Glossary

This page gives short definitions of terms used throughout the MTEX documentation. Each link leads to the page that develops the idea and shows how to use it. Terms that are easily confused appear together rather than in strict alphabetical order.

Commands and stored data

Command option and flag - controls appended to a command call. An option has a name and value, whereas a flag is switched on by its presence. See Options for the full calling convention.

Property and scan option - per-element data in ebsd.prop and whole-scan data in ebsd.opt, respectively. Only a property is indexed and subset in lockstep with the map. See Properties for the definition, examples, and the rule for deciding where a value belongs.

Header - scan-level information captured from a file's own preamble. It includes acquisition settings and vendor bookkeeping, but excludes phase and symmetry information already stored in CSList. It remains in the vendor's native shape, so field names are not normalised across file formats. See EBSD Import.

headerOnly - an import option for inspecting a large file without reading its per-point data. It returns an EBSD object with empty positions, orientations, and phase ids, but populated CSList, phaseMap, and opt.header.

Directions, symmetry, and reference frames

Antipodal - the flag marking a quantity as an axis rather than a direction, so 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, and square brackets [uvw] name a direction. Braces {hkl} and angle brackets <uvw> name the corresponding symmetric families. Planes and directions are not interchangeable: in quartz, the plane (100) and direction [100] are 30 degrees apart. See Miller Indices.

Point group - the symmetry operations that leave one point of a lattice fixed. There are 32 point groups.

Space group - a point group extended by translations. There are 230 space groups.

Laue group - a point group with an inversion centre added. There are 11 Laue groups, and a diffraction experiment can determine this symmetry. See Crystal Symmetries for all three groups.

Reference frame - the frame in which data is expressed. It has an identity, a basis, and a default plotting convention. A reference frame is distinct from both the symmetry attached to it and the way it is drawn.

Crystal frame - the Cartesian reference frame fixed to a phase's lattice basis. An alignment such as X||a*, Z||c belongs to this frame, not to its point group.

Specimen frame - the frame in which the sample is expressed. Measurement, rolling, and geological frames are named specimen frames. Reading a quantity in the crystal frame when it was written in the specimen frame, or conversely, causes nearly every confusing result. See Reference System.

Symmetry - the point group under which data is invariant. It is attached to a reference frame but is not the frame itself. Two datasets may share a symmetry while using differently aligned frames, or share a frame while carrying different symmetries.

Plotting convention - the layout of a reference frame on screen, such as which axis points east and which points out of the screen. The frame supplies a default, and a plot may override it. It is not merely a camera setting because import may also use its rotation as a frame relation. See Axes Alignment.

Frame change - re-expressing the same physical object in another reference frame with transformReferenceFrame. The object stays fixed. Rotating instead moves the physical object. See Reference System.

Frame-free - the state of a vector3d, S2Fun, or tensor whose frame is empty. Its frame is resolved against the session default when drawn. An object that points to the default frame is framed, not frame-free.

Fundamental sector - the part of the sphere containing exactly one representative of every set of symmetrically equivalent directions. An inverse pole figure is drawn on it. See Fundamental Sector.

Fundamental region - the corresponding set of representatives for orientations. See Fundamental Region.

Orientations and parent reconstruction

Orientation - the rotation that maps the crystal frame to the specimen frame. It describes how one crystal is placed in the sample. See Orientations.

Misorientation - the rotation relating two crystals, independent of the specimen frame.

Disorientation - the representative of a misorientation with the smallest rotation angle. It supplies the number in a phrase such as a 60 degree boundary. Symmetry lets many rotations describe the same relationship; disorientation selects one. See Theory.

Grain exchange symmetry - the additional ambiguity for two grains of the same phase. Their relationship has no natural direction, so a rotation and its inverse describe the same boundary.

Orientation relationship (OR) - the crystallographic mapping between a parent phase and a child phase.

Variant - one crystallographically equivalent child orientation predicted from one parent orientation by a known OR. It is the finest classification of a reconstructed child grain relative to its parent.

Packet - a grouping of variants that share a habit plane. In the usual martensite classification, this is the parent {111} plane to which the child lattice aligns.

Bain group - a grouping of variants by Bain correspondence. It records the parent {001} cube-axis plane to which the child lattice aligns. Packet and Bain group are independent classifications of the same variants, not two levels of one hierarchy. See Phase Transitions.

Transform - the first parent-reconstruction step. Each child grain is assigned a candidate parent orientation through the OR and changed to the parent phase.

Merge - the second parent-reconstruction step. Neighbouring transformed grains with compatible parent orientations are combined into one grain footprint.

