Glossary

Euler angles: a description of orientation involving sequential rotations of the crystal coordinate system through three angles with respect to the specimen coordinate system

Euler space: three-dimensional (usually Cartesian) space wherein Euler angles are represented

Friedel’s law: radiation is diffracted in the same fashion from both sides of a set of lattice planes, so that diffraction patterns are always

centrosymmetric, even if the crystals are not; this also causes the “ghost error” during ODF computation

fundamental zone of Rodrigues space: volume of Rodrigues space in which the lowest-angle crystallographically related solution of an orientation (or misorientation) resides

Geiger counter: counter to detect x-rays that is based on the potential of x-rays to ionize gas-today virtually obsolete in diffractometry

ghost error: error in ODF calculation by the series expansion method caused by the unavailability of the odd-order C coef cients

gnomonic projection: projection of a reference sphere in which the center of the sphere is the projection point and a plane tangential to the North Pole is the projection plane

goniometer: diffractometer to position the sample and the detector with respect to the incident beam

harmonic method of ODF calculation: see series expansion method high-resolution electron microscopy (HREM): technique for determination

of local orientations and orientation relationships based on direct imaging of the atoms

Hough transform: transformation of points in an image into sinusoidal curves in an accumulation space; a line in the original image is transformed into a point characterized by the angle θ and the distance ρ of the line in the original image

ideal orientation/Miller indices representation: orientation representation having the nearest Miller (or Miller-Bravais) indices of the crystal directions parallel to the specimen Z and X directions, respectively

interface-plane scheme: methodology for characterizing interfaces on the basis of the crystallographic orientation of the planar surface of the interface

interplanar angle: angle between two crystallographic planes interzonal angle: angle between two crystallographic directions inverse pole fi gure: angular distribution of a chosen specimen direction

with respect to the crystal coordinate system Kβ fi lter: foil positioned between sample and detector in x-ray diffractom-

etry and made of a material whose absorption edge lies just between the Kα and the Kβ peak of the x-ray tube; used to produce quasimonochromatic x-radiation

Kikuchi diffraction pattern: system of bright and dark lines (the Kikuchi lines) that form by the elastic (Bragg) re ection of diffusely scattered electrons at the atomic planes of a single crystalline volume in TEM; similar patterns form in SEM by SAC and EBSD; very well suited for orientation determination with the highest angular resolution

Kikuchi line: see Kikuchi diffraction pattern Laue group: eleven crystal classes out of the possible 32 point groups that

contain an inversion center Laue method: technique for orientation determination in single-crystal

volumes, which is based on the diffraction of polychromatic x-rays

Mackenzie distribution: distribution of disorientation angles and axes, where the latter are located in a stereographic unit triangle, for cubic crystals misoriented at random

macrotexture: an average texture determined from many grains obtained without reference to the location of individual grains within a specimen, or the experimental technique used to obtain this information

maximum entropy method: method for the correction of the ghost error in the series expansion method based on the assumption that, out of the possible range of complete ODFs, the solution with maximum entropy has the smoothest distribution with minimum additional information, that is, ghosts

mesotexture: the texture between grains, that is, the texture associated with grain boundaries

micro-Kossel diffraction: an SEM-based technique for obtaining crystallographic information from volumes of crystal down to approximately 10 μm, and based on the diffraction of x-ray generated within the sample under investigation

microdiffraction: generic term for techniques used to generate Kikuchi diffraction patterns in small volumes, with a spatial resolution beyond the limit of SAD, ~1 μm

microtexture: a sample population of orientation measurements that can be linked individually to their location within a specimen, or the experimental technique used to obtain this information

misorientation: the orientation difference between two individual orientation measurements, usually of the same phase (see also orientation relationship)

misorientation distribution function (MODF; MDF): continuous density distribution of misorientations, calculated either from discrete data or from a series expansion method

monochromator: crystal used in x-ray or neutron diffractometry to produce monochromatic radiation of a certain wavelength in accordance with Bragg’s law

normalization of pole fi gures: normalization of the pole gure intensities recorded in numbers of counts to standard units, commonly referred to as multiples of a random distribution independent of the experimental parameters

orientation correlation function (OCF): texture-reduced form of the MODF, derived by division of the MODF by the ODDF; yields information about the texture-reduced spatial correlation of misorientations

orientation difference distribution function (ODDF): statistical distribution of misorientations in a sample without consideration of the actual location of the orientations, only governed by the texture; used to normalize the MODF, but does not contain valuable information on the spatial arrangement of the individual orientations

orientation distribution function (ODF): continuous density distribution of orientations, calculated either from discrete data or from a series expansion method

orientation imaging microscopy (OIM™): see orientation mapping orientation mapping: depiction of the microstructure in terms of its orientation

constituents orientation matrix: cosines of angles between axes of the specimen coordi-

nate system and the crystal coordinate system, arranged to form a 3 × 3 matrix

orientation microscopy: automated measurement and storage of orientations according to a prede ned pattern of coordinates on the sampling plane of the specimen

orientation relationship: the difference between two individual orientation measurements, usually of different phases (see also misorientation)

