Symmetry in reciprocal space

Shmueli, U.; Hall, S. R.; Grosse-Kunstleve, R. W.

doi:10.1107/97809553602060000552

Affine transformation 1.4.4.4

Body-diagonal axes A1.4.2.6

Bravais lattices

centred 1.4.4.5

direct and reciprocal 1.4.4.5

Centred Bravais lattice 1.4.4.5

Centre of symmetry

false 1.4.2.2

Centring

translations 1.4.4.1

type 1.4.4.5

Centrosymmetry

status of A1.4.2.2

Change-of-basis matrix A1.4.2.1

Change of crystal axes 1.4.4.3

Computer-adapted space-group symbols 1.4.3.2, A1.4.1, A1.4.2.3, A1.4.2.3

Computer-algebraic languages A1.4.1

Crystal axes, change of 1.4.4.3

Crystal systems A1.4.2.2

Cubic space groups 1.4.3.3

Cyclic (even) permutation of coordinates 1.4.3.3, 1.4.3.3, A1.4.1

Data handling, Hall symbols in A1.4.2.1

Direct Bravais lattice 1.4.4.5

Direct inspection of structure-factor equation 1.4.2.2

Direct lattice 1.4.4.1

Direct methods 1.4.2.4

Direct-space transformations 1.4.4.3

Effects of symmetry on the Fourier image 1.4.2.1

Electron density 1.4.2.2

Even (cyclic) permutation of coordinates 1.4.3.3, 1.4.3.3, A1.4.1

Explicit-origin space-group notation A1.4.2.3

Explicit space-group symbols A1.4.2.1, A1.4.2.2, A1.4.2.1

Face-diagonal axes A1.4.2.5

False centre of symmetry 1.4.2.2

FORTRAN A1.4.1

FORTRAN interface A1.4.1

FORTRAN interpreter A1.4.1

Fourier images 1.4.1

effects of symmetry on 1.4.2.1

Fourier space 1.4.2.3

symmetry in 1.4.4.4

Fourier summations 1.4.2.3

space-group-specific 1.4.2.3

General conditions for possible reflections 1.4.2.2

Geometric structure factors 1.4.2.3, 1.4.2.4, A1.4.3

Group–subgroup relationship 1.4.3.3

Hall symbols A1.4.2.1, A1.4.2.3, A1.4.2.7

in data handling A1.4.2.1

in software A1.4.2.1

Hermann–Mauguin space-group symbol 1.4.3.4

Hexagonal axes 1.4.3.3

Hexagonal family 1.4.3.3

Hexagonal space groups 1.4.3.3

Improper rotations A1.4.2.2, A1.4.2.3, A1.4.2.4

Intrinsic component of translation part of space-group operation 1.4.2.2

Inverse rotation operator 1.4.2.1

Languages

computer-algebraic A1.4.1

numerically and symbolically oriented 1.4.3.2

Lattice

direct 1.4.4.1

reciprocal 1.4.4.1

Lattice-translation subgroup A1.4.2.2

Lattice type A1.4.2.2

Laue groups 1.4.2.2

Location-dependent component of translation part of space-group operation 1.4.2.2

