International
Tables for
Crystallography
Volume D
Physical properties of crystals
Edited by A. Authier

International Tables for Crystallography (2006). Vol. D, ch. 3.3, pp. 444-445

Section 3.3.11. Glossary

Th. Hahna* and H. Klapperb

aInstitut für Kristallographie, Rheinisch–Westfälische Technische Hochschule, D-52056 Aachen, Germany, and bMineralogisch-Petrologisches Institut, Universität Bonn, D-53113 Bonn, Germany
Correspondence e-mail:  hahn@xtal.rwth-aachen.de

3.3.11. Glossary

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(hkl) crystal face, lattice plane, net plane (Miller indices)
{hkl} crystal form, set of symmetrically equivalent lattice (net) planes
[uvw] zone axis, crystal edge, lattice direction, lattice row (direction indices)
[\langle uvw\rangle] set of symmetrically equivalent lattice directions (rows)
[{\cal G}] symmetry group of the (real or hypothetical) `parent structure' or high-symmetry modification or `prototype phase' of a crystal; group in general
[{\cal H}] eigensymmetry group of an (untwinned) crystal; symmetry group of the deformed (`daughter') phase of a crystal; subgroup
[{\cal H}_1], [{\cal H}_2], [\ldots], [{\cal H}_j] oriented eigensymmetries of domain states 1, 2, [\ldots], j
[{\cal H}_{1,2}^*], [{\cal H}^*] intersection symmetry group of the pair of oriented eigensymmetries [{\cal H}_1] and [{\cal H}_2], reduced eigensymmetry of a domain
[{\cal K}] composite symmetry group of a twinned crystal (domain pair); twin symmetry
[{\cal K}_{1,2}^*], [ {\cal K}^*] reduced composite symmetry of the domain pair (1, 2)
[{\cal K}(n)] extended composite symmetry of a twinned crystal with a pseudo n-fold twin axis
k, [k_1], [k_2], [\ldots], [k_i] twin operations ([k_1] = identity)
[2^{\prime}], [m^{\prime}], [{\bar 1}{^{\prime}}], [4'(2)], [6'(3)], [{\bar 3}{^\prime}(3)], [{\bar 6}{^\prime}(3)] twin operations of order two in colour-changing (black–white) symmetry notation
[\vert {\cal G}\vert], [\vert {\cal H}\vert], [\vert {\cal K}\vert] order of group [{\cal G}], [{\cal H}], [{\cal K}]
[i] index of [{\cal H}] in [{\cal G}], or of [{\cal H}] in [{\cal K}]
[j], [\Sigma] index of coincidence-site lattice (twin lattice, sublattice) with respect to crystal lattice
[\omega] twin obliquity
[{\bf b}_t] Burgers vector of twinning dislocations
f fault vector of a merohedral twin boundary
t twin displacement vector
[{\cal G}F{\cal H}] Aizu (1970a[link]) symbol of a ferroic phase transition (ferroic species); F = ferroic
W, [W^{\prime}] designation of non-merohedral ferroelastic twin boundaries (according to Sapriel, 1975[link])
[F_{hkl}] structure factor of reflection hkl
[{\bf g}_{hkl}] diffraction vector (reciprocal-lattice vector) of reflection hkl
[\varphi_{hkl}] phase angle of structure factor [F_{hkl}]
[\Psi_{hkl}], [\Phi_{hkl}] difference of phase angles (`phase jump') across twin boundary
[\rho] charge density of a ferroelectric twin boundary
P spontaneous polarization

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