orientation topography: spatial arrangement of the crystallographic orientations in the microstructure

orthonormal coordinate system: right-handed Cartesian coordinate system chosen as three mutually perpendicular unit vectors

peak separation: the means to separate intensities stemming from closely spaced re ectors, either experimentally or numerically

penetration depth: depth of the specimen from where the diffracted information arises

pole: normal to a set of crystallographic planes pole fi gure: angular distribution of a chosen crystal direction (usually a set

of plane normals) with respect to the specimen coordinate system pole fi gure inversion: calculation of the ODF from the data of (typically sev-

eral) pole gures position-sensitive detector (PSD): one-dimensional location-sensitive coun-

ter that simultaneously records a part of the diffraction spectrum positivity method: iterative method for the correction of the ghost error in

the series expansion method based on a generalization of the zerorange method

proportional counter: counter to detect x-rays that is based on the potential of x-rays to ionize a gas

pseudo-Kossel diffraction: an SEM-based technique for obtaining crystallographic information by Kossel diffraction, where the x-radiation is generated in a target layer of an appropriate material deposited on the sample under investigation

pulse-height analyzer: device that distinguishes between electrical pulses of different size and that is used to distinguish between x-rays of different energy, thus reducing background and uorescent radiation

Radon transform: Hough transform under consideration of the gray values of the individual pixels

random texture: sample population of orientations having no preferred crystallographic orientation

refl ection geometry: geometrical setup to study diffraction effects on thick bulk samples where the incident radiation is re ected in the surface layers

Rietveld texture analysis (RITA): a method for quantitative texture analysis by an iterative combination of crystallographic Rietveld pro le analysis of diffraction spectra and ODF calculation

Rodrigues space: three-dimensional Cartesian space wherein Rodrigues vectors are represented

Rodrigues vector (R vector): combination of the angle and axis of rotation into one mathematical entity

Rodrigues-Frank space (RF space): see Rodrigues space rotation matrix: see orientation matrix scintillation counter: counter to detect x-rays that is based on the potential

of x-rays to ionize a solid crystal selected-area channeling (SAC): an SEM-based technique for obtaining dif-

fraction information from volumes of crystal down to approximately 10 μm

selected-area diffraction pole fi gures: technique to derive the orientation distribution of smallest polycrystalline volumes in the TEM

selected-area electron diffraction (SAD): characteristic point patterns generated by electron diffraction in thin metallic foils, or the experimental technique to generate those patterns; the traditional method for orientation determination in the TEM before the advent of TEMs with microdiffraction facilities

semiconductor counter: counter to detect x-rays that is based on the possibility of x-rays to ionize a semiconductor crystal

series expansion method: method to calculate the ODF from pole gure data in Fourier space by tting pole gures and ODF by a series expansion with spherical harmonic functions

skeleton line: representation of the relative intensity maxima in the various ODF sections in the Euler space as a function of the corresponding Euler angle

spallation source: neutron source where the neutrons are produced by spallation, that is, the interaction of a high-energy proton beam with a target material; interesting for time-of- ight (TOF) applications because of the possibility to pulse the neutron beam

specimen coordinate system: coordinate system chosen as the geometry of the specimen

spiral scan: method to scan the pole gure on a spiral by a coupled changing of both pole gure angles (outdated)

step scan: method to scan the pole gure in distinct pole gure angles stereographic projection: projection of a reference sphere onto its equato-

rial plane such that equal angles between lines on the surface of the sphere retain their equality in the projection

structure factor: unit cell equivalent of the atomic scattering amplitude; summation over the waves scattered by each of the atoms in the unit cell gives the amplitude of the wave being re ected at a given plane

subvolume of the fundamental zone of Rodrigues space: volume obtained by subdivision of the fundamental zone such that the absolute value of the axis of rotation is given by H > K > L, where HKL are its Miller indices

synchrotron radiation: x-radiation generated in an electron synchrotron that is characterized by a high intensity and low angular divergence and which can be used for local texture analysis by means of the Laue and Debye-Scherrer methods

texture: distribution of the crystallographic orientations of a given sample texture fi bers: intensity distribution along certain prede ned paths through

the Euler space time-of-fl ight (TOF) measurements: method to separate several re ectors

by determining the ight time of the neutrons, which depends on their energy or wavelength (see also energy-dispersive diffractometry); requires a pulsed neutron source

transmission geometry: geometrical setup to study diffraction effects on thin samples that are penetrated by the incident radiation

truncation error: error in ODF calculation by the series expansion method caused by the necessity to truncate the series expansion of pole gure and ODF expansion

universal stage (U stage): sample stage that allows rotation of an optically anisotropic crystal until its optical axis is aligned parallel to the microscope axis; the rotation angles then yield the crystallographic orientation of the crystal

vector method: direct method for ODF computation based on subdivision of both pole gures and orientation space into small subregions, which are considered as components of vectors

WIMV method: direct method for ODF computation; acronym for the authors Williams, Imhof, Matthies, and Vinel

zero-range method: method for the correction of the ghost error in the series expansion method based on the assumption that ranges with zero intensity in the pole gures yield an approximation to the indeterminable part of the entire ODF