Matrix representation 1.4.2.1

Monoclinic family 1.4.3.3

Monoclinic space groups 1.4.3.3

Multiple reciprocal cell 1.4.4.5

Multiplicity 1.4.2.3

Non-cyclic (odd) permutation of coordinates 1.4.3.3, 1.4.3.3, A1.4.1

Numerically oriented languages 1.4.3.2

Obverse setting 1.4.4.5

Odd (non-cyclic) permutation of coordinates 1.4.3.3, 1.4.3.3, A1.4.1

Origin-shift vector A1.4.2.1

Orthorhombic space groups 1.4.3.3

Parity of the hkl subset 1.4.3.4

Periodic density function 1.4.1

Permissible symmetry 1.4.1

Permutation of coordinates

cyclic (even) 1.4.3.3, 1.4.3.3, A1.4.1

non-cyclic (odd) 1.4.3.3, 1.4.3.3, A1.4.1

Permutation operators 1.4.3.3

Point-group operators 1.4.2.2, A1.4.2.2

Point-group symmetry of reciprocal lattice 1.4.2.1

Principal axes A1.4.2.4

Proper rotation A1.4.2.2, A1.4.2.3, A1.4.2.4

Reciprocal Bravais lattice 1.4.4.5

Reciprocal cell, multiple 1.4.4.5

Reciprocal lattice 1.4.4.1

point-group symmetry of 1.4.2.1

weighted 1.4.1, 1.4.2.2

Reciprocal-space representation of space groups 1.4.1

Reciprocal space

symmetry in 1.4.4.1

REDUCE A1.4.1

Relationship between structure factors of symmetry-related reflections 1.4.2.2

Representation of space groups in reciprocal space 1.4.1

Representative operators of a space group A1.4.2.2

Rotation

improper A1.4.2.2, A1.4.2.3, A1.4.2.4

proper A1.4.2.2, A1.4.2.3, A1.4.2.4

Rotation operator

inverse 1.4.2.1

Rotation part of space-group operation 1.4.2.2

Shift of space-group origin 1.4.4.3

Software, Hall symbols in A1.4.2.1

Space-group algorithm 1.4.4.1

Space-group notation, explicit-origin A1.4.2.3

Space-group operation 1.4.2.2

intrinsic and location-dependent components of translation part 1.4.2.2

rotation part 1.4.2.2

translation part 1.4.2.2

Space-group origin, shift of 1.4.4.3

Space groups

cubic 1.4.3.3

hexagonal 1.4.3.3

in reciprocal space A1.4.4

monoclinic 1.4.3.3

orthorhombic 1.4.3.3

reciprocal-space representation of 1.4.1

representative operators of A1.4.2.2

tetragonal 1.4.3.3

triclinic 1.4.3.3

trigonal 1.4.3.3

Space-group-specific Fourier summations 1.4.2.3

Space-group-specific structure-factor formulae 1.4.2.4

Space-group-specific symmetry factors 1.4.1

Space-group symbols

computer-adapted 1.4.3.2, A1.4.1, A1.4.2.3, A1.4.2.3

explicit A1.4.2.1, A1.4.2.2, A1.4.2.1

Hall A1.4.2.1, A1.4.2.3, A1.4.2.7

Hermann–Mauguin 1.4.3.4

Space-group tables 1.4.4.1

Spherical atoms 1.4.2.4

Statistics

structure-factor 1.4.2.4

Status of centrosymmetry A1.4.2.2

Structure-factor formulae, space-group-specific 1.4.2.4

Structure factors

geometric 1.4.2.3, 1.4.2.4, A1.4.3

tables of 1.4.3, A1.4.3

trigonometric 1.4.2.3, 1.4.2.4, A1.4.3

Structure-factor statistics 1.4.2.4

Symbolically oriented languages 1.4.3.2

Symbolic programming techniques 1.4.1

Symmetry

effects on Fourier image 1.4.2.1

in Fourier space 1.4.4.4

in reciprocal space 1.4.4.1

permissible 1.4.1

Symmetry factors 1.4.2.3, 1.4.2.4

space-group-specific 1.4.1

tables of 1.4.1

Symmetry-generating algorithm A1.4.2.1

Symmetry-related reflections, relationship between structure factors of 1.4.2.2

Systematic absences 1.4.4.5

Tetragonal family 1.4.3.3

Tetragonal space groups 1.4.3.3

Text processing A1.4.1

Three-generator symbol A1.4.2.2

Transformation properties of direct and reciprocal base vectors and lattice-point coordinates 1.4.2.2

Transformations

affine 1.4.4.4

direct-space 1.4.4.3

Translation

part of space-group operation 1.4.2.2

part of space-group operation, intrinsic and location-dependent components of 1.4.2.2

Triclinic space groups 1.4.3.3

Trigonal space groups 1.4.3.3

Trigonometric structure factors 1.4.2.3, 1.4.2.4, A1.4.3

Type of rotation (proper or improper) A1.4.2.2

Vectors

origin-shift A1.4.2.1

Weighted reciprocal lattice 1.4.1, 1.4.2.2

Wyckoff position 1.4.2.2

Chapter 1.4. Symmetry in reciprocal space

Chapter index