Grain graph - a reconstruction graph with one node per grain and edges for shared grain boundaries. It reasons directly about grain-to-grain compatibility.

Variant graph - a reconstruction graph with one node for every grain-and-candidate-variant pair. Its edges describe compatible candidates in neighbouring grains, so it chooses variants before merging. See Grain Graph Based Reconstruction.

Fibre - all orientations that place one fixed crystal direction along one fixed specimen direction. It is a curve in orientation space and a common shape for real textures. See Fibres.

Distributions

Texture - a material's departure from a random orientation distribution.

ODF - orientation distribution function, the density of material over orientations. A single orientation has no volume fraction; a region of orientations does. See ODF.

MRD - multiples of a random distribution, the unit used for an ODF. A value of one everywhere means no texture. A value of 20 means that the material near that orientation is twenty times as frequent as randomness would predict.

Pole figure - the density of one selected crystal direction over specimen directions.

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

Ghost effect - the ODF error caused by pole figures being insensitive to the odd part of the harmonic expansion. It is a genuine gap in what diffraction can determine, not a numerical artefact. See The Ghost Effect.

Halfwidth - the angular distance over which each discrete measurement is spread during density estimation.

Bandwidth - the highest harmonic degree kept in a series representation. Halfwidth and bandwidth express the same trade-off between detail and noise from opposite sides. See Density Estimation.

Maps, grains, and boundaries

notIndexed - the phase assigned when a measured diffraction pattern cannot be indexed. It is a recorded measurement, not missing data. Like any phase, a connected notIndexed area can form a grain. A patch narrower than the alpha closing threshold is absorbed into a neighbouring grain. See Filling Missing Data.

Grain - a phase-homogeneous, spatially connected region of EBSD points produced by segmentation. A phase change between neighbours is always a boundary. Orientation-based methods commonly require neighbouring orientations to agree within a threshold. There is no canonical grain definition, so that threshold is a convention. See Grains.

Grain boundary - one segment between neighbouring EBSD points that belong to different grains. These atomic segments are stored in walk order.

Phase boundary - a grain boundary whose two neighbouring grains have different phases. It is a query on grain boundaries, not a separate type.

Enclosure - the relationship in which one grain lies entirely inside another. From outside, the containing grain has a hole; from inside, the contained grain is an inclusion. These are the same fact, and the hole is never empty because even a notIndexed patch is a grain.

Chain - a maximal run of grain-boundary segments laid end to end. It runs from one junction to the next without passing through one. Every segment belongs to one chain, and the same two grains lie on its sides throughout.

Junction - a vertex where the number of meeting boundary segments is not two. It includes outer-map endpoints and points where four segments cross.

Triple point - a junction where exactly three segments meet and separate three distinct grains. It is a strict subset of junctions; three segments meeting at the scanned-area edge do not make a triple point. See Triple Points.

Closed chain - a chain that ends where it began. A junction-free enclosed grain usually has one, but a chain may also leave a junction and return to that same junction. Closed therefore does not mean junction-free.

Gap - a run of absent measurements within one scan line, often created by selecting one phase before rebuilding the grid. Grid assignment recovers its lattice positions; a gap is not a notIndexed measurement.

Hole in a scan grid - a connected notIndexed area inside the region that was actually scanned. This is distinct from a gap and from a dummy cell.

Dummy cell - a synthetic filler cell beyond the scanned edge that bounds the spatial decomposition. It has no id, never represents a measurement, and never becomes a grain.

Local deformation model - the position correction used for gaps, holes, and dummy cells on a nonrigid scan grid. MTEX fits an ideal affine grid and interpolates measured local deviations into positions without measurements. See Scan Grids.

KAM - kernel average misorientation, the average orientation difference between a measurement and its neighbours. See KAM.

GROD - grain reference orientation deviation, the difference between a measurement and its grain's mean orientation. See Mis2Mean / GROD.

Material response

Slip system - a lattice plane together with a direction in that plane, along which a crystal shears plastically.

Schmid factor - the geometric factor relating applied stress to the shear stress resolved onto a slip system. It lies between zero and 0.5. See Plasticity.

Taylor model - the assumption that every grain undergoes the same strain. It is the plastic counterpart of the Voigt bound.

Sachs model - the assumption that every grain feels the same stress. It is the plastic counterpart of the Reuss bound. Taylor and Sachs bound real behaviour from above and below. See Tensors.

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

References

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Notation and Conventions collects the choices behind these terms, including angle units, Euler conventions, frame direction, and the action of a rotation.