamental region - the same idea for orientations. See Fundamental Sector and Fundamental Region.

Orientations

Orientation - the rotation relating the specimen frame to the crystal frame; how one crystal is placed in the sample. See Orientations.

Misorientation - the rotation relating two crystals to each other, independent of the specimen. Disorientation - the one representative of a misorientation with the smallest rotation angle, which is the number quoted when a boundary is called "a 60 degree boundary". Symmetry makes many rotations describe the same relationship; disorientation picks one. See Theory.

Grain exchange symmetry - the further ambiguity that a misorientation between two grains of the same phase has no natural direction, so a rotation and its inverse describe the same boundary.

Variant - one of the several child orientations a single parent orientation can produce under an orientation relationship. Packet - variants grouped by shared habit plane. Bain group - variants grouped by which parent cube axis the child aligns to. Packet and Bain group are independent classifications of the same variants, not two levels of one hierarchy. See Phase Transitions.

Fibre - the set of all orientations that put one fixed crystal direction along one fixed specimen direction. A curve in orientation space, and the shape many real textures take. See Fibres.

Distributions

Texture - the departure of a material's orientations from randomness.

ODF - orientation distribution function, the density of material over orientations. Being a density, it gives no volume fraction to a single orientation, only to a region of them. See ODF.

MRD - multiples of a random distribution, the unit an ODF is reported in. A value of 1 everywhere is no texture; a value of 20 means twenty times as much material near that orientation as chance would give.

Pole figure - the density of one chosen crystal direction over all specimen directions. Inverse pole figure - the reverse, the density of one chosen specimen direction over crystal directions. Both are projections of an ODF and both lose information. See Pole Figures.

Ghost effect - the ODF error that follows from pole figures being blind to the odd part of the harmonic expansion. Not a numerical artefact but a genuine gap in what diffraction can know. See The Ghost Effect.

Halfwidth - how far each measurement is spread when a density is estimated from discrete data. Bandwidth - the highest harmonic degree kept in a series representation. The two are the same trade-off between detail and noise, seen from opposite sides. See Density Estimation.

Maps, grains and boundaries

notIndexed - the phase given to a measurement whose pattern could not be indexed. A recorded value, not missing data, and a connected patch of it can form a grain of its own.

Grain - a connected, phase-homogeneous region of measurements whose orientations agree to within a threshold. There is no canonical definition; the threshold is a convention. See Grains.

Grain boundary - the segment between two neighbouring measurements that fell in different grains. Phase boundary - not a separate kind of object, just a grain boundary whose two grains differ in phase.

Hole and inclusion - one grain lying entirely within another, seen from outside and from inside. The same fact, not two.

Chain - a run of boundary segments laid end to end between two junctions. Junction - a vertex where the number of meeting segments is anything other than two. Triple point - a junction where exactly three segments meet and they separate three distinct grains, so it is a strict subset of the junctions. See Triple Points.

KAM - kernel average misorientation, the average orientation difference between a measurement and its neighbours. GROD - grain reference orientation deviation, the difference between a measurement and its own grain's mean. See KAM and Mis2Mean / GROD.

Material response

Slip system - a lattice plane together with a direction in it, along which a crystal shears plastically. Schmid factor - the geometric factor relating applied stress to the shear stress resolved onto a slip system, between 0 and 0.5. See Plasticity.

Taylor and Sachs models - the assumptions that every grain undergoes the same strain, and that every grain feels the same stress. They bound the real behaviour from above and below, and are the plastic counterparts of the Voigt and Reuss bounds in Tensors.

GND - geometrically necessary dislocations, the dislocation content implied by a gradient of orientation within a grain. See GND.

Next

The conventions behind these terms - Euler angles, frames, units and the direction a rotation acts in - are collected in Notation and Conventions.